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{"url":"http:\/\/math.stackexchange.com\/questions\/156351\/need-help-with-real-analysis-question?answertab=oldest","text":"# need help with real analysis question\n\nI really need help with this question: Prove that a metric space which contains a sequence with no convergent subsequence also contains an cover by open sets with no finite subcover.\n\nThanks a lot.\n\n-\nDo you know what a contrapositive is? Are you familiar with the various characterizations of compactness? \u2013\u00a0Potato Jun 10 '12 at 4:54\nJust so you know, a topological space is sequentially compact if every sequence has a convergent subsequence, and compact if every open cover admits a finite subcover. In the case of a metric space, these are equivalent. \u2013\u00a0talmid Jun 10 '12 at 5:43\n\nLet $(a_n)$ be a sequence in the metric space $M$ that doesn't have any convergent subsequence. The set $\\{a_n\\}$ consists of isolated points (that is, it doesn't have any accumulation points; otherwise you could take a convergent subsequence), and it's infinite (because if it wasn't, one of the points would repeat infinitely in the sequence and we could get a constant subsequence). Now, for each $n$ take an open ball $B_{r_n}(a_n)$ around $a_n$ with radius $r_n$ small enough not to contain any other terms in the sequence, constructing an (infinite) family of open sets $\\{B_{r_n}(a_n)\\}$.\n\nNow if you know some facts about compactness you could argue: The set $\\{a_n\\}$ is closed, and then since it's a subset of the metric space $M$, if $M$ is compact then so is $\\{a_n\\}$. However, note that $\\{B_{r_n}(a_n)\\}$ is an open cover of $\\{a_n\\}$, but contains no finite subcover. Then $\\{a_n\\}$ isn't compact, and neither is $M$ (that is, not every subcover of $M$ admits a finite subcover).\n\nOr otherwise, like suggested by Martin Sleziak (and showing a direct proof): consider the open cover $\\{B_{r_n}(a_n)\\} \\cup (M \\setminus \\{a_n\\})$, which doesn't admit a finite subcover.\n\nIt's a nice exercise trying to fill in the details.\n\nAn example is given in the space of bounded sequences of real numbers, with the supremum norm: for $i \\in \\mathbb{N}$, let $e_i$ to be the sequence with a one at the $i$-th position and zeroes elsewhere; then $(e_i)$ is a sequence with no convergent subsequence and $\\{e_i\\}$ doesn't have accumulation points (even more: it's uniformly discrete).\n\n-\nIf you want open cover of the whole space, you can slightly modify the solution in this answer by adding the open set $M\\setminus\\{a_n; n\\in\\mathbb N\\}$. \u2013\u00a0Martin Sleziak Jun 10 '12 at 5:09\n@MartinSleziak I was thinking of that. I'll add it. Thanks. \u2013\u00a0talmid Jun 10 '12 at 5:12","date":"2015-11-28 09:52:30","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9459584951400757, \"perplexity\": 114.7629556447476}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2015-48\/segments\/1448398451872.11\/warc\/CC-MAIN-20151124205411-00278-ip-10-71-132-137.ec2.internal.warc.gz\"}"} | null | null |
\section{Additional Test Results}
The objective of a continual learning algorithm is to continuously learn new knowledge on the current task, while maintaining its performance on past tasks. To achieve this, there are two components that needs to be quantified: 1) \textbf{backward transfer} and 2) \textbf{forward transfer}. We formally define them in the context of continual reinforcement learning as follow:
\noindent\textbf{Backward Transfer} First, let $r_{i, j}$ denote the test episodic (normalized) reward on task $i$ after training on task $j$. Retention for each task is then given by $f_i = r_{i, T} / r_{i, i}$ for all $i < T$. The average retention is $f = \frac{1}{T-1} \sum_{i=1}^{T-1} f_i$. If this measure is larger than 100\%, it indicates \textit{positive backward transfer}, which means the performance on previously seen tasks benefit from more recent experiences. If this measure of retention is lower than $100\%$, this means that the robot forgets some knowledge about older tasks and we call this \textit{negative backward transfer} or \textit{forgetting}.
\begin{table} [b!]
\vspace*{-0.2cm}
\begin{tabular}{ p{1.4cm}p{1.4cm}p{1.4cm}p{1.4cm} p{1.4cm} p{1.4cm} }
\hline
\multicolumn{6}{c}{ \textbf{\% Forward Transfer in terms of Task Reward (Pusher)}} \\
\hline
\textbf{Task} & \textbf{2} & \textbf{3} & \textbf{4} & \textbf{5} & \textbf{Average} \\
\hline
Multi-task& 118 $\pm$ 23 & 106 $\pm$ 12 & \textbf{105 $\pm$ 9} & 110 $\pm$ 21 & 109 $\pm$ 9 \\
HyperCRL & 127 $\pm$ 22 & 99 $\pm$ 12 & 94 $\pm$ 12 & 107 $\pm$ 20 & 107 $\pm$ 9 \\
SI & 114 $\pm$ 26 & 84 $\pm$ 13 & 98 $\pm$ 15 & 101 $\pm$ 20 & 99 $\pm$ 10 \\
EWC & 125 $\pm$ 23 & \textbf{109 $\pm$ 11} & 105 $\pm$ 10 & \textbf{110 $\pm$ 21} & \textbf{112 $\pm$ 9} \\
Coreset & 126 $\pm$ 20 & 99 $\pm$ 13 & 90 $\pm$ 17 & 106 $\pm$ 21 & 105 $\pm$ 9 \\
Finetuning & \textbf{138 $\pm$ 22} & 108 $\pm$ 9 & 94 $\pm$ 17 & 107 $\pm$ 23 & 112 $\pm$ 9 \\
\hline
\hline
\multicolumn{6}{c}{ \textbf{\% Forward Transfer in terms Task Normalized Reward (Door)}} \\
\hline
\textbf{Task} & \textbf{2} & \textbf{3} & \textbf{4} & \textbf{5} & \textbf{Average} \\
\hline
Multi-task& 103 $\pm$ 74 & \textbf{94 $\pm$ 34} & 122 $\pm$ 160 & 78 $\pm$ 78 & 96 $\pm$ 49 \\
HyperCRL & \textbf{106 $\pm$ 76} & 91 $\pm$ 31 & \textbf{168 $\pm$ 203} & \textbf{102 $\pm$ 67} & \textbf{117 $\pm$ 57} \\
SI & 69 $\pm$ 57 & 56 $\pm$ 40 & 107 $\pm$ 137 & 66 $\pm$ 66 & 75 $\pm$ 42 \\
EWC & 71 $\pm$ 62 & 78 $\pm$ 32 & 125 $\pm$ 151 & 71 $\pm$ 61 & 86 $\pm$ 44 \\
Coreset & 94 $\pm$ 80 & 83 $\pm$ 34 & 113 $\pm$ 145 & 57 $\pm$ 68 & 84 $\pm$ 46 \\
Finetuning & 73 $\pm$ 83 & 90 $\pm$ 43 & 101 $\pm$ 145 & 83 $\pm$ 77 & 87 $\pm$ 47 \\
\hline
\hline
\multicolumn{6}{c}{ \textbf{\% Forward Transfer in terms Task Reward (Block Sliding)}} \\
\hline
\textbf{Task} & \textbf{2} & \textbf{3} & \textbf{4} & \textbf{5} & \textbf{Average} \\
\hline
Multi-task& 71 $\pm$ 13 & 92 $\pm$ 20 & 99 $\pm$ 9 & 93 $\pm$ 14 & 89 $\pm$ 7 \\
HyperCRL & \textbf{92 $\pm$ 8} & 97 $\pm$ 14 & 82 $\pm$ 39 & \textbf{94 $\pm$ 14} & 91 $\pm$ 11 \\
SI & 91 $\pm$ 7 & 83 $\pm$ 48 & 102 $\pm$ 9 & 88 $\pm$ 14 & 91 $\pm$ 13 \\
EWC & 90 $\pm$ 9 & \textbf{115 $\pm$ 14} & 103 $\pm$ 11 & 94 $\pm$ 20 & \textbf{100 $\pm$ 7} \\
Coreset & 65 $\pm$ 22 & 108 $\pm$ 14 & \textbf{110 $\pm$ 16} & 94 $\pm$ 17 & 95 $\pm$ 9 \\
Finetuning & 48 $\pm$ 42 & 88 $\pm$ 19 & 97 $\pm$ 25 & 76 $\pm$ 29 & 77 $\pm$ 15 \\
\hline
\end{tabular}
\caption{\textbf{Forward Transfer on Pusher, Door and Block Sliding Envs}. We measure the average episodic reward at the end of training on task $t$ compared to training a single-task baseline on the same task from scratch. Results show the mean and one standard deviation, evaluated across four seeds and 10 episodes per seed. Greater than 100 indicates positive forward transfer, otherwise it indicates negative forward transfer.}
\label{table:transfer}
\end{table}
\noindent\textbf{Forward Transfer} Forward Transfer measures how the robot adapts to new tasks after training on older task(s). Specifically, let $r_i^*$ denote the test episodic reward on task $i$ for a single-task model trained from scratch using CEM planning. This single-task model serves as a baseline for performance. We then calculate forward transfer as $I_i = r_{i, i} / r_i^*$, and the average is $I = \frac{1}{T-1} \sum_{i=2}^{T} I_i$. If this measure is greater than 100\%, it indicates \textit{positive forward transfer}, which means that the robot benefits from older experiences when learning a new task. If this measure is lower than $100\%$, it means that the robot is unable to take advantage of past experience to solve new tasks, also known as \textit{negative forward transfer}.
To better illustrate the continual learning capability of \texttt{HyperCRL}, we provide an evaluation of the positive transfer capabilities defined above. We show the result on all three experiments in Table \ref{table:transfer}.
In the pusher experiment, \texttt{HyperCRL}~ achieves an average forward transfer of $100 \pm 11\%$. This means that our proposed method can adapt to new tasks and reach similar level of performances compared to a single-task baseline trained from scratch. In the door experiment, \texttt{HyperCRL}~ beats all baseline in terms of forward transferring capabilities. In the block sliding experiment, \texttt{HyperCRL}~ achieves slightly lower average forward transfer compared to the best baseline. A note of caution is that some results have very large variance across different random seeds. Better techniques to train hypernetworks or plan with learned dynamics model would improve the reliability of our approach, and we leave this to future work.
\section{Additional Experiment on HalfCheetah}
We ran another experiment using \texttt{HyperCRL}~following the environment setup from \cite{henderson2017benchmark}, changing the body of the robot. We modified body size (torso, leg) on the HalfCheetah environment to create a continual learning scenario with $T=5$ tasks. Our method outperforms other continual learning baselines (SI, EWC, coreset) and performs similarly to multi-task learning (Figure \ref{fig:cheetah_reward}).
\section{More Training Details}
In this section, we provide more details about the hyperparameters used during the experiments in Table \ref{table:hyperparameter}.
\begin{table}[h!]
\centering
\begin{tabular} {p{1.8cm} | p{1cm}| p{1cm} | p{1cm}|p{1cm} | p{1cm}|p{1cm} }
\hline
& $P$ & $M$ & $K$ & $S$ & $\alpha_H$ & $\alpha_\mathbf{e}$ \\
\hline
Pusher & 10 & 20 & 200 & 2000 & 0.0001 & 0.0001 \\
Door & 10 & 300 & 200 & 200 & 0.0001 & 0.0001 \\
Block Sliding & 10 & 100 & 150 & 500 & 0.0001 & 0.0001 \\
Half Cheetah & 10 & 100 & 1000 & 2000 & 0.0001 & 0.0001 \\
\hline
\hline
\end{tabular}
\begin{tabular}{p{1.85cm} | p{1cm} | p{1cm} | c | c }
& $\mathcal{B}$ & $\beta_\text{reg}$ & hnet non-linearity & hnet hidden layers \\
\hline
Pusher & 100 & 0.05 & ELU & [50, 50]\\
Door & 100 & 0.5 & ReLU & [256, 256]\\
Block Sliding & 100 & 0.5 & ReLU & [50, 50]\\
Half Cheetah & 100 & 0.05 & ReLU & [256, 256] \\
\hline
\end{tabular}
\caption{Hyper-parameter values of the proposed algorithm~\texttt{HyperCRL}~ on pusher pusher, door, block sliding and half cheetah environments.}
\label{table:hyperparameter}
\end{table}
\begin{figure*} [t!]
\vspace{-9cm}
\centering
{\includegraphics[width=\textwidth]{figure/half_cheetah_body_reward.pdf}}
{\caption{\textbf{Reward on HalfCheetah Environment} from \cite{henderson2017benchmark}. Shown are episodic rewards evaluated during training. Each task is trained for 100k steps, totaling 500k steps. Results are averaged across four random seeds, and shaded area marks one standard deviation.
\label{fig:cheetah_reward}}}
\end{figure*}
\section{Additional ``Oracle" baseline}
In Figure \ref{fig:door_reward}, the multi-head multi-task baseline slightly underperforms \texttt{HyperCRL}. We hypothesize that the hypernetwork architecture might be more effective for learning the task.
We consider another multi-task baseline that shares the same architecture of the hypernetwork used in \texttt{HyperCRL}, but is trained without regularization and has access to the entire replay buffer similar to the multi-task baseline. We call this \texttt{HyperCRL}\texttt{-MT}, and we believe this should serve as a better upper-bound on the continual learning performance of \texttt{HyperCRL}~. We compare results on the door-opening experiment in Figure \ref{fig:door_reward_supp_2}. With full access to all past experiences, \texttt{HyperCRL}\texttt{-MT} slightly outperforms \texttt{HyperCRL}~ on this experiment, which shows the efficacy of our proposed method.
\begin{figure*} [t!]
\vspace{-18cm}
\centering
{\includegraphics[width=\textwidth]{figure/door_pose_reward_supp_2.pdf}}
\caption{\textbf{Additional Hypernetwork Baseline on Door Environment} Shown are normalized episodic rewards evaluated during training. ~\texttt{HyperCRL}\texttt{-MT} is trained with access to the entire replay buffer. Results are averaged across four random seeds, and normalized with respect to a model trained from scratch separately on each task.}
\label{fig:door_reward_supp_2}
\end{figure*}
\section{Limitations and Future Work}
\vspace{-0.05cm}
While our proposed approach shows good results against the baselines we tested, there are many interesting prospects for future work. First, better techniques to train hypernetworks will significantly aid this line of work. Currently, the size of our hypernetwork is at least an order of magnitude larger than the target network, since it directly outputs all the weights. Hypernetworks are often sensitive to the choice of random seeds and architecture. Second, extending our method to image-based RL environments is worth investigating, as it will enable higher-capacity target networks.
Finally, \texttt{HyperCRL}~is not task agnostic, nor can it automatically detect task switching that happens continuously with no clear task boundaries. A possible direction is to use probabilistic inference models (i.e.~Bayesian non-parametrics \cite{xu2020taskagnostic}) or changepoint detection methods to perform task identification.
\section{Conclusion}
\vspace{-0.05cm}
In this paper we described \texttt{HyperCRL}, a task-aware method for continual model-based reinforcement learning using hypernetworks. In all of our experiments, we have demonstrated that \texttt{HyperCRL}~consistently outperforms alternative continual learning baselines in terms of overall performance at the end of training, as well as in terms of retaining performance on previous tasks.
By allowing the entire network to change between tasks, rather than just the output head layer of the dynamics network, \texttt{HyperCRL}~is more effective at accurately representing different dynamics, even with significant task switching, while only requiring a fixed-size hypernetwork and no training data from old tasks to generate task-conditional dynamics for lifelong planning.
\section{Experiments}
We perform multiple robot simulation experiments
to answer the following questions: (a) How does \texttt{HyperCRL}~compare with existing continual learning baselines in terms of overall performance across tasks? (b) How effective is \texttt{HyperCRL}~in preventing catastrophic forgetting across tasks?
\subsection{Pushing a block of non-uniform mass}
First, we look at an intuitively simple experiment simulated using Surreal Robotics Suite \cite{corl2018surreal}, in which a Panda robot tries to push a non-uniform-density block across the table (Figure \ref{fig:pusher_illustration}). The objective is to push the block to the goal position while \textit{maintaining its initial orientation}. We vary the densities of the left and right parts of the block across different tasks ($T=5$), changing the center of mass and moment of inertia. The robot needs to learn to maneuver the position of its end-effector on the side of the block to correct for orientation deviations while pushing the block forward. Each episode is 100-step long, which is 10 seconds of simulator time. At the start of each episode, we initialize the robot end-effector to a fixed position behind the block.
The state is represented as a concatenated vector $(x_\text{ee}, x_1,x_2, x_3, x_4)$.
Here $(x_1,x_2, x_3, x_4)$ represents the $xy$ positions of the four corners and $x_\text{ee}$ is the $xy$ position of the end-effector with respect to the block.
The input action vector, $\delta x_\text{ee}$, specifies a desired offset with respect to the current position $x_\text{ee}$. The robot is actuated using an operational space controller \cite{khatib1987unified}. It calculates the joint torques given an action that is updated at 10Hz. The reward function
is set to minimize the sum of distances between the current and goal pose of the block following $r(s, a) = \sum_{i=1}^4 ( 1 - \text{tanh}(10~||x_i - g_i||)) - 0.25||a||$, where ${g_i}$ is the goal position of the $i^{th}$ corner. The reward function consists of one term per corner within the range [0, 1], and to maximize reward the robot should minimize the corner distances to the goal pose.
\begin{figure} [t!]
\begin{subfigure}[b]{0.55\columnwidth}
\centering
\includegraphics[width=4cm]{figure/pusher_env.pdf}
\caption{Initial and goal poses of the block.}
\label{fig:pusher_setting}
\end{subfigure}
\begin{subfigure}[b]{0.42\columnwidth}
\begin{tabular} {p{0.5cm} p{0.7cm} p{0.7cm} }
\hline
\textbf{Task} & \textbf{Green} & \textbf{Blue} \\
\hline
1 & 500 & 500 \\
\hline
2 & 100 & 500 \\
\hline
3 & 500 & 100 \\
\hline
4 & 500 & 250 \\
\hline
5 & 250 & 500 \\
\hline
\end{tabular}
\label{table:pusher}
\caption{Density of the block in $kg/m^3$}
\label{fig:three sin x}
\end{subfigure}
\caption{\textbf{Setup of Pusher Environment}. The robot needs to solve 5 pushing tasks sequentially, each involving a block of different mass distribution. The objective is to push the block to the goal pose (indicated by the dotted frame) without changing its orientation.}
\label{fig:pusher_illustration}
\vspace{-0.6cm}
\end{figure}
\begin{figure}[h!]
\centering
\hspace*{-0.3cm}
\includegraphics[width=0.9\columnwidth]{figure/door_env.pdf}
\caption{\textbf{Setup of Door Environment}. For round and lever handles, the robot must first rotate the handle \textit{clockwise} before pulling the door open. Additionally, we introduce two more tasks by flipping the rotational direction to \textit{counter-clockwise} for the round and lever handles.}
\label{fig:panda}
\vspace*{-0.3cm}
\end{figure}
\begin{figure*} [h]
\centering
\includegraphics[width=\linewidth]{figure/pusher_reward.pdf}
\caption{\textbf{Reward on Pusher Environment}. Shown are episodic rewards evaluated during training. Results are averaged across four random seeds, and the shaded areas represent one standard deviation. Each task is trained for 4k steps, summing to 20k steps in total. Vertical dotted lines indicate task switches. The bottom-right subplot shows the average reward across all task $\leq t$ seen so far.}
\label{fig:pusher_reward}
\vspace{-0.3cm}
\end{figure*}
\vspace*{-0.2cm}
\subsection{Door Opening}
Next, we experiment on a more complex task to better demonstrate the flexibility of \texttt{HyperCRL}. We choose a door opening experiment, where the Panda robot has to open doors with different types of handles (Figure \ref{fig:panda}). Unlike the pushing example, the dynamic switches between tasks are much more discontinuous and the tasks require different motions to solve, due to the rotational joints imposed by some of the handles. A total of $T = 5$ tasks need to be solved sequentially, each involving a different handle type. Tasks 2 and 4 (similarily tasks 3 and 5) both have a round (lever) handle, but with different turning directions. The environment is modified from the DoorGym environment \cite{doorgym2019} and simulated in the Surreal Robotics Suite~\cite{robosuite}.
We model the environment as follow: (i) $\phi_d$ represents the angle of the door (ii) $\phi_k$ represents the angle of the door handle (iii) $x \in \mathbb{R}^3$ is the position, $q \in \mathbb{R}^4 $ is the quaternion representation of the rotation of the robot end-effector with respect to the handle (iv) $d \in \mathbb{R}$ is the state of the gripper (v) $q_j \in \mathbb{R}^7$ is the angle of the joints of the Panda arm. Concatenating all the above elements and their time derivative gives the full state vector $(\phi_d, \dot{\phi}_d, \phi_k, \dot{\phi}_k, x, q, d, q_j, \dot{q}_j) \in \mathbb{R}^{26}$.
Similar to the pushing environment, the robot is actuated with operational space control updated at 10Hz. The input action is a vector $(\delta x, \delta q, \delta d)$, which specifies a translation and rotational movement of the end-effector in the world frame. Finally, the reward function has five components as follows: $r(s, a) = -||x||_2 - \text{log}(||x||_2 + \epsilon) - ||q_{o}||_2 + 50\,\phi_d + 20\,\phi_k$, where $q_{o}$ is the difference between the orientation of the current end-effector and the required pose for opening the door.
\begin{figure}[h!]
\centering
\vspace*{-0.3cm}
\begin{minipage}[c]{0.64\columnwidth}
\includegraphics[width=0.95\columnwidth]{figure/slide_env.pdf}
\end{minipage}
\begin{minipage}[c]{0.3\columnwidth}
\caption{\textbf{Setup of Slide Environment}. The Panda arm should push block 1, which will kick block 2 in motion towards the goal pose. There are 5 tasks sequentially with different friction for block 2.}
\label{fig:slide}
\end{minipage}
\vspace*{-0.6cm}
\end{figure}
\vspace{-0.1cm}
\subsection{Block Sliding}
Our last experiment involves a Panda robot and two separate blocks placed on tabletop with low friction. The initial pose of the end-effector, the two blocks are placed along a straight line and we number the two blocks shown in Figure \ref{fig:slide}. To move block 2 to its goal pose, the manipulator should first hit block 1, which would slide away and in turn set the second block into sliding motion until stopped by friction. We vary the friction of block 2 across different tasks ($T$ = 5), while keeping friction of block 1 the same. Similar to the pusher experiment, we represent the state as a concatenated vector $(x_\text{ee}, x^1_{1:4}, x^2_{1:4})$, where $x_\text{ee}$ denotes the $xy$ position of the end-effector, and $(x^1_{1:4}, x^2_{1:4})$ denotes the $xy$ positions of the corners of both blocks. The reward function minimizes the distances between the current and goal pose of the second block $g_{1:4}$ as follows: $r(s, a) = \sum_{i=1}^4 (1 - \text{tanh}(10 ||x^2_i - g_i ||)) - 0.1||a||$. The robot must adjust the momentum of the first block in the initial push for different frictions to successfully deliver the second block to its goal. Each episode is 30-step long and equates 3 seconds in the simulator.
\vspace{-0.1cm}
\subsection{Baselines}
We compare the hypernetwork to the following baselines: (i) Multi-task learning with access to a buffer of all data from all previous tasks (an oracle) (ii) Coreset that remembers one percent of the state-action transition data per task, sampled randomly (iii) Synaptic Intelligence \cite{si} (iv) Elastic Weight Consolidation \cite{ewc} (v) Fine-tuning, where we optimize $f_{\theta_t}(\cdot)$ on each task's data without regularization. All the baseline models resemble the target model in our hypernetwork setup, except the multi-head output layer with one head per task. For coreset or multi-task learning, an additional batch of past data is sampled from the coreset or oracle every update step, and contributes to the total dynamics loss.
\setlength{\tabcolsep}{1pt}
\begin{table} [b!]
\vspace{-15pt}
\begin{tabular}{ p{1.4cm}p{1.4cm}p{1.4cm}p{1.4cm} p{1.4cm} p{1.4cm}}
\hline
\multicolumn{6}{c}{ \textbf{\% Retention in terms of Reward (Pusher)}} \\
\hline
\textbf{Task} & \textbf{1} & \textbf{2} & \textbf{3} & \textbf{4} & \textbf{Average} \\
\hline
Multi-task & \textbf{142 $\pm$ 74} & 91 $\pm$ 25 & 96 $\pm$ 9 & 91 $\pm$ 11 & \textbf{106 $\pm$ 20}\\
HyperCRL & 99 $\pm$ 10 & \textbf{107 $\pm$ 9} & \textbf{98 $\pm$ 13} &\textbf{103 $\pm$ 15} & 102 $\pm$ 6 \\
SI & 40 $\pm$ 54 & 88 $\pm$ 21 & 95 $\pm$ 21 & 92 $\pm$ 14 & 79 $\pm$ 16 \\
EWC & 7 $\pm$ 15 & 13 $\pm$ 8 & 6 $\pm$ 8 & 0 $\pm$ 3 & 4 $\pm$ 5 \\
Coreset & 87 $\pm$ 66 & 32 $\pm$ 46 & 39 $\pm$ 13 & 61 $\pm$ 43 & 55 $\pm$ 23 \\
Finetuning & 0 $\pm$ 2 & -2 $\pm$ 6 & 1 $\pm$ 3 & 13 $\pm$ 16 & 3 $\pm$ 4\\
\hline
\hline
\multicolumn{6}{c}{ \textbf{\% Retention in terms of Normalized Reward (Door, see Figure \ref{fig:door_reward})}} \\
\hline
\textbf{Task} & \textbf{1} & \textbf{2} & \textbf{3} & \textbf{4} & \textbf{Average} \\
\hline
Multi-task & 37 $\pm$ 70 & 81 $\pm$ 88 & 59 $\pm$ 60 & \textbf{93 $\pm$ 129} & 68 $\pm$ 45\\
HyperCRL & \textbf{113 $\pm$ 75} & \textbf{100 $\pm$ 76} & \textbf{99 $\pm$ 36} & 86 $\pm$ 68 & \textbf{100 $\pm$ 26} \\
SI & -17 $\pm$ 27 & 11 $\pm$ 61 & 6 $\pm$ 37 & 16 $\pm$ 60 & 4 $\pm$ 24 \\
EWC & -6 $\pm$ 33 & 17 $\pm$ 59 & 4 $\pm$ 25 & 16 $\pm$ 50 & 7 $\pm$ 22 \\
Coreset & -5 $\pm$ 28 & 26 $\pm$ 53 & 21 $\pm$ 34 & 45 $\pm$ 68 & 22 $\pm$ 24 \\
Finetuning & -14 $\pm$ 28 & 11 $\pm$ 58 & 3 $\pm$ 23 & 16 $\pm$ 65 & 4 $\pm$ 23 \\
\hline
\hline
\multicolumn{6}{c}{ \textbf{\% Retention in terms of Reward (Block Sliding)}} \\
\hline
\textbf{Task} & \textbf{1} & \textbf{2} & \textbf{3} & \textbf{4} & \textbf{Average} \\
\hline
Multi-task & \textbf{106 $\pm$ 36} & \textbf{131 $\pm$ 27} & 103 $\pm$ 39 & \textbf{113 $\pm$ 12} & \textbf{113 $\pm$ 16}\\
HyperCRL & 82 $\pm$ 56 & 98 $\pm$ 11 & \textbf{109 $\pm$ 16} & 95 $\pm$ 65 & 96 $\pm$ 22 \\
SI & 37 $\pm$ 14 & 92 $\pm$ 12 & 68 $\pm$ 56 & 103 $\pm$ 7 & 75 $\pm$ 15 \\
EWC & -5 $\pm$ 7 & 14 $\pm$ 20 & 13 $\pm$ 35 & 39 $\pm$ 27 & 15 $\pm$ 12 \\
Coreset & 58 $\pm$ 18 & 97 $\pm$ 72 & 65 $\pm$ 33 & 73 $\pm$ 21 & 73 $\pm$ 21 \\
Finetuning & -2 $\pm$ 8 & -12 $\pm$ 15 & -1 $\pm$ 4 & -7 $\pm$ 5 & -6 $\pm$ 5 \\
\hline
\end{tabular}
\caption{\textbf{Performance Retention on Pusher, Door and Block Sliding Envs}. We measure average episodic reward retained at the end of training all 5 tasks compared to the end of training on task $t$. Results show the mean and one std. deviation, evaluated across 4 seeds and 10 episodes per seed. Greater than 100 indicates positive backward transfer, otherwise it indicates forgetting.}
\label{table:pusher_forgetting}
\end{table}
\begin{figure*}[t]
\centering
\includegraphics[width=\linewidth]{figure/door_pose_reward.pdf}
\caption{\textbf{Normalized Reward on Door Environment} during training. Results are averaged across four random seeds, and the error bars represent one standard deviation. Each task is trained for 60k steps, totaling 300k steps. The reward is normalized with respect to a model trained from scratch separately on each task.}
\label{fig:door_reward}
\vspace{-0.6cm}
\end{figure*}
\vspace{-0.1cm}
\subsection{Results}
\noindent\textbf{Pusher} \texttt{HyperCRL}~is able to learn to push all 5 of the blocks across the table with minimal forgetting (Table \ref{table:pusher_forgetting}), and even shows signs of positive backward transfer. The average performance of our method is on par with the multi-task learning baseline (Figure \ref{fig:pusher_reward}), which has access to the entire history of data. \texttt{HyperCRL}~also outperforms other continual learning baselines, either regularization-based (SI, EWC), or replay-based (Coreset). Simple finetuning, however, catastrophically forgets and is unable to perform pushing for all 5 types of block at the end.
\noindent\textbf{Door}
\texttt{HyperCRL}~outperforms all continual learning baselines on the door opening task, and the multi-task baseline.
Figure \ref{fig:door_reward} shows the learning curves of all our evaluated methods, compared to a single-task baseline trained from scratch on each task. \texttt{HyperCRL}~virtually sees no performance degradation in terms of reward (Table \ref{table:pusher_forgetting}).
\noindent\textbf{Block Sliding} \texttt{HyperCRL}~ outperforms all the continual learning baselines although its performance falls short of the multi-task baseline. In Table \ref{table:pusher_forgetting}, \texttt{HyperCRL}~experiences a slight degree of forgetting on average. The learning curve is omitted here due to space constraint and is available on our project website.
\subsection{Training details}
For all experiments, we model the target network as a multi-layer perceptron (MLP) with two hidden layers (four for door opening) of 200 neurons each and ReLU non-linearity. Each task embedding is initialized as a $10d$ standard normal vector. The hypernetwork is also a MLP with two hidden layers of 50 neurons each (256 neurons for door opening). The parameters of the hypernetwork are initialized with Xavier initialization \cite{glorot2010understanding}. We use Adam with a learning rate of 0.0001 to optimize $\mathcal{L}_t$. During planning, we run CEM for 5 iterations to optimize the actions for a horizon of $h=20$ ($10$ for door opening) steps. Each iteration, we sample 500 (2000 for door opening) action sequences to maximize the sum of rewards. For SI and EWC, we use implementations from \cite{threescenario_cl}.
\section{Introduction}
Lifelong model-based robot learning is predicated upon continual adaptation to the dynamics of new tasks. For example, robots need to learn to manipulate unseen objects with various mass distributions, walk on new types of terrains with different friction, elasticity, and other physical properties, or even learn to adapt to different tasks, such as walking, running, or climbing stairs. This presents at least two challenges for many model-based reinforcement learning (MBRL) and model-predictive control (MPC) formulations, which typically comprise of a dynamics learning phase followed by a planning/policy optimization and execution phase. First, these methods are not scalable because the time required to train the dynamics model grows linearly with the size of the collected experience. Second, as the robot learner encounters and adapts to new tasks, it has to avoid catastrophic forgetting of the dynamics of old tasks.
In this work, we propose to extend the task-aware continual learning approach based on hypernetworks in \cite{continualhyper} to adapt to changing environment dynamics and to address the scalability and catastrophic forgetting challenges mentioned above in a reinforcement learning setting. We use task-conditional hypernetworks, which are neural network models that accept a learned task encoding as an input, and output the weights of another (target) network. In our case, the output is the dynamics model for that task. No additional information other than task transition boundary is needed. We show that continual learning with hypernetworks leads to effective model-based reinforcement learning, while reducing the number of updates of the dynamics model across planning sessions and preventing catastrophic forgetting.
We consider the setting where task boundaries are known in order to simplify the problem, although there are continual learning methods that have addressed the task-agnostic setting using Bayesian non-parametric methods \cite{xu2020taskagnostic}. In addition, we focus on fixed-capacity hypernetworks and target networks that can handle a sequence of tasks without adding new neurons or layers to the network, unlike many related works \cite{threescenario_cl, pnn} in which every new task adds capacity to the dynamics model. We argue that the fixed-capacity setting, together with storing only the most recent portion of the state transition experience, is more realistic and scalable for lifelong robot learning applications compared to approaches in which the training time or the model's size scales linearly with the size of collected experience.
\begin{figure}[t!]
\centering
\vspace{-0.3cm}
\includegraphics[width=\columnwidth]{figure/Corl2020Overview-crop.pdf}
\caption{Overview of our proposed method \texttt{HyperCRL}}
\vspace{-0.5cm}
\label{fig:main_diagram}
\end{figure}
Our work makes the following contributions: we show that task-aware continual learning with hypernetworks is an effective and practical way to adapt to new tasks and changing dynamics for model-based reinforcement learning without keeping state transitions from old tasks nor adding capacity to the dynamics model. We evaluate our method on locomotion and manipulation scenarios, where we show that our method outperforms related continual learning baselines.
\section{The Proposed Approach}
\subsection{Problem Setting and Method Overview}
We consider the following problem setting: A robot interacts with the environment to solve a sequence of $T$ goal-directed tasks, each of which brings about different dynamics while having
the same state-space $\mathcal{S}$ and action space $\mathcal{A}$. The robot is exposed to the tasks sequentially online without revisiting data collected in a previous task.
The robot also has finite memory and is not allowed to maintain a full history of state transitions for the purpose of re-training. Since the distribution of tasks changes over time and the agent does not know about it a priori, it must continually adapt to the streaming data of observations that it encounters, while trying to solve each task. The robot knows when a task switch occurs.
\begin{algorithm}[]
\caption{Continual Reinforcement Learning via Hypernetworks (\texttt{HyperCRL})}
\label{alg:lilac}
\begin{algorithmic}[1]
\STATE {\bfseries Input:} $T$ tasks, each with its own dynamics $\mathcal{S} \times \mathcal{A} \rightarrow \mathcal{S'}$, reward $r(s,a)$. Learning rates $\alpha_\Theta$, $\alpha_e$, and planning horizon $h$. \\
\STATE Randomly initialize hypernetwork weights $\Theta_1$
\FOR {task $t$ = 1, 2, $\dots$, $T$}
\STATE Initialize task-specific replay buffer $\mathcal{D}_t = \{\}$
\STATE Randomly initialize task embedding $e_{t}$
\STATE Collect $P$ episodes of trajectories $\tau$ using a random policy and add it to $\mathcal{D}_t$
\FOR {episode $m$ = 1, 2, \dots, $M$}
\STATE (Optionally) Reset the environment; Observe $s_0$
\STATE Generate target network weights $\theta_t = H_{\Theta_t}(e_{t})$
\STATE // \texttt{The dynamics model for the current episode is $f_{\theta_t}(\cdot)$}
\FOR {step $k$ = 1, 2, \dots, $K$}
\STATE Optimize action sequence $a_{k:k+h}$ using CEM with $f_{\theta_t}(\cdot)$ and known reward
\STATE Execute first action $a_k$, observe next state $ s_{k+1}$, add $(s_k, a_k, s_{k+1})$ to $\mathcal{D}_t$
\ENDFOR
\STATE // \texttt{Update hypernetwork and task embedding}
\FOR {$s$ = 1, 2, \dots, $S$}
\STATE Sample a batch $\mathcal{B}$ of state-action pairs $(s_k, a_k, s_{k+1})$ from $\mathcal{D}_t$ and compute $\mathcal{L}_t$
\STATE $\Theta_t \gets \Theta_t - \alpha_\Theta \nabla_{\Theta_t} \mathcal{L}_t(\Theta_t, e_t)$
\STATE $e_t \gets e_t - \alpha_e \nabla_{e_t} \mathcal{L}_t(\Theta_t, e_t)$
\ENDFOR
\ENDFOR
\STATE $\Theta_{t+1} = \Theta_{t}$
\ENDFOR
\end{algorithmic}
\end{algorithm}
We consider the solution setting of MBRL with a learned dynamics model, the parameters of which are inferred through a task-conditioned hypernetwork. Given learned task embeddings $e_t$ and parameters $\Theta_t$ of the hypernetwork $H(\cdot)$, we infer parameters $\theta_{t}$ of the dynamics neural network $f_{\theta_t}(\cdot)$. Using this dynamics model, we perform CEM optimization to generate action sequences and execute them in the environment for $K$ time-steps with MPC. We store the observed transitions in the replay dataset and update the parameters of the hypernetwork $\Theta_t$ and task-embeddings $e_t$ (off-policy optimization). We repeat this for $M$ episodes per task, and for each of the $T$ tasks sequentially.
\subsection{Training Procedure}
\noindent\textbf{Dynamics Learning.} The learned dynamics model is a feed-forward neural network whose parameters vary across tasks. One way to learn a dynamics network $f_\theta(\cdot)$ across tasks is to update it sequentially as training progresses. However, since our problem setting is such that the agent is not allowed to retain state-transition data from previous tasks in the replay buffer, adapting the weights of a single network sequentially across tasks is likely to lead to catastrophic forgetting~\cite{continualhyper}. In order to alleviate issues of catastrophic forgetting while trying to adapt the weights of the network, we learn a hypernetwork that takes task embeddings as input, and outputs parameters for the dynamics network corresponding to every task, learning different dynamics networks $f_{\theta_t}(\cdot)$ for each task $t$.
We assume that the agent has finite memory and does not have access to state-transition data across tasks. So, the task-specific replay buffer $\mathcal{D}_t$ is reset at the start of every task $t$. For the current episode, the agent generates a dynamics network $f_{\theta_t}$ using $\theta_t=H_{\Theta_t}(e_t)$. Then, for $k=1...K$ timesteps and planning horizon $h$, the agent optimizes action sequences $a_{k:k+h}$ using CEM, and executes the first action $a_k$ (MPC). $\mathcal{D}_t$ is augmented by a tuple $(s_k,a_k,s_{k+1})$, where $s_k$ is the current state, $a_k$ is the executed action, and $s_{k+1}$ is the next observed state under task $t$.
The parameters $\Theta_t$ of the hypernetwork and the task embeddings $e_t$ are updated by backpropagating gradients with respect to the sum of a dynamics loss $\mathcal{L}_\text{dyn}$ and a regularization term. We define the dynamics loss as $\mathcal{L}_{dyn}(\Theta_t, e_t)=\sum_{\mathcal{D}_t}||\hat{s}_{k+1}-s_{k+1} ||_2$, where the predicted next states are $\hat{s}_{k+1}=f_{\theta_t}(s_k,a_k)$ and $\theta_t=H_{\Theta_t}(e_t)$.
In practice, we infer the difference $\Delta_{k+1}$ through the dynamics network ($\Delta_{k+1}=f_{\theta_t}(s_k,a_k)$) such that $\hat{s}_{k+1} = s_k + \Delta_{k+1}$ for stable training.
In addition, inputs to the $f_{\theta_t}$ network are normalized, following the procedure in previous works~\cite{pets}. Similarly, a new $e_t$ is initialized at the start of every task and updated every episode during the task by gradient descent. Older task embeddings ($e_{1:t-1}$) could also be amenable to gradient descent, but we keep them fixed for simplicity.
\vspace{0.1cm}
\noindent\textbf{Regularizing the Hypernetwork.} To alleviate catastrophic forgetting, we regularize the output of the hypernetwork for all previous task embeddings $e_{1:t-1} $. After training for task $t-1$, a snapshot of the hypernetwork weights is saved as $\Theta_{t-1}$. For each of the past tasks $i=1...t-1$, we use a regularization loss to keep the outputs of the snapshot $H_{\Theta_{t-1}}(e_i)$ close to the current output $H_{\Theta_{t}}(e_i)$. This approach sidesteps the need to store all past data across tasks, preserves the predictive performance of dynamics networks $f_{\theta_t}$, and only requires a single point in the weight space (a copy of the hypernetwork) to be stored. The task embeddings are differentiable vectors learned along with parameters of the hypernetwork. The overall loss function for updating $\Theta_t$ and $e_t$ is given by the sum of the dynamics loss $\mathcal{L}_\text{dyn}(\cdot)$, which is evaluated on the data collected from task $t$ and the regularization term $\mathcal{L}_\text{reg}(\cdot)$:
\begin{eqnarray}
\begin{aligned}
\mathcal{L}_t(\Theta_t, e_t) = \mathcal{L}_\text{dyn} (\Theta_t, e_t) + \mathcal{L}_\text{reg}(\Theta_{t-1},\Theta_t, e_{1:t-1}) \\
\mathcal{L}_{\text{reg}}(\cdot)
= \frac{\beta_\text{reg}}{t-1} \sum_{i=1}^{t-1} \| H_{\Theta_{t-1}}(e_i) - H_{\Theta_t}(e_i)\|_2^2
\end{aligned}
\end{eqnarray}
The planning objective for CEM optimization of action sequences is given by the sum of rewards obtained by executing the sequence of actions $a_{k:k+h}$ under the learned dynamics model $f_{\theta_t}(\cdot)$ for the task. The reward function $r(s, a)$ is assumed to be known, but nothing precludes learning it from data under our current framework.
\section{Preliminaries}
\textbf{Hypernetworks for Continual Learning.} A hypernetwork~\cite{hypernetworks,Schmidhuber1991LearningTC} is a network that generates the weights of another neural network.
The hypernetwork $H_{\Theta}(e)=\theta$ with weights $\Theta$ can be conditioned on an embedding vector $e$ to output the weights $\theta$ of the main (target) network $f_{\theta}(x) = f(x;\theta) = f(x;H_{\Theta}(e))$ by varying the embedding vector $e$. The hypernetwork is typically larger with respect to the number of trainable parameters in comparison to the main network because the size of output layer in the hypernetwork is equal to the number of weights in the target network. Hypernetworks have been shown to be useful in the continual learning setting~\cite{continualhyper} for classification and generative models.
This has been shown to alleviate some of the issues of \textit{catastrophic forgetting}. They have also been used to enable gradient-based hyperparameter optimization~\cite{stn_vicol}.
\textbf{Planning with CEM and MPC.}
The Cross-Entropy Method (CEM)~\cite{cem} is a widely used online planning algorithm that samples action sequences from a time-evolving distribution which is usually considered to be a diagonal Gaussian $a_{1:h}\sim\mathcal{N}(\mu_{1:h},\texttt{diag}(\sigma^2_{1:h}))$, where $h$ is the planning horizon. Action sequences are iteratively re-sampled and evaluated under the currently learned dynamics model, and the sampling distribution parameters $\mu_{1:h},\sigma_{1:h}$ are re-fitted to the top percentile of trajectories. CEM for planning in MBRL has been successfully used in a number of previous approaches~\cite{pets,planet}, as it alleviates exploitation of model bias compared to purely gradient based optimizations~\cite{l4dc} and can better adapt to varying dynamics as compared to fully amortized policies~\cite{dreamer}.
\section{Related Works}
\textbf{Continual Learning in Neural Networks} Continual learning studies the problem of incrementally learning from a sequential stream of data with only a small portion of the data available at once~\cite{clsurvey}.
A simple yet effective approach is finetuning, which directly tunes the trained source task network on the target task~\cite{bengio2012deep}.
The efficacy of this approach for continual learning suffers from the well-established phenomenon of catastrophic forgetting~\cite{pnn}.
Sequential Bayesian posterior updates are a principled way to perform continual learning and naturally avoid the forgetting problem since the exact posterior fully incorporates all previous data but in practice approximations have to be made that may be prone to forgetting.
Elastic Weight Consolidation (EWC) uses a Laplace approximation to the posterior, storing previous tasks' empirical fisher matrices and regularizing future task weight deviations under their induced norms~\cite{ewc}. Other works have also employed variational mean-field approximations~\cite{vcl} or block-diagonal Kronecker factored Laplace approximations~\cite{kfac-cl}.
Synaptic Intelligence (SI) forgoes an obvious approximate Bayesian interpretation but operates similarly to EWC in that it computes a relative parameter importance measure, but through a linear approximation to the contribution in loss reduction due to each parameter on previous tasks~\cite{si}.
Coreset methods prevent catastrophic forgetting by choosing and storing a significantly smaller subset of the previous task's data, which is used to rehearse the model during or after finetuning~\cite{gem, agem, tinycoreset}. Similarly, the inducing points used in sparse Gaussian Process (GP) formulations, which can be seen as a type of coreset, has been used for continual learning ~\cite{Titsias2020FunctionalRF, vargp}.
Another type of approach learns separate task-specific network components. The most common version of this are multi-head networks that learn and switch between separate output layers depending on the task~\cite{lwf}. Progressive Neural Networks (PNN)~\cite{pnn} are an extreme version of this approach, in which an entirely new copy of the network is appended for each task, thereby eliminating any forgetting. These methods can incur significant memory and compute cost especially for larger models and many tasks.
\textbf{Model-based RL} Model-based reinforcement learning approaches incorporate model learning of the environment in solving the control task.
Traditionally, the model is trained to approximate the stationary dynamics and/or reward of the environment from all collected samples.
Various choices for the model have been proposed.
Many non-parametric models, such as commonly used GPs, rely on storing and making inferences with past data~\cite{deisenroth2011pilco}, although in many cases the amount of data needed to be stored can be drastically reduced through sparse variational inference~\cite{burt2018explicit}. Nonlinear parametric models typically do not admit efficient sequential update rules and therefore usually train on all past data as well~\cite{raiko2009variational}.
Typically, the trained model is then used to simulate imagined trajectories, either for the purpose of online planning~\cite{pets, planet} or as training data for an amortized policy~\cite{dreamer}.
In non-stationary environments, the dynamics can change over time.
In this setting, a lot of works focus on quickly adapting to the change in dynamics to minimize online regret, as opposed to retaining performance on previously experienced dynamics~\cite{basso2009reinforcementnonstat,padakandla2019reinforcement, hallak2015contextual}. Meta-learning is a popular tool in this paradigm where a global dynamics model is ``meta-trained" to quickly adapt to the true online dynamics from only a few samples. However, the meta-learning process typically requires updating the meta-model with data from a diverse set of dynamics that is obtained by storing previous experiences in a buffer and/or being able to simultaneously interact with many different environments~\cite{al2017continuous}.
\textbf{Relationship to Meta-Learning} Our work is different from meta-learning approaches in MBRL like \cite{mole_mbrl, learningtoadapt} in two ways. First, we focus on preventing catastrophic forgetting and do not explicitly train a model prior across multiple tasks for fast adaptation. This means that we do not need to design a set of tasks for meta-training and in principle, our work can continuously learn to perform new tasks from scratch. Second, we do not require the use of a replay buffer that grows linearly with the number of tasks or total length of collected state-transition pairs. We emphasize that this is consistent with the theme of continual learning, where storing past data is limited.
\textbf{Continual RL} Memory-efficient continual learning methods in the reinforcement learning setting have also been proposed. PNN was used in an on-policy actor-critic method and was demonstrated on sequential discrete action Atari games. The authors of~\cite{p&c} build on top of PNN and continual policy compression methods~\cite{Berseth2018ProgressiveRL} by compressing the extended model from PNN into a fixed size network after each task. For the compression stage, they propose a more scalable online EWC algorithm that eschews the linear cost of storing past fisher matrices.
The use of coresets has also been explored in this setting~\cite{abel2018state}. In~\cite{mole_mbrl}, a mixture model of separate task-specific neural networks is used for the environment model that requires adding a new model each time a task is instantiated.
A similar approach was also demonstrated using a mixture of GPs using an online clustering algorithm~\cite{abdollahi2015adaptive}. Our work is also related to MPC interpretations as a reduction to online learning~\cite{boots_mpc_online_learning}.
\textbf{Robust and Adaptive Control} Existing literature on control theory provides many related classes of approaches that handle changes in dynamics: adaptive control methods handle unknown parameters of a dynamics model by estimating them over time so as to execute a given trajectory, and robust control methods provide stability guarantees as long as the parameter or model disturbance is within bounds \cite{adaptivecontrol_book}. The setting we study in this work differs in that we learn the dynamics model from scratch, without assuming a reference model, and it may change over tasks without imposing any bounds on particular parameters.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,060 |
Q: Looping through a subset of an Oracle Collection I would like some help with a bit of recursive code I need to traverse a graph stored as a collection in PL/SQL.
---------
|LHS|RHS|
---------
| 1 | 2 |
| 2 | 3 |
| 2 | 4 |
| 3 | 5 |
---------
Assuming 1 is the start node, I would like to be able to find 2-3 and 2-4 without looping through the entire collection to check each LHS. I know one solution is to use a global temporary table instead of a collection, but I would really like to avoid reading and writing to and from disk if at all possible.
Edit: The expected output for the above example would be an XML like this:
<1>
<2>
<3>
<5>
</5>
</3>
<4>
</4>
</2>
</1>
Thanks.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,147 |
Various threads on Andrew Sullivan's Daily Dish over the last month or two, and the much-quoted opinion of Judge Vaughn Walker in the California gay marriage case, are calling me to put on my philosophical hat, to set out some philosophical drinks and snacks and a metaphorical water-pipe to try to entertain and inform my guests, on the subject of morality. Morality is one of the most human of concepts: every society has one or more, nearly everyone across the globe in all eras has been pretty sure that they understand what it is, and nearly everyone believes they use, hold or embody a significant piece of it in their lives.
I would just like to pound the point a little further and deeper: morality is not a great basis for any kind of civic discussion or rational argument in a diverse democracy, because in the final analysis morality is always subjective. As I first wrote 30 years ago, morality is a classic case of a "mental event," an event that occurs only within the minds of human beings. You may believe that your morality comes from a Holy Book, or from a Divine Judgement or some other source beyond the human mind, yet as a historical-philosophical kind of guy, I will forever argue that morality – just like several other abstract concepts that are near-universal in human thought such as beauty or justice – cannot be found in the real universe in any place but inside human heads, and I defy you to show me any other physical location where morality exists.
It's actually a touching tribute to our creativity, to our ingenuity in finding reasons to justify that which we already prefer, that so many people vaguely believe that there is some abstract ideal of morality that could be found if we would all just look for it nicely. This Platonic ideal of a universal morality is a strong enough stereotype to recur again and again in all types of utopian philosophies, but it just doesn't exist, as far as I can tell, in any type of reality. Even in societies much less diverse than our own, in which all individuals seem to follow one particular religious-ethical-moral set of beliefs, individual A can never be fully sure that individual B understands every situation calling for a moral judgement precisely the same way that A understands it. Even though their main beliefs may come from the same set of social institutions, from the same proverbs and the same books or traditions, their individual development and experiences brings about subtle or large differences in understanding.
Morality is essentially your own belief about which persons and what behaviors should be honored and respected, by you and by others, in a "proper" social order.
These differences in moral understanding, among individuals in a homogenous society, may not amount to much in the ordinary course of peaceful life. However, it's always in moments of crisis, in times of testing, that the differences in interpretation of the same tradition – and/or the willingness of B or C to sacrifice their goods or social positions, or other desired values, as morality may demand in moments of crisis – demonstrate the subjective basis of morality in human life, as individuals take actions that create individual and/or social conflicts. In short, even when everyone supposedly shares the same morality in societies much less diverse than our own, people find reasons to do things, and others find reasons to yell and scream and fight, because they say those things the first people did are immoral. This is one of the basic dynamics of both small-group and large-group historical action, in all lands and in all times.
On the other hand, the strength of social systems of morality is shown by the vast majority of individual cases, in which individuals do accept the dictates of the dominant moral system of their group, even though it "gores other parts of their ox," to alter the old proverb, and individuals do feel great regret for their lapses in being able to follow the dominant morality. And haven't we all known cases of people who are so prepared to accept a negative judgement on themselves, that it seems they are blaming themselves for self-imagined moral faults that no one else even noticed?
Despite the subjectivity of morality, and the slipperiness of individuals in choosing whether or not to be bound by social systems of morality when push really comes to shove, concepts of morality are deeply rooted in human thought, and will never disappear from human thought. If you understood my system for analyzing the four simultaneous, overlapping social sciences that each of us are creating in our every moment of choice in our every day of human action and interaction, you would find it easy to understand how thoughts of morality are oh-so-basic and constantly self-generated in the average human animal, since morality essentially arises from the intersection of the two most social of the four simultaneous, overlapping social sciences. These would be what I call "the science of explanations," which you would probably call by one of its more common names such as philosophy/ science/ religion/ ideology, in which humans are constantly creating and distributing explanations of what our world is about and how it works, and what I would call the science of politics, which begins on the most basic level with humans creating and distributing systems of what other persons they accord honor, status and rank to (which gives a foundation to the extreme elaboration and institutionalization of governmental structures in modern society, which house the narrow range of behaviors that are commonly called "politics" in American democracy in the era of idiotic electronic media).
You follow all that? In short, you (and everyone else) are constantly creating and distributing explanations of how the world works, and you are constantly creating and distributing ideas of persons and behaviors that you respect and honor. Morality is basically a combination of the two, a set of explanations of how the world works which depends on honoring and respecting certain behaviors in certain situations (and disrespecting other behaviors in those situations). Morality is essentially your own belief about which persons and what behaviors should be honored and respected, by you and by others, in a "proper" social order. You can't be much of a human being if you aren't constantly giving and receiving these two types of ideas, the philosophical and the political, if you aren't deeply affected by the explanations you choose to use and the social behaviors that you choose to respect or disrespect. To have and hold and use concepts of morality is a very, very deeply rooted structure in human personalities.
Yet despite how deeply they may be rooted in our personality structures, concepts of morality remain fundamentally subjective as well. I cannot get into your skull and understand your sense of morality in the same way you understand it; you cannot get into my skull and understand my sense of morality in the same way I understand it. In the typical society of a few hundred years ago, one could generally be sure that one's neighbors and acquaintances in a city would be members of one's same culture that shared the same basic moral postulates: the prevailing religion, an understanding of the local kinship systems and beliefs, and so on. In such circumstances, there's a small point in arguing about morality: while you and your interlocutors are unlikely to convince each other of your rightness, at least you might clarify differences in your interpretation of your overall shared moral system, or even find areas of contradiction or ambiguity in the moral system your society has evolved.
In today's diverse societies, however, while you may believe that your own morality is founded on the finest principles and supported by the most divine angels, you never know about your neighbor, your co-worker, the guy in the next car on the freeway or the passenger in the next seat on the transit system: she may believe herself to be a devotee of Cthulhu or Cheney, or any other variant of a bloodthirsty ideology which believes you should be cut down mercilessly if you get in their way. A modern American Christianist Palinite's moral system has little or no relation to the diverse sources and experiences that create and define the many subgroups of the American cultural left, for either side to make arguments based on their vision of "morality" and expect the other side to accept it, is to admit and announce that the speaker has no understanding of what drives the cultural opposition to their program.
We're going to have arguments: but let's try to keep them on sounder grounds than the subjective terrain of morality. Do argue about philosophy, about the explanations that we use to make sense of the world (and remember, I use the word "philosophy" to include all of the content implied by the words "science" and "religion"). These arguments aren't likely to be highly fruitful either, yet presumably there is an underlying reality that each side can claim to provide better explanations for, and over the centuries we might be able to say "the bulk of the evidence favors this particular side of the argument." Do argue about politics, about which persons and personality types should be respected, about what behaviors should be honored and rewarded and what behaviors should be dishonored and punished in various ways. This argument may often degenerate into arguments based on competing moral systems, yet again, keeping the focus on the basic question of political science in human societies, which persons are we respecting and why, may in time help clarify the issues and choices and improve people's decision-making skills, and improve the outcomes for human societies as a whole.
Even in the less diverse societies of the past, morality was always a subjective value, a mental event that existed only within the minds of human beings (even if they claimed that their morality had divine or eternal foundations of some sort). In today's society, morality has become so completely subjective, it is really quite useless to argue about it, or from it, in any way. The basic science of explanations, philosophy/science/religion, has itself been shattered into a million apparently subjective shards which give no compelling guidance to a diverse, even self-contradictory, social system we barely understand (and in which our major media channels seem to be actively trying to prevent understanding). Until we can come to a better consensus on basic explanations of reality – something we can hopefully do before we totally destroy the planet that supports our human lives – we won't have any hope of convincing anyone of anything based on concepts of what we call morality.
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{"url":"http:\/\/myatnanyone-npt.com\/smooth-pigweed-pjlxls\/pl8rods.php?tag=89b143-mythic-vital-strike-pathfinder","text":"You can beat this, probably. Vital Strike (Mythic) You can strike your foes with incredible force. Particularly beware of the Confounding Bandersnatch, which has additional methods of confusion (DC 29 Fort save injury poison). Making statements based on opinion; back them up with references or personal experience. Mythic Improved Vital Strike (Mythic) - Pathfinder_OGC. Yes, its important to make that distinction for non-native english speakers.. New comments cannot be posted and votes cannot be cast, More posts from the Pathfinder_RPG community, For info, news, resources, and anything else about the Pathfinder TTRPG! Our first test cases are going to be taken straight from the SRD so there's no building involved and it's clearer that these sorts of things ought to be expected: Bakekujira: dice and add the results together. Prerequisite(s): Vital Strike. die. Furthermore, this requires a Full-Round Action rather than a Standard Action. If you need to roll multiple dice of the same type, The only real problem is that you'll likely outshine or be overshadowed by most straight base-class characters; there isn't a whole lot in your power bracket at level 17. Normal: Vital Strike only applies on the first attack of each of your turns. So for Vital Strike, you should multiply your bonuses by 2: When you use the attack action, you can make one attack at your highest base attack bonus that deals additional damage. If you really care enough you can probably run her to ground eventually, you'd just have to be pretty determined. The Horned Champion must choose and prepare his feats ahead of time by getting 8 hours of sleep and spending 1 hour in physical training. (For weapons with more than one damage die, count all the weapon\u2019s base damage dice together as one.) Which was my goal to begin with! Am I correct in believing that it's the number of sets of dice (\u00d72, \u00d73 or \u00d74, for the 3 Vital Strike feats) that are rolled instead of the physical # of dice that are actually rolled? X2, X3, X4 are certainly more consistent with the effects of the prerequisite feats. A new Mythic worksheet has been added to increase support for the awesome (and free!) So people looking to become immune to your attack can do so between levels 9 and 13, generally, and at 17th level, when you get the attack, PC-equivalent enemies can easily render themselves immune. If you then add in foe biting, that becomes 6d8 weapon damage(3d8 for IMV, then doubled), 12d6 sneak attack, 2d6 fire, 2d6 electricity, and +86 base damage. MathJax reference. Is scooping viewed negatively in the research community? Prerequisites: Vital Strike, Improved Vital Strike, Greater Vital Strike, Mythic Vital Strike. Hope you brought an optimized T1 full-caster... or two... Rune Giant Benefit: Whenever you use Vital Strike, Improved Vital Strike, or Greater Vital Strike, multiply the Strength bonus, magic bonus, and other bonuses that would normally be multiplied on a critical hit by the number of weapon damage dice you roll for that feat. Mythic Vital Strike will allow me to multiply all modifiers by the number of damage dice I deal with Vital Strike. Shadow Body is a 5th-7th level spell that grants you incorporeality. Bandersnatch: Mythic Power (Su): Each day, he can expend a number of uses of mythic power equal to his mythic rank (10). Vital Strike: Forms with only one natural attack with high damage can capitalize on Vital Strike. The number of dice rolled for a Greataxe is one d12, that is, you roll one twelve-sided die. Can create illusions. If the weapon is normally 2d6 and your bonuses (strength, etc) are +10 (or 2d6+10), you would roll 4d6+10 with Vital Strike. You're pretty much dead. Mythic Vital Strike turns this all on its head, as that feat now makes every single modifier that would be multiplied by a crit now get multiplied on the Vital Strike standard action. It relies exclusively on stacking negative levels to kill stuff, and only does like 8 negative levels a round, tops, so if you hit its 31 AC within a couple rounds you're good. Thanks for contributing an answer to Role-playing Games Stack Exchange! This attack counts as a Vital Strike despite not using an attack action. Use MathJax to format equations. AC 32, but 36 with Blade Barrier's cover effect up. Our five mythic feats will be Mythic Eldritch Heritage, Mythic Power Attack, Mythic Vital Strike, Mythic Improved Vital Strike, and Mythic Weapon Specialization. (3) and (4) are never multiplied by anything ever... except for Mythic Improved Vital Strike, which lets you ignore that 'exception' and multiply (1), (2), (3), and (4) If you have Improved Vital Strike that becomes 6d6+30, and Greater Vital Strike it becomes 8d6+40. Let's say you have Improved Vital Strike, 6d6 sneak attack, Flaming and Shock on a +3 longsword, and +43 base damage(+20 strength, +10 dex, +10 int via mythic weapon finesse). Meanwhile the casters are spamming their most powerful spells at +2 CL for 1 mythic point, without even needing to know or prepare the spell, without using a spell slot, and that isn't even including any path abilities or feats, that's just lvl \u2026 Maralith Also grapples, which negates your abilities. Mythic vital strike is pretty crazy. Also can use binding and disguise and teleport and dominate monster and all that good stuff. Mythic Vital Strike says: Whenever you use Vital Strike, Improved Vital Strike, or Greater Vital Strike, multiply the Strength bonus, magic bonus, and other bonuses that would normally be multiplied on a critical hit by the number of weapon damage dice you roll for that feat. Vital Strike (Mythic) You can strike your foes with incredible force. Mostly the army is the problem. NUTS! AC 30 and you are blinded so there's also a 50% miss chance. Mythic Hero Mythic Hero is a class in Pathfinder: Wrath of the Righteous. Extra damage from sources that wouldn\u2019t normally be multiplied on a critical hit isn\u2019t multiplied by this feat. I greatly respect the work & effort of your argument, the dark wanderer. You can beat this, but it's not intended as a solo monster but rather as a minion of something more dangerous. Could try to disarm you with each. However, this nets you a semi-permanent increase in power since you get the defeated creature rather than just killing it and also it prevents the use of True Resurrection spam as a defense. Immortal Ichor: It's also probably somewhat faster than you, gets to do a bunch of stuff as swift actions that are normally standard actions, and generally can use the saved time to out-range you. From Two-Handed Fighter, we get Shattering Strike, Overhand Chop, Weapon Training, and Greater Power Attack. Vital Strike (Combat) You make a single attack that deals significantly more damage than normal. That's... a pretty rediculously good defense. with the \u201c#\u201d representing the number of sides on the Oh well, guess you sit this one out. Mythic rules from Paizo! The Vital Strike feat tree is simple compared to feat-starved trees like Two-Weapon Fighting. You're actually a pretty solid combatant against most dragons, but this one's secondarily a grapple monster so you're just really good rather than a shoo-in. It has greater teleport at will, and anyone teleporting near it loses at least one turn, no save. You can probably kill it, assuming you have your party for backup. This undead whale's long-range-strike capability allows it to close with you first, despite its massive size, ensuring that you begin your turn within its Undead Parasites effect. Not on how many die you roll for your damage. Role-playing Games Stack Exchange is a question and answer site for gamemasters and players of tabletop, paper-and-pencil role-playing games. Banning or nerfing a single specific feat is very unlikely to change the overall way the system plays, while making a feat more powerful does risk significant and problematic changes, from a theoretical standpoint. Even then it can grapple you with its AoO, is probably hidden requiring Perception to locate, and has 32 AC. Meh...I think you might of misunderstood it originally for I was talking about all 3 of the Mythic Vital Strikes, which is why I was quoting the disgusting 10k+ hits...etc. But it is published as CR 17 and Mythic and you can kill it real easy. Updating Pixel after many months. The latter is about as explicit as the could possibly be that you multiply the damage done by the total number of weapon dice rolled for the feat. ;). Vital Strike (Mythic) You can strike your foes with incredible force. Swarms! Lets look at what sorts of defences high-powered 17th level characters typically have, and whether an infinite-damage melee vital strike would be enough to overcome them. At only 5 feats, any fighter character could make use of Vital Strike and still have room in their feat list for other interesting feats. The masters of mythic at Legendary Games explain rules rationales and concepts and offer an array of alternate rules to deal with the most problematic elements in the mythic rule set like Mythic Vital Strike, wild arcana, foe-biter legendary weapons, and more! The Spell isn't affected by Vital Strike [Mythic].It is not part of the weapon.It is only delivered through a weapon attack, which is the thing enhanced by Vital Strike [Mythic]If your weapon was flaming would have an enchantement on it (like Greater Magic Weapon), that would be multiplied by Vital Strike [Mythic]. Can see through your illusions. To learn more, see our tips on writing great answers. Still generally better than your ability, though. Nothing in the rules says that. Imprisonment spam: single Will save at -4 or die-and-don't-come-back, melee range standard action. So the multiplier clearly goes up the really-big way and not the looks-really-big-but-is-actually-100%-a-trap way. Pathfinder Second Edition Beginner Box by Paizo Dungeon Master's Guide ... Great Cleave, Greater Vital Strike, Improved Critical M (Slam), Improved Vital Strike, Power Attack M , Toughness, Vital Strike. You can literally do nothing against this creature. Plus mind control is pretty easy to block. Their total should have been high enough to kill anything they were going to kill with regular Mythic Vital Strike; Improved Mythic Vital Strike is a wasted feat and power attack is ridiculously awful for this build. However, there is always the counter argument\/action that can be taken...the arms race. If you succeed at both checks, you kill the whale, if you fail you do nothing with your turn except possibly cause yourself more damage. Well, as everyone probably have noted, some of the mythic feats are pretty broken - especially Mythic vital Strike. Greater Vital Strike, Improved Vital Strike, Mythic Improved Vital Strike, Mythic Vital Strike, ... Latest Pathfinder products in the Open Gaming Store. Gets so many attacks each round. Grants 1 additional Vital Strike on the last attack of the turn. Even if mundane and melee characters aren't supposed to get anything nice ever, they feature largely in the faux-mythological material that 3.X is descendant from. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Phasmadaemon So, there's a bunch of fights where you can contribute to your party and a coordinated effort around you would lead you to probable victory, a number of fights where you're utterly useless, and a number of fights you could win even on your own maybe. You can kill this less well than most people, since it can actually attack you back, but a party of well-built level 5 characters could take it out if the felt like it. Can Vital Strike be used on a charge? The intro chapter covers this, saying: Whenever a roll is required, the roll is noted as \u201cd#,\u201d You aren't the wimpy ne'erdowell of the typical melee combatant, and you aren't the omniscient omnipotent deity of the typical magic-user. While training, the Horned Champion decides which feats to prepare. Why are fifth freedom flights more often discounted than regular flights? Mythic Vital Strike expands the power of Vital Strike to let you multiply (1) and (2) in the same way that a critical hit does, but it's not a critical hit. 1: Races of Nature Unleashed (PF1) Aegis of Empires 5: Race for Shataakh-Uulm (Pathfinder RPG) Like, it works across planes and without line of effect. It creates new permanent demiplanes or alters remote environments in pre-existing planes, seeds them with new life, then eventually abandons them. The following is a break down of the new options available to players; what\u2019s good, what\u2019s bad, and how things work. Press question mark to learn the rest of the keyboard shortcuts. Does Mythic Vital Strike count individual dice or sets of dice? It's a grapple monster with a save-or-suck gaze attack targeting Will. But what does this mean? For help with Vital Strike, see my Practical Guide to Vital Strike. Overkill, like I mention, is cool and mythic but doesn't actually do anything. Do look out for Improved Mythic Vital Strike, though, which allows the damage to rocket towards your initial estimates and makes this sort of problem available at 11th level. It's invisible, and can knock out magical methods of flight with greater dispel magic. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Benefit: Your Vital Strike is additionally applied to the last attack you make during your turn, not just the first.. Normal: Vital Strike only applies to the first attack you make each turn. You can deliver blows that shatter bone and liquefy internal organs. Deatch Clutch spam: hp-limited one-roll save-or-die, but always makes the opponent staggered and might deal serious Con damage against opponents with too much hp. Irminsul: It can charge through difficult terrain, and ignore most applyable conditions with ease. That's a lot, enough to one shot Cthulhu. What is the word to describe the \"degrees of freedom\" of an instrument? This amount is its maximum amount of mythic power. God Bless! Also can fly, which renders you irrelevant unless you can, too. Vital Strike Power Attack Calculator. Specifically, you multiply the applicable bonuses by 64 in the most extreme case. So if you do decide to make it work this way it will look and feel fine, basically. Also it gets PaO 3\/day, which is one of the most powerful spells in the game and allows it to ensure you are fighting whatever it wants as well as it. Grapples, rending your abilities irrelevant. It can fly, though. Can teleport at-will. I also read it wrong at first but common sense kicked. Furthermore, most save-or-die's in Pathfinder require two saves rather than one, and most of them are spells. Ancestral Anthologies Vol. I'm pretty sure you can't even get that high of a bonus. Can you use Vital Strike with Focused Attack for crit build? A mythic red dragon's body has cordlike muscles that allow it to move more quickly and gracefully than a creature of its size should have a right to. At high levels, where everything has telepathy, this becomes a contest of wills with any creature that makes its save-- whoever fails the will save first dies. Has the hp to take hits from your unarmed strikes, assuming that's not your main weapon (you do something like 2d6X4+strX8 damage, and provoke AoO with that). It only takes a minute to sign up. Vital Strike: Double weapon damage. It's quite a lot of damage if you go about it right. Fort +5. Druidic summoning spam: Druids get armies of increasingly powerful free-willed beings. Can fly. It possesses okayish ranged attacks that inflict the sickened condition on its targets, in addition to the ranged swift action confusion. Mythic Maraliths can Mythic Blade Barrier, which is an immediate action. She can probably escape you but that's hardly a victory, and being able to force her away from whatever you want is basically winning. The Bandersnatch confuses you (DC 29 Fort save to negate), possibly resulting in you OHKOing your party members. 20% chance you're fighting two of these. Prerequisites: Vital Strike, Improved Vital Strike, Greater Vital Strike, Mythic Vital Strike . You are correct on many points. In spite of this, they're still similar in many ways to other adventurers. So, you get to, on a hit, do ~2304 damage. I also have Mythic Power Attack through the Extra Mythic \u2026 The Paizo Pathfinder Roleplaying Game rules. ...This should not be CR 17. Roll the weapon\u2019s damage dice for the attack twice and add the results together before adding bonuses from Strength, weapon abilities (...). Does concealment negate all precision damage? While with Mythic Vital Strike that becomes 4d6+20. Uses illusions and misdirection to evade your attacks. (note for non-english speakers: the plural of 'die' is 'dice'). Spring Attack is a special kind of full-round action that includes the ability to make one melee attack, not one attack action. Prerequisites: Base attack bonus +6. Villains of the worst kind, mythic red dragons are unflinchingly evil in ways rarely matched even by other mythic evil creatures. The same goes for Improved Vital Strike (x3), and Greater Vital Strike (x4). (Not including Holy or energy damage, which are x32 also.) You don't really need to ever do more damage than that. My character is currently a level 11 Paladin, Mythic Tier 2, with Vital Strike and Improved Vital Strike, and Mythic Vital Strike, obviously. Since it has no realistic way of harming you, you can just get back up and continue trying to hit its 32 AC, even if that does happen. But it wouldn't matter too much since you can't cast and use Vital Strike in the same turn as they will both always be a standard action, making it very useless for a Magus. That's a different feat than you asked about in your question, and I already mention it in my last line. Does anyone has any idea of how to The same goes for Improved Vital Strike (x3), and Greater Vital Strike (x4). You can use it to select your Mythic path, set your Mythic Tier, as well as track your surge ability, Legendary Item (if you are lucky enough to have one!) So, instead of applying those bonuses (ie: strength) once, you apply them twice. Devastating Strike allows me to add +2 damage to my Vital Strike per additional set of weapon damage that I deal, so +2 with Vital Strike or +4 with Improved Vital Strike. Weapon = +6 (bane = +8) ST 36 (2h) = +19 Mythic power attack = +48 Sacred Bonus = +4 Morale Bonus = +5 (Skald & Bard) Luck Bonus = +3 Mythic Enlarge Person = Size H (sword Gigantic) Sword has Impact. HP. Class and Path Abilities. Not a good fight for you. Prerequisite: Vital Strike. Mostly, it's just different. Because Vital Strike only multiplies the weapon's base damage (just the dice; no enhancements), Vital Strike seems like a poor tactical option. Vital strike lets you do your 4 swings worth of damage in one single swing, mythic vital strike multiplies all bonuses as well The plan is to use vital strike instead of full attack, you concentrate on single standard action attacks and do a full 4 times damage when you hit CTP\u2019s Guide to Pathfinder Mythic Adventures Introduction A new pseudo-subsystem for Pathfinder has been released in the form of Mythic Adventures. The mythic optional rules are all about the players having overtly super-powered versions of normal characters. 135 After rolling the damage of a Vital Strike attack, you can spend 2 stamina points to reroll up to two of the weapon\u2019s damage dice. Vital Strike allows you to forego additional attacks in favor of making a single attack with high damage. Heck, a party of level one characters can kill this thing if you pick the right ones. By clicking \u201cPost Your Answer\u201d, you agree to our terms of service, privacy policy and cookie policy. Even your 10,000 damage estimate is far overblown. Final project ideas - computational geometry. It can shoot lightning bolts from 1200 ft away, including 1\/day an empowered chain lightning for 30d6 damage to everyone. Re: Mythic Vital Strike, in the tabletop any character that gets access to the 3rd-tier mythic ability Fleet Warrior doesn't need to even bother with Vital Strike stuff, though I don't know if \u2026 We can only say \"caught up\", Integral of a function defined with a loop. Prerequisites: Improved Vital Strike, Mythic Vital Strike, Vital Strike, base attack bonus +11, 5th mythic tier.. ;) Such as Dispel Magic against the spells you mentioned, etc. It's got a number of methods to neutralize you, though, obviously, if you get a hit off it's dead. Keep in mind this is a level 16 or higher character with mythic tier. It's got nausea poison and tree shape, mostly. For example, if using Improved Vital Strike, you would roll the weapon\u2019s damage dice for the attack four times before adding other damage bonuses, instead of three times. Has an army. So, basically, mythic vital strike states \"everything that is doubled in a critical, is doubled in your vital strike\", the normal vital strike states that you \"cannot apply your vital strike damage bonus to critical, but anything else can\" Employer telling colleagues I'm \"sabotaging teams\" when I resigned: how to address colleagues before I leave? The masters of mythic at Legendary Games explain rules rationales and concepts and offer an array of alternate rules to deal with the most problematic elements in the mythic rule set like Mythic Vital Strike, wild arcana, foe-biter legendary weapons, and more! Fights that aren't against solo monsters aren't your strong suit. Making this change punishes mundane characters to the advantage of casting classes, which is consistent with the Pathfinder design eidos. that would imply your damage modifiers summed to 30,000\/64, or ~469. Otherwise, I feel like you're correct, but could definitely see a GM ruling that it multiplies the Shocking Grasp too. It seems like you might be having touble understanding how big numbers of weapon damage could not be a big deal at higher levels. Constricts, rending anyone's abilities irrelevant with a DC 25 Fort save to negate. Power \u2026 It's got nothing, except the possibility that you'll slip because ice is slippery. Source Pathfinder Unchained pg. Just to do a comparison for a 6th level Fighter with a \u2026 Roll the weapon\u2019s damage dice for the attack twice and add the results together before adding bonuses from Strength, weapon abilities (such \u2026 That's not an 'overpowered' character, that's actually surprisingly balanced for high-level Pathfinder play. Also has its own suite of more traditional OHKOs. Unfortunately, is a mind-affecting illusion fear emotion effect, and thus vulnerable to almost every high-level mental defense ever. In Conclusion []. It's hard to compare their abilities to yours, but it generally seems like the army's versatility and resilience is superior to your single-target effect. Definitely a hard fight and not something you're likely to be a major factor in. In addition to confusion, the Bandersnatch is quite capable of grappling you with its grab special ability, rendering you unable to use your giant pile of feats. Mythic vital strike is pretty crazy. CTP\u2019s Guide to Pathfinder Mythic Adventures Introduction A new pseudo-subsystem for Pathfinder has been released in the form of Mythic Adventures. The effect is a little less reliable than yours, but the 60 ft range is a lot better than melee, so we'll call it even. Blowing up basically everything ever with a giant oversized doomsday attack is very much consistent with that design philosophy. Feats Awesome Blow, Bleeding Critical, Critical Focus, Greater Vital Strike, Improved Bull Rush, Improved Critical (battleaxe), Improved Initiative, Improved Vital Strike, Iron Will, Lightning Reflexes, Power Attack, Vital Strike Will I get all the missing monthly security patches? Once people see this correct way to read that terribly worded feat that I am sure any logical DM will now play the Mythic Vital Strike feats correctly once they read this post & the comments. Weapon Finesse: If you plan to use a lot of dexterity-dependent polymorphs, this is a must. The feat multiplies your bonuses based on how many extra times you roll the weapon's damage dice. Can force choke you out with telekinesis. Whenever you use Vital Strike, Improved Vital Strike, or Greater Vital Strike, multiply the Strength bonus, magic bonus, and other bonuses that would normally be multiplied on a critical hit by the number of weapon damage dice you roll for that feat. You can beat this, though! Benefit: When using any Vital Strike feat in an area of light or heavy gravity, roll the weapon\u2019s damage dice for the attack one additional time. Yeah, that's Mythic Improved Vital Strike. \"Mythic heroes are set apart from their contemporaries, capable of amazing feats of courage in the face of overwhelming odds. - Surge (Su): can expend one use of its mythic power to increase any d20 roll that he just made by rolling 1d12 and adding it to the result. Allowing a player, as a very high level ability, to make use of this build (Greater Vital Strike requires 16 BAB) is not a significant problem. So, basically, mythic vital strike states \"everything that is doubled in a critical, is doubled in your vital strike\", the normal vital strike states that you \"cannot apply your vital strike damage bonus to critical, but anything else can\". If your weapon was flamming or would have an enchantement on it, that would be multiplied by Vital Strike [Mythic]. And so we see that good 9th level offensive spells are generally better than your ability, but not by terribly much most of the time. Our five mythic feats will be Mythic Eldritch Heritage, Mythic Power Attack, Mythic Vital Strike, Mythic Improved Vital Strike, and Mythic Weapon Specialization. Whats the highest possible Charisma score a character can acquire in Pathfinder? Oh, no! You can beat this. Many players think that the multiplier to the damage is the total number of damage dice that are rolled instead of the number of sets of the dice that you are allowed due to the feat(s). You can strike your foes with incredible force. If you can get past that, her only really recourse is to run away. No. This site is an SRD (System Reference Document) for the Paizo Pathfinder Roleplaying Game. Does Vital Strike work with Overhand Chop? Prerequisites: Greater Vital Strike CRB, 10th mythic tier. This means that you must make a DC 28 Will Save or be nauseated and thus unable to attack (or spend some channel energy, if you have that ability, and have the Whale fail a save which it needs to roll a 1 to fail), and then hit AC 32. You would need someone to teleport you 40 ft away from it with your initiative next coming before the Protean's and hope you weren't teleporting directly into a Prismatic Sphere. In fact, even the fact that you roll a weapon's damage dice rather than it's damage die implies that the weapons may well have more than one such die to be rolled. How does vital strike work with magus spellstrike? The following is a break down of the new options available to players; what\u2019s good, what\u2019s bad, and how things work. A Greatsword rolls two d6, or two six-sided dice. Flaming isn't multiplied on a crit, so it would not be multiplied by Mythic Vital Strike. site design \/ logo \u00a9 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. This leads to very big damage numbers as a single standard action. You must take the second result, even if it\u2019s lower. The point is, that this feat reads like it's the # of damage dice but it's always been intended to work as a x2, x3 or x4 modifier. Greater Vital Strike (Combat, Mythic) You can deliver blows that shatter mountains and cut adamantine. What is the duration of the resistance effect of Swarming Dispersal for a Swarmkeeper Ranger? This is basically the same thing you do only slightly better because casters have to be better at everything :\/. We're probably looking at something more like 36*64=2304 damage for a very-damage-focused mid-op high-level character. Alas, the Frumious Bandersnatch is no more a threat to you than a regular one. You can't really do too much here, armies are a major weakness of yours, as are grapple attempts (let alone ranged insta-gib grapples). Pathfinder Vital Strike Power Attack Calculator. It functions for other Colossal mythic creatures in the same way, but not for non-mythic creatures or those of other sizes. Vital Strike (Mythic) You can strike your foes with incredible force. Alchemist's Bombs and Vital Strike: What is \u201cbonus damage?\u201d. However, it has no range. The time has come to seek out the heart of the Worldwound and strike a mortal blow against the Templars of the Ivory Labyrinth. Are any bonuses added when using Vital Strike in Pathfinder? Do size effects and Vital Strike actually work in conjunction? You can beat this. So if you happen to roll 6d6+20, that will become 24d6+80. An elohim is a strange being obsessed with creating miniature worlds populated with creatures of its choosing. Weird spam: Will save or die (succeeding the Fort save leaves you stunned, which is basically dead), AoE for any number of creatures within 30 ft of each other. are required to roll 4d6, you should roll four six-sided Has an army, also mind control, also Magic Jar at will and teleport. Mythic Vital Strike (Not administered by or affiliated with Paizo Publishing\u00ae in any way), Press J to jump to the feed. You can't fight swarms, they're just straight-up immune to you. Basically, you are so, so screwed, but so is everyone else in your party. Benefit: When you use the attack action, you can make one attack at your highest base attack bonus that deals additional damage. It creates new permanent demiplanes or alters remote environments in pre-existing planes, seeds them with new life, eventually... Weapon 's damage dice I deal with Vital Strike larger, the Horned decides! Service, privacy policy and cookie policy Strike in Pathfinder require two saves rather than a action... A nice way to handle invisible creatures to your attacks ( and free! injury poison ) spam! Of dice Stop spam: victory with no save, opposable only be used with the effects of resistance!, this requires a full-round action that includes the ability to make it work this way it will do lot! Let there be Mythic eventually, you can probably kill it real.! caught up '' versions of normal characters the Templars of the worst kind, Mythic Strike! Can probably run her to ground eventually, you 'd just have to be better everything... Effects and Vital Strike most applyable conditions with ease not intended as a single attack with high damage instead... Role-Playing Games Stack Exchange is a mind-affecting illusion fear emotion effect, and mythic vital strike pathfinder can your! 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Includes the ability to make it work this way it will do a lot of damage dice own suite more!\n\nKarachi Weather 14 Day Forecast, High Point Men's Soccer Id Camp, Jo\u00e3o Cancelo Fifa 21 Rating, Monster Hunter Rise Demo Review, Raging Thunder 1 Offline Multiplayer,","date":"2021-06-20 06:31:22","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.2731574475765228, \"perplexity\": 6164.540167817355}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-25\/segments\/1623487658814.62\/warc\/CC-MAIN-20210620054240-20210620084240-00560.warc.gz\"}"} | null | null |
layout: default
---
Identities
==========
Knowing who the users of your service are is a common need for service owners. When building Cougar we looked at existing
libraries and frameworks for modelling and resolving entities (users or other applications) and found them too restrictive,
so in time honoured tradition, we've implemented our own, although they are heavily based on JAAS, which we've used where we can.
Cougar's identity model
-----------------------
The base of Cougar's identity model is the concept of a Principal, which represents any entity, such as an individual,
a corporation, and a login id. An Identity consists of both the Principal (the logical identity) and the Credentials
that were used to resolve that Principal.
Service implementations interact with instances of Identity, however these in turn are resolved from IdentityTokens
(string key/value pairs) which are resolved on a per transport basis. This means that the logic to resolve the tokens can
vary by transport (as is needed, since the binary transport presents data rather differently from an HTTP transport).
Identity token resolution is performed in the transport thread, Identity resolution occurs on an EV thread. In the case of
transports supporting batch calls (e.g. JSON-RPC), Identity resolution is done once for the whole batch and the resolved Identity
list is sent to all executables.
Identity tokens can also be 'rewritten' back to the client, to support tokens which change (e.g. single use tokens or rotating
keys on an encrypted sso token).
Identity token resolution
-------------------------
Identity token resolution is performed through transport-specific implementations of `IdentityTokenResolver`:
public interface IdentityTokenResolver<I, O, C> {
public List<IdentityToken> resolve(I input, C transportAuthTokens);
public void rewrite(List<IdentityToken> credentials, O output);
public boolean isRewriteSupported();
}
The types of the generic parameters vary by transport and for custom transports you should consult specific documentation to ascertain these. Standard Cougar transports are as follows:
<table>
<tr><th>Name</th><th>I</th><th>O</th><th>C</th></tr>
<tr><td>Rescript</td><td>javax.servlet.http.HttpServletRequest</td><td>javax.servlet.http.HttpServletResponse</td><td>java.security.cert.X509Certificate[]</td></tr>
<tr><td>SOAP</td><td>org.apache.axiom.om.OMElement</td><td>org.apache.axiom.om.OMElement</td><td>java.security.cert.X509Certificate[]</td></tr>
<tr><td>Socket</td><td colspan="3">Custom identity token resolvers not supported</td></tr>
</table>
Each transport instance has a seperate, single identity token resolver (normally a compound one into which many individual resolvers can be registered).
Identity resolution
-------------------
Identity resolution is the transport-agnostic process of converting `IdentityToken`s into relevant instances of `Identity`.
As mentioned previously, identity resolution always occurs on an `ExecutionVenue` thread. If no `Executable`s are found for
an invocation, then the identities will never be resolved. Identity resolution occurs via implementations of `IdentityResolver`
only one of which (normally a compound one into which many individual resolvers can be registered) is set on an `ExecutionVenue`
instance.
Identity token emission
-----------------------
Finally, if you're making a call to a Cougar service using a provided Cougar client implementation, then the `Identity(s)`
passed in the client call are converted into `IdentityToken`s as part of the call serialisation. This makes use of the `tokenise`
call on `IdentityResolver`, the outputs of which are passed into an `IdentityTokenResolver`. This rather confusingly uses
the same interface as on the server, but effectively 'swaps' the input and output types from those you would expect to see
on a server side resolver. To explain more clearly here are the types of the generic parameters:
<table>
<tr><th>Name</th><th>I</th><th>O</th><th>C</th></tr>
<tr><td>Sync Rescript</td><td>org.apache.http.client.methods.HttpUriRequest</td><td>org.apache.http.client.methods.HttpUriRequest</td><td>java.security.cert.X509Certificate[]</td></tr>
<tr><td>Async Rescript</td><td>org.eclipse.jetty.client.api.Response</td><td>org.eclipse.jetty.client.api.Request</td><td>java.security.cert.X509Certificate[]</td></tr>
<tr><td>Socket</td><td colspan="3">Custom identity token resolvers not supported</td></tr>
</table>
To emit the tokens, a call is made to `rewrite`, but only if `isRewriteSupported()` returns `true`. There is currently no
mechanism for handling token rewrites by the server.
Each client instance has both an `IdentityResolver` and an `IdentityTokenResolver`.
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,808 |
\section{#1}}
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\begin{document}
\begin{titlepage}
\bigskip
\bigskip
\bigskip
\bigskip
\begin{center}
{\Large \bf Hair in the Back of a Throat:}
{\Large \bf Non-Supersymmetric Multi-Center Solutions from K\"ahler Manifolds}
\bigskip
\bigskip
{\bf Nikolay Bobev${}^{(1)}$,
Ben Niehoff${}^{(2)}$ and Nicholas P. Warner${}^{(2)}$ \\ }
\bigskip
${}^{(1)}$
Simons Center for Geometry and Physics\\
Stony Brook University\\
Stony Brook, NY 11794, USA\\
\vskip 5mm
${}^{(2)}$
Department of Physics and Astronomy \\
University of Southern California \\
Los Angeles, CA 90089, USA \\
\bigskip
nbobev@scgp.stonybrook.edu,~bniehoff@usc.edu,~warner@usc.edu \\
\end{center}
\begin{abstract}
\noindent We find a class of non-supersymmetric multi-center solutions of the STU model of five-dimensional ungauged supergravity. The solutions are determined by a system of linear equations defined on a four-dimensional K\"ahler manifold with vanishing Ricci scalar and a $U(1)$ isometry. The most general class of such K\"ahler manifolds was studied by LeBrun and they have non-trivial $2$-cycles that can support the topological fluxes characteristic of bubbled geometries. After imposing an additional $U(1)$ symmetry on the base we find explicit multi-center supergravity solutions. We show that there is an infinite number of regular multi-center solutions with non-trivial topology that are asymptotic to the near-horizon limit of a BMPV black hole.
\end{abstract}
\end{titlepage}
\tableofcontents
\section{Introduction}
The construction of microstate geometries for black holes and black rings is now a fairly well developed subject. The defining idea of such geometries is that they have the same asymptotics at infinity as a given black hole or black ring and yet the solutions are completely smooth and, as a consequence, they resolve the black-hole or black-ring singularity into smooth ``bubbled geometries.'' More generally, it is interesting to see what classes of smooth, multi-centered geometries can be inserted into a black-hole, or black-ring throat since such additional structure may be thought of as ``hair'' on the black object. Since the throat geometries are typically asymptotic to an anti de Sitter space, such geometric ``hair in the back of a throat'' can be studied quite precisely using holography. One of the primary purposes in finding such backgrounds is not only to elucidate the possible microstate geometries but also to obtain a better semi-classical description of black-hole microstates in general.
Most of the progress on microstate geometries has been for BPS solutions \cite{Bena:2005va,Berglund:2005vb, Bena:2007kg} because such solutions are generically far simpler and are, in fact, governed by a linear system of differential equations \cite{Bena:2004de}. However, recent work has shown that there are also linear systems of equations that govern very large families of extremal, non-BPS solutions \cite{Goldstein:2008fq,Bena:2009ev, Bena:2009en,Bena:2009fi,Bena:2009qv, Bobev:2009kn}. These families not only include most of the known extremal, non-BPS black holes and black rings but also greatly generalize these solutions by including more charges and extending the results to completely new non-BPS, multi-centered black-ring solutions. The construction of such solutions is a very important first step in understanding the structure and properties of non-BPS solutions in general, particularly since such solutions have played a pivotal role in the analysis of attractor flows \cite{Ferrara:1995ih, Ferrara:1996dd,Ceresole:2007wx, LopesCardoso:2007ky,Andrianopoli:2007gt, Ferrara:2008ap,Bellucci:2008sv}, black-hole bound states, deconstruction \cite{Denef:2007yt, Gaiotto:2007ag, Gimon:2009gk}, wall crossing and entropy enigmas \cite{Denef:2002ru, Bates:2003vx, Denef:2007vg}.
Ultimately one would like to find the non-BPS analogs of bubbled solutions in which the singularity of the underlying black object has been resolved and the black-hole, or black-ring, throat is rounded off in some form of smooth geometry. Such solutions have come to be known as {\it microstate geometries} and the requisite geometric transition to the bubbled geometries that lies at the heart of such objects has been found and extensively studied for BPS solutions \cite{Bena:2005va,Berglund:2005vb, Bena:2007kg}. However, there are very few examples of the corresponding smooth, non-BPS geometries \cite{Bena:2009fi, Bena:2009qv, Bobev:2009kn}. Indeed, there are rather few examples of non-BPS solutions with more than one non-trivial bubble in a black-hole background. One of the purposes of this paper is to investigate an interesting new class of bubbled geometries and to find new non-BPS bubbled solutions.
A crucial first step in finding bubbled geometries is to find smooth, four-dimensional ``base geometries'' with non-trivial homology (the ``bubbles'') that supports the cohomological fluxes that give rise to the charges of the solution. In BPS solutions (and in some non-BPS solutions) these base geometries are necessarily hyper-K\"ahler manifolds and are usually chosen to be asymptotic to $\mathbb{R}^4$ or $\mathbb{R}^3 \times S^1$ so that the final, five-dimensional geometry is asymptotic to five-dimensional, or four-dimensional, Minkowski space. There are a rich variety of such admissible base geometries because the metrics are allowed to be ambi-polar, that is, the base metric is allowed to reverse sign from regions with signature $+4$ to regions with signature $-4$. In spite of this apparent peculiarity, the presence of very non-trivial warp factors means that such base metrics can give rise to perfectly viable, smooth, Lorentzian five-dimensional geometries. The ambi-polar generalizations of Gibbons-Hawking (GH) metrics \cite{Gibbons:1979zt} have proven extremely valuable in that they have given rise to extensive and highly computable classes of BPS microstate geometries.
It was one of the important realizations of \cite{Bena:2009fi, Bena:2009qv} that one could relax the hyper-K\"ahler condition on the base geometry and still obtain non-BPS solutions from linear systems of equations. In particular, it was shown in \cite{Bena:2009fi} how this could be achieved by starting from a four-dimensional Euclidean solution to Einstein's equations coupled to an electromagnetic field. This led to some interesting examples based upon Israel-Wilson metrics but it turns out that many of these naturally arise as spectral flows of more standard non-BPS solutions based upon Gibbons-Hawking metrics. One can also construct a regular non-BPS solution with an Euclidean Kerr-Newman base \cite{Bobev:2009kn}, however the base has only one topological two-cycle and there is no obvious way to generalize it easily. A natural follow-up question is whether there are any other classes of Euclidean electrovac solutions that contain appropriate non-trivial homology and that can be used to generate non-BPS microstate geometries. It turns out that there is a relatively straightforward generalization of the Gibbons-Hawking metrics to K\"ahler electrovac solutions and these geometries were studied extensively by LeBrun in \cite{LeBrun:1991}.
The central result in \cite{LeBrun:1991} is to find the explicit local form of all Euclidean, four-dimensional K\"ahler metrics that have a $U(1)$ isometry and a vanishing Ricci scalar. It is then shown in a follow-up paper, \cite{LeBrun:2008kh}, that these solutions are necessarily electrovac solutions whose electromagnetic field is related to the K\"ahler form. This generalizes earlier work on the classification of hyper-K\"ahler metrics with $U(1)$ isometry \cite{Boyer:1982mm,DasGegenberg} in which it is shown that the metric is determined by a single function that is required to satisfy the Affine Toda equation. The Gibbons-Hawking metrics then emerge as precisely the metrics for which the $U(1)$ action preserves all three complex structures (that is, the $U(1)$ is tri-holomorphic). The ``LeBrun metrics'' in \cite{LeBrun:1991} are defined by two functions, one of which must satisfy the Affine Toda equation and the other of which must essentially be harmonic in a background defined by the Affine Toda solution. This family of solutions collapses to either the general class of $U(1)$-invariant hyper-K\"ahler metrics, or to the GH family if one makes an essentially trivial choice for one of the two functions.
Amongst the general class of LeBrun metrics is what we will call the ``LeBrun-Burns metrics,'' which provide a simple, explicit class of K\"ahler metrics on $\mathbb{C}^2$ with $n$ points blown up\footnote{One of the original motivations in \cite{LeBrun:1991} for finding this metric is that there is a simple conformal compactification that yields an explicit K\"ahler metric on the connected sum of several $\mathbb{C} \mathbb{P}_2$'s.}. The end result is rather similar to the Gibbons-Hawking metrics except that the $\mathbb{R}^3$ sections and the harmonic functions on $\mathbb{R}^3$ are now replaced by the hyperbolic space, $\mathbb{H}^3$, and its harmonic functions. The LeBrun-Burns metrics are also asymptotic to $\mathbb{R}^4$ and, interestingly enough, the $U(1)$ isometry on this $\mathbb{R}^4$ does {\it not} act in a manner that matches the tri-holomorphic $U(1)$ action on a Gibbons-Hawking metric that is similarly asymptotic to $\mathbb{R}^4$. Thus the solutions obtained from the LeBrun-Burns metrics will be intrinsically different from those obtained from GH solutions.
In this paper we explicitly solve the equations of motion of five-dimensional supergravity on an axisymmetric LeBrun-Burns base and thus provide an infinite class of non-supersymmetric multi-centered solution. We find that, due to the Maxwell flux on the four-dimensional K\"ahler base, the five-dimensional backgrounds are not asymptotically flat and have the asymptotics of a warped, rotating $AdS_2\times S^3$ space. For certain choices of parameters this becomes the near horizon limit of a BMPV black hole \cite{Breckenridge:1996is}. We would like to emphasize that although our approach to finding these solutions was inspired by the construction of BPS microstate geometries we find the most general axisymmetric solutions within the floating brane Ansatz \cite{Bena:2009fi} and with an axisymmetric LeBrun-Burns base. In particular our solutions include superpositions of non-supersymmetric concentric black rings and other potentially interesting solutions with horizons.
In section 2 of this paper we review the process through which one can construct five-dimensional non-BPS solutions using the floating-brane Ansatz \cite{Bena:2009fi}. In Section 3 we introduce the general LeBrun metrics and begin solving the linear system in this background, and in Section 4 we specialize to the LeBrun-Burns metrics, discuss their properties and further reduce the linear system and exhibit all the necessary Green functions. We will also show, in Section 4, that because the Maxwell field on the four-dimensional base involves the K\"ahler form, the energy-momentum tensor does not fall off at infinity and hence the LeBrun-Burns base metrics do not naturally lead to five-dimensional solutions that are asymptotic to flat space.
In Section 5 we start with the simplest possible LeBrun-Burns metric, $\mathbb{R}^4$, and use the linear system and Green functions of Section 4 to construct very simple, explicit examples of non-BPS solutions. We find that the natural asymptotic geometries that arise from LeBrun-Burns base metrics are a warped, rotating $AdS_2\times S^3$ space. In Section 6 we consider more general LeBrun-Burns base metrics with non-trivial topology and find the general axisymmetric solution to the system of non-BPS equations on such a base. Five-dimensional regularity and the absence of closed time-like curves (CTCs) puts very stringent conditions on our solutions but in spite of this we find a family of regular solutions with non-trivial bubbles that are asymptotic to the near-horizon region of a BMPV black hole. In Section 7 we present our conclusions and suggest some directions for further work. Some of the technical details of the construction of the solutions are relegated to the Appendix.
\section{The family of non-BPS solutions}
It is simplest to characterize our solutions in terms of ${\cal N} \! = \! 2$, five-dimensional ungauged supergravity with three $U(1)$ gauge fields. This theory may also be thought of as arising from a truncation of eleven-dimensional supergravity on $T^6$. The bosonic action is given by:
\begin{eqnarray}
S = \frac {1}{ 2 \kappa_{5}} \int\!\sqrt{-g}\,d^5x \Big( R -\coeff{1}{2} Q_{IJ} F_{\mu \nu}^I F^{J \mu \nu} - Q_{IJ} \partial_\mu X^I \partial^\mu X^J -\coeff {1}{24} C_{IJK} F^I_{ \mu \nu} F^J_{\rho\sigma} A^K_{\lambda} \bar\epsilon^{\mu\nu\rho\sigma\lambda}\Big) \,,
\label{5daction}
\end{eqnarray}
where we use the conventions of \cite{Bena:2009fi}. The matrix that defines the kinetic terms can be written as:
\begin{equation}
Q_{IJ} ~=~ \frac{1}{2} \,{\rm diag}\,\big((X^1)^{-2} , (X^2)^{-2},(X^3)^{-2} \big) \,.
\label{scalarkinterm}
\end{equation}
The scalar fields themselves are not independent and are most conveniently parametrized in terms of three other scalar fields, $Z_I$:
\begin{equation}
X^1 =\bigg( \frac{Z_2 \, Z_3}{Z_1^2} \bigg)^{1/3} \,, \quad X^2 = \bigg( \frac{Z_1 \, Z_3}{Z_2^2} \bigg)^{1/3} \,,\quad X^3 =\bigg( \frac{Z_1 \, Z_2}{Z_3^2} \bigg)^{1/3} \,,
\label{XZrelns}
\end{equation}
which satisfy the constraint $X^1 X^2 X^3 =1$. The reason why we use three scalars, $Z_I$, to parametrize two independent scalar fields becomes evident once we write the metric Ansatz
\begin{equation}
ds_5^2 ~=~ -Z^{-2} \,(dt + k)^2 ~+~ Z \, ds_4^2 \,,
\label{metAnsatz}
\end{equation}
and define $Z$ by:
\begin{equation}
Z ~\equiv~ \big( Z_1 \, Z_2 \, Z_3 \big)^{1/3} \,.
\label{Zdefn}
\end{equation}
This turns out to be an extremely convenient way to express both the scalar fields and the warp factors.
The electromagnetic fields are given by the ``floating brane'' Ansatz of \cite{Bena:2009fi}, which relates metric coefficient and scalar fields to the electrostatic potentials. In particular, the Maxwell potentials are given by:
\begin{equation}
A^{(I)} ~=~ - Z_I^{-1}\, (dt +k) + B^{(I)} \,,
\label{AAnsatz}
\end{equation}
where $B^{(I)}$ is a one-form on the base $ds_4^2$. It is convenient to introduce the magnetic two-from field strengths
\begin{equation}
\Theta^{(I)} ~\equiv~ d B^{(I)}\,.
\end{equation}
The four-dimensional base space, $ds^2_4$, has to be a solution of Euclidean Einstein-Maxwell equations\footnote{The normalization of the fields in this equation is different from most standard sources on general relativity and is chosen to agree with the four-dimensional conventions in \cite{Bena:2009fi}.}
\begin{equation}
{R}_{\mu\nu} = \coeff{1}{2}\, \big( {\cal F}_{\mu\rho} {{\cal F}_{\nu}}^{\rho} - \coeff{1}{4}\, g_{\mu\nu} {\cal F}_{\rho\sigma} {\cal F}^{\rho\sigma} \big)\,,
\label{electrovacequation}
\end{equation}
where all quantities are computed in the four-dimensional base metric. The Maxwell field is then decomposed as:
\begin{equation} \label{Fdecomp}
{\cal F} = \Theta^{(3)} - \omega^{(3)}_{-}\,.
\end{equation}
where $\Theta^{(3)}$ is self-dual and $\omega^{(3)}_{-}$ is anti-self-dual. The equations of motion $d {\cal F} = d * {\cal F} =0$ imply that $\Theta^{(3)}$ and $\omega^{(3)}_{-}$ are harmonic. As the notation implies, this defines the magnetic two-from field strength $\Theta^{(3)}$.
The linear system that solves the equations of motion can now be written as \cite{Bena:2009fi}:
\begin{eqnarray}
\hat \nabla^2 Z_1 &=& *_4 \big[ \Theta^{(2)} \wedge \Theta^{(3)} \big] \,, \qquad \big(\Theta^{(2)} - *_4 \Theta^{(2)} \big) ~=~ 2 \, Z_1 \, \omega^{(3)}_- \,, \label{ZMax1} \\
\hat \nabla^2 Z_2&=& *_4 \big[ \Theta^{(1)} \wedge \Theta^{(3)} \big] \,, \qquad
\big(\Theta^{(1)} - *_4 \Theta^{(1)} \big) ~=~ 2 \, Z_2 \, \omega^{(3)}_- \label{ZMax2}\,,
\end{eqnarray}
and
\begin{eqnarray}
\hat \nabla^2 Z_3 &=& *_4 \big[ \Theta^{(1)} \wedge \Theta^{(2)} ~-~ \omega^{(3)}_- \wedge( dk - *_4 dk ) \big] \,,
\label{Z3eqn} \\
dk ~+~ *_4 dk &=& \frac{1}{2} \, \sum_I \, Z_I \, \big(\Theta^{(I)} + *_4 \Theta^{(I)} \big) \,, \label{keqn}
\end{eqnarray}
%
where $\hat \nabla^2$ is the Laplacian on $ds^2_4$. Indeed, having chosen the electrovac solution that defines the base metric, one uses \eqref{Fdecomp} to read off $\Theta^{(3)}$ and $\omega_-^{(3)}$. As a result, \eqref{ZMax1} and \eqref{ZMax2} are two linear coupled equations for $Z_1$ and $\Theta^{(2)}$ and $Z_2$ and $\Theta^{(1)}$ respectively. Once these equations are solved, $k$ and $Z_3$ are solutions to the system of linear equations \eqref{Z3eqn} and \eqref{keqn}. Our purpose here is to implement this procedure for the LeBrun metrics.
\section{The non-BPS equations for the LeBrun metrics}
\subsection{The metric}
\label{LeBrunMet}
The LeBrun metric, \cite{LeBrun:1991}, is
\begin{equation}
ds^2_{4}~=~ w^{-1}\, (d\tau + A)^2 ~+~ w\, (e^{u} (dx^2+dy^2) +dz^2) \,,
\label{LBmet}
\end{equation}
where $u$ and $w$ are two functions of $(x,y,z)$ which obey the $su(\infty)$ Toda equation and its linearized form:
\begin{eqnarray}
&&\partial_{x}^2 \,u ~+~ \partial_{y}^2 \,u ~+~ \partial_z^2\, (e^u) ~=~ 0 \,, \label{Toda} \\
&&\partial_{x}^2 \,w ~+~ \partial_{y}^2 \,w ~+~ \partial_z^2\,(e^u\, w) ~=~ 0\,.\label{linearToda}
\end{eqnarray}
The one-form, $A$, satisfies:
\begin{equation}
dA ~=~ \partial_{x}w ~dy\wedge dz ~-~ \partial_{y}w~ dx\wedge dz ~+~ \partial_z(e^u w) ~dx \wedge dy\,, \label{Adefn}
\end{equation}
and the integrability of this differential, $d^2 A=0$, is equivalent to the equation (\ref{linearToda}).
The metric is K\"ahler, with K\"ahler form:
\begin{equation}
J ~=~ (d\tau + A) \wedge dz ~-~ w\, e^u \, dx\wedge dy \,. \label{Kform}
\end{equation}
It is convenient to introduce frames:
\begin{equation}
e^0 ~\equiv~ w^{-{1 \over 2}} \, (d\tau + A) \,, \qquad e^1 ~\equiv~ w^{ {1 \over 2}} \, e^{ {u \over 2}} \, dx \,,
\qquad e^2 ~\equiv~ w^{ {1 \over 2}} \, e^{ {u \over 2}} \, dy \,, \qquad e^3 ~\equiv~ w^{ {1 \over 2}} \, dz \,, \label{frames}
\end{equation}
and the self-dual forms
\begin{eqnarray}
&& \Omega^{(1)}_+ ~\equiv~ e^{- {u \over 2}} ( e^0 \wedge e^1 ~+~ e^2 \wedge e^3) ~=~ (d\tau + A) \wedge dx ~+~ w\, dy \wedge dz \,, \nonumber \\
&& \Omega^{(2)}_+ ~\equiv~ e^{- {u \over 2}} ( e^0 \wedge e^2 ~-~ e^1 \wedge e^3) ~=~ (d\tau + A) \wedge dy ~-~ w\, dx \wedge dz \,, \label{sdforms}\\
&& \Omega^{(3)}_+ ~\equiv~ ( e^0 \wedge e^3 ~+~ e^1 \wedge e^2) ~=~ (d\tau + A) \wedge dz ~+~ w\, e^u\, dx \wedge dy \,. \nonumber
\end{eqnarray}
We will also frequently denote the coordinates by $\vec y \equiv (y_1, y_2, y_3) =(x,y,z) $.
\subsection{Harmonic fluxes}
\label{harmflux}
One can then verify that:
\begin{equation}
\Theta ~\equiv~ \sum_{a=1}^3 \bigg( \partial_a \bigg( {H \over w} \bigg)\bigg) \, \Omega^{(a)}_+ \label{harmform1}
\end{equation}
is harmonic if and only if $H$ satisfies (\ref{linearToda}):
\begin{equation}
\partial_{x}^2\, H ~+~ \partial_{y}^2\, H ~+~ \partial_z^2\, (e^u \, H ) ~=~ 0 \,. \label{harm1}
\end{equation}
Note that if one differentiates (\ref{Toda}) with respect to $z$ one finds that $H = \partial_z u$ satisfies (\ref{harm1}) and (\ref{Toda}).
Define the Maxwell field, ${\cal F}$, by
\begin{equation}
{\cal F} ~\equiv~ \Theta ~+~ \alpha \, J \,, \quad {\rm with} \quad H ~=~ -{1 \over 2\, \alpha} \, \partial_z u \,. \label{MaxF}
\end{equation}
The metric, (\ref{LBmet}), is then a solution to the Einstein-Maxwell equations (\ref{electrovacequation}).
This fits the form of the linear system obtained in \cite{Bena:2009fi} and so we take:
\begin{equation}
\Theta^{(3)} ~=~ -{1 \over 2\, \alpha} \, \sum_{a=1}^3 \bigg( \partial_a \bigg( {\partial_z u \over w} \bigg)\bigg) \, \Omega^{(a)}_+ \,, \qquad \omega^{(3)}_- ~=~ - \alpha \, J \,. \label{Max3}
\end{equation}
One can now use this in the linear system \eqref{ZMax1}, \eqref{ZMax2}, \eqref{Z3eqn} and \eqref{keqn} to solve the equations of motion of supergravity. Note that we can absorb the constant $\alpha$ by rescaling the coordinate $\tau$ and the function $w$ (which in turn rescales the one-form, $A$). Throughout the rest of this paper, we set $\alpha = -1$.
\subsection{Solving the first layer}
\label{layer1}
One finds that the first part of the system is solved by an Ansatz:
\begin{equation}
\Theta^{(1)}~\equiv~ Z_2 \, J ~+~ \sum_{a=1}^3 p^{(1)}_a \, \Omega^{(a)}_+ \,, \qquad
\Theta^{(2)}~\equiv~ Z_1 \, J ~+~ \sum_{a=1}^3 p^{(2)}_a \, \Omega^{(a)}_+ \,, \label{Thetaforms}
\end{equation}
\begin{equation}
Z_1 ~=~ \frac{1}{2}\, \Big( {K^{(2)} \, \partial_z u \over w} \Big) ~+~L_1\,, \qquad Z_2 ~=~ \frac{1}{2}\, \Big( { K^{(1)} \, \partial_z u \over w} \Big) ~+~L_2 \,. \label{Z12form}
\end{equation}
The Bianchi identities imply the following relations
\begin{eqnarray}
&& p^{(1)}_1 ~=~ \partial_x \Big( {K^{(1)} \over w} \Big) \,, \qquad p^{(1)}_2 ~=~ \partial_y \Big( {K^{(1)} \over w} \Big) \,, \qquad p^{(1)}_3 ~=~ -\, Z_2 ~+~ \partial_z \Big( {K^{(1)} \over w} \Big) \,, \label{pfns1} \\
&&p^{(2)}_1 ~=~ \partial_x \Big( {K^{(2)} \over w} \Big) \,, \qquad p^{(2)}_2 ~=~ \partial_y \Big( {K^{(2)} \over w} \Big) \,, \qquad p^{(2)}_3 ~=~ -\, Z_1 ~+~ \partial_z \Big( {K^{(2)} \over w} \Big) \,. \label{pfns2}
\end{eqnarray}
One can add arbitrary functions of $z$ alone to the $p^{(I)}_3$, but these can be absorbed by a shift $K^{(I)} \to K^{(I)} + w \, g^{(I)}(z)$, for some function $g^{(I)}$.
The functions $L_1$ and $L_2$ can be any solution of (\ref{linearToda}), that is:
\begin{equation}
\partial_{x}^2 \,L_I ~+~ \partial_{y}^2 \,L_I ~+~ \partial_z^2\,(e^u\, L_I ) ~=~ 0\,, \qquad I =1,2\,,\label{Leqns1}
\end{equation}
and given these solutions the functions $K^{(1)}$ and $K^{(2)}$ are determined by the linear equations:
\begin{eqnarray}
&&\partial_{x}^2 \, K^{(1)} ~+~ \partial_{y}^2 \,K^{(1)} ~+~ \partial_z \,(e^u\, \partial_z \,K^{(1)} ) ~=~ 2\, \partial_z \,(e^u\, w\, L_2 ) \,, \label{lin2a} \\
&&\partial_{x}^2 \,K^{(2)} ~+~ \partial_{y}^2 \,K^{(2)} ~+~ \partial_z \,(e^u\, \partial_z \,K^{(2)} ) ~=~ 2\, \partial_z \,(e^u\, w\, L_1 ) \,. \label{lin2b}
\end{eqnarray}
\subsection{Solving the second layer}
\label{layer2}
As usual one makes the Ansatz
\begin{equation}
k ~\equiv~ \mu \, (d \tau + A) ~+~ \omega \,, \label{kansatz}
\end{equation}
where $\omega = \vec\omega \cdot d \vec y$ is a one-form on the three-dimensional base.
One then finds that the solution may be written as:
\begin{equation}
Z_3 ~=~ \Big( {K^{(1)} \, K^{(2)} \over w} \Big) ~+~L_3 \,, \label{Z3form}
\end{equation}
\begin{equation}
\mu ~=~ -\frac{1}{2}\, \Big( {K^{(1)} \, K^{(2)} \, \partial_z u \over w^2} \Big) - \frac{1}{2}\, \Big( {K^{(1)} \, L_1 + K^{(2)} \, L_2 \over w} \Big) ~-~ \frac{1}{4}\, \Big( {\partial_z u \, L_3 \over w} \Big) ~+~ M \,. \label{muform}
\end{equation}
The functions $L_3$ and $M$ must then satisfy the linear equations:
\begin{eqnarray}
&&\partial_{x}^2 \, M + \partial_{y}^2 \, M + \partial_z \,(e^u\, \partial_z \, M ) = \partial_z \,(e^u \, L_1 \, L_2 ) \,, \label{lin3a} \\
&& \partial_{x}^2 \, L_3 + \partial_{y}^2 \, L_3 + e^u\, \partial_z^2 \, L_3 = -2 \, e^u \big[ 2\, w \,(- L_1 L_2 + \partial_z M) + L_1 \, \partial_z K^{(1)} + L_2 \, \partial_z K^{(2)} \big] \,. \label{lin3b}
\end{eqnarray}
Finally, the components of $\vec \omega$ are determined from:
\begin{eqnarray}
(\partial_y \, \omega_z - \partial_z \, \omega_y ) ~+~ (M \partial_x w - w \partial_x M) &+&\frac{1}{2} \, \sum_{I=1}^2 (K^{(I)} \partial_x L_I - L_I \partial_x K^{(I)}) \notag\\
&+& \frac{1}{4} \, \big((\partial_z u) \, \partial_x L_3 - L_3 \partial_x (\partial_z u) \big) ~=~ 0 \,, \label{omx} \\
- (\partial_x \, \omega_z - \partial_z \, \omega_x ) ~+~ (M \partial_y w - w \partial_y M) &+&\frac{1}{2} \, \sum_{I=1}^2 (K^{(I)} \partial_y L_I - L_I \partial_y K^{(I)}) \notag\\
&+& \frac{1}{4} \, \big((\partial_z u) \, \partial_y L_3 - L_3 \partial_y (\partial_z u) \big) ~=~ 0 \,, \label{omy}
\end{eqnarray}
%
%
\begin{eqnarray}
(\partial_x \, \omega_y - \partial_y \, \omega_x ) &+& (M \partial_z (e^u \, w) - e^u \, w \, \partial_z M) ~+~ \frac{1}{2} \, \sum_{I=1}^2 (K^{(I)} \partial_z (e^u \, L_I) - e^u \, L_I \partial_z K^{(I)}) \notag\\
&+& \frac{1}{4} \, \big((\partial_z e^u) \, \partial_z L_3 - L_3 \partial_z^2 (e^u) \big)~+~ 2\, e^u \, w\, L_1 \,L_2 ~=~ 0 \,. \label{omz}
\end{eqnarray}
The integrability of these equations for $\vec \omega$ follows from the differential equations satisfied by all the other functions.
\subsection{The complete solution}
\label{summary1}
The complete solution is thus obtained by first choosing a background metric, (\ref{LBmet}), with functions $u$ and $w$ that satisfy (\ref{Toda}) and (\ref{linearToda}). The choice of background fixes one of the three electromagnetic fields, via (\ref{Kform})and (\ref{MaxF}) and, in particular, determines $\Theta^{(3)}$ via (\ref{Max3}). One then finds $L_1$ and $L_2$ as solutions to the homogeneous equations (\ref{Leqns1}) and uses these solutions as sources in the linear equations, (\ref{lin2a}) and (\ref{lin2b}), for $K^{(1)}$ and $K^{(2)}$. These functions then determine the remaining magnetic fluxes, $\Theta^{(j)}$, and the electrostatic potentials, or warp factors, $Z_j$, $j=1,2$ from (\ref{Thetaforms}), (\ref{Z12form}), (\ref{pfns1}) and (\ref{pfns2}). Next one solves the linear equation, (\ref{lin3a}), for $M$ with a source determined by $L_1 L_2$ and then solves the linear equation for $L_3$, (\ref{lin3b}), whose source is made from $L_j, K^{(j)}$ and $M$. The last step is to use all of these functions to solve the linear, first order system, (\ref{omx})--(\ref{omz}) for $\vec \omega$ and obtain $Z_3$ and the angular momentum vector from (\ref{Z3form}), (\ref{muform}) and (\ref{kansatz}). While complicated, this is a linear system of equations once one has chosen a solution for the metric function, $u$.
Before concluding, it is worth noting that taking the function, $u$, to be a constant is a trivial solution to (\ref{Toda}) and then (\ref{linearToda}) becomes the harmonic equation on $\mathbb{R}^3$ and the metric reduces to the familiar class of Gibbons-Hawking metrics. Similary, if one takes $w = \partial_z u$ then it also satisfies (\ref{linearToda}), as can be seen by differentiating (\ref{Toda}) with respect to $z$. This yields the general class of hyper-K\"ahler metrics with a non-triholomorphic $U(1)$ isometry \cite{Boyer:1982mm,DasGegenberg,Bena:2007ju}, which are based upon the Affine Toda equation. The resulting system of equations for non-BPS solutions in five dimensions does not, however, reduce to that considered in the bubbling BPS solutions \cite{Bena:2005va,Berglund:2005vb,Bena:2007kg} but is rather more akin to the fluxes considered in \cite{Bena:2009fi}. This is because the flux background is a mixture of self-dual and anti-self-dual fluxes and these break supersymmetry. In particular, the anti-self-dual flux is non-normalizable since it is proportional to the complex structure. Thus even the simple Gibbons-Hawking and Toda limits of the LeBrun backgrounds extend the class of solutions considered thus far.
The LeBrun solutions are four-dimensional Euclidean Einstein-Maxwell solutions and it is natural to ask whether some of them preserve supersymmetry. Supersymmetric solutions of four-dimensional Euclidean Einstein-Maxwell theory were classified in \cite{Gutowski:2010zs}. The maximally supersymmetric solutions are $\mathbb{R}^4$ or $H_2\times S^2$. There are two classes of solutions which preserve half of the supersymmetries - the well-known Gibbons-Hawking solutions and the Euclidean Israel-Wilson metrics discussed in \cite{Dunajski:2006vs}. Therefore the classification of \cite{Gutowski:2010zs} also demonstrates that the general LeBrun solutions, albeit K\"ahler, are non-supersymmetric solutions of Einstein-Maxwell theory.
\section{The LeBrun-Burns metrics}
\label{BurnsSec}
The LeBrun-Burns metrics represent a very natural generalization of the Gibbons-Hawking metrics in that they are four-dimensional K\"ahler metrics with $n$ 2-cycles and associated moduli and they satisfy Einstein's equations coupled to a $U(1)$ gauge field. They were constructed \cite{LeBrun:1991} (see also [3] as cited in \cite{LeBrun:1991}) as explicit metrics on a decompactification of $n\mathbb{C}\mathbb{P}_2$, the connected sum of $n$ $\mathbb{C}\mathbb{P}_2$'s.
\subsection{Defining the metric}
\label{LBBDef}
The simplest class of metrics arises if one takes:
\begin{equation}
u ~=~ \log (2 \, z)\,, \label{LBBuform}
\end{equation}
and it is then convenient to reparametrize by defining:
\begin{equation}
z ~\equiv~ \coeff{1}{2}\, \zeta^2 \,, \qquad V ~\equiv~ e^u \, w ~=~ 2\, z\, w ~=~ \zeta^2 \, w \,. \label{zetaVdefn}
\end{equation}
The LeBrun-Burns metric can then be written as
\begin{equation}
ds^2_4 ~=~ \zeta^2 \Big[ V^{-1} \, (d\tau+A)^2 + V \Big( \frac{dx^2 + dy^2 + d \zeta ^2}{\zeta ^2} \Big) \Big] \label{LBB2}\,.
\end{equation}
Note that the three-dimensional metric is the standard constant-curvature metric on the hyperbolic plane, $\mathbb{H}^3$:
\begin{equation}
ds^2_{\mathbb{H}^3} ~=~ \displaystyle\frac{dx^2 + dy^2 + d\zeta^2}{\zeta ^2} \,. \label{HypMet}
\end{equation}
The equations (\ref{linearToda}) and (\ref{Adefn}) that define the four-dimensional base imply that $V$ is a harmonic function on the hyperbolic plane and that $A$ is an appropriate one-form on $\mathbb{H}^3$:
\begin{equation}
\nabla^2_{\mathbb{H}^3} V ~=~ 0\,, \qquad\qquad dA ~=~ *_{\mathbb{H}^3} dV \,. \label{Hypconds}
\end{equation}
\subsection{Geometry of the LeBrun-Burns metric}
\label{LBBGeom}
\subsubsection{Asymptotics}
\label{LeBrunAsym}
To avoid a conical singularity at $\zeta =0$, one must have $V \to 1$ at this point so that the metric in the $(\zeta, \tau)$ direction limits to that of $\mathbb{R}^2$ in polar coordinates. Thus the metric in the neighborhood of $\zeta =0$ is that of $\mathbb{R}^4$ and regularity requires that one restrict the space to $\zeta \ge 0$. Similarly, if one requires $V \to 1$ at infinity, the space is asymptotic to $\mathbb{R}^4 = \mathbb{C}^2$. Note that the circle defined by $\tau$ lies in an $\mathbb{R}^2$ plane of the $\mathbb{R}^4$, and the associated isometry therefore only commutes with another $U(1)$ factor in the generic $SO(4)$ holonomy of the base metric. This is quite different from the way in which the isometry associated with the $U(1)$ fiber behaves in GH spaces.
The Green functions of the Laplacian on $\mathbb{H}^3$ are the functions:
\begin{eqnarray}
G(x,y,\zeta; a,b,c) &\equiv& \bigg( \frac{(x-a)^2+(y-b)^2+ \zeta^2+ c^2} { \sqrt{((x-a)^2+(y-b)^2+ \zeta ^2+ c^2)^2 - 4\, c^2\, \zeta^2 }}~-~1 \bigg) \nonumber\\
&=& \bigg( \frac{(x-a)^2+(y-b)^2+ \zeta^2+ c^2} { \sqrt{((x-a)^2+(y-b)^2+ (\zeta-c)^2) ((x-a)^2+(y-b)^2+ (\zeta+c)^2) }}~-~1 \bigg) \,, \nonumber\\
\label{Gdefn}
\end{eqnarray}
where one should remember that $\zeta \ge 0$ on $\mathbb{H}^3$ and so this function only has one singularity in the domain of definition.
The constant has been added so that $G$ vanishes at infinity. Given $G$, we can then solve for $A$ in \eqref{Hypconds}. Putting $A = D(x,y,\zeta; a,b,c) \; d\phi$, we obtain
\begin{eqnarray}
D(x,y,\zeta; a,b,c) &\equiv& \frac{(x-a)^2+(y-b)^2+ \zeta^2 - c^2} { \sqrt{((x-a)^2+(y-b)^2+ \zeta ^2+ c^2)^2 - 4\, c^2\, \zeta^2 }} \nonumber\\
&=& \frac{(x-a)^2+(y-b)^2+ \zeta^2 - c^2} { \sqrt{((x-a)^2+(y-b)^2+ (\zeta-c)^2) ((x-a)^2+(y-b)^2+ (\zeta+c)^2) }} \,. \nonumber\\
\label{Ddefn}
\end{eqnarray}
One can then take:
\begin{equation}
V~=~ \varepsilon_0 ~+~ \sum_{j=1}^N \, q_j \, G(x,y,\zeta; a_j,b_j,c_j)
\label{Vblowup}
\end{equation}
\begin{equation}
A ~=~ \sum_{j=1}^N \, q_j \, D(x,y,\zeta; a_j,b_j,c_j) \, d\phi
\label{Ablowup}
\end{equation}
With these choices and $ \varepsilon_0=1$, the LeBrun-Burns metric is a smooth K\"ahler metric on $\mathbb{C}^2$ blown up at $N$ points. It is thus a K\"ahler, electrovac generalization of the Gibbons-Hawking metrics.
Near $(a_j,b_j,c_j)$, one has
\begin{equation}
G(x,y,\zeta; a_j,b_j,c_j) ~\sim~ \frac{c_j} { \sqrt{ (x-a_j)^2+(y-b_j)^2+ (\zeta-c_j)^2 }} ~\equiv~ \frac{c_j}{r}\,,
\label{Gasympsing}
\end{equation}
\begin{equation}
D(x,y,\zeta; a_j,b_j,c_j) ~\sim~ \frac{\zeta - c_j} { \sqrt{ (x-a_j)^2+(y-b_j)^2+ (\zeta-c_j)^2 }} ~\equiv~ \cos \theta\,,
\label{Dasympsing}
\end{equation}
and the metric (\ref{LBB2}) behaves as:
\begin{eqnarray}
ds^2_4 &=& c_j\, q_j \big[ q_j^{-2} r \, (d\tau+\cos \theta \, d\phi)^2 + r^{-1} (dr^2 + r^2 d \theta^2+ r^2 \sin^2 \theta \, d \phi^2 ) \big] \nonumber \\
&=& c_j\, q_j \big[ d\rho^2 + \coeff{1}{4} \rho^2( d \theta^2+ \sin^2 \theta \, d \phi^2 + q_j^{-2} \, (d\tau+\cos \theta \, d\phi)^2) \big] \,,
\label{metasymp}
\end{eqnarray}
where we have introduced spherical polar coordinates about $(a_j,b_j,c_j)$ and made a change of variable $r = {1\over 4} \rho^2$. Thus near the singular points of $V$, the metric is locally $\mathbb{R}^4/\mathbb{Z}_{q_j}$, and hence may be viewed as regular in string theory.
At infinity one has:
\begin{equation}
G(x,y,\zeta; a_j,b_j,c_j) ~\sim~ \frac{2\, c_j^2 \, \zeta^2 } {( x^2+ y^2+ \zeta^2)^2}\,,
\label{Gasympinf}
\end{equation}
\begin{equation}
D(x,y,\zeta; a_j,b_j,c_j) ~\sim~ 1\,,
\label{Dasympinf}
\end{equation}
and hence $V \to \varepsilon_0$ and $A \to d\phi$, and the metric is asymptotic to $\mathbb{R}^4 = \mathbb{C}^2$ for $\varepsilon_0 = 1$.
\subsubsection{Homology and periods}
\label{Topology}
Exactly as in Gibbons-Hawking geometries, the LeBrun-Burns metrics have non-trivial two-cycles defined by the $U(1)$ fibers over any curve between the poles of $V$. More specifically, the $U(1)$ fiber (defined by $\tau$) taken over a generic line interval in the $\mathbb{H}^3$ base describes a cylinder. However, if one runs this interval between two poles of $V$ at points, $\vec y^{(i)}$ and $\vec y^{(j)}$ then the fiber is pinched off at the ends and the result is essentially a topological two-sphere. The asymptotic behavior of the metric at each end of the interval, (\ref{metasymp}), means that this two-sphere may, in fact, be modded out by some discrete group that depends upon the values of $q_i$ and $q_j$. The two-cycles defined in this way will be denoted as $\Delta_{ij}$ and are depicted in Fig. \ref{cycles}.
\begin{figure}
\centering
\includegraphics[height=3cm]{cycles.eps}
\caption{\it \small The non-trivial cycles of the LeBrun-Burns metrics are defined by sweeping the $U(1)$ fiber along a path, in $\mathbb{H}^3$, between
any two poles of the potential, $V$. The fiber is pinched off at the poles. Here the fibers sweep out a pair of intersecting two-cycles.}
\label{cycles}
\end{figure}
The periods of these cycles are trivial to compute using (\ref{Kform}):
\begin{equation}
\frac{1}{2\, \pi} \, \int_{\Delta_{ij}} \, J ~=~ \frac{1}{2\, \pi} \, \int_{\Delta_{ij}} d\tau \wedge dz ~=~ 2(z_j - z_i) ~=~ \zeta_j^2 - \zeta_i^2 \,, \label{perint}
\end{equation}
where $z_i = \frac{1}{2} \zeta_i^2$ denote the $z$-coordinates of the corresponding poles of $V$.
The Maxwell fields, $\Theta^{(1)}$, $\Theta^{(2)}$ and $\Theta^{(3)}$ defined in (\ref{Thetaforms}) and (\ref{Max3}) have components along the fiber of the form
\begin{equation}
\Theta^{(I)} ~=~ \vec \nabla \bigg( \frac{K^{(I)}}{w} \bigg) \,\cdot \, d\tau \wedge d\vec y \,, \qquad I=1,2,3 \,, \label{tauparts}
\end{equation}
where $K^{(1)}$ and $K^{(2)}$ satisfy (\ref{lin2a}) and (\ref{lin2b}) and
\begin{equation}
K^{(3)} ~\equiv~ {1 \over 2} \, \partial_z u \,. \label{p3defn}
\end{equation}
From this it follows that these fields have fluxes
\begin{equation}
\Pi_{ij}^{(I)} ~\equiv~ \frac{K^{(I)}}{w}\Big|_{\vec y^{(j)}} ~-~ \frac{K^{(I)}}{w} \Big |_{\vec y^{(i)}} \,, \qquad I=1,2,3 \,. \label{fluxes}
\end{equation}
Note, in particular, that for the LeBrun-Burns metric ${K^{(3)}}w^{-1} = V^{-1}$ which vanishes at all the $\vec y^{(i)}$. Therefore $\Theta^{(3)}$ has {\it no non-trivial} fluxes on the compact two cycles.
On the other hand, the complete Maxwell field, ${\cal F}$, (\ref{MaxF}), does have non-trivial fluxes because it has an anti-self-dual component involving $J$.
\begin{equation}
\frac{1}{2\, \pi} \, \int_{\Delta_{ij}} \, {\cal F} ~=~ -\frac{1}{2\, \pi} \, \int_{\Delta_{ij}} \, J ~=~ -(\zeta_j^2 - \zeta_i^2) \,, \label{Fflux}
\end{equation}
There is potentially a similar contribution from the ``electric parts'' of the complete gauge fields defined in (\ref{AAnsatz}). Specifically, the complete Maxwell fields, $F^{(I)}$, have a component along the fiber:
\begin{equation}
F^{(I)} ~\equiv~ dA^{(I)} ~=~ d\tau \wedge d \big(Z_I^{-1} \, \mu \big) ~+~ \dots \,. \label{Ftaucomps}
\end{equation}
This will generically lead to fluxes of the form
\begin{equation}
\widehat \Pi_{ij}^{(I)} ~\equiv~ \frac{\mu}{Z_I}\bigg |_{\vec y^{(j)}} ~-~ \frac{\mu}{Z_I} \bigg |_{\vec y^{(i)}} \,, \qquad I=1,2,3 \,, \label{otherfluxes}
\end{equation}
however, regularity of the metric and the absence of closed time-like curves typically requires that $Z_I$ be finite and $\mu$ vanish at the points $\vec y^{(i)}$. Thus these fluxes are usually zero.
In summary, the bubbled non-BPS solutions generically have non-vanishing fluxes for all three Maxwell fields but the self-dual part of the third Maxwell field, $\Theta^{(3)}$, will have trivial fluxes.
\subsection{Solving the non-BPS system}
\label{LBBSoln}
The differential operators of interest are:
\begin{eqnarray}
{\cal L}_1 H & \equiv& \partial_{x}^2 H ~+~ \partial_{y}^2 \, H ~+~ \zeta^{-1} \, \partial_\zeta \, (\zeta \partial_\zeta H ) \,, \label{diffop1} \\
{\cal L}_2 G & \equiv& \partial_{x}^2 G ~+~ \partial_{y}^2 \, G ~+~\zeta \, \partial_\zeta \, \big (\zeta^{-1} \, \partial_\zeta G \big) \,. \label{diffop2}
\end{eqnarray}
Note that $\zeta^2 {\cal L}_2$ is simply the Laplacian on $\mathbb{H}^3$. The operator, ${\cal L}_1$ has been introduced for later convenience because it appears in the equations of motion and it is also useful to note that it has a simple geometric interpretation. Observe that the Laplacian on $\mathbb{R}^4 = \mathbb{R}^2 \times \mathbb{R}^2$ may be written as
\begin{equation}
\hat {\cal L}_1 H ~=~ \partial_{x}^2 H ~+~ \partial_{y}^2 \, H ~+~ \zeta^{-1} \, \partial_\zeta \, (\zeta \partial_\zeta H ) ~+~ \zeta^{-2}\, \partial_\varphi^2 \, H\,, \label{diffop3}
\end{equation}
where $(x,y)$ are Cartesians on the first $\mathbb{R}^2$ and $(\zeta,\varphi)$ are polars on the second $\mathbb{R}^2$. Thus solving equations that involve ${\cal L}_1$ may simply be viewed as looking for $\varphi$-independent solutions with the flat Laplacian on $\mathbb{R}^4$. The equations and solutions that involve ${\cal L}_1$ are thus extremely familiar from the extensive literature on black rings. In particular, it is useful to note that the following are Green functions for ${\cal L}_1$:
\begin{eqnarray}
H(x,y,\zeta; a,b,c) &\equiv& \frac{1} { \sqrt{((x-a)^2+(y-b)^2+ \zeta ^2 + c^2)^2 - 4\, c^2\, \zeta^2 }} \nonumber\\
&=& \frac{1} { \sqrt{((x-a)^2+(y-b)^2+ (\zeta-c)^2) \, ((x-a)^2+(y-b)^2+ (\zeta+c)^2) }} \,. \nonumber\\
\label{Fdefn}
\end{eqnarray}
At infinity one has:
\begin{equation}
H(x,y,\zeta; a,b,c) ~\sim~ \frac{1} {( x^2+ y^2+ \zeta^2) }\,.
\label{Fasympinf}
\end{equation}
To solve the linear system, one first solves the homogeneous equations:
\begin{equation}
{\cal L}_2 V ~=~ 0 \,, \qquad {\cal L}_2 \, (\zeta^2 \, L_1) ~=~ 0 \,, \qquad {\cal L}_2 (\zeta^2 \, L_2) ~=~ 0 \,, \label{VLeqns}
\end{equation}
and then uses these solutions in the equations that define the magnetic fluxes and the angular momentum function, $M$:
\begin{eqnarray}
{\cal L}_1 \, K^{(1)} &=& 2\, \zeta^{-1} \partial_\zeta \,(V\, L_2 ) \,, \qquad {\cal L}_1 \, K^{(2)} ~=~ 2\, \zeta^{-1} \partial_\zeta \,(V \, L_1 ) \,, \label{peqns} \\
{\cal L}_1 \, M &=& \zeta^{-1} \partial_\zeta \, (\zeta^2 \, L_1 \, L_2 ) \,. \label{Meqn1}
\end{eqnarray}
The last step is to use these solutions in:
\begin{equation}
{\cal L}_2 \, L_3 ~=~ 4 \, V \,( L_1 L_2 - \zeta^{-1} \partial_\zeta M) - 2 \, \zeta \, (L_1 \, \partial_\zeta K^{(1)} + L_2 \,\partial_\zeta K^{(2)} )\,. \label{L3eqn1}
\end{equation}
The physical functions now have the form
\begin{equation}
Z_1 ~=~ {K^{(2)} \over V} ~+~L_1\,, \quad Z_2 ~=~ { K^{(1)} \over V } ~+~L_2 \,, \quad Z_3 ~=~ {\zeta^2 \,K^{(1)} \, K^{(2)} \over V } ~+~L_3 \,, \label{BurnsZforms}
\end{equation}
\begin{equation}
\mu ~=~ -{\zeta^2 \, K^{(1)} \, K^{(2)} \over V^2} - \frac{1}{2}\, {\zeta^2 \, (K^{(1)} \, L_1 + K^{(2)} \, L_2 ) \over V} ~-~ \frac{1}{2}\, { L_3 \over V} ~+~ M \,. \label{Burnsmuform}
\end{equation}
The equations for $\omega$ reduce to
\begin{eqnarray}
&& (\partial_y \omega_{\zeta} - \partial_{\zeta} \omega_y ) + \displaystyle\frac{1}{\zeta}(M \partial_x V - V \partial_x M) + \frac{1}{2\zeta} \sum_{j=1}^2 (K^{(j)} \partial_x (\zeta^2 L_j) - \zeta^2L_j \partial_x K^{(j)}) + \frac{1}{2 \zeta} \partial_x L_3 = 0 \,, \notag \\
&& (\partial_{\zeta} \omega_x -\partial_x \omega_{\zeta}) + \displaystyle\frac{1}{\zeta}(M \partial_y V - V \partial_yM) + \frac{1}{2\zeta} \sum_{j=1}^2 (K^{(j)} \partial_y (\zeta^2 L_j) - \zeta^2L_j \partial_y K^{(j)}) + \frac{1}{2 \zeta} \partial_y L_3 = 0 \,, \notag \\
&& (\partial_{x} \omega_y -\partial_y \omega_{x}) + \displaystyle\frac{1}{\zeta}(M \partial_{\zeta} V - V \partial_{\zeta} M) + \frac{1}{2\zeta} \sum_{j=1}^2 (K^{(j)} \partial_{\zeta} (\zeta^2 L_j) - \zeta^2L_j \partial_{\zeta} K^{(j)}) \label{Burnsomega}\\
&&+ \frac{1}{2 \zeta} \partial_{\zeta} L_3 + 2 V L_1L_2 = 0 \,. \notag
\end{eqnarray}
This system of equations has a gauge invariance that leaves the physical solution completely invariant. See Appendix \ref{gauge invariance} for details.
\subsection{Asymptotics}
\label{Asymp1}
Ideally one would like to find solutions that are asymptotically flat and for the metric (\ref{metAnsatz}) this means that one must have $Z_I \to 1$ at infinity. However, this is generically not possible because the Maxwell fields, ${\cal F}$, in (\ref{Fdecomp}) and $\Theta^{(j)}, j=1,2$ in (\ref{Thetaforms})
involve the K\"ahler form and thus the norm of these fields does not vanish at infinity.
To see this, suppose that the $Z_I$ go to constants at infinity, then the space-space and time-time components of the full five-dimensional Einstein's equations imply that, at infinity,
\begin{equation} \label{5d_Einstein_ij}
\sum_{I=1}^3 \big( {\Theta^{(I)}}_{ik} {\Theta^{(I)}}_j{}^k - \frac14 \delta_{ij} {\Theta^{(I)}}_{kl} {\Theta^{(I)}}^{kl} \big) ~\to~ 0 \,,
\end{equation}
\begin{equation} \label{5d_Einstein_00}
\sum_{I=1}^3 {\Theta^{(I)}}_{kl} {\Theta^{(I)}}^{kl} ~\to~ 0 \,.
\end{equation}
The self-dual parts of the $\Theta^{(I)}$ can be made to vanish at infinity, and so \eqref{5d_Einstein_ij} can be satisfied. However, the left-hand-side of \eqref{5d_Einstein_00} is positive-definite, and so this equation cannot be satisfied because the $\Theta^{(j)}, j=1,2$ always have a non-vanishing anti-self-dual part (given by the K\"ahler form $J$). This is in contrast to the solutions based on Gibbons-Hawking metrics for which the $\Theta^{(I)}$ vanish at infinity.
One cannot, therefore, arrange to have $Z_I \to 1$ at infinity. On the other hand, we will now show that there are solutions that are asymptotic to the near-horizon limit of a BMPV black hole.
\section{Solutions with a flat base space}
\label{FlatSolutions}
Here we consider solutions in which the base space is completely flat, taking $V \equiv 1$ in the LeBrun-Burns metric. One of the purposes in doing this is to see
what kind of asymptotic geometries and black-object geometries can be generated from the LeBrun-Burns metric using the solution technique of Section \ref{BurnsSec}.
Indeed, we will show that the natural boundary conditions correspond to the near-horizon regions of black holes and black rings. It is also important to note that even though we have set $V=1$ and thus trivialized the metric on the base, the Maxwell field, ${\cal F}$, is still non-zero but is now purely anti-self-dual\footnote{This means that ${\cal F}$ has vanishing energy-momentum tensor, consistent with the flatness of the base.} and proportional to the complex structure, $J$. Similarly, the other Maxwell fields (\ref{Thetaforms}) have both anti-self-dual and self-dual parts on the base. This will generically mean that supersymmetry is completely broken and that the solutions we get will be non-BPS.
\subsection{The near-horizon limit of a black hole}
\label{flatsol1}
Perhaps the simplest non-trivial solution is a spherically symmetric one, whose sources necessarily lie at $(x, y, \zeta)=(0,0,0)$. In addition we set some of the electric potentials to zero:
\begin{equation}
L_1 ~\equiv~L_2 ~\equiv~ 0\,. \label{BHsol1}
\end{equation}
It is also convenient to introduce polar coordinates in $\mathbb{R}^2$ and $\mathbb{R}^4$: We already have $\zeta$ and $\tau$ in one copy of $\mathbb{R}^2$ and so we define\footnote{The coordinate $\theta$ here is not the same as the one in \eqref{metasymp}. }
\begin{equation}
x ~=~ \eta \cos \phi\,, \quad y ~=~ \eta \sin \phi\,; \qquad \zeta ~=~ \rho \cos \theta \,, \quad \eta ~=~ \rho \sin \theta \,; \qquad \rho ~\equiv~ x^2+y^2+ \zeta^2 \,. \label{polars1}
\end{equation}
The functions $K^{(I)}$ and $M$ are then homogeneous solutions to ${\cal L}_1 H =0$ and the spherically symmetric solutions are proportional to $H(x,y,\zeta; 0,0,0) = \rho^{-2}$ (see (\ref{Fdefn})). We therefore take
\begin{equation}
Z_1 ~=~ K^{(2)} ~=~ \frac{\beta_2}{ \rho^2} \,, \qquad Z_2 ~=~ K^{(1)} ~=~ \frac{ \beta_1}{ \rho^2} \,, \qquad M ~=~ \frac{\gamma}{ \rho^2} \label{BHsol2} \,,
\end{equation}
where $\beta_1, \beta_2 $ and $\gamma$ are constant parameters.
It is easy to see that one can satisfy (\ref{L3eqn1}) by taking:
\begin{equation}
L_3 ~=~\hat L_3 + 2 \, M \,, \qquad {\cal L}_2 \hat L_3 ~=~ 0\,, \label{BHsol3}
\end{equation}
for some function, $\hat L_3$. The natural choice for $\hat L_3$ is the function $G$ in (\ref{Gdefn}), but this vanishes for $c=0$, and one must take a limit:
\begin{equation}
\hat L_3 = \beta_3 \, \lim_{c \to 0} \, \frac{ 1}{ 2\,c^2} \, G(x,y,\zeta; 0,0,c) ~=~ \beta_3 \, \frac{ \zeta^2}{ \rho^4} ~=~ \beta_3 \, \frac{ \cos^2 \theta}{ \rho^2}\,, \label{BHsol4}
\end{equation}
One then has
\begin{eqnarray}
Z_3 &=& \zeta^2 \, K^{(1)} \, K^{(2)} + L_3 ~=~ (\beta_1 \,\beta_2\, + \beta_3 )\, \frac{ \cos^2 \theta}{ \rho^2} ~+~ \frac{2\, \gamma}{ \rho^2} \,, \label{BHsol5} \\
\mu &=& -\, \zeta^2 \, K^{(1)} \, K^{(2)} ~-~ \frac{1}{2}\, \hat L_3 ~=~ - \frac{1}{2}\, (2\,\beta_1 \,\beta_2 + \beta_3) \, \frac{ \cos^2 \theta}{ \rho^2} \,. \label{BHsol6}
\end{eqnarray}
The last step is to solve for $\vec \omega$, for which we can choose the gauge $\omega_z =0$. Equations (\ref{omx})--(\ref{omz}) then reduce to:
\begin{equation}
\zeta \, \partial_\zeta \omega_y ~=~ \frac{1}{2}\, \partial_x \hat L_3 \,, \quad \zeta \, \partial_\zeta \omega_x ~=~ - \frac{1}{2} \, \partial_y \hat L_3 \,, \qquad \partial_x \omega_y - \partial_y \omega_x ~=~ - \frac{1}{2}\, \zeta^{-1} \, \partial_\zeta \hat L_3 \label{BHsol7}
\end{equation}
for which the solution is:
\begin{equation}
\omega ~=~ - \frac{\beta_3}{2} \, \frac{1}{\rho^4} \,( y \, dx -x \, dy )~=~ \frac{\beta_3}{2} \, \frac{ \sin^2 \theta}{ \rho^2} \, d \phi\,, \label{BHsol8}
\end{equation}
where the homogeneous solutions have been chosen so that $\omega$ goes to zero at infinity.
The five-dimensional metric is then:
\begin{eqnarray}
ds_5^2 &=& - W_0(\theta)^{-2} \, \rho^4\,\bigg(dt - \frac{1}{2}\, ( \beta_3+ 2\,\beta_1 \,\beta_2 ) \, \frac{ \cos^2 \theta}{ \rho^2} d\tau + \frac{\beta_3}{2} \,\frac{ \sin^2 \theta}{ \rho^2} \, d \phi \bigg)^2 \nonumber \\
&&\quad ~+~ W_0(\theta) \, \Big( \frac{d\rho^2}{ \rho^2} + d \theta^2 + \cos^2 \theta d\tau^2 + \sin^2 \theta d \phi^2 \Big) \,,
\label{BHmet}
\end{eqnarray}
where
\begin{equation}
W_0(\theta) ~\equiv~ \big(\beta_1 \beta_2( 2\, \gamma+ (\beta_1 \,\beta_2\, + \beta_3 )\, \cos^2 \theta ) \big)^\frac{1}{3} \,. \label{BHsol9}
\end{equation}
The conditions for absence of causal pathologies for solutions of our Ansatz are discussed in Appendix \ref{causality}. For the simple solution in this section there is no Dirac-Misner string in $\omega$ and the condition for absence of CTC's is that all constants $\gamma$, $\beta_1$, $\beta_2$ are non-negative and
%
\begin{equation}
8 \gamma\beta_1\beta_2 \geq \beta_3~. \label{noCTCBMPV}
\end{equation}
%
For generic choice of parameters satisfying \eqref{noCTCBMPV} the metric \eqref{BHmet} has the form of a warped rotating $AdS_2\times S^3$. The general solution has unequal angular momenta in each $\mathbb{R}^2$, and has a distorting warp factor, function, $W_0(\theta)$. For the special choice $\beta_3 = - \beta_1 \beta_2$ the function $W_0$ becomes a constant and the two angular momenta become equal. The metric then is precisely the near horizon limit of the BMPV black hole \cite{Breckenridge:1996is}. It is worth emphasizing that the BMPV black hole (and its near horizon limit) is a supersymmetric solution of supergravity whereas our solution has anti-self-dual flux that breaks supersymmetry.
\subsection{Near-horizon limit of a black ring with two dipole charges}
\label{flatsol2}
\subsubsection{Solving the equations}
\label{SolEqns}
To get the black ring (or supertube) generalization of the foregoing solution, we simply need to use the source functions (\ref{Gdefn}) and (\ref{Fdefn}) with $c \ne 0$. We can, without loss of generality, take $a=b=0$ since we are going to consider a single source. We therefore start by taking:
\begin{equation}
\qquad L_J ~=~ \displaystyle\frac{\ell_J}{\zeta^2} \, G(x,y,\zeta; 0,0,c) \,, \qquad J=1,2 \,, \label{BRsol1}
\end{equation}
for some constants $\ell_J $. The supertube will thus be located at $(0,0,c)$.
The functions $K^{(I)}$ now have a source part and a homogeneous part that is proportional to $H$:
\begin{eqnarray}
K^{(1)} &=& - \frac{\ell_2}{\zeta^2}\, G(x,y,\zeta; 0,0,c) + \beta_1 \, H(x,y,\zeta; 0,0,c) ~=~ - L_2 + \beta_1 \, H(x,y,\zeta; 0,0,c) \,, \label{BRsol2} \\
K^{(2)} &=& - \frac{\ell_1}{\zeta^2}\, G(x,y,\zeta; 0,0,c) + \beta_2 \, H(x,y,\zeta; 0,0,c) ~=~ - L_1 + \beta_2 \, H(x,y,\zeta; 0,0,c) \label{BRsol3} \,,
\end{eqnarray}
and hence
\begin{equation}
Z_1 = K^{(2)} + L_1 = \beta_2\, H(x,y,\zeta; 0,0,c) \,, \qquad Z_2 = K^{(1)} + L_2 = \beta_1\, H(x,y,\zeta; 0,0,c) \,, \label{BRsol4} \\
\end{equation}
where, once again, $\beta_1$ and $\beta_2 $ are constants. The next step is to solve (\ref{Meqn1}) and (\ref{L3eqn1}) for $M$ and $L_3$, and as in (\ref{BHsol3}) it is convenient to shift $L_3$ by $M$. One finds
\begin{equation}
L_3 ~=~\hat L_3 + 2 \, M \,, \qquad {\cal L}_2 \hat L_3 ~=~ -2\, (\beta_1\ell_1 + \beta_2 \ell_2) \, \zeta^{-1} \, G \, \partial_\zeta H \,. \label{BRsol5}
\end{equation}
It is straightforward to show that this and (\ref{Meqn1}) are satisfied by:
\begin{eqnarray}
\hat L_3 &=& (\beta_1\ell_1 + \beta_2 \ell_2) \, \big[\, (\rho^2 + c^2 - 2 \, \zeta^2) H^2 ~-~H\,\big] + \ell_3 \, G \,, \label{BRsol6} \\
M &=& - \frac{ \ell_1 \, \ell_2}{2} \, \big( \zeta^{-2} \, G^2 ~-~ 4 \, \rho^2\, H^2 \label{BRsol7} \big) ~+~ \mu_0\, H \,,
\end{eqnarray}
where the constants $\ell_3$ and $\mu_0$ multiply homogeneous solutions to the relevant differential equations. Combining these results in
(\ref{Z3form}) and (\ref{muform}) one obtains:
\begin{eqnarray}
Z_3 &=& \big((2\,\ell_2-\beta_1) (2\,\ell_1-\beta_2) \zeta^2 ~+~ 4\, \ell_1\,\ell_2 (\rho^2 -\zeta^2) \big)\, H^2 + \ell_3 \, G ~+~ 2\, \mu_0 \, H\,, \label{BRsol8} \\
\mu &=& - \frac{1}{ 2}\, \big[2\, (\beta_1 \beta_2 - (\beta_1\ell_1 + \beta_2 \ell_2) ) \, \zeta^2 \, H^2 ~+~ \ell_3 \, G \big] \,. \label{BRsol9}
\end{eqnarray}
The last step is to solve for (\ref{omx})--(\ref{omz}) for $\omega$ and one can easily verify that:
\begin{equation}
\omega = \Big[ - \frac{\ell_3}{2} \big( G - 2\, c^2 \, H \big) ~-~ (\beta_1\ell_1 + \beta_2 \ell_2) \, H^2 \, \rho^2 \sin^2 \theta \Big] \, d \phi \,, \label{BRsol10}
\end{equation}
where a constant of integration has been adjusted so that $\omega$ goes to zero at infinity.
The Green functions, $G$ and $H$, and the metric that we construct here are, of course, familiar from the standard description of black rings. This is explained further in Appendix \ref{CanCoords}.
\subsubsection{Regularity near the supertube}
\label{STreg}
The first step in checking regularity of the metric is to look for closed time-like curves (CTC's) in the $\tau$ and $\phi$ directions near the ring. Indeed there is a divergent negative coefficient of $d \tau^2$ unless one requires:
\begin{equation}
\beta_1 \, \ell_1 ~=~ \beta_2 \, \ell_2\,, \label{CTCcond1}
\end{equation}
which we will use to eliminate $\ell_2$. This condition is a familiar regularity requirement for the three-charge, two-dipole charge supertube
\cite{Bena:2004wt,Bena:2004wv}.
Once this term is dealt with there is a sub-leading divergence that then requires
\begin{equation}
\beta_2 \mu_0 = - 2 c^2 \ell_1 \ell_3~. \label{radiusST}
\end{equation}
Since the radius of the supertube\footnote{See Appendix A.4 for more details on this.} is related to $c$ we can interpret this relation as a radius formula for the supertube. There is a Dirac-Misner string in $\omega$ that leads to CTC's for $x = y =0$ and $\zeta < c$, and this requires that $\ell_3 =0$ and so we must fix the homogeneous solutions by taking:
\begin{equation}
\ell_3 ~=~ \mu_0 ~=~ 0 \,. \label{CTCcond2}
\end{equation}
With these choices the five-dimensional metric simplifies significantly and it is convenient to introduce two manifestly non-negative functions:
\begin{equation}
W_1(\rho, \theta) \equiv \rho^4 \,\big( (\rho^2+ c^2)^2 - 4 \, c^2 \, \rho^2\,\cos^2 \theta \big)^{-1} \,, \quad W_2(\theta) \equiv (2\, \ell_1-\beta_2)^2 \, \cos^2 \theta + 4 \, \ell_1^2 \, \sin^2 \theta \,, \label{H12defn}
\end{equation}
and define
\begin{equation}
\widehat Z(\rho,\theta) ~\equiv~ \bigg(\beta_1^2 \, W_1^2 \, W_2\bigg)^{1/3} \,. \label{Zhatdefn}
\end{equation}
The angular momentum vector simplifies to:
\begin{equation}
k ~=~ \rho^{-2}\, W_1(\rho, \theta) \, \Big[ \big( (\beta_1\ell_1 + \beta_2 \ell_2) - \beta_1\, \beta_2\, \big) \, \cos^2 \theta \, d \tau ~-~ (\beta_1\ell_1 + \beta_2 \ell_2) \, \sin^2 \theta \, d \phi \Big] \,, \label{kang1}
\end{equation}
and the five dimensional metric may be written as:
\begin{equation}
ds_5^2 ~=~ - \widehat Z(\rho,\theta)^{-2} \, \rho^4\, (dt + k)^2 ~+~ \widehat Z(\rho,\theta) \, \Big( \frac{d\rho^2}{ \rho^2} + d \theta^2 + \cos^2 \theta \, d\tau^2 + \sin^2 \theta \, d \phi^2 \Big) \,.
\label{BRmet}
\end{equation}
This form of the metric is reminiscent of the ``decoupling limit" for supersymmetric black rings/supertubes discussed in \cite{Elvang:2004ds}. It would be interesting to dualize our solutions to the D1-D5 duality frame and compare in more detail with the background in \cite{Elvang:2004ds}.
This metric has no CTC's but is singular at the location of the supertube. This is a generic property of the supertube with two dipole charges and is familiar from the corresponding supersymmetric solutions \cite{Bena:2004wt}.
\subsubsection{Asymptotics at infinity}
\label{AsympInf}
At infinity one has:
\begin{equation}
Z_1 ~\sim~ \frac{\beta_2}{\rho^2} \,, \qquad Z_2~\sim~ \frac{\beta_1}{\rho^2} \,, \qquad Z_3~\sim~ \frac{\beta_1}{\beta_2} \, \frac{W_2(\theta)}{\rho^2} \,, \label{asymp1}
\end{equation}
\begin{equation}
k ~\sim~ \rho^{-2}\, \Big[ \big( (\beta_1\ell_1 + \beta_2 \ell_2) - \beta_1\, \beta_2\, \big) \, \cos^2 \theta \, d \tau ~-~ (\beta_1\ell_1 + \beta_2 \ell_2) \, \sin^2 \theta \, d \phi \Big] \,, \label{asymp2}
\end{equation}
and hence:
\begin{equation}
\big( Z_1 Z_2 Z_3 \big)^{1 \over 3} ~\sim~ \, \frac{\Big( \beta_1^2 \, W_2(\theta) \Big)^{1 \over 3}}{\rho^2} \label{Warpasymp1}
\end{equation}
The five-dimensional asymptotic metric, (\ref{BRmet}), now takes the form:
\begin{eqnarray}
ds_5^2 ~=~ && - \Big(\beta_1^2 \, W_2(\theta) \Big)^{-2/3} \, \rho^4\, (dt + k)^2 \nonumber \\
&&\quad ~+~ \Big(\beta_1^2 \, W_2(\theta) \Big)^{1/3}\, \Big( \frac{d\rho^2}{ \rho^2} + d \theta^2 + \cos^2 \theta \, d\tau^2 + \sin^2 \theta \, d \phi^2 \Big) \,,
\label{BRmetasymp}
\end{eqnarray}
which is precisely of the form discussed in Section \ref{flatsol1}, {\it i.e.} a warped form of rotating $AdS_2 \times S^3$. For the special choice $\beta_2=4\ell_1$ we have $W_2(\theta)=4\ell_1^2$ and \eqref{BRmetasymp} reduces to the near horizon BMPV metric. Therefore we can consider the metric \eqref{BHmet} as the metric to which all black hole, black ring and multi-center solutions within our Ansatz will asymptote for $\rho\to\infty$. We will describe this in more detail in the next section.
\section{Multi-centered solutions}
\label{BlowingBubbles}
We have been able to solve in complete generality the system of differential equation \eqref{VLeqns}, \eqref{peqns}, \eqref{Meqn1}, \eqref{L3eqn1} and\eqref{Burnsomega} on an axisymmetric LeBrun-Burns base. This provides an infinite class of explicit five-dimensional multi-centered solutions with (at least) one time-like and two space-like Killing vectors $(\partial_{t},\partial_{\tau},\partial_{\phi})$. Amongst our solutions are multi-center generalizations of the solutions in Section \ref{flatsol1} and \ref{flatsol2} as well as a class of regular bubbled geometries that we discuss in some detail in Section \ref{Burnsasymptotics} below.
\subsection{General axisymmetric solutions}
\label{GenAxi}
We will look for solutions on an axisymmetric LeBrun-Burns base in which the geometry at infinity has the form (\ref{BHmet}). The singular points of the harmonic function, $V$, that determines the LeBrun-Burns base are located along the $\zeta$ axis at points $c_j$:
\begin{equation}
V~=~ \varepsilon_0 ~+~ \sum_{j=1}^N \, q_j \, G_j ~.
\end{equation}
Where for convenience we have defined
\begin{eqnarray}
G_{i} &\equiv& G(x,y,\zeta;0,0,c_i) = \displaystyle\frac{\rho^2 +c_i^2}{\sqrt{(\rho^2+c_i^2)^2-4 \zeta^2 c_i^2}} ~-~ 1, \\
H_{i} &\equiv& H(x,y,\zeta;0,0,c_i) = \displaystyle\frac{1}{\sqrt{(\rho^2+c_i^2)^2-4 \zeta^2 c_i^2}}~,\\
D_{i} &\equiv& D(x,y,\zeta; 0,0,c_i) = \displaystyle\frac{\rho^2 -c_i^2}{\sqrt{(\rho^2+c_i^2)^2-4 \zeta^2 c_i^2}}~,
\end{eqnarray}
where we will assume that $c_i\neq 0$. It is trivial to solve \eqref{VLeqns} for the functions $L_1$ and $L_2$
\begin{equation}
L_{a} = \displaystyle\frac{1}{\zeta^2} \left(\ell_a^{0} +\displaystyle\sum_{i=1}^{N}\ell_{a}^{i}G_{i}\right)~, \qquad a=1,2~. \label{L12axi}
\end{equation}
Solving \eqref{peqns} and \eqref{Meqn1} for $K^{(a)}$ and $M$ one finds
\begin{eqnarray}
K^{(1)} &=& k_1^{0} + \displaystyle\frac{\beta_1}{\rho^2}+\displaystyle\sum_{i=1}^{N}k_{1}^{i}H_{i} - V L_{2}+ 4\rho^2 \displaystyle\sum_{i,j=1}^{N} q_{i} \ell_2^{j}H_iH_j~, \label{K1axi}\\
K^{(2)} &=& k_2^{0} + \displaystyle\frac{\beta_2}{\rho^2}+\displaystyle\sum_{i=1}^{N}k_{2}^{i}H_{i} - V L_{1} + 4\rho^2 \displaystyle\sum_{i,j=1}^{N} q_{i} \ell_1^{j}H_iH_j~, \label{K2axi}\\
M &=& m_{0}+ \displaystyle\frac{\gamma}{\rho^2} +\displaystyle\sum_{i=1}^{N}m_{i}H_{i} - \displaystyle\frac{\zeta^2}{2} L_{1}L_2 + 2\rho^2 \displaystyle\sum_{i,j=1}^{N} \ell_1^{i} \ell_2^{j}H_iH_j~.\label{Maxi}
\end{eqnarray}
After a somewhat tedious exercise\footnote{Some of the identities used to solve the equations for $K^{(a)}$, $M$, $L_3$ and $\omega_{\phi}$ are collected in Appendix \ref{UseIdents}.} one can also solve equation \eqref{L3eqn1}
\begin{eqnarray}
\label{L3axi}
&& L_3 = \ell_3^{0} + \displaystyle\sum_{i=1}^{N} \ell_3^i G_i - \zeta^2 VL_1 L_2 + \displaystyle\sum_{i=1}^{N} (2(\varepsilon_0 - Q)m_{i} +(\ell_1^0-\Lambda_1) k_1^i+(\ell_2^0-\Lambda_2) k_2^i)H_{i} \notag\\
&&+ \beta_3\displaystyle\frac{\zeta^2}{\rho^4}+(2(\varepsilon_0 - Q)\gamma +(\ell_1^0-\Lambda_1) \beta_1+(\ell_2^0-\Lambda_2)\beta_2)\displaystyle\frac{1}{\rho^2}+ 2\gamma \displaystyle\sum_{i=1}^{N} \displaystyle\frac{q_{i} }{c_i^2} \displaystyle\frac{\rho^{-2}-H_i}{H_i}~, \notag\\
&&+ \displaystyle\sum_{i=1}^{N} (2q_{i}m_{i} + \ell_1^i k_1^i + \ell_2^i k_2^i) (\eta^2-\zeta^2+c_i^2)H_{i}^2 + \displaystyle\sum_{i\neq j =1}^{N} \displaystyle\frac{(2q_{i}m_{j} + \ell_1^i k_1^j + \ell_2^i k_2^j)}{c_i^2-c_j^2} \displaystyle\frac{H_j-H_i}{H_i} \notag\\
&&+4\displaystyle\sum_{i,j=1}^{N} ((\varepsilon_0 - Q) \ell_1^i \ell_2^j+ (\ell_1^0-\Lambda_1) q_i \ell_2^j + (\ell_2^0-\Lambda_2)q_i \ell_1^j)\rho^2 H_i H_j \\
&&+ 4 \displaystyle\sum_{i,j,k=1}^{N} q_i \ell_1^j \ell_2^k \rho^2 (3\rho^2 - 4 \zeta^2+c_i^2+c_j^2+c_k^2) H_{i} H_j H_k~. \notag
\end{eqnarray}
where we have defined
\begin{equation}
Q \equiv \displaystyle\sum_{i=1}^{N}q_i~, \qquad\qquad \Lambda_{1} \equiv \displaystyle\sum_{i=1}^{N} l_1^{i}~, \qquad\qquad \Lambda_{2} \equiv \displaystyle\sum_{i=1}^{N} l_2^{i}~.
\end{equation}
The one form $\omega = \omega_{\phi} d\phi$ is given by
\begin{eqnarray}
\omega_{\phi} &=& \omega_{0}+ \displaystyle\frac{\beta_3}{2} \displaystyle\frac{\sin^2\theta}{\rho^2} - \gamma\displaystyle\sum_{i=1}^{N} \displaystyle\frac{q_i}{c_i^2} D_i - \displaystyle\sum_{j=1}^{N} \left( m_0q_j + k_1^0 \ell_1^j + k_2^0 \ell_2^j + \displaystyle\frac{\ell_3^j}{2} \right)D_j\notag\\ &&- \displaystyle\sum_{j=1}^{N} (2m_jq_j+k_1^j \ell_1^j + k_2^j \ell_2^j)\eta^2 H_j^2 - \displaystyle\sum_{i\neq j =1}^{N} \displaystyle\frac{(2q_{i} m_{j}+k_1^i \ell_1^j + k_2^i \ell_2^j)}{2(c_i^2-c_j^2)} (D_iD_j + 4\eta^2c_i^2 H_i H_j) \notag \\
&& - 8 \displaystyle\sum_{i,j,k=1}^{N} q_i \ell_1^j \ell_2^k \eta^2\rho^2 H_iH_jH_k ~, \label{omegasoln}
\end{eqnarray}
where $\omega_{0}$ is a constant which should be fixed so as to avoid CTCs and Dirac-Misner strings.
Substituting \eqref{L12axi}, \eqref{K1axi}, \eqref{K2axi}, \eqref{Maxi} and \eqref{L3axi} in the expressions for $Z_1$, $Z_2$, $Z_3$ and $\mu$, \eqref{BurnsZforms} and \eqref{Burnsmuform}, one finds the most general non-BPS solution on an axisymmetric LeBrun-Burns base captured by the floating brane Ansatz of \cite{Bena:2009fi}. For easy comparison with the solution in Section \ref{flatsol1} we have chosen to single out the terms in the solution which have poles at $\rho=0$, {\it i.e.} the terms with coefficients involving $\beta_1$, $\beta_2$, $\beta_2$ and $\gamma$.
In addition to the parameters $\beta_1$, $\beta_2$, $\beta_3$ and $\gamma$, the solution in general has $(8N+7)$ parameters: $\{c_i,\varepsilon_0, q_i, \ell_I^0, \ell_I^i, k_a^0, k_a^i,m_0, m_i\}$. As we will see in the next subsection imposing regularity and absence of causal pathologies will greatly reduce the number of independent parameters.
\subsection{Regular bubbled solutions}
\label{Burnsasymptotics}
The solution we construct here will be asymptotic to the metric \eqref{BHmet}, which can be viewed as the ``elementary" solution within our Ansatz. These regular solutions on a base with non-trivial topology can be viewed as a non-supersymmetric generalization of the BPS bubbled solutions of \cite{Bena:2005va, Berglund:2005vb}.
We begin by defining a radial coordinate around each of the poles of the harmonic functions
\begin{equation}
\rho_i^2= \eta^2 + (\zeta-c_i)^2~.
\end{equation}
We will be interested in constructing a solution that is regular at the locations of the poles of the harmonic functions, $\rho_i \to 0$, and is free of CTCs and Dirac-Misner strings.
For $\rho_i \to 0$ we have the following expansion of the harmonic functions
\begin{equation}
G_i \sim \displaystyle\frac{c_i}{\rho_i} ~, \qquad\qquad H_i \sim \displaystyle\frac{1}{2 c_i\rho_i} ~.
\end{equation}
Since we are looking for a regular bubbled solution in five dimensions we will assume that all functions in the solution have the same singular points (excluding the point $\rho=0$ which, as discussed in the previous section, will be treated separately). The functions $Z_1$ and $Z_2$ near a singular point, $\rho_i \to 0$, diverge as
\begin{equation}
Z_1 \sim \displaystyle\frac{\ell_1^i}{c_i\rho_i} ~, \qquad\qquad Z_2 \sim \displaystyle\frac{\ell_2^i}{c_i\rho_i} ~.
\label{ZIsing}
\end{equation}
To ensure regularity we should set
\begin{equation}
\ell_1^i=\ell_2^i = 0~, \qquad \forall ~i ~.
\label{ellzero1}
\end{equation}
The function $Z_3$ near a singular point, $\rho_i \to 0$, is
\begin{equation}
Z_3 \sim \left(\ell_3^i c_i + \displaystyle\frac{k_1^ik_2^i}{4c_i q_i}\right)\displaystyle\frac{1}{\rho_i} + \displaystyle\frac{m_i}{c_i \rho_i}\left(\varepsilon_0+ \displaystyle\sum_{k=1,k\neq i}^{N} q_k \text{sign}(c_k^2-c_i^2)\right) + \displaystyle\frac{q_i m_i (\eta^2 -\zeta^2 + c_i^2)}{2 c_i^2 \rho_i^2}~.
\end{equation}
The last term in the expression above is divergent and could be made to vanish only for $m_i=0$. Therefore for a regular $Z_3$ one should set
\begin{equation}
m_i= 0~,\qquad\qquad \ell_3^i = -\displaystyle\frac{k_1^ik_2^i}{4 c_i^2 q_i}~, \qquad \forall ~i ~.
\end{equation}
It is not hard to show that with this choice of constants the function $\mu$ will limit to a constant near a singular point. The condition for absence of CTC's\footnote{This comes from $\mathcal{Q} \geq 0$, where $\mathcal{Q}$ is defined in Appendix \ref{causality}.} requires that $\mu$ should vanish at a singular point of $V$ and this leads to the constraint:
\begin{equation}
m_0 + \displaystyle\frac{\gamma}{ c_i^2} - \displaystyle\frac{k_1^ik_2^i}{8 c_i^2 q_i^2} = 0~, \qquad \forall ~i ~. \label{muregrhoi}
\end{equation}
There is one more condition on the constant parameters of the solutions coming from removing a possible Dirac-Misner string in $\omega$. However it turns out that after setting $\omega_0=0$ the absence of a Dirac-Misner string in $\omega$ is guaranteed by \eqref{muregrhoi}.
To summarize, the conditions for regularity and absence of CTC's and Dirac-Misner strings near the poles of the harmonic functions requires that we set:
\begin{equation}
m_i=\ell_1^i=\ell_2^i = 0~, \qquad \ell_3^i = -\displaystyle\frac{k_1^ik_2^i}{4 c_i^2 q_i}~,\qquad m_0 + \displaystyle\frac{\gamma}{ c_i^2} - \displaystyle\frac{k_1^ik_2^i}{8 c_i^2 q_i^2} = 0 ~,\qquad \forall ~i ~. \label{singconstr}
\end{equation}
Note that these conditions are quite different from the regularity and causality constraints for BPS bubbled solutions with a GH base \cite{Bena:2007kg}. In particular for the class of bubbled solutions discussed here there is no analogue of the ``bubble equations" (or integrability conditions) familiar from the supersymmetric multi-center solutions \cite{Bena:2007kg, Bates:2003vx}. However we still have an equation that fixes the locations of the poles in the harmonic functions (but not the distance between them) in terms of the parameters $\{\gamma,m_0,k_1^i,k_2^i,q_i\}$.
Our analysis so far does not guarantee the regularity of the supergravity scalars ({\it i.e.} the K\"ahler moduli of the tori in M-theory) and the absence of causal pathologies at asymptotic infinity. To ensure that we should study the behavior of the solution at $\rho \to \infty$. The harmonic functions have the following expansion
\begin{equation}
G_i \sim 2c_i^2 \displaystyle\frac{\zeta^2}{\rho^4}~, \qquad\qquad H_i \sim \displaystyle\frac{1}{\rho^2} ~.
\end{equation}
Imposing the regularity and causality constraints at $\rho\to \infty$ one finds the following constraints on the parameters of the solution:
\begin{equation}
m_0=k_1^0k_2^0=0~, \qquad \ell_3^0- (k_1^0\ell_1^0+k_2^0\ell_2^0)=0~,\qquad k_1^0\beta_2 + k_2^0\beta_1 + k_1^0\displaystyle\sum_{i=1}^{N}k_2^i + k_2^0\displaystyle\sum_{i=1}^{N}k_1^i =0~. \label{asympconstr}
\end{equation}
The constraints are easily solved by imposing $\ell_3^0=k_1^0=k_2^0=m_0=0$, however there are in principle other ways to satisfy the relations in \eqref{asympconstr}, so we will not commit to a specific solution.
The asymptotic expansion ($\rho\to\infty$) of the metric functions in the solution is
\begin{eqnarray}
Z_1 &\sim& \frac{1}{\varepsilon_0} \Big(\beta_2 + \sum_{i=1}^{N} k_2^i \Big) \frac{1}{\rho^2}~, \qquad Z_2 ~\sim~ \frac{1}{\varepsilon_0} \Big(\beta_1 + \sum_{i=1}^{N} k_1^i \Big) \frac{1}{\rho^2}~, \notag\\
Z_3 &\sim& 2(\varepsilon_0 - Q) \frac{\gamma}{\rho^2} + \frac{1}{\varepsilon_0} \Big(\beta_3\varepsilon_0 + \beta_1\beta_2 + \sum_{i=1}^{N} \Big(\beta_2k_1^i+\beta_1k_2^i - \varepsilon_0 \frac{k_1^i k_2^i}{2 q_i} \Big) + \sum_{i,j = 1}^{N} k_1^i k_2^j -4\varepsilon_0\gamma Q \Big)\,\frac{\zeta^2}{\rho^4}~. \notag\\
\mu &\sim& - \frac{1}{2\varepsilon_0^2} \Big(\beta_3\varepsilon_0 + 2\beta_1\beta_2 + 2 \sum_{i=1}^{N}(\beta_2k_1^i+\beta_1k_2^i)+ 2 \sum_{i,j = 1}^{N} k_1^i k_2^j - \varepsilon_0\sum_{i=1}^{N} \frac{k_1^i k_2^i}{2 q_i} -4\varepsilon_0\gamma Q \Big) \frac{\zeta^2}{\rho^4}~.\notag
\end{eqnarray}
The constraints \eqref{asympconstr} together with \eqref{singconstr} lead to
\begin{equation}
\omega = \frac{\beta_3}{2} \frac{\sin^2 \theta}{\rho^2} d\phi \,,
\end{equation}
It is clear that at $\rho \to \infty$ these regular bubbled solutions are asymptotic to the warped, rotating $AdS_2\times S^3$ solution presented in Section \ref{flatsol1}. The parameters of the solution can be arranged such that the warp factor in the metric is a constant and the solution is asymptotic to the near horizon BMPV black hole.
The axisymmetric multi-center solutions have $8N+11$ parameters. The regularity and causality constraints studied in this section impose $5N+4$ relations on them, therefore we have a $(3N+7)$-parameter family of regular solutions with non-trivial topology on the base. It should be emphasized that we have only analyzed in detail the condition for absence of CTC's near the singularity of the harmonic functions and at asymptotic infinity. In principle one needs to ensure that there are no CTC's globally and for this one usually has to rely on numerics \cite{Bena:2006kb}. On the other hand, experience with many examples suggests that once one has addressed this at singular points and ensured that the metric coefficients are well-behaved then there are no CTC's globally.
It is interesting to note that there is no analog of the bubble equations \cite{Bena:2007kg, Bates:2003vx} for our regular non-BPS solutions. Bubble equations can be viewed as a form of angular momentum balance that constrains the location of sources and with pure flux solutions, non-trivial bubble equations require non-zero sources for all three fluxes. In our solutions, the magnetic flux of $\Theta^{(3)}$ is trivial on the topological two-cycles and the complete Maxwell field ${\cal F}$, has no localized sources. Thus one should not be too surprised at the absence of constraints on the location of the remaining flux sources.
\section{Conclusions}
\label{Conclusions}
Using the floating brane Ansatz of \cite{Bena:2009fi} we have constructed a large class of non-BPS multi-centered supergravity solutions. The solutions are determined by a four-dimensional K\"ahler base with non-trivial topology and that is a solution of the Euclidean Einstein-Maxwell equations. To find explicit solutions one has to solve a coupled linear system of inhomogeneous differential equations on this base. We managed to construct the most general explicit solution of these equations on the axisymmetric LeBrun-Burns base. The generic multi-centered solutions will have horizons but we showed explicitly that by a judicious choice of parameters one can make the solutions completely smooth and regular. Due to the Maxwell flux on the four-dimensional base the five-dimensional solutions are not asymptotically flat but can be arranged to look like a warped, rotating $AdS_2\times S^3$ space at asymptotic infinity. For specific choice of parameters the asymptotic metric is exactly the near horizon throat metric of the BMPV black hole. We have thus constructed ``hair in the back of a throat".
There are a number of possible directions for further work in this area. First, it well-known that BPS supertubes with two electric and one magnetic dipole charge are regular in six dimensions in the D1-D5 duality frame \cite{Lunin:2001jy,Lunin:2002iz,Bena:2008dw}. Such solutions can thus potentially provide richer classes of regular geometries. Indeed, five-dimensional regularity requires that all the $Z_I$ be non-singular but supertubes allow two of the $Z_I$ to have poles and the singularities are resolved as Kaluza-Klein monopoles in six dimensions. The solutions presented in Section \ref{GenAxi}, before five-dimensional regularity was imposed, include solutions that correspond to families of concentric supertubes. Removing the singularities as in (\ref{ZIsing}) required us to set some of the parameters to zero (see (\ref{ellzero1})) and while we still found regular solutions with microstate structure, it restricted that family of solutions quite strongly and led us to solutions for which the bubble equations were trivial. We expect that for solutions with supertubes there will be some analog of the familiar radius formula arising from the bubble equations, or integrability conditions. We therefore expect there to be even richer classes of bubbles and ``hair'' if one allows solutions that are regular in six dimensions but not necessarily in five.
It is also worth recalling that there are spectral flow methods that map regular, six-dimensional supertube geometries onto five-dimensional, regular bubbled geometries \cite{Bena:2008wt}. For BPS solutions, these transformations do not substantially modify the geometry of the four-dimensional base, though they can modify the asymptotics at infinity. On the other hand, for non-BPS solutions such spectral flows can completely change the geometry of the base, for example, mapping a hyper-K\"ahler geometry onto an Israel-Wilson electrovac solution \cite{Bena:2009fi}. It would be interesting to see how such spectral flows might modify the solutions considered here, particularly if one first includes supertube configurations. It will almost certainly move one beyond the LeBrun class of solutions and perhaps give a richer class of geometries at infinity.
There are other natural generalizations of the solutions considered here. Our solutions can be uplifted to eleven dimensions where they are sourced by intersecting M2 and M5 branes on $T^6$ \cite{Bena:2007kg}. It is fairly evident that there will also be solutions that can be obtained from intersecting M2 and M5 branes wrapping two-cycles and four-cycles in a more general Calabi-Yau three-fold. Going in the opposite direction, any solution with a LeBrun base has a space-like Killing vector (defined by $\tau$-translations) and so one can perform a dimensional reduction along this direction to find supergravity solutions in four dimensions. These solutions will clearly be non-BPS and will represent an infinite class of multi-center four-dimensional solutions that are non-supersymmetric generalizations of the solutions of \cite{Bates:2003vx}.
It would be interesting to explore the attractor mechanism for our solutions and make connections with recent discussions on non-BPS attractors. The multi-centered solutions of Section \ref{BlowingBubbles} may realize non-BPS split attractors. It is interesting to note that in a recent discussion on non-supersymmetric split attractor flows the authors of \cite{Nampuri:2010um} also found that there are no bubble equations (or integrability conditions). This fits with our analysis in Section \ref{BlowingBubbles} and it will be very interesting to make this connection more precise.
Since our solutions are asymptotic to anti-de Sitter space one can do holographic analysis of the ``hair'' corresponding to our geometries and understand them as duals to states (or thermal ensembles) in the corresponding CFT. The solutions presented here have a warped and rotating $AdS_2$ region and while the $AdS_2/CFT_1$ correspondence is not understood in such detail as its higher dimensional analogs\footnote{For a recent discussion on holography for backgrounds with and $AdS_2$ factor see \cite{Sen:2011cn}.} there might be some effective approach similar to the one in \cite{Guica:2008mu}.
Alternatively, one might use a series of dualities and transform the solutions to the D1-D5-P IIB duality frame \cite{Bena:2008dw} and study the states in the D1-D5 CFT. One might then be able to study the stability of the solutions and make some connection with the recent discussion of Hawking radiation from non-supersymmetric solutions of the D1-D5 system \cite{Chowdhury:2007jx,Avery:2009tu,Avery:2010hs}.
One would also very much like to find explicit non-supersymmetric solutions that have a throat region that looks like the solutions discussed in this paper but are asymptotically flat at infinity. To achieve this, one will probably have to find a way of breaking the relationship between the background electromagnetic field and the K\"ahler form. To achieve this one will probably have to relax some of the simplifying assumptions of the floating brane Ansatz \cite{Bena:2009fi} and work with more general (and complicated) equations of motion. However, there are almost certainly even broader classes of non-supersymmetric solutions that are determined by linear systems of equations and thus such explicit non-BPS solutions may well be within reach.
\bigskip
\bigskip
\leftline{\bf Acknowledgements}
\smallskip
We would like to thank Chris Beem, Iosif Bena and Cl\'ement Ruef for useful conversations. NB would like to dedicate this work to the memory of his grandparents Kunka and Nedelcho. NB is grateful to the USC Department of Physics and Astronomy for warm hospitality while part of this work was completed. This work was supported in part by DOE grant DE-FG03-84ER-40168.
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{"url":"https:\/\/mathspace.co\/textbooks\/syllabuses\/Syllabus-410\/topics\/Topic-7275\/subtopics\/Subtopic-97168\/?activeTab=theory","text":"NZ Level 7 (NZC) Level 2 (NCEA)\nThe Trigonometric Ratios\nLesson\n\nRight-angled triangle\n\n## Trigonometric Ratios\n\nA ratio is a statement of a\u00a0mathematical relationship comparing two quantities, often represented as a fraction. If we consider an angle\u00a0$\\theta$\u03b8\u00a0in a right-angled triangle, we can construct various ratios to compare the lengths of the sides.\u00a0Special relationships that exist in right-angled triangles are called trigonometric ratios.\n\nThrough investigation we can see that there is a definite relationship between the angles in a right-angled triangle and the ratio of sides.\u00a0We can use these trigonometric ratios to find unknown angles and sides of a triangle.\n\nThere are 3 basic trigonometric ratios that relate sides and angles together. \u00a0They have the special names of tangent, sine and cosine. \u00a0The names of the relationships date back to 499AD, with ties to Latin and Sanskrit. \u00a0Actually the word sine is thought to be derived from a translation gone wrong! Regardless\u00a0the names for these relationships have stuck.\n\nWe often shorten the names tangent, sine and cosine to tan, sin and cos respectively.\n\nTrigonometric ratios\n\n$\\sin\\theta$sin\u03b8\u00a0=\u00a0$\\frac{Opposite}{Hypotenuse}$OppositeHypotenuse\u00a0\u00a0=\u00a0$\\frac{b}{c}$bc\n\n$\\cos\\theta$cos\u03b8\u00a0=\u00a0$\\frac{Adjacent}{Hypotenuse}$AdjacentHypotenuse\u00a0=\u00a0$\\frac{a}{c}$ac\n\n$\\tan\\theta$tan\u03b8\u00a0=\u00a0$\\frac{Opposite}{Adjacent}$OppositeAdjacent\u00a0=\u00a0$\\frac{b}{a}$ba\n\nThe mnemonic SOHCAHTOA can be useful to help remember the ratios.\n\n## Another relationship\n\nLet's have a look at just one more special relationship.\n\nIf we know the\u00a0sine and cosine ratios for a particular angle,\n\n$\\sin\\theta=\\frac{Opposite}{Hypotenuse}$sin\u03b8=OppositeHypotenuse\n\n$\\cos\\theta=\\frac{Adjacent}{Hypotenuse}$cos\u03b8=AdjacentHypotenuse\n\nThen we can construct a new relationship for $\\text{sine }\\div\\text{cosine }$sine \u00f7\u200bcosine\n\n $\\frac{\\sin\\theta}{\\cos\\theta}$sin\u03b8cos\u03b8\u200b $=$= $\\frac{\\left(\\frac{Opposite}{Hypotenuse}\\right)}{\\left(\\frac{Adjacent}{Hypotenuse}\\right)}$(OppositeHypotenuse\u200b)(AdjacentHypotenuse\u200b)\u200b $=$= $\\frac{Opposite}{Hypotenuse}\\times\\frac{Hypotenuse}{Adjacent}$OppositeHypotenuse\u200b\u00d7HypotenuseAdjacent\u200b $=$= $\\frac{Opposite}{Adjacent}$OppositeAdjacent\u200b $=$= $\\tan\\theta$tan\u03b8\n\nAlgebraically we have just shown that $\\tan\\theta=\\frac{\\sin\\theta}{\\cos\\theta}$tan\u03b8=sin\u03b8cos\u03b8\n\nThat is, the tangent ratio of an angle is the same as dividing its sine ratio by its cosine ratio.\n\n## Special triangles\n\nWe can create right-angled triangles of varying side lengths and angle combinations. There are, however, two\u00a0very special triangles that are referred to often in trigonometric studies. \u00a0These triangles are called exact value triangles, and they look like this.\n\n### Observations\n\n- Any right-angled triangle with a $45^\\circ$45\u00b0 angle will be isosceles. This means it will have two equal sides (here we have the simplest case where they measure $1$1 unit each). How can we obtain the hypotenuse?\n\n- The right-angled triangle with $30^\\circ$30\u00b0 and $60^\\circ$60\u00b0 angles can be obtained by cutting an equilateral triangle in half. See if you can start with an equilateral triangle of side length $2$2 to obtain the exact side lengths in the above triangle.\n\nFrom these 2 triangles we can construct trigonometric ratios\u00a0for the angles 30, 45 and 60 degrees.\n\nNow, an isosceles right-angled triangle may not have its sides measuring $1$1,$1$1 and $\\sqrt{2}$2, but however large it is, it will always have two $45^\\circ$45\u00b0 angles and\u00a0the ratios of the sides will always be the same as in the table. The same applies to the triangle with $60^\\circ$60\u00b0 and $30^\\circ$30\u00b0 angles.\n\nThese particular values are ones that we need to be familiar with for our continued study in high school trigonometry, as they will help us obtain exact rather than rounded values. \u00a0Personally, I find that\u00a0one of the best ways to remember them is through the use of the triangle diagrams.\n\nLet's have a look at these worked examples.\n\n##### Question 1\n\nFind the value of $\\theta$\u03b8 if $\\tan\\theta=\\sqrt{3}$tan\u03b8=3, given that $0^\\circ\\le\\theta\\le90^\\circ$0\u00b0\u03b890\u00b0.\n\n##### Question 2\n\nFind the value of $\\theta$\u03b8 if $\\sin\\theta=\\frac{\\sqrt{3}}{2}$sin\u03b8=32, given that $0^\\circ\\le\\theta\\le90^\\circ$0\u00b0\u03b890\u00b0.\n\n##### Question 3\n\nFind the value of $\\theta$\u03b8 if $\\cos\\theta=\\frac{8}{17}$cos\u03b8=817, given that $0^\\circ\\le\\theta\\le90^\\circ$0\u00b0\u03b890\u00b0.\n\n##### Question 4\n\nGiven that $\\tan\\theta=\\frac{1}{\\sqrt{3}}$tan\u03b8=13, find $\\sin\\theta$sin\u03b8 to two decimal places.\n\n1. First, find the value of $\\theta$\u03b8, given that $0^\\circ\\le\\theta\\le90^\\circ$0\u00b0\u03b890\u00b0.\n\n2. Hence, find the value of $\\sin\\theta$sin\u03b8.\n\n### Outcomes\n\n#### M7-4\n\nApply trigonometric relationships, including the sine and cosine rules, in two and three dimensions\n\n#### 91259\n\nApply trigonometric relationships in solving problems","date":"2021-09-26 10:39:20","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7987464666366577, \"perplexity\": 1204.1566682245495}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-39\/segments\/1631780057857.27\/warc\/CC-MAIN-20210926083818-20210926113818-00111.warc.gz\"}"} | null | null |
package main
import (
"context"
pb "golang-x/grpcx/hello"
"google.golang.org/grpc"
"log"
)
const address = "localhost:7000"
func main() {
conn, err := grpc.Dial(address, grpc.WithInsecure())
if err != nil {
log.Fatalf("failed to connect: %v", err)
}
defer conn.Close()
c := pb.NewGreeterClient(conn)
r, err := c.SayHello(context.Background(), &pb.HelloRequest{ParaFoo: "foo"})
if err != nil {
log.Fatalf("failed to say hello %v", err)
}
log.Printf("Greeting: %s", r.Message)
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 316 |
package com.takisoft.talkr.data;
import java.util.ArrayList;
import java.util.Collections;
import java.util.regex.Matcher;
import java.util.regex.Pattern;
import org.neo4j.graphdb.Node;
import org.neo4j.graphdb.Relationship;
/**
*
* @author Gericop
*/
public class Word {
public static enum WordType {
UNKNOWN(null),
NOUN(DetailConstants.TYPE_NOUN),
VERB(DetailConstants.TYPE_VERB),
ADVERB(DetailConstants.TYPE_ADVERB),
ADJECTIVE(DetailConstants.TYPE_ADJECT),
PREFIX(DetailConstants.TYPE_PREFIX),
GEO(DetailConstants.TYPE_GEO),
NUMERAL(DetailConstants.TYPE_NUMERAL),
EMOTION(DetailConstants.TYPE_EMOTION),
CONJUNCTION(DetailConstants.TYPE_CONJ),
PROPERTY(DetailConstants.TYPE_PROP);
private final String regex;
WordType(String regex) {
this.regex = regex;
}
public String getRegex() {
return regex;
}
}
String wordString;
ArrayList<Synonym> synonyms;
private ArrayList<Antonym> antonyms;
private ArrayList<Coverb> coverbs;
private ArrayList<Category> categories;
WordType type = WordType.UNKNOWN;
public Word(Node node, boolean getAllElements) {
if (getAllElements) {
new Word(node);
} else {
wordString = (String) node.getProperty(DetailConstants.PROP_KEY_OBJECT_ID);
type = WordType.valueOf((String) node.getProperty(DetailConstants.PROP_KEY_WORD_TYPE));
}
}
public Word(Node node) {
wordString = (String) node.getProperty(DetailConstants.PROP_KEY_OBJECT_ID);
type = WordType.valueOf((String) node.getProperty(DetailConstants.PROP_KEY_WORD_TYPE));
if (node.hasRelationship(DetailConstants.RelTypes.SYNONYM)) {
Iterable<Relationship> rels = node.getRelationships(DetailConstants.RelTypes.SYNONYM);
for (Relationship rel : rels) {
if (synonyms == null) {
synonyms = new ArrayList<>();
}
synonyms.add(new Synonym(new Word(rel.getOtherNode(node), false).getWord()));
}
}
if (node.hasRelationship(DetailConstants.RelTypes.ANTONYM)) {
Iterable<Relationship> rels = node.getRelationships(DetailConstants.RelTypes.ANTONYM);
for (Relationship rel : rels) {
if (antonyms == null) {
antonyms = new ArrayList<>();
}
antonyms.add(new Antonym(new Word(rel.getOtherNode(node), false).getWord()));
}
}
}
private Word() {
this(null, WordType.UNKNOWN);
}
private Word(String wordString) {
this(wordString, WordType.UNKNOWN);
}
private Word(String wordString, WordType type) {
this.wordString = wordString;
this.type = type;
}
public static ArrayList<Word> getWords(PageData data) {
ArrayList<Word> words = new ArrayList<>();
ArrayList<RegionHolder> regions = new ArrayList<>();
Matcher matcher = null;
Pattern pattern;
for (WordType wordType : WordType.values()) {
if (wordType == WordType.UNKNOWN) {
continue;
}
pattern = Pattern.compile(wordType.getRegex(), Pattern.CASE_INSENSITIVE | Pattern.UNICODE_CASE | Pattern.MULTILINE);
if (matcher == null) {
matcher = pattern.matcher(data.getText());
} else {
matcher.usePattern(pattern);
matcher.reset();
}
if (matcher.find()) {
regions.add(new RegionHolder(wordType, matcher.start()));
}
}
regions.add(new RegionHolder(WordType.UNKNOWN, matcher.regionEnd()));
Collections.sort(regions);
for (int i = 0; i < regions.size() - 1; i++) {
RegionHolder currentRegion = regions.get(i);
Word word = new Word(data.getTitle(), currentRegion.type);
Matcher region = matcher.region(currentRegion.start, regions.get(i + 1).start);
//System.out.println(currentRegion.type.name() + " | " + currentRegion.start + " - " + regions.get(i + 1).start);
ArrayList<Synonym> synonyms = searchSynonyms(region);
word.setSynonyms(synonyms);
// reset does not work properly
region = matcher.region(currentRegion.start, regions.get(i + 1).start);
ArrayList<Antonym> antonym = searchAntonyms(region);
word.setAntonyms(antonym);
if (word.getType() == WordType.NOUN || regions.size() == 2) {
word.setCategories(Category.getCategoriesForWord(data.getText()));
}
if (word.getType() == WordType.VERB) {
ArrayList<Coverb> coverbs = searchCoverbs(word, data.getText());
word.setCoverbs(coverbs);
}
words.add(word);
}
return words;
}
private static ArrayList<Coverb> searchCoverbs(Word word, String text) {
ArrayList<Coverb> coverbs = new ArrayList<>();
Pattern pattern = Pattern.compile(DetailConstants.MISC_COVERB, Pattern.CASE_INSENSITIVE | Pattern.UNICODE_CASE | Pattern.DOTALL);
Matcher matcher = pattern.matcher(text);
if (matcher.find()) {
pattern = Pattern.compile(DetailConstants.MISC_COVERB_WORD, Pattern.CASE_INSENSITIVE | Pattern.UNICODE_CASE | Pattern.MULTILINE);
matcher = pattern.matcher(matcher.group());
while (matcher.find()) {
coverbs.add(new Coverb(matcher.group() + word.getWord()));
}
}
return coverbs;
}
private static ArrayList<Synonym> searchSynonyms(Matcher region) {
ArrayList<Synonym> synonyms = new ArrayList<>();
Pattern pattern = Pattern.compile(DetailConstants.INTYPE_SYN, Pattern.CASE_INSENSITIVE | Pattern.UNICODE_CASE | Pattern.MULTILINE);
region.usePattern(pattern);
if (region.find()) {
//System.out.println("Found: " + DetailConstants.INTYPE_SYN);
int start = region.start();
int end = region.regionEnd();
pattern = Pattern.compile(DetailConstants.P_START, Pattern.CASE_INSENSITIVE | Pattern.UNICODE_CASE | Pattern.MULTILINE);
region.usePattern(pattern);
if (region.find()) {
end = region.start();
//System.out.println("Found: " + DetailConstants.P_START + " | end: " + end);
}
// get the words
Matcher regionSyn = region.region(start, end);
pattern = Pattern.compile(DetailConstants.MISC_WORDS, Pattern.CASE_INSENSITIVE | Pattern.UNICODE_CASE | Pattern.MULTILINE);
regionSyn.usePattern(pattern);
while (regionSyn.find()) {
String raw = regionSyn.group();
synonyms.add(new Synonym(raw));
//synonyms.add(new Synonym(raw.substring(raw.indexOf("[[") + 2, raw.indexOf("]]"))));
//String word = raw.substring(raw.indexOf("[[")+2, raw.indexOf("]]"));
//System.out.println(word);
}
}
return synonyms;
}
private static ArrayList<Antonym> searchAntonyms(Matcher region) {
ArrayList<Antonym> antonyms = new ArrayList<>();
Pattern pattern = Pattern.compile(DetailConstants.INTYPE_ANT, Pattern.CASE_INSENSITIVE | Pattern.UNICODE_CASE | Pattern.MULTILINE);
region.usePattern(pattern);
if (region.find()) {
//System.out.println("Found: " + DetailConstants.INTYPE_SYN);
int start = region.start();
int end = region.regionEnd();
pattern = Pattern.compile(DetailConstants.P_START, Pattern.CASE_INSENSITIVE | Pattern.UNICODE_CASE | Pattern.MULTILINE);
region.usePattern(pattern);
if (region.find()) {
end = region.start();
//System.out.println("Found: " + DetailConstants.P_START + " | end: " + end);
}
// get the words
Matcher regionSyn = region.region(start, end);
pattern = Pattern.compile(DetailConstants.MISC_WORDS, Pattern.CASE_INSENSITIVE | Pattern.UNICODE_CASE | Pattern.MULTILINE);
regionSyn.usePattern(pattern);
while (regionSyn.find()) {
String raw = regionSyn.group();
antonyms.add(new Antonym(raw));
//antonyms.add(new Antonym(raw.substring(raw.indexOf("[[") + 2, raw.indexOf("]]"))));
//String word = raw.substring(raw.indexOf("[[")+2, raw.indexOf("]]"));
//System.out.println(word);
}
}
return antonyms;
}
public String getWord() {
return wordString;
}
private void setWord(String wordString) {
this.wordString = wordString;
}
public WordType getType() {
return type;
}
private void setType(WordType type) {
this.type = type;
}
public ArrayList<Synonym> getSynonyms() {
return synonyms;
}
private void setSynonyms(ArrayList<Synonym> synonyms) {
this.synonyms = synonyms;
}
public ArrayList<Antonym> getAntonyms() {
return antonyms;
}
private void setAntonyms(ArrayList<Antonym> antonyms) {
this.antonyms = antonyms;
}
public ArrayList<Coverb> getCoverbs() {
return coverbs;
}
private void setCoverbs(ArrayList<Coverb> coverbs) {
this.coverbs = coverbs;
}
public ArrayList<Category> getCategories() {
return categories;
}
private void setCategories(ArrayList<Category> categories) {
this.categories = categories;
}
static class RegionHolder implements Comparable<RegionHolder> {
WordType type;
int start;
public RegionHolder(WordType type, int start) {
this.type = type;
this.start = start;
}
@Override
public int compareTo(RegionHolder o) {
return this.start - o.start;
}
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 2,388 |
\section{Introduction}
The problem of establishing sufficient conditions for the complementation of the subspace of compact linear operators $\mathcal{L}_{K}(E;F)$ in the space $\mathcal{L}(E;F)$ of all continuous linear operators, has been widely studied by many authors. For example, see Kalton \cite{KALTON}, Emmanuelle \cite{EM}, John \cite{KA}, Bator and Lewis \cite{LEW} and Ghenciu \cite{IOANA}, among others.
Emmanuele \cite{EM} and John \cite{KA} showed that if $c_{0}$ embeds in $\mathcal{L}_{K}(E;F)$ then $\mathcal{L}_{K}(E;F)$ is not complemented in $\mathcal{L}(E;F)$ for every $E$ and $F$ infinite dimensional Banach spaces.
John \cite{KA} proved that if $E$ and $F$ are arbitrary Banach spaces and $T: E\rightarrow F$ is a non compact
operator which admits a factorization $T = A\circ B$ through a Banach space
$G$ with an unconditional basis, then the subspace $\mathcal{L}_{K}(E;F)$
of compact operators contains an isomorphic copy of $c_{0}$ and thus $\mathcal{L}_{K}(E;F)$ is not
complemented in $\mathcal{L}(E;F)$.
John \cite{KA} also proved that if $E$ and $F$ are infinite dimensional Banach spaces, such that each
non compact operator $T \in \mathcal{L}(E;F)$ factors through a Banach space $G$ with an unconditional basis, then the following conditions are equivalent:
\begin{enumerate}
\item $\mathcal{L}_{K} (E; F)=\mathcal{L} (E;F)$.
\item $\mathcal{L} (E; F)$ contains no copy of $\ell_{\infty}$.
\item $\mathcal{L}_{K} (E; F)$ contains no copy of $c_{0}$.
\item $\mathcal{L}_{K} (E; F)$ is complemented in $\mathcal{L} (E; F)$.
\end{enumerate}
Ghenciu \cite{IOANA} obtained the following result:
Let $E$ and $F$ be Banach spaces, and let $G$ be a Banach space with an unconditional basis $(g_{n})$ and coordinate functionals $(g^{\prime}_{n})$.
\begin{enumerate}
\item [(a)] If there exist operators $R\in\mathcal{L}(G; F)$ and $S\in\mathcal{L}(E; G)$ such that $(R(g_{n}))$ is a seminormalized basic sequence
in $F$ and $(S^{\prime}(g^{\prime}_{n}))$ is not relatively compact in $E^{\prime}$, then $\mathcal{L}_{K}(E; F)$ is not complemented in
$\mathcal{L}(E; F)$.
\item [(b)] If there exist operators $R\in\mathcal{L}(G; F)$ and $S\in\mathcal{L}(E; G)$ such that $(R(g_{n}))$ is a seminormalized basic sequence
in $F$ and $(S^{\prime}(g^{\prime}_{n}))$ is not relatively weakly compact in $E^{\prime}$, then $\mathcal{L}_{wK}(E; F)$ is not complemented in
$\mathcal{L}(E; F)$.
\end{enumerate}
This result generalizes results of several authors \cite{EMA},\cite{LEW}, \cite{FEDER}.
In this paper, we obtain polynomial versions of the preceding results.
This paper is based on part of the author's doctoral thesis at the Universidade Estadual de Campinas. This research has been supported by CAPES and CNPq.
The author is grateful to his thesis advisor, Professor Jorge Mujica, for his advice and help.
\section{Preliminaries}
Let $E$ and $F$ denote Banach spaces over $ \mathbb{K}$, where $ \mathbb{K}$ is $ \mathbb{R}$ or $\mathbb{C}$. Let $E^{\prime}$
denote the dual of $E$. Denote by $ \mathcal{L}(E;F)$, $\mathcal{L}_{K}(E;F)$ and $\mathcal{L}_{wK}(E;F)$, respectively, the spaces of all bounded, all compact and all weakly compact linear operators of $E$ into $F$. Let $\mathcal{P}(^{n}E; F)$ denote the Banach space of all continuous $n$-homogeneous polynomials from $E$ into $F$. We omit $F$ when $F = \mathbb{K}$.
Let $\mathcal{P}_{w}(^{n}E; F)$ denote the subspace of all $P\in\mathcal{P}(^{n}E; F)$
which are weakly continuous on bounded sets, that is
the restriction $P|_{B}: B \rightarrow F $ is continuous for each bounded set $B\subset E$,
when $B $ and $F$ are endowed with the weak topology and the norm topology,
respectively. Let $\mathcal{P}_{K}(^{n}E; F)$ denote the
subspace of all $P\in \mathcal{P}(^{n}E; F)$ which map bounded sets onto relatively compact sets.
Let $\mathcal{P}_{wK}(^{n}E; F)$ denote the
subspace of all $P\in \mathcal{P}(^{n}E; F)$ which map bounded sets onto relatively weakly compact sets.
We always have the inclusions
$$ P_{w}(^{n}E; F)\subset \mathcal{P}_{K}(^{n}E; F)\subset\mathcal{P}_{wK}(^{n}E; F)\subset \mathcal{P}(^{n}E; F).$$
We refer to \cite{SEAN} or \cite{LMUJICA} for background information on the theory of polynomials on Banach spaces.
$E$ is isomorphic to a complemented subspace of $F$ if and only if there are $A \in
\mathcal{L}(E; F)$ and $B\in \mathcal{L}(F;E)$ such that $B\circ A = I$. $E$ is said to have an unconditional finite dimensional expansion of the identity if there is a sequence of bounded linear operators $A_{n}:E\rightarrow E$ of finite rank, such that for $x\in E$
$$\sum_{n=1}^{\infty}A_{n}(x)=x$$
unconditionally.
We will say that the series $\displaystyle\sum_{n=1}^{\infty}x_{n}$ of elements of $X$ is weakly unconditionally Cauchy if $\displaystyle\sum_{n=1}^{\infty}|x^{\prime}(x_{n})|<\infty$ for all $x^{\prime}\in X^{\prime}$ or, equivalently if
$$\sup\bigg\{\bigg\|\sum_{n\in F}x_{n}\bigg\| ; F\subset \mathbb{N}, F finite\bigg\}<\infty.$$
A sequence $(x_{n})\subset E$ is a semi-normalized basic sequence if $(x_{n})$ is a Schauder basis for the closed subspace $M =
\overline{[x_{n} : n\in \mathbb{N}]}$, and moreover there are constant $a$ and $b$ such that $0< a<\|x_{n}\|<b$ for all $n\in\mathbb{N}$.
We denote by $(e_{n})$ the canonical basis of $c_{0}$. If $\Sigma$ is an algebra of subsets of a set $\Omega$, then a finitely additive vector
measure $\mu:\Sigma\rightarrow E$ is said to be strongly additive if the series $\displaystyle\sum_{n=1}^{\infty}\mu(A_{n})$ converges in norm for each
sequence $(A_{n})$ of pairwise disjoint members of $\Sigma$.
The Diestel-Faires theorem (see \cite[p.20, Theorem 2]{DIESTEL}) asserts that if $\Sigma$ is a $\sigma-$ algebra and $\mu:\Sigma\rightarrow E$
is not strongly additive, then $E$ contains an isomorphic copy of $\ell_{\infty}$.
\section{The main results}
The proof of our main results rests mainly on the following theorem of Ghenciu \cite{IOANA}, which generalizes results of several authors
\cite{EMA},\cite{LEW}, \cite{FEDER}.
\bigskip
\begin{theorem} \label{thm:(Teorema 10)}(\cite[Theorem 1]{IOANA})
Let $E$ and $F$ be Banach spaces, and let $G$ be a Banach space with an unconditional basis $(g_{n})$ and coordinate functionals $(g^{\prime}_{n})$.
\begin{enumerate}
\item [(a)] If there exist operators $R\in\mathcal{L}(G; F)$ and $S\in\mathcal{L}(E; G)$ such that $(R(g_{n}))$ is a seminormalized basic sequence
in $F$ and $(S^{\prime}(g^{\prime}_{n}))$ is not relatively compact in $E^{\prime}$, then $\mathcal{L}_{K}(E; F)$ is not complemented in
$\mathcal{L}(E; F)$.
\item [(b)] If there exist operators $R\in\mathcal{L}(G; F)$ and $S\in\mathcal{L}(E; G)$ such that $(R(g_{n}))$ is a seminormalized basic sequence
in $F$ and $(S^{\prime}(g^{\prime}_{n}))$ is not relatively weakly compact in $E^{\prime}$, then $\mathcal{L}_{wK}(E; F)$ is not complemented in
$\mathcal{L}(E; F)$.
\end{enumerate}
\end{theorem}
Emmanuele \cite{EM} and John \cite{KA} independently proved that if $\mathcal{L}_{K}(E; F)$ contains a copy of $c_{0}$, then $\mathcal{L}_{K}(E; F)$ is not complemented in $\mathcal{L}(E; F)$ (see \cite[Theorem 2]{EM} and \cite[Theorem 1]{KA}). They also proved that if there exists a noncompact operator
$T\in \mathcal{L}(E; F)$ which factors through a Banach space with an unconditional basis, then $\mathcal{L}_{K}(E; F)$ contains a copy of $c_{0}$.
Clearly Theorem \ref{thm:(Teorema 10)} $(a)$ follows from these results.
\begin{theorem} \label{thm:(Teorema 11)}
Let $E$ and $F$ be Banach spaces, and let $G$ be a Banach space with an unconditional basis $(g_{n})$ and coordinate functionals $(g^{\prime}_{n})$.
\begin{enumerate}
\item [(a)] If there exist operators $R\in\mathcal{L}(G; F)$ and $S\in\mathcal{L}(E; G)$ such that $(R(g_{n}))$ is a seminormalized basic sequence
in $F$ and $(S^{\prime}(g^{\prime}_{n}))$ is not relatively compact in $E^{\prime}$, then $\mathcal{P}_{K}(^{n}E; F)$ is not complemented in
$\mathcal{P}(^{n}E; F)$ for every $n\in\mathbb{N}$.
\item [(b)] If there exist operators $R\in\mathcal{L}(G; F)$ and $S\in\mathcal{L}(E; G)$ such that $(R(g_{n}))$ is a seminormalized basic sequence
in $F$ and $(S^{\prime}(g^{\prime}_{n}))$ is not relatively weakly compact in $E^{\prime}$, then $\mathcal{P}_{wK}(^{n}E; F)$ is not complemented in
$\mathcal{P}(^{n}E; F)$ for every $n\in\mathbb{N}$.
\end{enumerate}
\end{theorem}
\begin{proof}
$(a)$ The case $n=1$ follows from Theorem \ref{thm:(Teorema 10)} $(a)$. If $n\in\mathbb{N}$, then by a result of Ryan \cite{RYAN} there exists an isomorphism
$$P\in\mathcal{P}(^{n}E; F)\rightarrow T_{P}\in\mathcal{L}(\hat{\otimes}_{n,s,\pi}E; F).$$
Furthermore $P\in \mathcal{P}_{K}(^{n}E; F)$ if and only if $T_{P}\in\mathcal{L}_{K}(\hat{\otimes}_{n,s,\pi}E; F)$.
Suppose that $\mathcal{P}_{K}(^{n}E; F)$ is complemented in $\mathcal{P}(^{n}E; F)$. Then $\mathcal{L}_{K}(\hat{\otimes}_{n,s,\pi}E; F)$ is complemented
in $\mathcal{L}(\hat{\otimes}_{n,s,\pi}E; F)$. Let $\pi:\mathcal{L}(\hat{\otimes}_{n,s,\pi}E; F)\rightarrow \mathcal{L}_{K}(\hat{\otimes}_{n,s,\pi}E; F)$
be a projection. By a result of Blasco \cite[Theorem 3]{BLASCO} $E$ is isomorphic to a complemented subspace of $\hat{\otimes}_{n,s,\pi}E$. Hence there exist operators $A\in\mathcal{L}(E;\hat{\otimes}_{n,s,\pi}E)$ and $B\in\mathcal{L}(\hat{\otimes}_{n,s,\pi}E; E)$ such that $B\circ A=I$. Consider the operator
$$\rho: T\in\mathcal{L}(E;F)\rightarrow \pi(T\circ B)\circ A\in \mathcal{L}_{K}(E; F).$$
If $T\in\mathcal{L}_{K}(E; F)$, then $T\circ B\in\mathcal{L}_{K}(\hat{\otimes}_{n,s,\pi}E; F)$ and therefore $\pi(T\circ B)\circ A=T\circ B\circ A=T$.
Thus $\rho: \mathcal{L}(E;F)\rightarrow \mathcal{L}_{K}(E; F)$ is a projection, contradicting the case $n=1$.
$(b)$ The proof of $(b)$ is almost identical to the proof of $(a)$, but using that $P\in \mathcal{P}_{wK}(^{n}E; F)$ if and only if $T_{P}\in \mathcal{L}_{wK}(\hat{\otimes}_{n,s,\pi}E; F)$, a result which is also due to Ryan \cite{RYAN}.
\end{proof}
\begin{theorem} \label{thm:(Teorema 12)}
Let $E$ and $F$ be Banach spaces, and let $G$ be a Banach space with an unconditional basis $(g_{n})$ and coordinate functionals $(g^{\prime}_{n})$.
If there exist operators $R\in \mathcal{L}(G; F)$ and $S\in\mathcal{L}(E; G)$ such that $(R(g_{n}))$ is a seminormalized basic sequence
in $F$ and $(S^{\prime}(g^{\prime}_{n}))$ is not relatively compact in $E^{\prime}$, then $\mathcal{P}_{w}(^{n}E; F)$ is not complemented in
$\mathcal{P}(^{n}E; F)$ for every $n\in \mathbb{N}$.
\end{theorem}
\begin{proof}
The method of proof of Theorem \ref{thm:(Teorema 11)} does not work here, since it is not true in general that $P\in\mathcal{P}_{w}(^{n}E; F)$ if and only if
$T_{P}\in \mathcal{L}_{w}(\hat{\otimes}_{n,s,\pi}E; F)$. Thus we have to proceed differently.
It follows from results of Aron and Prolla \cite{ARON} and Aron, Hervés and Valdivia \cite{VALDIVIA} that $\mathcal{P}_{w}(^{n}E; F)\subset \mathcal{P}_{K}(^{n}E; F)$ for every $n\in \mathbb{N}$, and it is easy to see that $\mathcal{P}_{w}(^{n}E; F)=\mathcal{P}_{K}(^{n}E; F)$ when $n=1$.
Thus the case $n=1$ follows from Theorem \ref{thm:(Teorema 10)} $(a)$. To prove the theorem by induction on $n$ it suffices to prove that
if $\mathcal{P}_{w}(^{n+1}E; F)$ is complemented in $\mathcal{P}(^{n+1}E; F)$, then $\mathcal{P}_{w}(^{n}E; F)$ is complemented in
$\mathcal{P}(^{n}E; F)$. Aron and Schottenloher \cite[Proposition 5.3]{AR} proved that $\mathcal{P}(^{n}E; F)$ is isomorphic to a complemented subspace of
$\mathcal{P}(^{n+1}E; F)$ when $F$ is the scalar field, but their proof works equally well when $F$ is an arbitrary Banach space. Thus there
exist operators $A\in\mathcal{L}(\mathcal{P}(^{n}E; F); \mathcal{P}(^{n+1}E; F))$ and $B\in\mathcal{L}(\mathcal{P}(^{n+1}E; F);\mathcal{P}(^{n}E; F))$
such that $B\circ A=I$. The operator $A$ is of the form
$$A(P)(x)=\varphi_{0}(x)P(x)$$
for every $P\in\mathcal{P}(^{n}E; F)$ and $x\in E$, where $\varphi_{0}\in E^{\prime}$ verifies that $\|\varphi_{0}\|=1=\varphi_{0}(x_{0})$, where
$x_{0}\in E$ and $\|x_{0}\|=1$. It is clear that if $P\in \mathcal{P}_{w}(^{n}E; F)$, then $A(P)\in \mathcal{P}_{w}(^{n+1}E; F)$.
Let us assume that $\mathcal{P}_{w}(^{n+1}E; F)$ is complemented in $\mathcal{P}(^{n+1}E; F)$, and let $\pi: \mathcal{P}(^{n+1}E; F)\rightarrow \mathcal{P}_{w}(^{n+1}E; F)$ be a projection. Consider the operator
$$\rho=B\circ \pi\circ A: \mathcal{P}(^{n}E; F)\rightarrow \mathcal{P}_{w}(^{n}E; F).$$
If $P\in \mathcal{P}_{w}(^{n}E; F)$, then $A(P)\in \mathcal{P}_{w}(^{n+1}E; F)$, and therefore
$$\rho(P)=B\circ \pi\circ A(P)=B\circ A(P)=P.$$
Thus $\rho:\mathcal{P}(^{n}E; F)\rightarrow \mathcal{P}_{w}(^{n}E; F)$ is a projection, and therefore $\mathcal{P}_{w}(^{n}E; F)$ is complemented
in $\mathcal{P}(^{n}E; F)$. This completes the proof.
\end{proof}
Ghenciu \cite{IOANA} derived as corollaries of Theorem \ref{thm:(Teorema 10)} results of several authors \cite{EMA}, \cite{LEW}, \cite{FEDER}, \cite{KALTON} and \cite{KA}. We now apply Theorems \ref{thm:(Teorema 11)} and \ref{thm:(Teorema 12)} to obtain polynomials versions of those corollaries.
\begin{corollary}\label{thm:(Teorema 13)}
If $F$ contains a copy of $c_{0}$ and $E^{\prime}$ contains a weak-star null sequence which is not weakly null, then $\mathcal{P}_{wK}(^{n}E; F)$ is
not complemented in $\mathcal{P}(^{n}E; F)$ for every $n\in \mathbb{N}$.
\end{corollary}
\begin{corollary}\label{thm:(Teorema 14)}
If $F$ contains a copy of $c_{0}$ and $E$ contains a complemented copy of $c_{0}$, then $\mathcal{P}_{wK}(^{n}E; F)$ is
not complemented in $\mathcal{P}(^{n}E; F)$ for every $n\in \mathbb{N}$.
\end{corollary}
\begin{corollary}\label{thm:(Teorema 15)}
If $F$ contains a copy of $\ell_{1}$ and $\mathcal{L}(E; \ell_{1})\neq \mathcal{L}_{K}(E; \ell_{1})$, then $\mathcal{P}_{wK}(^{n}E; F)$ is
not complemented in $\mathcal{P}(^{n}E; F)$ for every $n\in\mathbb{N}$.
\end{corollary}
When $n=1$ Corollaries \ref{thm:(Teorema 13)}, \ref{thm:(Teorema 14)} and \ref{thm:(Teorema 15)} correspond to \cite[Corollaries 2,3 and 5]{IOANA}.
Ghenciu derived those corollaries by observing that $E$ and $F$ satisfy the hypothesis of Theorem \ref{thm:(Teorema 10)} $(b)$. Since the hypothesis
of Theorem \ref{thm:(Teorema 10)} $(b)$ coincide with the hypothesis of Theorem \ref{thm:(Teorema 11)} $(b)$, we see that Corollaries \ref{thm:(Teorema 13)}, \ref{thm:(Teorema 14)} and \ref{thm:(Teorema 15)} follow from Theorem \ref{thm:(Teorema 11)} $(b)$.
\begin{corollary}\label{cor 33}
If $F$ contains a copy of $c_{0}$ and $E$ is infinite dimensional, then:
\begin{enumerate}
\item [(a)] $\mathcal{P}_{K}(^{n}E; F)$ is not complemented in
$\mathcal{P}(^{n}E; F)$ for every $n\in \mathbb{N}$.
\item [(b)] $\mathcal{P}_{w}(^{n}E; F)$ is not complemented in
$\mathcal{P}(^{n}E; F)$ for every $n\in \mathbb{N}$.
\end{enumerate}
\end{corollary}
\begin{corollary}\label{cor 34}
If $E$ contains a complemented copy of $\ell_{1}$ and $F$ is infinite dimensional, then:
\begin{enumerate}
\item [(a)] $\mathcal{P}_{K}(^{n}E; F)$ is not complemented in
$\mathcal{P}(^{n}E; F)$ for every $n\in \mathbb{N}$.
\item [(b)] $\mathcal{P}_{w}(^{n}E; F)$ is not complemented in
$\mathcal{P}(^{n}E; F)$ for every $n\in \mathbb{N}$.
\end{enumerate}
\end{corollary}
When $n=1$ Corollaries \ref{cor 33} and \ref{cor 34} correspond to \cite[Corollaries 4 and 6]{IOANA}.
Ghenciu derived those corollaries by observing that $E$ and $F$ satisfy the hypothesis of Theorem \ref{thm:(Teorema 10)} $(a)$. Since the hypothesis
of Theorem \ref{thm:(Teorema 10)} $(a)$ coincide with the hypothesis of Theorems \ref{thm:(Teorema 11)} $(a)$ and \ref{thm:(Teorema 12)}, we see that Corollaries \ref{cor 33} and \ref{cor 34} follow from Theorems \ref{thm:(Teorema 11)} $(a)$ and \ref{thm:(Teorema 12)}.
\begin{corollary}\label{cor 35}
If $E$ contains a copy of $\ell_{1}$ and $F$ contains a copy of $\ell_{p}$, with $2\leq p<\infty$, then:
\begin{enumerate}
\item [(a)] $\mathcal{P}_{K}(^{n}E; F)$ is not complemented in
$\mathcal{P}(^{n}E; F)$ for every $n\in \mathbb{N}$.
\item [(b)] $\mathcal{P}_{w}(^{n}E; F)$ is not complemented in
$\mathcal{P}(^{n}E; F)$ for every $n\in \mathbb{N}$.
\end{enumerate}
\end{corollary}
\begin{proof}
We follow an argument of Emmanuele \cite[p. 334 ]{EM}. By a result of Pelczynski \cite{PELC}, if $E$ contains a copy of $\ell_{1}$,
then $E$ has a quotient isomorphic to $\ell_{2}$ (see also the proof of \cite{ARONLIBRO}). Let $S:E\rightarrow \ell_{2}$ be the quotient
mapping, and let $R:\ell_{2}\hookrightarrow \ell_{p}\subset F$ be the natural inclusion.
Since $S^{\prime}:\ell_{2}\rightarrow E^{\prime}$ is an embedding, the hypothesis of Theorems \ref{thm:(Teorema 11)} $(a)$ and \ref{thm:(Teorema 12)}
are clearly satisfied.
\end{proof}
\begin{proposition}\label{cor 366}
Let $E$ and $F$ be infinite dimensional Banach spaces. If $\mathcal{P}_{K} (^{n}E; F)$ contains a copy of $c_{0}$, then $\mathcal{P}_{K} (^{n}E; F)$ is not complemented in $\mathcal{P} (^{n}E; F)$.
\end{proposition}
\begin{proof}
By an aforementioned result of Ryan \cite{RYAN} we have that $P\in \mathcal{P}_{K}(^{n}E; F)$ if and only if $T_{P}\in\mathcal{L}_{K}(\hat{\otimes}_{n,s,\pi}E; F)$. Thus the result follows from \cite[Theorem 2]{EM} or \cite[Theorem 1]{KA}.
\end{proof}
The next proposition is a polynomial version of \cite[Theorem 2]{EM} and \cite[Theorem 1]{KA}. The proof is based in ideas of \cite[Corollary 11 ]{LEWIS}.
\begin{proposition}\label{cor 36}
Let $E$ be an infinite dimensional Banach space and $n>1$. If $\mathcal{P}_{w} (^{n}E; F)$ contains a copy of $c_{0}$, then $\mathcal{P}_{w} (^{n}E; F)$ is not complemented in $\mathcal{P} (^{n}E; F)$.
\end{proposition}
\begin{proof}
By Corollary \ref{cor 33} and \cite[Lemma 5 ]{GONZALEZ M} we may suppose without loss of generality that $F$ contains no copy of $c_{0}$ and $E$ contains no complemented copy of $\ell_{1}$. By \cite[Theorem 3 ]{GONZALEZ M} $\mathcal{P}_{w} (^{n}E; F)$ contains no copy of $\ell_{\infty}$. Let $(P_{i})$ be a copy of the unit vector basis $(e_{i})$ of $c_{0}$ in $\mathcal{P}_{w} (^{n}E; F)$. Then $$\sup\bigg\{\bigg\|\sum_{i\in F}e_{i}\bigg\| ; F\subset\mathbb{N}, F finite\bigg\}=1.$$ By a result of Bessaga and Pelczynski \cite{BES} (see also \cite[p.44, Theorem 6]{DIESTELL}) the series $\displaystyle\sum_{i=1}^{\infty} e_{i}$ is weakly unconditionally Cauchy in $c_{0}$. This implies that the series
$\displaystyle\sum_{i=1}^{\infty} P_{i}$ is weakly unconditionally Cauchy in $\mathcal{P}_{w} (^{n}E; F)$. For every $\varphi\in F^{\prime}$ and $x\in E$ we consider the continuous linear functional $$\psi: P\in\mathcal{P}_{w} (^{n}E; F)\rightarrow \varphi(P(x))\in \mathbb{C}.$$ Since the series
$\displaystyle\sum_{i=1}^{\infty} P_{i}$ is weakly unconditionally Cauchy in $\mathcal{P}_{w} (^{n}E; F)$,
$\displaystyle\sum_{i=1}^{\infty}|\psi( P_{i})|=\displaystyle\sum_{i=1}^{\infty}|\varphi( P_{i}(x))|<\infty$ for every $\varphi\in F^{\prime}$ and $x\in E$. This shows that
$\displaystyle\sum_{i=1}^{\infty} P_{i}(x)$ is weakly unconditionally Cauchy in $F$ for each $x\in E$. Finally since $F$ contains no copy of $c_{0}$, an
application of \cite[p.45, Theorem 8 ]{DIESTELL} shows that $\displaystyle\sum_{i=1}^{\infty} P_{i}(x)$ converges unconditionally in $F$ for each $x\in E$. Let $\mu: \wp(\mathbb{N})\rightarrow \mathcal{P} (^{n}E; F)$ be the finitely additive vector measure defined by $\mu(A)(x)=\displaystyle\sum_{i\in A}P_{i}(x)$ for each $x\in E$ and $A\subset \mathbb{N}$.
Suppose there is a projection $\pi:\mathcal{P}(^{n}E; F)\rightarrow \mathcal{P}_{w} (^{n}E; F)$. Then $\pi(P_{i})=P_{i}$ for each $i\in \mathbb{N}$.
If the sequence $(\|P_{i}\|)$ does not converge to zero, then there is $\epsilon>0$ and a subsequence $(i_{k})$ of $\mathbb{N}$, such that $\|P_{i_{k}}\|>\epsilon$ for each $k\in \mathbb{N}$. But this implies that the measure $\pi\circ\mu:\wp(\mathbb{N})\rightarrow \mathcal{P}_{w}(^{n}E; F)$ is not strongly additive. Then the Diestel-Faires Theorem would imply that $\mathcal{P}_{w} (^{n}E; F)$ contains a copy of $\ell_{\infty}$. Therefore $\|P_{i}\|\rightarrow 0$, but this is absurd too, because $(P_{i})$ is a copy of $(e_{i})$. This complete the proof.
\end{proof}
The following theorem is a polynomial version of \cite[Theorem 2 ]{KA}.
\begin{theorem} \label{thm:(Teorema 17)}
Let $E$ and $F$ be Banach spaces and $P\in \mathcal{P}(^{n}E; F)$ such that $P\notin \mathcal{P}_{w}(^{n}E; F)$. Suposse that $P$ admits a factorization $P=Q\circ T$ through a Banach space $G$ with an unconditional finite dimensional expansion of the identity, where $T\in \mathcal{L}(E;G)$ and $Q\in \mathcal{P}(^{n}G;F)$. Then $\mathcal{P}_{w} (^{n}E;F)$ contains a copy of $c_{0}$ and thus $\mathcal{P}_{w} (^{n}E;F)$ is not complemented in
$\mathcal{P}(^{n}E;F)$.
\end{theorem}
\begin{proof}
The case $n=1$ follows from \cite[Theorem 2 ]{KA}.
Case $n> 1$: Since $G$ has an unconditional finite dimensional expansion of the identity, by \cite[Lemma 6 ]{GONZALEZ M} there is a sequence $(Q_{i})\subset \mathcal{P}_{w} (^{n}G; F)$ so that $Q(z)=\displaystyle\sum_{i=1}^{\infty}Q_{i}(z)$ unconditionally for each $z\in G$, hence $P(x)=\displaystyle\sum_{i=1}^{\infty}Q_{i}(T(x))$ unconditionally for each $x\in E$. Since $Q_{i}\in \mathcal{P}_{w} (^{n}G; F)$ for every $i\in \mathbb{N}$, it follows that $Q_{i}\circ T\in \mathcal{P}_{w} (^{n}E; F)$ for every $i\in \mathbb{N}$. By the uniform boundedness principle, we have $$\sup\bigg\{\bigg\|\sum_{i\in F}Q_{i}\circ T\bigg\| ; F\subset\mathbb{N}, F finite\bigg\}<\infty.$$
Again by \cite[p.44, Theorem 6]{DIESTELL} the series $\displaystyle\sum_{i=1}^{\infty}Q_{i}\circ T$ é weakly unconditionally Cauchy in $\mathcal{P}_{w} (^{n}E; F)$.
Since $P\notin \mathcal{P}_{w} (^{n}E; F)$, an application of \cite[p.45, Theorem 8]{DIESTELL} shows that $\mathcal{P}_{w} (^{n}E; F)$ contains a copy of $c_{0}$, and therefore by Proposition \ref{cor 36} $\mathcal{P}_{w} (^{n}E;F)$ is not complemented in $\mathcal{P}(^{n}E;F)$.
\end{proof}
\begin{corollary}\label{cor 300}
Let $E$ and $F$ be Banach spaces, with $E$ infinite dimensional, and let $n>1$. If each $P\in \mathcal{P}(^{n}E; F)$ such that $P\notin \mathcal{P}_{w}(^{n}E; F)$ admits a factorization $P=Q\circ T$, where $T\in \mathcal{L}(E;G)$, $Q\in \mathcal{P}(^{n}G;F)$ and $G$ is a Banach space with an unconditional finite dimensional expansion of the identity, then the following conditions are equivalent:
\begin{enumerate}
\item [(1)] $\mathcal{P}_{w} (^{n}E; F)$ contains a copy of $c_{0}$,
\item [($1^{\prime}$)] $\mathcal{P}_{K} (^{n}E; F)$ contains a copy of $c_{0}$,
\item [(2)] $\mathcal{P}_{w} (^{n}E; F)$ is not complemented in $\mathcal{P} (^{n}E; F)$,
\item [($2^{\prime}$)] $\mathcal{P}_{K} (^{n}E; F)$ is not complemented in $\mathcal{P} (^{n}E; F)$,
\item [(3)] $\mathcal{P}_{w} (^{n}E; F)\neq \mathcal{P} (^{n}E; F)$,
\item [($3^{\prime}$)] $\mathcal{P}_{K} (^{n}E; F)\neq \mathcal{P} (^{n}E; F)$,
\item [(4)] $\mathcal{P}(^{n}E; F)$ contains a copy of $c_{0}$,
\item [(5)] $\mathcal{P}(^{n}E; F)$ contains a copy of $\ell_{\infty}$.
\end{enumerate}
\end{corollary}
\begin{proof}
$(1)\Rightarrow (2)$ by Proposition \ref{cor 36}.
$(2)\Rightarrow (3)$ is obvious.
$(3)\Rightarrow (1)$ by Theorem \ref{thm:(Teorema 17)}.
$(1)\Rightarrow (4)$ is obvious.
$(4)\Rightarrow (3)$ suppose $(4)$ holds and $(3)$ does not hold. Then $\mathcal{P}_{w} (^{n}E; F)=\mathcal{P}(^{n}E; F)\supset c_{0}$. Thus $(1)$ holds,
and therefore $(3)$ holds, a contradiction.
$(5)\Rightarrow (4)$ is obvious.
$(4)\Rightarrow (5)$ by a result of Ryan \cite{RYAN} $\mathcal{P}(^{n}E; F)$ is isometrically isomorphic to $\mathcal{L}(\widehat{\otimes}_{n,s,\pi}E; F)$.
Thus the result follows from (\cite[Remark 3 e) ]{KA} part $2\Rightarrow 3$).
Thus $(1)$, $(2)$, $(3)$, $(4)$ and $(5)$ are equivalent.
$(1)\Rightarrow(1^{\prime})$ is obvious.
$(1^{\prime})\Rightarrow (2^{\prime})$ by Proposition \ref{cor 366}.
$(2^{\prime})\Rightarrow (3^{\prime})$ is obvious.
$(3^{\prime})\Rightarrow (3)$ is obvious.
Since $(3)\Rightarrow (1)$ and $(1)\Rightarrow (1^{\prime})$, the proof of the corollary is complete.
\end{proof}
In particular if $E$ has an unconditional finite dimensional expansion of the identity we obtain \cite[Theorem 7]{GONZALEZ M}.
The assumptions of this corollary apply also if $F$ is a complemented subspace of a space with an unconditional basis.
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\section{Introduction}
Matrix completion is one of the cornerstone problems in machine learning and has a diverse range of applications. One of the original motivations for it comes from the {\em Netflix Problem} where the goal is to predict user-movie ratings based on all the ratings we have observed so far, from across many different users. We can organize this data into a large, partially observed matrix where each row represents a user and each column represents a movie. The goal is to fill in the missing entries. The usual assumptions are that the ratings depend on only a few hidden characteristics of each user and movie and that the underlying matrix is approximately \emph{low rank}. Another standard assumption is that it is incoherent, which we elaborate on later. How many entries of $M$ do we need to observe in order to fill in its missing entries? And are there efficient algorithms for this task?
There have been thousands of papers on this topic and by now we have a relatively complete set of answers. A representative result (building on earlier works by Fazel \cite{Fa}, Recht, Fazel and Parrilo \cite{RFP}, Srebro and Shraibman \cite{SS}, Candes and Recht \cite{CR}, Candes and Tao \cite{CT}) due to Keshavan, Montanari and Oh~\cite{KMO2} can be phrased as follows: Suppose $M$ is an unknown $n_1 \times n_2$ matrix that has rank $r$ but each of its entries has been corrupted by independent Gaussian noise with standard deviation $\delta$. Then if we observe roughly
$$m = (n_1 + n_2) r \log (n_1 + n_2)$$
of its entries, the locations of which are chosen uniformly at random, there is an algorithm that outputs a matrix $X$ that with high probability satisfies
$$\mbox{err}(X) = \frac{1}{n_1 n_2} \sum_{i,j} \Big | X_{i,j} - M_{i,j} \Big | \leq O(\delta) \;.$$
There are extensions to non-uniform sampling models \cite{LS, CBSW}, as well as various efficiency improvements \cite{JNS, Ha}. What is particularly remarkable about these guarantees is that the number of observations needed is within a logarithmic factor of the number of parameters \---- $(n_1 +n_2)r$ \---- that define the model.
In fact, there are benefits to working with even higher-order structure but so far there has been little progress on natural extensions to the tensor setting. To motivate this problem, consider the {\em Groupon Problem} (which we introduce here to illustrate this point) where the goal is to predict user-activity ratings. The challenge is that which activities we should recommend (and how much a user liked a given activity) depends on {\em time} as well \---- weekday/weekend, day/night, summer/fall/winter/spring, etc. or even some combination of these. As above, we can cast this problem as a large, partially observed tensor where the first index represents a user, the second index represents an activity and the third index represents the time period. It is again natural to model it as being close to low rank, under the assumption that a much smaller number of (latent) factors about the interests of the user, the type of activity and the time period should contribute to the rating. How many entries of the tensor do we need to observe in order to fill in its missing entries? This problem is emblematic of a larger issue: Can we always solve linear inverse problems when the number of observations is comparable to the number of parameters in the mode, or is computational intractability an obstacle?
In fact, one of the advantages of working with tensors is that their decompositions are unique in important ways that matrix decompositions are not. There has been a groundswell of recent work that uses tensor decompositions for exactly this reason for parameter learning in phylogenetic trees \cite{MR}, HMMs \cite{MR}, mixture models \cite{HK}, topic models \cite{AFHKL} and to solve community detection \cite{AGHK}. In these applications, one assumes access to the entire tensor (up to some sampling noise). But given that the underlying tensors are low-rank, can we observe fewer of their entries and still utilize tensor methods?
A wide range of approaches to solving tensor completion have been proposed \cite{LMWY, GRY, SDS, THK, MHWG, KSV, JO, BSa, YZ}. However, in terms of provable guarantees none\footnote{Most of the existing approaches rely on computing the tensor nuclear norm, which is hard to compute \cite{Gu, HM}. The only other algorithms we are aware of \cite{JO, BSa} require that the factors be orthogonal. This is a rather strong assumption. First, orthogonality requires the rank to be at most $n$. Second, even when $r\leq n$, most tensors need to be ``whitened'' to be put in this form and then a random sample from the ``whitened" tensor would correspond to a (dense) linear combination of the entries of the original tensor, which would be quite a different sampling model. } of them improve upon the following n\"aive algorithm. If the unknown tensor $T$ is $n_1 \times n_2 \times n_3$ we can treat it as a collection of $n_1$ matrices each of size $n_2 \times n_3$. It is easy to see that if $T$ has rank at most $r$ then each of these slices also has rank at most $r$ (and they inherit incoherence properties as well). By treating a third-order tensor as nothing more than an {\em unrelated} collection of $n_1$ low-rank matrices, we can complete each slice separately using roughly $m = n_1 (n_2 + n_3) r \log (n_2 + n_3)$
observations in total. When the rank is constant, this is a {\em quadratic} number of observations even though the number of parameters in the model is {\em linear}.
Here we show how to solve the (noisy) tensor completion problem with many fewer observations. Let $n_1 \leq n_2 \leq n_3$. We give an algorithm based on the sixth level of the sum-of-squares hierarchy that can accurately fill in the missing entries of an unknown, incoherent $n_1 \times n_2 \times n_3$ tensor $T$ that is entry-wise close to being rank $r$ with roughly
$$m = (n_1)^{1/2} (n_2 + n_3) r \log^4 (n_1 + n_2 + n_3)$$
observations. Moreover, our algorithm works even when the observations are corrupted by noise. When $n = n_1 = n_2 = n_3$, this amounts to about $n^{1/2} r $ observations per slice which is much smaller than what we would need to apply matrix completion on each slice separately. Our algorithm needs to leverage the structure between the various slices.
\subsection{Our Results}
We give an algorithm for noisy tensor completion that works for third-order tensors. Let $T$ be a third-order $n_1 \times n_2 \times n_3$ tensor that is entry-wise close to being low rank. In particular let
\begin{equation}\label{eq:tensor}
T = \sum_{\ell = 1}^r \sigma_\ell \mbox{ } a_\ell \otimes b_\ell \otimes c_\ell + \Delta
\end{equation}
where $\sigma_\ell$ is a scalar and $a_\ell, b_\ell$ and $c_\ell$ are vectors of length $n_1$, $n_2$ and $n_3$ respectively. Here $\Delta$ is a tensor that represents noise. Its entries can be thought of as representing model misspecification because $T$ is not exactly low rank or noise in our observations or both. We will only make assumptions about the average and maximum absolute value of entries in $\Delta$. The vectors $a_\ell, b_\ell$ and $c_\ell$ are called {\em factors}, and we will assume that their norms are roughly $\sqrt{n_i}$ for reasons that will become clear later. Moreover we will assume that the magnitude of each of their entries is bounded by $C$ in which case we call the vectors $C$-incoherent\footnote{Incoherence is often defined based on the span of the factors, but we will allow the number of factors to be larger than any of the dimensions of the tensor so we will need an alternative way to ensure that the non-zero entries of the factors are spread out}. (Note that a random vector of dimension $n$ and norm $\sqrt{n}$ will be $O(\sqrt{\log n_i})$-incoherent with high probability.)
The advantage of these conventions are that a typical entry in $T$ does not become vanishingly small as we increase the dimensions of the tensor. This will make it easier to state and interpret the error bounds of our algorithm.
Let $\Omega$ represent the locations of the entries that we observe, which (as is standard) are chosen uniformly at random and without replacement. Set $|\Omega| = m$. Our goal is to output a hypothesis $X$ that has small entry-wise error, defined as:
$$\mbox{err}(X) = \frac{1}{n_1 n_2 n_3} \sum_{i,j,k} \Big | X_{i,j,k} - T_{i,j,k} \Big |$$
This measures the error on both the observed and unobserved entries of $T$. Our goal is to give algorithms that achieve {\em vanishing} error, as the size of the problem increases. Moreover we will want algorithms that need as few observations as possible.
Here and throughout let $n_1 \leq n_2 \leq n_3$ and $n = \max\{ n_1,n_2,n_3\}$. Our main result is:
\begin{theorem}[Main theorem] \label{thm:predict}
Suppose we are given $m$ observations whose locations are chosen uniformly at random (and without replacement) from a tensor $T$ of the form (\ref{eq:tensor}) where each of the factors $a_\ell, b_\ell$ and $c_\ell$ are $C$-incoherent. Let $\delta = \frac{1}{n_1 n_2 n_3} \sum_{i,j,k} | \Delta_{i,j,k}|$. And let $r^* = \sum_{\ell = 1}^r |\sigma_\ell|$. Then there is a polynomial time algorithm that outputs a hypothesis $X$ that with probability $1- \epsilon$ satisfies
$$\mbox{err}(X) \leq 4 C^3 r^* \sqrt{\frac{ (n_1)^{1/2} (n_2 + n_3) \log^4 n + \log 2/\epsilon}{ m } }\ + 2 \delta$$
provided that $\max_{i,j,k} |\Delta_{i,j,k}| \leq \sqrt{\frac{m}{\log 2/\epsilon}} \delta$.
\end{theorem}
Since the error bound above is quite involved, let us dissect the terms in it. In fact, having an additive $\delta$ in the error bound is unavoidable. We have not assumed anything about $\Delta$ in (\ref{eq:tensor}) except a bound on the average and maximum magnitude of its entries. If $\Delta$ were a random tensor whose entries are $+\delta$ and $-\delta$ then no matter how many entries of $T$ we observe, we cannot hope to obtain error less than $\delta$ on the unobserved entries\footnote{The factor of $2$ is not important, and comes from needing a bound on the empirical error of how well the low rank part of $T$ itself agrees with our observations so far. We could replace it with any other constant factor that is larger than $1$.}. The crucial point is that the remaining term in the error bound becomes $o(1)$ when $m = \widetilde{\Omega}((r^*)^2 n^{3/2})$ which for polylogarithmic $r^*$ improves over the n\"aive algorithm for tensor completion by a {\em polynomial} factor in terms of the number of observations. Moreover our algorithm works without any constraints that factors $a_\ell, b_\ell$ and $c_\ell$ be orthogonal or even have low inner-product.
In non-degenerate cases we can even remove another factor of $r^*$ from the number of observations we need. Suppose that $T$ is a tensor as in (\ref{eq:tensor}), but let $\sigma_\ell$ be Gaussian random variables with mean zero and variance one. The factors $a_\ell, b_\ell$ and $c_\ell$ are still fixed, but because of the randomness in the coefficients $\sigma_\ell$, the entries of $T$ are now random variables.
\begin{corollary} \label{corr:inf2}
Suppose we are given $m$ observations whose locations are chosen uniformly at random (and without replacement) from a tensor $T$ of the form (\ref{eq:tensor}), where each coefficient $\sigma_\ell$ is a Gaussian random variable with mean zero and variance one, and each of the factors $a_\ell, b_\ell$ and $c_\ell$ are $C$-incoherent.
Further, suppose that for a $1-o(1)$ fraction of the entries of $T$, we have $\operatorname{var}(T_{i,j,k}) \geq r/\operatorname{polylog}(n) = V$ and that $\Delta$ is a tensor where each entry is a Gaussian with mean zero and variance $o(V)$. Then there is a polynomial time algorithm that outputs a hypothesis $X$ that satisfies
\[
X_{i,j,k} = \Big (1\pm o(1) \Big )T_{i,j,k}
\]
for a $1 - o(1)$ fraction of the entries. The algorithm succeeds with probability at least $1 - o(1)$ over the randomness of the locations of the observations, and the realizations of the random variables $\sigma_\ell$ and the entries of $\Delta$. Moreover the algorithm uses $m = C^6 n^{3/2} r \operatorname{polylog}(n)$ observations.
\end{corollary}
\noindent In the setting above, it is enough that the coefficients $\sigma_\ell$ are random and that the non-zero entries in the factors are spread out to ensure that the typical entry in $T$ has variance about $r$. Consequently, the typical entry in $T$ is about $\sqrt{r}$. This fact combined with the error bounds in Theorem~\ref{thm:predict} immediately yield the above corollary . Remarkably, the guarantee is interesting even when $r = n^{3/2 - \epsilon}$ (the so-called overcomplete case). In this setting, if we observe a subpolynomial fraction of the entries of $T$ we are able to recover almost all of the remaining entries almost entirely, even though there are no known algorithms for decomposing an overcomplete, third-order tensor even if we are given {\em all} of its entries, at least without imposing much stronger conditions that the factors be nearly orthogonal \cite{GM}.
We believe that this work is a natural first step in designing practically efficient algorithms for tensor completion. Our algorithms manage to leverage the structure across the slices through the tensor, instead of treating each slice as an independent matrix completion problem. Now that we know this is {\em possible}, a natural follow-up question is to get more efficient algorithms. Our algorithms are based on the sixth level of the sum-of-squares hierarchy and run in polynomial time, but are quite far from being practically efficient as stated. Recent work of Hopkins et al. \cite{HSSS} shows how to speed up sum-of-squares and obtain {\em nearly linear time} algorithms for a number of problems where the only previously known algorithms ran in a prohibitively large degree polynomial running time. Another approach would be to obtain similar guarantees for alternating minimization. Currently, the only known approaches \cite{JO} require that the factors are orthonormal and only work in the undercomplete case. Finally, it would be interesting to get algorithms that recover a low rank tensor exactly when there is no noise.
\subsection{Our approach}
All of our algorithms are based on solving the following optimization problem:
\begin{equation}\label{eq:conv}
\qquad \min \|X\|_\mathcal{K} \mbox{ s.t. } \exists X \mbox{ with } \frac{1}{m} \sum_{(i,j,k) \in \Omega} | X_{i,j,k} - T_{i,j,k}| \leq 2 \delta
\end{equation}
and outputting the minimizer $X$, where $\|\cdot\|_\mathcal{K}$ is some norm that can be computed in polynomial time. It will be clear from the way we define the norm that the low rank part of $T$ will itself be a good candidate solution. But this is not necessarily the solution that the convex program finds. How do we know that whatever it finds not only has low entry-wise error on the observed entries of $T$, but also on the unobserved entries too?
This is a well-studied topic in statistical learning theory, and as is standard we can use the notion of Rademacher complexity as a tool to bound the error. The Rademacher complexity is a property of the norm we choose, and our main innovation is to use the sum-of-squares hierarchy to suggest a suitable norm. Our results are based on establishing a connection between noisy tensor completion and refuting random constraint satisfaction problems. Moreover, our analysis follows by embedding algorithms for refutation within the sum-of-squares hierarchy as a method to bound the Rademacher complexity.
A natural question to ask is: Are there other norms that have even better Rademacher complexity than the ones we use here, and that are still computable in polynomial time?
It turns out that {\em any} such norm would immediately lead to much better algorithms for refuting random constraint satisfaction problems than we currently know. We have not yet introduced Rademacher complexity yet, so we state our lower bounds informally:
\begin{theorem} [informal]
For any $\epsilon > 0$, if there is a polynomial time algorithm that achieves error
$$\mbox{err}(X) \leq r^* \sqrt{\frac{n^{3/2-\epsilon}}{ m } }$$ through the framework of Rademacher complexity then there is an efficient algorithm for refuting a random $3$-SAT formula on $n$ variables with $m = n^{3/2 - \epsilon}$ clauses. Moreover the natural sum-of-squares relaxation requires at least $n^{2\epsilon}$-levels in order to achieve the above error (again through the framework of Rademacher complexity).
\end{theorem}
\noindent These results follow directly from the works of Grigoriev \cite{G}, Schoenebeck \cite{Sch} and Feige \cite{Fe}. There are similar connections between our upper bounds and the work of Coja-Oghlan, Goerdt and Lanka \cite{COGL} who give an algorithm for strongly refuting random $3$-SAT. In Section~\ref{sec:connect} we explain some preliminary connections between these fields, at which point we will be in a better position to explain how we can borrow tools from one area to address open questions in another. We state this theorem more precisely in Corollary~\ref{cor:3sat} and Corollary~\ref{corr:3lb}, which provide both conditional and unconditional lower bounds that match our upper bounds.
\subsection{Computational vs. Sample Complexity Tradeoffs}
It is interesting to compare the story of matrix completion and tensor completion. In matrix completion, we have the best of both worlds: There are efficient algorithms which work when the number of observations is close to the information theoretic minimum. In tensor completion, we gave algorithms that improve upon the number of observations needed by a polynomial factor but still require a polynomial factor more observations than can be achieved if we ignore computational considerations.
We believe that for many other linear inverse problems (e.g. sparse phase retrieval), there may well be gaps between what can be achieved information theoretically and what can be achieved with computationally efficient estimators. Moreover, proving lower bounds against the sum-of-squares hierarchy offers a new type of evidence that problems are hard, that does not rely on reductions from other average-case hard problems which seem (in general) to be brittle and difficult to execute while preserving the {\em naturalness} of the input distribution. In fact, even when there are such reductions \cite{BR}, the sum-of-squares hierarchy offers a methodology to make sharper predictions for questions like: Is there a quasi-polynomial time algorithm for sparse PCA, or does it require exponential time?
\subsection*{Organization}
In Section~\ref{sec:connect} we introduce Rademacher complexity, the tensor nuclear norm and strong refutation. We connect these concepts by showing that any norm that can be computed in polynomial time and has good Rademacher complexity yields an algorithm for strongly refuting random $3$-SAT. In Section~\ref{sec:using} we show how a particular algorithm for strong refutation can be embedded into the sum-of-squares hierarchy and directly leads to a norm that can be computed in polynomial time and has good Rademacher complexity. In Section~\ref{sec:spectral} we establish certain spectral bounds that we need, and prove our main upper bounds. In Section~\ref{sec:lb} we prove lower bounds on the Rademacher complexity of the sequence of norms arising from the sum-of-squares hierarchy by a direct reduction to lower bounds for refuting random $3$-XOR. In Appendix~\ref{app:extensions} we give a reduction from noisy tensor completion on asymmetric tensors to symmetric tensors. This is what allows us to extend our analysis to arbitrary order $d$ tensors, but the proofs are essentially identical to those in the $d = 3$ case but more notationally involved so we omit them.
\section{Noisy Tensor Completion and Refutation}\label{sec:connect}
Here we make the connection between noisy tensor completion and strong refutation explicit. Our first step is to formulate a problem that is a special case of both, and studying it will help us clarify how notions from one problem translate to the other.
\subsection{The Distinguishing Problem}\label{sec:dist}
Here we introduce a problem that we call the {\em distinguishing problem}. We are given random observations from a tensor and promised that the underlying tensor fits into one of the two following categories. We want an algorithm that can tell which case the samples came from, and succeeds using as few observations as possible. The two cases are:
\begin{enumerate}
\item Each observation is chosen uniformly at random (and without replacement) from a tensor $T$ where independently for each entry we set
\begin{equation*}
T_{i,j,k}=
\begin{cases}
a_i a_j a_k &\mbox{ with probability } 7/8\\
\mbox{ } \mbox{ } 1 &\mbox { with probability } 1/16\\
-1 &\mbox{ else}
\end{cases}
\end{equation*}
where $a$ is a vector whose entries are $\pm 1$.
\item Alternatively, each observation is chosen uniformly at random (and without replacement) from a tensor $T$ each of whose entries is independently set to either $+1$ or $-1$ and with equal probability.
\end{enumerate}
\noindent In the first case, the entries of the underlying tensor $T$ are {\em predictable}. It is possible to guess a $15/16$ fraction of them correctly, once we have observed enough of its entries to be able to deduce $a$. And in the second case, the entries of $T$ are completely unpredictable because no matter how many entries we have observed, the remaining entries are still random. Thus we cannot predict any of the unobserved entries better than random guessing.
Now we will explain how the distinguishing problem can be equivalently reformulated in the language of refutation. We give a formal definition for strong refutation later (Definition~\ref{def:strongref}), but for the time being we can think of it as the task of (given an instance of a constraint satisfaction problem) certifying that there is no assignment that satisfies many of the clauses. We will be interested in $3$-XOR formulas, where there are $n$ variables $v_1, v_2, ..., v_n$ that are constrained to take on values $+1$ or $-1$. Each clause takes the form
$$v_i \cdot v_j \cdot v_k = T_{i,j,k}$$
where the right hand side is either $+1$ or $-1$. The clause represents a parity constraint but over the domain $\{+1, -1\}$ instead of over the usual domain $\mathbb{F}_2$. We have chosen the notation suggestively so that it hints at the mapping between the two views of the problem. Each observation $T_{i,j,k}$ maps to a clause $v_i \cdot v_j \cdot v_k = T_{i,j,k}$ and vice-versa. Thus an equivalent way to formulate the distinguishing problem is that we are given a $3$-XOR formula which was generated in one of the following two ways:
\begin{enumerate}
\item Each clause in the formula is generated by choosing an ordered triple of variables $(v_i, v_j, v_k)$ uniformly at random (and without replacement) and we set
\begin{equation*}
v_i \cdot v_j \cdot v_k=
\begin{cases}
a_i a_j a_k &\mbox{ with probability } 7/8\\
\mbox{ } \mbox{ } 1 &\mbox { with probability } 1/16\\
-1 &\mbox{ else}
\end{cases}
\end{equation*}
where $a$ is a vector whose entries are $\pm 1$. Now $a$ represents a planted solution and by design our sampling procedure guarantees that many of the clauses that are generated are consistent with it.
\item Alternatively, each clause in the formula is generated by choosing an ordered triple of variables $(v_i, v_j, v_k)$ uniformly at random (and without replacement) and we set
$v_i \cdot v_j \cdot v_k = z_{i,j,k}$
where $z_{i,j,k}$ is a random variable that takes on values $+1$ and $-1$.
\end{enumerate}
\noindent In the first case, the $3$-XOR formula has an assignment that satisfies a $15/16$ fraction of the clauses in expectation by setting $v_i = a_i$. In the second case, any fixed assignment satisfies at most half of the clauses in expectation. Moreover if we are given $\Omega(n \log n)$ clauses, it is easy to see by applying the Chernoff bound and taking a union bound over all possible assignments that with high probability there is no assignment that satisfies more than a $1/2 + o(1)$ fraction of the clauses.
This will be the starting point for the connections we establish between noisy tensor completion and refutation.
Even in the matrix case these connections seem to have gone unnoticed, and the same spectral bounds that are used to analyze the Rademacher complexity of the nuclear norm \cite{SS} are also used to refute random $2$-SAT formulas \cite{GK}, but this is no accident.
\subsection{Rademacher Complexity}\label{sec:rad}
Ultimately our goal is to show that the hypothesis $X$ that our convex program finds is entry-wise close to the unknown tensor $T$. By virtue of the fact that $X$ is a feasible solution to (\ref{eq:conv}) we know that it is entry-wise close to $T$ on the observed entries. This is often called the empirical error:
\begin{definition}
For a hypothesis $X$, the empirical error is
$$\mbox{emp-err}(X) = \frac{1}{m} \sum_{(i,j,k) \in \Omega} | X_{i,j,k} - T_{i,j,k}|$$
\end{definition}
Recall that $\mbox{err}(X)$ is the average entry-wise error between $X$ and $T$, over all (observed and unobserved) entries. Also recall that among the candidate $X$'s that have low empirical error, the convex program finds the one that minimizes $\|X\|_\mathcal{K}$ for some polynomial time computable norm. The way we will choose the norm $\|\cdot\|_\mathcal{K}$ and our bound on the maximum magnitude of an entry of $\Delta$ will guarantee that the low rank part of $T$ will with high probability be a feasible solution. This ensures that $\|X\|_\mathcal{K}$ for the $X$ we find is not too large either. One way to bound $\mbox{err}(X)$ is to show that no hypothesis in the unit norm ball can have too large a gap between its error and its empirical error (and then dilate the unit norm ball so that it contains $X$). With this in mind, we define:
\begin{definition}
For a norm $\|\cdot\|_{\mathcal{K}}$ and a set $\Omega$ of observations, the generalization error is
$$\sup_{\|X\|_\mathcal{K} \leq 1} \Big | \mbox{err}(X) - \mbox{emp-err}(X) \Big | $$
\end{definition}
\noindent It turns out that one can bound the generalization error via the Rademacher complexity.
\begin{definition}\label{def:rad}
Let $\Omega = \{(i_1, j_1, k_1), (i_2, j_2, k_2), ..., (i_m, j_m, k_m)\}$ be a set of $m$ locations chosen uniformly at random (and without replacement) from $[n_1] \times [n_2] \times [n_3]$. And let $\sigma_1, \sigma_2, ..., \sigma_\ell$ be random $\pm 1$ variables.
The Rademacher complexity of (the unit ball of) the norm $\|\cdot\|_\mathcal{K}$ is defined as
$$R^m(\|\cdot\|_\mathcal{K}) = \mathop{\bf E\/}_{\Omega, \sigma} \Big [ \sup_{\|X\|_\mathcal{K} \leq 1} \Big | \sum_{\ell =1}^m \sigma_\ell X_{i_\ell, j_\ell, k_\ell} \Big | \Big ] $$
\end{definition}
It follows from a standard symmetrization argument from empirical process theory \cite{KP, BM} that the Rademacher complexity does indeed bound the generalization error.
\begin{theorem}\label{thm:generalize}
Let $\epsilon\in (0,1)$ and suppose each $X$ with $\|X\|_{\mathcal{K}} \leq 1$ has bounded loss \---- i.e. $|X_{i,j,k} - T_{i,j,k}| \leq a$ and that locations $(i, j, k)$ are chosen uniformly at random and without replacement. Then with probability at least $1- \epsilon$, for every $X$ with $\|X\|_{\mathcal{K}} \leq 1$, we have
$$\mbox{err}(X) \leq \mbox{emp-err}(X) + 2 R^m(\|\cdot\|_\mathcal{K}) + 2 a \sqrt{\frac{\ln(1/\epsilon)}{m}}$$
\end{theorem}
We repeat the proof here following \cite{BM} for the sake of completeness but readers familiar with Rademacher complexity can feel free to skip ahead to Definition~\ref{def:Z}. The main idea is to let $\Omega'$ be an independent set of $m$ samples from the same distribution, again without replacement. The expected generalization error is:
\begin{equation}\label{eqn:generalization}
\mathop{\bf E\/}_{\Omega} \Big [ \sup_{\|X\|_\mathcal{K} \leq 1} \Big | \frac{1}{m} \sum_{\ell =1}^m | X_{i_\ell, j_\ell, k_\ell} - T_{i_\ell, j_\ell, k_\ell} | - \mathop{\bf E\/}_{i,j,k} [ | X_{i,j,k} - T_{i,j,k} | ] \Big | \Big ]\tag{$\ast$}
\end{equation}
Then we can write
\begin{eqnarray*}
(\mbox{\ref{eqn:generalization}}) &=& \mathop{\bf E\/}_{\Omega} \Big [ \sup_{\|X\|_\mathcal{K} \leq 1} \Big | \frac{1}{m} \sum_{\ell =1}^m | X_{i_\ell, j_\ell, k_\ell} - T_{i_\ell, j_\ell, k_\ell} | - \frac{1}{m} \mathop{\bf E\/}_{\Omega'} [\sum_{\ell =1}^m | X_{i'_\ell, j'_\ell, k'_\ell} - T_{i'_\ell, j'_\ell, k'_\ell} | ] \Big | \Big ] \\
&\leq& \mathop{\bf E\/}_{\Omega, \Omega'} \Big [ \sup_{\|X\|_\mathcal{K} \leq 1} \Big | \frac{1}{m} \Big ( \sum_{\ell =1}^m | X_{i_\ell, j_\ell, k_\ell} - T_{i_\ell, j_\ell, k_\ell} | - | X_{i'_\ell, j'_\ell, k'_\ell} - T_{i'_\ell, j'_\ell, k'_\ell} | \Big ) \Big | \Big ]
\end{eqnarray*}
where the last line follows by the concavity of $\sup(\cdot)$. Now we can use the Rademacher (random $\pm 1$) variables $\{\sigma_\ell\}_\ell$ and rewrite the right hand side of the above expression as follows:
\begin{eqnarray*}
(\mbox{\ref{eqn:generalization}}) &\leq& \mathop{\bf E\/}_{\Omega, \Omega', \sigma} \Big [ \sup_{\|X\|_\mathcal{K} \leq 1} \Big | \frac{1}{m} \sum_{\ell =1}^m \sigma_\ell \Big ( | X_{i_\ell, j_\ell, k_\ell} - T_{i_\ell, j_\ell, k_\ell} | - | X_{i'_\ell, j'_\ell, k'_\ell} - T_{i'_\ell, j'_\ell, k'_\ell} | \Big ) \Big | \Big ] \\
&\leq& \mathop{\bf E\/}_{\Omega, \Omega', \sigma} \Big [ \sup_{\|X\|_\mathcal{K} \leq 1} \Big | \frac{1}{m} \sum_{\ell =1}^m \sigma_\ell | X_{i_\ell, j_\ell, k_\ell} - T_{i_\ell, j_\ell, k_\ell} | \Big | + \Big | \frac{1}{m} \sum_{\ell =1}^m \sigma_\ell | X_{i'_\ell, j'_\ell, k'_\ell} - T_{i'_\ell, j'_\ell, k'_\ell} | \Big | \Big ] \\
&\leq& 2 \mathop{\bf E\/}_{\Omega, \sigma} \Big [ \sup_{\|X\|_\mathcal{K} \leq 1} \Big | \frac{1}{m} \Big ( \sum_{\ell =1}^m \sigma_\ell | X_{i_\ell, j_\ell, k_\ell} - T_{i_\ell, j_\ell, k_\ell} | \Big ) \Big | \Big ] \\
&\leq& 2 \mathop{\bf E\/}_{\Omega, \sigma} \Big [ \sup_{\|X\|_\mathcal{K} \leq 1} \Big | \frac{1}{m} \Big ( \sum_{\ell =1}^m \sigma_\ell \Big ( | X_{i_\ell, j_\ell, k_\ell}| + |T_{i_\ell, j_\ell, k_\ell} | \Big ) \Big ) \Big | \Big ] \\
&\leq& 2 \mathop{\bf E\/}_{\Omega, \sigma} \Big [ \Big | \frac{1}{m} \sum_{\ell =1}^m \sigma_\ell |T_{i_\ell, j_\ell, k_\ell}| \Big | \Big ] + 2 \mathop{\bf E\/}_{\Omega, \sigma} \Big [ \sup_{\|X\|_\mathcal{K} \leq 1} \Big | \frac{1}{m} \sum_{\ell =1}^m \sigma_\ell |X_{i_\ell, j_\ell, k_\ell}| \Big | \Big ]\\
&=& 2 \mathop{\bf E\/}_{\Omega, \sigma} \Big [ \Big | \frac{1}{m} \sum_{\ell =1}^m \sigma_\ell T_{i_\ell, j_\ell, k_\ell} \Big | \Big ] + 2 \mathop{\bf E\/}_{\Omega, \sigma} \Big [ \sup_{\|X\|_\mathcal{K} \leq 1} \Big | \frac{1}{m} \sum_{\ell =1}^m \sigma_\ell X_{i_\ell, j_\ell, k_\ell} \Big | \Big ]
\end{eqnarray*}
where the second, fourth and fifth inequalities use the triangle inequality. The equality uses the fact that the $\sigma_\ell$'s are random signs and hence can absorb the absolute value around the terms that they multiply. The second term above in the last expression is exactly the Rademacher complexity that we defined earlier. This argument only shows that the Rademacher complexity bounds the expected generalization error. However it turns out that we can also use the Rademacher complexity to bound the generalization error with high probability by applying McDiarmid's inequality. See for example \cite{Bal}. We also remark that generalization bounds are often stated in the setting where samples are drawn i.i.d., but here the locations of our observations are sampled without replacement. Nevertheless for the settings of $m$ we are interested in, the fraction of our observations that are repeats is $o(1)$ \---- in fact it is subpolynomial \---- and we can move back and forth between both sampling models at negligible loss in our bounds.
In much of what follows it will be convenient to think of $\Omega = \{(i_1, j_1, k_1), (i_2, j_2, k_2), ..., (i_m, j_m, k_m)\}$ and $\{\sigma_\ell\}_\ell$ as being represented by a sparse tensor $Z$, defined below.
\begin{definition}\label{def:Z}
Let $Z$ be an $n_1 \times n_2 \times n_3$ tensor such that
$$Z_{i,j,k} = \begin{cases}
0, \mbox{ if } (i,j,k) \notin \Omega \\
\sum_{\ell \mbox{ s.t. } (i, j, k) = (i_\ell, j_\ell, k_\ell)} \sigma_\ell
\end{cases} $$
\end{definition}
This definition greatly simplifies our notation.
In particular we have
$$\sum_{\ell = 1}^m \sigma_\ell X_{i_\ell, j_\ell, k_\ell} =\sum_{i,j,k} Z_{i,j,k} X_{i,j,k} = \langle Z, X \rangle$$
where we have introduced the notation $\langle \mbox{ }\cdot\mbox{ },\mbox{ }\cdot\mbox{ } \rangle$ to denote the natural inner-product between tensors. Our main technical goal in this paper will be to analyze the Rademacher complexity of a sequence of successively tighter norms that we get from the sum-of-squares hierarchy, and to derive implications for noisy tensor completion and for refutation from these bounds.
\subsection{The Tensor Nuclear Norm}
Here we introduce the tensor nuclear norm and analyze its Rademacher complexity. Many works have suggested using it to solve tensor completion problems \cite{LMWY, SDS, YZ}. This suggestion is quite natural given that it is based on a similar guiding principle as that which led to $\ell_1$-minimization in compressed sensing and the nuclear norm in matrix completion \cite{Fa}. More generally, one can define the atomic norm for a wide range of linear inverse problems \cite{CRPW}, and the $\ell_1$-norm, the nuclear norm and the tensor nuclear norm are all special cases of this paradigm. Before we proceed, let us first formally define the notion of incoherence that we gave in the introduction.
\begin{definition}\label{def:balanced}
A length $n_i$ vector $a$ is \emph{$C$-incoherent} if $\|a\| = \sqrt{n_i}$ and $\|a\|_\infty \leq C$.
\end{definition}
Recall that we chose to work with vectors whose typical entry is a constant so that the entries in $T$ do not become vanishingly small as the dimensions of the tensor increase.
We can now define the tensor nuclear norm\footnote{The usual definition of the tensor nuclear norm has no constraints that the vectors $a$, $b$ and $c$ be $C$-incoherent. However, adding this additional requirement only serves to further restrict the unit norm ball, while ensuring that the low rank part of $T$ (when scaled down) is still in it, since the factors of $T$ are anyways assumed to be $C$-incoherent. This makes it easier to prove recovery guarantees because we do not need to worry about sparse vectors behaving very differently than incoherent ones, and since we are not going to compute this norm anyways this modification will make our analysis easier.}:
\begin{definition}[tensor nuclear norm]\label{def:anorm}
Let ${\mathcal{A}} \subseteq \mathbb R^{ n_1 \times n_2 \times n_3 }$ be defined as
$${\mathcal{A}} = \Big \{ X \mbox{ s.t. } \exists \mbox{ distribution } \mu \mbox{ on triples of $C$-incoherent vectors with } X_{i,j,k} = \mathop{\bf E\/}_{(a,b,c) \leftarrow \mu}[a_i b_j c_k]\Big \}$$
The {\em tensor nuclear norm} of $X$ which is denoted by $\|X\|_{{\mathcal{A}}}$ is the infimum over $\alpha$ such that $X/\alpha \in \calA$.
\end{definition}
\noindent In particular $\|T - \Delta \|_{{\mathcal{A}}} \leq r^*$. Finally we give an elementary bound on the Rademacher complexity of the tensor nuclear norm. Recall that $n = \max(n_1, n_2, n_3)$.
\begin{lemma}\label{radnuc}
$R^m(\| \cdot\|_{\mathcal{A}}) = O(C^3\sqrt{\frac{n}{m}})$
\end{lemma}
\begin{proof}
Recall the definition of $Z$ given in Definition~\ref{def:Z}. With this we can write
$$\mathop{\bf E\/}_{\Omega, \sigma} \Big [ \sup_{\|X\|_{\mathcal{A}} \leq 1} \Big | \sum_{\ell =1}^m \sigma_\ell X_{i_\ell, j_\ell, k_\ell} \Big | \Big ] = \mathop{\bf E\/}_{\Omega, \sigma} \Big [\sup_{\mbox{{\small $C$-incoherent} } a, b, c} | \langle Z, a\otimes b \otimes c \rangle| \Big ]$$
We can now adapt the discretization approach in \cite{FKS}, although our task is considerably simpler because we are constrained to $C$-incoherent $a$'s. In particular, let $$S = \left \{ a \Big | a \mbox{ is $C$-incoherent and } a \in \Big (\epsilon \mathbb{Z} \Big )^n \right \}$$
By standard bounds on the size of an $\epsilon$-net \cite{Mat}, we get that $|S| \leq O(C/\epsilon)^n$. Suppose that $|\langle Z, a\otimes b \otimes c \rangle| \leq M$ for all $a, b, c \in S$. Then for an arbitrary, but $C$-incoherent $a$ we can expand it as $a = \sum_i \epsilon^i a^i$ where each $a^i \in S$ and similarly for $b$ and $c$. And now
$$ |\langle Z, a\otimes b \otimes c \rangle| \leq \sum_i \sum_j \sum_k \epsilon^i \epsilon^j \epsilon^k |\langle Z, a^i \otimes b^i \otimes c^i \rangle| \leq (1-\epsilon)^{-3} M$$
Moreover since each entry in $a \otimes b \otimes c$ has magnitude at most $C^3$ we can apply a Chernoff bound to conclude that for any particular $a, b, c \in S$ we have $$|\langle Z, a\otimes b \otimes c \rangle | \leq O\Big(C^3\sqrt{m \log 1/\gamma}\Big)$$
with probability at least $1-\gamma$. Finally, if we set $\gamma = (\frac{\epsilon}{C})^{-n}$ and we set $\epsilon = 1/2$ we get that
$$R^m({\mathcal{A}}) \leq \frac{(1-\epsilon)^{-3}}{m} \max_{a, b, c \in S}|\langle Z, a\otimes b \otimes c \rangle | = O\Big(C^3\sqrt{\frac{n}{m}}\Big)$$
and this completes the proof.
\end{proof}
The important point is that the Rademacher complexity of the tensor nuclear norm is $o(1)$ whenever $m = \omega(n)$. In the next subsection we will connect this to refutation in a way that allows us to strengthen known hardness results for computing the tensor nuclear norm \cite{Gu, HM} and show that it is even hard to compute in an average-case sense based on some standard conjectures about the difficulty of refuting random $3$-SAT.
\subsection{From Rademacher Complexity to Refutation}
Here we show the first implication of the connection we have established. Any norm that can be computed in polynomial time and has good Rademacher complexity immediately yields an algorithm for strongly refuting random $3$-SAT and $3$-XOR formulas. Next let us finally define strong refutation.
\begin{definition}
For a formula $\phi$, let $\operatorname{opt}(\phi)$ be the largest fraction of clauses that can be satisfied by any assignment.
\end{definition}
In what follows, we will use the term {\em random $3$-XOR formula} to refer to a formula where each clause is generated by choosing an ordered triple of variables $(v_i, v_j, v_k)$ uniformly at random (and without replacement) and setting
$v_i \cdot v_j \cdot v_k = z$
where $z$ is a random variable that takes on values $+1$ and $-1$.
\begin{definition}\label{def:strongref}
An algorithm for strongly refuting random $3$-XOR takes as input a $3$-XOR formula $\phi$ and outputs a quantity $\mbox{alg}(\phi)$ that satisfies
\begin{enumerate}
\item For any $3$-XOR formula $\phi$, $\operatorname{opt}(\phi) \leq \mbox{alg}(\phi)$
\item If $\phi$ is a random $3$-XOR formula with $m$ clauses, then with high probability $\mbox{alg}(\phi) = 1/2 + o(1)$
\end{enumerate}
\end{definition}
\noindent This definition only makes sense when $m$ is large enough so that $\mbox{opt}(\phi) = 1/2 + o(1)$ holds with high probability, which happens when $m = \omega(n)$. The goal is to design algorithms that use as few clauses as possible, and are able to certify that a random formula is indeed far from satisfiable (without underestimating the fraction of clauses that can be satisfied) and to do so as close as possible to the information theoretic threshold.
Now let us use a polynomial time computable norm $\|\cdot\|_\mathcal{K}$ that has good Rademacher complexity to give an algorithm for strongly refuting random $3$-XOR. As in Section~\ref{sec:dist}, given a formula $\phi$ we map its $m$ clauses to a collection of $m$ observations according to the usual rule: If there are $n$ variables, we construct an $n \times n \times n$ tensor $Z$ where for each clause of the form $v_i \cdot v_j \cdot v_k = z_{i,j,k}$ we put the entry $z_{i,j,k}$ at location $(i, j, k)$. All the rest of the entries in $Z$ are set to zero. We solve the following optimization problem:
\begin{equation} \label{eq:refute}
\max \eta \mbox{ s.t. } \exists X \mbox{ with } \|X\|_{\mathcal{K}} \leq 1 \mbox{ and } \frac{1}{m} \langle Z, X \rangle \geq 2 \eta
\end{equation}
Let $\eta^*$ be the optimum value. We set $\mbox{alg}(\phi) = 1/2 + \eta^*$. What remains is to prove that the output of this algorithm solves the strong refutation problem for $3$-XOR.
\begin{theorem}\label{thm:radtoref}
Suppose that $\|\cdot\|_{\mathcal{K}}$ is computable in polynomial time and satisfies $\|X\|_\mathcal{K} \leq 1$ whenever $X = a \otimes a \otimes a$ and $a$ is a vector with $\pm 1$ entries. Further suppose that for any $X$ with $\|X\|_{\mathcal{K}} \leq 1$ its entries are bounded by $C^3$ in absolute value. Then (\ref{eq:refute}) can be solved in polynomial time and if $R^m(\|\cdot\|_\mathcal{K}) = o(1)$ then setting $\mbox{alg}(\phi) = 1/2 + \eta^*$ solves strong refutation for $3$-XOR with $O(C^6 m \log n)$ clauses.
\end{theorem}
\begin{proof}
The key observation is the following inequality which relates (\ref{eq:refute}) to $\operatorname{opt}(\phi)$.
$$ 2\operatorname{opt}(\phi) -1 \leq \frac{1}{m} \sup_{\|X\|_\mathcal{K} \leq 1} \langle Z, X \rangle$$
To establish this inequality, let $v_1, v_2, ... , v_n$ be the assignment that maximizes the fraction of clauses satisfied. If we set $a_i = v_i$ and $X = a \otimes a \otimes a$ we have that $\|X\|_\mathcal{K} \leq 1$ by assumption. Thus $X$ is a feasible solution. Now with this choice of $X$ for the right hand side, every term in the sum that corresponds to a satisfied clause contributes $+1$ and every term that corresponds to an unsatisfied clause contributes $-1$. We get $ 2\operatorname{opt}(\phi) -1$ for this choice of $X$, and this completes the proof of the inequality above.
The crucial point is that the expectation of the right hand side over $\Omega$ and $\sigma$ is exactly the Rademacher complexity. However we want a bound that holds with high probability instead of just in expectation. It follows from McDiarmid's inequality and the fact that the entries of $Z$ and of $X$ are bounded by $1$ and by $C^3$ in absolute value respectively that if we take $O(C^6 m \log n)$ observations the right hand side will be $o(1)$ with high probability. In this case, rearranging the inequality we have
$$\operatorname{opt}(\phi) \leq 1/2 + \frac{1}{m} \sup_{\|X\|_\mathcal{K} \leq 1} \langle Z, X \rangle $$
The right hand side is exactly $\mbox{alg}(\phi)$ and is $1/2 + o(1)$ with high probability, which implies that both conditions in the definition for strong refutation hold and this completes the proof.
\end{proof}
We can now combine Theorem~\ref{thm:radtoref} with the bound on the Rademacher complexity of the tensor nuclear norm given in Lemma~\ref{radnuc} to conclude that if we could compute the tensor nuclear norm we would also obtain an algorithm for strongly refuting random $3$-XOR with only $m = \Omega(n \log n)$ clauses. It is not obvious but it turns out that any algorithm for strongly refuting random $3$-XOR implies one for $3$-SAT. Let us define strong refutation for $3$-SAT. We will refer to any variable $v_i$ or its negation $\bar{v}_i$ as a literal. We will use the term {\em random $3$-SAT formula} to refer to a formula where each clause is generated by choosing an ordered triple of literals $(y_i, y_j, y_k)$ uniformly at random (and without replacement) and setting
$y_i \vee y_j \vee y_k = 1$.
\begin{definition}\label{def:strongref2}
An algorithm for strongly refuting random $3$-SAT takes as input a $3$-SAT formula $\phi$ and outputs a quantity $\mbox{alg}(\phi)$ that satisfies
\begin{enumerate}
\item For any $3$-SAT formula $\phi$, $\operatorname{opt}(\phi) \leq \mbox{alg}(\phi)$
\item If $\phi$ is a random $3$-SAT formula with $m$ clauses, then with high probability $\mbox{alg}(\phi) = 7/8 + o(1)$
\end{enumerate}
\end{definition}
The only change from Definition~\ref{def:strongref} comes from the fact that for $3$-SAT a random assignment satisfies a $7/8$ fraction of the clauses in expectation. Our goal here is to certify that the largest fraction of clauses that can be satisfied is $7/8 + o(1)$. The connection between refuting random $3$-XOR and $3$-SAT is often called ``Feige's XOR Trick" \cite{Fe}. The first version of it was used to show that an algorithm for $\epsilon$-refuting $3$-XOR can be turned into an algorithm for $\epsilon$-refuting $3$-SAT. However we will not use this notion of refutation so for further details we refer the reader to \cite{Fe}. The reduction was extended later by Coja-Oghlan, Goerdt and Lanka \cite{COGL} to strong refutation, which for us yields the following corollary:
\begin{corollary}\label{cor:3sat}
Suppose that $\|\cdot\|_{\mathcal{K}}$ is computable in polynomial time and satisfies $\|X\|_\mathcal{K} \leq 1$ whenever $X = a \otimes a \otimes a$ and $a$ is a vector with $\pm 1$ entries. Suppose further that for any $X$ with $\|X\|_{\mathcal{K}} \leq 1$ its entries are bounded by $C^3$ in absolute value and that $R^m(\|\cdot\|_\mathcal{K}) = o(1)$. Then there is a polynomial time algorithm for strongly refuting a random $3$-SAT formula with $O(C^6 m \log n)$ clauses.
\end{corollary}
Now we can get a better understanding of the obstacles to noisy tensor completion by connecting it to the literature on refuting random $3$-SAT. Despite a long line of work on refuting random $3$-SAT \cite{GK, FGK, FO, FKO, COGL}, there is no known polynomial time algorithm that works with $m = n^{3/2 - \epsilon}$ clauses for any $\epsilon > 0$. Feige \cite{Fe} conjectured that for any constant $C$, there is no polynomial time algorithm for refuting random $3$-SAT with $m = Cn$ clauses\footnote{In Feige's paper \cite{Fe} there was no need to make the conjecture any stronger because it was already strong enough for all of the applications in inapproximability.}. Daniely et al. \cite{DLSS1} conjectured that there is no polynomial time algorithm for $m = n^{3/2 - \epsilon}$ for any $\epsilon > 0$. What we have shown above is that any norm that is a relaxation to the tensor nuclear norm and can be computed in polynomial time but has Rademacher complexity is $R^m(\|\cdot\|_\mathcal{K}) = o(1)$ for $m = n^{3/2 - \epsilon}$ would disprove the conjecture of Daniely et al. \cite{DLSS1} and would yield much better algorithms for refuting random $3$-SAT than we currently know, despite fifteen years of work on the subject.
This leaves open an important question. While there are no known algorithms for strongly refuting random $3$-SAT with $m = n^{3/2 - \epsilon}$ clauses, there are algorithms that work with roughly $m = n^{3/2}$ clauses \cite{COGL}. Do these algorithms have any implications for noisy tensor completion? We will adapt the algorithm of Coja-Oghlan, Goerdt and Lanka \cite{COGL} and embed it within the sum-of-squares hierarchy. In turn, this will give us a norm that we can use to solve noisy tensor completion which uses a polynomial factor fewer observations than known algorithms.
\section{Using Resolution to Bound the Rademacher Complexity}\label{sec:using}
\subsection{Pseudo-expectation}
Here we introduce the sum-of-squares hierarchy and will use it (at level six) to give a relaxation to the tensor nuclear norm. This will be the norm that we will use in proving our main upper bounds. First we introduce the notion of a pseudo-expectation operator from \cite{BKS1, BKS2, BS}:
\begin{definition}[Pseudo-expectation \cite{BKS1}]\label{def:pseudo-exp}
Let $k$ be even and let $P_k^{n'}$ denote the linear subspace of all polynomials of degree at most $k$ on $n'$ variables. A linear operator $\widetilde{\mathop{\bf E\/}}:P_k^{n'}\rightarrow \mathbb R$ is called a \emph{degree $k$ pseudo-expectation operator} if it satisfies the following conditions:
\begin{description}
\item(1) $\widetilde{\mathop{\bf E\/}}[1] = 1$ ({\em normalization})
\item(2) $\widetilde{\mathop{\bf E\/}}[P^2] \geq 0$, for any degree at most $k/2$ polynomial $P$ ({\em nonnegativity})
\end{description}
Moreover suppose that $p \in P_k^{n'}$ with $\mbox{deg}(p) = k'$. We say that $\widetilde{\mathop{\bf E\/}}$ satisfies the constraint $\{p = 0\}$ if $\widetilde{\mathop{\bf E\/}}[pq] = 0$ for every $q \in P_{k - k'}^{n'}$. And we say that $\widetilde{\mathop{\bf E\/}}$ satisfies the constraint $\{ p \geq 0\}$ if $\widetilde{\mathop{\bf E\/}}[p q^2] \geq 0$ for every $q \in P_{\lfloor (k-k')/2 \rfloor}^{n'}$.
\end{definition}
The rationale behind this definition is that if $\mu$ is a distribution on vectors in $\mathbb R^{n'}$ then the operator $\widetilde{\mathop{\bf E\/}}[p] = \mathop{\bf E\/}_{Y \leftarrow \mu}[p(Y)]$ is a degree $d$ pseudo-expectation operator for every $d$ \---- i.e. it meets the conditions of Definition~\ref{def:pseudo-exp}. However the converse is in general not true. We are now ready to define the norm that will be used in our upper bounds:
\begin{definition}[$SOS_k$ norm]\label{def:rnorm}
We let $\mathcal{K}_k$ be the set of all $X \in \mathbb R^{ n_1 \times n_2 \times n_3}$ such that there exists a degree $k$ pseudo-expectation operator on $P_k^{n_1 + n_2 + n_3}$ satisfying the following polynomial
constraints (where the variables are the $Y^{(a)}_i$'s)
\begin{enumerate}
\item[(a)] $\{ \sum_{i=1}^{n_1} (Y^{(1)}_i)^2 = n_1 \}$, $\{ \sum_{i=1}^{n_2} (Y^{(2)}_i)^2 = n_2 \}$ and $\{ \sum_{i=1}^{n_3} (Y^{(3)}_i)^2 = n_3 \}$
\item[(b)] $\{ (Y^{(1)}_i)^2 \leq C^2 \}$, $\{ (Y^{(2)}_i)^2 \leq C^2 \}$ and $\{ (Y^{(3)}_i)^2 \leq C^2 \}$ for all $i$ and
\item[(c)] $X_{i,j,k} = \widetilde{\mathop{\bf E\/}}[ Y^{(1)}_i Y^{(2)}_j Y^{(3)}_k ]$ for all $i,j$ and $k$.
\end{enumerate}
The {\em $SOS_k$ norm} of $X \in \mathbb R^{ n_1 \times n_2 \times n_3}$ which is denoted by $\|X\|_{\mathcal{K}_k}$ is the infimum over $\alpha$ such that $X/\alpha \in \calK_k$.
\end{definition}
The constraints in Definition~\ref{def:pseudo-exp} can be expressed as an $O(n^k)$-sized semidefinite program. This implies that given any set of polynomial constraints of the form $\{p = 0\}$, $\{p \geq 0\}$, one can efficiently find a degree $k$ pseudo-distribution satisfying those constraints if one exists. This is often called the {\em degree $k$ Sum-of-Squares algorithm} \cite{Sho, N, Las, P}. Hence we can compute the norm $ \|X\|_{\mathcal{K}_k}$ of any tensor $X$ to within arbitrary accuracy in polynomial time. And because it is a relaxation to the tensor nuclear norm which is defined analogously but over a distribution on $C$-incoherent vectors instead of a pseudo-distribution over them, we have that $\|X\|_{\mathcal{K}_k} \leq \|X\|_{{\mathcal{A}}} $ for every tensor $X$. Throughout most of this paper, we will be interested in the case $k = 6$.
\subsection{Resolution in $\mathcal{K}_6$}\label{sec:resolution}
Recall that any polynomial time computable norm with good Rademacher complexity with $m$ observations yields an algorithm for strong refutation with roughly $m$ clauses too. Here we will use an algorithm for strongly refuting random $3$-SAT to guide our search for an appropriate norm. We will adapt an algorithm due to Coja-Oghlan, Goerdt and Lanka \cite{COGL} that strongly refutes random $3$-SAT, and will instead give an algorithm that strongly refutes random $3$-XOR. Moreover each of the steps in the algorithm embeds into the sixth level of the sum-of-squares hierarchy by mapping resolution operations to applications of Cauchy-Schwartz, that ultimately show how the inequalities that define the norm (Definition~\ref{def:rnorm}) can be manipulated to give bounds on its own Rademacher complexity.
Let's return to the task of bounding the Rademacher complexity of $\| \cdot \|_{\mathcal{K}_6}$. Let $X$ be arbitrary but satisfy $\| X\|_{\mathcal{K}_6} \leq 1$. Then there is a degree six pseudo-expectation meeting the conditions of Definition~\ref{def:rnorm}. Using Cauchy-Schwartz we have:
\begin{equation}
\Big ( \langle Z, X \rangle \Big )^2 = \Big ( \sum_{i} \sum_{j,k} Z_{i,j,k} \widetilde{\mathop{\bf E\/}}[Y^{(1)}_i Y^{(2)}_j Y^{(3)}_k] \Big )^2 \leq n_1 \Big ( \sum_i \Big ( \sum_{j,k} Z_{i,j,k} \widetilde{\mathop{\bf E\/}}[Y^{(1)}_i Y^{(2)}_j Y^{(3)}_k] \Big )^2 \Big )\label{eq:sdgfdh}
\end{equation}
To simplify our notation, we will define the following polynomial
$$Q_{i,Z}(Y^{(2)}, Y^{(3)}) = \sum_{j,k} Z_{i,j,k} Y^{(2)}_j Y^{(3)}_k $$
which we will use repeatedly.
If $d$ is even then any degree $d$ pseudo-expectation operator satisfies the constraint $(\widetilde{\mathop{\bf E\/}}[p])^2 \leq \widetilde{\mathop{\bf E\/}}[p^2]$ for every polynomial $p$ of degree at most $d/2$ (e.g., see Lemma $A.4$ in \cite{BBH}). Hence the right hand side of (\ref{eq:sdgfdh}) can be bounded as:
\begin{equation}
n_1 \Big ( \sum_i \Big ( \widetilde{\mathop{\bf E\/}}[Y^{(1)}_i Q_{i,Z}(Y^{(2)}, Y^{(3)})] \Big )^2 \Big ) \leq n_1 \sum_i \widetilde{\mathop{\bf E\/}}\Big [\Big (Y^{(1)}_i Q_{i,Z}(Y^{(2)}, Y^{(3)}) \Big )^2 \Big]
\label{eq:bound-rad}
\end{equation}
It turns out that bounding the right-hand side of (\ref{eq:bound-rad}) boils down to bounding the spectral norm of the following matrix.
\begin{definition}\label{def:randmat}
Let $A$ be the $n_2 n_3 \times n_2 n_3$ matrix whose rows and columns are indexed over ordered pairs $(j,k')$ and $(j',k)$ respectively, defined as
$$A_{j,k',j',k} = \sum_{i} Z_{i,j,k} Z_{i,j',k'}$$
\end{definition}
We can now make the connection to resolution more explicit: We can think of a pair of observations $Z_{i,j,k}, Z_{i,j',k'}$ as a pair of $3$-XOR constraints, as usual. Resolving them (i.e. multiplying them) we obtain a $4$-XOR constraint $$x_j \cdot x_k \cdot x_{j'} \cdot x_{k'} = Z_{i,j,k}Z_{i,j',k'}$$ $A$ captures the effect of resolving certain pairs of $3$-XOR constraints into $4$-XOR constraints. The challenge is that the entries in $A$ are not independent, so bounding its maximum singular value will require some care. It is important that the rows of $A$ are indexed by $(j, k')$ and the columns are indexed by $(j', k)$, so that $j$ and $j'$ come from different $3$-XOR clauses, as do $k$ and $k'$, and otherwise the spectral bounds that we will want to prove about $A$ would simply not be true! This is perhaps the key insight in \cite{COGL}.
It will be more convenient to decompose $A$ and reason about its two types of contributions separately. To that end, we let $R$ be the $n_2 n_3 \times n_2 n_3$ matrix whose non-zero entries are of the form
$$R_{j,k,j,k} = \sum_{i} Z_{i,j,k} Z_{i,j,k}$$
and all of its other entries are set to zero. Then let $B$ be the $n_2 n_3 \times n_2 n_3$ matrix whose entries are of the form
$$B_{j,k',j',k} = \begin{cases}
0, \mbox{ if } j = j' \mbox{ and } k = k' \\
\sum_{i} Z_{i,j,k} Z_{i,j',k'} \mbox{ else }
\end{cases} $$
By construction we have $A = B + R$. Finally:
\begin{lemma}\label{lemma:schur2}
$$ \sum_i \widetilde{\mathop{\bf E\/}} \Big [\Big (Y^{(1)}_i Q_{i,Z}(Y^{(2)}, Y^{(3)}) \Big )^2 \Big] \leq C^2 n_2 n_3 \|B\| + C^6 m $$
\end{lemma}
\begin{proof}
The pseudo-expectation operator satisfies $\{ (Y^{(1)}_i)^2 \leq C^2 \}$ for all $i$, and hence we have
$$\sum_i \widetilde{\mathop{\bf E\/}}\Big [\Big (Y_i Q_{i,Z}(Y^{(2)}, Y^{(3)}) \Big )^2 \Big] \leq C^2 \sum_i \widetilde{\mathop{\bf E\/}}\Big [\Big ( Q_{i,Z}(Y^{(2)}, Y^{(3)}) \Big )^2 \Big] = C^2 \sum_i \sum_{j,k,j',k'} \widetilde{\mathop{\bf E\/}}\Big [ Z_{i,j,k} Z_{i,j',k'} Y^{(2)}_j Y^{(3)}_k Y^{(2)}_{j'} Y^{(3)}_{k'}\Big]$$
Now let $Y^{(2)} \in \mathbb R^{n_2}$ be a vector of variables where the $i$th entry is $Y^{(2)}_i$ and similarly for $Y^{(3)}$. Then we can re-write the right hand side as a matrix inner-product:
$$C^2\sum_i \sum_{j,k,j',k'} Z_{i,j,k} Z_{i,j',k'} \widetilde{\mathop{\bf E\/}}[ Y^{(2)}_j Y^{(3)}_k Y^{(2)}_{j'} Y^{(3)}_{k'}] = C^2 \langle A, \widetilde{\mathop{\bf E\/}}[(Y^{(2)} \otimes Y^{(3)}) (Y^{(2)} \otimes Y^{(3)})^T] \rangle$$
We will now bound the contribution of $B$ and $R$ separately.
\begin{claim}
$\widetilde{\mathop{\bf E\/}}[(Y^{(2)} \otimes Y^{(3)}) (Y^{(2)} \otimes Y^{(3)})^T]$ is positive semidefinite and has trace at most $ n_2 n_3$
\end{claim}
\begin{proof}
It is easy to see that a quadratic form on $\widetilde{\mathop{\bf E\/}}[(Y^{(2)} \otimes Y^{(3)}) (Y^{(2)} \otimes Y^{(3)})^T]$ corresponds to $\widetilde{\mathop{\bf E\/}}[p^2]$ for some $p \in P_2^{n_2 + n_3}$ and this implies the first part of the claim. Finally $$\mbox{Tr}(\widetilde{\mathop{\bf E\/}}[(Y^{(2)} \otimes Y^{(3)}) (Y^{(2)} \otimes Y^{(3)})^T]) = \sum_{j,k} \widetilde{\mathop{\bf E\/}}[(Y^{(2)}_j)^2 (Y^{(3)}_k)^2] \leq n_2 n_3$$
where the last equality follows because the pseudo-expectation operator satisfies the constraints $\{ \sum_{i=1}^{n_2} (Y^{(2)}_i)^2 = n_2 \}$ and $\{ \sum_{i=1}^{n_3} (Y^{(3)}_i)^2 = n_3 \}$.
\end{proof}
Hence we can bound the contribution of the first term as
$C^2 \langle B, \widetilde{\mathop{\bf E\/}}[(Y^{(2)} \otimes Y^{(3)}) (Y^{(2)} \otimes Y^{(3)})^T]] \rangle \leq C^2 n_2 n_3 \|B\|$.
Now we proceed to bound the contribution of the second term:
\begin{claim}\label{claim:jk}
$\widetilde{\mathop{\bf E\/}}[(Y^{(2)}_j)^2 (Y^{(3)}_k)^2] \leq C^4$
\end{claim}
\begin{proof}
It is easy to verify by direct computation that the following equality holds:
$$C^4 - (Y^{(2)}_j)^2 (Y^{(3)}_k)^2 = \Big (C^2 - (Y^{(2)}_j)^2 \Big ) \Big (C^2 - (Y^{(3)}_k)^2 \Big) + \Big (C^2 - (Y^{(3)}_k)^2\Big ) (Y^{(2)}_j)^2 + \Big (C^2 - (Y^{(2)}_j)^2 \Big )(Y^{(3)}_k)^2$$
Moreover the pseudo-expectation of each of the three terms above is nonnegative, by construction. This implies the claim.
\end{proof}
Moreover each entry in $Z$ is in the set $\{-1, 0, +1\}$ and there are precisely $m$ non-zeros. Thus the sum of the absolute values of all entries in $R$ is at most $m$. Now we have:
$$C^2 \langle R, \widetilde{\mathop{\bf E\/}}[(Y^{(2)} \otimes Y^{(3)}) (Y^{(2)} \otimes Y^{(3)})^T] \rangle \leq C^2 \sum_{j,k} R_{j, k, j, k} \widetilde{\mathop{\bf E\/}}[(Y^{(2)}_j)^2 (Y^{(3)}_k)^2] \leq C^6 m $$
And this completes the proof of the lemma.
\end{proof}
\section{Spectral Bounds}\label{sec:spectral}
Recall the definition of $B$ given in the previous section. In fact, for our spectral bounds it will be more convenient to relabel the variables (but keeping the definition intact):
$$B_{j,k,j',k'} = \begin{cases}
0, \mbox{ if } j = j' \mbox{ and } k = k' \\
\sum_{i} Z_{i,j,k'} Z_{i,j',k} \mbox{ else }
\end{cases} $$
\noindent Let us consider the following random process: For $r = 1, 2, ..., O(\log n)$ partition the set of all ordered triples $(i,j,k)$ into two sets $S_r$ and $T_r$. We will use this ensemble of partitions to define an ensemble of matrices $\{\mathsf{B}^r\}_{r =1}^{O(\log n)}$: Set $U_{i,j,k'}^r$ as equal to $Z_{i,j,k'}$ if $(i,j,k') \in S_r$ and zero otherwise. Similarly set $V_{i,j',k}^r$ equal to $Z_{i,j',k}$ if $(i,j',k) \in T_r$ and zero otherwise. Also let $E_{i,j,j',k,k',r}$ be the event that there is no $r' < r$ where $(i,j,k') \in S_{r'}$ and $(i,j',k) \in T_{r'}$ or vice-versa. Now let
$$\mathsf{B}^r_{j,k,j',k'} = \sum_{i} U_{i,j,k'}^r V_{i,j',k}^r \mathbbm{1}_{E}$$
where $\mathbbm{1}_E$ is short-hand for the indicator function of the event $E_{i,j,j',k,k',r}$. The idea behind this construction is that each pair of triples $(i,j,k')$ and $(i,j',k)$ that contributes to $B$ will be contribute to some $\mathsf{B}^r$ with high probability. Moreover it will not contribute to any later matrix in the ensemble. Hence with high probability $$B = \sum_{r = 1}^{O(\log n)} \mathsf{B}^r$$
Throughout the rest of this section, we will suppress the superscript $r$ and work with a particular matrix in the ensemble, $\mathsf{B}$. Now let $\ell$ be even and consider
$$\Tr(\underbrace{\mathsf{B} \mathsf{B}^T \mathsf{B} \mathsf{B}^T ... \mathsf{B} \mathsf{B}^T}_{\ell \mbox{ times }})$$
As is standard, we are interested in bounding $\mathop{\bf E\/}[\Tr(\mathsf{B} \mathsf{B}^T \mathsf{B}\mathsf{B}^T ... \mathsf{B} \mathsf{B}^T)]$ in order to bound $\|\mathsf{B}\|$. But note that $\mathsf{B}$ is {\em not} symmetric. Also note that the random variables $U$ and $V$ are not independent, however whether or not they are non-zero is non-positively correlated and their signs are mutually independent. Expanding the trace above we have
\begin{eqnarray*}
\Tr(\mathsf{B} \mathsf{B}^T \mathsf{B}\mathsf{B}^T ... \mathsf{B} \mathsf{B}^T) &=& \sum_{j_1, k_1} \sum_{j_2, k_2} ... \sum_{j_{\ell-1}, k_{\ell -1}} \mathsf{B}_{j_1,k_1,j_2, k_2} \mathsf{B}_{j_3, k_3, j_2, k_2} ... \mathsf{B}_{j_1,k_1, j_{\ell }, k_{\ell } }\\
&=& \sum_{j_1, k_1} \sum_{i_1} \sum_{j_2, k_2} \sum_{i_2} ... \sum_{j_{\ell }, k_{\ell }} \sum_{i_\ell} U_{i_1,j_1,k_2} V_{i_1,j_2,k_1} \mathbbm{1}_{E_1} U_{i_2,j_3,k_2} V_{i_2,j_2,k_3} \mathbbm{1}_{E_2}... U_{i_\ell,j_{1},k_\ell} V_{i_\ell,j_\ell,k_1}\mathbbm{1}_{E_\ell}
\end{eqnarray*}
where $\mathbbm{1}_{E_1}$ is the indicator for the event that the entry $\mathsf{B}_{j_1,k_1,j_2,k_2}$ is not covered by an earlier matrix in the ensemble, and similarly for $\mathbbm{1}_{E_2}, ..., \mathbbm{1}_{E_\ell}$.
Notice that there are $2 \ell$ random variables in the above sum (ignoring the indicator variables). Moreover if any $U$ or $V$ random variable appears an odd number of times, then the contribution of the term to $\mathop{\bf E\/}[\Tr(\mathsf{B} \mathsf{B}^T \mathsf{B}\mathsf{B}^T ... \mathsf{B} \mathsf{B}^T)]$ is zero. We will give an encoding for each term that has a non-zero contribution, and we will prove that it is injective.
Fix a particular term in the above sum where each random variable appears an even number of times. Let $s$ be the number of distinct values for $i$. Moreover let $i_1, i_2, ..., i_s$ be the order that these indices first appear. Now let $r^j_1$ denote the number of distinct values for $j$ that appear with $i_1$ in $U$ terms \---- i.e. $r^j_1$ is the number of distinct $j$'s that appear as $U_{i_1, j, *}$. Let $r^k_1$ denote the number of distinct values for $k$ that appear with $i_1$ in $U$ terms \---- i.e. $r^k_1$ is the number of distinct $k$'s that appear as or $U_{i_1, *, k}$. Similarly let $q^j_1$ denote the number of distinct values for $j$ that appear with $i_1$ in $V$ terms \---- i.e. $q^j_1$ is the number of distinct $j$'s that appear as $V_{i_1, j, *}$. And finally let $q^k_1$ denote the number of distinct values for $k$ that appear with $i_1$ in $V$ terms \---- i.e. $q^k_1$ is the number of distinct $k$'s that appear as $V_{i_1, *, k}$.
We give our encoding below. It is more convenient to think of the encoding as any way to answer the following questions about the term.
\begin{itemize}
\item[(a)] What is the order $i_1, i_2, ..., i_s$ of the first appearance of each distinct value of $i$?
\item[(b)] For each $i$ that appears, what is the order of each of the distinct values of $j$'s and $k$'s that appear along with it in $U$? Similarly, what is the order of each of the distinct values of $j$'s and $k$'s that appear along with it in $V$?
\item[(c)] For each step (i.e. a new variable in the term when reading from left to right),
has the value of $i$ been visited already? Also, has the value for $j$ or $k$ that appears along with $U$ been visited? Has the value for $j$ or $k$ that appears along with $V$ been visited? Note that whether or not $j$ or $k$ has been visited (together in $U$) depends on what the value of $i$ is, and if $i$ is a new value then the $j$ or $k$ value must be new too, by definition. Finally, if any value has already been visited, which earlier value is it?
\end{itemize}
Let $r_j = r^j_1 + r^j_2 + ... + r^j_s$ and $r_k = r^k_1 + r^k_2 + ... + r^k_s$. Similarly let $q_j = q^j_1 + q^j_2 + ... q^j_s$ and $q_k = q^k_1 + q^k_2 + ... q^k_s$. Then the number of possible answers to \textbf{$(a)$} and \textbf{$(b)$} is at most $n_1^s$ and $n_2^{r_j} n_3^{r_k} n_2^{q_j} n_3^{q_k}$ respectively. It is also easy to see that the number of answers to \textbf{$(c)$} that arise over the sequence of $\ell$ steps is at most $8^\ell (s( r_j + r_k)( q_j + q_k))^\ell$. We remark that much of the work on bounding the maximum eigenvalue of a random matrix is in removing any $\ell^\ell$ type terms, and so one needs to encode re-visiting indices more compactly. However such terms will only cost us polylogarithmic factors in our bound on $\|B\|$.
It is easy to see that this encoding is injective, since given the answers to the above questions one can simulate each step and recover the sequence of random variables. Next we establish some easy facts that allow us to bound $\mathop{\bf E\/}[\Tr(\mathsf{B} \mathsf{B}^T \mathsf{B}\mathsf{B}^T ... \mathsf{B} \mathsf{B}^T)]$.
\begin{claim}\label{claim1}
For any term that has a non-zero contribution to $\mathop{\bf E\/}[\Tr(\mathsf{B} \mathsf{B}^T \mathsf{B}\mathsf{B}^T ... \mathsf{B} \mathsf{B}^T)]$, we must have $s \leq \ell/2$ and $r_j + q_j + r_k + q_k \leq \ell$
\end{claim}
\begin{proof}
Recall that there are $2 \ell$ random variables in the product and precisely $\ell$ of them correspond to $U$ variables and $\ell$ of them to $V$ variables. Suppose that $s > \ell/2$. Then there must be at least one $U$ variable and at least one $V$ variable that occur exactly once, which implies that its expectation is zero because the signs of the non-zero entries are mutually independent. Similarly suppose $ r_j + q_j + r_k + q_k > \ell$. Then there must be at least one $U$ or $V$ variable that occurs exactly once, which also implies that its expectation is zero.
\end{proof}
\begin{claim}\label{claim2}
For any valid encoding, $s \leq r_j + q_j$ and $s \leq r_k+ q_k$.
\end{claim}
\begin{proof}
This holds because in each step where the $i$ variable is new and has not been visited before, by definition the $j$ variable is new too (for the current $i$) and similarly for the $k$ variable.
\end{proof}
Finally, if $s, r_j, q_j, r_k$ and $q_k$ are defined as above then for any contributing term
$$U_{i_1,j_1,k_2} V_{i_1,j_2,k_1} U_{i_2,j_3,k_2} V_{i_2,j_2,k_3} ... U_{i_\ell,j_{1},l_\ell} V_{i_\ell,j_\ell,k_1}$$
its expectation is at most $p^{r_j + r_k} p^{q_j + q_k}$ where $p = m/n_1 n_2 n_3$ because there are exactly $r_j + r_k$ distinct $U$ variables and $q_j + q_k$ distinct $V$ variables whose values are in the set $\{-1, 0, +1\}$ and whether or not a variable is non-zero is non-positively correlated and the signs are mutually independent.
This now implies the main lemma:
\begin{lemma}\label{lem:walks}
$\mathop{\bf E\/}[\Tr(\mathsf{B} \mathsf{B}^T \mathsf{B}\mathsf{B}^T ... \mathsf{B} \mathsf{B}^T)] \leq n_1^{\ell/2} (\max(n_2, n_3))^{\ell} p^\ell (\ell)^{3 \ell + 3}$
\end{lemma}
\begin{proof}
Note that the indicator variables only have the effect of zeroing out some terms that could otherwise contribute to $\mathop{\bf E\/}[\Tr(\mathsf{B} \mathsf{B}^T \mathsf{B}\mathsf{B}^T ... \mathsf{B} \mathsf{B}^T)]$. Returning to the task at hand, we have
$$\mathop{\bf E\/}[\Tr(\mathsf{B} \mathsf{B}^T \mathsf{B}\mathsf{B}^T ... \mathsf{B} \mathsf{B}^T)] \leq \sum_{s, r_j, r_k, q_j, q_k} n_1^s n_2^{r_j} n_3^{r_k} n_2^{q_j} n_3^{q_k} p^{r_j + r_k} p^{q_j + q_k} 8^\ell (s( r_j + r_k)( q_j + q_k))^\ell
$$
where the sum is over all valid triples $s, r_j, r_k, q_j, q_k$ and hence $s, r, q \leq \ell/2$ and $s \leq r_j + r_k$ and $s \leq q_j + q_k$ using Claim~\ref{claim1} and Claim~\ref{claim2}. We can upper bound the above as
\begin{eqnarray*}
\mathop{\bf E\/}[\Tr(\mathsf{B} \mathsf{B}^T \mathsf{B}\mathsf{B}^T ... \mathsf{B} \mathsf{B}^T)] &\leq& \sum_{s, r_j, r_k, q_j, q_k} n_1^s (pn_2)^{r_j + q_j} (pn_3)^{r_k + q_k} (\ell)^{3 \ell + 3} \\
&\leq& \sum_{s, r_j, r_k, q_j, q_k} n_1^s (p \max(n_2, n_3))^{r_j + q_j + r_k + q_k} (\ell)^{3 \ell + 3}
\end{eqnarray*}
Now if $p \max(n_2, n_3) \leq 1$ then using Claim~\ref{claim2} followed by the first half of Claim~\ref{claim1} we have:
$$\mathop{\bf E\/}[\Tr(\mathsf{B} \mathsf{B}^T \mathsf{B}\mathsf{B}^T ... \mathsf{B} \mathsf{B}^T)] \leq n_1^s (p \max(n_2, n_3))^{2s} (\ell)^{3 \ell + 3} \leq n_1^{\ell/2} (p \max(n_2, n_3))^{\ell} (\ell)^{3 \ell + 3}$$
where the last inequality follows because $p n_1^{1/2} \max(n_2, n_3) > 1$. Alternatively if $p \max(n_2, n_3) > 1$ then we can directly invoke the second half of Claim~\ref{claim1} and get:
$$\mathop{\bf E\/}[\Tr(\mathsf{B} \mathsf{B}^T \mathsf{B}\mathsf{B}^T ... \mathsf{B} \mathsf{B}^T)] \leq n_1^s (p \max(n_2, n_3))^\ell (\ell)^{3 \ell + 3} \leq n_1^{\ell/2} (p \max(n_2, n_3))^{\ell} (\ell)^{3 \ell + 3}$$
Hence $\mathop{\bf E\/}[\Tr(\mathsf{B} \mathsf{B}^T \mathsf{B}\mathsf{B}^T ... \mathsf{B} \mathsf{B}^T)] \leq n_1^{\ell/2}\max(n_2, n_3)^\ell p^\ell (\ell)^{3 \ell + 3}$ and this completes the proof.
\end{proof}
As before, let $n = \max(n_1, n_2, n_3)$. Then the last piece we need to bound the Rademacher complexity is the following spectral bound:
\begin{theorem}\label{thm:spectral}
With high probability, $\|B\| \leq O\Big( \frac{m \log^4 n}{n_1^{1/2}\min(n_2, n_3)} \Big)$
\end{theorem}
\begin{proof}
We proceed by using Markov's inequality:
$$
\Pr[\|\mathsf{B}\| \geq n_1^{1/2} \max(n_2, n_3) p (2 \ell)^3 ] = \Pr \Big [\|\mathsf{B}\|^\ell \geq \Big (n_1^{1/2}\max(n_2, n_3) p (2 \ell)^3 \Big )^\ell \Big ] \\
\leq \frac{\mathop{\bf E\/}[\Tr(\mathsf{B} \mathsf{B}^T \mathsf{B}\mathsf{B}^T ... \mathsf{B} \mathsf{B}^T)]}{n_1^{\ell/2}\max(n_2, n_3)^\ell p^{\ell} (2 \ell)^{3\ell}} \leq \frac{\ell^3}{2^{3 \ell}}
$$
and hence setting $\ell = \Theta(\log n)$ we conclude that $\|\mathsf{B}\| \leq 8 n_1^{1/2} \max(n_2, n_3) p \log^3 n$ holds with high probability. Moreover $B = \sum_{r =1}^{O(\log n)} \mathsf{B}^r$ also holds with high probability. If this equality holds and each $\mathsf{B}^r$ satisfies $\|\mathsf{B}^r\| \leq 8 n_1^{1/2}\max(n_2, n_3) p \log^3 n$, we have
$$\|B\| \leq \max_r O(\|\mathsf{B}^r\| \log n) = O\Big( \frac{m \log^4 n}{n_1^{1/2}\min(n_2, n_3)} \Big)$$ where we have used the fact that $p = m/n_1 n_2 n_3$. This completes the proof of the theorem.
\end{proof}
\subsection*{Proofs of Theorem~\ref{thm:predict} and Corollary~\ref{corr:inf2}}
We can now bound the Rademacher complexity of the norm that we get from the six level sum-of-squares relaxation to the tensor nuclear norm:
\begin{theorem}\label{thm:k6rad}
$R^m(\|\cdot\|_{\mathcal{K}_6}) \leq O\Big(\sqrt{\frac{ (n_1)^{1/2} (n_2 + n_3) \log^4 n}{ m} }\Big)$
\end{theorem}
\begin{proof} Consider any $X$ with $\|X\|_{\mathcal{K}_6} \leq 1$. Then using Lemma~\ref{lemma:schur2} and Theorem~\ref{thm:spectral} we have
$$\Big ( \langle Z, X \rangle \Big )^2 \leq n_1 \Big ( \sum_i \Big ( \sum_{j,k} Z_{i,j,k} X_{i,j,k} \Big )^2 \Big ) \leq C^2 n_1 n_2 n_3 \|B\| + C^6 m n_1 = O\Big( m n_1^{1/2} \max(n_2, n_3) \log^4 n + m n_1 \Big) $$
Recall that $Z$ was defined in Definition~\ref{def:Z}. The Rademacher complexity can now be bounded as
$$\frac{1}{m} (\langle Z, X \rangle ) \leq O\Big(\sqrt{\frac{ (n_1)^{1/2} (n_2 + n_3) \log^4 n}{ m } }\Big)$$
which completes the proof of the theorem.
\end{proof}
Recall that bounds on the Rademacher complexity readily imply bounds on the generalization error (see Theorem~\ref{thm:generalize}). We can now prove Theorem~\ref{thm:predict}:
\begin{proof}
We solve (\ref{eq:conv}) using the norm $\| \cdot \|_{\mathcal{K}_6}$. Since this norm comes from the sixth level of the sum-of-squares hierarchy, it follows that (\ref{eq:conv}) is an $n^6$-sized semidefinite program and there is an efficient algorithm to solve it to arbitrary accuracy. Moreover we can always plug in $X = T - \Delta$ and the bounds on the maximum magnitude of an entry in $\Delta$ together with the Chernoff bound imply that with high probability $X = T - \Delta$ is a feasible solution. Moreover $\|T - \Delta\|_{\mathcal{K}_6} \leq r^*$. Hence with high probability, the minimizer $X$ satisfies $\|X\|_{\mathcal{K}_6} \leq r^*$. Now if we take any such $X$ returned by the convex program, because it is feasible its empirical error is at most $2 \delta$. And since $\|X\|_{\mathcal{K}_6} \leq r^*$ the bounds on the Rademacher complexity (Theorem~\ref{thm:k6rad}) together with Theorem~\ref{thm:generalize} give the desired bounds on $\mbox{err}(X)$ and complete the proof of our main theorem.
\end{proof}
Finally we prove Corollary~\ref{corr:inf2}:
\begin{proof}
Our goal is to lower bound the absolute value of a typical entry in $T$. To be concrete, suppose that $\operatorname{var}(T_{i,j,k}) \geq f(r, n)$ for a $1-o(1)$ fraction of the entries where $f(r, n) = r^{1/2}/ \log^D n$.
Consider $T_{i,j,k}$, which we will view as a degree three polynomial in Gaussian random variables. Then the anti-concentration bounds of Carbery and Wright \cite{CW} now imply that $|T_{i,j,k}| \geq f(r, n)/\log n $ with probability $1 - o(1)$. With this in mind, we define
$$ \mathcal{R} = \{ (i, j, k) \mbox{ s.t. } |T_{i,j,k}| \geq f(r, n)/\log n\}$$
and it follows form Markov's bound that that $|\mathcal{R}| \geq (1 - o(1)) n_1 n_2 n_3$. Now consider just those entries in $\mathcal{R}$ which we get substantially wrong:
$$\mathcal{R}' = \{ (i, j, k) \mbox{ s.t. } (i, j, k) \in \mathcal{R} \mbox{ and } |X_{i,j,k} - T_{i,j,k}| \geq 1/\log n\}$$
We can now invoke Theorem~\ref{thm:predict} which guarantees that the hypothesis $X$ that results from solving (\ref{eq:conv}) satisfies $\mbox{err}(X) = o(1/\log n)$ with probability $1-o(1)$ provided that $m = \widetilde{\Omega}( n^{3/2} r )$. This bound on the error immediately implies that $|\mathcal{R}'| = o(n_1 n_2 n_3)$ and so $|\mathcal{R} \setminus \mathcal{R}'| = (1-o(1))n_1 n_2 n_3$. This completes the proof of the corollary.
\end{proof}
\section{Sum-of-Squares Lower Bounds}\label{sec:lb}
Here we will show strong lower bounds on the Rademacher complexity of the sequence of relaxations to the tensor nuclear norm that we get from the sum-of-squares hierarchy. Our lower bounds follow as a corollary from known lower bounds for refuting random instances of $3$-XOR \cite{G, Sch}. First we need to introduce the formulation of the sum-of-squares hierarchy used in \cite{Sch}: We will call a Boolean function $f$ a $k$-junta if there is set $S \subseteq [n]$ of at most $k$ variables so that $f$ is determined by the values in $S$.
\begin{definition}\label{def:constr1}
The $k$-round Lasserre hierarchy is the following relaxation:
\begin{enumerate}
\item[(a)] $\|v_0\|^2 = 1$, $\|v_C\|^2 = 1$ for all $C \in {\mathcal{C}}$
\item[(b)] $\langle v_f, v_g \rangle = \langle v_{f'}, v_{g'} \rangle$ for all $f, g, f', g'$ that are $k$-juntas and $f \cdot g \equiv f' \cdot g'$
\item[(c)] $v_f + v_g = v_{f + g}$ for all $f, g$ that are $k$-juntas and satisfy $f \cdot g \equiv 0$
\end{enumerate}
\end{definition}
\noindent Here we define a vector $v_f$ for each $k$-junta, and ${\mathcal{C}}$ is a class of constraints that must be satisfied by any Boolean solution (and are necessarily $k$-juntas themselves). See \cite{Sch} for more background, but it is easy to construct a feasible solution to the above convex program given a distribution on feasible solutions for some constraint satisfaction problem. In the above relaxation, we think of functions $f$ as being $\{0, 1\}$-valued. It will be more convenient to work with an intermediate relaxation where functions are $\{-1, 1\}$-valued and the intuition is that $u_S$ for some set $S \subseteq [n]$ should correspond to the vector for the character $\chi_S$.
\begin{definition}\label{def:constr2}
Alternatively, the $k$-round Lasserre hierarchy is the following relaxation:
\begin{enumerate}
\item[(a)] $\|u_\emptyset \|^2 = 1$, $\langle u_{\emptyset}, u_S \rangle = (-1)^{Z_S}$ for all $(\oplus_S, Z_S) \in {\mathcal{C}}$
\item[(b)] $\langle u_S, u_T \rangle = \langle u_{S'}, u_{T'} \rangle$ for sets $S, T, S', T'$ that are size at most $k$ and satisfy $S \Delta T = S' \Delta T'$, where $\Delta$ is the symmetric difference.
\end{enumerate}
\end{definition}
\noindent Here we have explicitly made the switch to XOR-constraints \---- namely $(\oplus_S, Z_S)$ has $Z_S \in \{0, 1\}$ and correspond to the constraint that the parity on the set $S$ is equal to $Z_S$. Now if we have a feasible solution to the constraints in Definition~\ref{def:constr1} where all the clauses are XOR-constraints, we can construct a feasible solution to the constraints in Definition~\ref{def:constr2} as follows. If $S$ is a set of size at most $k$, we define $$u_S \equiv v_g - v_f$$ where $f$ is the parity function on $S$ and $g = 1 - f$ is its complement. Moreover let $u_\emptyset = v_0$.
\begin{claim}\label{claim:red1}
$\{u_S\}$ is a feasible solution to the constraints in Definition~\ref{def:constr2}
\end{claim}
\begin{proof}
Consider Constraint $(b)$ in Definition~\ref{def:constr2}, and let $S, T, S', T'$ be sets of size at most $k$ that satisfy $S \oplus T = S' \oplus T'$. Then our goal is to show that
$$ \langle v_{g_S} - v_{f_S}, v_{g_T} - v_{f_T} \rangle = \langle v_{g_{S'}} - v_{f_{S'}}, v_{g_{T'}} - v_{f_{T'}} \rangle$$
where $f_S$ is the parity function on $S$, and similarly for the other functions. Then we have $f_S \cdot f_T \equiv f_{S'} \cdot f_{T'}$ because $S \oplus T = S' \oplus T'$, and this implies that $\langle v_{f_S}, v_{f_T} \rangle = \langle v_{f_{S'}}, v_{f_{T'}} \rangle$. An identical argument holds for the other terms. This implies that all the Constraints $(b)$ hold. Similarly suppose $(\oplus_S, Z_S) \in {\mathcal{C}}$. Since $f_S \cdot g_S \equiv 0$ and $f_S + g_S \equiv 1$ it is well-known that $(1)$ $ v_{f_S}$ and $v_{g_S}$ are orthogonal $(2)$ $v_{f_S} + v_{g_S} = v_0$ and $(3)$ since $f_S \in {\mathcal{C}}$ in Definition~\ref{def:constr1}, we have $v_{g_S} = 0$ (see \cite{Sch}). Thus $$\langle u_\emptyset, u_S \rangle = \langle v_0, v_{g_S} \rangle - \langle v_0, v_{f_S} \rangle = -1$$ and this completes the proof.
\end{proof}
Now following Barak et al. \cite{BBH} we can use the constraints in Definition~\ref{def:constr2} to define the operator $\widetilde{\mathop{\bf E\/}}[\cdot]$. In particular, given $p \in P_k^n$ where $p \equiv \sum_S c_S \prod_{i \in S} Y_i$ and $p$ is multilinear, we set $$\widetilde{\mathop{\bf E\/}}[p)] = \sum_S c_S \langle u_\emptyset, u_S \rangle$$ Here we will also need to define $\widetilde{\mathop{\bf E\/}}[p]$ when $p$ is not multilinear, and in that case if $Y_i$ appears an even number of times we replace it with $1$ and if it appears an odd number of times we replace it by $ Y_i$ to get a multilinear polynomial $q$ and then set $\widetilde{\mathop{\bf E\/}}[p] = \widetilde{\mathop{\bf E\/}}[q]$.
\begin{claim}\label{claim:red2}
$\widetilde{\mathop{\bf E\/}}[\cdot]$ is a feasible solution to the constraints in Definition~\ref{def:rnorm}, and for any $(\oplus_S, Z_S) \in {\mathcal{C}}$ we have $\widetilde{\mathop{\bf E\/}}[\prod_{i \in S} Y_i] = (-1)^{Z_S} $.
\end{claim}
\begin{proof}
Then by construction $\widetilde{\mathop{\bf E\/}}[1] = 1$, and the proof that $\widetilde{\mathop{\bf E\/}}[p^2] \geq 0$ is given in \cite{BBH}, but we repeat it here for completeness. Let $p = \sum_S c_S \prod_{i \in S} Y_i$ be multilinear where we follow the above recipe and replace terms of the form $Y_i^2$ with $(1/n)$ as needed.
Then $p^2 = \sum_{S,T} c_S c_T \prod_{i \in S} Y_i \prod_{i \in T} Y_i$
and moreover
\begin{eqnarray*}
\widetilde{\mathop{\bf E\/}}[p^2] &=& \sum_{S, T} c_S c_T \langle u_\emptyset, u_{S \Delta T} \rangle = \sum_{S, T} c_S c_T \langle u_S, u_{T} \rangle = \Big \| \sum_S c_S u_S \Big \|^2 \geq 0
\end{eqnarray*}
as desired. Next we must verify that $\widetilde{\mathop{\bf E\/}}[\cdot]$ satisfies the constraints $\{\sum_{i = 1}^n Y_i^2 = n\}$ and $\{Y_i^2 \leq C^2\}$ for all $i \in \{1, 2, ..., n\}$, in accordance with Definition~\ref{def:pseudo-exp}. To that end, observe that
$$\widetilde{\mathop{\bf E\/}}\Big[\Big(\sum_{i=1}^n Y_i^2 - n \Big) q\Big] = 0$$
which holds for any polynomial $q \in P_{k - 2}^n$. Finally consider
$$\widetilde{\mathop{\bf E\/}}\Big[ \Big(C^2 - Y_i^2\Big) q^2\Big ] = \widetilde{\mathop{\bf E\/}}\Big[ \Big(C^2 - 1 \Big) q^2\Big ] \geq 0$$
which follows because $C^2 \geq 1$ and holds for any polynomial $q \in P_{\lfloor (d-d')/2 \rfloor}^n$. This completes the proof.
\end{proof}
\begin{theorem}\cite{G, Sch}
Let $\phi$ be a random $3$-XOR formula on $n$ variables with $m = n^{3/2 - \epsilon}$ clauses. Then for any $\epsilon > 0$ and any $c < 2$, the $k = \Omega(n^{c \epsilon})$ round Lasserre hierarchy given in Definition~\ref{def:constr1} permits a feasible solution, with probability $1 - o(1)$.
\end{theorem}
\noindent Note that the constant in the $\Omega(\cdot)$ depends on $\epsilon$ and $c$. Then using the above reductions, we have the following as an immediate corollary:
\begin{corollary}\label{corr:3lb}
For any $\epsilon > 0$ and any $c < 2$ and $k = \Omega(n^{c \epsilon})$, if $m = n^{3/2 - \epsilon}$ the Rademacher complexity $R^m(\| \cdot \|_{\mathcal{K}_k}) =1 - o(1)$.
\end{corollary}
\noindent Thus there is a sharp phase transition (as a function of the number of observations) in the Rademacher complexity of the norms derived from the sum-of-squares hierarchy. At level six,
$R^m(\|\cdot\|_{\mathcal{K}_6}) = o(1)$ whenever $m = \omega(n^{3/2} \log^4 n)$. In contrast, $R^m(\|\cdot\|_{\mathcal{K}_k}) = 1- o(1)$ when $m = n^{3/2 - \epsilon}$ even for very strong relaxations derived from $n^{2 \epsilon}$ rounds of the sum-of-squares hierarchy. These norms require time $2^{n^{2 \epsilon}}$ to compute but still achieve essentially no better bounds on their Rademacher complexity.
\subsection*{Acknowledgements}
We would like to thank Aram Harrow for many helpful discussions.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 7,250 |
\section*{Author summary}
\section{Introduction}
Effective response to disease outbreaks depends on reliable estimates of their status.
This process of identifying new outbreaks and monitoring ongoing ones — \vocab{disease surveillance} — is a critical tool for policy makers and public health professionals~\cite{horstmann1974}.
The traditional practice of disease surveillance is based upon gathering information from in-person patient visits.
Clinicians make a diagnosis and report that diagnosis to the local health department.
These health departments aggregate the reports to produce local assessments and also pass information further up the government hierarchy to the national health ministry, which produces national assessments~\cite{mondor2012}.
Our previous work describes this process with a mathematical model~\cite{priedhorsky2018flow}.
This approach is accepted as sufficient for decision-making~\cite{johnson2004, rolfes2018annual} but is expensive, and results lag real time by anywhere from a week~\cite{cdc2016} to several months~\cite{bahk2015comparing, jajosky2004}.
Novel surveillance systems that use disease-related internet activity traces such as social media posts, web page views, and search queries are attractive because they would be faster and cheaper~\cite{priedhorsky2017cscw, santillana2015}.
One can conjecture that an increase of influenza-related web searches is due to an increase in flu observations by the public, which in turn corresponds to an increase in real influenza activity.
These systems use statistical techniques to estimate a mapping from past activity to past traditional surveillance data, then apply that map to current activity to predict current (but not yet available) traditional surveillance data, a process known as \vocab{nowcasting}.
\begin{figure}
\includegraphics[width=\textwidth]{us_ili_and_deceptive.pdf}
\caption{
\caphead{Simple deceptive models for influenza-like illness (ILI)}
This figure shows five one-feature models that map U.S.\ Google volume for contagiousness-related searches to ILI data from the CDC (``how long are you contagious'', ``flu contagious'', ``how long am i contagious'', ``influenza contagious'', ``when are you contagious'').
We fit using ordinary least squares linear regression over the first three seasons of the study period.
Despite a good fit during the training period, these models severely overestimate the peaks of the fourth and fifth seasons, demonstrating that a model's history of accuracy does not yield accurate predictions in the future if it uses deceptive input features, such as these contagiousness searches.
Our \vocab{deceptiveness} metric quantifies the risk of such divergence.
}
\label{fig:us-ili-deceptive}
\end{figure}
One specific concern with this approach is that these models can learn coincidental, rather than informative, relationships~\cite{priedhorsky2018flow}.
For example, Bodnar and Salathé found a correlation between zombie-related Twitter messages and influenza~\cite{bodnar2013}.
More quantitatively, Ginsberg \etal\ built a flu model using search queries selected from 50~million candidates by a purely data-driven process that considered correlation with influenza-like-illness in nine regions of the United States~\cite{ginsberg2008}.
Of the 45 queries selected by the algorithm for inclusion in the model, 6~(13\%) were only weakly related to influenza (3~categorized as ``antibiotic medication'', 2~``symptoms of an unrelated disease'', 1~``related disease'').
Of the 55 next-highest-scoring candidates, 8~(15\%) were weakly related (3, 2, and 3 respectively) and 19~(35\%) were ``unrelated to influenza'', e.g. ``high school basketball''.
That is, even using a high-quality, very computationally expensive approach that leveraged demonstrated historical correlation in nine separate geographic settings, one-third of the top 100 features were weakly related or not related to the disease in question.
\Figure{fig:us-ili-deceptive} illustrates this problem for flu using contagiousness-related web searches.
Such features, with a dubious real link to the quantity of interest, pose a risk that the model may perform well during training but then provide erroneous estimates later when coincidental relationships fail, especially if they do so suddenly.
We have previously proposed a metric called \vocab{deceptiveness} to quantify this risk~\cite{priedhorsky2018flow}.
This metric quantifies the fraction of an estimate that depends on noise (coincidental relationships between input and output data) rather than signal (informative relationships) and is a real number between 0 and 1 inclusive.
We hypothesize that disease nowcasting models that leverage the deceptiveness of input features have better accuracy than those that do not.
This is an important question because disease forecasting is improved by better nowcasting.
For example, Brooks \etal's top-performing entry~\cite{brooks2018nonmechanistic} to the CDC's flu forecasting challenge~\cite{cdcchallenge2017} was improved by nowcasting.
Lu \etal\ tested autoregressive nowcasts using several internet data sources and found that they improved 1-week-ahead forecasts~\cite{lu2018accurate}.
Kandula \etal\ measured the benefit of nowcasting to their flu forecasting model at 8–35\%~\cite{kandula2018evaluation}.
Finally, our own work shows that a Bayesian seasonal flu forecasting model using ordinary differential equations benefits from filling a one-week reporting delay with internet-based nowcasts~\cite{osthus2018good}.
The present work tests this hypothesis using five seasons of influenza-like-illness (ILI) in the United States (2011–2016).
We selected U.S.\ influenza because high-quality reference data are easily available and because it is a pathogen of great interest to the public health community.
Although flu is often considered a mild infection, it can be quite dangerous for some populations, including older adults, children, and people with underlying health conditions.
Typical U.S.\ flu seasons kill ten to fifty thousand people annually~\cite{rolfes2018annual}.
Our experiment is a simulation study followed by validation using real data.
This lets us test our approach using fully-known deceptiveness as well as a more realistic setting with estimated deceptiveness.
We trained linear estimation models to nowcast ILI using an extension of ridge regression~\cite{hoerl1970} called \vocab{generalized ridge}~\cite{hemmerle1975gridge} or \vocab{gridge regression} that lets us apply individual weights to each feature, thus expressing a prior belief on their value: higher value for lower deceptiveness.
We used three classes of input features:
(1)~synthetic features constructed by adding plausible noise patterns to ILI,
(2)~Google search volume on query strings related to influenza,
and (3)~Google search volume on inferred topics related to influenza.
We found that accurate deceptiveness knowledge did indeed reduce prediction error, and in the case of the automatically-generated query string features, as much or more than topic features that require human curation. We also found that semantic distance as derived from the Wikipedia article category tree served as a useful proxy for deceptiveness.
The remainder of this paper is organized as follows.
We next describe our data sources, regression approach, and experiment structure.
After that, we describe our results and close with their implications and suggestions for future work.
\section{Methods}
Our study period was five consecutive flu seasons, 2011–2012 through 2015–2016, using weekly data.
The first week in the study was the week starting Sunday, July 3, 2011, and the last week started Sunday, June 26, 2016, for a total of 261 consecutive weeks.
We considered each season to start on the first Sunday in July, and the previous season to end on the day before (Saturday).
We used gridge regression to fit input features to U.S.\ ILI over a subset of the first three seasons, then used the fitted coefficients to estimate ILI in the fourth and fifth seasons.
(We used this training schedule, rather than training a new model for each week as one might do operationally, in order to provide a more challenging setting to better differentiate the models.)
We assessed accuracy by comparing the estimates to ILI using three metrics: $r^2$ (the square of Pearson correlation), root mean squared error (RMSE), and hit rate.
The experiment is a full factorial experiment with four factors, yielding a total of 225 models:
\begin{enumerate}
\item \inhead{Class of input features} (3 levels): synthetic features, search query string volume, and search topic volume.
\item \inhead{Training period} (3): one, two, or three consecutive seasons.
\item \inhead{Noise added to deceptiveness} (5): perfect knowledge of deceptiveness to none at all.
\item \inhead{Model type} (5): ridge regression and four levels of gridge regression.
\end{enumerate}
This procedure is implemented in a Python program.
The remainder of this section describes our data sources, regression algorithm, experimental factors, and assessment metrics in detail.
\subsection{Data sources}
We used four types of data in this experiment:
\begin{enumerate}
\item \inhead{Reference data.}
U.S.\ national ILI from the Centers for Disease Control and Prevention (CDC).
This is a weekly estimate of influenza incidence.
\item \inhead{Synthetic features.}
Weekly time series computed by adding specific types of systematic and random noise to ILI.
These simulated features have known deceptiveness.
\item \inhead{Flu-related concepts.}
We used the crowdsourced Wikipedia category tree to enumerate a set of concepts and estimate the semantic relatedness of each to influenza.
\item \inhead{Real features.}
Two types of weekly time series: Google search query strings and Google search topics.
These features are based on the flu-related concepts above and use estimated flu relatedness as a proxy for deceptiveness.
\end{enumerate}
This section explains the format and quirks of the data, how we obtained them, and how readers can also obtain them.
\subsubsection{Reference data: U.S.\ influenza-like illness (ILI) from CDC}
\vocab{Influenza-like illness} (ILI) is a syndromic metric that estimates influenza \vocab{incidence}, i.e., the number of new flu infections.
It is the fraction of patients presenting to the health care system who have symptoms consistent with flu and no alternate explanation~\cite{cdc2016}.
The basic process is that certain clinics called \vocab{sentinel providers} report the total number of patients seen during each interval along with those diagnosed with ILI.
Local, provincial, and national governments then collate these data to produce corresponding ILI reports~\cite{cdc2016}.
U.S.\ ILI values tend to range between 1–2\% during the summer and 7–8\% during a severe flu season~\cite{cdc2016, cdc2018percentage}.
While an imperfect measure (for example, it is subject to reporting and behavior biases if some groups, like children, are more commonly seen for ILI~\cite{lee2015detecting}), it is considered sufficiently accurate for decision-making purposes by the public health community~\cite{johnson2004, rolfes2018annual}.
In this study, we used weekly U.S.\ national ILI downloaded from the Centers for Disease Control and Prevention (CDC)'s FluView website~\cite{cdc2017fluview} on December 21, 2016, six months after the end of the study period.
This delay is enough for reporting backfill to settle sufficiently~\cite{osthus2018good}.
\Figure{fig:us-ili-deceptive} illustrates these data, and they are available as an Excel spreadsheet in S1~Dataset\ (\code{ILI.xls}).
\subsubsection{Synthetic features: Computed by us}
\label{sec:features-synthetic}
These simulated features are intended to model a plausible way in which internet activity traces with varying usefulness might arise.
Their purpose is to provide an experimental setting with features that are sufficiently realistic and have known deceptiveness.
\begin{figure}
\includegraphics[width=\textwidth]{bases.pdf}
\caption{
\caphead{Systematic noise basis functions for synthetic features}
These functions model plausible mechanisms of how features are affected by exogenous events.
}
\label{fig:bases}
\end{figure}
Each synthetic feature $x$ is a random linear combination of ILI $y$, Gaussian random noise $\varepsilon$, and systematic noise $\sigma$ (all vectors with 261 elements, one for each week):
\begin{align}
x &= w_\text{i} y + w_\text{r} \varepsilon + w_\text{s} \sigma \\
\label{eq:three-1}
1 &= w_\text{i} + w_\text{r} + w_\text{s}
\end{align}
A feature's deceptiveness $g \in [0,1]$ is simply the weight of its systematic noise: $g = w_\text{s}$.
Random noise $\varepsilon$ is a random multivariate normal vector with standard deviation 1.
Systematic noise $\sigma$ is a random linear combination of seven basis functions $\sigma_j$:
\begin{align}
w_\text{s} \sigma &= \sum_{j=1}^7 w_{\text{s}j} \sigma_j \\
w_\text{s} &= \sum_{j=1}^7 w_{\text{s}j}
\end{align}
These basis functions, illustrated in \Figure{fig:bases}, simulate sources of systematic noise for internet activity traces.
They fall into three classes:
\begin{itemize}
\item \inhead{Oprah effect~\cite{priedhorsky2018flow}:} 3 types.
These simulate pulses of short-lived traffic driven by media interest.
For example, U.S.\ Google searches for measles were 10 times higher in early 2015 than any other time during the past five years~\cite{google2017trends}, but measles incidence peaked in 2014~\cite{cdc2018measles}.
The three specific bases are: \vocab{annual}~$\sigma_1$, a pulse every year shortly after the flu season peak; \vocab{fore}~$\sigma_2$, pulses during both the training and test seasons (second, fourth, and fifth); and \vocab{late}~$\sigma_3$, pulses only during the test seasons (fourth and fifth).
The last creates features with novel divergence after training is complete, producing deceptive features that cannot be detected by correlation with reference data.
\item \inhead{Drift:} 2 types.
These simulate steadily changing public interest.
For example, as the case definition of autism was modified, the number of individuals diagnosed with autism increased~\cite{hill2015}.
The two bases are: \vocab{steady}~$\sigma_4$, a slow change over the entire study period of five seasons, and \vocab{late}~$\sigma_5$, a transition from one steady state to another over the fourth season.
The latter again models novel divergence.
%
%
\item \inhead{Cycle:} 2 types.
This simulates phenomena that have an annual ebb and flow correlating with the flu season.
An example is the U.S.\ basketball season noted above.
The two bases are: \vocab{annual}~$\sigma_6$, cycles continuing for all five seasons, and \vocab{ending}~$\sigma_7$, cycles that end after the training seasons.
The latter again models novel divergence.
\end{itemize}
In order to build one feature, we need to sample the nine elements of the weight vector $w = ( w_\text{i}, w_\text{r}, w_{\text{s}1}, ...\, w_{\text{s}7} )$, which sums to 1.
This three-step procedure is as follows.
First, $w_\text{i}$, $w_\text{r}$, and $w_\text{s}$ are sampled from a Dirichlet distribution:
\begin{gather}
(w_\text{i}, w_\text{r}, w_\text{s}) \sim \text{Dir}(1.0, 0.5, 1.5) \\
\text{E}(w_\text{i}) = \frac{1}{3} \quad , \quad
\text{E}(w_\text{r}) = \frac{1}{6} \quad , \quad
\text{E}(w_\text{s}) = \frac{1}{2}
\end{gather}
Next, the relative weight of the three types of systematic noise is sampled:
\begin{align}
(w_\text{so}, w_\text{sd}, w_\text{sc})
&\sim w_\text{s} \text{Dir}(0.3,0.3,0.3)
\end{align}
Finally, all the weight for each type is randomly assigned with equal probability to a single basis function:
\begin{align}
(w_{\text{s}1}, w_{\text{s}2}, w_{\text{s}3})
&\sim w_\text{so} \text{Multinomial}(1, [\frac{1}{3}, \frac{1}{3}, \frac{1}{3}]) \\
(w_{\text{s}4}, w_{\text{s}5})
&\sim w_\text{sd} \text{Multinomial}(1, [\frac{1}{2}, \frac{1}{2}]) \\
(w_{\text{s}6}, w_{\text{s}7})
&\sim w_\text{sc} \text{Multinomial}(1, [\frac{1}{2}, \frac{1}{2}]) \\
\end{align}
\begin{figure}
\includegraphics[width=\textwidth]{synthetic_examples.pdf}
\caption{
\caphead{Example synthetic features}
This figure shows the least and most deceptive features and a third with medium deceptiveness.
}
\label{fig:synthetic-examples}
\end{figure}
\begin{figure}
\includegraphics[width=\textwidth]{decept_hist.pdf}
\caption{
\caphead{Deceptiveness histogram for all three feature types}
Synthetic features have continuous deceptiveness and are grouped into ten bins, while the two types of search features have seven discrete deceptiveness levels.
}
\label{fig:decept-all}
\end{figure}
This procedure yields a variety of high- and low-quality synthetic features.
We sampled 500 of them.
\Figure{fig:synthetic-examples} shows three examples, and \Figure{fig:decept-all} shows the deceptiveness histogram.
The features we used are available in S3~Dataset\ (\code{synthetic.xlsx}).
\subsubsection{Flu-related concepts: Wikipedia}
\label{sec:flu-concepts}
In order to build the flu nowcasting model based on web search queries described in the next section, we first needed a set of influenza-related concepts.
We used the Wikipedia inter-article link graph to generate a set of candidate concepts and the Wikipedia article category hierarchy to estimate the semantic relatedness of each concept to influenza, which we use as a proxy for deceptiveness.
An important advantage of this approach is that it is automated and easily generalizable to other diseases.
Wikipedia is a popular web-based encyclopedia whose article content and metadata are crowdsourced~\cite{ayers2008}.
We used two types of metadata from a dataset~\cite{priedhorsky2017cscwdata} collected March 24, 2016 for our previous work~\cite{priedhorsky2017cscw} using the Wikipedia API.
First, Wikipedia articles contain many hyperlinks to other articles within the encyclopedia.
This work used the article ``Influenza'' and the 572 others it links to, including clearly related articles such as ``Infectious disease'' and apparently unrelated ones such as ``George W.\ Bush'', who was the U.S.\ president immediately prior to 2009 H1N1.
Second, Wikipedia articles are leaves in a category hierarchy.
Both articles and categories have one or more parent categories.
For example, one path from ``Influenza'' to the top of the tree is: \emph{Healthcare-associated infections}, \emph{Infectious diseases}, \emph{Diseases and disorders}, \emph{Health}, \emph{Main topic classifications}, \emph{Articles}, and finally \emph{Contents}.
This tree can be used to estimate semantic relatedness between two articles.
The number of levels one must climb the tree before finding a common category is a metric called \vocab{category distance}~\cite{priedhorsky2017cscw}; the distance between an article and itself is 1.
For example, the immediate categories of ``Infection'' include \emph{Infectious diseases}.
Thus, the distance between these two articles is~2, because we had to ascend two levels from ``Influenza'' before discovering the common category \emph{Infectious diseases}.
We used category distance between each of the 573 articles and ``Influenza'' to estimate the semantic relatedness to influenza.
The minimum category distance was 1 and the maximum 7.
The basic intuition for this approach is that Wikipedia category distance is a reasonable proxy for how related a concept is to influenza, and this relatedness is in turn a reasonable proxy for deceptiveness.
For example, consider a distance-1 feature and a distance-7 feature that are both highly correlated with ILI.
Standard linear regression will give equal weight to both features.
However, we conjecture that the distance-7 feature's correlation is more likely to be spurious than the distance-1's; i.e., we posit that the distance-7 feature is more deceptive.
Thus, we give the distance-1 feature more weight in the regression, as described below.
Because category distance is a discrete variable $d \in [1,7] \cap \mathbb{Z}$, while deceptiveness $g \in [0,1]$ is continuous, we convert category distance into a deceptiveness estimate $\hat g$ as follows:
\begin{equation}
\hat g = (1-2\epsilon) \frac{d-1}{6} + \epsilon
\end{equation}
The purpose of $\epsilon \ne 0$ is to ensure that features with minimum category distance of~1 receive regularization from the linear regression, as described below.
In our initial data exploration, the value of $\epsilon$ had little effect, so we used $\epsilon = 0.05$; therefore, $\hat g \in \{ 0.05, 0.20, 0.35, 0.50, 0.65, 0.80, 0.95 \}$.
We emphasize that category distance is already a noisy proxy for deceptiveness.
Even with zero noise added to deceptiveness, $\hat g \ne g$.
It is important to realize that because Wikipedia is continually edited, metadata such as links and categories change over time.
Generally, mature topic areas such as influenza and infectious disease are more stable than, for example, current events.
The present study assumes that the dataset we used is sufficiently correct despite its age; i.e., freshly collected links and categories might be somewhat different but not necessarily more correct.
The articles used and their category distances are in S2~Dataset\ (\code{en+Influenza.xlsx}).
\subsubsection{Real features: Google searches}
\label{sec:features-search}
Typically, each feature for internet-based disease surveillance estimates public interest in a specific concept.
This study uses Google search volume as a measure of public interest.
By mapping our Wikipedia-derived concepts to Google search queries, we obtained a set of queries with estimated deceptiveness.
Then, search volume over time for each of these queries, as well as their deceptiveness, are input for our algorithms.
We tested two types of Google searches.
\vocab{Search query strings} are the raw strings typed into the Google search box.
We designed an automated procedure to generate query strings from Wikipedia article titles.
\vocab{Search topics} are concepts assigned to searches by Google using proprietary and unspecific algorithms.
We built a map from Wikipedia article titles to topics manually.
Our procedure to map articles to query strings is:
\begin{enumerate}
\item Decode the percent notation in the title portion of the article's URL~\cite{wikipedia2018percent}.
\item Change underscores to spaces.
\item Remove parentheticals.
\item Approximate non-ASCII characters with ASCII using the Python package \code{unidecode}~\cite{solc2018}.
\item Change upper case letters to lower case. (This serves a simplifying rather than necessary purpose, as the Google Trends API is case-insensitive.)
\item Remove all characters other than alphanumeric, slash, single quote, space, and hyphen.
\item
Remove \vocab{stop phrases} we felt were unlikely to be typed into a search box.
Matches for the following regular expressions were removed (note leading and trailing spaces):
\begin{itemize}
\item ``\code{ and\b}''
\item ``\code{^global }''
\item ``\code{^influenza .? virus subtype }''
\item ``\code{^list of }''
\item ``\code{^the }''
\end{itemize}
\end{enumerate}
This produces a query string for all 573 articles.
The map is 1-to-1: each article maps to exactly one query string, and each query string maps to exactly one article.
The process is entirely automated once the list of stop phrases is developed.
Google search topics is a somewhat more amorphous concept.
Searches are assigned to topics by Google's proprietary machine learning algorithms, which are not publically available~\cite{google2018trendshelp}.
A given topic is identified by its name or a hexadecimal code.
For example, the query string ``apple'' might be assigned to ``Apple (fruit)'' or ``Apple (technology company)'' based on the content of the full search session or other factors.
\begin{table}
\makebox[\textwidth][c]{
\begin{tabular}{lllc}
\toprule
\textbf{Article}
& \textbf{Query string}
& \textbf{Topic name}
& \textbf{Topic code} \\
\midrule
Sense (molecular biology) & sense & Sense (Molecular biology) & \code{/m/0dpw95} \\
Influenza A virus subtype H9N2 & h9n2 & Influenza A virus subtype H9N2 (Virus) & \code{/m/0b3dc1} \\
George W.\ Bush & george w bush & George W. Bush (43rd U.S. President) & \code{/m/09b6zr} \\
\bottomrule
\end{tabular}
}
\caption{
\caphead{Sample Wikipedia articles and the queries to which they map}
}
\label{tab:sample-queries}
\end{table}
To manually build a mapping between Wikipedia articles and Google search topics,
we entered the article title and some variations into the search box on the Google Trends website~\cite{google2017trends} and then selected the most reasonable topic named in the site's auto-complete box.
The topic code was in the URL.
If the appropriate topic was unclear, we discussed it among the team.
Not all articles had a matching topic; we identified 363 topics for the 573 articles (63\%).
Among these 363 articles, the map is 1-to-1.
\Table{tab:sample-queries} shows a few examples of both mappings, and \Figure{fig:decept-all} shows the deceptiveness histograms.
\begin{figure}
\includegraphics[width=\textwidth]{ght_examples.pdf}
\caption{
\caphead{Search volume for two queries presented to our model}
The topic ``Influenza A virus (Virus)'' shows a seasonal pattern roughly corresponding to ILI, while the raw query ``respiratory system'' shows a seasonal pattern that does not correspond to ILI.
}
\label{fig:ght-examples}
\end{figure}
We downloaded search volume for both query strings and topics from the Google Health Trends API~\cite{stocking2017} on July 31, 2017.
This gave us a weekly time series for the United States for each search query string and topic described above.
These data appear to be a random sample, changing slightly from download to download.
Each element of the time series is the probability that the reported search session contains the string or topic, multiplied by 10 million.
Searches without enough volume to exceed an unspecified privacy threshold are set to zero, i.e., we cannot distinguish between few searches and no searches.
For this reason, we removed from analysis searches with more than 2/3 of the 261 weeks having a value of zero.
This resulted in 457 usable of 573 query strings (80\%) and 349 of 363 topics (96\%).
\Figure{fig:ght-examples} shows two of these time series.
Our map and category distances are in S2~Dataset\ (\code{en+Influenza.xlsx}).
Google's terms of service prohibit redistribution of the search volume data.
However, others can request the data using the same procedure we used~\cite{google2018ghtform}.
We used the script \code{ght_get} in the experiment source code for downloading.
This script depends on a patched source code file originally provided by Google that has an unclear license; therefore, we cannot redistribute this code.
Access to the Google source code is granted with the data, and we do provide the patch.
\subsection{Gridge regression}
Linear regression is a popular approach for mapping features (inputs) to observations (output).
This section describes the algorithm and the extensions we used in our experiment to incorporate deceptiveness information.
The model for linear regression is
\begin{equation}
y = X\beta + \varepsilon
\end{equation}
where $y$ is an $N \times 1$ observation vector, $X = [1, x_1, x_2, \ldots, x_p]$ is an $N \times (p+1)$ feature matrix where $x_i$ is the $N \times 1$ standardized feature vector (i.e., mean centered and standard deviation scaled) corresponding to feature $i$, $\beta$ is a $(p+1) \times 1$ coefficient vector, $\varepsilon \sim \text{MVN}(0,\sigma^2 I)$, where $\text{MVN}(\mu,\Sigma)$ is a multivariate normal distribution with mean $\mu$ and covariance matrix $\Sigma$, $\sigma^2 > 0$ is a scalar, and $I$ is an $N \times N$ identity.
Standardizing the features of $X$ is a convention that places all features on the same scale.
The goal of linear regression is to find the estimate of $\beta$ that minimizes the sum-of-squared residual errors. The \vocab{ordinary least squares} (OLS) estimator $\hat{\beta}^\text{OLS}$ solves the following:
\begin{equation}
\label{eq:leastsquares}
\hat{\beta}^{\text{OLS}}
= \argmin_{\beta}
\sum_{j=1}^N \Bigg(y_j - \beta_0 - \sum_{i=1}^p \beta_i x_{ji}\Bigg)^2
\end{equation}
or in matrix form:
\begin{equation}
\hat{\beta}^{\text{OLS}}
= (X'X)^{-1} Xy
\end{equation}
$\hat{\beta}^\text{OLS}$ is the unbiased, minimum variance estimator of $\beta$, assuming $\varepsilon$ is normally distributed~\cite[ch.~1–2]{scheffe1959variance}.
A prediction corresponding to a new feature vector $\ddot{x}$ is $\hat{y}^\text{OLS} = \ddot{x} \hat{\beta}^\text{OLS}$.
While $\hat{y}^\text{OLS}$ is unbiased, it is often possible to construct an estimator with smaller \vocab{expected prediction error} — i.e., with predictions on average closer to the true value — by introducing some amount of bias through \vocab{regularization}, which is the process of introducing additional information beyond the data.
Also, regularization can make regression work in situations with more features than observations, like ours.
One popular regularization method is called \vocab{ridge regression}~\cite{hoerl1970}, which extends OLS by encouraging the coefficients $\beta$ to be small.
This minimizes:
\begin{equation}
\label{eq:ridge_min}
\hat{\beta}^{\text{ridge}}_{\lambda}
= \argmin_{\beta} \left\{
\sum_{j=1}^N
\left( y_j - \beta_0 - \sum_{i=1}^p \beta_i x_{ji} \right)^{\!\!2}
+ \lambda \sum_{i=1}^p \beta_i^2
\right\}
\end{equation}
or equivalently:
\begin{equation}
\label{eq:ridge_closed_form}
\hat{\beta}^{\text{ridge}}_{\lambda}
= (X'X + \lambda I )^{-1} X'y.
\end{equation}
The additional parameter $\lambda \geq 0$ controls the strength of regularization. When $\lambda=0$, this is equivalent to OLS.
As $\lambda$ increases, the coefficient vector $\beta$ is constrained towards zero more vociferously.
Ridge regression applies the same degree of regularization to each feature, as $\lambda$ is common to all features.
A second extension, called \vocab{generalized ridge regression}~\cite{hemmerle1975gridge} or \vocab{gridge regression}, adds a feature-specific modifier $\kappa_i$ to the regularization:
\begin{equation}
\label{eq:fridge_min}
\hat{\beta}^{\text{gridge}}_{\lambda\kappa}
= \argmin_{\beta} \left\{
\sum_{j=1}^N
\left( y_j - \beta_0 - \sum_{i=1}^p \beta_i x_{ji} \right)^{\!\!2}
+ \lambda \sum_{i=1}^p \kappa_i \beta_i^2
\right\}
\end{equation}
$\kappa_i \geq 0$ adjusts the regularization penalty individually for each feature (ridge regression is a special case where $\kappa_i = 1\ \forall\ i$).
Gridge retains closed-form solvability:
\begin{equation}
\label{eq:gridge_closed_form}
\hat{\beta}^{\text{gridge}}_{\lambda\kappa}
= (X'X + \lambda K)^{-1} X'y
\end{equation}
where $K$ is a diagonal matrix with $\kappa_i$ on the diagonal and zero on the off-diagonals.
Gridge regression allows us to incorporate feature-specific deceptiveness information by making $\kappa_i$ a function of feature $i$'s deceptiveness.
The more deceptive feature $i$, the larger $\kappa_i$.
\subsection{Experiment factors}
Our experiment had 225 conditions.
This section describes its factors:
input feature class~(3 levels),
training period~(3),
deceptiveness noise added~(5),
and regression type~(5).
\subsubsection{Input feature class}
We tested three classes of input features:
\begin{enumerate}
\item \inhead{Synthetic.} Randomly generated transformations of ILI, as described above in~\S\ref{sec:features-synthetic}.
\item \inhead{Search query string.} Volume of Google searches entered directly by users, as described above in \S\ref{sec:features-search}.
\item \inhead{Search topic.} Volume of Google search topics inferred by Google's proprietary algorithms, as described above in \S\ref{sec:features-search}.
\end{enumerate}
Each feature comprises a time series of weekly data, with frequency and alignment matching our ILI data.
\subsubsection{Training period}
We tested three different training periods:
1st through 3rd seasons inclusive (three season),
2nd and 3rd (two seasons),
and 3rd only (one season).
Because the 4th season contains transitions in the synthetic features, we did not use it for training even when testing on the 5th season.
\subsubsection{Deceptiveness noise added}
The primary goal of our study is to evaluate how much knowledge of feature deceptiveness helps disease incidence models.
In the real world, this knowledge will be imperfect.
Thus, one of our experiment factors is to vary the quality of feature deceptiveness knowledge.
Our basic approach is to add varying amounts of noise to the best available estimate of each feature's deceptiveness $\hat g \in [0,1]$.
Recall that for synthetic features, $\hat g = g$ is known exactly, while for the search-based features, $\hat g$ is an estimate based on the Wikipedia category distance.
To compute the noise-added deceptiveness $\tilde g_i$ for feature $i$, for noise added $\gamma$, we simply select a random other feature $j$ and mix with its deceptiveness: $\tilde g_i = (1-\gamma) \hat g_i + \gamma \hat g_j$.
There are five levels of this factor:
\begin{itemize}
\item Zero noise: $\gamma = 0$, i.e., the model gets the best available estimate of $g_i$.
\item Low noise: $\gamma = 0.05$.
\item Medium noise: $\gamma = 0.15$.
\item High noise: $\gamma = 0.4$.
\item Total noise: $\gamma = 1$, i.e., the model gets no correct information at all about $g_i$.
\end{itemize}
Models do not know what condition they are in; they get only $\tilde g_i$, not $\gamma$.
\subsubsection{Regression type}
We tested five types of gridge regression:
\begin{enumerate}
\item Ridge regression: $\kappa_i = 1$, i.e., ignore deceptiveness information.
\item
Threshold gridge regression: keep features with category distance $d_i \leq 3$ and discard them otherwise, as in \cite{priedhorsky2017cscw}.
This is implemented as a threshold $\tilde g_i = 0.35$, which is applicable to both search and synthetic features (which have no $d_i$).
%
\begin{equation}
\kappa_i = \begin{cases}
0.1 & \text{if } \tilde g_i \leq 0.35 \\
1 & \text{otherwise}
\end{cases}
\end{equation}
\item Linear fridge: $\kappa_i = \tilde g_i$.
\item Quadratic fridge: $\kappa_i = \tilde g_i^2$.
\item Quartic fridge: $\kappa_i = \tilde g_i^4$.
\end{enumerate}
These levels are in rough ascending order of deceptiveness importance.
(We additionally tested, but do not report, a few straw-man models to help identify bugs in our code.)
All models used $\lambda = 150.9$, obtained by 10-fold cross-validation~\cite{james2013introduction}.
For each model, we tested 41 values of $\lambda$ evenly log-spaced between $10^{-1}$ and $10^7$; each fold fitted a model on the 9 folds left in and then evaluated its RMSE on the one fold left out.
The $\lambda$ with the lowest mean RMSE (plus a bias of up to 0.02 to encourage $\lambda$s in the middle of the range) across the 10 folds, was reported as the best $\lambda$ for that model.
We then used the mean of these best $\lambda$s for our experiment.
\subsection{Assessment of models}
To evaluate a model, we apply its coefficients learned during the training period to input features during the 52 weeks of the fourth and fifth seasons respectively, yielding estimated ILI $\hat y$.
We then compare $\hat y$ to reference ILI $y$ for each of the two test seasons.
For each model and metric, this yields two scalars.
We report three metrics:
\begin{enumerate}
\item \inhead{$\boldsymbol{r^2}$},
the square of the Pearson correlation $r$.
Most previous work reports this unitless metric.
\item \inhead{Root mean squared error} (RMSE),
defined as:
\begin{equation}
\sqrt{\frac{1}{N} \sum_{j=1}^N (y_j - \hat{y}_j)^2}
\end{equation}
has interpretable units of ILI.
\item \inhead{Hit rate}
is a measure of how well a prediction captures the direction of change.
It is defined as the fraction of weeks when the direction of the prediction (increase or decrease) matches the direction of the reference data~\cite{santillana2015}:
\begin{equation}
\frac{\sum_{j=2}^N \text{sign}(y_j - y_{j-1})
\overset{?}{=}
\text{sign}(\hat y_j - \hat y_{j-1} )}
{N-1}
\end{equation}
Because it captures the trend (is the flu going up or down?), it directly answers a simple, relevant, and practical public health question.
\end{enumerate}
\section{Results}
\begin{figure}
\includegraphics[width=\textwidth]{selected_models.pdf}
\caption{
\caphead{ILI predictions for zero-added-noise, 3-season-trained models}
This figure shows the 15 models in the ``ideal'' situation: no noise added to deceptiveness, and trained on all three training seasons.
The different types of gridge regression show subtle yet distinct differences, with the models taking into account deceptiveness more generally being closer to the ILI reference data.
}
\label{fig:selected-models}
\end{figure}
Output of our regression models is illustrated in \Figure{fig:selected-models}, which shows 15 selected conditions.
These conditions are close to what would be done in practice: use all available training information and add no noise.
The differences between gridge regression types are subtle, but they are real, and close examination shows that the stronger gridge models that place higher importance on deceptiveness information are closer to the ILI reference data.
The remainder of this section analyzes these differences across all the conditions.
\begin{figure}
\includegraphics[width=\textwidth]{results_rmse_4.pdf}
\caption{
\caphead{Gridge regression error compared to plain ridge, 5th season}
Gridge algorithms that take into account deceptiveness \textit{usually} have lower RMSE than plain ridge, which does not.
Further, adding deceptiveness noise usually gives the appropriate trend: worse deceptiveness knowledge means worse predictions.
$r^2$ and RMSE on the 4th season show similar trends, while hit rate shows limited benefit from gridge; these figures are available in S4~Figure.
}
\label{fig:results-rmse}
\end{figure}
\Figure{fig:results-rmse} illustrates the effect on error (RMSE) of adding noise to deceptiveness information; $r^2$ is similar.
Generally, the gridge algorithms have lower error than plain ridge in lower-added-noise conditions and higher error in higher-added-noise situations.
That is, conditions with better knowledge of deceptiveness outperform the baseline, and performance declines as deceptiveness knowledge worsens, which is the expected trend.
This supports our hypotheses that (a)~incorporating knowledge of feature deceptiveness can improve estimates of disease incidence based on internet data and (b)~semantic distance, as expressed in the Wikipedia article category tree, is an effective proxy for deceptiveness.
(Hit rate shows limited benefit for gridge, as we discuss below.)
\begin{figure}
\vspace{-24pt}
\includegraphics[width=\textwidth]{summary_boxplot.pdf}
\caption{
\caphead{Improvement over ridge in zero- and low-noise conditions}
This figure illustrates performance of the gridge algorithms divided by plain ridge in the same condition.
The third group compares \emph{query string} gridge models against \emph{topic} ridge.
Boxes plot the median with first and third quartiles, and the whiskers show the maximum and minimum.
Each box-and-whiskers summarizes 12 data points.
For the two error metrics, increasing the importance of deceptiveness through quadratic gridge yields increasing improvement over plain ridge, but the trend ends at quartic gridge.
Notably, this is true even when comparing query string models (which are completely automatic) against topic ridge (which requires lots of manual attention), suggesting that deceptiveness information can be used to replace expensive human judgement.
Hit rate, however, seems to gain limited benefit from deceptiveness in this experiment.
}
\label{fig:results-summary}
\end{figure}
\Figure{fig:results-summary} summarizes the improvement of the four gridge algorithms over plain ridge for all three metrics in the zero- and low-noise conditions.
These results suggest that adding low-noise knowledge of deceptiveness to ridge regression improves error but not hit rate.
It also appears that the benefits of gridge level off between quadratic (deceptiveness squared) and quartic (deceptiveness raised to the fourth power): while quartic sometimes beats quadratic ridge, it frequently is worse than plain ridge.
We speculate that the lack of observed benefit of gridge on hit rate is due to one or both of two reasons.
First, plain ridge may be sufficiently good on this metric that it has already reached diminishing returns; recall that in \Figure{fig:selected-models} all five algorithms captured the overal trend of ILI well.
Second, ILI is noisy, with lots of ups and downs from week to week regardless of the medium-term trend.
This randomness may limit the ability of hit rate to assess performance on a weekly time scale without overfitting.
That is, we believe that gridge's failure to improve over plain ridge on hit rate is unlikely to represent a concerning flaw in the algorithm.
\section{Discussion}
Our previous work introduced \vocab{deceptiveness}, which quantifies the risk that a disease estimation model's error will increase in the future because it uses features that are coincidentally, rather than informatively, correlated with the quantity of interest~\cite{priedhorsky2018flow}.
This work tests the hypothesis that incorporating deceptiveness knowledge into a disease nowcasting algorithm reduces error; to our knowledge, it is the first work to quantitatively assess this question.
To do so, we used simulated features with known deceptiveness as well as two types of real web search features with deceptiveness estimated using semi- and fully-automated algorithms.
\subsection{Findings}
Our experiment yielded three main findings:
\begin{enumerate}
\item
Deceptiveness information does help our linear regression nowcasting algorithms, and it helps more when it is more accurate.
\item
A readily available, crowdsourced semantic relatedness measure, Wikipedia category distance, is a useful proxy for deceptiveness.
\item
Deceptiveness information helps automatically generated features perform the same or better than similar, semi-automated features that require human curation.
\end{enumerate}
The effects we measured are stronger for the synthetic features than the real ones.
We speculate that this is for two reasons.
First, the web search feature types are skewed towards low deceptiveness, because they are based on Wikipedia articles directly linked from ``Influenza'', while the synthetic features lack this skew.
Second, the synthetic features can have zero-noise deceptiveness information, while the real features cannot, because they use Wikipedia category distance as a less-accurate proxy.
If verified, the second would further support the hypothesis that more accurate deceptiveness information improves nowcasts.
The third finding is interesting because it is relevant to a long-standing tension regarding how much human intervention is required for accurate measurements of the real world using internet data: more automated algorithms are much cheaper, but they risk oversimplifying the complexity of human experience.
For example, our query strings were automatically generated from Wikipedia article titles, which are written for technical accuracy rather than salience for search queries entered by laypeople.
To select features for disease estimation, one could use a fully-automated approach (e.g., our query strings), a semi-automated approach (e.g., our topics, which required a manual mapping step), or a fully-manual approach (e.g., by expert elicitation of search queries or topics, which we did not test).
One might expect that a trade-off would be present here: more automatic is cheaper, but more manual is more accurate.
However, this was not the case in our results.
The third box plot group in \Figure{fig:results-summary} compares the gridge models using query string features to a baseline of plain ridge on \emph{topic} features.
Query strings perform favorably regardless of whether the baseline is plain ridge on query strings or topics, and sometimes the improvement is greater than gridge using topic features.
This suggests that there is not really a trade-off, and fully automatic features might be among the most accurate.
\subsection{Limitations}
All experiments are imperfect.
Due to its finite scope, this work has many limitations.
We believe that the most important ones are:
\begin{itemize}
\item
Wikipedia is changing continuously.
While we believe that these changes would not have a material effect on our results, we have not tested this.
\item
Wikipedia has non-semantic categories, such as the roughly 20,000 articles in category \emph{Good article} that our algorithm that would assign distance~1 from each other.
We have not yet encountered any other relevant non-semantic categories, and ``Influenza'' is not a \emph{Good article}, so we believe this limitation does not affect the present results.
However, any future work extending our algorithms should exclude these categories from the category distance computation.
\item
The mapping from Wikipedia articles to Google query strings and topics has not been optimized.
While we have presented mapping algorithms that are reasonable both by inspection and supported by our current and prior~\cite{priedhorsky2017cscw} results, we have not compared these algorithms to alternatives.
\item
Linear regression algorithm metaparameters were not fully evaluated.
For example, $\epsilon$ in §\ref{sec:flu-concepts} was thoughtfully but arbitrarily assigned rather than experimentally optimized.
\item
Other methods of feature generation may be better.
This experiment was not designed to evaluate the full range of feature generation algorithms.
In particular, direct elicitation of features such as query strings and topics should be evaluated.
\end{itemize}
\subsection{Future work}
This is an initial feasibility study using a fairly basic nowcasting model.
At this point, the notion of deceptiveness for internet-based disease estimation is promising, but continued and broader positive results are needed to be confident in this hypothesis.
In addition to addressing the limitations above, we have two groups of recommendations for future work.
First, multiple opportunities to improve nowcasting performance should be investigated.
Additional deceptiveness-aware fitting algorithms such as generalized lasso~\cite{tibshirani2011glasso} and generalized elastic net~\cite{sokolov2016glasticnet} should be tested.
Category distance also has opportunities for improvement.
For example, it can be made finer-grained by measuring path length through the Wikipedia category tree rather than counting the number of levels ascended: the distance between ``Influenza'' and ``Infection'' would become~3, taking into account that \emph{Infectious diseases} was a direct category of the latter.
Finally, alternate deceptiveness estimates need testing, for example category distance based on the medical literature.
In addition to better nowcasting, utility needs to be demonstrated when deceptiveness-aware nowcasts augment best-in-class forecasting models, such as those doing well in the CDC's flu forecasting challenge~\cite{cdcchallenge2017}.
Second, we are optimistic that our algorithms will generalize well to different diseases and locations.
This is because our best feature-generation algorithm is fully automated, making it straightforward to generalize by simply offering new input.
For example, to generate features for dengue fever in Colombia, one could: start with the article ``Dengue fever'' in Spanish Wikipedia; write a set of Spanish stop phrases; use the Wikipedia API to collect links from that article and walk the category tree; pull appropriate search volume data from Google or elsewhere; and then proceed as described above.
Future studies should evaluate generalizability to a variety of disease and location contexts.
\subsection{Conclusion}
We present a study testing the value of deceptiveness information for nowcasting disease incidence using simulated and real internet features and generalized ridge regression. We found that incorporating such information does in fact help nowcasting; to our knowledge, ours is the first quantitative evaluation of this question.
Based on these results, we hypothesize that other internet-based disease estimation methods may also benefit from including feature deceptiveness estimates. We look forward to further research yielding deeper insight into the deceptiveness question.
\section*{Author contributions}
Experiment concept: RP~ARD~DO.
Methods: RP~ARD~DO (experiment), MB~FO (mapping Wikipedia articles to Google searches), DO (statistical approach).
Data curation, investigation, and software: RP~ARD.
Visualization: RP.
Literature review: RP~ARD.
Writing: RP~ARD~DO.
Review and editing: RP~ARD~MB~FO~DO.
Funding acquisition and project administration: RP.
\section*{Acknowledgments}
We thank the Wikipedia editing community for building the link and category networks used to compute semantic distance and Google, Inc.\ for providing us with search volume data.
We also appreciate the helpful feedback provided by anonymous reviewers.
\bibliographystyle{plainurl}
| {
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} | 2,771 |
Beata Barbara Kubiak Ho-Chi (ur. 29 listopada 1958) – polska doktor habilitowana nauk humanistycznych. Kulturoznawczyni, literaturoznawczyni, orientalistka. Specjalizuje się w zagadnieniach z zakresu japonistyki, w tym pisma, sztuki i estetyki tego kraju. Wykładowca w Katedrze Japonistyki na Wydziale Orientalistycznym Uniwersytetu Warszawskiego.
Życiorys
Absolwentka studiów filologicznych na Uniwersytecie Warszawskim (rocznik 1982). Jej praca magisterska dotyczyła tradycji rycerskiej w hanie Aizu. W 1995 roku otrzymała dyplom DEA paryskiej szkoły wyższej Institut national des langues et civilisations orientales. Doktoryzowała się w 2001 roku na Wydziale Orientalistycznym UW na podstawie pracy zatytułowanej Mishima Yukio: estetyka klasyczna w twórczości prozatorskiej i dramaturgicznej w latach 1941-1960. Habilitowała się w 2012 roku na tej samej uczelni, pisząc rozprawę pt. Tragizm w japońskim teatrze lalkowym bunraku. Doświadczenie naukowe zdobywała na Uniwersytecie Tokijskim i w International Research Center for Japanese Studies w Kioto. W 2015 roku została profesorem nadzwyczajnym.
W 2020 została nominowana do Nagrody Literackiej Gdynia w kategorii przekład na język polski za tłumaczenie książki pt. Wyznanie maski autorstwa Yukio Mishimy.
Książki
Beata Kubiak Ho-Chi jest autorką lub współautorką następujących pozycji książkowych:
Mishima Yukio: estetyka klasyczna w prozie i dramacie 1941-1960
Dwa filary kultury japońskiej: literatura i sztuki performatywne (materiały konferencyjne)
Estetyka i sztuka japońska: wybrane zagadnienia
Tragizm w japońskim teatrze lalkowym bunraku
Film japoński a kultura europejska: obcość przezwyciężona?
East Asian theatres: traditions - inspirations - European/Polish contexts
Publikacje naukowe
Afektywna topografia współczesnego Tokio w powieści Yoriko Shōno "Kombinat zakrzywionej czasoprzestrzeni" (Taimu surippu konbināto)
Dialog with a Ghost: Modern Nō Plays by Mishima Yukio on the Stages of Polish Theatre
Blade Runner w kombinacie zakrzywionej czasoprzestrzeni, czyli film Ridleya Scotta w powieści Shōno Yoriko
Uwagi
Przypisy
Absolwenci Uniwersytetu Warszawskiego
Polscy japoniści
Polscy kulturoznawcy
Polscy literaturoznawcy
Urodzeni w 1958
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Label: Denomination of Origin Tigernut from Valencia
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} | 7,262 |
Addiction is a perpetual issue with organic, mental, social and ecological elements impacting its advancement and support. Regularly, it falls under two classes, substance reliance, or medication Addiction, and social enslavement, for example, a betting habit. Elevated want to re-encounter utilization of the substance or conduct, possibly impacted by mental (e.g., stretch, history of injury), social (e.g., family or companions' utilization of a substance), and ecological elements (e.g., openness of a substance, minimal effort) can prompt general utilize/introduction, with endless, utilize/presentation prompting mind changes. These cerebrum changes incorporate modifications in cortical (pre-frontal cortex) and sub-cortical (limbic framework) areas including the neuro-hardware of reward, inspiration, memory, motor control and judgment. This can prompt sensational increments in desires for a medication or movement, and in addition hindrances in the capacity to effectively manage this drive, despite the learning and experience of numerous outcomes identified with the addictive conduct.
Disregarding the way that already, passionate prosperity disarranges, and impulse issues were every now and again treated freely, we currently understand that co-happening mental prosperity and substance use jumbles influence each other and must be managed together. Treating just a single issue won't gain the other thusly ground. Likewise, divided, parallel watch out for the disarranges does not achieve one, great treatment outline. To be great, the two issues must be managed meanwhile, in a comparable place, by a comparable treatment gathering. This is called composed treatment.
Different headways in enslavement treatment strategies will help in the giving quality care to individuals with the undesirable liquor, tobacco, or other medications utilize. Among them, Cognitive conduct treatment is a type of psychotherapy intended to treat the social impacts of substance mishandle. Neurorehabilitation and treatment offer complex therapeutic process which plans to help recuperation from sensory system damage because of enslavement. 12step recuperation treatment includes a functioning commitment procedure intended to improve the probability of a substance abuser getting to be partnered with and effectively engaged with 12-step self-improvement gatherings, consequently advancing restraint. It has for quite some time been a vital piece of the recuperation procedure and the reason for some, recuperation programs.
Addiction causes dependable changes in the in defenseless people. The industriousness of these social changes is because of enduring changes in quality articulation keeping in mind the end goal to drive these enduring changes in quality articulation epigenetic systems assume a pivotal part. It is an essential system used to comprehend compulsion science. Different components incorporate the biochemical system of medication poisonous quality, Genetic linkage thinks about, the biochemical measure is additionally conveyed for constant liquor abuse. Hereditarily a man does not acquire a substance manhandle they acquire a defenselessness to it. Individuals having defenselessness may not build up an issue of medication or liquor manhandle if they are not presented to elements of dependence.
Addictive clutters are caused by various components, including inherited shortcoming, natural stressors, social weights, personality characteristics and mental issues. From a neurological perspective, addictive scrambles develop when a substance changes the way the customer's cerebrum feels, please. Addictive substances change the cerebrum's ability to send and get synthetic concoctions called neurotransmitters, which cause enchant. The addictive substances can foresee nerves in the psyche called neurons from getting these bliss synthetics, which implies the solution customer relies upon the pharmaceutical, rather than his or her regular cerebrum synthetic substances, for estimations of joy. A couple of youngsters are more in peril of making addictive disperses, joining adolescents with no less than one of the going with conditions show 1) Children of substance abusers. 2) Adolescents who are setbacks of physical, sexual or mental abuse. 3) Adolescents with mental prosperity issues, especially debilitated and foolish high schoolers. 4) Physically crippled adolescents.
Animal models have contributed colossally to our comprehension of enslavement essentially sedate mishandle, its results and aversion and treatment. Creature examines have yielded principal bits of knowledge into why individuals mishandle medications and how tranquilizes cause the impulse and cluttered reasoning found independence. It is a profitable research instrument since they enable researchers to lead analyzes that they would never perform on people. It effectively affects humans, comes about because of creature studies ought to be extrapolated to people with alert, their esteem is inestimable. Case reports are additionally joined in compulsion inquire about.
The utilization of unlawful medications shows numerous dangers to the well-being of individuals living with HIV including unsafe consequences for the body and the dangers related with infusion sedate utilize, and dangers related with sexual transmission of HIV. Distinctive medications effects affect the body, and they can influence your judgment, emotional well-being, and physical wellbeing in an unexpected way. Utilizing medications can make you more inclined to hazardous practices, for example, sharing needles or not utilizing condoms. Unobtrusive utilization of liquor can help your heart wellbeing in a few conditions, yet it can likewise prompt long-haul impacts that are destructive and lessen your capacity to ward off HIV. On the off chance that you infuse drugs, you might be at expanded hazard for transmitting or getting HIV. Liquor and medication utilize can be hurtful to your wellbeing and escape hand for a few people. Utilizing medications can make it difficult for you to look after wellbeing.
A noteworthy segment of the conduct effects of drug addiction fuse Paranoia, Aggressiveness, Impulsiveness, and Loss of Self-Control. A noteworthy element of dependence is the loss of control in notice admission of the addictive substance. Express that you will give two cases of the contact between drugs that are addictive, their cell questions in the cerebrum, and the reward. The latest research demonstrates that the reward pathway might be considerably more imperative in the craving-related with compulsion, contrasted with the reward itself. Researchers have taught an incredible arrangement about the biochemical, cell, and atomic underlying foundations of dependence; plainly fixation is an ailment of the cerebrum. Fixation is a state in which an animal includes in an urgent conduct, notwithstanding when looked with negative qualities. Thusly, uncontrolled substance use achieves lethality of the psyche. Medication Addiction is a cerebrum contamination that is depicted by incautious solution pursuing, disregarding its dangerous results. It causes changes in the normal development of the tangible framework hurting the nerve tissues, executing neurons and this prompts dis-control of the neural system. The doctor suggested drugs that are as often as possible mauled are opioids, rest solutions.
Yoga and withdraw approaches-have been intended to give natural cures, which represses the drawn-out utilization of any substance. Individuals who are rationally sick are endorsed to run with yoga as it reestablishes brains dopamine capacities and keeps worry. Meditation brings the mid the condition of rest, in which a human considers exhibit. Move and music treatments are given to individuals to bring a beam of expectation inside them that regardless they can perform superior to others. Recovery facilities give exceptional time-frame to petition, quietness, rest, straightforwardness and consideration. It is an exit plan from life's day by day worries and additionally a chance to develop one's understanding of self and the widespread vitality that encompasses and backings us. Backslide offers an orderly technique for training the abuser to perceive and oversee backslide cautioning signs.
Dual diagnosis happens when somebody has both a psychological issue and a liquor or medication troublesome. These conditions happen together often Dual diagnosis or co-occurring issue is a term for somebody who hones a psychological sickness considering enjoy drinking, or the individual mishandling heroin amid times of lunacy. Liquor and medication issue probably happen with misery, uneasiness issue, schizophrenia, identity issue, and so on. The indications of substance mishandle include: sudden changes in conduct, withdrawal from loved ones, loss of control over utilization of materials, creating resistance and expulsion side effects. The results can be various and brutal. People with co-happening issue have a factually more noteworthy penchant for savagery, medicine rebelliousness, and inability to react to treatment than clients with just substance manhandle or a psychological instability. These issues additionally stretch out to these client's families, companions and colleagues.
Addiction treatment and recovery includes different medications and treatments. Substance misuse treatment includes Motivational treatment in which we urge a patient to build up a negative perspective of them mishandle, alongside a craving to change their conduct. It is one of the vital treatments incorporated into Rehabilitation house treatment approaches. Social conduct in habit can be dealt with by conduct treatment methodologies and medication actuated dependence treatment.
Addiction has extreme therapeutic outcomes like a tumor, HIV/AIDS, Hepatitis, Respiratory Disease, perpetual agony, and suicide. Abundance liquor utilization causes alcoholic hepatitis, greasy liver and ceaseless hepatitis with hepatic fibrosis or cirrhosis. Perilous utilization of infused drugs brings about HIV/AIDS. Medication and liquor compulsion prompt an assortment of respiratory issues like bronchitis, emphysema and lung growth, tranquilize Induced Pulmonary Toxicity and Alcoholic long illness.
On behalf of 8th World Congress on Addictive Disorders And Addiction Therapy 2019 Organizing Committee, we cordially invite professors, scientific communities, therapists, counsellors, students and business delegates to attend the 8th World Congress on Addictive Disorders and Addiction Therapy 2019 which is to be held on May 09-10 | 2019 in London, UK.
Addiction Therapy 2019 intends to unite researchers, specialists, and leading academic scientists to trade and offer their encounters and research comes about all parts of unsafe impact of Addiction and Treatment and Therapy. It additionally gives the head interdisciplinary gathering to specialists, experts and instructors to show and talk about the latest advancements, patterns, and concerns, viable difficulties experienced, and the arrangements embraced in the field of dependence treatment and treatment.
In the Global Market Brain disorders caused by Addiction and Addiction induced neurological disorders cost $ 500-700 billion and Europe alone spends 6 billion euros per year. Addiction Diagnosis, Treatment, Recovery, and Rehabilitation business has been on rising in recent years. Anxiety and psychotic disorders cost 76 billion euros to Europe. Yoga retreat therapy alone does the business of $ 27-30 billion in the USA in a year. There is also a lot of research is going on combating addiction disorders of alcohol, cocaine, opioid, methamphetamine, cannabis, and tobacco using new neuro-receptors/peptides and antibody therapies. Around 280 million people in the part of America and Europe are at the danger of addiction habit of drugs for non-medical use. The United States of America have around 14000-15000 rehab centers which did the business of $35 billion in the year of 2016. The Europe spends 212.6 billion euros per year for the addiction induced neurological disorders. Alcohol and illegal drug addiction treatments cost European people more than 76 billion euros.
Addiction treatment is planned to help dependent people from impulsive chasing. Medication misuse and are given in a few unique settings by utilizing various social and pharmacological methodologies. The worldwide Addiction treatment advertise was esteemed at around US$ 4.0 Bn in 2016 and is foreseen to grow at a CAGR of more than 6.0% from 2017 to 2025 to achieve estimation of roughly US$ 7.0 Bn by 2025. Great repayments for smoking suspension treatment, developing misuse of professionally prescribed medications, and ascend in government activities to bring issues to light about medication Addiction are a few components driving the Addiction treatment advertise from 2017 to 2025.
Addiction is a developing worry over the globe. As per the 2015 National Survey on Drug Use and Health (NSDUH), 15.1 million grown-ups matured multi year or more had liquor utilize clutter, which included about 9.8 million men. Around 1.3 million grown-ups got treatment for AUD at a specialized facility in 2015. More than 16 million individuals in the U.S. are living with an ailment caused by smoking. As indicated by CDC review, tobacco utilize causes almost 6 million deaths internationally every year. Current patterns show that tobacco utilize is probably going to cause more than 8 million deaths yearly by 2030. Medication mishandle treatment suppliers and makers of treatment items are concentrating on bringing issues to light among individuals and medication store proprietors about unfavorable impacts of medication misuse and significance of abuse treatment to expand the client pool. Additionally, organizations are putting forth preparing for recognizable proof of potential medication abusers and liquor abusers and utilization of medication mishandle testing to law authorization offices. Mindfulness through TV promotions, data pamphlets, daily papers, and other media have turned out to be powerful in checking substance mishandle emergency.
The worldwide Addiction treatment advertise has been divided in view of treatment write, medicate type, treatment focuses, dissemination channel, and topography. As far as treatment write, tobacco/nicotine Addiction treatment portion is anticipated to overwhelm the market and is required to proceed with this pattern amid the estimate time frame took after by the opioid Addiction treatment section. Ascend sought after for nicotine gum in creating markets is probably going to impel the fragment. Nicotine gum is quick acting, moderately more affordable, and can be devoured according to client's decision, these points of interest are relied upon to move the section. Considering medication write, nicotine substitution items were the main income producing section in 2016 and it is probably going to proceed with its strength amid the conjecture time frame. As far as treatment focuses, outpatient treatment focus portion is probably going to pick up piece of the pie amid the conjecture time frame as it cost lesser than private or inpatient treatment focuses and can be appropriate for the individuals who can't take expanded leaves from work or individual commitments. Considering dispersion channels, doctor's facility drug stores were the main circulation direct in 2016 and is probably going to represent predominant offer of the market amid the conjecture time frame.
Topographically, North America represented a significant offer of the worldwide cardiovascular medications advertise in 2016. This is because of ascend in the quantity of smokers in the U.S. has expanded concerns regarding wellbeing dangers for the two smokers and inactive smokers. The market in Asia Pacific is anticipated to pick up piece of the pie amid the conjecture time frame and is probably going to create extensive income sooner rather than later. Activities by neighborhood governments to accomplish in Addiction in assembling pharmaceuticals and motivating forces for the generation of generics in nations, for example, Brazil, South Africa, and Saudi Arabia are probably going to help the market in Latin America and Middle East and Africa.
Enter organizations working in the worldwide Addiction treatment showcase and profiled in the report incorporate Cipla Ltd., Allergan plc, Alkermes plc, Pfizer Inc., Orexo AB, GlaxoSmithKline plc, Cipla Ltd, Purdue Pharma L.P, Mallinckrodt, and Reckitt Benckiser. These players receive natural and inorganic development techniques to grow their item contributions, reinforce their geological achieve, increment client base, explore and advancement action, and gather piece of the overall industry. For example, in September 2015, the Purdue Pharma L.P. worked together with Rhodes Pharmaceuticals for the advancement of methylphenidate broadened discharge tablets for grown-ups.
This cover the Addiction treatment showcase breaks down the present and future situation of the worldwide market. Ascend in mindfulness activities by various medication makers and government bodies and increment in manhandle of physician recommended drugs are relied upon to drive the worldwide habit treatment advertise amid the figure time frame.
The worldwide Addiction treatment advertise report contains a point by point and expand official rundown, which incorporates showcase preview that gives data about the different portions. It likewise gives data and information investigation of the nation's market as for the portions considering treatment compose, tranquilize type, treatment focus, and dispersion channel. An expounded subjective investigation of drivers and patterns has been given in the market outline area. This segment likewise gives showcase appeal investigation regarding nation, hence exhibiting an intensive examination of the general focused situation in the worldwide Addiction treatment advertises.
Considering treatment focuses, the worldwide Addiction treatment showcase has been characterized into liquor Addiction treatment, tobacco/nicotine Addiction treatment, opioid habit treatment, and other substance Addiction treatment. The sections have been breaking down considering consciousness of Addiction treatment, genuine rate getting to various protection strategies for treatment, and therapeutic situations. The market size and gauge for every one of these fragments have been accommodated the period from 2017 to 2025, alongside their separate CAGRs for the estimate time frame from 2017 to 2025, thinking about 2016 as the base year.
Considering medication compose, the market has been portioned into bupropion, varenicline, acamprosate, disulfiram, naltrexone, methadone, buprenorphine, nicotine substitution items, and others. In term of treatment focuses, the market has been portioned into outpatient treatment focuses, private treatment focuses, and inpatient treatment focuses. The sections have been broadly breaking down considering medications and items utilized as a part of the treatment of Addiction, focuses that have been generally utilized for treatment and therapeutic repayment. The market size and conjecture as far as esteem (US$ Mn) for each fragment have been accommodated the period from 2015 to 2025. The report additionally gives compound yearly development rate (CAGR %) for each market portion for the estimate time frame from 2017 to 2025, thinking about 2016 as the base year.
As far as dispersion channels, the habit treatment advertise has been divided into healing facility drug store, therapeutic stores, and others. The circulation channels division has been done based on buy of medications which is recommended for Addiction treatment.
Geologically, the worldwide Addiction treatment advertise has been sectioned into North America, Europe, Asia Pacific, Latin America, and Middle East and Africa. The market size and gauge for every one of these areas have been accommodated the period from 2015 to 2025, alongside their individual CAGRs for the conjecture time frame from 2017 to 2025, thinking about 2016 as the base year.
The report additionally profiles significant players in the worldwide Addiction treatment advertise considering different qualities, for example, organization review, budgetary diagram, item portfolio, business methodologies, SWOT investigation, and late advancements. Enter players working in the worldwide habit treatment advertise are Cipla Ltd., Allergan plc, Alkermes plc, Pfizer Inc., Orexo AB, GlaxoSmithKline plc, Purdue Pharma L.P, Mallinckrodt, and Reckitt Benckiser (Indivior PLC).
Addiction is a chronic disorder with biological, psychological, social and environmental factors influencing its development and maintenance. Typically, it falls under two categories, substance dependence, or drug addiction, and behavioral addiction such as a gambling addiction. Heightened desire to re-experience use of the substance or behavior, potentially influenced by psychological (e.g., stress, history of trauma), social (e.g., family or friends' use of a substance), and environmental factors (e.g., accessibility of a substance, low cost) can lead to regular use/exposure, with chronic use/exposure leading to brain changes. These brain changes include alterations in cortical (pre-frontal cortex) and sub-cortical (limbic system) regions involving the neuro-circuitry of reward, motivation, memory, impulse control and judgment. This can lead to dramatic increases in cravings for a drug or activity, as well as impairments in the ability to successfully regulate this impulse, despite the knowledge and experience of many consequences related to the addictive behavior.
Dependence puts an extraordinary weight on influenced people and their families, causing across the board horribleness and behavioral brokenness. Wrongdoing related with sedate mishandle and the control of addictive therapeutics posture awesome legitimate and societal difficulties. Medications of fixation incite crucial changes in cerebrum organic chemistry, enacting neuronal reward circuits and going about as neuronal and cardiovascular stimulants. Research in the Department of Pharmacology plans to see how addictive specialists, for example, nicotine, amphetamines or cocaine influence neurotransmitter receptors and transporters, and how they change neuronal flag transduction to start habit. Different endeavors concentrate on the disclosure of novel analgesics that may supplant addictive analgesics medications later on.
Dysfunctional behaviors can expand the hazard for Alcohol abuse or medication manhandle, infrequently in view of self-sedating. Then again, Alcohol addiction can prompt huge uneasiness and dejection that may seem vague from an emotional instability. At long last, one issue can be more regrettable than the other.
New advances in brain research and neuroscience have revealed insight into the progressions that long haul utilization of Alcohol and different medications brings into the cerebrum particularly in mind remunerate framework, to encourage proceeded and perpetual examples of enthusiastic medication mishandle. New research points in enslavement incorporate Behavioral Pharmacology Research, Relationship between youth viciousness and substance mishandle, impact of Alcohol on intellectual working and cocaine antibodies and dependence epidemiological research. Behavioral Pharmacology Research infers wide based substance mishandle clinical research program incorporating both human lab research and outpatient treatment look into. Cocaine mishandle is a continuous and essential issue along these lines immunizations against cocaine are being produced.
Alcohol addiction is the most genuine type of issue drinking, and depicts a solid, frequently wild, want to drink. A dipsomaniac is a man, while alcohol abuse is the sickness. Sufferers of Alcohol addiction will frequently put drinking most importantly different commitments, including work and family, and may develop a physical resilience or experience withdrawal side effects on the off chance that they stop.
Alcohol abuse is at times known as Alcohol habit or Alcohol reliance. It's marginally extraordinary to 'unsafe drinking' which is an intermittent example of drinking which can cause harm your wellbeing.
A case of unsafe drinking will be drinking excessively at a gathering, and gambling a fall or contention. This example may form into Alcohol abuse if that sort of unsafe drinking turns into a propensity and occurs all the time.
In this reliance, different mental and clinical changes happen in the human body including alcoholic liver maladies. Ladies Alcohol abuse amid pregnancy may bring about fetal Alcohol disorder which is an example of extreme physical and mental imperfections in the creating embryo. Alcoholic polyneuropathy is harm to the nerves that outcomes from extreme drinking of Alcohol, incessant pancreatitis and Peptic ulcers is additionally a genuine malady caused because of Alcohol habit. Insanity tremens (DTs) is caused by Alcohol withdrawal after a time of overwhelming drinking and prompt serious mental and sensory system changes. Different chemotherapeutic specialists like methadone are utilized for Alcohol detoxification.
Professionally prescribed medication manhandle is the utilization of a pharmaceutical without a medicine, in a path other than as endorsed, or for the experience or emotions inspired. As per a few national studies, professionally prescribed meds, for example, those used to treat torment, consideration shortage issue, and uneasiness, are being mishandled at a rate second just to weed among illegal medication clients. The results of this mishandle have been consistently exacerbating, reflected in expanded treatment confirmations, crisis room visits, and overdose passings.
Medication habit is a perpetual sickness portrayed by habitual, or wild, tranquilize looking for and use notwithstanding destructive results and changes in the cerebrum, which can be dependable. These adjustments in the cerebrum can prompt the unsafe practices found in individuals who utilize drugs. Medication dependence is likewise a backsliding malady. Backslide is the arrival to tranquilize manhandle after an endeavor to stop.
The way to tranquilize fixation starts with the willful demonstration of taking medications. However, after some time, a man's capacity to pick not to do as such progresses toward becoming traded off. Looking for and taking the medication ends up plainly habitual. This is generally because of the impacts of long haul sedate introduction on cerebrum work. Fixation influences parts of the mind associated with reward and inspiration, learning and memory, and control over conduct.
Enslavement is an infection that influences both the mind and conduct.
Substance mishandle alludes to the destructive or perilous utilization of psychoactive substances, including liquor and illegal medications. Utilization of a substance in a way or sum which is exceptionally hurtful to the client and its encompassing is named as substance manhandle. For some high schoolers, illegal utilization of focal stimulants, for example, methamphetamine and dopamine turn out to be a piece of the scene of their young years.
Psychoactive substance utilize can prompt reliance disorder - a bunch of behavioral, intellectual, and physiological marvels that create after rehashed substance utilize and that regularly incorporate a powerful urge to take the medication, challenges in controlling its utilization, continuing in its utilization in spite of hurtful results, a higher need given to tranquilize use than to different exercises and commitments, expanded resistance, and some of the time a physical withdrawal state.
Arrangements which impact the levels and examples of substance utilize and related mischief can altogether decrease the general medical issues inferable from substance utilize, and intercessions at the social insurance framework level can work towards the rebuilding of wellbeing in influenced people.
Dual Diagnosis is a condition when a person experiences both a substance misuse issue and another psychological well-being issue, for example, sorrow or a nervousness issue. Some of the time utilize liquor or medications are because of mental issues. People who are managing Autism range issue are at high danger of substance manhandle. They may feel that substance misuse encourages them to cover their social incompetence however after some time it starts to cause significant issues throughout their life. Consideration Deficit Hyperactivity Disorder is likewise identify with dependence. Self-prescription hypothesis is broadly utilized for the treatment of co-happening issue.
Habit psychiatry concentrates on the assessment, conclusion, and treatment of individuals who are experiencing at least one issue and emotional wellness issues identified with compulsion. Directing and dependence treatment is extremely fundamental for such people. Because of most recent headway in innovations like Mobile wellbeing, now days it has turned out to be so natural for the general population to get associated with wellbeing administrations and being refreshed with all the data. Country and underserved groups regularly experience the ill effects of restricted access to forte treatment programs this can be overwhelmed by Tele-emotional well-being. Online Recovery programs give the chance to Alcohol and medication compulsion treatment via prepared specialists by means of the Internet, in a way that is helpful and private. | {
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} | 4,467 |
Q: Why am I getting a parse error on input `|' takeEveryNth :: [Int] -> Int -> [Int]
takeEveryNth g destination
| [] destination == []
| otherwise = [g !! destination] ++ takeEveryNth (drop (destination+1) g) destination
I keep getting the error message in the title for line 4 of this code ( | otherwise =…)
I have tried changing the indentation but can't figure why I am getting this error
A: The reason it doesn't work is because your first guard expression does not evaluate to a boolean expression where = follows.
I think this should do it:
takeEveryNth :: [Int] -> Int -> [Int]
takeEveryNth g destination
| length g <= destination = []
| otherwise = [g !! destination] ++ takeEveryNth (drop (destination+1) g) destination
Demo
Test:
takeEveryNth [1..10] 2
Produces:
[3,6,9]
and
takeEveryNth [1..10] 1
Produces:
[2,4,6,8,10]
A: The reason that this does not work is because the parser expects a singe =, not a == for a guard. That being said, you use guards as if they are patterns. Guards work with expressions that have type Bool. So a guard like | [] destination = ... makes no sense.
You likely want to implement something like:
takeEveryNth :: [Int] -> Int -> [Int]
takeEveryNth [] _ = []
takeEveryNth g destination = [g !! destination] ++ takeEveryNth (drop (destination+1) g) destination
This however is still not sufficient, since if the list g contains less than n elements, the g !! destination will error. Furthermore wrapping the values in a singleton list is not necessary, you can use the "cons" function (:) :: a -> [a] -> [a]. You can make use of drop :: Int -> [a] -> [a] to safely split at a given element, and then perform pattern matching, for example in a pattern guard on that result:
takeEveryNth :: [Int] -> Int -> [Int]
takeEveryNth g n
| (x:xs) <- drop (n-1) g = x : takeEveryNth xs n
| otherwise = []
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,715 |
\section{Introduction}
Tablet computers are widely used to complement education and provide entertainment at home and school. In the UK, 44\% of children aged between 5 to 11 have their own tablet computers or use them as the major means to go online~\cite{ofcom2016}. Tablet computers are used in over 70\% of UK schools to complement education. A similar trend is also observed in the US, where ownership of tablets by young children has grown 5 times between 2011 and 2013 \cite{commonsense2013}. This is transforming the learning experience for young children~\cite{judge2015using,papadakis2016comparing,neumann2014touch,schacter2016improving}.
However, these new ways of online access pose new privacy risks to families and young children. The large number of applications (`apps') that can be downloaded for free are a major way in which children interact with these devices. Currently these `free' apps are largely supported by monetisation of user's personal information~\cite{acquisti2016economics,kummer2016private}. While the use of cute characters may suggest benign practices, a large amount of personal information and online behaviour may be collected from children's apps and shared with third party online marketing and advertising industry~\cite{reyes2017our}. Such practices are not unique to children's apps, but young children are particularly vulnerable to this type of exposure and less capable to resist the resulting (personalised) in-app advertisements and game promotions~\cite{digital2017}.
Previous work~\cite{zhang2016nosy,kumar2018cscw} have discussed different types of online privacy threats that are recognisable by young children interacting with mobile devices, but personal data collection by mobile apps has not been specifically discussed. Exiting research has shown that this opaque data privacy risk is unknown to most users and extremely challenging to manage~\cite{van2017better,vallina2016tracking}. Current internet safeguarding advice for young children mainly focuses on the management of content, cyberbullying or social media~\cite{digital2017}. We argue that approaches to raising young children's awareness of data privacy risk are under-researched, yet are critical for scaffolding children's mental models of privacy.
Our work thus focuses on understanding the current practices applied by parents for safeguarding the online privacy of their children, and identifying barriers faced by families for mediating data privacy risks effectively. We aim to explore three questions:
\begin{itemize}
\item What privacy risks are children aged 6-10 aware of when interacting with their tablets?
\item How much are parents aware of the possibility of personal data collection by the apps regularly used by their children?
\item What technical and social practices are used by parents for safeguarding their young children's online privacy, and what support do they need to mediate data privacy risks?
\end{itemize}
To achieve this, we conducted semi-structured interviews with 12 parent-child pairs from the South East area of the UK, complemented by an online survey with 220 parents from western developed countries (78.6\% UK residence). Our analysis shows that current privacy tools on tablet devices provide good support for parents in our study to set up basic content control and filtering, but offer only limited capabilities for supporting them to gain awareness of data privacy risks or help their children establish this understanding. Although savvy tablet users, children in our study did not demonstrate a consistent understanding of their risk coping actions. Similarly, their parents -- who are largely relied upon by young children -- had limited awareness of the implicit personal data collection by third-parties or how to safeguard their children from this kind of risks. Our findings suggest that we are in need of new tools to raise parents' awareness of the current personal data collection practices of mobile applications, and help both parents and young children to gain the skills for coping with data privacy threats on mobile platforms.
\section{Background}
\subsection{Children and Mobile Technology}
In 2016, UK children aged 5-15 were for the first time reported to spend more time online than watching TV ~\cite{ofcom2016}. Tablets and smartphones are becoming the most popular devices used by children to go online, overtaking laptops or computers. However, little is known about the impact of these technologies on children's online safety and general well-being~\cite{digital2017}.
Research has shown that teenagers and tweens have a reasonable understanding about privacy risks online and their implications, and strategies to protect themselves~\cite{davis2013tweens,mostmans2014would}, although they are facing increasing challenges related to the use of Social Media platforms and smartphone devices~\cite{wisniewski2017parental}.
However, younger children are generally expected to be less capable to engage with the Internet in a safe and mindful way~\cite{shmueli2010privacy,holloway2013zero}. Using hypothetical scenarios and the contextual integrity framework, Kumar et al.~\cite{kumar2018cscw} unpacked young children's (aged 5-11) understandings of online privacy and identified key gaps in their recognition of how information is transmitted from/to their devices. Zhang-Kenney et al.~\cite{zhang2016nosy} found that children aged 7-11 perceived privacy related to their use of mobile devices as being alone, hiding secrets, keeping things to yourself, or not talking to strangers, largely drawing on their offline life experiences. We extend this existing body of work and examine children's understanding about data privacy on the mobile platforms in a contextualised and nuanced way.
\subsection{Parental Mediation of Mobile Technology}
Researchers have found that parents are generally concerned about their children's online privacy risks~\cite{ofcom2016,zhang2016nosy}, and employ a range of mechanisms in an attempt to safeguard their children, such as password protections, supervising them, or setting up social practices at home (e.g. limiting access to the Internet)~\cite{ofcom2016}.
Our work aims to investigate whether UK parents of young children are effectively supported to choose less privacy-invasive mobile apps for their children and what parents may struggle with.
A large body of previous research has investigated parents' role in regulating their children's' interactions with technologies, such as TV or computers~\cite{lin1989parental,austin1993exploring,valkenburg1999developing,lwin2008protecting,valcke2010internet,shin2011parental}. Parents' role in mediating children's usage of the new mobile technologies are largely investigated for parents of older children~\cite{wisniewski2017parental,wisniewski2017parents} or parents battling with young children's screentime control~\cite{hiniker2016screen,hiniker2016not} or content filtering~\cite{hashish2014involving}. These studies highlighted the challenges that parents face with fully grasping the new technologies or socially engaging their young children.
Literature suggests that parents' engagement largely falls into three patterns~\cite{hiniker2016not}: \textit{active mediation}, where parents take time to discuss with children about usage of technologies~\cite{livingstone2008parental}; \textit{restrictive mediation}, where access to technologies is controlled and limited; and \textit{co-engagement}, where parents consume technologies together with their children without injecting any critiques~\cite{hashish2014involving}.
Existing parental mediation approaches for managing older children's online privacy and safety have largely focused on a \textit{restriction} approach, for example, controlling or monitoring teens' interaction with their mobile phones using parental control software. However, the usability of these tools and their effectiveness has been questioned~\cite{livingstone2008parental,anderson2016parents,wisniewski2017parental,wisniewski2017parents}. For managing younger children's use of mobile technologies, new solutions are developed to promote active mediation and co-engagement between parents and young children, for example, for setting up content filtering~\cite{hashish2014involving} or limiting smartphone use~\cite{ko2015familync}. Results show that a combination of technical and social mediation can lead to a more productive learning experience and positive parent-child relationship. We extend this literature by investigating approaches currently taken by the parents to manage online privacy risks for their young children (under 11) and their effectiveness.
\subsection{Personal Data Collection on Mobile Platforms}
More broadly, concerns about the collection and use of personal information have been discussed prior to the emergency of the web and smartphones. Westin~\cite{westin1968privacy} describes privacy as the notion of personal autonomy over what information is communicated, by whom, and when. Nissenbaum~\cite{nissenbaum2004privacy} views privacy as a dynamic, dialectical process of boundary negotiation, and argues that there are no universal norms: privacy preferences ought to differ according to distinct culture or context.
Major smartphone operating systems like Android and iOS have endeavoured to improve on their existing privacy permission settings with the introduction of more granular controls. Despite such improvements, studies suggest that existing mechanisms are still inadequate, failing to raise users' awareness of these settings or convey implications to their privacy risks~\cite{balebako2014privacy,Liccardi2013,van2017better}. In response to these problems, researchers have explored alternative, novel presentations of privacy notifications, by raising users' awareness on the collection of sensitive personal information~\cite{almuhimedi2015your}, making complex privacy notices easier to digest~\cite{kelley2009nutrition,liccardi2014no}, or easing the process of decision by predicting personal privacy preferences~\cite{lin2012expectation,liu2016follow}. More recently, we have seen a growing body of work revealing third-party data collection practices to the users in various ways, such as in an augmented permission interface~\cite{balebako2014privacy} or through alternative visualisations~\cite{van2017better}. The goal of these studies is to reveal the opaque personal data flows, from the mobile apps to first-party app developers as well as third-party online advertising and marketing trackers, and investigate the impact on users' privacy mental model~\cite{vallina2016tracking,yu2016tracking,binns2018toit}. Our study explores the effectiveness of current privacy setting mechanisms for helping parents safeguard their children, and parents' possible needs for the alternative, transparent presentation of personal data risks.
\input{method}
\input{result}
\section{Discussions}
We found that child participants in our lab study demonstrated an awareness of risks that were directly experience-able, such as in-app promotions or inappropriate content. However, they had limited knowledge about any of the more insidious personal data privacy threats and they currently largely relied on parents' help to safeguard their online safety or provide guidance. These risks were neither fully recognised by their parents nor regularly discussed with them.
Our lab study and survey results further showed that our parent participants played a key role in mediating their children's interactions with mobile technologies. However, our analysis of both the lab interviews and the online survey showed that our parent participants largely had limited understanding about personal data collection by mobile apps, and their current concerns largely centred around app content, in-app promotions and exposure to strangers online. Parent participants in both studies largely took a passive approach to safeguarding their children, by setting up technical barriers or strict family rules. Our interviews showed possible reasons behind our parent participants' mediation approaches, including their perception that their children were too young to understand privacy risks, and their struggle of communicating with their children effectively. Existing literature has suggested that it is critical to consider active parental mediation of children's technology usage from an early age~\cite{hashish2014involving,kumar2018cscw}, when they are still interested in developing trusty relationship with grown-ups. This suggests that there might be a critical gap in exiting technologies and resources for not only raising parents' privacy awareness, but also their recognition of the importance of combining technical controls with active social interaction and mediation.
\subsection{Helping Parents to Raise Their Privacy Awareness}
Our parent participants' current concerns about their children's usage of mobile devices in terms of privacy risks are largely misplaced. Our data suggest that this is partially due to the difficulty parents expressed about keeping up with rapid developing technologies, and the lack of available tools that would be focused on raising users' awareness of privacy risks.
Privacy researchers have explored various ways to enhance the current opaque and passive privacy `permission' models on mobile devices, by contextualising data access purposes~\cite{shih2015privacy}, summarising risks~\cite{lin2012expectation}, augmenting permission interfaces~\cite{liccardi2014no}, and exploring just-in-time notification/nudging~\cite{almuhimedi2015your,balebako2013little}. However, in our study, we still found parents in our lab study struggling with having to scroll down to the bottom of the app page to read a piece of lengthy and jargon-laden privacy policy as their only option. This suggests that these technologies are not yet becoming accessible in the mainstream platforms.
Communicating privacy risks---especially those without immediate impacts---to busy parents can be challenging. As we see, even though our parent participants in our survey largely focused on the importance of content appropriateness, their young children were still exposed to apps that were probably inappropriate to their age (see Table~\ref{tab:apps}). The age rating of apps can be obscure (depending on the device and platform), and recognising apps that are indeed designed for young children in the general app store can be challenging even for trained eyes. This suggests that designing for parents may require careful consideration about information accessibility and usability. A summarised presentation of app risks~\cite{lin2012expectation} can provide a convenient shortcut for parents to quickly sift through apps with less risks. However, privacy risks can be a personal and contextualised decision making process~\cite{nielsen2002getting}, and a one-fit-all might not work for everyone's need.
Another challenge is that parents can face a more complicated social context, such as the peer pressure their children feel from their friends or siblings~\cite{zhang2016nosy,wisniewski2017parents}. These unique social factors could lead to either a more complex mental model or compromises to be made. Designing for parents thus needs to consider additional social context related to the technologies, such as experience comments from peers or other parents. They may provide as valuable inputs to their decision making as knowing
the specific companies or jurisdictions that have access to their children's personal data.
\subsection{Filling in the Parental Mediation Void}
Our study not only highlighted the knowledge gap in parent participants' awareness of personal data privacy threats, but also the even bigger knowledge gap of their young children's. This is alarming, given that our results showed that our child participants were already exposed to the risks, and they were unclear when to ask for help from their parents. In our study, our child participants showed a strong reliance on their parents' help, and a strong and trusty relationship with their parents. This indicates that there might be a great opportunity for parents to take a more proactive role in facilitating children's understanding about privacy risks.
However, currently our parent participants largely believed either that their children were too young to understand or they found themselves ill-equipped to mediate their children. This suggests there might be a critical gap in modern parents' awareness of the importance of active mediation and in technologies supporting parents to take an interactive approach.
This is analogous to the situation of parenting approaches to teenage online habits. A recent review of parental control tools~\cite{wisniewski2017parental} has shown that current technologies largely focus on parental restrictions/monitoring for parents of teenagers, and provide limited support for increasing parents' awareness or facilitating parent-child discussions, which is in fact desired by both parents and their teens. Existing studies have demonstrated that a co-learning process can facilitate a more effective mediation of technology usage between parents and young children~\cite{hiniker2016screen,hashish2014involving}
Our findings suggest the need to provide more support in raising parents' awareness on the importance of discussing these issues with their children from a young age. Existing resources online are largely focused on older children (like tweens or teenagers) and do not support younger children or cover this type of emerging personal data privacy risks. Although apps or smart toys targeted for young children are currently in the limelight due to rumours about them being unsafe and prompting children to reveal personal information~\cite{anglea2014,mcreynolds2017toys}, understanding of the risks associated with smart apps or smart toys is still scarce, and parents are only provided with generic cautions instead of specific advices.
Technologies should also consider incentivising parents to actively discuss these issues with their young children by providing specific age options, and content specially targeted for a younger age group. Literature has suggested that parents of teenagers often face stronger push-back from their older children for interfering or mediating their use of technologies~\cite{wisniewski2017parents}. Kumar et al~\cite{kumar2018cscw} argue that parents could miss a critical opportunity to establish a mediation relationship with their young children if they choose to delay the discussions, because ``[young] children are more focused on adult/parent relationships''.
\subsection{Scaffolding Children's Understanding}
The biggest challenges faced by our child participants in the lab study were that they found it hard to understand how information was used by mobile apps, who could access information and where information could go, and how to react to different risks, by recognising when to ask for help. This can be regarded as a complex topic for young children, and the ICT curriculum in the UK is still forming and going through rapid changes in the last few years. However, we argue that children's early understandings could have potential long-term impact on their mental model when they grow older and have more freedom with their smartphone devices~\cite{kumar2018cscw}.
The Zone of Proximal Development (ZPD) theory from Education Psychology~\cite{chaiklin2003zone} suggests that children's learning is better supported if education starts with individual child's current zone of knowledge and supports their learning process according to their individual needs and environment. A recent report in the UK on Digital Childhood also highlighted a gradual change of focus is needed for mediating young children's use of digital technologies according to their developmental stages~\cite{digital2017}. The critical knowledge gaps identified in our study could provide initial indicators to future privacy education technologies.
Furthermore, the web prototype we used in the last part of our lab study provided some possible future design directions for us to explore. While walking through children's favorite apps in the prototype (see Figure~\ref{fig:tracker}), we observed that older children (aged 8-10) found it ``very interesting''. They demonstrated an understanding of the information transmissions through interactions with the map view, and engaged in the discussions about the companies and countries to which their favorite apps might be sending their personal information. They responded that they believed that ``\textit{it's not right for companies from another country to access my information}'' [C9, aged 10] or that ``\textit{[I am ] sort of surprised, but not much. because people would do anything to make more money these days}'' [C1, aged 10].
At the same time we observed that the application enabled an engagement between parents and their children. Parents found it a useful tool to explain to their children the implications (``\textit{now you think that these companies are kind of using these as clever tools to gather your data?
you know it [means] that it's more than a game, did you?}''[P4]). This suggests that a child-friendly visusalisation of the information transmissions behind mobile apps could have the potential to not only increase children and parents' understanding of personal data privacy risks but also provide an interactive tool for co-learning.
\subsection{Limitations}
The primary limitation of this study is our sample population; our lab study participants were all residents of the affluent South East area in the UK and highly educated. We fully acknowledge that this is not representative of the populations. The complementation of this interview data with an online survey that incorporated a wider and more diverse population was one step towards validating the main themes. Furthermore, we have also participated in a large-scale science outreach activity for young children in the Autumn of 2017, with $>$100 families participating on the day. We observed similar reactions from the children, who came from a wider part of the area.
The second limitation is the lab study setting, where the presence of parents and children in the same room might influence the responses from the child participants. Furthermore, the unfamiliar setting and time constraints of the study might also limit their ability of reflective thinking. We plan to explore focus group studies with young children in future research, to reduce the influence from the interviewers and parents, and observe them in their familiar settings, like schools. Through this we aim to achieve a deeper understanding about the familiar terms used by the young children to describe risks and the building blocks required for them to adapt their existing knowledge to understanding new kinds of information transmission and associated risks.
\section{Conclusions}
In this report we presented the results of a mixed-method study towards understanding what data privacy threats children ages 6-10 and their parents were aware of during the interaction with tablet computers. We found that although our child participants had a reasonable awareness of familiar risks, like in-app promotions or inappropriate content, they (particularly younger children) largely struggled to understand the information transmissions of mobile apps, and how their personal data might be collected and pose threats to their personal privacy. Older children in our study demonstrated some strategies of declining access to information, however, our child participants still mostly relied on parents' help to mitigate risks.
Our parents also showed limited understanding regarding what data was collected by the apps and shared with whom. Their primary privacy concerns were about content and screen time controls. To mitigate their concerns, they sought passive technical restrictions, app limitations, or external information sources. However, these tools and resources largely focused on content control and provided no support for raising parents' awareness or facilitating discussions with their children. This is therefore a critical gap in the current landscape.
Based on these findings, we recommend 1) raising the general awareness of considering scaffolding children's knowledge about data privacy from an early age, where they are still at an age of seeking for a positive relationship with grown-ups, and are already facing risks at a regular basis; and 2) tool and resource developments that focus on facilitating skill and knowledge building for both parents and their young children, and encouraging an active co-learning experience. Our identification of children's key knowledge gaps and feedback to an exiting prototype could provide potential inputs for the design of future privacy education technologies.
\section{Selection and Participation of Children}
In our ethics approved study, children were recruited through public invitations shared with parents on social media, posters in permitted public spaces, mailing lists, and snowball sampling. The study took place over school summer holiday. Thus, no recruitment took place through schools. Participants lived in the South East area of the U.K. Children were limited to the ages of between six and ten inclusively. All children from each family were encouraged to participate in the study as long as they were within the age limit and did not express distress. Parents signed an informed consent and children signed an assent form with their parents' help (if needed). The forms explicitly requested consent for the study to be audio-recorded for the purposes of transcription.
\bibliographystyle{SIGCHI-Reference-Format}
\section{Methodology}
We undertook a mixed method study, including qualitative semi-structured interviews and an online survey. The former allowed us to look into the practices and understandings of individual child and parent, and the latter complemented these thick descriptions with quantitative data from a larger sample. Our study was reviewed and approved by our university's research ethics committee.
\subsection{Semi-structured Interviews to Parents and Children}
The parent-child interviews were designed to last no longer than one hour, and consisted of three parts. For safeguarding reasons, parents and children participants of the study stayed in the same room throughout each interview. We acknowledge that the presence of parents in the interviews may impact on the responses provided by the children.
In the first part, each child participant was asked to show us two of their favourite apps or games on their tablet, which was brought along to the study. They were also asked to explain how the apps were found, e.g. by themselves or together with the parents. In this way we were able to look into both the technical and social safeguarding practice at home from the child's point of view. The parent was then asked to comment on their privacy concerns of these favourite apps.
In the second part of the study, we used three hypothetical scenarios to explore how children felt about personal data collection by the apps, and how they might cope with them. In the three scenarios the child was asked to imagine that an app was asking for access to their camera, microphone or location information and how they felt about it. We then showed each child how to check access permissions on their device, and asked how they felt about their favorite apps having access to their e.g. camera or location. At the end of this session, parents were asked to comment on how they felt about their children's responses.
In the final part of the interview, we showed parents and children a new way of examining possible personal data leakage of their favorite apps using a prototype application from our prior work~\cite{vankleek2018chi} (see Figure~\ref{fig:tracker}). Although this platform was not specifically designed for children, we wanted to see how the explicit presentation of information transmission of mobile apps in this tool would impact participating children and parents' mindset about data privacy risks and their existing safeguarding practices. After giving each child five minutes to explore the interface by themselves, we asked them how they felt about their data being collected by various companies. We concluded the interview by asking some open questions to parents concerning their opinions about current technology and legal support for safeguarding their children's privacy online.
\begin{figure*}[ht!]
\centering
\setlength\fboxsep{0pt}
\setlength\fboxrule{0pt}
\fbox{\includegraphics[width=5.2in]{tracker.pdf}}
\caption{The web application used in the last phase of the lab study shows destinations to which personal data may be sent through each app, in a stacked bar chart view (left) and a map view (right). Hovering over an app (in the legend) highlights data trackers specific to that app.}
\label{fig:tracker}
\end{figure*}
\subsection{Online Surveys to Parents}
To confirm the themes observed from the 12 families in the lab study, we designed an online survey to parents of young children who regularly interact with mobile devices. The online survey was supported by the Prolific Academic system (\url{http://prolific.ac}), a crowdsourced online survey platform that is capable of recruiting participants fitting specific criteria. In our survey, participants were required to be parents or guardians to at least one child aged between 6 and 10, who has regular access to a tablet computer or smartphone. The survey was set up to be completed within 15 minutes, and each participant was rewarded \textsterling1.4 for completing the survey. Prolific provides comprehensive demographic information about the participants, such as their levels of family income or residential areas, which enabled us to collect data from a more diverse population than was the case in our lab study.
The online survey contained 3 parts. It started with some basic demographic questions about the parent and child, such as their age, level of education and usage of devices. The parent was then asked to choose one child aged 6-10 to complete the main survey.
There are two themes in the second/main part of the study: parents' privacy concerns in relation to their children's use of tablets or smartphones, and their knowledge of existing privacy control technologies, including password controls, kids app stores, and app privacy permissions. It started with \textit{generic concerns} considered by parents when choosing apps for their children and then focused on their opinions to specific personal data collection behaviours, such as accessing cameras, location information or sensitive personal information.
Finally the survey was concluded with a reflection section, asking whether the parents felt they learnt anything new about safeguarding their children's privacy and whether they would communicate this new knowledge to their child.
\subsection{Participants}
Our lab study participants were recruited through social media, public posters, mailing lists, and snowball sampling. All interviews were conducted in person, and parents and children stayed in the same room throughout. The interview protocol was designed to take 30-45 minutes. Each participant child received a \textsterling15 Amazon Gift Voucher as a token of appreciation. In total we had 12 families and 14 children, with at least one child from each family aged between 6 and 10 (inclusive). Mean age of the children was 7.7. More mothers (10 participants) than fathers accompanied the child to the study. Siblings were included in the same interview if they were both within the age of 6-10.
The online survey received 250 responses. 29 responses were excluded because their children were outside the age range of 6 and 10. Of the remaining 221 responses, the average age of the parents was 35.9, and 69.5\% were female. Most of our respondents (78\%) were UK residents, 15\% US residents, and the remaining 7\% reside in other western countries. The UK residents were evenly distributed in different regions of the country. The respondents had on average 2.27 children (range 1-5, SD = 0.88), and the average age of the child selected for completing the survey was 7.91 (range 6-10, SD = 1.41).
\subsection{Data Analysis Method}
We collected 10.5 hours of interview audio in total. The audio files were carefully transcribed and Thematic Analysis~\cite{braun2013successful} was applied by 2 researchers to identify common themes. Thematic Analysis allows us to take a ground-up approach to data analysis, without being confined to a prior theoretical framework. The two researchers started by coding half of the transcripts independently. We then discussed the codes that emerged, consolidated them, and organised them into 5 themes: children's understanding, children's coping strategies, parents' concerns, parental mediation methods and parents' expectations of support. Both researchers used the new codes to code all the transcripts and differences were discussed and resolved. The survey data was mostly analysed using a quantitative data analysis approach, although the three free-text questions were analysed using Thematic Analysis following the same process as above.
\section{Findings}
In what follows, we first describe how our parents perceive and manage risks. We then outline children's understandings of and coping abilities with online privacy risks. Finally, we highlight parents' needs for managing their children's data privacy risks related to their children's use of mobile devices.
\subsection{Parents' Concerns}
In both the lab study and online survey, parents said that they were generally very concerned of their children's use of these devices: only 2 families in the lab study mentioned that they never thought about privacy issues related to their children's use of mobile devices; and 44\% parents in the survey said they thought about their children's online privacy ``very often'' and 31.3\% said that they thought about it ``sometimes''. However, our online survey data also suggests that our parents' primary concerns were centred on \textit{app content} (86.8\%), followed by the \textit{cost of the apps} (70\%). This is consistent with parents from the lab study, as said by P1, ``\textit{before privacy, I want to know what does this do?}''.
Furthermore, despite parents' expressed concerns, our survey results suggest that many children in these families could still be using apps that were inappropriate for their age (i.e. content) or accessing their sensitive personal information. Table~\ref{tab:apps} shows children's top favorite apps that were mentioned more than 5 times in the online survey responses. For example, only 4 (out of 14) of these required no access to sensitive personal data, such as contact details on the device, location information or unique identification of the device; and five of these popular apps had an age rating inappropriate for young children aged 6-10 and would require parental guidance\footnote{The information about each app is retrieved from Google Play Store, accessed in December 2017. The UK-specific interpretation of the content rating can be found \url{https://support.google.com/googleplay/answer/6209544?hl=en-GB}. PEGI 3-7 are probably more appropriate for young children aged 6-10, than those rated ``requiring parental guidance''.}, including YouTube as well as some popular social media apps.
The level of privacy concerns expressed by the parent participants in the survey also did not significantly correlate with the type of favorite apps used by the children: parents who were generally very concerned might still choose apps having inappropriate age rating or excessive access to their children's personal information.
In our lab study, most (10/12) parent participants expressed that they were unaware of what data about them or their children was being collected, by whom, and how it was shared with (``\textit{We have not been worried about this sharing of information before}''[P2]). Only very few parents (2/14) had gone through the privacy settings on the device prior to the study (``\textit{basically I will just check the permissions and [if] there is anything that I can turn it off then I will}''[P1]). This indicates that there is a gap between our parent participants' concerns and their actual level of awareness of technologies and information about apps.
\begin{table}[ht!]
\centering
\begin{tabular}{c|l|l|l}
App & Number of use & Age rating & Sensitive personal data access \\ \hline
YouTube & 110 & Parental guidance & YES \\
Minecraft & 40 & PEGI 7 & YES \\
Roblox & 29 & Parental guidance & YES \\
Netflix & 14 & Parental guidance & YES \\
CBeebies & 10 & PEGI 3 & \textbf{NO} \\
WhatsApp & 10 & PEGI 3 & YES \\
YouTube Kids & 9 & PEGI 3 & YES \\
Clash Royale & 9 & PEGI 7 & \textbf{NO} \\
Candy Crush & 8 & PEGI 3 & \textbf{NO} \\
Facebook & 8 & Parental guidance & YES \\
Angry Birds & 6 & PEGI 3 & YES \\
Pokemon Go & 5 & PEGI 3 & YES \\
Temple Run & 5 & PEGI 3 & \textbf{NO} \\
Music.ly & 5 & Parental guidance & YES\\
\end{tabular}
\caption{Top Favorite Apps Mentioned in the Online Survey}
\label{tab:apps}
\end{table}
\subsection{Parents' Approach to Risk Minimisation}
\subsubsection{Parental restrictions}
The main strategy to enact parental restriction by parent participants in our study was the use of password control: this was widely applied by families from both the lab study and the online survey. For example, only 24\% parents reported \textit{no} password control in the online survey; and 43\% of them stated that they had controls of installation of even free apps, which seems to indicate a level of vigilance. This was consistent with our lab study participants, where all (but two) families had password controls for any app installations and device log-ins.
Furthermore, in the lab study, we also observed that a few families sought for Internet access restrictions. However, our interviews showed that parents did not necessarily fully understand the implications of their controls. For example, 2 (out of 12) families mentioned that they took out the SIM cards from the smartphones given to their children, and they only realised later that their children could still access to the Internet through wifi.
Taken together, this suggests that restrictions might not be always effective; and even so, tend to be on the level of binary control (install/not install). The example of online connectivity restrictions highlights the challenges that parents in our study faced in fully comprehending their choice of technologies, and hence their ability to provide sufficient protection support for their children's online safety and privacy.
\subsubsection{Passive parent-led app screening}
A common pattern observed in our study was reliance on parental vetting (or direct selection) of the apps to be installed. The majority of the parents (73\%) in the online survey reported that they installed the apps for children after having screened them themselves and only 13\% thought their children might have installed the apps by themselves.
Parents from the lab study reported a higher vigilance of app screening. The majority of the parents (10/12) in the lab study believed that their children could not install any apps without their permissions (``\textit{my mum has the password, so I can't just get it myself}'' [C5]) or their awareness (``\textit{[as they use my email address], I can see what comes in}''[P1]). Furthermore, some parents in the lab study would regularly go through the app store (``\textit{I search for free games, and categories, and then put in their ages, and type in educational}''[P5]) or external recommendations to identify suitable apps for their children and install for them. Sometimes children were involved in the process; sometimes not.
2 families in the lab study mentioned that to mitigate their children's risks, they minimised the number of apps installed on their devices. For example, P11 mentioned that
\begin{quote}
``\textit{I am always very weary with apps. For me what I would really encourage are educational apps to learn for example maths and this kind of thing}''.
\end{quote}
Although these families were generally very vigilant with their children's access to apps, their primary focus remained on apps' content appropriateness and controlling their children's access. None of the above approaches would raise our parents' awareness of personal data collection by mobile apps; nor manage these risks effectively for them.
\subsubsection{Setting home norms}
We found no consistent patterns in how in-home norms about app usage would be set or enforced by the parents.
The majority of the parents in the lab study believed that their children would `naturally' know when to ask for help, and would require their children to seek for parents' guidance by deploying family rules or technical restrictions. However, our interviews showed that the rules were not always consistently carried out either by the parents or children. For example, C8 described that ``\textit{I ask my mum and sometimes she allows it sometime not}''.
Despite this belief, several families from the lab study also mentioned that they required their children to use their devices in a common family area. P7, a mother of 10-year old mentioned that ``\textit{We try to keep them downstairs. So they are not doing things we are not aware of}'', and P11 said that ``\textit{When she is on YouTube, I try to make sure I am around. To keep an eye on her}.''
These observations do not suggest that family rules are ineffective, but that executing family rules against technologies can be a challenging task.
\subsubsection{Active mediation sparingly used}
In our lab study, only 2 families explicitly talked about personal data access on mobile devices with their children. For example, when being asked how he might go and install new apps on the device, the 8-year old boy responded with the following: \textit{ ... she [my mum] is strict about privacy settings, she has told me ... only apps that really need it... She doesn't want our data to go to other people...they can break into your home''} [C8]. This shows how the parent (not present in the study) was being explicit about data privacy risks with the child and trying to discuss the implications of the risks as well as setting up restrictions. Both families used simple real-world threats to help children understand the possible consequences of oversharing. No additional technologies or online resources were mentioned.
We observed two themes in the rest of the families from the lab study, who did not take any active mediation approaches yet at home. One theme was that some parents believed that privacy was a concept too hard for young children and they would avoid active mediations and take a parent-led protective approach.
For example, the mother of a 6-year old girl concluded that
\begin{quote}
``\textit{... she can't understand. .. it's my responsibility and it's hard to expect a child to understand that these companies are actually manipulating their naivety}''[P9]
\end{quote}
The other theme was that a few parents were open to introducing early discussions with their children, but they struggled with communicating to their children, for example, P11 described that ``\textit{This mostly comes from the school. When it comes from the parents, they don't really [listen].}'', or felt ill-equipped with their own understandings ``\textit{I feel [the other parent] is more equipped to have these conversations. I barely know how to install an app.}''[P5].
This suggests that the importance of actively mediating their children's awareness from a young age is not yet widely recognised by parents in our study, and these parents showed their struggle with keeping up with the technologies or finding a way to discuss these issues with their children effectively.
\subsection{Children's Awareness of Personal Data Privacy Threats}
Most parents in the online survey were not concerned about their child's awareness of online privacy risks: 83.3\% parents reported that they were ``very'' or ``somewhat'' happy, and a high proportion of them (77.7\%) expected that their children would ask for help or click 'no' to unnecessary requests for personal information access by the apps.
However, these patterns were not supported in the lab study. Despite indications of emerging understanding about sensitive information by our child participants, and good coping strategies from older children (above 8 years old) to directly experience-able risks, like in-app promotions or inappropriate content, children largely demonstrated a knowledge gap regarding personal data privacy threats related to their use of mobile devices and younger children particularly struggled.
Although most of our child participants (9/14) demonstrated recognition of sensitive types of information for them, including pictures, location information, passwords, email addresses, medical records, bank details etc, the main threats perceived by them resulting from exposing their personal information would come from \textit{strangers}.
The majority of the children (12/14) in the lab study mentioned that they could notice risks like \textit{in-app promotions}, \textit{inappropriate content}, or \textit{requests to sensitive information like credit card details or passwords}; and they used approaches like \textit{skipping/declining access} or \textit{asking for help from parents}. However, when an advert or promotion was skipped, the main reason was mainly about being bored or annoyed ("\textit{I don't really want to watch. because I want to watch something else}''[C10]). When help was sought from parents, it was more likely to be due to insufficient access to the device or a vague feeling of something not right (``...\textit{I didn't really like the look of, so I go to my Daddy}..'' [C2]). This suggests that our children may not always fully comprehend the actual risks or recognise the privacy-invasive context.
When we asked the child participants what they thought about one of their favorite apps requesting access to their device's camera, location information or photos,
most of the children couldn't answer, or gave unintelligible replies, such as ``\textit{I don't know what would happen. I will press yes}''[C11: a 6-yo boy].
Only a few older children (4/14) demonstrated some abilities of recognising potential risks, and associate specific social norms for different contents, like different apps, different types of personal data, or different data recipients. For example, C8, an 8-year old boy, when being asked why he thought location information was sensitive, he mentioned that ``\textit{only apps that really need it, like maps and stuff ... you won't even let the app that tracks weather and stuff to have location [because] they can break into your home}''.
\subsection{Children's Coping Strategies}
\subsubsection{Relying on parents' help}
Parents' guidance was widely sought by our child participants to the lab study. However, we observed two themes in children's reliance on parents: 1) a few children were consciously recognising potential risks and followed strict family norms, while 2) most children were generally motivated by a vague feeling about the situations or were restricted by what they could do on the devices by themselves.
For example, a 10-year old boy [C1] recognised the risk of an app asking for access to his audio and described that ``\textit{I do know when to ask...}'' and C8, an 8-year old boy, responded to our question about ``\textit{how he would respond to an app requesting for access to his camera}'', by saying that ``\textit{i ask my mum ... because she is strict about privacy settings}''. The majority of the children reacted passively to the risks, for example, C7 mentioned that ``\textit{Dad normally test whether these things send photos}''[C7]), and she would rely on Mummy to safeguard her privacy settings.
This implies a demand on parents' technical competence and also a need to raise children's ability of recognising risky situations. It is hard to be thorough with parental controls, given the complexity of technologies. Helping children, who are in the frontier of these risks, to recognise and flag risks, is a crucial piece in safeguarding children's privacy online.
\subsubsection{Declining access}
Our child participants' ability of declining personal data access request by mobile apps correlates to their awareness about personal data collection practices of the apps.
The majority of the children in the lab study showed a reasonably good ability of declining in-app game promotions or adverts. However, they were largely unable to make a conscious decision with apps asking for access to cameras or personal details. Most children had not been told about what they can/should do. If there were a ``cross'' button and they were annoyed and wanted to get on with their games, they would just tick it away.
Only a few children demonstrated some more developed mental model regarding their decisions, which took into consideration of the needs or purposes of an app asking for access to particular information. For example, an 8-year old boy described that ``\textit{I don't want `chrome' to have access to my phones... so it can show to others. and 'stickbot' doesn't really [need] either}'' [C5].
This indicates a critical gap in our child participants' awareness and coping skills regarding personal data collection by mobile apps. This is contributed by parent participants' own lack of awareness of the risks but also their lack of engagement with the children, believing that they are too young to understand these issues.
\subsection{Parents' Reflections on Personal Data Collection}
\subsubsection{Technologies hard to follow}
In the survey, parents expressed a high level of concerns about apps accessing their children's location information (93\%) or cameras (64\%). However, less than 20\% of the parents checked their children's privacy permission settings regularly or when they installed an app. On the conclusion of the survey, nearly 86\% of them felt that they learnt something through the survey and would need to go and check their children's apps and privacy settings more carefully. This suggests that parents' needs are largely unmet, and there is a critical gap between what parents are concerned about and what they are supported with.
In our lab study 7 parent participants expressed that they found it hard to understand technologies and keep up to speed. They often relied on the other partner, who may be a Dad or Mum, to take a lead on safeguarding the children. For example, P2, a mother of a 7-year old girl, expressed at the conclusion of the interview that ``\textit{he [my husband] understands more than I do. I don't know how to do that. We keep on discussing...at some point you need to show me how to do that.}''.
Four parents thought they had been careful with the device controls by applying restricted access to Internet or content. However, once knowing more about the personal data privacy threats, they found it hard to be thorough, ``\textit{I thought I was in a good control of what they have access to, and what they have told me. We ought to be more sensitive}'' [P4].
\subsubsection{Feeling losing control}
At the conclusion of the lab interviews, the majority of the parents (9/12) expressed an increase of concerns and their surprises of not being made known. They demanded for \textit{more transparency} in this space (``\textit{when you choose an app very clearly just one page just say this is what we do with your information. this is where this is going, rather than some kind of hidden secret}''[P10]) or legal regulations (``\textit{Legally ... we should be protected by law. They [these companies] should simply and very clearly show all these things that they are doing}''[P3]).
A few parents in the lab study reacted more passively to the issue, expressing that they believed that these issues should be dealt with by relevant authorities in due course (``\textit{I am trusting other people do know, and exercising the influence and pressure}'' [P5]) or felt that this type of personal data collections was unsurprising and hard to avoid given how the current app ecosystem works (``\textit{There is nothing to stop trackers, it's just a polite thing that you subscribe to a mailing list, but they don't have a way to unsubscribe me}''[P1]).
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,113 |
package com.amazonaws.services.cloudtrail.model.transform;
import java.math.*;
import javax.annotation.Generated;
import com.amazonaws.services.cloudtrail.model.*;
import com.amazonaws.transform.SimpleTypeJsonUnmarshallers.*;
import com.amazonaws.transform.*;
import com.fasterxml.jackson.core.JsonToken;
import static com.fasterxml.jackson.core.JsonToken.*;
/**
* Event JSON Unmarshaller
*/
@Generated("com.amazonaws:aws-java-sdk-code-generator")
public class EventJsonUnmarshaller implements Unmarshaller<Event, JsonUnmarshallerContext> {
public Event unmarshall(JsonUnmarshallerContext context) throws Exception {
Event event = new Event();
int originalDepth = context.getCurrentDepth();
String currentParentElement = context.getCurrentParentElement();
int targetDepth = originalDepth + 1;
JsonToken token = context.getCurrentToken();
if (token == null)
token = context.nextToken();
if (token == VALUE_NULL) {
return null;
}
while (true) {
if (token == null)
break;
if (token == FIELD_NAME || token == START_OBJECT) {
if (context.testExpression("EventId", targetDepth)) {
context.nextToken();
event.setEventId(context.getUnmarshaller(String.class).unmarshall(context));
}
if (context.testExpression("EventName", targetDepth)) {
context.nextToken();
event.setEventName(context.getUnmarshaller(String.class).unmarshall(context));
}
if (context.testExpression("ReadOnly", targetDepth)) {
context.nextToken();
event.setReadOnly(context.getUnmarshaller(String.class).unmarshall(context));
}
if (context.testExpression("AccessKeyId", targetDepth)) {
context.nextToken();
event.setAccessKeyId(context.getUnmarshaller(String.class).unmarshall(context));
}
if (context.testExpression("EventTime", targetDepth)) {
context.nextToken();
event.setEventTime(DateJsonUnmarshallerFactory.getInstance("unixTimestamp").unmarshall(context));
}
if (context.testExpression("EventSource", targetDepth)) {
context.nextToken();
event.setEventSource(context.getUnmarshaller(String.class).unmarshall(context));
}
if (context.testExpression("Username", targetDepth)) {
context.nextToken();
event.setUsername(context.getUnmarshaller(String.class).unmarshall(context));
}
if (context.testExpression("Resources", targetDepth)) {
context.nextToken();
event.setResources(new ListUnmarshaller<Resource>(ResourceJsonUnmarshaller.getInstance())
.unmarshall(context));
}
if (context.testExpression("CloudTrailEvent", targetDepth)) {
context.nextToken();
event.setCloudTrailEvent(context.getUnmarshaller(String.class).unmarshall(context));
}
} else if (token == END_ARRAY || token == END_OBJECT) {
if (context.getLastParsedParentElement() == null || context.getLastParsedParentElement().equals(currentParentElement)) {
if (context.getCurrentDepth() <= originalDepth)
break;
}
}
token = context.nextToken();
}
return event;
}
private static EventJsonUnmarshaller instance;
public static EventJsonUnmarshaller getInstance() {
if (instance == null)
instance = new EventJsonUnmarshaller();
return instance;
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 8 |
Produced by Chris Curnow, Lindy Walsh, Christine P. Travers
and the Online Distributed Proofreading Team at
http://www.pgdp.net
THE SECOND WAR WITH ENGLAND.
[Illustration: The Constitution and Java.]
THE SECOND WAR
WITH
ENGLAND.
BY J. T. HEADLEY,
AUTHOR OF "NAPOLEON AND HIS MARSHALS," "WASHINGTON AND HIS GENERALS,"
"THE OLD GUARD," "SCOTT AND JACKSON," ETC. ETC.
IN TWO VOLUMES.
VOL. I.
NEW YORK:
CHARLES SCRIBNER, 145 NASSAU STREET.
1853.
Entered, according to Act of Congress, in the year 1853, by
CHARLES SCRIBNER,
In the Clerk's Office of the District Court of the United States for
the Southern District of New York.
C. W. BENEDICT,
STEREOTYPER AND PRINTER,
12 Spruce Street, N. Y.
PREFACE.
More books, probably, have been written on the War of 1812 than on any
other portion of our history. The great political leaders of that time
were so vindictive in their animosities, and took such strong and
decided ground on all political questions, that the success of one or
the other afterwards in public life depended very much on his conduct
during the war. Hence, much detached and personal history has been
written in order to clear up or illustrate some particular event. A
candidate for public office was often chosen for his services in the
war; hence, every portion of it in which he took part was thoroughly
investigated by both friends and foes. So if one had failed in that
trying period of the country, the world was sure to hear of it when he
came up for the suffrages of the people. The war proved very
unfortunate for some of the leaders, and court martials and disgrace
closed the career of many which had hitherto been bright and
prosperous. These men have written long pamphlets and books in
self-defence, or they have been written by their descendants, so that
if hearing both sides would aid the reader in coming to a correct
conclusion, he was pretty sure to reach it. When so many quarrels are
to be settled the public will not fail to be informed all about the
origin of them. Another class of works have been written, designed
only to furnish a synopsis of the war, and scarcely reach to the value
of histories. Others have been confined solely to the military and
naval movements--others still are devoted almost exclusively to
political matters of that period; so that notwithstanding the large
supply of works on the War of 1812, I know of none in which all these
different topics are even attempted to be combined in proper
proportions. The present work is an effort to accomplish that end
without being too voluminous on the one hand, or too general on the
other. I have endeavored to give impressions as well as facts--to
trace the current and depict the phases of public feeling, rather than
inflict on the reader long documents and longer debates, in which
everything that gave them life and interest was carefully excluded by
the reporter.
The effects of the fierce conflict waged between the Federalists and
Democrats during the war have not yet passed away, and many of the
actors in it are still living, who retain their old prejudices and
hatred. Their near descendants and relatives, though so many of them
are found in the ranks of democracy, still defend the memory of those
whose names they bear, and endeavor to throw discredit on the writer
who would rob them of reputation, and consign them to the obloquy they
deserve. In a war like the late one with Mexico, where almost every
officer was a hero, and in narrating the progress of which the
historian is called upon only to eulogize, his task is an easy one.
But in one like that of 1812, in which the most conspicuous leaders
met with signal defeat and disgrace, and instead of winning
reputation, lost that which had illustrated them in the revolutionary
struggle, the historian necessarily recalls feuds and assails
character, which is sure to bring down on him the maledictions and
open condemnation of friends and relations. A noble man and true
patriot, like General Dearborn, will never want friends who will deny
his incompetency as commander-in-chief, while one who had won so brave
a name in the revolution, and was so estimable a man in social life as
General Hull, must always be defended by those in whose veins his
blood flows. The inefficiency and blunders of the government remain to
this day to many a sufficient apology for the conduct of Wilkinson,
Hampton and others.
Having no animosities to gratify, and no prejudices to favor, I have
set down nought in malice, but have endeavored to ascertain, amid
conflicting testimony, the exact truth, without regarding the friendly
or hostile feelings the declaration of it might awaken. In many cases
I have withheld much that was personal, because it was not necessary
to my purpose, and useless only in self-defence. That I should
reconcile difficulties which have never yet been healed, and please
rivals who have ever hated each other, was not to be expected. I have
attempted also to give a clear impression of the political and social
feelings of the times, and make the reader, as far as lay in my power,
live amid the scenes I depict.
Two new features have been introduced into the present work, which I
though necessary to a complete history of the war, viz., privateering
and the Dartmoor Prison.
It would be impossible to give all the authorities to which I am
indebted. State papers, records, journals, Gazettes of the time have
been consulted, as well as histories, while I have earnestly sought
for information from the survivors of the war. In many cases I have
omitted references to books in which facts I state are found recorded,
because I came across them in old pamphlets, letters, and newspaper
paragraphs, where, probably, the original compiler also obtained them.
I cannot omit, however, acknowledging the vast aid I have derived from
Niles' Register. A more valuable periodical was never published in
this country. Ingersoll's History also, though very deficient in
arrangement, contains more valuable material than any other work
embracing the same period.
CONTENTS OF VOL. I.
CHAPTER I.
A REVIEW OF THE CAUSES LEADING TO THE SECOND WAR WITH ENGLAND.
Duplicity and oppressive acts of the British Government
contrasted with the forbearance of the United States --
Character of Madison -- Debates in Congress on War measures
-- Declaration of War, 15
CHAPTER II.
Different feelings with which the Declaration of War was
received -- State of the parties at the commencement --
Federalists and Democrats -- Their hostility -- Absurd
doctrines of the Federalists -- Hostility of New England --
Unprepared state of the country -- Culpable neglect of the
government -- Comparative strength of the two navies --
Empty state of the Treasury -- Inefficiency of the Cabinet, 58
CHAPTER III.
Plan of the Campaign -- General Hull sent to Detroit --
British officers first receive news of the declaration of
war -- Capture of Hull's baggage, etc. -- Enters Canada and
issues a proclamation, and sends out detachments -- Colonels
McArthur and Cass advance on Maiden -- Hull refuses to
sustain them -- Recrosses to Detroit -- Van Horne's defeat
-- Colonel Miller defeats the enemy, and opens Hull's
communications -- Strange conduct of Hull -- Advance of the
British -- Surrender of Detroit -- Indignation of the
officers -- Review of the Campaign -- Rising of the people
-- Harrison takes command -- Advance of the army, 70
CHAPTER IV.
Operations on the New York frontier -- Battle of Queenstown
-- Death of Brock -- Scott a prisoner -- General Smythe's
Proclamation and abortive attempts -- Cursed by the army --
Duel with General Porter -- Retires in disgrace --
Dearborn's movements and failures -- Review of the campaign
on the New York frontier -- Character of the officers and
soldiers, 98
CHAPTER V.
THE NAVY.
The Cabinet resolves to shut up our ships of war in port --
Remonstrance of Captains Bainbridge and Stuart -- Rodgers
ordered to sea -- Feeling of the crews -- Chase of the
Belvidere -- Narrow escape of the Constitution from an
English fleet -- Cruise of the Essex -- Action between the
Constitution and Guerriere -- Effect of the victory in
England and the United States -- United States takes the
Macedonian -- Lieutenant Hamilton carries the captured
colors to Washington -- Presented to Mrs Madison in a
ball-room -- The Argus -- Action between the Wasp and Frolic
-- Constitution captures the Java -- Hornet takes the
Peacock -- Effect of these Victories abroad, 125
CHAPTER VII.
Harrison plans a winter campaign -- Advance of the army --
Battle and massacre at the River Raisin -- Baseness of
Proctor -- Promoted by his Government -- Tecumseh, his
character and eloquence -- He stirs up the Creeks to War --
Massacre at Fort Mimms -- Investment of Fort Meigs --
Advance of Clay's reinforcements and their destruction --
Successful sortie -- Flight of the besiegers -- Major
Croghan's gallant defence of Fort Stephenson, 177
CHAPTER VIII.
Chauncey ordered to Lake Erie to build a fleet -- A plan of
the campaign -- Woolsey -- Attack on York -- Death of
General Pike -- His character -- Capture of Fort George --
Gallantry of Scott -- Repulse of the British at Sackett's
Harbor by General Brown -- Dearborn pursues Vincent -- Night
attack on the American encampment -- Generals Winder and
Chandler taken prisoners -- Retreat of the army --
Reinforced by General Lewis -- Dearborn at Fort George --
Defeat of Colonel Boestler at Beaver Dams -- Attack on Black
Rock -- Dearborn withdrawn from the command of the northern
army, 205
CHAPTER IX.
SECOND SESSION OF THE TWELFTH CONGRESS.
Army bill -- Quincy and Williams -- Debate on the bonds of
merchants given for British goods imported in contravention
of the non-importation act -- Debate on the bills increasing
the army to 55,000 men -- Williams' report -- Quincy's
attack -- Clay's rejoinder -- Randolph, Calhoun, Quincy,
Lowndes and Clay -- State of the Treasury, 224
CHAPTER X.
Action between the Chesapeake and Shannon -- Rejoicing in
England over the victory -- The Enterprise captures the
Boxer -- Death of Lieutenant Burrows -- Daring cruise of the
Argus in the English and Irish channels -- Lieutenant
Allen's humanity -- Action with the Pelican -- Death of
Allen -- His character, 244
CHAPTER XI.
Cost of transportation to the northern frontier -- English
fleet on our coast -- Chesapeake blockaded -- Blockade of
the whole coast -- Cockburn attacks Frenchtown -- Burns
Havre De Grace -- Attacks Georgetown and Frederickstown --
Arrival of British reinforcements -- Attack on Craney Island
-- Barbarities committed in Hampton -- Excitement caused by
these outrages -- Commodore Hardy blockades the northern
coast -- Torpedoes -- Hostile attitude of Massachusetts --
Remonstrances of its legislature -- Feeling of the people, 257
CHAPTER XII.
Perry obtains and equips a fleet on Lake Erie -- Puts to sea
-- Kentucky marines -- Description of the battle -- Gallant
bearing of Perry -- Slaughter on the Lawrence -- Perry after
the battle -- Burial of the officers -- Exultation of the
people -- Harrison advances on Maiden -- flight of Proctor
-- Battle of the Thames, and death of Tecumseh, 271
CHAPTER XIII.
Wilkinson takes command of the northern army -- Plan of the
campaign -- Hampton entrusted with the 5th military district
and takes position at Plattsburg -- Quarrel between the two
Generals -- Hampton advances, against orders, into Canada:
is defeated -- Concentration of Wilkinson's army -- Moves
down the St. Lawrence -- Its picturesque aspect -- Harassed
by the enemy -- Battle of Chrystler's field -- Hampton
refuses to join him -- The expedition abandoned and the
armies retire to winter-quarters -- Disappointment and
indignation of the war party, and gratification of the
Federalists -- Abandonment of Fort George and burning of
Newark -- Loss of Fort Niagara and burning of Buffalo and
the settlements along the river -- Retaliation -- Gloomy
close of the campaign, 291
CHAPTER XIV.
1813--1814.
Winter operations -- Decatur challenges Commodore Hardy to
meet the United States and Macedonian with two of his
frigates -- Wilkinson's second invasion, of Canada -- Battle
of la Cole Mill -- Holmes' expedition into Canada --
Romantic character of our border warfare -- Inroad of the
British marines to Saybrook and Brockaway's Ferry, 310
CHAPTER XV.
THIRTEENTH CONGRESS. MAY 27, 1813.
Democratic gain in Congress -- Spirit in which the two
parties met -- Russian mediation offered and accepted, and
commerce opened -- State of the Treasury -- Debate
respecting a reporter's seat -- Direct Tax -- Webster's
resolutions -- Governor Chittenden -- Strange conduct of
parties in New Hampshire -- The embargo -- England proposes
peace -- Commissioners appointed -- Army bill -- Webster's
speech upon it -- Sketch of him -- The loan bill -- Defended
by Mr. Eppes -- Sketch of Mr. Pickering, with his speech --
Sketch of John Forsyth, and his speech -- Calhoun --
Grosvenor -- Bill for the support of military establishments
-- Speech of Artemus Ward -- Resolutions of Otis in the
Massachusetts Senate -- Repeal of the embargo -- Calhoun and
Webster -- Strange reversal of their positions -- Strength
of our navy and army, 319
HISTORY OF THE SECOND WAR WITH ENGLAND.
CHAPTER I.
A REVIEW OF THE CAUSES LEADING TO THE SECOND WAR WITH ENGLAND.
Duplicity and oppressive acts of the British Government
contrasted with the forbearance of the United States --
Character of Madison -- Debates in Congress on War measures
-- Declaration of War.
The peace which closed our revolutionary struggle was like a wound
healed only at the surface, and which must be opened anew before a
permanent cure can be effected. The desire for territory had become
the ruling passion of the British Empire, and the loss of the most
promising part of her vast possessions could not, therefore, be borne
with equanimity. The comparatively barren and inhospitable tract lying
north of the St. Lawrence and the lakes, which still belonged to her,
was but a sorry substitute for the rich alluvial bottoms that
stretched along the western rivers, while the mouth of the St.
Lawrence furnished but a meagre outlet compared with the noble rivers
and capacious harbors that seamed the inland and indented the coasts
of the Atlantic <DW72>. Some have supposed that England had never
abandoned the design of recovering a part, if not the whole of the
possessions she had lost on this continent. If this be true, that
purpose was doubtless a very vague one, and it depended entirely on
circumstances whether it ever assumed a definite form. One thing,
however, is certain, she had determined to narrow down our limits
wherever it was practicable, and to the fullest extent of her power.
This is evident from the eagerness with which she urged us to
acknowledge the various Indian tribes on our frontier, as independent
nations. She wished to have them placed on a footing with other
sovereign States, so that they could form treaties and dispose of
territory to foreign governments. Numerous and powerful tribes then
roamed undisturbed over vast tracts which have since become populous
States. Could Great Britain have purchased these, or had them
colonized by other foreign powers, nearly the whole line of lakes and
the territory west of Lake Erie would have presented an impenetrable
barrier to our growth in the north-west. Not succeeding in this
policy, she determined that the Indians should retain possession of
the land as her allies. This is evident from the constant disturbance
kept up on our north-western frontiers--from Lord Dorchester's
speeches instigating the Indians to war, and from the fact that an
English fort was erected within the territory of the republic. So
resolved was the British Government on this course that it for a long
time refused to carry out the stipulations of the treaty of 1783, and
still retained American posts captured by its forces during the
revolutionary war. The defeat of General Harmar, in 1790, and of St.
Clair, in 1791, were not wholly owing to our inefficiency or to Indian
prowess, but to British interference and encouragement.
The victory of Wayne, which followed these disastrous expeditions,
proved this true. Canadian militia and volunteers were found in the
Indian armies, while the battle that completed their overthrow ended
under the walls of a British fort standing on American ground. These
violations of a sacred treaty, and undisguised encroachments upon our
territory on the frontier, were afterwards surpassed by still greater
outrages at sea.
The French revolution exploding like a volcano in the heart of Europe,
followed by a republic whose foundation stones were laid in the
proudest blood of France--the extinction of the Bourbon dynasty, and
the loud declaration of rights which startled every despot from the
Archangel to the Mediterranean like a peal of thunder, had covered the
continent with hostile armies. The European powers who rejoiced in the
success of the revolutionary struggle on these distant shores, because
it inflicted a blow on their proud rival, saw with consternation the
principle that sustained it at work in their midst. Like the first
crusade against the infidels, which at once healed all the animosities
of the princes of Europe, a second crusade, harmonizing powers
hitherto at variance, was formed against this principle of human
rights, and the allied armies moved down upon the infant republic of
France. The devastating flood of feudalism would soon have swept
everything under but for the appearance of that strange embodiment of
power, Napoleon Bonaparte. Rolling it back from the French borders, he
commenced that long and fearful struggle which ended only at Waterloo.
England rashly formed a coalition with the continental powers,
anticipating an easy overthrow to the plebeian warrior, but soon found
herself almost alone in the conflict; and instead of treading down her
ancient rival, began to tremble for her own safety. The long and
deadly strife that followed exhausted her resources and crippled her
strength. Her war ships stretched from Copenhagen to the Nile, and to
supply these with seamen, she resorted to impressment not only on her
own shores, amid her own subjects, but on American ships, among
American sailors. Our merchant vessels were arrested on the high seas,
and men, on the groundless charge of being deserters, immediately
coerced into the British service. To such an extent was this carried,
that in _nine months_ of the years 1796 and '97, Mr. King, the
American minister at London, had made application for the release of
_two hundred and seventy-one seamen_,[1] most of whom were American
citizens.
[Footnote 1: Vide letter of Mr. King to the Secretary of State.]
At first the British Government claimed only the right to seize
deserters; but its necessities demanding a broader application to
right of search, her vessels of war arrested American merchantmen to
seek for _British seamen_, and later still, for British
subjects--finally, every sailor was obliged to prove himself a citizen
of the United States on the spot, or he was liable to be forced into
British service. American merchants were thus injured while
prosecuting a lawful commerce, and worse than all, great distress was
visited on the friends and relatives of those who were illegally torn
from their country and pressed into the hated service of a hated
nation. Over six thousand were known to have been thus seized, while
the actual number was much greater.
Not content with committing these outrages on the high seas, English
vessels boarded our merchantmen and impressed our seamen in our own
waters. That line which runs parallel to the sea coast of every
nation, and which is considered its legitimate boundary, presented no
obstacles to British cruisers.
In 1804, the frigate Cambria boarded an American merchantman in the
harbor of New York, and in direct opposition to the port officers,
carried off several of her seamen. To complete the insult, the
commander declared, in an official letter to the British Minister,
that he "considered his ship, while lying in the harbor of New York,
as _having dominion around her within the distance of her buoys_." Not
long after a coasting vessel while going from one American port to
another, was hailed by a British cruiser, and, refusing to stop, was
fired into and one of her crew killed. Thus an American citizen was
murdered within a mile of shore, and while going from port to port of
his own country.[2]
[Footnote 2: Vide Letter of Madison to Mr. Rose, the British Minister,
dated March 5th, 1808.]
These aggressions on land and insults at sea continued, at intervals,
down to 1806, when our commerce received a more deadly blow from the
British orders in council, and Napoleon's famous Berlin and Milan
decrees. To annoy and <DW36> her adversary, England declared the
whole coast of France, from Brest to the Elbe, in a state of blockade.
Napoleon retaliated by the Berlin decree, in which he declared the
British Islands in a state of blockade. The next year the English
government issued other orders in council, blockading the whole
continent, which were met by Napoleon's Milan decree.
These famous orders in council, so far as they affected us, declared
all American vessels going to and from the harbors of France and her
allies, lawful prizes, except such as had first touched at, or cleared
from an English port. The Berlin and Milan decrees, on the other hand,
pronounced all vessels that had so touched at an English port, or
allowed themselves to be searched by a British cruiser, the property
of France, while British goods, wherever found, were subject to
confiscation. In short, if we did not confine our commerce to England,
the latter would seize our merchantmen, wherever found, as lawful
prizes, while if we did trade with her, or even touch at her ports at
all, France claimed them as her property.
England, without the slightest provocation, had commenced a war
against France, and irritated at her want of success, declared her
coast in a state of blockade--thus violating an established law of
nations. The principle has long been admitted and acted upon by the
principal maritime nations of the world, that neutral flags have a
right to sail from port to port of the belligerent powers, to carry
any merchandise whatever, except those contraband of war, such as
arms, munitions of war, or provisions for the enemy. The only
exception to it is an actual blockade of a port where neutrals are
forbidden an entrance. This principle is founded in common justice;
otherwise two strong maritime nations might make a third neutral power
the greatest sufferer from the war. Besides, if the right to create
paper blockades is allowed, no restrictions can be placed upon it, and
in case of another war with England, she could declare the whole coast
of America, from Maine to Mexico, and that portion of our territory on
the Pacific, in a state of blockade, while the naval force of the
world could not maintain an _actual_ one.
The injustice of these retaliatory measures was severely felt by our
government. They placed us, a neutral power, in a worse attitude than
if allied to one or the other we had been at open war with the third,
for in the latter case our war ships could have defended our commerce,
which would also have been under the protection of the cruisers of our
ally. But now our men-of-war were compelled to look silently on and
see American merchantmen seized, while two nations, instead of one,
claimed the right to plunder us. Our commerce for the last few years
had advanced with unparalleled strides--so that at this time our
canvass whitened almost every sea on the globe, and wealth was pouring
into the nation. Suddenly, as if the whole world, without any
forewarning, had declared war against us; the ocean was covered with
cruisers after American vessels, and the commerce of the country was
paralyzed by a single blow.
But the most extraordinary part of the whole proceeding was, that
while England, by her orders in council, shut the Continent from us
and confiscated as a smuggler every American vessel that attempted to
enter any of its ports, she herself, with _forged_ papers, under the
American flag, carried on an extensive trade. The _counterfeit_
American vessel was allowed to pass unmolested by British cruisers,
while the real American was seized. It was estimated that England made
fifteen thousand voyages per annum in these disguised vessels, thus
appropriating to herself all the advantages to be gained by a neutral
nation in trading with the Continent, and using our flag as a
protection.
These were the prominent causes of the war, sufficient, one would
think, to justify the American Government in declaring it.
One-hundredth part of the provocation which we then endured, would now
bring the two governments in immediate and fierce collision.
But, notwithstanding England's desires and necessities, she would
never have committed these outrages, had she not entertained a supreme
contempt for our power, and cherished an inextinguishable hatred of
the nation, rendering her utterly indifferent to our rights. The
treaty of 1783, by which our independence was acknowledged, was wrung
from her by stern necessity. It was not an amicable settlement of the
quarrel--a final and satisfactory adjustment of all difficulties. On
the part of England it was a morose and reluctant abandonment of a
strife which was costing her too dear--the unwilling surrender of her
best provinces under circumstances dishonorable to her flag, and
humbling to her national pride. This hatred of the rebel colony was
mingled with contempt for our institutions and national character,
exhibited in a proud assumption of superiority and disregard of our
rights and our demands. A nation sunk in helpless weakness may submit
to tyrannical treatment, but one rapidly growing in strength and
resources, is sure to have a day of reckoning, when it will demand a
swift and complete settlement of the long-endured wrongs.
Our wisest statesmen, aware of this state of feeling, foresaw an
approaching rupture. The elder Adams, as far back as 1785, says, in
writing from England: "Their present system (the English) as far as I
can penetrate it, is to maintain a determined peace with all Europe,
in order that they may war singly against America."[3] In 1794,
Washington, in a letter to Mr. Jay, after speaking of the retention of
posts which the British Government had, by treaty, ceded to us, and of
the conduct of its agents in stirring up the Indians to hostilities,
says: "Can it be expected, I ask, so long as these things are known in
the United States, or at least firmly believed, and suffered with
impunity by Great Britain, that there ever will or can be any
cordiality between the two countries? I answer, No. And I will
undertake, without the gift of prophecy, to predict, that it will be
impossible to keep this country in a state of amity with Great Britain
long, if those posts are not surrendered." Still later, Jefferson,
writing home from England, says: "In spite of treaties, England is our
enemy. Her hatred is deep-rooted and cordial, and nothing with her is
wanted but power, to wipe us and the land we live in out of
existence."
[Footnote 3: Letter of Adams to the Secretary of Foreign Affairs, 19th
of July, 1785.]
Having scarcely recovered from the debility produced by the long
revolutionary struggle--just beginning to feel the invigorating
impulse of prosperity, the nation shrunk instinctively from a war
which would paralyze her commerce and prostrate all her rising hopes.
The Government hesitated to take a bold and decided stand on its
rights, and urge their immediate and complete acknowledgment. This
forbearance on our part, and apparent indifference to the honor of the
nation, only increased the contempt, and confirmed the determination
of the British Government. Still, remonstrances were made. Soon after
the arrival of the British Minister, Mr. Hammond, in 1791, Jefferson
stated the causes of complaint, followed up the next year by an able
paper on the charges made by the former against our Government. This
paper remained unanswered, and two years after Jefferson resigned his
secretaryship.
The next year, 1794, the British Government issued an order of
council, requiring her armed ships to arrest all vessels carrying
provisions to a French colony, or laden with its produce. The American
Government retaliated with an embargo, and began to make preparations
for immediate hostilities. In a few months the order was revoked, and
one less exceptionable issued, that calmed for awhile the waters of
agitation, and Mr. Jay was sent as Minister to England, to negotiate a
new treaty, which was to settle all past difficulties, establish some
principles of the law of nations, especially those affecting
belligerents and neutrals, and to regulate commerce. This treaty
removed many of the causes of complaint, but like all treaties between
a weak and strong government, it secured to England the lion's
portion. But with all its imperfections and want of reciprocity, it
was ratified in the spring of 1796, and became a law. Met at every
step by a determined opposition, its discussion inflamed party spirit
to the highest point, while its ratification was received with as many
hisses as plaudits. Still, it brought a partial, hollow pacification
between the two governments, which lasted till 1806, when the orders
in council before mentioned were issued. Great Britain, however,
hesitated not to impress our seamen and vex our commerce during the
whole period, with the exception of the short interval of the peace of
Amiens. In 1803, with the renewal of the war between her and France,
impressment was again practiced, though met at all times by
remonstrance, which in turn was succeeded by negotiation.
Those orders in Council seemed, at first, to preclude the possibility
of an amicable adjustment of difficulties. The country was on fire
from Portland to New Orleans. Cries of distress, in the shape of
memorials to Congress, came pouring in from every sea port in the
Union. Plundered merchants invoked the interposition of the strong arm
of power to protect their rights, and demanded indemnity for losses
that beggared their fortunes. Scorn and rage at this bold high-handed
robbery, filled every bosom, and the nation trembled on the verge of
war. Jefferson, however, sent Mr. Pinckney as envoy extraordinary to
cooperate with Mr. Monroe, our minister to England, in forming a
treaty which should recognize our maritime rights.
In the spring of the next year Jefferson received the treaty from
London. It having arrived the day before the adjournment of Congress,
and containing so much that was inadmissible, he did not submit it to
that body.
In the first place, there was no provision against the impressment of
seamen; and in the second place, a note from the British ministers
accompanied it, stating that the British government reserved to
itself the right to violate all the stipulations it contained, if we
submitted to the Berlin decree, and other infractions of our rights by
France. This reservation on the part of England was an assumption of
power that required no discussion. To declare that she would annul her
own solemn treaty, the moment she disapproved of our conduct towards
other nations, was to assume the office of dictator.
In the mean time, the death of Fox, whose character and conduct the
short time he was in power had given encouragement that a permanent
peace could be established, and the election of the dashing and fiery
Canning to his place, involved the negotiations in still greater
embarrassments. To indicate his course, and reveal at the outset the
unscrupulous and treacherous policy England was henceforth determined
to carry out, he had ready for promulgation long before it could be
ascertained what action our government would take on that treaty,
those other orders in Council, blockading the continent to us. He
declared, also, that all further negotiations on the subject were
inadmissible; thus leaving us no other alternative, but to submit or
retaliate. Thus our earnest solicitations and fervent desire to
continue on terms of amity--our readiness to yield for the sake of
peace what now of itself would provoke a war, were met by deception
and insult. England not only prepared orders violating our rights as
a neutral nation while submitting a treaty that protected them, but
plundered our vessels, impressed our seamen, and threatened the towns
along our coast with conflagration.
We could not allow our flag to be thus dishonored, our seamen
impressed, and our commerce vexed with impunity, and declared common
plunder by the two chief maritime nations of Europe. Retaliation,
therefore, was resolved upon; and in December of 1807, an embargo was
laid upon all American vessels and merchandize. In the spirit of
conciliation, however, which marked all the acts of government, the
President was authorized to suspend it soon as the conduct of European
powers would sanction him in doing so. This embargo prohibited all
American vessels from sailing from foreign ports, all foreign ships
from carrying away cargoes; while by a supplementary act, all coasting
vessels were compelled to give bonds that they would land their
cargoes in the United States.
This sudden suspension of commerce, threatening bankruptcy and ruin to
so many of our merchants, and checking at once the flow of produce
from the interior to the sea-board, was felt severely by the people,
and tried their patriotism to the utmost. Still the measure was
approved by the majority of the nation. New England denounced it, as
that section of the republic had denounced nearly every measure of
the administration from its commencement. The effect of the embargo
was to depress the products of our own country one half, and increase
those of foreign countries in the same proportion. There being no
outlet to the former, they accumulated in the market, and often would
not bring sufficient to pay the cost of mere transportation, while the
supply of the latter being cut off, the demand for them became
proportionably great. Thus it fell as heavy on the agricultural
classes as on the merchant, for while a portion of their expenses were
doubled, the produce with which they were accustomed to defray them
became worthless. But ship owners and sailors suffered still more, for
the capital of the one was profitless, and the occupation of the other
gone. It is true it helped manufacturers by increasing the demand for
domestic goods; it also saved a large amount of property, and a vast
number of American ships, which, if they had been afloat, would have
fallen into the hands of French and English cruisers.
But, while the embargo pressed so heavily on us, it inflicted severe
damage also on France and England, especially the latter. The United
States was her best customer, and the sudden stoppage of all the
channels of trade was a heavy blow to her manufactures, and would, no
doubt, have compelled a repeal of the orders in council to us, had
not she known that we were equal, if not greater sufferers. But while
the two nations thus stood with their hands on each other's throats,
determined to see which could stand choking the longest, it soon
became evident that our antagonist had greatly the advantage of us,
for the embargo shut ourselves out from the trade of the whole world,
while it only cut England off from that of the United States. Besides,
being forced to seek elsewhere for the products she had been
accustomed to take from us, other channels of trade began to be
opened, which threatened to become permanent.
A steady demand will always create a supply somewhere, and this was
soon discovered in the development of resources in the West Indies,
Spain, Spanish America, and Brazil, of which the British Government
had hitherto been ignorant.
The loud outcries from the opponents of this measure, especially from
New England, also convinced her that our government must soon repeal
the obnoxious act.
Under the tremendous pressure with which the embargo bore on the
people, New England openly threatened the government. John Quincy
Adams, who had sustained the administration in its course, finding his
conduct denounced by the Massachusetts Legislature, resigned his seat,
declaring to the President that there was a plan on foot to divide New
England from the Union, and that a secret emissary from Great Britain
was then at work with the ruling federalists to accomplish it. Whether
this was true or false, one thing was certain, an ominous cloud was
gathering in that quarter that portended evil, the extent of which no
one could calculate.
[Sidenote: 1809.]
Under these circumstances the embargo was repealed, and the
non-intercourse law, prohibiting all commercial intercourse with
France and Great Britain substituted.
While these things were transpiring an event occurred which threatened
to arrest all negotiations.
The Chesapeake, an American frigate, cruising in American waters, had
been fired into by the Leopard, a British 74, and several of her crew
killed. The commander of the latter claimed some British deserters,
whom he declared to be on board the American ship. Capt. Barron denied
his knowledge of any such being in the Chesapeake; moreover, he had
instructed, he said, his recruiting officer not to enlist any British
subjects. The captain of the Leopard then demanded permission to
search. This, of course, was refused, when a sudden broadside was
poured into the American frigate. Captain Barron not dreaming of an
encounter, had very culpably neglected to clear his vessel for action,
and at once struck his flag. An officer from the Leopard was
immediately sent on board, who demanded the muster-roll of the ship,
and selecting four of the crew, he retired. Three of these were
native Americans, the other was hung as a deserter. This daring
outrage threw the country into a tumult of excitement. Norfolk and
Portsmouth immediately forbade all communication with British ships of
war on the coast. [Sidenote: July 2.] The war spirit was aroused, and
soon after Jefferson issued a proclamation, prohibiting all vessels
bearing English commissions from entering any American harbor, or
having any intercourse with the shore.
[Sidenote: 1808.]
The act of the Leopard was repudiated by the English Government; but
the rage that had been kindled was not so easily laid, especially, as
no reparation was made. Mr. Monroe, our Minister to England, and
Canning could not adjust the matter; neither could Mr. Rose, the
English Minister, afterwards sent over for that especial purpose. The
British Government would not consent to mingle it up with the subject
of impressment generally, and refused to take any steps whatever
towards reparation, until the President's hostile proclamation was
withdrawn. Jefferson replied that if the minister would disclose the
terms of reparation, and they were satisfactory, their offer and the
repeal of the proclamation should bear the same date. This was refused
and Mr. Rose returned home.
[Sidenote: March.]
In the midst of this general distress and clamor, and strife of
political factions, Mr. Madison, who had been elected President, began
his administration.
Jefferson had struggled in vain against the unjust insane policy of
England. Embargoes, non-intercourse acts, all efforts at commercial
retaliation, remonstrances, arguments and appeals were alike
disregarded. Proud in her superior strength, and blind to her own true
interests, she continued her high-handed violation of neutral rights
and the laws of nations. In the mean time, the republic itself was
torn by factions which swelled the evils that oppressed it. It was
evident that Madison's seat would not be an easy one, and it was
equally apparent that he lacked some most important qualities in a
chief magistrate who was to conduct the ship of State through the
storms and perils that were gathering thick about her. The commanding
mind overshadowing and moulding the entire cabinet, the prompt
decision, fearless bearing and great energy were wanting. His manifest
repugnance to a belligerent attitude encouraged opposition and invited
attack. Small in stature and of delicate health, with shy, distant,
reserved manners, and passionless countenance, he was not fitted to
awaken awe or impart fear. Still he was a thorough statesman. His
official correspondence, while Jefferson's Secretary of State, his
dissertation on the rights of neutral nations and the laws that should
govern neutral trade, are regarded to this day as the most able
papers that ever issued from the American cabinet. His knowledge of
the Constitution was thorough and practical, and his adherence to it
inflexible. The exigencies of war, which always afford apologies, and
sometimes create demands for an illegal use of power, never forced him
beyond the precincts of law or provoked him to an improper use of
executive authority. His integrity was immovable, and though assailed
by envenomed tongues and pursued by slanders, his life at the last
shone out in all its purity, the only refutation he deigned to make.
But Madison possessed one quality for which his enemies did not give
him credit, and which bore him safely through the perils that
encompassed his administration--a calm tenacity--a silent endurance
such as the deeply-bedded rock presents in the midst of the waves. Men
knew him to be in his very nature repugnant to war, and when they saw
him go meekly, nay, shrinkingly into it, they expected to laugh over
his sudden and disgraceful exit. But while he was not aggressive and
decided in his conduct, he boldly took the responsibilities which the
nation placed upon his shoulders, and bore them serenely,
unshrinkingly to the last. His hesitation in approaching a point
around which dangers and responsibilities clustered prepared the
beholder for weak and irresolute conduct, but he was amazed at his
steadiness of character. This apparent contradiction arose from two
conflicting elements. Incapable of excitement and opposed to strife,
he naturally kept aloof from the place where one was demanded, and the
other to be met. Yet, at the same time, he had a knowledge of the
right, and an inflexible love for it which made him immovable when
assailed.
On the whole, perhaps the character he possessed was better fitted to
secure the permanent good of the country than that of a more executive
man. A bold, decided chief magistrate, possessing genius, and calming
by his superior wisdom and strength, the disturbed elements about him,
and developing and employing the resources of the country at the
outset, would probably have ended the war in six months. But the
knowledge the country gained and communicated also to other
governments of its own weakness and power, was, perhaps, better than
the misplaced confidence which sudden success, obtained through a
great leader would have imparted. In the vicissitudes of the war, we
worked out a problem which needs no farther demonstration.
Madison's administration was based on those principles which had
governed that of Jefferson, and the same restrictive measures were
persevered in to compel England to adopt a system more conformable to
our rights and the laws of neutrality. In the mean time Mr. Erskine
was appointed Minister on the part of Great Britain to adjust the
difficulties between the two countries. [Sidenote: April 19, 1809.]
At first this seemed an easy task, for he declared that his government
would revoke the orders in council on condition the non-intercourse
act was repealed. The proposal was at once communicated to Congress
when it assembled in May, and accepted by it. The 10th of June was
agreed upon as the day on which commercial intercourse should
recommence between the two countries, and the President issued a
proclamation to that effect. In July, however, it was ascertained that
the British Government repudiated the agreement entered into by its
Minister, declaring that he had exceeded his instructions. A second
proclamation reestablishing non intercourse was instantly issued, and
the two countries were farther than ever from a reconciliation.
The conduct of Great Britain, at this period, presents such a strong
contrast to her loud declarations before the world, or rather stamps
them as falsehoods so emphatically, that the historian is not
surprised at the utter perversion of facts with which she endeavored
to cover up her turpitude, and quiet her conscience. Without any
provocation, she had declared war against the infant republic of
France. In order to shield herself from the infamy which should follow
such a violation of the rights of nations, and waste of treasure and
of blood, she planted herself on the grand platform of principle, and
insisted that she went to war to preserve human liberty, and the
integrity of governments. In this violent assault on a people with
whom she was at peace, she made a great sacrifice for the common
interests of states, and hence deserved the gratitude, and not the
condemnation of men. With these declarations on her lips, she turned
and deliberately annulled her agreements with the United States, and
invaded her most sacred rights. She impressed our seamen, plundered
our commerce, held fortresses on our soil, and stirred up the savages
to merciless warfare against the innocent inhabitants on our frontier.
While with one hand she professed to strike for the rights of nations,
with the other she violated them in a hardihood of spirit never
witnessed, except in a government destitute alike of honor and of
truth. So, also, while sacrificing her soldiers and her wealth, to
prevent the aggressions of Napoleon; nay, sending a fleet and troops
to Egypt, for the noble purpose of saving that barbarous state from a
reckless invader; her armies were covering the plains of India with
its innocent inhabitants, and robbing independent sheikhs of their
lawful possessions, until, at last, she tyrannized over a territory
_four times_ as large as that of all France, and six times greater
than her own island. Such unblushing falsehoods were never before
uttered by a civilized nation in the face of history. The most
unscrupulous government does not usually cover up its tyranny and
aggressions by pharisaic mummeries. There are all shades of hypocrisy,
but to do the most damning acts under pretence of religious principle,
has generally been considered the sole prerogative of the Spanish
inquisition.
The disavowal of Mr. Erskine's treaty by the English government, and
the consequent renewal of the non-intercourse act, threw the country
into the fiercest agitation. The conduct of Great Britain appeared
like mockery. Forcing us into conciliation by promises, and then
withdrawing those promises; proposing to settle all difficulties by
negotiation, and yet, in the progress of it, refusing to touch one of
them, she determined to try the patience of the American people to the
utmost. The disavowal of a treaty made by her own minister, which
buoyed up the nation with the hope of returning peace and prosperity,
well nigh exhausted that patience; and there is little doubt but that
an immediate declaration of war would have been sustained by a large
majority of the American people. In passing from town to town, the
traveller saw groups of angry men discussing and denouncing the
tyranny of England. The shout of "_Free trade and sailors' rights_,"
shook the land, while flashing eyes and clenched fists told how
aroused the national feeling had become.
Mr. Jackson was sent, in the place of Mr. Erskine, to negotiate a
treaty; but his proposals were the same as those which the
administration had already rejected, while his insulting insinuation
that the President knew when he made the arrangement with Mr. Erskine,
that the latter was acting without authority, abruptly terminated all
intercourse, and he was recalled.
[Sidenote: 1810.]
On the first of May, Congress passed an act which revoked the
restrictive system, yet excluded British and armed vessels from the
waters of the United States.[4] It provided, however, that it should
be renewed in March against the nation, which did not before that time
so revoke or modify its edicts, as to protect the neutral commerce of
the United States. This was regarded as the ultimatum, and beyond it,
war against which ever government refused our just demands, was the
only resort. Messrs. Pinckney and Armstrong, our ministers at the
courts of England and France, were urged to press the repeal of those
obnoxious orders in council and decrees, in order that such a
catastrophe might be prevented. France receded, and Mr. Armstrong was
notified that the decrees were to cease to have effect after the first
of November, provided England withdrew her orders in council; or, if
she refused, that the United States should force her to acknowledge
the rights that France had, in a spirit of kindness, conceded. This
glad intelligence was made known by the President in a proclamation,
in which he also declared, that unless the British government repealed
her orders in council, within three months from that date, the
non-intercourse law should be revived against it.
[Footnote 4: Act of Congress, passed 1st of May, 1810.]
In the mean time Mr. Pinckney urged, with all the arguments in his
power, the English Cabinet to recede from its unjustifiable position.
The latter endeavored, by prevarication and duplicity, to avoid coming
to a definite understanding, but being closely pushed, it at length
gave our minister to understand that the United States must force
France to take the first step in revoking those odious acts against
which we complained. But as England had been the aggressor, this was
plainly unjust and impossible, and all hope of a peaceful settlement
was given up, and on the 1st of March, 1811, he took a formal leave of
the Prince Regent. At the same time Congress had passed an act,
authorizing the President to arrest the non-intercourse Act at any
moment that England should revoke her orders in council. [Sidenote:
April, 1811.] On the 38th of the next month, Napoleon definitely
revoked his Berlin and Milan decrees, so far as they related to
us--the repeal to be ante-dated November 1st, 1810. This decree was
forwarded by our minister, Mr. Barlow, who had succeeded Armstrong, to
the English Government, but it still refused to repeal its orders in
council on the ground that the decree did not embrace the continental
states, and affected only the United States. It soon became apparent,
therefore, to every one, that war was inevitable. The American
Government had placed itself, where it could not recede without
disgrace, while England was evidently resolved not to change her
attitude.
[Sidenote: 1811.]
Another collision at sea between two armed vessels inflamed still more
the war spirit that was pervading the land. On the 16th of May a
British sloop of war, the Little Belt, fired into the frigate
President, thinking doubtless to repeat the outrage committed on the
Chesapeake, but found her fire returned with such heavy broadsides
that in a few minutes thirty-two of her crew were killed or wounded.
The commander of the English ship declared that the American frigate
fired first. This Rodgers denied, and his denial was sustained by all
his officers.
The election of members of Congress, which took place in 1810 and 11,
had given a majority to the administration, so that there could be
harmony of action between the Legislature and the Executive. Beset
with difficulties, treading on the brink of a war, whose issues could
not be foreseen, anxious and uncertain, the President, by
proclamation, called the Twelfth Congress together a month before the
appointed time. It met Nov. 8th, and Henry Clay was chosen speaker.
From the outset he had been a warm supporter of the Administration,
and his eloquent voice had rung over the land, rousing up its warlike
spirit, and inspiring confidence in the ability of the nation to
maintain its rights. James Fisk, of Vermont, Peter B. Porter, and
Samuel L. Mitchell, of New York, Adam Leybert, of Penn., Robert
Wright, of Md., Hugh Nelson, of Va., Nathaniel Macon, of N. C.,
Calhoun, Langdon, Cheeves, and Wm. Lowndes, of S. C., Wm. M. Bibb and
George M. Troup, of Ga., Felix Grundy, of Tenn., and Wm. P. Duval, of
Ky., rallied round the young speaker, and presented a noble phalanx to
the anxious President. On the other side were Josiah Quincy, of Mass,
and Timothy Pitkin and Benjamin Talmadge, of Conn.
In the Senate the democratic leaders were Samuel Smith, of Md., Wm. B.
Giles, of Va., Wm. H. Crawford, of Ga., George W. Campbell, of Tenn.,
and George M. Bibb, of Ky. Leading the opposition were James Lloyd, of
Mass., and James A. Bayard, of Del.[5]
[Footnote 5: Vide Madison's Administration, by John Quincy Adams.]
The great accession of strength which the democratic members had
received, showed clearly the state of public feeling, especially south
and west, and the doubtful, hesitating policy of the last four years
was thrown aside. The tone of the President's Message was also
decidedly warlike, and no hope was held out of an amicable adjustment
of the difficulties with England. They were invoked as the
"Legislative guardians of the nation," to put the country "into an
armed attitude, demanded by the crisis." The halls of Congress
resounded with the cry of "to arms." The nightmare of fear and doubt
which had weighed down its councils was removed, and bold and fearless
speakers called aloud on the nation to defend its injured honor and
insulted rights. The might of England had ceased to be a bugbear--the
Rubicon of fear was passed. Mr. Madison, deprecating precipitate
measures, saw with alarm the sudden belligerent attitude which
Congress had assumed. The democratic leaders however told him the
nation was for war--that timidity would be his ruin--that those who
were resolved to make Mr. Clinton their candidate at the next
presidential election were taking advantage of his hesitation. In the
mean time bills providing for the enlistment of twenty-five thousand
men in the regular army; for repairing and equipping frigates and
building new vessels; authorizing the President to accept the services
of fifty thousand volunteers, and to require the Governors of the
several States and territories to hold their respective quotas of a
hundred thousand men in readiness to march at a moment's warning,[6]
were rapidly pushed through Congress. [Sidenote: Nov. 7, 1811.] The
brilliant victory, gained three days after Congress met by Harrison,
over the Indians at Tippecanoe, helped also to kindle into higher
excitement the martial spirit of the West and South-west, and for a
while opposition seemed to be struck powerless before the rising
energy of the nation.
[Footnote 6: Vide Madison's Administration, by John Quincy Adams.]
The bill authorizing the President to accept and organize certain
military corps to the number of 50,000, reported by Mr. Porter,
Chairman of the Committee on Foreign Affairs, called forth a long and
exciting debate. Mr. Grundy, one of the committee, defended the
resolution in a bold and manly speech. Referring to the Indian
hostilities on our north-western frontier, he unhesitatingly declared
that they were urged forward by British influence, and war, therefore,
was already begun. Some of the richest blood of the country had
already been shed, and he pledged himself for the western country,
that its hardy sons only waited for permission to march and avenge
those who had fallen. He was answered by Randolph, who denied that
Great Britain had stimulated the Indians to their merciless border
warfare--stigmatized the war to which this resolution looked as a war
of conquest--declared it was another mode of flinging ourselves into
the arms of Bonaparte and becoming "the instruments of him who had
effaced the title of Atilla 'the scourge of God.'"
He ridiculed the idea which had been started of conquering Canada, as
an insane project, and useless if accomplished. "Suppose it is ours,"
he exclaimed, "are we any nearer to our point? As his minister said to
the king of Epirus, "may we not as well take our bottle of wine before
as after the exploit? Go march to Canada--leave the broad bosom of the
Chesapeake and her hundred tributary rivers--the whole line of
sea-coast from Machias to St. Mary's unprotected. You have taken
Quebec--have you _conquered England_? Will you seek for the deep
foundations of her power in the frozen depths of Labrador?
'Her march is on the mountain wave,
Her home is on the deep.'
Will you call upon her to leave your ports and harbors untouched only
just till you can return from Canada to defend them? The coast is to
be left defenceless whilst men in the interior are revelling in
conquest and spoil." He pronounced the country to be in a state wholly
unfit for war.
Mr. Clay answered him in an eloquent speech. He defended the character
of our troops, and expressed his full confidence in the loyalty and
bravery of the country. "Gentlemen," he said, "had inquired what would
be gained by the contemplated war? Sir, I ask in turn, what will you
not lose by your mongrel state of peace with Great Britain? Do you
expect to gain anything in a pecuniary view? No sir. Look at your
treasury reports. Yon now receive only $6,000,000 of revenue annually,
and this amount must be diminished in the same proportion as the
rigorous execution of the orders in council shall increase. Before
these orders existed you received _sixteen millions_." He declared
that war was inevitable unless we tamely sacrificed our own interests,
rights and honor. In answering the objection that we ought only to go
to war when we were invaded, he exclaimed in thrilling tones, while
the house gazed in breathless silence on his excited features, "_How
much better than invasion is the blocking of your very ports and
harbors, insulting your towns, plundering your merchants and scouring
your coasts? If your fields are surrounded, are they in a better
condition than if invaded? When the murderer is at your door will you
meanly skulk to your cells? or will you boldly oppose him at his
entrance?_"
Every part of his speech told with tremendous effect. Many of the
members opposed the bill, which continued the subject of debate for
several days. Mr. Williams of South Carolina, defended it in a
fearless speech. In reply to a remark made by one of the members, that
it was unjust to go to war with England, as she was fighting for her
existence, he exclaimed in a loud sonorous voice that pealed through
the chamber, "_If her existence, sir, depends upon our destruction,
then I say down let her go._ She is contending for the liberties of
the world too, it seems. I would as soon have expected to hear that
the devil had espoused the cause of Christianity. Sir, we may trace
her progress for years through blood. Did she raise the standard of
liberty in India? Was it for liberty she offered up so many human
hecatombs on the plains of Hindostan? Was it to plant the standard of
_liberty_ in this country that she immolated even infant innocence
during the war of the Revolution? Is it to extend or secure the
blessings of freedom to us that the fireside and the cradle are
exposed to savage incursions in the west at this time?" This part of
his speech created a marked sensation.
The bill finally passed by 44 to 34.[7] The winter passed in exciting
debates, both in Congress and in the State Legislatures, while every
hamlet in the land was agitated with the notes of hostile
preparations. [Sidenote: March 9.] In the midst of this excitement,
the country was startled by the transmission of documents to Congress
showing that a man by the name of Henry had been sent by the Governor
of Canada to sound the disaffected New England States and endeavor to
form some connection with the leading federalists.[8]
[Footnote 7: Vide Report of proceedings in the House of
Representatives, Dec. 1811.]
[Footnote 8: This adventurer after staying some months in Boston, in
constant communication with the Secretary of Sir James Craig, Governor
of Canada, to whom he asserted that Massachusetts, in case of war,
would separate from the Union and ally herself, probably, with
England, visited the latter country to obtain remuneration for his
services. The Home Government, however, sent him back to Sir James
Craig as better able to appreciate the value of his labors. Indignant
at this neglectful treatment, he returned to Boston and obtained a
letter of introduction from Governor Gerry to Madison, to whom he
offered to divulge the whole conspiracy, of which he had been the head
and soul, for a certain sum of money. Madison gave him $50,000, and
the swindler embarked for France. There is but little doubt that Henry
made a fool of the Governor of Canada, and completely overreached the
President. The publication of the correspondence, however, increased
the hatred both against the federalists and the English nation.
He was an Irish adventurer of commanding person and most engaging
address. At one time he was editor of a paper and afterwards wine
dealer in Philadelphia. In 1798 he was appointed captain in the army,
and stationed at Fort Adams in Newport. Thence he was transferred to
Boston where he mingled freely in the best society of the city.
Becoming tired of a military life, he bought land in Vermont, and
settled down as a farmer. Finding agricultural pursuits unsuited to
his taste, he removed to Montreal and studied law for several years.
Being an aspiring man he made strenuous efforts to obtain the office
of Attorney General. Indignant at his failure, he turned his attention
to politics, in which he was more successful, for in a few months he
acquired the snug little sum of $50,000, paid over to him out of the
public treasury. He however did not enjoy the fruits of his labors. A
Frenchman styling himself Count, and who had accompanied him in his
last voyage from England, wheedled him into the purchase of large
estates held by the former in France. Relieved of most of his money,
and well supplied with deeds, etc., Henry sailed for France. But
failing to find the locality of these large possessions of which he
had become the purchaser, he was again compelled to fall back on his
genius for the means of subsistence, and became a distinguished
correspondent of a London Journal.]
[Sidenote: Apr. 8.]
In the mean time, Jonathan Russell, of Rhode Island, who had been
appointed _charge d'affaires_ to the English Court on the return of
Mr. Pinckney, wrote home that there was no prospect that the British
government would revoke its orders in council; and the President,
therefore, on the first of April, recommended an embargo to be laid on
all vessels in port, or which should arrive, for the term of sixty
days. The message was received with closed doors, and the house felt
that this was preparatory to a declaration of war. When Mr. Porter, in
accordance with the recommendation of the message, brought in a bill
to lay this embargo, there was great sensation in the house. In reply
to the interrogation, whether this was a peace measure or preparatory
to war, Mr. Grundy, one of the committee, arose and said, "it is a
_war_ measure, and it is meant that it shall lead directly to it." Mr.
Stow, of New York, said, "if it was a precursor to war, there were
some very serious questions to be asked. What is the situation of our
fortresses? What is the situation of our country generally?" Mr. Clay
then left the chair, and, in a short speech, made it apparent that
after what had passed, to shrink from this because it was a war
measure, would cover the nation with disgrace. Randolph, in reply,
said, that he was so impressed with the importance of the subject, and
the solemnity of the occasion, that he could not keep silent. "Sir,"
said he, "we are now in conclave--the eyes of the surrounding world
are not upon us. We are shut up here from the light of Heaven, but the
eyes of God are upon us. He knows the spirit of our minds. Shall we
deliberate on this subject with the spirit of sobriety and candor, or
with that spirit which has too often characterized our discussions
upon occasions like the present? We ought to realize that we are in
the presence of that God who knows our thoughts and motives, and to
whom we must hereafter render an account for the deeds done in the
body." He spoke at some length and earnestly. Clay seeing the effect
of his solemn adjurations on some members of the house, left the
speaker's chair and replied, that the gentleman from Virginia need not
have reminded them in the manner he had, of the presence of that Being
who watches and surrounds us. He thought that consciousness should
awaken different sentiments from those which had been uttered. It
ought to inspire us to patriotism, to the display of those qualities
which ennobled man. God always was with the right, and extended his
protection to those who performed their duty fearlessly, scorning the
consequences. The discussion of the bill continued through several
days, and exhibited, in a striking manner, the different effect of an
event so momentous and fearful as war on different characters. In one,
the overwhelming responsibility and direful results of adopting a
measure leading to it, shut out all other considerations. To another,
its chances and calamities were a matter of mere calculation to be
taken and met by any nation that expected to exist; while many hailed
it with the delight of true patriotism, feeling that the country had,
at last, risen from its humiliating attitude. Mr. Bleecker addressed
the house more like a clergyman than a statesman, warning the members
to desist from the perilous course. On the other hand, Mr. Mitchell,
from New York, declared, that the country was not to "be frightened by
political screech-owls;" and, alluding to the profligate character of
the Prince Regent, said, "he did not think any one should be afraid to
face a nation, at whose head stood such a man--one who was some years
since expelled a jockey club, and who was lately turned out of doors
for his unworthy conduct to his neighbor's wife. The power with which
we are to contend is not so terrific and almighty as is imagined."
[Sidenote: Apr. 4.]
The bill finally passed, 69 to 36. In the senate, 17 to 11.[9] About
the same time another dispatch was received from Mr. Russell, closing
with, "I no longer entertain a hope that we can honorably avoid war."
[Footnote 9: Vide Journal of Secret Session of Congress, of April,
1812.]
This was the feeling of the majority of the nation. In establishing
certain fixed limits beyond which it would not go, and erecting
certain barriers over which it would not allow England to pass, the
American Government had taken a position from which there was no
receding, with honor. While every thing was thus rapidly tending to
war, and the public was eager with expectation, waiting for the next
movement that should precipitate it, with all its horrors, on the
land, a despatch, received by the British Minister, Mr. Foster,[10]
from Castlereagh, closed at once every avenue towards a peaceful
adjustment of the existing difficulties. In it he declared "that the
decrees of Berlin and Milan must not be repealed singly and specially
in relation to the United States, but must be repealed, also, as to
all other neutral nations, and that in no less extent of a repeal of
the French decrees, had the British Government ever pledged itself to
repeal the orders in council."[11] This was saying, that unless the
United States instituted herself lawgiver between France and all other
European powers, and through her own unaided efforts obtained that
which England, with all her maritime strength could not enforce, the
latter would consider herself perfectly justified in withholding from
us our national rights. This awkward attempt to cover up under the
mask of diplomacy, duplicity and falsehood, from which an honorable
mind would have shrunk, was perfectly characteristic of the man who
carried the English and Irish Union by the most stupendous frauds and
bribery and corruption that can be found in the annals of modern
civilization.
[Footnote 10: Mr. Foster had succeeded Mr. Jackson as British Minister
at Washington, in the summer of 1811.]
[Footnote 11: Correspondence between the Secretary of State and Mr.
Foster, British Minister, 1812.]
I know the quasi denial of Mr. Foster, that this construction was a
just one, yet the language used can convey no other. To place it
beyond dispute, Lord Castlereagh, as late as May 22d, 1812, declared
as British Minister, to the House of Commons, that as the Berlin and
Milan decrees "were not unconditionally repealed, as required by his
Majesty's declaration, but only repealed so far as they regarded
America, he had no objection to state it, as his own opinion, that
this French decree, so issued, made no manner of alteration in the
question of the orders in council."[12]
[Footnote 12: Vide Niles' Register, vol. ii. page 332.]
It is rare to find such unscrupulous conduct on the part of a
Ministry, protected by so miserable a subterfuge. It could not be
supposed that the American Government would be deceived for a moment
by it, but the belief that we could not be _forced_ into a war,
rendered ordinary care and cunning superfluous. Occupied with
continental affairs alone, England looked upon the American Republic
as only a means to accomplish her ends there. The administration, at
Washington, was thus _compelled_ by the arbitrary conduct of its
enemy, to declare war, or forfeit all claim to the respect of the
nations of the earth, and all right to an independent existence.
Under these circumstances, Mr. Madison no longer hesitated, but on the
1st day of June transmitted a warlike message to Congress. After
recapitulating, in a general way, the history of past negotiations and
past injuries, he says: "Whether the United States shall continue
passive under these progressive usurpations and accumulating wrongs,
or opposing force to force in defence of their natural rights shall
commit a just cause into the hands of the Almighty Disposer of events,
avoiding all connections which might entangle it in the contests or
views of other powers, and preserving a constant readiness to concur
in an honorable reestablishment of peace and friendship, is a solemn
question, which the constitution wisely confides to the legislative
department of the Government. In recommending it to their early
deliberations, I am happy in the assurance that the decision will be
worthy the enlightened and patriotic councils of a virtuous, a free
and a powerful nation." This message was referred at once to the
Committee on Foreign Relations, who reported ten days after in favor
of an immediate appeal to arms. The deliberations on this report were
conducted with closed doors.
A bill drawn up by Mr. Pinckney, and offered by Mr. Calhoun, declaring
war to exist between Great Britain and the United States, was rapidly
pushed through the House, passing by a vote of 79 to 49. In the
Senate, being met not only by the opposition of the Federalists, but
by the friends of De Witt Clinton, who voted with them, it passed by a
majority of only six.[13] Congress, after passing an act, granting
letters of marque, and regulating prizes and prize goods, authorizing
the issue of Treasury notes to the amount of $5,000,000, and placing a
hundred per cent. additional duties on imports, adjourned. [Sidenote:
July 8.] In accordance with a resolution of Congress, the President
appointed a day of public humiliation and prayer, in view of the
conflict in which the nation had entered.
[Footnote 13: 19 to 13. Mr. Clinton's friends professed not to _oppose
the war_, but the declaration of it as premature.
The members from New Hampshire, most of those from Massachusetts, then
including Maine, those of Connecticut, Rhode Island, New Jersey, and
Delaware, with several from New York, some from Virginia and North
Carolina, one from Pennsylvania, and three from Maryland, opposed the
war. The members from Vermont, some from New York, all but one from
Pennsylvania, most from Maryland, Virginia, and North Carolina, all
from South Carolina, Georgia, Kentucky, Tennessee, Ohio, and
Louisiana, supported it.--_Ingersoll's History of the War._]
CHAPTER II.
Different feelings with which the Declaration of War was
received -- State of the parties at the commencement --
Federalists and Democrats -- Their hostility -- Absurd
doctrines of the Federalists -- Hostility of New England --
Unprepared state of the country -- Culpable neglect of the
government -- Comparative strength of the two navies --
Empty state of the Treasury -- Inefficiency of the Cabinet.
The proud and sensitive American of to-day can scarcely comprehend
how, under the heavy and protracted provocations which I have traced
in the preceding chapter, the country could have been kept for so long
a time from open hostilities. It would seem that the most arbitrary
exercise of executive and legislative power, could not have prevented
the people from rushing spontaneously to arms, and demanding their
rights at the bayonet's point. He is still more astounded, when he
remembers that this declaration of war was received with a storm of
indignation by a large party in the Union--that all New England, with
the exception of Vermont, anathematized it. The pulpit and the press
thundered forth their maledictions, and the wrath of heaven was
invoked on the heads of its authors. The flags of the shipping in
Boston harbor were hoisted at half-mast, in token of mourning, and the
spot rendered immortal by the patriots of the revolution, became the
rallying place of the disaffected, and the hope of the enemy. A common
welfare and a common country, could not allay this hostility, which
strengthened instead of diminishing to the last, and which was so
fanatical and blind in its violence, that it exhibited itself in the
most monstrous forms. Our defeats were gloried in, and the triumphs of
our oppressors hailed as an evidence that God was on their side, while
downright insubordination, plots, and incipient rebellion, crippled
the efforts of an already weak government, and swelled the disasters
on which they fattened.
But to one who knows to what a height the spirit of faction will
reach, nothing in all this unnatural hostility will seem strange. The
country, at this time, was divided into Federalists and Democrats, who
were scarcely less vindictive in their animosities, than the Whigs and
Tories of the revolution. New England was the furnace of Federalism,
and Boston the focal point from which issued incessant and bitter
assaults on Jefferson's, and afterwards on Madison's administration.
Thus, in the most trying period of our existence since the adoption of
the constitution, the country was divided and torn by the fiercest
spirit of faction with which it has ever been cursed.
I shall not enter into a history of the feuds of these two parties.
The principle which originally divided them was plain. One was for a
consolidated government, and more power in the executive; the other
for a larger distribution of power among the separate states of the
confederacy; one was strongly conservative, and the other tending to
radicalism; one was for putting the strictest construction on the
constitution, the other for giving it the greatest possible latitude.
These two parties had grown up with the republic. Their germs were
seen in the first convention that met after the achievement of our
independence, to settle the form of government. On one point all were
agreed--that our mutual safety and welfare depended on a confederacy,
but a difference of opinion arose on the amount of power the separate
states should confer on the Federal head. The constitution which was
finally adopted was not stringent enough to suit the Federalists; but
as a compromise, it was on the whole the best that could be secured.
Besides, by standing firmly with the general government in all
conflicts with the separate states, and with the executive when
brought in collision with Congress, and by the great patronage of the
President, that power which they preferred to see directly delegated
might practically be obtained. This party numbered among its leaders,
the first statesmen of the land.
Nor should these views be considered strange, nor the patriotism of
those who held them be assailed. Some of the noblest men who offered
their lives and fortunes to the cause of liberty, looked upon the
British Government as the best in the world, and stripped of some of
its peculiarities, and purged of its corruptions, would be the best
that human ingenuity could devise. They did not originally war against
a form of government, but to be free from its oppressive acts. They
did not hate, they admired the British constitution, and took up arms
not to destroy it, but to enjoy the rights it guaranteed to its
subjects. The government, in the principles of which they had been
educated, was the most prosperous and the strongest on the globe, and
common wisdom dictated that all its good points should be retained and
incorporated into our own. Why enter on an entirely new experiment
when we had so much to build upon in the experience of the mother
country? One of the grand features of that government was the central
power lodged in the throne; so ours should be characterized by a
strong executive. The very reason, the force of which was felt by all,
and that made a confederacy indispensable, viz., that a number of
independent states, separated by only imaginary lines, would,
inevitably, lead to frequent collisions and final civil war, operated
they thought with equal force against a _loose_ confederacy. The same
results would follow. The wisdom of these fears is seen at the present
day, in the separate power demanded by some of the states, and alas
was soon exhibited by the Federalists themselves in the spirit of
disobedience they instilled into the people against the general
government.
The Democrats, on the other hand, saw in all this a decided leaning
towards a monarchy, and afterwards boldly accused their adversaries of
conspiring to erect a throne in the midst of this republic. They were
taunted with sycophancy to England, and a craving after English
distinctions and aristocratic preeminence. The _principles_ on which
the two parties rested had their birth in true patriotism, and their
effect on the character of the Constitution was, doubtless, healthful.
Nor was there anything in their nature adapted to awaken such
vindictive hate. But like a strife between two individuals, the origin
of which is soon lost sight of in the passion engendered by the
conflict, so these two factions, in the heat of party rancor, forgot
in the main the theories on which they split. In the proposition of
every measure by either party for the welfare of the state, some
secret plot was supposed to be concealed.
The embarrassments in which this fierce hostile spirit placed the
administration, rendering it timid and cautious, was increased by the
form it took. The levelling and radical notions of the French
revolution, followed as they were by such atrocities, disgusted the
federalists, while the democrats, though they denounced the violence,
sympathized with the people, and saw in the commotion the working of
their own principles amid the oppressed masses of France. They not
only loved France, as their old ally, but they sympathized with her in
her efforts to hurl back the banded oppressors who sought to
reestablish a hated throne in her midst. So while the former party
stood charged with hating republics and wishing the domination of
England, the latter was accused of seeking an alliance with the
usurper Napoleon.
Many of the reasons given by the Federalists for their opposition,
furnish another exhibition of the blinding power of party spirit. As
to the simple question between England and America, it would seem that
no sane man could doubt, that sufficient provocation had been given to
justify us in a resort to arms. The impressment of six or seven
thousand seamen, most of them American citizens, the destruction of
nearly a thousand merchantmen, and the insults every where heaped upon
our flag, were wrongs which could not be justified. They therefore
endeavored to cover them up, by saying that the Democrats were
assisting Bonaparte, whom they regarded as a monster in human form,
and whose success would be the downfall of all liberty. The wrongs we
suffered were thus lost sight of, in the greater wrong of crippling
England in her desperate struggle with this modern Attila. Rather than
endanger the success of that conflict, they would suffer for a time
from the effect of her odious measures. They felt that England, in her
conduct, was not governed by hostile feelings towards this
country--that the evils she inflicted on us, were only incidental to
the war she was waging against a tyrant. Placed in imminent peril, as
the champion of freedom, she was compelled to resort to extraordinary
measures, which though they injured us, were intended only to crush a
common enemy. Hence the absurd interrogatory so incessantly urged by
wise statesmen: "Why do you not declare war against France as well as
England?"--as if the neglect to protect the interests and honor of the
country in one quarter, rendered it obligatory on the government to
neglect them in all quarters. The law which would redress one wrong,
is none the less right, because he who administers it refuses to apply
it to a second wrong. The injustice is in the person, not in the deed.
Besides, when a nation is insulted and outraged by two powers, it has
a perfect right to choose which it will first assault and chastise.
And yet the false doctrine was constantly promulgated, that we had no
right to declare war with England, without including France, because
she was equally criminal. In other words, the nation was bound to bear
quietly the evils under which it groaned, or embrace in the contest,
France, which stood ready to do us justice the moment that England
would.
It seems incredible that so absurd a dogma was soberly defended by
clear-headed statesmen. Strictly applied, it would require a nation,
for the sake of consistency, to submit to wrongs that degrade and ruin
her, or enter on a war equally ruinous, from its magnitude, when there
was a safe mode of procedure. Besides, all the circumstances pointed
out England as our antagonist. She harassed our frontiers--had taken
the first step against our commerce, and impressed our seamen. France
was guilty only of violating the laws of neutrality, while she always
stood pledged to recede from her position, if England would do the
same, and finally did recede, leaving no cause for war. The seizures
under the Rambouillet decree, were matters for negotiation before a
declaration of war could be justified.
As Jefferson was the head of the Democratic party, the Federalists
bent all their energies against his administration, and on his
retirement transferred their hostility to that of Madison.
But the Federalists were not all opposed to the war. The elder Adams,
the noblest chief of Federalism, was too clear-headed and high-minded
a statesman to let party spirit come between him and his country's
good, and he firmly advocated it, which brought down on him the
condemnation of many of his friends. Said he--"It is utterly
incomprehensible to me that a rational, social, or moral creature can
say the war is unjust; how it can be said to be unnecessary is very
mysterious. I have thought it both just and necessary for five or six
years." His son, John Quincy, deserted the party to uphold the war. On
the other hand, many friends of the administration and several members
of the cabinet were wholly opposed to it. There seemed to be an awe of
England oppressing our older statesmen that rendered them insensible
to insult, and willing to see the country the scorn and contempt of
the world, for its base submission under the unparalleled indignities
heaped upon it, rather than risk a conflict with that strong power.
Many of the merchants, also, who saw that their own ruin would
inevitably follow hostilities, were averse to it--indeed, the learning
and intelligence of the land was against it--but the people of the
South and West, between whom and their country's honor and rights
selfish interests and bitter party hate did not come, nobly sustained
it.
The gloomy prospect with which a nation always enters on an unequal
war, was in our case saddened by these divided feelings of the people,
and by the open animosity of several of the States. In order to
paralyze us still more, and render our complete humiliation certain,
provided England would strike a bold and decided blow, no preparation
had been made for the struggle. Although we had been for many years on
the verge of war, we had done comparatively nothing to meet its
exigences, but stood and stupidly gazed into its fearful abyss.
The income from the customs, in 1811, was $13,000,000. This, of
course, the Government knew would decrease in time of war, as it did,
to $9,500,000. Our debt at this period was $45,000,000. Yet a loan of
$11,000,000, five millions of Treasury Notes, and the revenue from the
imposts, which were doubled, was all the money furnished to carry on a
war, which was to cost over thirty millions a year. Congress, however,
did, as a last act of wisdom, appropriate $100,000 to the support,
expense, exchange, &c., of prisoners of war. The utter blindness which
had fallen on the Government was exhibited more fully in its neglect
of the Navy. Under the "peace establishment" of 1801, our navy had
been reduced, and from that time to 1812, "a period of eleven eventful
years, during which the nation was scarcely a day without suffering a
violation of its neutral rights, _not a single frigate_ had been added
to the navy." Gun-boats had been built for the protection of our
harbors, and the marine corps increased by seven hundred men, and
$200,000 per annum was appropriated to rebuild three frigates that had
been suffered to decay. Beyond this, nothing was done, and with but
nine frigates and a few other cruising vessels of less rate, while
seven thousand of our merchant ships were scattered over the ocean
claiming our protection, we plunged into a war with a nation that had
a hundred ships of the line in commission, and more than a thousand
vessels of war which bore her flag of defiance over the deep.
Superadded to all, the President, commander-in-chief of the army, was
utterly ignorant of war, and by nature and in principle wholly
repugnant to it. Conscious of his high and responsible position, he
resolved to press it with vigor. But he was unfortunate in his
Cabinet. Mr. Monroe, Secretary of State, had seen a little military
service, but only in a subordinate capacity. Mr. Gallatin, Secretary
of the Treasury, first opposed the declaration of war, and afterwards
insisted that the only hope of the country lay in a speedy peace.
Hamilton, Secretary of the Navy, and Eustis, Secretary of War, were
both ignorant of the duties of their respective departments. Pinckney,
the Attorney-General, shook his head at our prospects, while Gideon
Granger, Postmaster-General,[14] openly declared that the war could
not but end in failure, while Madison conducted its operations. To
complete the climax, a General wholly unfit for his position, was to
open the campaign. At this critical juncture, too, we had scarcely any
representatives abroad to enlist sympathy with us in our struggle. Mr.
Adams had been sent to Russia, and Joel Barlow was our Minister to
France. The latter, however, died in Poland a few months after he
received the news of our declaration of war, leaving us with scarcely
a representative in Europe.
[Footnote 14: The Postmaster-General was not at that time a member of
the Cabinet.]
It is not a matter of surprise that such a commencement to the war was
disastrous; the wonder is, that five, instead of two years of defeat,
were not meted out to us, as a just punishment for such stupidity and
neglect. Nothing but the momentous events transpiring in Europe,
distracting the attention of England, and rendering the presence of
her armies necessary at home, prevented her from striking us a blow,
from which it would have taken years to recover. May our Government
never be left to try such an experiment again!
CHAPTER III.
Plan of the Campaign -- General Hull sent to Detroit --
British officers first receive news of the declaration of
war -- Capture of Hull's baggage, etc. -- Enters Canada and
issues a proclamation, and sends out detachments -- Colonels
McArthur and Cass advance on Malden -- Hull refuses to
sustain them -- Recrosses to Detroit -- Van Horne's defeat
-- Colonel Miller defeats the enemy, and opens Hull's
communications -- Strange conduct of Hull -- Advance of the
British -- Surrender of Detroit -- Indignation of the
officers -- Review of the Campaign -- Rising of the people
-- Harrison takes command -- Advance of the army.
In determining the course to be pursued in carrying on hostilities the
administration selected Canada as the only field of operations
promising any success. The navy was to be shut up in port, leaving our
seven thousand merchantmen to slip through the hands of British
cruisers, and reach home as they best could. It was to be a war on
land and not on the sea, and the conquest of Canada would undoubtedly
be the result of the first campaign. General Dearborn, who had served
in the revolution, was appointed commander-in-chief of the northern
forces, and soon repaired to Plattsburgh, while General Van
Rensalaer, of the New York militia, and General Smith were stationed
on the Niagara frontier.
In anticipation of the war, General Hull, Governor of Michigan, had
been ordered to occupy his territory with an army of two thousand men,
for the purpose of defending the north-western frontier from the
Indians, and in case of war to obtain the command of Lake Erie, and
thus be able to cooperate with Dearborn and Van Rensalaer in the
invasion of Canada. The command naturally descended on him as Governor
of Michigan. Having, also, been an officer of merit under Washington,
the appointment was considered a very judicious one.
With part of the first regiments of United States infantry, and three
companies of the first regiment of artillery, the balance made up of
Ohio volunteers and Michigan militia, and one company of rangers, he
left Dayton, in Ohio, the first of June, just eighteen days before the
declaration of war. On the tenth, he was joined at Urbana by Colonel
Miller, with the fourth regiment of infantry, composed of three
hundred men. Here the little army entered the untrodden wilderness,
and slowly cut its way through the primeval forest, two hundred miles
in extent, to Detroit. It reached Maumee the latter part of June,
where, on the second of July, Hull received the news of the
declaration of war. The letter of the Secretary of War had been
_fourteen days_ reaching him. The British officer, at Maiden, had
been officially notified of it _two days before_. "On this occasion,
the British were better served. Prevost received notice of it, on the
24th of June, at Quebec. Brock on the 26th, at Newark. St. George on
the 30th, at Malden; and Roberts on the 8th of July, at St. Joseph's.
But, a fact still more extraordinary than the celerity of these
transmissions, is, that the information thus rapidly forwarded to the
British commanders, at Malden and St. Joseph, was received under
envelopes, franked by the Secretary of the American Treasury."[15]
But, if the Secretary of the Treasury had been the victim of a shrewd
trick, the Secretary of War had commenced his career by a most
egregious blunder. On the day of the declaration of war, he wrote two
letters to General Hull, one announcing the fact, and the other making
no mention of it. The latter despatched by a special messenger,
reached the General on the 24th of June. The former being intrusted to
the public mail as far as Cleveland, thence to be forwarded as it best
could, did not arrive at head quarters till the 2nd of July, or two
days after the news which it contained had been received by the
British officer at Malden.[16] By this unpardonable carelessness of
the Secretary of War, General Hull not only lost all the advantage to
be derived from having the knowledge of the declaration of hostilities
six days before the enemy, but he had to suffer from the preparations
which this previous information gave the latter time to make.
[Footnote 15: Vide Armstrong's Notices of the War of 1812.]
[Footnote 16: Vide Hull's Memoirs, and Armstrong's Notices of the
War.]
The first disaster that resulted from this culpability of the
Secretary of War, was the loss of General Hull's baggage, "hospital
stores, intrenching tools, and sixty men," together with the
instructions of the government, and the returns of the army. Having
received a letter from the Secretary of War, dated as late as the 18th
of June, in which he was urged to march with all possible despatch to
Detroit, and containing no announcement of a rupture, he naturally
supposed that the two governments were still at peace, and so to carry
out the instructions of the secretary, and expedite matters, he
shipped his baggage, stores, &c., to go by water to Detroit, while he
took his army by land. But the day previous the British commander, at
Malden, had received official notice of the declaration of war, and
when the packet containing the stores, &c., attempted to pass the
fort, it was stopped by a boat containing a British officer and six
men, and its cargo seized.
This first advantage gained over him so unexpectedly, by the enemy,
had a most depressing effect on the General. Instead of rousing him to
greater exertion, it filled him with doubt and uncertainty. He had a
dozen subordinates, either of whom, with that army, would in a few
days have seized Malden, and recovered all he had lost, and inflicted
a heavy blow on the enemy.
At length, however, he seemed to awake to the propriety of doing
something to carry out the objects of the campaign, and on the 12th
crossed the Detroit River and marched to Sandwich, only eighteen miles
from Malden. But here, with an unobstructed road leading to the enemy
before him, he paused and issued a proclamation to the Canadians, and
sent out detachments which penetrated sixty miles into the province.
The friendly disposition of the inhabitants was apparent, while the
Indians were overawed into a neutral position.
Four days after crossing the river, General Hull sent Colonels Cass
and Miller, with a detachment of two hundred and eighty men, towards
Malden. These gallant officers pushed to the river Canards, within
four miles of the fort, and driving the British pickets who held the
bridge from their position, took possession of it, and immediately
dispatched a messenger to General Hull, announcing their success. They
described the occupation of the post as of the utmost importance in
carrying out the plan of the campaign, and begged that if the army
could not be moved there, that they might be allowed to hold it
themselves--the General sending reinforcements as occasion demanded.
Instead of being gratified at this advantage gained over the enemy,
General Hull seemed irritated, condemned the attack as a breach of
orders, and directed the immediate return of the detachment. These
brave officers persisting in their request, he gave them permission to
retain the position, provided they were willing to do so on their own
responsibility, and without any aid from him.
This he knew they would not do. Such a proposition, from the
commanding officer, indicated a weakness of judgment, and a
willingness to resort to the most transparent trickery to escape
responsibility, that no apology can excuse. From the statements of the
British afterwards, it appeared that the approach of this detachment
filled the garrison with alarm; the shipping was brought up to the
wharves, and the loading of baggage commenced, preparatory to flight.
On two sides the fort was in a dilapidated state, while seven hundred
men, of whom only one hundred were regular troops, constituted the
entire garrison. From the panic which the approach of Cass and Miller
created, there is no doubt that the appearance of the whole army, of
two thousand men before the place, would have been followed by an
immediate surrender. One thing is certain, if General Hull supposed
that a garrison of seven hundred men behind such works, could make a
successful defence against nearly three times their number, he had no
right to regard his strong position at Detroit, when assailed by only
an equal force, untenable. Either Malden could have been taken, or
Detroit was impregnable. The troops felt certain of success, and were
impatient to be led to the attack, but he pronounced it unsafe to
advance without heavy artillery; besides, he wished to wait the effect
of his proclamation on the enemy. The Indians and Canadian militia, he
said, had begun to desert, and in a short time the force at Malden
might be "materially weakened." Two thousand men sat quietly down to
wait for this miserable garrison of seven hundred, six hundred of whom
were Canadian militia and Indians, to dwindle to less force, before
they dared even to approach within shot. The army was kept here three
weeks, till two twenty-four pounders and three howitzers could be
mounted on wheels strong enough to carry them, and yet a few weeks
after, behind better works than those of Malden, and with a force
fully equal to that of his adversary, he felt authorized to surrender,
though the largest guns brought forward to break down his defences,
were six pounders.
The cannon at length, being mounted, were with the ammunition placed
on floating batteries, ready to move on Malden, when the order to
march was countermanded, and the army, instead of advancing against
the enemy, recrossed the river to Detroit, over which it had passed a
few weeks before to the conquest of Canada. General Hull had issued a
proclamation, sent out two detachments, mounted two heavy cannon and
three howitzers, and then marched back again. Such were the
astonishing results accomplished by the first grand army of invasion.
The gathering of the Indian clans, and reinforcements pouring into the
British garrison, had alarmed him. The news seemed to take him by
surprise, as though it for the first time occurred to him that during
these three or four weeks in which he remained idle, the enemy might
possibly be active.
The surrender, at this time, of Fort Mackinaw, situated on the island
of the same name in the straits between Lakes Huron and Michigan, was
a severe blow to him, for it opened the flood-gates to all the
Indians, Canadians and British in the north-west. This fort was the
key to that section of the country, and the grand depot of the fur
companies. By its position it shielded General Hull from all attack in
that direction. Lieutenant Hanks commanded it, with a garrison of
sixty men. As soon as the British commander of St. Joseph's, just
above it, received news of the declaration of war, he took with him
some two hundred Canadians and British, and four hundred Indians, and
suddenly appearing before the fort demanded its surrender. This was
the first intimation to Lieutenant Hanks of the commencement of
hostilities. He capitulated without offering any resistance, and the
Indians at once rallied around the British standard. Here was another
blunder, a double one. In the first place, private enterprise had
outstripped the action of Government. The British officer at St.
Joseph's, though more remote than Mackinaw, received the declaration
of war _nine_ days before it reached the American commander at the
latter place, or rather, Lieutenant Hanks did not receive it at all,
either from the Government or General Hull. Colonel Roberts, of St.
Joseph's, with his band of Canadians and Indians, was kind enough to
convey the information.
It is surprising that General Hull, after his experience, did not at
once provide that a post so vital to him, should not become the victim
of the same criminal negligence which had paralyzed his efforts.
_Fifteen days_ intervened between his receiving the notification of
war, and the taking of Fort Mackinaw, and yet no messenger from him,
the Governor of the Territory, and commander-in-chief of the forces in
that section, reached the garrison. Were it not for the calamitous
results which followed, the whole campaign might be called a "comedy
of errors."
Three days previous, however, to the retreat of Hull from Canada, he
committed another error which increased his embarrassments. Proctor,
who had arrived at Malden with reinforcements, threw a small
detachment across the river to Brownstown, to intercept any provisions
that might be advancing from Ohio to the army. Captain Brush, who was
on the way with the mail, flour and cattle, was thus stopped at the
River Raisin. To open the communication and bring up the provisions,
Major Van Horne was dispatched with two hundred volunteers and
militia. But the detachment, marching without sufficient caution, was
led into ambush, and utterly defeated. Only about one-half returned to
the army. Both Gen. Hull and Major Van Horne were to blame in this
affair--the former for not sending a larger detachment, when he knew
the enemy must be on the march, while at the same time he was ignorant
of his force. This error is the more culpable, because he did not
expect an immediate attack; for, after the detachment was despatched,
he remained quietly in Canada, and then crossed at his leisure to
Detroit. He therefore could, without danger, have spared a larger
force, and should have done so, especially when the want of provisions
was one of the evils he would be called upon to encounter. On the
other hand, Major Van Horne should have heeded the information he
received, that the enemy were in advance, in position, and not allowed
his little army to rush into an ambuscade.
General Hull's position had now become sufficiently embarrassing.
"The whole northern hive was in motion." Reinforcements were hastening
to the support of Malden; his communications on the lake were cut off
by British vessels, while the defeat of Van Horne announced that his
communications by land were also closed. The latter he knew must be
opened at all hazards, and Colonel Miller was dispatched on the route
which Van Horne had taken with four hundred men to clear the road to
the river Raisin. Leaving Detroit on the 8th of August, he next day in
the afternoon, as he was approaching Brownstown, came upon the enemy
covered with a breast work of logs and branches of trees, and
protected on one side by the Detroit river, and on the other by swamps
and thickets. The British and Canadians were commanded by Muir, and
the Indians by Tecumseh. Captain Snelling leading the advance guard
approached to within half musket shot, before he discovered the enemy.
A fierce and deadly fire was suddenly opened on him, which he
sustained without flinching, till Colonel Miller converting his order
of march into order of battle, advanced to his support. Seeing,
however, how destructive the fire of the enemy was, while the bullets
of his own men buried themselves for the most part in the logs of the
breastwork; perceiving, also, some symptoms of wavering, Miller
determined to carry the works by the bayonet. The order to charge was
received with loud cheers; and the next moment the troops poured
fiercely over the breastwork, and routing the British and Canadians
pressed swiftly on their retiring footsteps. Tecumseh, however,
maintained his post, and Van Horne, who commanded the right flank of
the American line, supposing from his stubborn resistance that it
would require more force than he possessed to dislodge him, sent to
Colonel Miller for reinforcements. The latter immediately ordered a
halt, and with a reluctant heart turned from the fugitives now almost
within his grasp, and hastened to the relief of his subordinate. On
arriving at the breastwork, he found the Indian chief in full flight.
He then started again in pursuit, but arrived in view of the enemy
only to see him on the water floating away beyond his grasp.
He, however, had established the communication between the army and
the river Raisin, and dispatched Captain Snelling to Detroit with the
account of the victory, and a request for boats to remove the wounded,
and bring provisions for the living, and reinforcements to supply the
place of the dead and disabled. General Hull immediately sent Colonel
McArthur with a hundred men and boats, but with provisions sufficient
only for a single meal.[17]
[Footnote 17: Miller's testimony on the trial of Hull.]
Colonel Miller was some twenty miles from the supplies, but not
deeming it prudent with the slender reinforcements he had received,
and the still scantier provisions, to proceed, remained on the battle
field, and sent another messenger declaring that the communication was
open, and it required only a few more men and a supply of provisions,
to keep it so. The next evening, the messenger returned, bringing
instead of provisions a peremptory order to return to Detroit. It is
doubtful whether Colonel Miller ought not to have advanced without
waiting for further reinforcements, and formed a junction with Captain
Brush, who had an abundance of provisions, and a detachment of a
hundred and fifty men. But, after the communications were established,
he did not probably see so much necessity for dispatch as for
security. But General Hull seemed to be laboring under a species of
insanity. After sending forth two detachments to open his
communications, and finally succeeding, he deliberately closed them
again, and shut from his army all those provisions, the want of which
he a few days after gave as a reason for surrendering. The rapid
concentration of the enemy's forces, in front of him, might have been
given as a sufficient cause for suddenly calling in all his troops to
defend Detroit, had he not two days after sent Colonel McArthur,
accompanied by Cass, with a detachment of four hundred men, to obtain
by a back, circuitous and almost wholly unknown route through the
woods that which Colonel Miller had secured, and then been compelled
to relinquish.
[Sidenote: Aug. 7.]
When General Hull recrossed the river to Detroit, he left some hundred
and fifty, convalescents and all, "to hold possession of that part of
Canada," which he had so gallantly won, "to defend the post to the
last extremity against musketry, but if overpowered by artillery to
retreat."[18] In the mean time, General Brock, the commander of the
British forces, approached, and began to erect a battery opposite
Detroit to protect his army, and cover it in crossing the river. Not a
shot was fired to interrupt his proceedings, no attempt made to
destroy his shipping which had arrived. Daliba offered "to clear the
enemy from the opposite shores from the lower batteries," to which
General Hull replied, "I will make an agreement with the enemy, that
if they will not fire on me I will not fire on them." Major Jessup
asked permission to cross the river and spike the guns, but this was
considered a too desperate undertaking. In short, every project that
was proposed was rejected, and the twenty-four pounders and the
howitzers slept dumb on their carriages, in the midst of these hostile
preparations of the enemy.
[Footnote 18: McAfee's History.]
At length, on the morning of the 15th, a messenger arrived from
General Brock demanding an immediate surrender of the town and fort.
To this summons Hull replied in a decided and spirited manner; but
this did not seem to daunt the British commander. He immediately
opened his fire from a newly erected battery, which, after knocking
down some chimneys, and disabling a few soldiers, finally ceased at
ten o'clock in the evening. The next morning it re-commenced, and
under cover of its harmless thunder the British, in broad daylight,
commenced crossing a river more than three thousand feet wide. This
presumptuous attempt succeeded without the loss of a man. The troops
then formed in column twelve deep, and marching along the shore, soon
emerged into view, about five hundred yards from the fort. The
opposing forces were nearly equal, but the position of the Americans
gave them vastly the advantage. The fort proper was of great strength,
surrounded by a deep, wide ditch, and strongly palisaded with an
exterior battery of two twenty-four pounders. It was occupied by four
hundred men, while four hundred more lay behind a high picket fence,
which flanked the approach to it. Three hundred more held the town.
Against this formidable array, General Brock, preceded by five light
pieces of artillery, boldly advanced. He did not even have a vanguard,
and rode alone in front of his column. To the most common observer,
they were marching on certain and swift destruction. The militia who
had never been under fire, were eager for the conflict, so confident
were they of victory. On swept the apparently doomed column upon which
every eye was sternly bent, while every heart beat with intense
anxiety to hear the command to fire. In this moment of thrilling
excitement, a white flag was lifted above the works, and an order came
for all the troops to withdraw from the outer posts and stack their
arms. Such a cry of indignation as followed, probably never before
assailed the ears of a commander. Lieutenant Anderson in a paroxysm of
rage, broke his sword over one of his guns and burst into tears. The
shameful deed was done, and so anxious was General Hull that all
should receive the benefit of this capitulation, that he included in
it Colonels McArthur and Cass, and their detachment whom he had sent
to the river Raisin, together with that entrusted with the supplies.
To enhance the regret and shame of this sudden surrender, it was soon
discovered that McArthur and Cass, having heard the cannonading
twenty-four hours before, had returned, and at the moment the white
flag was raised were only a mile and a half from the fort, and
advancing so as to take the enemy in rear. The result of a defence
would have been the entire destruction of the British army. Ah! what a
different scene was occurring on this same day, in another hemisphere.
On this very morning Napoleon crossed the Dnieper, on his way to
Moscow, and Murat and Ney, at the head of eighteen thousand splendid
cavalry, fell on the Russian rear guard, only six thousand strong. Yet
this comparatively small band, composed like most of the troops under
Hull, of new levies, never thought of surrendering. First in two
squares, and then in one solid square they continued their retreat all
day--sometimes broken, yet always re-forming and presenting the same
fringe of glittering steel, and the same adamantine front. Forty times
were the apparently resistless squadrons hurled upon them, yet they
still maintained their firm formation, and at night effected a
junction with the main army, though with the loss of more than
one-sixth of their number. It was to be left to Scott and Brown and
Miller and Jessup and Jackson, to show that Russian serfs were not
braver troops than American freemen.
It sometimes happens that events widely different in their character,
and presenting still wider contrast in the magnitude and grandeur of
the circumstances that attend them, are in their remote results alike,
both in character and in their effect on the destiny of the world.
Thus, six days after our declaration of war, Napoleon crossed the
Niemen, on his march to Moscow. This first step on Russian territory
was the signal for a long train of events to arise, which in the end
should dash to earth the colossal power of Napoleon, while our
movement was to break the spell which made Great Britain mistress of
the seas; and two nations, one an unmixed despotism and the other a
pure republic, from that moment began to assume a prominence they
never before held, and from that time on, have been the only powers
which have rapidly increased in resources and strength, till each
threatens, in time, to swallow up its own hemisphere.
Much has been written of this campaign of Hull, and in the
controversy, statistics differ as widely as opinions. He was tried by
Court Martial, of which Martin Van Buren was Judge Advocate, acquitted
of treason, but found guilty of cowardice and sentenced to be shot.
Being pardoned by the President, his life was saved, but he went forth
a blighted and ruined man.
On many points there is room for a diversity of judgment, but one
thing is certain, General Hull was unfit for the station to which he
was assigned. He had been a gallant subordinate officer in the
revolution, but a man may be a good major, or even colonel, but a bad
commander-in-chief. There are many officers who are fit only to act
under orders, whom personal danger never agitates, but who are
unnerved by responsibility. Let the latter rest on some other person
and they will cheerfully encounter the peril. Hull may have been one
of these, at least it seems more rational to attribute a portion of
his conduct to some mental defect rather than to cowardice. It is
hard to affix such a stain on a man who moved beside Washington in the
perilous march on Trenton--stood firmly amid the hottest fire at
Princeton--gallantly led his men to the charge at Bemis' Heights, and
faced without flinching the fiery sleet that swept the column pressing
up the rugged heights of Stony Point. Gray hairs do not make a coward
of such a man, though they should render him imbecile.
It is not easy at this remote period to appreciate the difficulties of
the position in which Hull eventually found himself. At first he
refused to take command of the expedition, but being urged by the
government, accepted, though with the express understanding that in
case of hostilities, he was to be sustained both by a fleet on Lake
Erie, and an army operating on the northern and western frontier of
New York. He knew that the conquest of Canadian territory would be of
slight importance, if the lake and river communication was controlled
by the enemy, for they could pass their troops from one point to
another with great rapidity, cut off his supplies and reinforcements,
and hem him in till a force sufficient to overwhelm him was
concentrated.
On arriving near Malden, he was astounded to hear that the enemy had
received notice of the war before him, and hence had time to make more
or less preparations. The second blow was the loss of hospital
stores, intrenching tools, army baggage, private papers, &c. The third
came in the fall of Mackinaw, thus removing the only barrier that kept
back the northern hordes. He knew the enemy had possession of the
water communication, and were therefore able to threaten his retreat.
Dearborn, who ought to have been pressing the British on the Niagara
frontier, and thus attracted their forces from Malden, had entered
into an armistice with the Governor of Canada, leaving the latter at
full liberty to reinforce the troops opposed to Hull, a privilege of
which he was not slow to avail himself. There was not a gleam of
sunshine in the whole gloomy prospect that spread out before the
American commander. His own army diminishing, while that of his
adversary was rapidly increasing--behind him a wilderness two hundred
miles in extent, his situation was disheartening enough to make a
strong man sad. The difficulties in which he found himself environed
must always produce one of two effects on every man--either rouse him
to tenfold diligence and effort and daring, or sink him in
corresponding inactivity and despondency. There can be no middle
state. That the latter was the effect produced on General Hull, there
can be no doubt. He proved plainly that he was not one of those whom
great emergencies develope into an extraordinary character worthy to
command and worthy to be obeyed. The very first misfortune unmanned
him, and from that hour to the sad close of the campaign, when he
acted at all he did nothing but heap blunder on blunder. His mind
having once got into a morbid state, his position and his prospects
appeared to his diseased imagination ten times more desperate than
they really were.
With the failure of General Dearborn to invade Canada from the New
York frontier, and more especially with the lakes entirely under the
control of the enemy, his campaign, according to all human
calculations, must prove a failure. Detroit must fall, and Michigan be
given up to the enemy. The only chance by which this catastrophe could
have been prevented, was offered by General Brock when he crossed the
river to storm Detroit. If Hull had possessed a spark of genius or
military knowledge, he would have seen in this rash movement of his
enemy, the avenue opened for his release, and the sure precursor of
his fortunes. With that broad river cutting off its retreat, the
British army would have been overthrown; provisions and arms obtained,
and the enemy received a check which in all probability would have
enabled Hull to sustain himself till reinforcements arrived. But he
had made up his mind to surrender, and thus save Detroit from the
cruelties of the savage, and the enemy could not commit a blunder of
sufficient magnitude to arouse his hopes and spur him into
resistance; and having scarcely heard the report of his guns from
first to last, he veiled the banner of his country in the dust.
This explanation of his conduct would correspond more with his former
life, than to admit the charge of either treason or cowardice, and be
perfectly satisfactory, but for the _mode_ of his surrender. There is
a mystery here, that neither General Hull nor his friends have ever
cleared up. After having shown the imbecility of government, by which
failure became inevitable, they stop as though their task was done.
But the criminality of government being conceded, and the fall of
Detroit acknowledged to be an inevitable consequence, it does not
follow that the surrender of the army was necessary. Why, after
Colonel Miller opened the communications with supplies and
reinforcements, did not General Hull retreat at once? The enemy would
not have attempted a pursuit through that wilderness. With a rear
guard left to man the works, he could have gained two days' march,
while Detroit was able to make as good terms without him as with him.
He could have had no reason for staying, except the determination to
hold his position and defend Detroit to the last. If he had not fully
resolved to do so, the way of retreat was open, and he was bound to
occupy it; if he _had_, why did he not keep to that determination? No
new elements had entered into the struggle--no unforeseen events
occurred to affect the conclusions he had adopted. The enemy was not
in greater force than he imagined, but on the contrary, in less. He
understood the strength of his own position; his troops were never in
greater spirits; why then did he so suddenly and totally change his
purpose? It is impossible to reconcile this grievous inconsistency in
his conduct. Nor is this all that is dark and mysterious; supposing
new conditions had occurred to alter his determination, and affect the
relative position of the armies--an entirely new order of things had
taken place, requiring another mode of procedure than the one adopted
by himself and the army; why did he not call a council of war, and
submit those new features to its consideration? When his troops wished
to attack Malden, he considered the question so momentous as to
require a council of his officers. When a simple repulse was the only
misfortune that could happen, he regarded it his duty to take advice
from his subordinates; but when it came to an absolute surrender of
his whole army, no such obligation was felt. This man, who was so
afraid to compromise his force, lest it should meet with a repulse,
did not in the end hesitate to surrender it entire, and cover it with
dishonor on his own responsibility. Military history rarely records
such an event as this, and never unless either treason or cowardice
was apparent as noonday. Not a faltering word--not a doubtful
movement--not a sign of flinching, till the white flag was seen
flaunting its cowardly folds before the banner of his country. No
general has a right to assume such a responsibility, at least, until
the question has been submitted to his officers. He may peril his
troops in an unsuccessful attack, but never _dishonor_ them without
consulting their wishes. The act was that of a timorous commander, or
of a bold and unscrupulous man, like Gorgey. The rash and unmilitary
advance of Brock, which notwithstanding its success, met the
disapproval of his superior, seems wholly unaccountable, except some
one, in the confidence of Hull, had whispered in his ears, that the
latter intended no defence.
The _manner_ of surrender, conflicts with the explanation of the act
itself, and involves the conduct of Hull in a mystery. To tell us he
was neither a traitor nor a coward, and yet leave those violations of
military rules and contradictions of character unexplained and
unreconciled, is to leave the same painful doubt on the mind as though
no defence had been attempted. A morbid state of mind equivalent to
insanity, thus changing for a time the whole character of the man, is
the only charitable construction.
The blame, however, was not distributed impartially. The Secretary of
War should have been immediately removed from office, Dearborn
withdrawn as commander-in-chief, and the whole administration
thoroughly overhauled, and its policy changed. As it was, the swelling
curses of the land smote the single head of General Hull. The news of
his surrender fell on the country like a thunderbolt at noonday. The
march of his army had been watched with intense interest, but with
scarcely any misgivings. So large a force appearing with the
declaration of war in their hands on the weak and unprepared posts of
the north-western frontier was expected to sweep everything before it.
Its defeat was considered impossible, its entire, shameful surrender,
therefore, could hardly be credited. The nation was stunned, but with
surprise, not fear, at least that portion west of the Alleghanies.
Indignation and a spirit of fierce retaliation swelled every bosom.
But eastward, where party spirit and divided feelings and views, had
rendered the war party cautious and timid, the effect was for a time
paralyzing. If defeated at the outset, while England could bring into
the field scarcely any but her colonial force, what would be our
prospects of success when her veterans drilled in the wars of the
continent should appear? The government, however, awoke to the
vastness of the undertaking, but still remained ignorant of the means
by which it was to be accomplished.
To save the north-western frontier, now laid open to the incursions
of savages, Kentucky, Ohio, Pennsylvania and Virginia, sent forth
crowds of volunteers, eager to redeem the tarnished reputation of the
country. Several members of Congress from Kentucky enlisted as private
soldiers--the young and ardent Clay was seen at the musters, thrilling
the young men who surrounded him, as though he wielded the fiery cross
in his hands. Ten thousand men were raised in an incredible short
space of time, and placed under General Harrison, the hero of
Tippecanoe. To these were added portions of the 17th and 19th
regiments of regular infantry and two regiments from Kentucky and
Ohio, for government was apparently determined to make up for the
insufficient, niggardly expenditures of the first campaign by its
useless prodigality in preparing for the second.
Four thousand men raised by order of Gov. Shelby, of Kentucky, all
mounted on horseback, were put under Major General Hopkins, of the
militia, who, jointly with three regiments already sent to Vincennes
by Harrison, were to defend the frontiers of Indiana and Illinois.
[Sidenote: Oct. 10.]
Reaching Fort Harrison, which Captain, afterwards General Taylor, with
scarcely thirty efficient men, had gallantly defended against the
attacks of four or five hundred Indians, this motley crowd of horsemen
started on the 14th for the Indian villages which lay along the
Illinois and Wabash rivers. But the long and tedious march and the
uncomfortable bivouacs by night, obscured the visions of glory that
had dazzled them, and the fourth day, the enthusiasm which from the
first had been rapidly subsiding, reached zero, and open mutiny seized
the entire body of the troops. A major rode up to General Hopkins and
peremptorily ordered him to wheel about. The General refusing to obey,
he was compelled next day to constitute the rear guard of this
splendid corps of cavalry, whose horses' tails were towards the enemy
and their heads towards Fort Harrison.
[Sidenote: Sept. 12.]
In the mean time, Harrison, with about 2,500 men reached Fort Deposit,
and relieved the garrison composed of seventy men who had gallantly
withstood the attacks of hordes of Indians. Here he paused till the
arrival of other troops, and occupied the time in sending out various
detachments against the Indian villages, all of which were successful.
On the 18th, Harrison returned to Fort Wayne, where he met General
Winchester, with reinforcements from Ohio and Kentucky, in all about
two thousand men. Winchester ranked Harrison, and the latter finding
himself superseded, was about to retire. The President, however,
restored him to his original command, and he continued his march
northward. [Sidenote: Sept.] In the latter part of this month he was
at Fort Defiance. Leaving his troops there, he returned to the
settlements to organize and hasten up the forces designed to
constitute the centre and right wing of his army. Abandoning his
original plan of boldly marching on Detroit and recapturing it at
once, he determined to advance in three different columns, by as many
different routes, to the Miami Rapids, thence move suddenly to
Brownstown, cross the river and seize Malden, which had so annoyed
Hull. All along the highways and rude half-trodden paths, and skirting
the banks of rivers that rolled through nothing but primeval forests
from their sources to the lakes, squads of men, some mounted, some in
uniform, but the most part in the rough frontiersman costume, were
seen toiling northward, to avenge the disgrace of Hull. Their
camp-fires lit up the wilderness by night, and their boisterous mirth
filled it with echoes by day. A more motley band of soldiers were
never seen swarming to battle.
CHAPTER IV.
Operations on the New York frontier -- Battle of Queenstown
-- Death of Brock -- Scott a prisoner -- General Smythe's
Proclamation and abortive attempts -- Cursed by the army --
Duel with General Porter -- Retires in disgrace --
Dearborn's movements and failures -- Review of the campaign
on the New York frontier -- Character of the officers and
soldiers.
While Harrison's forces were thus scattered amid the forests and
settlements of Ohio and Indiana, the army along the Niagara frontier
had begun to move. At this time every eye in the land was turned
northward. That long chain of Mediterraneans, whose shores were
fringed with hostile armies, from Sackett's Harbor to where they lost
themselves in the forests of the north-west, became an object of the
deepest interest. Every rumor that the wind bore across the
wilderness, or that, following the chains of settlements along the
rivers reached the haunts of civilization, was caught up with avidity.
The discomfiture of Hull had filled every heart with trembling
solicitude for the fate of our other armies. Defeat in the west, and
incomprehensible delays in the east, had changed the Canadas from a
weak province, to be overrun by the first invader, into a Gibraltar
against which the entire strength of the nation must be hurled.
I have stated before that Dearborn, commanding the forces on the
Niagara and northern frontier, instead of making a diversion in favor
of Hull, by crossing the Niagara and drawing attention to himself, had
been coaxed into an armistice with Provost, the English Governor, in
which Hull had been left out. This armistice was asked and granted, on
the ground that dispatches had been received, announcing the
revocation of the orders in council. One great cause of the war being
thus removed, it was hoped that peace might be restored. The result
was as we have seen; the British commander immediately dispatched
Brock to Malden, to capture Hull, from which successful expedition he
was able to return before the armistice was broken off. General
Dearborn clung to this absurd armistice, as if it were the grandest
stroke of diplomacy conceivable. He carried his attachment so far as
to disobey the express command of his Government, to break it off.
[Sidenote: August 24.] At length, however, this nightmare ended, and
preparations were made for a vigorous autumnal campaign.
The northern army, numbering between eight and ten thousand soldiers,
was principally concentrated at two points. One portion was encamped
near Plattsburg and Greenbush, commanded by General Dearborn, in
person, the other at Lewistown, was under the direction of General
Stephen Van Rensalaer, of the New York militia, while 1,500 regulars,
under General Smythe, lay at Buffalo, a few miles distant. There were
a few troops stationed also at Ogdensburg, Sackett's Harbor, and Black
Rock.
The discontent produced by Hull's surrender, and the loud complaints
against the inaction of the northern army, together with the
consciousness that something must be done to prevent the first year of
war from closing in unmixed gloom, induced General Van Rensalaer to
make a bold push into Canada, and by a sudden blow attempt to wrest
Jamestown from the enemy, and there establish his winter quarters.
The cutting out of two English brigs[19] from under the guns of Fort
Erie, by Lieutenant Elliot with some fifty volunteers, created an
enthusiasm in the American camp of which General Van Rensalaer
determined to avail himself.
[Footnote 19: One of those, the Caledonia, afterwards did good service
as a part of the fleet of Perry on Lake Erie. The other having gone
aground, was burnt, to prevent recapture.]
The command of the expedition was given to his cousin, Col. Solomon
Van Rensalaer, a brave and chivalric officer, who on the 13th of
October, at the head of three hundred militia, accompanied by Col.
Chrystie with three hundred regular troops, prepared to cross the
river. It wanted still an hour to daylight when the two columns stood
in battle array on the shore. Through carelessness, or inability to
obtain them, there were not sufficient boats to take all over at once,
and they were compelled to cross in detachments. The boat which
carried Col. Chrystie being badly managed, was swept away by the
current, and finally compelled to re-land on the American shore. This
gallant officer was wounded while thus drifting in the stream, yet
soon after he made another attempt to cross, and succeeding, led his
troops nobly until the close of the action.
Col. Van Rensalaer having effected a landing, formed on the shore and
marched forward. The whole force at this time did not exceed one
hundred men. These, however, were led up the bank where they halted to
wait the junction of the other troops that kept arriving, a few boat
loads at a time. But daylight now having dawned, the exposed position
of this detachment rendered it a fair mark for the enemy, who
immediately opened their fire upon it. In a few minutes every
commissioned officer was either killed or wounded. Col. Van Rensalaer
finding that the bank of the river afforded very little shelter,
determined with the handful under him to storm the heights. But he had
now received four wounds, and was compelled to surrender the command
to Captains Ogilvie and Wool,[20] who gallantly moved forward, and
carried the fort and heights. The enemy were driven into a strong
stone house, from which they made two unsuccessful attempts to recover
the ground they had lost. Brock, flushed with the easy victory he had
gained over Hull, rallied them by his presence, and while attempting
to lead on the grenadiers of the 49th, fell mortally wounded. This for
a time gave the Americans undisturbed possession of the heights, and
great efforts were made to bring over the other troops. General Van
Rensalaer, after the fall of his cousin, crossed and took the command,
but hastening back to urge on the embarkation of the militia, it
devolved on General Wadsworth.
[Footnote 20: Now General Wool.]
Daylight had seen this brave little band form on the shores of the
river under a galling fire--the morning sun glittered on their
bayonets from the heights of Queenstown, and the victory seemed won.
The day so gloriously begun would have closed in brighter effulgence,
had not the militia on the farther side refused to cross over to the
assistance of their hard-pressed comrades. A stone house near the bank
defended by two light pieces of artillery, still played on the boats
that attempted to cross, and the Americans on the Canada side, having
no heavy artillery, were unable to take it. The firing from this, and
soon after the appearance of a large body of Indians on the field of
battle, so frightened the militia, that neither entreaties nor threats
could induce them to embark. Through utter want of orderly management,
half of the twenty boats had been destroyed or lost; still it was not
the lack of means of transportation that held them back, but
_conscientious scruples about invading an enemy's territory_.
Attempting to mask their cowardice under this ridiculous plea, they
stood and saw the dangers thicken around their comrades who had relied
on their support, without making a single effort to save them from
destruction.
Lieutenant-colonel Scott by a forced march through mud and rain, had
arrived at Lewistown with his regiment at four o'clock in the morning,
just as the troops were embarking. He begged permission to take part
in the expedition, but the arrangements having all been made, his
request was denied. He therefore planted his guns on the shore and
opened his fire on the enemy. But seeing how small a proportion of the
troops were got across, and perceiving also the peril of Van
Rensalaer's detachment, his young and gallant heart could not allow
him to remain an idle spectator, and taking one piece of artillery he
jumped into a boat with his adjutant Roach, and pushed for the
opposite shore. Wadsworth immediately gave the command of the troops
to him, and his chivalric bearing and enthusiastic language soon
animated every heart with new courage. Six feet five inches in height
and in full uniform, he presented a conspicuous mark for the enemy and
a rallying point to the troops. Had his regiment been with him,
Queenstown would have been a second Chippewa.
Considerable reinforcements, however, had arrived, swelling the
number to six hundred, of whom three hundred and fifty were regular
troops. These, Scott, assisted by the cool and skillful Capt.
Zitten, soon placed in the most commanding positions, and waited for
further reinforcements. Just before, a body of five hundred Indians,
whom the firing had suddenly collected, joined the beaten light
troops of the English. Encouraged by this accession of strength, the
latter moved again to the assault, but were driven back in
confusion. Still the enemy kept up a desultory engagement. On one
occasion, the Indians, issuing suddenly from the forest, surprised a
picket of militia, and following hard on their flying traces,
carried consternation into that part of the line. Scott, who was in
the rear, showing the men how to unspike a gun, hearing the tumult,
hastened to the front, and rallying a few platoons, scattered those
wild warriors with a single blow. But while the day was wearing away
in this doubtful manner, a more formidable foe appeared on the
field. General Sheaffe, commanding at Fort George, had heard the
firing in the morning; and a little later the news of the death of
Brock was brought him. His forces were immediately put in motion,
and soon after midday the little band that had from day dawn bravely
breasted the storm, saw from the heights they had so bravely won, a
column eight hundred and fifty strong, approaching the scene of
combat--not in haste or confusion, but with the slow and measured
tread of disciplined troops. These few hundred Americans watched its
progress with undaunted hearts, and turned to catch the outlines of
their own advancing regiments, but not a bayonet was moving to their
help. At this critical moment news arrived of the shameful mutiny
that had broken out on the opposite shore. The entreaties of Van
Rensalaer, and the noble example of Wadsworth, and the increasing
peril of their comrades, were wholly unavailing--not a soul would
stir. This sealed the fate of the American detachment. A few
hundred, sustained by only one piece of artillery against the
thirteen hundred of the enemy--their number when the junction of the
advancing column with the remaining troops and the Indian allies
should be effected--constituted hopeless odds. General Van
Rensalaer, from the opposite shore, saw this, and sent word to
Wadsworth to retreat at once, and he would send every boat he could
lay hands on to receive the fugitives. He, however, left everything
to the judgment of the latter. Colonels Chrystie and Scott, of the
regulars, and Mead, Strahan, and Allen of the militia, and officers
Ogilvie, Wool, Totten, and Gibson McChesney, and others, presented a
noble yet sorrowful group, as they took council over this message of
the commander-in-chief. Their case was evidently a hopeless one, yet
they could not make up their minds to retreat. Col. Scott, mounting
a log in front of his troops, harangued them in a strain worthy of
the days of chivalry. He told them their condition was desperate,
but that Hull's surrender must be redeemed. "Let us then die," he
exclaimed, "arms in hand. Our country demands the sacrifice. The
example will not be lost. The blood of the slain will make heroes of
the living. Those who follow will avenge our fall, and our country's
wrongs. Who dare to stand?" A loud "ALL!" rang sternly along the
line.[21] In the mean time Gen. Sheaffe had arrived, but instead of
advancing immediately to the attack, slowly marched his column the
whole length of the American line, then countermarched it, as if to
make sure that the little band in front of him was the only force he
had to overcome. All saw at a glance that resistance was useless,
and retreat almost hopeless. The latter, however, was resolved
upon, but the moment the order was given to retire, the whole broke
in disorderly flight towards the river. To their dismay, no boats
were there to receive them, and a flag of truce was therefore sent
to the enemy. The messenger, however, never returned; another and
another shared the same fate. At last Scott tied a white
handkerchief to his sword, and accompanied by Captains Totten and
Gibson, crept under one of the precipices, down the river, till he
arrived where a gentle <DW72> gave an easy ascent, when the three
made a push for the road, which led from the valley to the heights.
On the way they were met by Indians, who firing on them, rushed
forward with their tomahawks, to kill them. They would soon have
shared the fate of the other messengers, but for the timely arrival
of a British officer, with some soldiers who took them to Gen.
Sheaffe, to whom Scott surrendered his whole force. Two hundred and
ninety-three were all that survived of the brave band who had
struggled so long and so nobly for victory. Several hundred militia,
however, were found concealed along the shore, who had crossed over,
but skulked away in the confusion.
[Footnote 21: Mansfield's Life of Scott.]
The entire loss of the Americans in this unfortunate expedition,
killed and captured, was about one thousand men.
General Van Rensalaer, disgusted with the conduct of the militia, soon
after sent in his resignation.
Brock was buried the following day "under one of the bastions of Fort
George," and at the request of Scott, then a prisoner, minute guns
were fired from Fort Niagara during the funeral ceremonies. Above the
dull distant roar of the cataract, the minute guns of friends and foes
pealed over the dead, as with shrouded banners the slowly marching
column bore him to his last resting place. Cannon that but a few hours
before had been exploding in angry strife on each other, now joined
their peaceful echoes over his grave. Such an act was characteristic
of Scott, who fierce and fearless in battle, was chivalrous and kind
in all his feelings.
While a prisoner in an inn at Niagara, Scott was told that some one
wished to see the "tall American." He immediately passed through into
the entry, when to his astonishment he saw standing before him two
savage Indian chiefs, the same who had attempted to kill him when he
surrendered himself a prisoner of war. They wished to look on the man
at whom they had so often fired with a deliberate aim. In broken
English, and by gestures, they inquired where he was hit, for they
believed it impossible that out of fifteen or twenty shots not one had
taken effect. The elder chief, named Jacobs, a tall, powerful savage,
became furious at Scott's asserting that not a ball had touched him,
and seizing his shoulders rudely, turned him round to examine his
back. The young and fiery Colonel did not like to have such freedom
taken with his person by a savage, and hurling him fiercely aside,
exclaimed, "Off, villain, you fired like a squaw." "We kill you now,"
was the quick and startling reply, as knives and tomahawks gleamed in
their hands. Scott was not a man to beg or run, though either would
have been preferable to taking his chances against these armed
savages. Luckily for him, the swords of the American officers who had
been taken prisoners, were stacked under the staircase beside which he
was standing. Quick as thought he snatched up the largest, a long
sabre, and the next moment it glittered unsheathed above his head. One
leap backward, to get scope for play, and he stood towering even above
the gigantic chieftain, who glared in savage hate upon him. The
Indians were in the wider part of the hall, between the foot of the
stairs and the door, while Scott stood farther in where it was
narrower. The former, therefore, could not get in the rear, and were
compelled to face their enemy. They manoeuvred to close, but at every
turn that sabre flashed in their eyes. The moment they should come to
blows, one, they knew, was sure to die, and although it was equally
certain that Scott would fall under the knife of the survivor before
he could regain his position, yet neither Indian seemed anxious to be
the sacrifice. While they thus stood watching each other, a British
officer chanced to enter, and on beholding the terrific tableau, cried
out, "The guard," and at the same instant seized the tallest chief by
the arm and presented a cocked pistol to his head. The next moment the
blade of Scott quivered over the head of the other savage, to protect
his deliverer. In a few seconds the guards entered with levelled
bayonets, and the two chieftains were secured. One of them was the son
of Brant, of revolutionary notoriety.
The prisoners were all taken to Quebec, whence they were sent in a
cartel to Boston. As they were about to sail, Scott, who was in the
cabin of the transport, hearing a noise on deck, went up to ascertain
the cause, and found that the British officers were separating the
Irishmen, to exclude them from mercy due to the other prisoners, and
have them taken to England and tried for treason. Twenty-three had
thus been set apart when he arrived. Indignant at this outrage, he
peremptorily ordered the rest of the men to keep silent and not answer
a question of any kind, so that neither by their replies or voice they
could give any evidence of the place of their birth. He then turned to
the doomed twenty-three, and denounced the act of the officers, and
swore most solemnly that if a hair of their heads was touched, he
would avenge it, even if he was compelled to refuse quarter in battle.
Soon after he reached Boston, he was sent to Washington, and in a
short time was exchanged. He then drew up a report of the whole affair
to the Secretary of War, and it was presented the same day to
Congress. The result was the passage of an act of retaliation (March
3d, 1813.)
[Sidenote: Nov. 10.]
General Van Rensalaer having resigned his commission, making the
second general disposed of since the commencement of hostilities, the
command on the Niagara frontier devolved on General Smythe, who issued
a proclamation to the "men of New York," which was of itself a
sufficient guarantee that he would soon follow Hull into worse than
oblivion. In it, after speaking of the failure of the former
expedition, he said, "Valor had been conspicuous, but the nation
unfortunate in the selection of some of those directing it"----"the
commanders were popular men, destitute alike of theory and experience
in the art of war." "In a few days," said he, "the troops under my
command will plant the American standard in Canada to conquer or die."
He called on all those desirous of honor or fame, to rally to his
standard. He was not one of the incompetent generals whose plans
failed through ignorance. Portions of his proclamations, however, were
well adapted to rouse the military spirit of the state, and in less
than three weeks he had nearly five thousand men under his command.
His orders from the Secretary of War, were, not to attempt an
invasion with "less than three thousand combatants," and with
sufficient boats to carry the whole over together.
Seventy boats and a large number of scows having been collected at
Black Rock, he issued his orders for the troops to be in readiness
early on the morning of the 28th of November, to cross over and attack
the enemy.
Previous to the main movement, however, he sent over two detachments,
one under Colonel Boestler, and the other under Captain King--the
former to destroy a bridge five miles below Fort Erie, in order to cut
off the communication between it and Chippewa, while the latter, with
a hundred and fifty regular troops and seventy seamen, was to carry
the "Red House," and storm the British batteries on the shore.
The boats pushed off at midnight, and were soon struggling in the
centre of the stream. Of Colonel Boestler's seven boats, containing
two hundred men, only three reached the Canada shore. With less than
half his force he advanced and easily routed the guard, but hearing
that a British reinforcement was marching up, he retreated without
destroying the bridge, and re-embarked his men. Captain King started
with ten boats, but six of them were scattered in the darkness, and
only four reached the point of attack. Among these, however, were the
seventy seamen. The advance of the boats having been seen by the
sentinels on watch, the little detachment was compelled to land under
a shower of grape shot and musketry.
The sailors without waiting the order of a regular march, rushed up
the bank with their boarding pikes and cutlasses, stormed the
position, and carried it with loud huzzas. After securing some
prisoners and tumbling two cannon and their caissons into the river,
Lieutenant Angus began to look around for Captain King. The latter
directing his force on the exterior batteries, carried the first by
the bayonet, when the other was abandoned. The position and all the
batteries being taken, the firing had ceased, and Lieutenant Angus
marched his sailors, with the wounded and prisoners, to the shore to
wait for Captain King, and recross the river. Finding only four boats
there, and ignorant that no more had landed, he concluded that the
former had already re-embarked his troops; he therefore launched these
and made good his retreat to the American shore. In a short time
Captain King arrived, and to his amazement found all the boats gone.
After a short search, however, he discovered two belonging to the
enemy, in which he despatched the prisoners he had taken, and as many
of his men as they would hold. He remained behind with the remainder
of his detachment, and was soon after compelled to surrender himself
prisoner of war.
On the return of Boestler and Angus without Captain King and the rest
of the detachment, Colonel Winder volunteered to go in search of them.
But, as he approached the opposite shore, he found all the batteries
re-established, which opened their fire upon him, compelling him to
return with the loss of six killed and twenty-six wounded. In fact his
own boat was the only one that touched land at all--the others being
carried down by the force of the stream.
Through some unaccountable delay, the main body, to which the two
detachments sent off at midnight were designed as an advance guard,
did not embark till twelve o'clock next day. But at length two
thousand men under General Porter, were got on board, while General
Tannehill's volunteers and M'Clure's regiment were drawn up on the
shore ready to follow. As if on purpose to give his adversary time for
ample preparation, thus imitating the fatal examples of Dearborn and
Hull, Smythe kept his men paraded on the beach in full view of the
Canada shore, till late in the afternoon. He then, instead of giving
the anxiously expected order to advance, commanded the whole to
debark. Indignation and rage at this vacillating, pusillanimous
conduct seized the entire army, and curses and loud denunciations were
heard on every side. General Porter boldly and openly accused his
commander of cowardice. The latter, frightened at the storm he had
raised, promised that another attempt should be made the next day. It
was resolved to cross at a place five miles below the navy yard, and
the following day, at four o'clock, nearly the entire army was
embarked. General Porter with the American colors floating from the
stern of his boat, was in advance, to show that he asked no man to go
where he would not lead. But when all was ready, and at the moment
when every one expected to hear the signal to move forward, an order
was passed along the line directing the troops to be relanded,
accompanied with the announcement that the invasion of Canada was for
that season abandoned. A shout of wrath burst from the whole army.
Many of the militia threw away their arms and started for their homes,
while fierce threats against the General's life were publicly made by
the remaining troops. He was branded as a coward, shot at in the
streets, and without even the form of a trial, was driven in scorn and
rage from the army, and chased and mobbed by an indignant people from
the state he had dishonored. Before he retired, however, he made an
absurd attempt to retrieve his honor by challenging General Porter to
mortal combat. They met on Grand Island and exchanged shots without
effect. The seconds having published the transaction in a Buffalo
paper, "congratulated the public on the happy issue." In commenting on
this, Ingersoll very pithily remarks, "The public would have
preferred a battle in Canada."
Beginning at the extreme north-west, and continuing along the lakes to
Niagara, we had met with nothing but defeat. Only one more army was
left to lift the nation out of the depths of gloom by its
achievements, or deepen the night in which the year 1812 was closing.
General Dearborn, the commander-in-chief, had an army of three
thousand regulars and as many more militia, with the power to swell
his force to ten thousand if he thought proper. The plan of government
to conquer Canada through Hull's invasion from Detroit, Van
Rensalaer's and Smythe's from Niagara, both to be supported and their
triumph secured by the advance of Dearborn, had fallen to the ground,
and the latter was passing the autumn in idleness.
General Brown, who commanded the militia appointed for the defence of
the eastern shore of Lake Ontario and southern shore of St. Lawrence,
exhibited, at Ogdensburg, the first indications of those qualities of
a great commander which afterwards developed themselves on the scene
of Van Rensalaer's and Smythe's defeats and failures. Colonel Forsyth
having made a successful incursion into Canada with a noble body of
riflemen, twice defeating double his numbers and burning a block house
with stores; the British, in retaliation, attacked Ogdensburg. On the
2d of October they commenced a cannonade from their batteries at
Prescott, on the opposite side of the river. This harmless waste of
ammunition was continued for two days, when it was resolved to storm
the town. Six hundred men were embarked in forty boats, and under
cover of the batteries, pulled steadily across the river. General
Brown could collect but four hundred militia to oppose them, but
having posted these judiciously, they were able to keep up such a
deadly fire on the enemy that every attempt to land proved abortive,
and the whole detachment was compelled to withdraw to the Canada
shore.
There was, during the summer, a good deal of skirmishing along the
frontier, forming interludes to the more important movements. Colonel
Pike on the 19th of the same month made an incursion into Canada,
surprised a body of British and Indians, and burnt a block-house.
Three days after, Captain Lyon captured forty English at St. Regis,
together with a stand of colors and despatches from the Governor
General to an Indian tribe. The colors were taken by William M. Marcy.
[Sidenote: Nov. 20.]
Thus the autumn wore away, till at last, Dearborn seemed to awake
from his torpor. Moving his army from the little town of Champlain,
he forded the La Cole, and attacked and captured an English
block-house. The grand movement had now commenced, and the British
Governor-General prepared to meet the most serious invasion that had
yet been attempted. But to his astonishment he discovered that all
this display of force was to obtain possession of a guard-house, and
retain it for half an hour. This feat being accomplished, General
Dearborn, amid much confusion, marched his six thousand men back
again, and resting on his honors soon after retired into winter
quarters. After protracted delays and unaccountable inaction, he
seemed at last to feel the necessity of obeying the urgent orders of
the government, "_not to lose a moment in attacking the British
posts in his front_." These he had now obeyed to the letter--he had
_attacked_ a block-house and fled. The great tragedy had begun and
ended in a farce. The surrender of Hull was an unmitigated disgrace,
and the nation turned towards Niagara for relief. The failure of Van
Rensalaer was not unmixed with consolation. He and the officers and
men who bore the brunt of that day's battle, had shown what American
troops could do. Van Rensalaer has been charged with acting rashly,
and exposing himself to discomfiture, when success would have been
of no advantage. But those who suppose that a victory is fruitless,
because no important position is gained, or territory is wrested
from the enemy, commit a vital error. They forget that _moral_ power
is half, even when every thing depends on hard blows. When
confidence is lost, and despondency has taken the place of courage
and hope, a battle that should restore these would be a victory, at
almost any sacrifice. So Van Rensalaer thought, and justly. His
preparations and mode of procedure were not careful and prudent, as
they should have been, exhibiting a want of thoroughness which a
longer experience would have rectified; still, his plan might have
succeeded but for the dastardly conduct of the militia, and a new
impulse been given to the movements along the northern frontier.
This cowardly behavior of his troops he could not anticipate, for
they had hitherto shown no disinclination to fight. At Hull's
surrender there were no indications of a craven spirit--on the
contrary, the soldiers cursed their commander, and the general
feeling was, that give the men a gallant leader and they would fight
bravely. Van Rensalaer knew that his troops would not fail through
reluctance on his part to lead them to battle, and it was enough to
break his noble heart, as he stood bleeding from four wounds, to see
them refuse to come to his rescue.
General Smythe's conduct admits of no apology. His excuse for
countermanding his last order, after the troops had embarked, is
groundless. He says that his orders were strict, not to attempt an
invasion of Canada with less than three thousand men, and that he but
fifteen hundred. Yet in his last attempt all but some two hundred of
his troops were actually embarked, when he commanded them to re-land.
He was either not aware how many soldiers composed his army until he
counted them as they lay off in their boats, ready to pull for the
opposite shore, or he knew it before. If the latter be true, why all
this display, designed to eventuate in nothing? On the other hand, the
confession of ignorance is still worse. This much is clear, all these
difficulties and objections could not have occurred to him for the
first time when he saw the army drawn up on shore or afloat. The
excuse, if honest, is worse than the act itself.
[Sidenote: Aug. 1.]
Dearborn's inactivity furnished less salient points of criticism, but
it was fully as culpable as Smythe's failure. In the first place, he
received orders from the Secretary of War to make a diversion in favor
of _Hull at Niagara and Kingston, as soon as possible_. His position
might have been such that no blame could attach to him for not making
such diversion, but nothing could warrant him in entering into an
armistice with the enemy, in which Hull was excluded. If he assumed
such a responsibility in the hope that peace would be secured, he was
bound to make as one of the first conditions, that no reinforcements
should be sent to Malden and Detroit. One such act is sufficient to
cause the removal of a commander, for he can never be an equal match
against a shrewd and energetic enemy. Prevost wrote to Gen. Brock: "_I
consider it_ most fortunate that I have been able to prosecute this
object of Government, (the armistice,) _without interfering with your
operations on the Detroit. I have sent you men, money, and stores of
all kinds._"[22]
[Footnote 22: Vide Life and Services of Sir George Provost.]
One cannot read this letter without feeling chagrin that the Senior
Major-General of the American army could be so easily overreached.
In the second place, his delay in breaking off this armistice when
peremptorily ordered by government, was clearly reprehensible, while
the fact that with an army of six thousand men under his immediate
command, he accomplished absolutely nothing, is incontrovertible proof
of his inefficiency as a commander. The isle of Aux Noix was
considered the key of Central Canada, and this he could have taken at
any moment and held for future operations; yet he went into winter
quarters without having struck a blow.
The troops, regular and militia, under his general direction, amounted
in the latter part of September to thirteen thousand men. Six thousand
three hundred were stationed along the Niagara, two thousand two
hundred at Sackett's Harbor, and five thousand on Lake Champlain. To
oppose this formidable force, Sir George Provost had not more than
three thousand troops,[23] and yet not even a battle had been fought,
if we except that of Van Rensalaer's detachment, while instead of
gaining we had lost both fortresses and territory.
[Footnote 23: Vide Armstrong's Notices of the War of 1812.]
One naturally inquires what could be the cause of such a complete
failure where success was deemed certain. In the first place, there
was not a man in the cabinet fit to carry out a campaign, however well
planned. The sudden concentration of so large a force on our northern
frontier, before reinforcements could arrive from England, was a wise
movement, and ought to have accomplished its purpose. But there the
wisdom ended, and vacillation and doubt took the place of promptness,
energy and daring.
In the second place, inefficient commanders were placed at the head of
our armies. Both Dearborn and Hull had been gallant officers in the
Revolution, but they were wholly unaccustomed to a separate command,
and while imitating the caution of their great exemplar, exhibited
none of his energy and daring. They remembered his Fabian inactivity,
but they forgot the overwhelming reasons that produced it, and forgot,
also, Trenton, Princeton and Monmouth.
In the third place, the militia were undisciplined and could not be
relied upon. The insubordination, unmilitary conduct, and recklessness
of rules which force a commander into extreme caution, lest his
semblance of an army should be annihilated, are not known to the
persons who coolly criticise him at a distance. These things are
doubtless an ample excuse for much that is unsparingly condemned.
Hence it is unjust to pronounce judgment on this or that action,
because it might apparently have been avoided, unless those actions
and the declarations of their author contradict each other, or stand
condemned by every interpretation of military rules.
In the commencement of the war we had neither an army nor generals
that could be trusted. The troops lacked confidence in their leaders,
and the latter had no confidence in their troops. Such mutual distrust
can result in nothing but failure. Our commanders were in an
embarrassing position, but they ought to have been aware that to
_fight_ their way out was the only mode of escape left them. Battles
make soldiers and develop generals. In the tumult and dangers of a
fierce fight, the cool yet daring officers, fertile in resources,
fierce in the onset, and stubborn and unconquered in retreat, are
revealed, and soon men are found who will follow where they lead, even
into hopeless combat. A spirit of emulation and valor succeeds
timidity and distrust.
The administration at this period was surrounded with great and
perplexing difficulties. With but the germ of a military academy,
efficient officers were scarce. The establishment of the school at
West Point was one of the wisest acts ever performed by this
government, and the attempt, a few years since, to destroy it, one
of the most unscrupulous, reckless and dangerous ever put forth by
ignorant demagogues. Our volunteers and militia have confidence in
men bred to the profession of arms. They yield them ready
obedience--submit to rigid discipline--while the method and skill
with which everything is conducted, impart confidence and
steadiness. A country like ours will never submit to the expense and
danger of a large standing army, nor do we need it if we can keep
well supplied with military schools. A few West Point officers on
the Canada frontier would have brought the campaign of 1812 to a
different close.
CHAPTER V.
THE NAVY.
The Cabinet resolves to shut up our ships of war in port --
Remonstrance of Captains Bainbridge and Stuart -- Rodgers
ordered to sea -- Feeling of the crews -- Chase of the
Belvidere -- Narrow escape of the Constitution from an
English fleet -- Cruise of the Essex -- Action between the
Constitution and Guerriere -- Effect of the Victory in
England and the United States -- United States takes the
Macedonian -- Lieutenant Hamilton carries the captured
colors to Washington -- Presented to Mrs. Madison in a
ball-room -- The Argus -- Action between the Wasp and Frolic
-- Constitution captures the Java -- Hornet takes the
Peacock -- Effect of these Victories abroad.
Having gone through the first campaigns on the Canadian frontier, I
leave for awhile the army of Harrison, swallowed up in the forests of
Ohio and surrounded by the gloom of a northern winter, toiling its way
towards Malden, and turn with a feeling of relief to the conduct of
our little navy during the summer that had passed.
As I stated before, our naval force amounted to but nine frigates and
a few sloops of war, while Great Britain had a hundred ships of the
line in commission, and more than a thousand vessels in all, bearing
the royal flag. Added to this stupendous difference in the number of
ships, was the moral power attached to the universally acknowledged
superiority of the British navy. England was recognized mistress of
the seas. The fleets of Spain, France and Holland had one after
another submitted to her sway, and fresh with still greater laurels
won under Nelson, her navy was looked upon as irresistible. A naval
contest on our part, therefore, was not dreamed of, and hence arose
the determination on the part of the Administration at Washington, to
convert our frigates into mere floating batteries for the protection
of harbors. But it must be remembered, weak as our navy appeared, it
was stronger at the declaration of war than the whole British force on
our coast. We had ships enough to blockade Halifax and Bermuda, and
bear undisputed sway until reinforcements could be sent across the
Atlantic. Our privateers in the revolution--the conduct of our ships
in the Bay of Tripoli had given evidence of what could be done, and
the determination of the Cabinet, therefore, to lay up the ships of
war before their metal had been tested--to leave the waters around our
coast vexed with British cruisers, when at least for six weeks we
could have kept them clear of the enemy, and in all probability
captured their entire squadron on the American station, is another
painful evidence of the utter incapacity of the administration to
carry on the war. If, in anticipation of hostilities, our whole fleet
had been collected and put in such order that it could have sailed at
an hour's notice, results would have been accomplished far greater
than those which followed.
Against our nine frigates, the President, United States, and
Constellation, of the first class, the Congress, Constitution, and the
Chesapeake of the second, the Essex, Adams, Boston and New York,[24]
together with several smaller vessels, there were on the Halifax
station but five frigates and some smaller vessels. The Africa,
sixty-four, was the only two decker on our coast, in active service.
The Halifax station could have been reinforced by the other two
stations, the Jamaica and Leeward Island, but not within a month,
which would have given us an opportunity of cutting them up in detail.
England, at this time, was so occupied with the momentous affairs in
Europe, that she kept her fleets on the eastern board of the Atlantic,
and ignorant of our naval strength, supposed the ships on the Halifax
station more than a match for the whole American navy. Had the British
fleet on this coast been captured, and an alliance offensive and
defensive formed with France, we should have struck the maritime power
of England a blow from which she never would have recovered. But the
outcries of the Federalists filled the administration with as much
dread of French alliance, as it entertained of the naval power of
England.
[Footnote 24: The Boston and New York were not ready for sea, but
could and would have been, had there been a determination on the part
of the Government to use the navy.]
Not only was the American Government innocent of all such plans for
the navy, but it did not even provide for the merchantmen which might
be approaching the American coast, and liable to be captured by the
most contemptible cruiser that sailed unmolested along our shores. No
nation ever before had the opportunity of doing so much with small
means, as circumstances placed in the hands of the American Government
at the commencement of the war, and threw it away so foolishly, so
unpardonably.
The insane project to lay up the American ships in harbor, was
defeated by two naval officers, to whom the nation owes perpetual
gratitude. Captains Bainbridge and Stewart were at Washington when the
subject was under discussion, and being shown the written orders to
Commodore Rodgers, to keep his fleet in the harbor of New York, as a
part of its defence, they sought an interview with the Secretary of
the Navy, and boldly remonstrated against this death-blow to the navy.
"If laid up in war, who would support it in peace?" Although told that
the thing was settled, so far as regarded the fleet in New York Bay,
they appealed with still greater urgency, and in the true spirit of
their profession, declared that the American commanders were capable
of taking care of their own ships; nay, in noble enthusiasm asserted,
that eight times out of ten, an American frigate would capture an
antagonist of equal metal.
The secretary was moved by their appeal, backed as it was with solid
argument, and took them to see the President. They made to him the
same statements which had so deeply impressed the Secretary of the
Navy. Moreover, they promised _victories_, a dream which had never
visited the brain of a member of the cabinet. "Eight times out of
ten," said they, "with equal force we can hardly fail--our men are
better men, and better disciplined; our midshipmen are not mere boys,
only fit to carry orders, but young men capable of reflection and
action. Our guns are sighted, which is an improvement of our own the
English know nothing of. While we can fire cannon with as sure an aim
as musketry, or almost rifles, striking twice out of every three
shots, they must fire at random, without sight of their object or
regard to the undulations of the sea, shooting over our heads, seldom
hulling us or even hitting our decks. We may be captured, and probably
shall be, even after taking prizes from them, because their numbers
are so much greater than ours. But the American flag will never be
dishonored, seldom if ever struck to equal force."[25] The President,
as well as the Secretary of the Navy, was swept away by the arguments
and gallant spirit of those officers, and suddenly remembered the
daring and success of the few ships of war and the privateersmen
during the Revolution.
[Footnote 25: Vide Ingersoll's History of the War of 1812.]
Seeing their advantage, these officers pressed it with redoubled
energy, until the President called a meeting of the cabinet to consult
on the matter. But Mr. Gallatin, to whose sagacity and foresight all
paid the most profound deference, treated the project as absurd. He
had studied European affairs too much, and the rising genius of this
country too little. Like many other wise statesmen, he could not
introduce into the elements from which he drew his conclusions, the
gallant spirit, lofty enthusiasm and indomitable courage, which then
pervaded our little navy. He saw only the tremendous maritime
preponderance against us, and hence, with all his patriotism and
wisdom, acted as a perpetual clog to the government till he was sent
abroad, and his counsels could no longer influence the cabinet.
But his advice that all maritime efforts should be confined to
privateers, prevailed, and Bainbridge and Stewart were told that the
decision which had been made respecting the national ships, could not
be changed. Undaunted by their repulse, they spent nearly the whole
night after this resolve had been made known to them, in drawing up a
remonstrance to the President. Having witnessed the effect of their
personal appeal to him, they determined to address him once more by
letter.
The language of that address was not softened by well rounded periods,
but plain and direct, placed the subject in its true aspect before Mr.
Madison, and put on him as Chief Magistrate of the Union, the
responsibility of keeping the navy from its legitimate field of
action. When this joint communication was laid before the Secretary of
the Navy, he objected to it as too strong and stern to present to the
President, and advised them to modify its language. They refused to do
so, and Mr. Madison instead of being offended at their plainness of
speech, took upon himself the responsibility of acting independent of
his cabinet, and assured them the vessels should be ordered to sea. No
one can tell the joy of these brave men, when they found the navy they
loved so well, was not to be dishonored, and elate with pride,
determined that the flag they had so long carried over the sea, should
never be struck but with honor.
The naval officers knew that the country reposed no confidence in its
marine force, and Captains Bainbridge and Stewart, anticipating the
doom they had struggled so noble to avert, had determined to go to
sea in a privateer which the latter had purchased.[26] With a band of
hardy seamen about them, and each serving in rotation as captain and
first officer, they resolved to claim the right of the American flag
to the high seas.[27]
[Footnote 26: The Snapper, which, under Peregrine Green, was soon
after captured off the Capes of the Delaware.]
[Footnote 27: Vide Cooper's Naval History; Harris' Life of Bainbridge;
Memoir of Commodore Stewart; Naval Chronicle; and Ingersoll's History
of the War of 1812.]
At this time there were in the port of New York, the President,
forty-four; Essex, thirty-two; and Hornet, eighteen; to which, on the
21st of June, were added the United States, forty-four; Congress,
thirty-eight; and Argus, sixteen, all ready to sail in an hour's
notice, with the exception of the Essex, which was repairing her
rigging and restowing her hold. As soon as the President had
determined to send the vessels to sea, this squadron was put under the
command of Commodore Rogers, and he ordered to get under way at once,
and intercept a large fleet of Jamaica men which were reported to have
sailed, and by this time should be off the American coast. An hour
after Commodore Rogers received his orders, he was leading his
squadron down the Bay, and soon his canvas disappeared in the
distance.
From the joy that pervaded this little squadron, as the sails were
given to the wind, one would have supposed it was going to witness a
grand regatta, instead of to unequal and deadly strife with an enemy.
In the gallant hearts that trod those decks, existed none of the
timidity and distrust that weighed down the government. There was not
merely the determination of brave men entering on a desperate
conflict, but the buoyancy of confidence, the joy of those who were to
wipe out with their heavy broadsides the imputations cast on them by
their own countrymen, and hush forever, with their shouts of victory,
the boasting and mockery of their foe. The sailors partook of the
excitement, for it was a common enemy against which they were
going--the oppressor of seamen as well as the invader of national
rights. Says a midshipman on board the Hornet, in his Diary: "This
morning the declaration of war by the United States against Great
Britain was read. *** At ten o'clock, A. M., Commodore Rodgers hove
out the signal to weigh; never was anchor to the cathead sooner, nor
topsail sheeted home[28] to the masthead with more dispatch, than upon
the present occasion; the smallest boy on board seems anxious to meet
what is now looked upon as the common tyrant of the ocean, for they
had heard the woeful tales of the older tars. ** When the ship was
under way, Captain Lawrence had the crew called to their quarters,
and told them that if there were any amongst them who were
disaffected, or one that had not rather sink than surrender to the
enemy, with gun for gun, that he should be immediately and uninjured,
landed and sent back in the pilot boat. The reply fore and aft
was--not one." Not one hesitating voice, but instead, three hearty
cheers, that made the vessel ring. With such a spirit did the first
squadron put to sea, and make its first claim, at the cannon's mouth,
to equal rights.
[Footnote 28: Vide Ingersoll's History of the War.]
[Sidenote: June 23.]
Two days after, Rodgers discovered, at six o'clock in the morning, an
English frigate to the north-east, and instantly crowded sail in
pursuit. The chase led down the wind, and the President being a fast
sailer when going free, soon gained on the stranger, leaving the
squadron far astern. At four o'clock she got within gunshot, but the
wind falling, gave the enemy the advantage, and Rodgers seeing that he
no longer gained on the chase, attempted to <DW36> it. The first gun
was pointed by the commodore himself, the shot of which struck the
English frigate in the stern, and passed on into the gun-room. This
was the first hostile gun fired on the sea after war was declared. The
second was pointed by Lieutenant Gamble, which also struck the enemy.
The third shot, directed by Rodgers himself, killed two men and
wounded five others. At the fourth shot, fired by Lieutenant Gamble,
the gun bursted, killing and wounding sixteen men. The Commodore was
flung into the air by the explosion, and fell back on deck with such
violence that his leg was broken. The enemy took heart at this
unexpected accident, and opened his fire. The President, however, soon
began to heave her shot again with such precision, that the British
frigate was compelled to cut away her anchors, throw overboard her
boats, and spring fourteen tons of water in order to lighten her. She
was by these means enabled to gain on her pursuers. Commodore Rodgers
finding the distance between them increasing, fired three broadsides,
which falling short, he abandoned the chase. The loss of the
President, in killed and wounded, was twenty-two, only six of whom
were damaged by the shot of the enemy. The Belvidera, for such she was
afterwards ascertained to be, reported seven killed and wounded. After
repairing damages Rodgers again cruised for the Jamaica men, and at
length supposing he had got in their wake, kept on until near the
mouth of the English Channel, when seeing nothing of them, he returned
by way of Maderia and the Western Islands to Boston. It was a barren
cruise, only seven merchantmen being taken during the whole seventy
days the squadron was absent.
In the mean time the report of the Belvidera, which had put into
Halifax, caused the enemy to collect a fleet, which early in July was
off New York, where it captured a great many American merchantmen.
Among the prizes was the schooner Nautilus, the first vessel of war
taken on either side. [Sidenote: July 12.] While the squadron was thus
cruising off the coast, in the hope of meeting the American fleet
under Rodgers, the Constitution, a forty-four, sailed from Annapolis
on her way to New York. Her crew was newly shipped, a hundred men
having joined her on the night before she sailed. The orders which
Captain Hull, the commander, received from the Secretary of the Navy,
exhibit the timidity and weakness of the Government. In the first
place, after giving directions respecting the destination of the ship,
he said: "I am informed that the Belvidera is in our waters, but you
are not to understand me as impelling you to battle previously to your
having confidence in your crew, unless attacked, or with a reasonable
prospect of success, of which you are to be at your discretion the
judge." In a later order he says: "If on your way thither (_i. e._
from Annapolis to New York) you should fall in with the enemy's
vessel, you will be guided in your proceeding by your own judgment,
bearing in mind, however, that you are not voluntarily to encounter a
force superior to your own." One can imagine the smile of contempt
that curled the lip of the stern commander of the Constitution, when
he received this pitiful order, so well adapted in its tone and
language to make timorous officers, and hence ensure defeat. The
Secretary had witnessed the confidence and daring spirit of Bainbridge
and Stewart, and he was afraid such men would fight, when prudence
would dictate flight. But he might have known that when officers like
them were once fairly out to sea, on the decks of their own ships,
beneath their own flag streaming aloft, they would pay no more
attention to orders like the above, than to the sighing of the wind
through their cordage.
On the 17th the Constitution was out of sight of land, though still
within soundings and going under easy canvas, when at two o'clock she
discovered four sail in the north. At four she discovered another a
little to the eastward of the first. Towards evening, the wind blowing
light from the southward, the Constitution beat to quarters and
cleared for action. At ten o'clock she showed the private signal,
which remained unanswered; and concluding she had fallen in with a
squadron of the enemy, made all sail. Just before daybreak the
Guerriere, one of the fleet, sent up a rocket and fired two guns. As
the light broadened over the deep, Capt. Hull, who was anxiously on
the look-out, discerned seven ships closing steadily upon him. This
was the squadron of Commodore Broke, consisting of the Africa 64,
Guerriere 38, Shannon 38, Belvidera 36, Eolus 32, together with the
captured Nautilus and a schooner. As the sun rose over the ocean and
lifted the mist that lay on the water, Capt. Hull had a full view of
his position. Two frigates were beating down from the north upon him,
while the Africa, two frigates, a brig and schooner were following in
his wake, and all with English colors flying. To increase the painful
uncertainty that now hung over the fate of his vessel, the breeze
which had been light all night entirely died away, and the sails
flapped idly against the masts. Hull, however, resolved that his ship
should not be lost, if human energy and skill could save her, and
immediately sent all his boats forward to tow. But he soon found that
the enemy, by putting the boats of two ships on one, were slowly
closing on him. He then took all the rope he could spare and run a
kedge out nearly a half a mile ahead and dropped it. The crew seized
the rope, and springing to it with a will, soon made the ship walk
through the water. As she came up with the kedge she overran it, and
while still moving on under the headway she had obtained, another
kedge was carried ahead, and the noble vessel glided away, as if by
magic, from her pursuers. It was not long, however, before the enemy
discovered the trick the Yankee was playing, and began also to kedge.
A little air was felt at half-past seven, but at eight it fell calm
again, when the vessels resorted to boats, long sweeps and the kedge.
The Shannon, which was astern, having, at last, got most of the boats
of the squadron on her, slowly gained on the Constitution, while the
Guerriere was walking down on her larboard quarter. The prospect for
the American was now gloomy enough--there was scarcely a ray of hope.
The unruffled sea seemed to heave in mockery of the anguish of those
whose every thought was a prayer for wind, and slowly, like the
unpitying approach of death, the hostile fleet kept closing on that
helpless ship. One more hour like the last, would bring her under the
guns of two frigates. Still, there was not a craven heart within those
ribs of oak. Each man, as he looked sternly on his comrade, read in
his face the determination to fight while a gun was left. Hull,
chafing at his desperate position, resolved to close fiercely with the
first vessel that approached; and judging from his after conduct, he
would have made wild work with his antagonist. The men in the boats
strove nobly, but it was a contest of mere physical strength, in which
there was not the least hope of success. But adverse fate seemed at
last to relent, and a light breeze sprung up from the southward. Hull
no sooner saw it approaching on the water than he ordered the sails to
be trimmed, and the moment the vessel felt its gentle pressure, she
was brought up into the wind--the boats fell alongside and were
hoisted to their davits or swung, just clear of the water--the men
working coolly at their posts, although the shot of the Guerriere
were dashing the sea into spray around them.
But in an hour it again fell nearly calm, and the boats were once more
put on. The crew strove to make up by effort what they lacked in
force, but the Shannon steadily gained. With the exception of a little
rest obtained when slight breezes struck the vessel, the men were kept
incessantly at work all the day. At two o'clock, the Belvidera opened
with her bow guns, to which the Constitution responded with her stern
chasers. In half-an-hour, however, Captain Hull ordered the firing to
cease, and the men were again ordered to the boats, and rowing and
kedging were kept up till eleven at night. They were fast becoming
exhausted under the tremendous strain that had been put upon them
since early in the morning, when to their great relief a breeze sprung
up, and every sail that would draw was set. It lasted, however, only
for an hour. At midnight, it was calm again; but the crews of both
vessels had been overtasked, and no boats were sent out. In the
morning, Captain Hull discovered that some of the vessels had gained
on him, and four frigates were within long gun shot. It was now
apparent that the least unfavorable change would settle the fate of
the Constitution. The officers had snatched a little sleep at their
posts, and were ready to defend their flag to the last. It was a
lovely summer morning, and as the orb of day slowly rolled into view,
it lighted up a scene of thrilling interest and transcendant beauty.
The ocean lay slumbering in majestic repose, reflecting from its
unruffled bosom the cloudless sky. A light breeze was fanning the sea,
and every stitch of canvas that would draw was set. All the vessels
had now got on the same tack, the gallant American leading the van.
"The five frigates were clouds of canvas from their trucks to the
water," as slowly and proudly they swept along the deep. The
Constitution looked back on her eager pursuers, each eye on her decks
watching the relative speed of the vessels, and each heart praying for
wind. But, at noon, it again fell calm, when the Belvidera was found
to be two miles and a half astern, the next frigate three miles
distant, and the others still farther to leeward. This was a great
gain on the position of the day before, and with a steady breeze,
there would be no doubt of the issue. About half-past twelve, a light
wind sprung up, and although it kept unsteady during the afternoon, it
was evident the Constitution was walking away from her pursuers. Every
sail was tended, and every rope watched with scrupulous care, that
showed the American frigate to be a thorough man of war. The day which
had been so beautiful threatened a stormy close, for a heavy squall
was rising out of the southern sea. Captain Hull narrowly watched its
approach, with every man at the clew lines. Just before it struck the
ship, the order was given, and the vessel was stripped of her canvas
as by a single blow. The British vessels began to take in sail without
waiting for the near approach of the squall. As soon as the strength
of the gale had been felt, the Constitution was again put under a
press of canvas, and bowing gracefully, as if in gratitude to the
rising sea, she flung the foam joyfully from her bows, and was soon
rushing through the water at the rate of eleven knots an hour. When
the rain cloud had passed, and an observation of the enemy's ships
could be obtained, they were far astern, and with the last rays of the
setting sun, the Constitution bade farewell to her pursuers. It was
gallantly and gloriously done.
Cool and steady action on the part of the commander, met by
corresponding conduct on the part of the officers and crew, thorough
seamanship exhibited in every manoeuvre she attempted, saved the noble
vessel from capture. What a contrast does this conduct of the nephew,
thus surrounded by a superior force and beset with apparently
insurmountable difficulties, present to that of the uncle at Detroit.
In the one, desperate circumstances produced great effort, in the
other none at all. One with no thought of surrendering, while a spar
was left standing, the other meekly laying down his arms without
firing a shot. Shortly after, the Constitution arrived in Boston.
Previous to the sailing of this vessel from Annapolis, the Essex,
under Capt. Porter, having been got ready for sea at New York, started
on a cruise to the southward. Making several prizes of merchantmen,
she again stood to the southward, when she fell in with a fleet of
British transports, convoyed by a frigate and bomb vessel. She
endeavored to get along side of the former, but one of the transports
which Capt. Porter had spoken, threatening to make signal to the other
vessels, he was obliged to take possession of her. To accomplish this,
as the prize had a hundred and fifty soldiers aboard, consumed so much
time that the rest of the fleet escaped.
The Essex having disguised herself as a merchant man continued her
cruise, and in a few days discovered a strange sail, which, deceived
by her appearance, boldly attacked her. The latter having got the
enemy in close range, knocked out her ports, which had been closed,
and poured in her broadsides. This sudden metamorphosis and tremendous
firing completely stunned the stranger, and he immediately hauled down
his colors. The prize proved to be the ship Alert, mounting twenty-two
eighteen-pound carronades. This was the first British war vessel
taken by an American cruiser.
Captain Porter having converted the Alert into a cartel, sent her with
the prisoners into St. John's. The English Admiral, at Newfoundland,
remonstrated against this course, as it deprived the British of the
chances of recapture before entering an American port. He however
could not well refuse to carry out the arrangements which the Captain
of the Alert had entered into.
The Essex, after an unsuccessful cruise and some narrow escapes,
finally reached the Delaware, where she replenished her stores.
[Illustration: The Constitution and Guerriere.]
On the 28th of July an order was sent from the Secretary of the Navy,
to Capt. Hull, at Boston, to deliver up the Constitution to Commodore
Bainbridge, and take charge of the frigate Constellation. [Sidenote:
Aug. 2.] But fortunately for him and the navy, just before this order
reached him he had again set sail, and was out on the deep, where the
anxieties of the department could not disturb him. Cruising eastward
along the coast, he captured ten small prizes near the mouth of the
St. Lawrence and burned them. In the middle of the month he recaptured
an American merchantman and sent her in, and then stood to the
southward. On the 19th he made a strange sail, one of the vessels that
a few weeks before had pressed him so hard in the chase. When the
Constitution had run down to within three miles of him, the Englishman
laid his maintop sail aback, and hung out three flags, to show his
willingness to engage. Capt. Dacres, the commander, surprised at the
daring manner in which the stranger came down, turned to the captain
of an American merchantman whom he had captured a few days before, and
asked him what vessel he took that to be. The latter replied, as he
handed back the glass to Dacres, that he thought from her sails she
was an American. It cannot be possible, said Dacres, or he would not
stand on so boldly. It was soon evident, whoever the stranger might
be, he was bent on mischief. Hull prepared his vessel for action
deliberately, and after putting her under close fighting canvas and
sending down her royal yards, ordered the drums to beat to quarters.
It was now five o'clock, and as the Constitution bore steadily down
towards her antagonist, the crew gave three cheers. The English vessel
was well known, for she had at one of her mast-heads a flag proudly
flying, with the "Guerriere" written in large characters upon it. When
the Constitution arrived within long gun shot, the Guerriere opened
her fire, now waring to bring her broadside to bear, and again to
prevent being raked by the American, which slowly but steadily
approached. The Englishman kept up a steady fire, for nearly an hour,
to which the Constitution replied with only an occasional gun. The
crew at length became excited under this inaction. The officer below
had twice come on deck to report that men had been killed standing
idly at their guns, and begged permission to fire; but Hull still
continued to receive the enemy's broadsides in silence. The Guerriere
failing to <DW36> the Constitution, filled and moved off with the
wind free, showing that she was willing to receive her and finish the
conflict in a yard-arm to yard-arm combat. The Constitution then drew
slowly ahead, and the moment her bows began to lap the quarters of the
Guerriere, her forward guns opened, and in a few minutes after, the
welcome orders were received to pour in broadside after broadside as
rapidly as possible. When she was fairly abeam, the broadsides were
fired with a rapidity and power that astounded the enemy. As the old
ship forged slowly ahead with her greater way, she seemed moving in
flame. The mizen mast of the enemy soon fell with a crash, while her
hull was riddled with shot, and her decks slippery with gore. The
carnage was so awful that the blood from the wounded and mangled
victims, as they were hurried into the cockpit, poured over the ladder
as if it had been dashed from a bucket. As Hull passed his antagonist
he wheeled short round her bows to prevent a raking fire. But in doing
this he came dead into the wind--his sails were taken aback--the
vessel stopped--then getting sternway, the Guerriere came up, her bows
striking the former abeam. While in this position, the forward guns of
the enemy exploded almost against the sides of the Constitution,
setting the cabin on fire. This would have proved a serious event but
for the presence of mind of the fourth lieutenant, Beekman Verplanck
Hoffman, who extinguished it. As soon as the vessels got foul both
crews prepared to board. The first lieutenant, Morris,[29] in the
midst of a terrific fire of musketry, attempted to lash the ships
together, which were thumping and grinding against each other with the
heavy sea, but fell, shot through the body. M. Alwyn, the master, and
Lieut. Bush of the marines, mounting the taffrail to leap on the
enemy's decks were both shot down, the latter killed instantly with a
bullet through the head. Finding it impossible to board under such a
tremendous fire, the sails of the Constitution were filled, when the
vessels slowly and reluctantly parted. As the Constitution rolled away
on the heavy swell, the foremast of the Guerriere fell back against
the mainmast, carrying that down in its descent, leaving the frigate a
helpless wreck, "wallowing in the trough of the sea." Hull seeing that
his enemy was now completely in his power, ran off a little way to
secure his own masts and repair his rigging which was badly cut up.
In a short time he returned, and taking up a position where he could
rake the wreck of the Guerriere at every discharge, prepared to finish
her. Capt. Dacres had fought his ship well, and when every spar in her
was down, gallantly nailed the jack to the stump of the mizen-mast.
But further resistance was impossible, and to have gone down with his
flag flying, as one of the English journals declared he ought to have
done, would have been a foolish and criminal act. A few more
broadsides would have carried the brave crew to the bottom, and to
allow his vessel to roll idly in the trough of the sea, a mere target
for the guns of the American, would neither have added to his fame nor
lessened the moral effect of the defeat. He therefore reluctantly
struck her flag, and Lieutenant Read was sent on board to take
possession.
[Footnote 29: Afterwards Commodore Morris.]
As he stepped over the vessel's side, a disgusting scene presented
itself. When the vessel struck, Captain Dacres told the crew they
might go and get some refreshments, which was another mode of giving
them liberty to drink. In a short time, all the petty officers and
their wives, together with the sailors, were wallowing together in
filth. The vessel being dismasted lay in the trough of the sea, and as
she rolled backwards and forwards the water came in the ports on one
side, and poured out of those on the other, mingling in a loathsome
mass the motley multitude.
This vessel, as well as all the English ships, presented another
striking contrast to the American. Impressment was so abhorred, that
British officers were afraid of being shot down by their topmen during
an engagement; and hence dared not wear their uniforms, while ours
went into action with their epaulettes on, knowing that it added to
their security, for every sailor would fight for his commander as he
would for a comrade.
Captain Hull kept hovering around his prize during the night; and at
two o'clock, "sail ho," was sent aft by the watch, when the
Constitution immediately beat to quarters. The weary sailors tumbled
up cheerfully at the summons, the vessel was cleared for action, and
there is no doubt that if another Guerriere had closed with the
Constitution, she would have been roughly handled, crippled as the
latter was from her recent conflict.
After deliberating for an hour, the stranger stood off. In the
morning, the Guerriere was reported to have four feet water in the
hold, and was so cut up that it would be difficult to keep her afloat.
The prisoners were, therefore, all removed, and the vessel set on
fire. The flames leaped up the broken masts, ran along the bulwarks,
and wrapped the noble wreck in a sheet of fire. As the guns became
heated, they went off one after another, firing their last salute to
the dying ship. At length, the fire reached the magazine, when she
blew up with a tremendous explosion. A huge column of smoke arose and
stood for a long time, as if petrified in the calm atmosphere, and
then slowly crumbled to pieces, revealing only a few shattered planks
to tell where that proud vessel had sunk. The first English frigate
that ever struck its flag to an American ship of war, had gone down to
the bottom of the ocean, a gloomy omen of England's future. The sea
never rolled over a vessel whose fate so startled the world. It
disappeared for ever, but it left its outline on the deep, never to be
effaced till England and America are no more.
The loss of the Constitution was seven killed and seven wounded, while
that of Guerriere was fifteen killed and sixty-four wounded, a
disparity that shows with how much more precision the American had
fired. It is impossible, at this period, to give an adequate idea of
the excitement this victory produced. In the first place, it was
fought three days after the surrender of General Hull, the uncle of
the gallant captain. The mortifying, stunning news of the disaster of
the North-western army met on the sea-board, the thundering shout that
went up from a people delirious with delight over this naval victory.
From one direction the name of Hull came loaded with execrations--from
the other overwhelmed with blessings. But not only was the joy
greater, arriving as the news did on the top of a disaster, but it
took the nation by surprise. An American frigate had fearlessly stood
up in single combat on the deep with her proud foe, and giving gun for
gun, torn the crown from the "mistress of the sea." The fact that the
Constitution had four guns more and a larger crew, could not prevent
it from being practically an even-handed fight. The disparity of the
crews was of no consequence, for it was an affair of broadsides, while
the vast difference in the execution done, proved that had the
relative weight of metal and the muster roll been reversed, the issue
would have been the same.
Captain Hull on his return to Boston, surrendered the frigate to
Bainbridge, who soon after hoisted his broad pennant on board, but did
not put to sea till the 26th of October.
[Sidenote: Oct. 12.]
In the mean time, Commodore Rodgers having refitted again, started on
a cruise, having the United States, forty-four, commanded by Commodore
Decatur, and the Argus, sixteen, Captain Sinclair, in company.
Commodore Rodgers having captured on the 17th, the British packet
Swallow, with two hundred thousand dollars on board, continued his
cruise to the eastward. Just before, in a heavy gale, the United
States and Argus had parted company with him. The former directed her
course so as to fall in the track of East Indiamen, but on Sunday
morning, the 25th, she saw a large sail to the southward, which proved
to be the English frigate Macedonian. After some manoeuvering, the two
vessels approached within a mile of each other, when the firing
commenced. After the United States delivered her second broadside, she
ceased manoeuvering and took the same tack with her enemy, both
steering free. The Macedonian, however, was to windward, and hence
could make it a yard-arm-to-yard-arm combat whenever she chose. But
she preferred a longer range, and the two vessels swept on, delivering
their rapid broadsides within musket shot. The distance at which they
kept, together with the heavy sea that was rolling, rendered the aim
imperfect and protracted the conflict, so that it continued for an
hour after the guns of both vessels began to bear, before any material
effect was visible. The broadsides of the United States were delivered
so rapidly that she was constantly enveloped in flame and smoke, and
the crew of the Macedonian several times thought her on fire and
cheered. Decatur, with his fine face lit up with that chivalric valor
that was wont to illumine it in battle, moved amid his men with words
of encouragement and praise. As the mizen-mast of the enemy went by
the board, hearing a sailor say to his comrade, "Jack, we've made a
brig of her;" he replied, "Take good aim, Jack, and she will soon be
a sloop." Turning to a captain of the gun, he said, "Aim at the yellow
streak, her spars and rigging are going fast enough, she must have a
little more hulling." Soon after her fore and main top mast went over.
At length, the mizen mast was cut in two by a shot, about ten feet
from the deck, while with every roll of the ship the weakened foremast
threatened to swell the wreck. The Englishman, perceiving that his
vessel would soon become unmanageable, made an effort to close, for
the purpose of boarding. But Decatur saw his advantage too plainly, to
risk it in a desperate encounter, and putting on sail shot ahead. The
enemy mistaking this movement for a rapid flight gave three cheers,
and all the flags having come down with the spars, set a union Jack in
the main rigging in token of triumph. But when the United States was
seen to tack and approach, as if about to close, it was hauled down.
On this same Sabbath, while the cheers of the United States' crew rang
over the deep, Napoleon was traversing in gloom the fatal, bloody
field of Malo-Jaraslowitz, and with two kings and three marshals by
his side, was deliberating on that retreat which was to change the
face of the world.
The superiority of American gunnery, in this combat, was placed beyond
dispute. It was a simple cannonade on a very rough sea. Yet the United
States had but five killed and seven wounded, while out of three
hundred men, the Macedonian had one hundred and four killed or
wounded. So, also, the former lost her top-gallant masts, and had been
hulled but a few times. It is true her rigging suffered severely, but
the English frigate had almost every spar in her more or less
shattered, while her hull was pierced with a hundred shot. In this, as
in the former engagement between the Constitution and Guerriere, the
United States carried _four more guns_ than her antagonist. She was a
heavier ship, but therefore a better mark, and yet the enemy's shot
rarely hulled her. The decks of the latter presented a revolting
spectacle. "Fragments of the dead were distributed in every
direction--the decks covered with blood--one continued agonizing yell
of the unhappy wounded,"[30] filled the ship.
[Footnote 30: Statement of an American officer.]
Decatur having arrived with his prize in New London, dispatched Lieut.
Hamilton, son of the Secretary of the Navy, to Washington, with an
account of the victory, and the captured colors. [Sidenote: Dec. 8.]
Hurrying on, greeted with the acclamations of the multitude as he
passed, he arrived at the capital in the evening. On that very night a
ball had been given to the officers of the navy, at which Hull and
Stewart and the Secretary of the Navy were present. Young Hamilton
walked into the gay assemblage and delivered his message to his
overjoyed father, who immediately announced it to the company. Shout
after shout shook the hall--all crowded around the young lieutenant,
eager to hear the incidents of the action. As he narrated how they
fought and how they conquered, tears of joy and gratitude streamed
from the eyes of his mother, who stood fondly gazing on him. Captured
colors of the enemy decorated the room, and a delegation was sent to
bring those of the Macedonia and add them to the number. Captains
Stewart and Hull bore them in, and presented them, amid the loud
acclamations of the throng, to the wife of the President--the band
struck up an inspiring air, and intense excitement and exultation
filled every bosom.
The Argus met with but little success. The seamanship of her officers
was, however, tested during the cruise. She was chased three days and
nights by an English squadron, and yet not only managed to escape, but
having come upon an English merchantman during the chase, actually
captured it in sight of the fleet, though by the time she had manned
it the enemy had opened on her with his guns. Having made five prizes
in all, she returned to port.
In the meanwhile the Wasp, Captain Jones, which was returning from
Europe with dispatches, the time war was declared, had refitted and
started on a cruise. Sailing northward to the latitude of Boston, she
made a single capture and returned to the Delaware. On the 13th of
October, the very day of Van Rensalaer's defeat at Queenstown, she
again put to sea, and after being four days out, on the night of the
17th, made five strange sail. Not knowing their strength or character,
Captain Jones deemed it prudent to keep off till daylight, when he
would have a better opportunity for observing them. In the morning he
discovered there were six ships under the convoy of a brig of war. Two
of them were armed, but the brig deeming herself alone a match for the
American, sent them all forward, and waited for the latter to
approach. The sea was rough from the effects of a storm that had swept
those latitudes the day before, in which Captain Jones had lost his
jib boom and two of his crew. There was no manoeuvering attempted in
this tumultuous sea, and the Wasp surged on in dead silence, the only
sound heard on her decks being the roar of the waves as they burst
along her sides. She closed on her antagonist with a deadliness of
purpose seldom witnessed in naval combats. She never delivered her
broadside till within a hundred and eighty feet, and then with fearful
effect. At first this heroism seemed doomed to a poor reward. The fire
of the Frolic was incessant. Seldom had an Englishman been known to
deliver such rapid broadsides. In five minutes the main topmast of
the Wasp fell amid the rigging--in two minutes more the gaft and mizen
top-gallant mast followed. Thus, in eight minutes from the time the
vessels closed, the Wasp was so disabled that her destruction seemed
almost certain. But while cut up herself so terribly aloft, she had
struck with every broadside the heart of her antagonist. As she rolled
on the heavy seas her guns were frequently under water, and the
sailors staggered around their pieces like drunken men. Delivering her
broadsides as she sunk, she hulled her antagonist at every discharge;
while the latter, firing as she rose, made sad work with the rigging
of the former. Jones seeing his spars and rigging so dreadfully cut
up, was afraid that his vessel would become unmanageable, and
therefore determined to run foul of his adversary and board. But when
the vessels closed, the bows of the Frolic struck abaft the midships
of the Wasp, which so swung the head of the latter around that she was
enabled to throw a raking fire into the former. The order, therefore,
to board was countermanded, and a fresh broadside directed to sweep
her decks. In loading some of the guns, the rammers struck against the
bows of the Frolic. The shot went crashing the whole length of the
ship, and the crew, excited by this hand-to-hand fight, could no
longer be restrained from boarding. Mr. Biddle, the first lieutenant,
leaped into the rigging, followed by Lieut. Rodgers and other men,
and soon gained the decks of the Frolic--but, in looking round for the
enemy, they saw but three or four officers standing aft, and bleeding.
None but the dead and wounded cumbered the decks. Not one was left to
haul down the colors. The officers threw down their swords in token of
submission, and Lieutenant Biddle, springing into the rigging, lowered
the English flag with his own hand. The carnage was horrible for so
small a vessel--nearly a hundred of the officers and crew being killed
or wounded. The decks were literally covered with the mangled forms of
men and officers. The corpses presented a ghastly appearance as they
rolled from side to side with the tossing vessel, while shivered spars
and masts covered the wreck, and still hanging by the ropes, swung
with every lurch against its shattered hull. There can scarcely be a
more mournful sight than a noble ship dismantled in mid ocean, her
decks crimsoned with blood, while on every side, amid broken and rent
timbers, her gallant crew dismembered and torn, are stretched in
death.
The Frolic was a brig carrying in all twenty-two guns, while the Wasp,
though a ship, carried but eighteen, thus making a difference in favor
of the former of four guns.
The Wasp had, therefore, captured a superior force in single combat.
But in this, as in the two former engagements I have detailed, the
same extraordinary disparity in the respective losses of the two
vessels was exhibited. While near a hundred were killed or wounded in
the Frolic, there were only five killed and as many wounded in the
American ship. It is not a matter of surprise that the belief became
prevalent in England that our vessels were filled with Kentucky
riflemen. These men had become famous for their accuracy of aim; and
it was supposed we had introduced them into our navy. In no other way
could they account for the awful carnage that followed every single
combat of ship with ship. In all her naval history, such destructive
work had never been witnessed in so short a space of time. The moment
an American vessel opened her broadsides, death began to traverse the
decks of her antagonist with such a rapid footstep, that men were
appalled.
This was doubtless owing in a great measure to our guns being sighted,
an improvement introduced by American officers, rendering the aim
infinitely more accurate.
The Wasp in this engagement had been fought nobly, but her victory
proved worse than a barren one to her gallant commander and crew.
Scarcely had the English Jack been lowered to the Stars and Stripes,
before the latter were struck to the English flag. The Poictiers an
English seventy-four, soon hoved in sight and bore down on the two
vessels lying to and clearing away the wreck. The Wasp endeavored to
make use of her heels, but on turning out her sails, they were found
completely riddled. Flight was out of the question, and both vessels
surrendered. They were taken into Bermuda, where the Americans were
parolled and allowed to return home.
On the 26th of October, Commodore Bainbridge left Boston, accompanied
by the Hornet, with the intention of joining Captain Porter, in the
Essex, and passing into the Pacific Ocean, where the British fisheries
and commerce could be easily struck. Captain Lawrence, cruising
southward, at length arrived at St. Salvador, where he found a British
sloop of war, the Bonne Citoyenne. The latter being in a neutral port,
was safe. She was superior to the Hornet, but Lawrence, determined to
provoke her out to single combat, sent a challenge to her
commander--Commodore Bainbridge, in the meanwhile, promising to keep
out of the way. The challenge was declined, and if the fact that she
had a large amount of specie on board, had been given as the reason of
her refusal, the conduct of Captain Green, the commander would have
been unobjectionable. But to intimate, as he did, that the frigate
would interfere, after Bainbridge had pledged his word, and the
American Consul offered guarantees, evinced a contemptible spirit,
almost as degrading as cowardice.
Captain Lawrence determined, however, not to let the vessel go to sea
without him, and he therefore blockaded the port.
The Constitution left the Hornet blockading the Bonne Citoyenne, and
steered south, keeping along the coast, and on the 29th discovered two
sail between her and the land, which was about thirty miles distant
and in full view. One of the vessels being small, kept standing in
towards the shore, while the larger one, a British frigate, the Java,
of thirty-eight guns, directed her course towards the American.
Bainbridge, wishing to get farther from the land, tacked and steered
to the south-east for two hours, the Englishman following after. About
half-past one, finding himself clear of the land, Bainbridge tacked
and stood towards the stranger. At 2 o'clock the two vessels were only
half a mile apart, the Englishman to windward, and showing no colors.
The order to fire a shot to make the latter set his ensign being
misunderstood, a whole broadside was delivered, and the battle
commenced. A tremendous cannonade followed. The wind was light and the
sea smooth, so that full scope was given for manoeuvering and accurate
aim. Bainbridge, who at the commencement of the war, had urged the
President to send the national ships to sea, and was now in his first
fight, felt not only the promise he had given the Secretary of the
Navy weighing on him, but his responsibility as commander of the
Constitution, fresh with laurels from the capture of the Guerriere.
He managed his ship with consummate skill, and not only foiled every
attempt of the enemy to get a raking position, but soon obtained one
himself, and delivered a broadside that swept the decks of the Java.
The vessels had at length approached within pistol shot, and the
effect of the rapid broadsides of the Constitution delivered so
closely and on that smooth sea, could be heard in the rending timbers
of the enemy's ship. Bainbridge, in the mean time, received a musket
ball in his thigh. He however still walked the quarter deck, watching
every movement of his antagonist, and the effect of every broadside.
In a few minutes later, a cannon shot plunged into the wheel,
shattering it in fragments, and sending a copper bolt into his leg.
Crippled and bleeding--refusing even to sit down--he continued to limp
over the quarter deck, watching the progress of the combat, and
directing the movements, apparently unconscious of pain. The
destruction of the wheel he felt to be a more serious affair than his
wounded leg, for he was no longer able to give verbal orders to the
helmsman. The tiller was of course worked below the second deck by
ropes and tackles, where the helmsman unable to see the sails and
steer accordingly, depended entirely on orders transmitted to him.
This would have been of minor consequence in a steady yard to yard-arm
fight, but in the constant manoeuvering of the two vessels, either to
get or prevent a raking fire, it was a serious inconvenience. Still,
the Constitution managed to secure this advantage in almost every
evolution. The tremendous fire she kept up, so staggered the
Englishman, that he resolved to run his vessel aboard at all hazards.
He came stern on, and his bowsprit passed through the mizen rigging of
the Constitution. The next moment, however, it was cut in two by a
cannon shot, when the two vessels parted. At length the Constitution,
after wearing twice to get the right position, threw herself fairly
alongside her antagonist, and they moved on together, yard-arm and
yard-arm, pouring in incessant broadsides. In a few minutes the mizen
mast of the Java went over, and as her foremast had gone long before,
nothing but the main mast was left standing. Her fire had now ceased,
and Bainbridge, under the impression she had struck, set his sails and
passed off to windward to repair damages, make his masts secure, and
be ready for any new combat that might be forced on him, in a sea
filled with the enemy's cruisers. After an hour spent in overhauling
his ship he returned, and finding the enemy's ensign still flying, he
passed directly across her bows, and was about to deliver a raking
fire, when she struck. The combat lasted for more than two hours, and
from the number of evolutions on both sides, was brought to a
termination several miles from where it commenced. The Java was
completely dismantled. Her mizen mast had been cut away close to the
deck--the mainmast fell soon after the firing ceased, while nothing
but a stump of the foremast, some twenty or thirty feet long, was left
standing. Her bowsprit, too, was gone; in fact, every spar had been
shot out of her. The Constitution, on the contrary, at the close of
the long severe conflict, had every spar standing. An eighteen pound
shot had made an ugly hole through her mizen mast, and another had cut
a deep gash in the foremast, and a quantity of ropes swinging loose in
the wind, showed that she had been in the midst of cannon balls, but
she came out of the conflict as she went in, every spar erect and her
royal yards across. The outward appearance of the ships did not
present a more striking contrast than their decks. Those of the Java
were rent and torn, and strewed with the dead. A hundred and sixty-one
had been killed or wounded, while nine killed and twenty-five wounded
covered the entire loss of the Constitution.
Among the prisoners taken was Lieutenant-General Hislop, with his
staff, on his way to Bombay, as Governor. They were all treated with
that kindness and generosity which ever characterizes a truly brave
man--conduct which the English, in the very very few opportunities
offered them, did not generally reciprocate.
The severe wounds of Commodore Bainbridge could not force him to leave
the deck, even after the action was over. In his anxiety for his ship
and the prize, and care of the wounded and prisoners, he forgot his
sufferings, keeping his feet till eleven o'clock at night. These eight
hours of constant exertion increased the inflammation to an alarming
degree, and well nigh cost him his life.
It was a proud day for him; he had redeemed his pledge to the
government, and added another wreath to the laurels that already
crowned the American navy.
The Constitution lay by the Java for two or three days, in order that
the wounded might be removed with care and safety. When this was
accomplished, the latter vessel being so completely riddled that it
would be impossible to get her into an American port, was blown up.
Our gunners fired with too accurate an aim; they so destroyed the
vessels of the enemy, that they could not be secured as prizes.
The Constitution was carried into St. Salvador, where her arrival did
not improve the prospect before the Bonne Citoyenne, should she
venture to break a lance with the Hornet. She was apparently preparing
to go to sea that night, with the intention of avoiding her
antagonist if convenient, and fighting her if necessary. The capture
of the Java, however, produced a change in her plans, and she took
eighteen days longer to reflect on the subject.
Commodore Bainbridge dismissed the private passengers found on board
the Java, without regarding them as prisoners of war, while all the
others were released on their parol. Governor Hislop presented him
with an elegant sword, as a token of his esteem and an acknowledgment
of the kindness with which he had been treated. Captain Lambert,
commander of the Java, was mortally wounded, and just before his
removal to the shore, Bainbridge, leaning on the shoulders of two
officers, hobbled into his room to restore to him his sword. It was a
touching spectacle, the wounded victor presenting to his dying
antagonist, the sword he never would wield again, accompanying it with
expressions of esteem and kindly hopes. Captain Lambert received it
with emotion, and returned his thanks. Two days after, it was laid
across his breast. It was not dishonored in its owner's hand, for his
ship had been gallantly fought to the last, and surrendered only when
not a sail could be set.
Bainbridge, at this time, was not quite forty years of age. Six feet
in height, of commanding person, and an eye that burned like fire in
battle, he moved over his quarter deck the impersonation of a hero.
His noble conduct to the prisoners, won him the praise even of his
enemies. An English Admiral, when told of it, shook his head,
remarking, that it had an ominous look when a young commander, in a
navy unaccustomed to victory, could treat his foes so like an old
Spanish cavalier.[31]
[Footnote 31: There is a curious incident connected with this battle.
A few nights before it occurred, Bainbridge dreamed, that he had a
long encounter with a British vessel, and finally captured her. On
board were several officers, and among them a general. It made such an
impression on him, that he entered the facts in his journal, and spoke
of them to his officers. After the engagement, as he was standing on
deck surrounded by his officers, waiting to receive the commander of
the Java, he saw the boats carrying General Hislop approach. Turning
to lieutenant Parker, he said, "that is the man I saw in my dream."]
The Constitution, in this engagement, carried fifty-four guns, and the
Java forty-nine. On this difference of five guns, the English
attempted to erect a prop to support their naval pride. The effort to
prove a superiority in weight of metal and number of men, in every
victorious American vessel, and the changes rung on the difference of
a single gun, exhibited a sensitiveness that enhanced instead of
lessened the defeats. If a battle is never to be considered equal,
until both ships have the same tonnage to a pound, the same number of
cannon, and the muster roll be equal to a man, it is to be feared
there never will be one fought. Not only did the English allege that
the Constitution was greatly superior in weight of metal, but
declared that her success was owing, in a large measure, to her
musketry; and yet the Java had not a spar standing at the close of the
battle. Muskets do not dismantle vessels, and leave them mere hulks at
the mercy of their foe.[32] The English court of enquiry appointed to
investigate the subject, asked the boatswain, "if they had suffered
much on the forecastle from musketry." "Yes," he very frankly replied,
"_and, likewise, from round and grape_." The latter was, no doubt,
true, and very probably the former.
[Footnote 32: Some time after the peace of 1815, a distinguished
officer of the English navy, visited the Constitution, then just
fitted anew at Boston, for a Mediterranean cruise. He went through the
ship, accompanied by Captain ---- of our service. "Well, what do you
think of her?" asked the latter, after the two had gone through the
vessel, and reached the quarter deck again. "She is one of the finest
frigates, if not the finest frigate I ever put my foot on board of,"
returned the Englishman; "but, as I must find some fault, I'll just
say, that your wheel is one of the clumsiest things I ever saw, and is
unworthy of the vessel." Captain ---- laughed, and then explained the
appearance of the wheel, saying, "When the Constitution took the Java,
the former's wheel was shot out of her. The Java's wheel was fitted on
the Constitution to steer with, and although we think it ugly, as you
do, we keep it as a trophy."]
Bainbridge returned to Boston, and resigned the command of the
Constitution, which stood greatly in need of repairs.
Lawrence continued, as before stated, to blockade the Bonne Citoyenne,
until the latter part of January, when a British seventy-four heaving
in sight, he was compelled to run in beside his adversary. The tables
were now turned upon him, and he had the prospect of seeing the
man-of-war playing the part of keeper at the mouth of the port, while
his own prisoner making use of this protection could pass out, and
continue his voyage. This was a predicament he did not relish, and
taking advantage of the night, quietly slipped out to sea, and
continued his cruise. He made a few prizes, and among them a brig of
ten guns, with $12,500 in specie on board. Arriving, at length, at the
mouth of the Demarara river, he discovered an English brig of war, and
gave chase to her. The latter running in shore, led him into such
shoal water, that he deemed it prudent to haul off. He, however, did
not abandon the hope of forcing the ship into an engagement, and while
beating down on a different tack to get within reach of her, he
discovered another brig apparently seeking to close. He immediately
put the head of his vessel toward that of the stranger. Both were
close on the wind, and as they continued to approach, it was evident
from their course they must pass each other with their yard-arms
almost touching. It was now nearly half-past five, and the lurid rays
of the sun, just sinking behind the hills of the main land, flooded
the two vessels as they silently closed. The moment they began to draw
abeam, so that the guns bore, the firing began. When fairly abreast,
the vessels were not more than fifty feet apart. The words of command
and the shrieks of the wounded could be distinctly heard in either
vessel, as broadside crashed against broadside. It was a stern meeting
and parting. As soon as the guns ceased to bear, the Englishman wore,
in order to get a raking fire on the Hornet. The latter, however, was
too quick for him; he was first about, and coming down on his quarter
in "a perfect blaze of fire," poured in his broadsides with such close
range and destructive effect, that in ten minutes more the enemy not
only struck, but hoisted a signal of distress. Mr. Shubrick being sent
on board to take possession, reported that the vessel was the sloop of
war, Peacock, and that she had six feet water in the hold. Every
effort was made to save the prize, and to get out the wounded. Both
vessels were anchored; the pumps were rigged on board the Peacock, and
bailing was resorted to. The vessel, however, continued to sink, and
at last went down, carrying nine of her own crew and three of the
Hornet with her. Two American officers, and many more seamen came near
losing their lives, in their gallant effort to save the prisoners.
The foremast of the ill-fated vessel protruded from the sea, where she
went down, remaining for some time to mark the place of the battle and
the victory.
The superiority of American gunnery and American seamanship was again
established beyond dispute. The Hornet was slightly superior in weight
of metal,[33] but she not only out-maneuvered her antagonist, but
surpassed her incomparably in the effective use of her guns. The
former had but one man killed and two wounded, while of the latter
there were thirty-eight killed and wounded, and among them the
commander. The Hornet had but a single shot in her hull, while the
Peacock was so riddled that she sunk in a few minutes after the
action.
[Footnote 33:
Peacock. Hornet.
Broadside guns, 9 10
Crew, 130 135]
The thrill of exultation that passed over the land at the announcement
of the first naval victory, was alloyed by the reflection that it was
but an isolated instance, and hence could hardly justify a belief in
our naval superiority. But as frigate after frigate and ship after
ship struck, all doubt vanished, and the nation was intoxicated with
delight. The successive disasters that befel our land forces along the
Canada line, could not check the outburst of enthusiasm on every side.
As the news of one victory succeeding another was borne along the
great channels of communication, long shouts of triumph rolled after
it, and the navy from being unknown and uncared for, rose at once to
be the bulwark and pride of the nation. All faces were turned to the
ocean to catch the first echo of those resistless broadsides, that
proudly asserted and made good the claim to "free trade and sailor's
rights." Where we had been insulted and wronged the most, there we
were chastising the offender with blows that astounded the world. If
the American Government had been amazed at the failure of its deep
laid schemes against Canada, it was no less so at the unexpected
triumphs at sea. Saved from the deepest condemnation by the navy,
which it had neglected--forced to fall back on its very blunders for
encouragement, it could say with Hamlet--
"Let us know,
Our indiscretion sometimes serves us well
When our deep plots do pall."
But our astonishment at these successive and brilliant victories could
scarcely exceed that of the old world. The British navy had been so
long accustomed to victory, that a single-handed contest of an English
frigate with that of any other nation, had ceased to be a matter of
solicitude to her. The maritime nations of Europe had, one after
another, yielded to her sway, till her flag in every sea on the globe
extorted the respect and fear which the declaration, "I am a Roman
citizen" did, in the proudest days of the Empire. Her invincibility on
the ocean was a foregone conclusion. The victories of Napoleon
stopped with the shore--even his "star" paled on the deep. His
extraordinary efforts and energies could not tear from the British
navy the proud title it had worn so long. His fleets, one after
another, had gone down before the might of British broadsides, and the
sublime sea fights of Aboukir and Trafalgar, were only corroborations
of what had long been established. If this was the common feeling of
the Continent it is no wonder that "the English were stunned as by the
shock of an earthquake."[34] The first victory surprised them, but did
not disturb their confidence. They began to discuss the causes of the
unlooked for event with becoming dignity, but before the argument was
concluded, another and another defeat came like successive thunder
claps, till discussion gave way to alarm. The thoughtful men of
England were too wise to pretend that disasters occurring in such
numbers and wonderful regularity, could be the result of accident, and
feared they beheld the little black cloud which the prophet saw rising
over the sea, portending an approaching storm. If, in so short a time,
a maritime force of only a few frigates and sloops of war could strike
such deadly blows and destroy the prestige of English invincibility,
what could not be done when that navy should approximate her own in
strength. Some of the leading journals indulged in foolish boasting
and detraction of American valor, and held up to derision those who
saw portents of evil in the recent defeats. But the Times spoke the
sentiments of those whose opinions were of any weight. Said the
latter: "We witnessed the gloom which the event (the capture of the
Guerriere) cast over high and honorable minds. We participated in the
vexation and regret, and it is the first time we ever heard that the
striking of the flag on the high seas to any thing like an equal
force, should be regarded by Englishmen with complacency or
satisfaction." *** "It is not merely that an English frigate has been
taken, after what we are free to confess, may be called a brave
resistance, but that it has been taken by a _new enemy_, an enemy
unaccustomed to such triumphs, and likely to be rendered insolent and
confident by them." Another declared: "Our maritime superiority is in
fact a part of the nation's right. It has been the right of the
conqueror, since men associated together in civilization, to give laws
to the conquered, and is Great Britain to be driven from the proud
eminence which the blood and treasures of her sons have attained for
her among nations, by a piece of striped bunting flying at the
masthead of a few _fir-built frigates_, manned by a handful of
bastards and outlaws?"
[Footnote 34: Vide Alison.]
Such were the different sentiments entertained and expressed in
England at the outset, but as the war progressed, anxiety and alarm
took the place of boasting.
The war vessels at length grew timorous, and lost all their desire to
meet an American ship of equal rank. It was declared that our frigates
were built like seventy-fours, and therefore English frigates were
justified in declining a battle when offered. The awful havoc made by
our fire affected the seamen also, and whenever they saw the stars and
stripes flaunting from the masthead of an approaching vessel, they
felt that no ordinary battle was before them. English crews had never
been so cut up since the existence of her navy. In the terrific battle
of the Nile, Nelson lost less than three out of one hundred, and in
his attack on Copenhagen, less than four out of every hundred. In
Admiral Duncan's famous action off Camperdown, the proportion was
about the same as that of the Nile. In 1793, the French navy was in
its glory, and the victories obtained over its single ships by English
vessels were considered unparalleled. Yet in fourteen single
engagements, considered the most remarkable, and in which the ships,
with one exception, ranged from thirty-six guns to fifty-two, the
average of killed and wounded was only seventeen per ship, while in
four encounters with American vessels, the Constitution, United States
and Wasp, the average was a hundred and eleven to each vessel.
[Sidenote: Jan. 2.]
This success of the navy at length roused Congress to do something in
its aid, and an act was passed on the 2d of January, authorizing the
President to build four seventy-fours, and six ships of forty-four
guns, thus increasing the force of the navy tenfold. On the 3d of
March, by another act, it authorized the building of such vessels on
the lakes as was deemed necessary to their protection. Sums were also
voted to the officers and crews as prize money.
CHAPTER VII.
Harrison plans a winter campaign -- Advance of the army --
Battle and massacre at the River Raisin -- Baseness of
Proctor -- Promoted by his Government -- Tecumseh, his
character and eloquence -- He stirs up the Creeks to war --
Massacre at Fort Mimms -- Investment of Fort Meigs --
Advance of Clay's reinforcements and their destruction --
Successful sortie -- Flight of the besiegers -- Major
Croghan's gallant defence of Fort Stephenson.
The army of General Harrison, which in October was slowly pushing its
way towards Malden to Detroit, soon became involved in difficulties
that compelled him to abandon his original design of an autumnal
campaign. The lakes being in possession of the enemy, provisions,
ammunition and cannon had to be transported by land, through swamps
and along forest paths which could be traced only by blazed trees, and
traversed only when the ground was frozen. He therefore occupied his
time in sending out detachments and hurrying up his forces, in order
to be ready to advance when the frozen ground, and especially the ice
along the margin of the lake would facilitate the transportation of
his guns and munitions of war.
General Tupper made two attempts, first from Fort Defiance and
afterwards from Fort McArthur, to dislodge the Indians at the Rapids,
but failed in both. Another detachment under Col. Campbell left
Franklintown in December, to attack the Indian villages on the
Missisineway, which were reached on the 18th, and four out of five
destroyed.
At length the column which formed the right of this army, nominally of
ten thousand men, having arrived at Sandusky with the park of
artillery, Gen. Harrison gave the order for the whole to move forward.
In three divisions, one from Sandusky, one from Fort McArthur, and the
third under General Winchester, from Fort Defiance, were to advance to
the Rapids of the Maumee, there take in their supply of ordnance and
provisions, and proceed at once to invest Malden. Harrison, commanding
the central division, started on the 31st of December. Gen.
Winchester, who had moved six miles from Fort Defiance, to Camp No. 3,
did not commence his march till the 8th of January. It was a cold
bitter day and the snow lay over two feet deep in the forest when that
doomed column, one thousand strong, set out for the Rapids,
twenty-seven miles distant. The troops, most of whom were Kentuckians,
were brave and hardy, and cheerfully harnessing themselves to sledges
dragged their baggage through the deep snow. Gen. Winchester was
ordered to fortify himself at the Rapids and wait the arrival of the
other troops. But three days after he reached the place, while
constructing huts to receive the supplies on the way, and sleds for
their transportation to Malden, he received an urgent request from the
inhabitants of Frenchtown, a small settlement nearly forty miles
distant, on the River Raisin, to come to their rescue. Feeling,
however, the importance of fulfilling his orders, he gave the
messengers no encouragement. But another express on the next day, and
a third the day after, telling him that the whole settlement was
threatened with massacre by the Indians--that only a small force of
the enemy held possession of the place, and by a prompt answer to
their prayer the ruin of all would be prevented, he called a council
of war. Col. Allen, and other gallant officers, pleaded the cause of
the helpless settlers with all the eloquence of true sympathy. They
declared that the chief object of the expedition was to protect the
frontiers from the merciless Indians, and that brave men spurned
danger when the prayers of women and children were sounding in their
ears. [Sidenote: Jan. 20.] Such appeals prevailed over the cooler and
safer arguments drawn from the necessity of not damaging the success
of the whole campaign by perilling one of the wings of the advancing
army, and a detachment of five hundred men, under Colonel Lewis was
sent forward to Presque Isle, there to await the arrival of the main
column. But this officer hearing at the latter place that an advance
party of French and Indians were already in possession of Frenchtown,
hurried forward, and the next day in the afternoon arrived on the
banks of the stream opposite the village. The river being frozen, he
immediately ordered the charge to be sounded. The column advanced
steadily across on the ice, and entering the village under a heavy
fire of the British, forced them from their position and soon drove
them to the woods, when darkness closed the combat. Two days after,
General Winchester arrived with a reinforcement of two hundred and
fifty men. He had sent a dispatch to Gen. Harrison, then on the Lower
Sandusky, announcing his departure from his orders, and asking for
reinforcements. [Sidenote: Jan. 23.] The latter sent forward a
detachment of three hundred, and followed himself the same day with a
corps of three hundred and sixty men. The assistance, however, came
too late, for on the day before they started, the fate of Gen.
Winchester's army was sealed. Gen. Proctor, at Malden, only eighteen
miles distant, hearing of Col. Lewis' advance on Frenchtown, hurried
down with about 1500 men and six pieces of artillery to attack him.
The latter had stationed the main force behind pickets, in the form of
a half circle, but the two hundred and fifty men who had arrived with
Gen. Winchester were, through some strange fatuity, placed outside,
four hundred yards distant, and wholly uncovered. Just as the drums
beat the morning reveille, Proctor advanced to the assault. The troops
came on steadily till within range of the Kentucky rifles, when they
were met by such a fierce and deadly fire that they wheeled and fled
in confusion.
But, while the attack in front was thus repulsed, that on the
unprotected left wing of two hundred and fifty men was, in a few
minutes, completely successful. Such a preposterous position, as that
to to which it was assigned, no sane man could dream of holding.
Outflanked, and almost surrounded by yelling Indians, its danger was
perceived when too late to remedy it. General Winchester and Colonel
Lewis, however, each with a detachment of fifty men, rushed forward to
the rescue, but they only swelled the disaster. Their followers were
cut down and tomahawked, and they themselves captured, and taken to
Proctor. The latter had paused after his attack on the pickets, for
nearly one-fourth of the regular troops had fallen in that one
assault, and he hesitated about exposing himself again to the deadly
fire of Kentucky rifles. It is very doubtful whether he would have
ventured on a second attack. He, however, represented to General
Winchester, that he could easily set the town on fire, and reduce the
garrison; but, in that case, he would not guarantee the lives of the
soldiers, or the inhabitants from the barbarity of the Indians.
General Winchester fully believing that the five hundred men, who
still gazed undauntedly on the foe, must be sacrificed, agreed to a
capitulation; and an officer was sent with a flag to Major Madison, on
whom the command had devolved, informing him of the unconditional
surrender of all the troops by his superior officer. The brave major,
who did not at all look upon himself and gallant band as vanquished
men, indignantly refused to obey so unworthy a summons, even from his
rightful commander, and coolly told the officer, "he should do no such
thing; nay, would not surrender at all, unless the side arms of the
officers would be restored to them at Amhertsburg, the wounded
promptly and securely transported to that post, and a guard sufficient
for their safety assigned them."[35] If the British commander refused
to grant these terms, he and his men would fight to the last, and, if
necessary, die with their arms in their hands. This proposition, to
which any officer fit to wear a sword would have cheerfully accepted,
Proctor at first rejected, and yielded at last only because no other
terms would be listened to. But no sooner did the garrison surrender,
than in direct violation of the conditions, he gave unbridled license
to the soldiers and Indians. The latter were allowed to scalp and
mutilate the dead and wounded, whose bleeding corpses crimsoned the
snow on every side. Proctor, fearing the approach of Harrison, made
all haste to depart, and the next night reached Amhertsburg with the
prisoners, who were there crowded into a "small and muddy wood yard,
and exposed throughout the night to a cold and constant rain, without
tents or blankets, and with only fire enough to keep them from
freezing." He had brutally left the dead at French town unburied, and
sixty of the wounded, who were too feeble to march, unprotected. By a
great stretch of kindness, he allowed two American surgeons to remain
and take care of them. He had promised to send sleds the next day, to
convey them to Malden. These never arrived; but, instead, there came a
party of his Indian allies, who tomahawked a portion of the wounded,
and then set fire to the houses, consuming the dead and dying
together, and responding to the shrieks of the suffering victims with
yells and savage laughter. Captain Hart, a relative of Henry Clay, was
among the number, as was also a member of Congress. Hart, and indeed a
large majority of them, belonged to the most respectable families of
Kentucky. One officer was scalped in presence of his friends, and with
the blood streaming down his pallid features, rose on his knees, and
silently and most piteously gazed on their faces. While in this
position, an Indian boy was told by his father to tomahawk him. The
unskilful stripling struck again and again, only producing faint
groans from the sufferer, till at length the father, in showing how a
blow should be planted, ended the tragedy. The secretary of General
Winchester was shot while on horseback, and scalped, and his body
stripped and cast into the road. The dead, to the number of two
hundred, were left unburied; and, for a long time after, hogs and dogs
were seen devouring the bodies, and running about crunching human
skulls and arms in their teeth. Most of these facts were sworn to
before a justice of the peace, and forwarded by Judge Woodward, of the
supreme court of Michigan, to Colonel Proctor, with the remark, "The
truth will undoubtedly eventually appear, and that unfortunate day
must meet the steady and impartial eye of history." General Harrison
was at the Rapids, hurrying on the reinforcements, when he heard of
the catastrophe. A few days after, he dispatched Dr. M'Kechen with a
flag of truce to the river Raisin, to pass thence, if possible, to
Malden. Seized by the Indians and stript, he was at length taken to
Captain Elliot, who kindly forwarded him to Colonel Proctor. The
latter denied his mission, declaring he was a spy, and would not
recognize him, in his official character, till the fifth of February.
Three weeks after, he was accused of carrying on a secret
correspondence with the Americans, and without the form of a trial
thrown into a filthy dungeon below the surface of the ground, where he
lay for a whole month, and was finally liberated, only to carry the
seeds of disease, implanted by this brutal treatment, to his grave.
[Footnote 35: Vide Armstrong's Notices of the War of 1812.]
When the news of this horrid massacre reached Kentucky, the State
was filled with mourning, for many of her noblest sons had fallen
victims to the savage. The Governor and his suite were in the
theatre at the time the disastrous tidings arrived in Frankfort. The
play was immediately stopped, the building deserted, and the next
morning a funereal sadness rested on the town, and the voice of
lamentation--like that which went up from Egypt when the first born
of every house was slain--arose from almost every dwelling. But amid
it all there was a smothered cry for vengeance, which never ceased
ringing over the State, until it was hushed in the shout of victory
that rose from the battle-field of the Thames.
Language has no epithets sufficiently opprobrious with which to stamp
this atrocious deed of Colonel Proctor. It combines all the inhuman
elements necessary to form a perfect monster--deceit, treachery,
falsehood, murder, and that refinement of cruelty which looks with
derision on slow torture, and the brutality which can insult the dead.
The very apologies which his countrymen made for him only blackened
his character. It was said that the prisoners surrendered at
discretion, and he never pledged his word for their protection--a
falsehood as afterwards fully proved by the prisoners, and a
statement, whether true or false, utterly useless, only to make the
whole transaction complete and perfect in every part. No man who was
sufficiently acquainted with honor to simulate it successfully, would
have attempted to cover an act so damning with such an excuse. The
annals of civilized warfare present no instance of the massacre and
torture of troops who have surrendered themselves prisoners of war on
a fair battle-field. An act like this, committed by a British officer
on the plains of Europe, sustained only by such an apology, would cost
him his head. Absolute inability, on the part of a commander to
protect his captives, is the only excuse a _man_ would ever offer.
This Proctor had not, for his allies were under his control and he
knew it. At all events he never attempted to save the prisoners. No
guard was left over the wounded, as he had stipulated to do--no
sleighs were sent back the next morning to fetch them to Fort Malden,
as promised--no effort whatever made in their behalf. He never
designed to keep his promises or fulfil his engagements--he had
abandoned the dead and wounded at Frenchtown to his savage allies, as
their part of the reward. Our troops frequently employed Indian
tribes, but no such atrocities were ever suffered to sully the
American flag. The whole transaction, from first to last, is black as
night. His deceit, treachery, cruelty to officers and men, neglect of
the dead and abandonment of the wounded to worse than death--his after
falsehood, meanness and cupidity are all natural and necessary parts
to the formation of a thoroughly base and brutal man. He was a
disgrace to his profession, a disgrace to the army and to the nation
which rewarded him for this act with promotion. His memory shall be
kept fresh while the western hemisphere endures, and the transaction
hold a prominent place in the list of dark deeds that stand recorded
against the English name. Just a month from this date three American
seamen went down in the Peacock, while nobly struggling to save the
prisoners. A few years before, some Turkish captives, in Egypt, being
paroled by Napoleon, were afterwards retaken in a desperate battle and
sentenced by a council of war to be shot. Although they had forfeited
their lives by the laws of all civilized nations, in thus breaking
their parole, and proved by their conduct that a second pardon would
simply be sending them as a reinforcement to the enemy, and though
Bonaparte only carried into execution the decision of a council of
war, yet for this act of his, English historians to this day heap
upon him the epithets of murderer and monster; while not the mere
murder, which would have been comparative kindness, but the
abandonment of American prisoners to slow torture by fire and the
scalping knife, was rewarded with promotion in the army.
The difficulties which our volunteers and new levies unaccustomed to
such hardships, had to contend with on the western frontier, may be
gathered from the march of the three hundred men dispatched to the aid
of Winchester, but who did not arrive till after the massacre.
Starting with twenty pieces of artillery, in a heavy snow storm, they
boldly pierced the wilderness, but made the first day only a short
march. The next day, a courier arrived toiling through snow and mud,
ordering the artillery to advance with all speed. But under the weight
of the heavy guns, the wheels sunk to their axles with every slow
revolution, and it was only by dint of great effort, they were got on
at all. After a weary day's march, they encamped around a blazing
fire, and were just making their scanty meal, when a messenger entered
the camp, stating, that Harrison had retreated from the Rapids. A
portion immediately resolved to push on to his help, and snatching a
few hours of repose, they, at two o'clock in the morning, tumbled up
from their couch of snow, and falling into marching order, hurried
forward through the gloom. To add to their discomfort and sufferings,
a January rain-storm had set in, making the whole surface one
yielding mass, into which they sunk sometimes to their waists.
Drenched to the skin with the pelting rain, stumbling and falling at
almost every step in the dissolving snow, they kept on, and at length
reached the black swamp, near Portage river. This was four miles
across, and was covered with a broad sheet of water as far as the eye
could reach. Out of the untroubled surface rose the trunks of sickly
looking and decayed trees, presenting amid the black and driving rain,
a spectacle sufficient to chill and benumb the most manly heart. Ice
was beneath, but of its strength, or of the depth below, no one could
tell. The soldiers, however, hurried forward into the water, and
though the rotten, treacherous ice under their feet would often give
way, letting them down, till their farther descent was arrested by
their arms; they kept intrepidly on, till, at length, the last mile
was won, and weary and staggering they emerged on the farther side.
Although on the whole route, there were but eight miles where they did
not sink below the knee, and often to the middle, this gallant band
accomplished thirty miles by night fall. Weary, dispirited and
benumbed, they then encamped, and without an axe, cooking utensils, or
a tent to cover them, sat down on logs, and having kindled a feeble
fire made their meagre repast. They then placed two logs together to
keep them from the melting snow, and lay in rows across them, exposed
to the pitiless storm. Next morning, they continued their march, and
effected a junction with the army.
To such hardships and exposures were the sons of gentlemen and farmers
subjected, in those disheartening northern campaigns which ended only
in failure.
While such scenes were transpiring in the north, there occurred one of
those events which form the romance and poetry of the American
wilderness. At this time, Michigan was an unbroken forest, with the
exception of Detroit, and a few settlements along the line of the
lakes, containing in all, but five or six thousand inhabitants. Ohio
had but 300,000, while 2,000 Indians still held their lands within its
limits. Thirteen thousand constituted the entire white population of
Illinois. These states, which now number by millions, were then almost
wholly unknown, except on the borders of the lakes and the Ohio river.
All through the interior, numerous tribes of Indians roamed
undisturbed, and hung, in black and threatening war clouds, around the
borders of civilization. The English had succeeded in exciting many of
these to hostilities against the settlers. Their efforts were aided in
a masterly manner by Tecumseh, a Shawnee warrior, who had imbibed a
bitter, undying hostility to the Americans. Brave, temperate,
scorning a lie, and despising the spoils of war, he fought to restore
his race to their ancient rights and power. Unable to cope with the
Americans alone, he gladly availed himself of our declaration of war
to form an alliance with the British. Lifted by native genius above
the vices of savages, he also exhibited a greatness of intellect, and
loftiness of character, which, in civilized life, would have led to
the highest renown. Despising the petty rivalries of tribes and
chiefs, he became absorbed in the grand idea of uniting all the Indian
clans in one great and desperate struggle for mastery with the whites.
He had succeeded in carrying out his scheme, to a great extent,
throughout the North and West. Of erect, athletic frame, noble,
commanding appearance, with the air of a king, and the eloquence of a
Demosthenes when rousing the Greeks to arms against Philip, he went
from tribe to tribe electrifying them with his appeals, and rousing
them to madness by his fiery denunciations against their oppressors.
His brother, the prophet, accompanied him,--a dark, subtle, cunning
impostor, to whose tricks Tecumseh submitted for awhile, because they
foiled the hatred and deceit of rival chiefs. As he arose before his
savage audiences, his imposing manner created a feeling of awe; but
when he kindled with his great subject, he seemed like one inspired.
His eye flashed fire, his swarthy bosom heaved and swelled with
imprisoned passion, his whole form dilated with excitement, and his
strong untutored soul poured itself forth in eloquence, wild,
headlong, and resistless, as the mountain torrent. Thoughts, imagery
leaped from his lips in such life and vividness that the stoicism of
the Indian vanished before them, and his statue-like face gleamed with
passion. The people he always carried with him; but the chiefs, who
feared his power over their followers, often thwarted his plans. When
not addressing the clans, he was reserved, cold, and haughty. His
withering sarcasm, when Proctor proposed to retreat from Malden; his
reply to the interpreter, who offering him a chair in the presence of
Harrison, said, "Your father wishes you to be seated;" "My father! the
sun is my father, and the earth my mother," as he stretched himself
proudly on the ground, reveal a nature conscious of its greatness, and
scorning the distinctions which the white man arrogated to himself.
After passing through the northern tribes, he took his brother, and
went south to the Creeks, to complete the plan of a general alliance.
The journey of nearly a thousand miles through the wilderness, of
these two brothers,--the discussion of their deep-laid scheme at night
around their camp-fire,--the day-dreams of Tecumseh, as gorgeous as
ever flitted before the imagination of a Caesar,--the savage empire
destined to rise under his hand, and the greatness he would restore
to his despised race, would make a grand epic. Pathless mountains and
gloomy swamps were traversed; deep rivers swam, and weariness and toil
endured, not for spoils or revenge, but to carry out a great idea.
There is a rude, Tuscan grandeur about him, as he thus moves through
the western wilderness impelled by a high purpose,--a barbaric
splendor thrown about even the merciless measures he means to adopt,
by the great moral scheme to which they are to be subject. His
combinations exhibited the consummate general. While England occupied
us along the sea-coast, he determined to sweep in one vast semi-circle
from Michilimackinac to Florida upon the scattered settlements. Fires
were to be kindled North and South, and West, to burn towards the
centre, while civilized warfare should desolate the eastern <DW72> of
the Alleghanies. Tecumseh had seen Hull surrender, and knew that the
British had been victorious all along the frontier. His prospects were
brightening, and with this glorious news to back his burning
eloquence, he had no doubt of exciting the Southern tribes to war. The
Chickasaws and Choctaws in Mississippi, numbered over thirty thousand;
the Creeks twenty-five thousand, while south of them dwelt the large
and warlike tribe of the Seminoles. His chief mission was to the
Creeks, from whom, on his mother's side, he was descended. This
powerful clan stretched from the southern borders of Tennessee nearly
to Florida. The sun in his course looked on no fairer, richer land
than the country they held. Some of them had learned the arts of
civilization, and, hitherto, had evinced a friendly disposition
towards the whites. But British influence working through the Spanish
authorities in Florida, had already prepared them for Tecumseh's
visit. An alliance, offensive and defensive, had been formed between
England and Spain; and the armies of the former were then in the
Peninsula, endeavoring to wrest the throne from Bonaparte. The latter,
therefore, was bound to assist her ally on this continent, and so lent
her aid in exciting the Southern Indians to hostility.
The year before, General Wilkinson had been dispatched to take
possession of a corner of Louisiana, still claimed by the Spanish. He
advanced on Mobile, and seized without opposition the old fort of
Conde, built in the time of Louis the XIV. He here found abundant
evidence of the machinations of the Spanish and English. Runners had
been sent to the Seminoles and Creeks offering arms and bribes, if
they would attack the frontier settlements. But for this, Tecumseh,
with all his eloquence, might have failed. Co-operating with the
British agents in Florida, as he had done with Brock and Proctor in
Canada, he at length saw his cherished scheme about to be fulfilled.
The old and more peaceful,--those who had settled in well-built towns,
with schools, and flocks, and farms about them,--opposed the war which
would devastate their land, and drive them back to barbarism. But the
eloquence of Tecumseh, as he spoke of the multiplied wrongs of the
Indians, and their humiliation, described the glories to be won, and
painted in glowing colors the victories he had gained in the North,
kindled into a blaze the warlike feelings of the young; and soon
ominous tidings came from the bosom of the wilderness that stretched
along the Coosa and Talapoosa rivers. Having kindled the flames, he
again turned his footsteps northward.
Anxiety and alarm soon spread among the white settlers, and the
scattered families sought shelter in the nearest forts. Twenty-four
had thus congregated at Fort Mimms, a mere block-house, situated on
the Alabama, near the junction of the Tombigbee. It was garrisoned by
a hundred and forty men, commanded by Major Beasely, and, with proper
care, could have resisted the attacks of the savages. But the rumors
of a rising among the Indians were discredited. A <DW64> who stated he
had seen them in the vicinity, was chastised for spreading a false
alarm. The night preceding the massacre, the dogs growled and barked,
showing that they scented Indians in the air. But all these warnings
were unheeded, when suddenly, in broad midday, the savages, some
seven hundred strong, made their appearance before the fort, and
within thirty feet of it, before they were discovered. The gate was
open, and with one terrific yell they dashed through into the outer
enclosure, driving the panic-stricken soldiers into the houses within.
Mounting these they set them on fire, and shot down every soul that
attempted to escape. Seeing, at once, their inevitable doom, the
soldiers fought with the energy of despair. Rushing madly on their
destroyers, they gave blow for blow, and laid sixty of them around the
burning buildings before they were completely overpowered. At last, a
yell of savage triumph rose over the crackling of flames, and cries
and shrieks of terrified women and children. Then followed a scene
which may not be described. The wholesale butchery,--the ghastly
spectacle of nearly three hundred mutilated bodies, hewed and hacked
into fragments, were nothing to the inhuman indignities perpetrated on
the women. Children were ripped from the maternal womb, and swung as
war-clubs against the heads of the mothers, and all those horrible
excesses committed, which seem the offspring of demons.
When Tecumseh reached again the British camp in Canada, he found the
American army at fort Meigs. Harrison, after Winchester's defeat,
instead of boldly pushing on in pursuit, had retreated. He was a brave
general, but lacked the energy and promptness necessary to an
efficient commander. Thus far these qualities seemed confined solely
to the English officers, leaving to ours the single one of caution.
Fort Meigs was erected on the Maumee, just above where it debouches
into Lake Erie. Here the army remained inactive, serving only as a
barrier to the Indians, who otherwise would have fallen on the Ohio
settlements, till the latter part of April. General Harrison employed
the winter in getting reinforcements from Ohio and Kentucky, and did
not reach the fort till the first of the month.
In the mean time, Proctor and Tecumseh had organized a large force for
its reduction. On the twenty-third, the sentinel on watch reported
that the boats of the enemy, in great numbers, were entering the mouth
of the river. The fort, at this time, contained about a thousand men,
and was well supplied with every thing necessary for a long and stout
defence, while twelve hundred Kentuckians, under General Clay, were
marching to its relief.
Finding the fortifications too strong to be carried by assault,
Proctor sat down before them in regular siege. The light troops and
Indians were thrown across the river, and heavy batteries erected on
the left bank. A well-directed cannonade from the fort so annoyed the
besiegers, that they were compelled to perform most of their work by
night. The garrison, at first, suffered very little, except from
scarcity of water. The well in the fort having dried up, they were
compelled to draw their supply from the river. But the men detailed
for this purpose, were constantly picked off by skulking Indians, who
becoming emboldened by success gradually drew closer around the
besieged; and climbing into tall trees, and concealing themselves in
the thick foliage, rained their balls into the works. On the first of
May, Proctor having completed his batteries, opened his fire. He sent,
also, a summons to surrender, which was scornfully rejected by
Harrison, who maintained a brisk cannonade for four days, when the
welcome intelligence was received, that Clay with his twelve hundred
Kentuckians was close at hand. Harrison determined, at once, to raise
the siege, and dispatched a messenger to him, to land eight hundred
men on the left bank of the river, and carry the batteries erected
there by storm, and spike the guns; while the remaining four hundred
should keep down the right bank towards the batteries, against which
he would make a sortie from the fort. The eight hundred were placed
under Colonel Dudley, who crossing the river in good order, advanced
fiercely on the batteries and swept them. Flushed with the easy
victory, and burning to revenge their comrades massacred at river
Raisin, the men refused to halt and spike the guns, but drove
furiously on after the flying troops, or turned aside to fight the
Indians, who clung to the forest. In the mean time, Proctor, aroused
by this unexpected onset, hastened up from his camp a mile and a half
below with reinforcements, and rallied the fugitives. At this critical
moment, Tecumseh also joined him, with a large body of Indians. These
advancing against the disordered Kentuckians, drove them back on the
river. The latter fought bravely, but discipline and numbers told too
heavily against them, and but one hundred and fifty of these gallant,
but imprudent men reached the farther bank in safety. Colonel Dudley
while struggling nobly to repair the error they had committed in
refusing to obey his orders, fell mortally wounded. The small, but
disciplined band of three hundred and fifty, led by Colonel Miller, of
the nineteenth infantry, against the batteries on the right bank,
carried them with the bayonet, and spiking the guns returned with
forty-two prisoners.
The two succeeding days, the armies remained inactive. In the mean
time, the Indians began to return home in large numbers; and Proctor
deserted by his savage allies, resolved to abandon the siege.
Embarking his heavy ordnance and stores under a galling fire from the
fort, he made a hasty and disorderly retreat down the river. The loss
of the Americans during the siege, was two hundred and seventy men
killed and wounded, exclusive of the destruction of a large portion of
Clay's command. That of the British was much less, so that although
the attack on the fort had failed, the Americans were by far the
heaviest sufferers.
Harrison leaving the fort in command of Colonel Clay, repaired to
Franklinton, the place appointed for the rendezvous of the regiments
newly raised in Ohio and Kentucky. In the mean time, a deputation of
all the friendly Indian tribes in Ohio waited on him, offering their
services in the approaching conflict on the borders. They were
accepted on the conditions, they should not massacre their prisoners,
or wage war against women and children.
After Harrison's departure, Proctor again appeared before Fort Meigs.
But finding it well garrisoned, he did not attempt another attack; but
taking five hundred regulars and a horde of Indians, seven hundred in
number, suddenly appeared before Fort Stephenson in Lower Sandusky.
[Sidenote: Aug. 1.] Major Croghan, a young man only twenty-one years
of age, held the post, with but a hundred and sixty men. He had only
one cannon, a six pounder, while the fortifications having been
hastily constructed, were not strong enough to resist artillery.
Knowing this, and the smallness of Croghan's force, Harrison had
previously ordered him to destroy the works, and retire on the
approach of the enemy. But this was impossible, for Proctor took
measures at once to cut off his retreat. When this was accomplished,
he sent a flag demanding the immediate surrender of the place, saying,
if the garrison resisted, they would be given up to massacre. This
mere stripling, not old enough to be frightened, like Hull and
Wilkinson, coolly replied, that when he got possession of the fort,
there would be none left to massacre. River Raisin was fresh in his
memory, and lay not far off; but neither the fear of Indian
barbarities, nor the dark array, ten times his number, closing
steadily upon him, could shake his gallant young heart. He was such
stuff as heroes are made of.
This was on Sunday evening, and immediately after receiving the bold
answer of Croghan, Proctor opened on the fort from his gun boats, and
a howitzer on shore. The cannonading was kept up all night, lighting
up the forest scenery with its fire, and knocking loudly on that
feeble fort for admission. At day break, Croghan saw that the enemy
had planted three sixes within two hundred and fifty yards of the
fort. Against this battery, he could reply with only his single gun,
whose lonely report seemed a burlesque on the whole affair. Finding
that Proctor concentrated his fire against the north-western angle, he
strengthened it with bags of flour and sand. The firing was kept up
till late in the afternoon, when seeing that but little impression
was made on the works, Proctor resolved to carry them by storm, and a
column, five hundred strong, was sent against them. With undaunted
heart, young Croghan saw it approach, while his little band, proud of
their heroic leader, closed firmly around him, swearing to stand by
him to the last. Some time previously, a ditch six feet deep and nine
feet wide had been dug in front of the works, and the six pounder,
loaded with slugs and grape, was now placed, so as to rake that part
of it where it was conjectured the enemy would cross. Colonel Short
commanded the storming column, which he led swiftly forward to the
assault. As it came within range, a well directed volley of musketry
staggered it for a moment, but Colonel Short rallying them, leaped
first into the ditch, crying out, "Give the d--d Yankees no quarter."
In a moment, the ditch was red with scarlet uniforms. At that instant,
the six pounder was fired. A wild shriek followed, and when the smoke
cleared away, that section of the column which had entered the ditch
lay stretched on the bottom, with their leader among them. The
remainder started back aghast at such sudden and swift destruction,
but being rallied they again advanced, only to be swept away. All
efforts to rally them the third time, were fruitless; they fled first
to the woods, and then to their boats, and next morning before
daybreak disappeared altogether. This garrison of striplings had
behaved nobly, and notwithstanding the brutal order of the British
commander to give no quarter, exhibited that humanity without which
bravery is not a virtue. Moved with pity at the groans and prayers for
help from those who lay wounded in the ditch, they, not daring to
expose themselves outside in presence of the enemy, handed over the
pickets during the night, jugs, and pails of water to allay the fever
of thirst; and made a hole through which they pulled with kindly
tenderness many of the wounded, and carried them to the surgeon. These
men knew that, if the attack had proved successful, not one would have
been left to tell how they fought, or how they fell, yet this
consciousness did not deaden, for a moment, the emotions of pity. This
generosity and kindness have always characterized the American
soldier, from the commencement of our national existence. The
merciless warfare inflicted by England through the savages during the
revolution, could not make him forget his humanity; nor the haughty,
insulting conduct of English officers in this second war, force him to
throw aside his kind and generous feelings.
This attack closed, for the time, the efforts of Proctor to get
possession of our forts, and he retired with his savage allies to
Detroit. Our whole western frontier was now in a most deplorable
condition. Instead of carrying the war into the enemy's country, we
had been unable to protect our own borders. Notwithstanding the
repulse at Fort Meigs, the savages still hung around our settlements,
making frequent and successful dashes upon them; while the powerful
tribe of the Osages lying west of the Mississippi, threatened to come
into Tecumseh's grand scheme, for the extermination of the whites.
Forts Madison and Mason were evacuated, leaving Fort Howard, only
forty miles above St. Louis, our most northern post on the
Mississippi.
CHAPTER VIII.
Chauncey ordered to Lake Erie to build a fleet -- A plan of
the campaign -- Woolsey -- Attack on York -- Death of
General Pike -- His character -- Capture of Fort George --
Gallantry of Scott -- Repulse of the British at Sackett's
Harbor by General Brown -- Dearborn pursues Vincent -- Night
attack on the American encampment -- Generals Winder and
Chandler taken prisoners -- Retreat of the army --
Reinforced by General Lewis -- Dearborn at Fort George --
Defeat of Colonel Boestler at Beaver Dams -- Attack on Black
Rock -- Dearborn withdrawn from the command of the northern
army.
While Harrison was pushing forward his winter campaign, Dearborn
remained quietly in winter quarters, but soon as he saw the river St.
Lawrence clear of ice, he prepared to renew his invasion of Canada.
Armstrong having resigned the post of minister to France, was
appointed Secretary of War in place of Eustis. Being an officer of
distinction, it was thought he would throw more energy into the war
department, than his predecessor. His plan of the campaign was simple,
and if prosecuted with energy, promised success. Dearborn was to
concentrate his forces at the mouth of the Niagara river, and fall
successively on Kingston, York, and Fort George, thus cutting off all
communication between Montreal and Upper Canada. To carry this out
successfully, naval superiority on the lake, for the safe
transmission of troops and ordnance, was indispensable. From the
commencement of the war, the only vessel of any pretension which the
United States had on lake Ontario was the Oneida, of sixteen guns,
commanded by Lieutenant, afterwards Commodore Woolsey. This gallant
officer managed to preserve his ship, notwithstanding the great
efforts of the enemy to get possession of it, beating off, in one
instance, while lying in Sackett's Harbor, six British armed vessels.
At this time, a vast forest fringed the southern shore of Ontario.
With the exception of here and there a clearing, Sackett's Harbor
containing some half a dozen miserable houses, and Oswego not much
larger, were the only settlements on the American side, while strong
forts and old towns lined the Canada shore. This large body of water,
the control of which was of such vast consequence to the protection of
New York state, could be reached from the Hudson, two hundred miles
distant, only by highways nearly impassable, except in midsummer and
winter. But, whatever difficulties might attend the attempt to build
and man vessels of war on those remote waters, it was evident that
until it was made, all movements against Canada must prove abortive.
Captain Isaac Chauncey was, therefore, ordered thither the summer
previous, to take command, and build and equip vessels. [Sidenote:
1812.] He arrived in Sackett's Harbor in October, with forty
carpenters, and a hundred officers and seamen. To control the lake in
the mean time, he purchased and armed several American schooners. With
these, he on the eighth of November set sail, and soon after chased
the Royal George under the guns of the fort at Kingston, and there
maintained a spirited contest for half an hour. After various
skirmishes with the enemy, he at length returned to Sackett's Harbor,
and spent the winter in building vessels. [Sidenote: Nov. 26.] In the
mean time, the Madison, of twenty-four guns, had been completed and
launched. Nine weeks before, her hull and spars were growing in the
forest. By spring, when Dearborn was ready to commence operations,
Chauncey had a snug little fleet under his command, composed of the
Madison, Oneida, and eleven armed schooners.
It having been ascertained that three British vessels were getting
ready for sea at York, it was resolved to destroy them. The original
plan, therefore, of commencing the campaign by an attack on Kingston,
was by the recommendation of Chauncey changed, and the former place
designated as the first point of attack.
This fleet of thirteen sail could carry but 1700 men. With these
Chauncey, at length, set sail, and on the twenty-fifth of April,
anchored off York. Although it blew a gale from the eastward, the
boats were hoisted out, and the landing of the troops under General
Pike was commenced. The wind carried the boats west of the place
designated, which was an open field, to a thickly wooded shore, filled
with Indians and sharp shooters. Major Forsythe with a corps of
rifles, in two batteaux, first approached the shore. Assailed by a
shower of balls, he commanded the rowers to rest on their oars and
return the fire. General Pike, who was standing on the deck of his
vessel, no sooner saw this pause, than he exclaimed to his staff with
an oath, "I can't stand here any longer; come, jump into the boat."
Ordering the infantry to follow at once, he leaped into a boat, and
with his staff was quickly rowed into the hottest of the fire. Moving
steadily forward amid the enemy's balls, he landed a little distance
from Forsythe. The advance boats containing the infantry reaching the
shore at the same time, he put himself at the head of the first
platoon he met, and ordered the whole to mount the bank and charge.
Breasting the volleys that met them, the Americans with loud cheers
scaled the bank, and routed the enemy. At that moment, the sound of
Forsythe's bugles was heard ringing through the forest. This completed
the panic, and the frightened savages, with a loud yell, fled in all
directions. The landing of the remaining troops, under cover of the
well directed fire of Chauncey's vessels, was successfully made.
Captains Scott and Young led the van, and with the fifteenth regiment,
under command of Major King, covered themselves with honor. The troops
were then formed in sections, and passing through the woods, advanced
towards the fort. The bridges having been destroyed over the streams
that intersected the road, only one field piece and a howitzer could
be carried forward to protect the head of the column, which at length
came under the fire of a battery of twenty-four pounders. Captain
Walworth, of the sixteenth, was ordered to advance with trailed
bayonets at the charge step, and storm this battery. Moving rapidly
across the intervening space, this gallant company approached to
within a short distance of the guns, when at the word, "recover
charge," the enemy deserted their pieces and fled. The column then
continued to move on up a gentle ascent, and soon silenced the
remaining battery, and took possession of the works. But just at this
moment, when a flag of surrender was momentarily expected, a magazine
containing five hundred barrels of powder, exploded with terrific
violence. Huge stones, fragments of shivered timber, and blackened
corpses were hurled heavenward together, and came back in a murderous
shower on the victorious column. Forty of the enemy, and more than two
hundred Americans were killed or wounded by the explosion. The army
was stunned for a moment, but the band striking up Yankee Doodle, the
rent column closed up with a shout, and in five minutes was ready to
charge. General Pike at the time of the explosion was sitting on the
stump of a tree, whither he had just removed a wounded British
soldier. Crushed by the falling fragments, he together with a British
sergeant, who had been taken prisoner, and Captain Nicholson, was
mortally wounded. Turning to his aid, he exclaimed, "I am mortally
wounded." As the surgeons and aid were bearing him from the field, he
heard the loud huzzas of his troops. Turning to one of his sergeants,
he with an anxious look mutely inquired what it meant. The officer
replied, "_The British Union Jack is coming down and the stars are
going up._" The dying hero heaved a sigh, and smiled even amid his
agony. He was carried on board the commodore's ship, and the last act
of his life was to make a sign, that the British flag which had been
brought to him should be placed under his head.
[Illustration: Death of Pike.]
Thus fell one of the noblest officers in the army. Kind, humane, the
soul of honor and of bravery, he was made after the model of the
knights of old. His father had fought in the war of the Revolution,
and though too old to serve, was still an officer in the army. In a
letter to his father, dated the day before the expedition, he, after
stating its character, said: "Should I be the happy mortal destined
to turn the scale of war--will you not rejoice, O, my father? May
heaven be propitious, and smile on the cause of my country. But if we
are destined to fall, may my fall be like Wolfe's--to sleep in the
arms of victory." His prayer was answered, and the country mourned the
loss of a gallant officer, a pure patriot, and a noble man.
Colonel Pearce, on whom the command devolved after the fall of Pike,
took possession of the barracks and then advanced on the town. As he
approached he was met by the officers of the Canadian militia,
proposing a capitulation. This was done to produce a delay, so that
the English commander, General Sheaffe, with the regulars could
escape, and the vessels and military stores be destroyed. The plan was
successful, the regular troops made good their retreat, one magazine
of naval and military stores was burned, together with two of the
vessels undergoing repairs. The third had sailed for Kingston a short
time before the attack.
Owing to the explosion of the magazine the loss of the Americans was
severe, amounting to three hundred killed and wounded. Notwithstanding
the exasperation of the victors at the wanton, and as they supposed
premeditated destruction of life, they treated the inhabitants with
kindness and courtesy. Such had been the strict orders of their
commander before his death. The only violence committed was the
burning of the house of Parliament, and this was owing, doubtless, to
the fact that a scalp was found suspended over the speaker's mace. The
sight of an American scalp, hanging as a trophy in a public building,
would naturally exasperate soldiers, whose friends and relatives had
fallen beneath the knife of the savage.[36]
[Footnote 36: Major Eustis, Captains Scott, Walworth, M'Glarpin, Young
and Moore, and Lieutenants Irvine, Fanning and Riddle, behaved with
great gallantry in the engagement.]
The troops were at once re-embarked, for the purpose of proceeding
immediately to Niagara, but owing to foul weather they were a week on
the way. At length, being reinforced by troops from Sackett's Harbor
and Buffalo, Dearborn, with some five thousand men, sailed for Fort
George. This fort was situated on a peninsula, which it commanded.
Dearborn resolved to make the landing in six divisions of boats, under
cover of the fire of the armed schooners. The first division,
containing five hundred men, was commanded by Winfield Scott, who
volunteered for the service, followed by Colonel Porter with the field
train. The gallant Perry offered to superintend the landing of the
boats, which had to be effected under a heavy fire and through an ugly
surf. The 27th of May, early in the morning, the debarkation began,
and soon the boats, in separate divisions, were moving towards the
shore. Fifteen hundred British lined the bank, which rose eight or ten
feet from the water. Scott rapidly forming his men under the plunging
fire of these, shouted, "Forward!" and began to scale the ascent. But,
pressed by greatly superior numbers, they were at length borne
struggling back. Dearborn, who was standing on the deck of Chauncey's
vessel, watching the conflict through his glass, suddenly saw Scott,
while waving his men on, fall heavily back down the steep. Dropping
his glass he burst into tears, exclaiming: "_He is lost!--He is
killed!_" The next moment, however, Scott sprang to his feet again,
and shouting to his men, he with a rapid and determined step remounted
the bank, and, unscathed by the volley that met him, knocked up with
his sword the bayonets leveled at his breast, and stepped on the top.
Crowding furiously after, the little band sent up their shout around
him, on the summit. Dressing his line under the concentrated fire of
the enemy, Scott then gave the signal to charge. The conflict was
fierce but short; the British line was rent in twain, and the
disordered ranks were driven over the field. Scott, seizing a
prisoner's horse, mounted and led the pursuit.
Fort George was abandoned, and the garrison streamed after the
defeated army. They, however, set fire to the train of the magazines
before they left. This was told to Scott, and he instantly returned
with two companies to save them. Before he could arrive, one magazine
exploded, sending the fragments in every direction. A piece of timber
struck him on the breast, and hurled him from his horse. Springing to
his feet he shouted, "To the gate!" Rushing on the gate, they tore it
from its hinges and poured in--Scott was the first to enter, and
ordering the brave Captains Hindman and Stockton to extinguish the
matches, he ran forward and pulled down the flag. Quickly re-mounting
his horse he put himself at the head of his column and pressed
fiercely after the enemy, chasing the fugitives for five miles, and
halted, only because commanded to do so by Colonel Boyd, in person. He
had already disobeyed two orders to stop the pursuit, and had he not
been arrested by his superior officer in person, would soon have been
up with the main body of the British.
The loss of the enemy in this short but spirited combat was two
hundred and fifty killed and wounded and one hundred prisoners, while
that of the Americans was only seventy-two.
The British army, under Gen. Vincent, retreated towards Burlington
Heights, followed soon after by General Winder, with eight hundred
men.
But while Chauncey and Dearborn were thus destroying the forts on the
Niagara, Sir George Provost made a sudden descent on Sackett's Harbor.
The protection of this place was of vital importance to us. Here was
our naval depot--here our ship yard with vessels on the stocks, and in
fact, this was the only available port on the lake for the
construction and rendezvous of a fleet. Yet the garrison left to
protect it consisted of only two hundred and fifty dragoons under
Lieutenant Colonel Backus, Lieutenant Fanning's artillery, two hundred
invalid soldiers and a few seamen, making in all some five hundred
men. Two days after the capture of Fort George, the fleet of Sir James
Yeo, carrying a thousand men, commanded by Provost, appeared off the
harbor. Alarm guns were instantly fired and messengers dispatched to
General Brown, who resided eight miles distant at Brownville, to
collect the militia and hasten to the defence of the place. The year
before Brown had joined the army and been appointed brigadier-general
in the militia, but at the close of the campaign, being disgusted with
its management and disgraceful termination, he retired to his farm.
His heart, however, was in the struggle, and the courier sent from
Sackett's Harbor had scarcely finished his message, before he was on
his horse and galloping over the country. Rallying five or six hundred
militia he hastened to the post of danger. He was one of those whom
great exigences develop. Brave, prudent, resolute, and rock fast in
his resolution, he was admirably fitted for a military leader, while
by his daring and gallant behavior, he acquired great influence over
raw troops. Acquainted with all the localities and resources of the
place, he at the request of Lieutenant Backus readily assumed the
command. A breastwork was hastily erected on the only spot where a
landing could be effected, and the militia placed behind it. The
regulars formed a second line near the barracks and public buildings,
while Fanning, with the artillerists, held the fort proper, and
Lieutenant Chauncey, with his men, defended the stores at Navy Point.
The night of the 28th passed in gloomy forebodings. The troops slept
on their arms, and Brown and his officers passed the hours in silently
and cautiously reconnoitering the shores of the lake. That little
hamlet embosomed in the vast primeval forest that stretched away on
either side along the water's edge and closed darkly over the solitary
highway that led to the borders of civilization, presented a lonely
aspect. As hour after hour dragged heavily by, every ear was bent to
catch the muffled sound of the enemy's sweeps, but only the wind
soughing through the tree-tops and the monotonous dash of waves on the
beach disturbed the stillness of the scene. But as the long looked for
dawn began to streak the water, the fleet of British boats were
observed rapidly pulling towards the breastwork. Brown bade the
militia reserve their fire till the enemy were within pistol shot, and
then deliver it coolly and accurately. They did so, and the first
volley checked the advance of the boats. After the second volley,
however, the militia were seized with a sudden panic, and broke and
fled. Colonel Mills, who commanded the volunteers, was shot while
bravely attempting to arrest the disorder. Brown succeeded in stopping
some ninety of them, whom he posted on a line with the regulars. The
British having landed, formed in good order, and moved steadily
forward on this little band of regulars. The latter never wavered, but
maintained their ground with stubborn resolution, and as they were
gradually forced back by superior numbers, took possession of the
barracks, behind which they maintained a rapid and galling fire.
Backus had fallen, mortally wounded, and Lieutenant Fanning was also
severely wounded, but he still clung to his gun and directed its fire
with wonderful accuracy. Finding the troops able to maintain their
position for some time yet, Brown exhorted them to hold firm while he
endeavored to rally the fugitive militia. Riding up to them, he
rebuked and entreated them by turns, until, at last, when he told them
how courageously and nobly the strangers were defending the homes they
had basely abandoned to pillage, they promised to return and do their
duty. Not daring, however, to trust men in an open attack who had
just fled from a breastwork, although he solemnly swore he would cut
down the first that faltered, he led them by a circuitous route along
the edge of the forest, as if he designed to seize the boats and cut
off the enemy's retreat. The stratagem succeeded, and the British made
a rush for their boats, leaving their killed and wounded behind.
Having lost, in all, between four and five hundred men, they dared not
venture on a second attack, and withdrew, humbled and mortified, to
the Canada shore. The American loss was about one hundred.
The successful defence of Sackett's Harbor following so quickly the
capture of Forts York and George, promised well for the summer
campaign. But disasters soon checked the rising hopes of the nation.
General Winder, who had started in pursuit of Vincent, found, on his
arrival at Forty Mile Creek, that the enemy had been reinforced.
Halting here, therefore, he dispatched a messenger to Dearborn for
more troops. General Chandler, with another brigade, was sent, when
the whole force was put in motion, and crossing Stony Creek, arrived
at night-fall, within a short distance of the British encampment. Here
the army halted, preparatory to an attack the next morning. General
Vincent, although greatly inferior in numbers, felt that his future
success depended entirely on his retaining his present position, and,
therefore, resolved to hazard a second battle. But, having, by a
careful reconnoissance, discovered that the American camp guards were
scattered and careless, while the whole encampment was loose and
straggling, he immediately changed his plan, and determined to make a
bold and furious night onset, and endeavor by one well-directed blow
to break the American army in pieces. Following up this determination,
he, with seven hundred men, set out at midnight, and arriving at three
o'clock in the morning at the American pickets silently and adroitly
captured every man before he could give the alarm. Pressing with the
main column directly for the centre of the encampment, he burst with
the appalling war-cry of the savage on the astonished soldiers. The
artillery was surrounded, and several pieces, with one hundred men,
were taken prisoners, and among them the two generals, Winder and
Chandler. General Vincent having lost his column in the darkness, the
second in command ignorant what course to pursue, or what to do,
concluded to retreat with his trophies. The attack had been well
planned and boldly carried out, and but for the blunder made by
Vincent would no doubt have been completely successful. As it was the
loss was nearly equal; so that the American army was still in a good
condition to take the initial and advance. But the command devolving
on Colonel Burns, a cavalry officer, who declared he was incompetent
to direct infantry movements, a retreat was resolved upon. The army
arriving at Forty Mile Creek, a messenger was despatched to Dearborn,
asking for orders. General Lewis, with the sixth regiment, was
immediately sent forward, with directions to engage the enemy at once.
An hour after his arrival at camp the British fleet was seen slowly
beating up abreast of it. A schooner was towed near the shore and
opened its fire, but Lieutenant Eldridge, heaving a few hot shot into
her, compelled her to withdraw. In the mean time, some vessels
appearing off Fort George, Dearborn conjectured that an attack upon
him was meditated, and recalled this division of the army. The boats,
however, sent to bring them, were overtaken by an armed schooner, and
many of them captured.
After these catastrophes Dearborn remained at Fort George an entire
fortnight, wholly inactive. The British, on the other hand, made
diligent use of this interval, in taking possession of mountain
passes, and thus accomplished the double purpose of securing their own
position and narrowing the limits of Dearborn's possessions, and
destroying his communication. The latter, at length, being aroused to
the danger in which these posts placed him, despatched Col. Boestler,
with six hundred men, to break up one of them, seventeen miles
distant. Acting under wrong information, this small detachment arrived
without molestation at Beaverdams, within two miles of the "Stone
House" where the enemy had fortified themselves. But here they were
suddenly surrounded by a body of British and Indians, and a conflict
ensued. Believing it impossible to effect a safe retreat through the
forest, pressed by such a force, Colonel Boestler surrendered his
whole detachment prisoners of war. This ended Dearborn's campaign, and
his military services. Colonel Bishop, who showed great activity in
carrying out the plan of the British commander, finding Fort Erie
ungarrisoned, took possession of it, and crossing suddenly to Black
Rock, with 250 men, drove out the militia and destroyed the guns and
stores. But the news reaching Buffalo, a few regulars, together with
some militia and friendly Indians hastened to the fort and expelled
the invaders, killing their commander.
The successful attacks on York and Fort George had removed much of the
odium with which the disasters of the previous years had covered
Dearborn, and great results were expected from so brilliant an opening
of the campaign. But his after inaction and efforts ending only in
failure, disgusted the people and Congress. Broken down by disease and
demoralized by their long camp life, the soldiers but poorly
represented the vigor and energy of the republic. Dearborn, like the
other generals, received all the blame that properly attached to him,
together with that which belonged to the Government, and when the news
of Boestler's defeat arrived in Washington, the House of
Representatives was thrown into a state of indignant excitement. Mr.
Ingersoll was deputed to wait on the President and demand Dearborn's
removal, as Commander-in-Chief of the Western army. The request was
granted, and on the 15th of July he resigned his command. He had
accomplished, literally nothing, in two campaigns, and though he was
surrounded with difficulties, crippled, and rendered cautious by the
indifferent and unsuitable troops under his command, yet, after making
a large allowance for all, there is margin wide enough to secure his
condemnation. His materials became worse instead of better under his
management, and the prospects on our northern border grew gloomier the
longer he held command. The energy and vigor of his younger days were
gone, and the enfeebled commander of 1812 was a very different man
from the daring and gallant officer of the Revolution. He had stood on
the deck of his vessel and seen Pike carry York, and young Scott Fort
George with mere detachments. He had witnessed the bravery of his
troops under gallant officers, and it needed only energy and activity
in himself to have made the army the pride of the nation.
[Sidenote: 1813.]
Colonel Boyd assumed the command till the arrival of Wilkinson in
September, but with the exception of some skirmishing, the summer
passed away in inactivity.
The British, by capturing two American sloops that ventured into a
narrow part of the lake, near the garrison of Aux Noix, obtained
command of this water communication, which they held the remainder of
the season.
CHAPTER IX.
SECOND SESSION OF THE TWELFTH CONGRESS.
Army bill -- Quincy and Williams -- Debate on the bonds of
merchants given for British goods imported in contravention
of the non-importation act -- Debate on the bills increasing
the army to 55,000 men -- Williams' report -- Quincy's
attack -- Clay's rejoinder -- Randolph, Calhoun, Quincy,
Lowndes and Clay -- State of the Treasury.
The members of Congress, when they assembled in October, did not
exchange those congratulations they promised each other at their
adjournment, after declaring war. Every plan had proved abortive,
every expectation been disappointed. True, the gallant little navy was
left to fall back on. Its successes, however, did not reflect much
credit on their sagacity, but rather by returning good for evil, had
administered a severe rebuke to their neglect. The Federalists could
claim the chief honor there, and make both the victories on the sea
and defeats on land the grounds of attack. They had always said leave
Canada alone and go to the sea, there is the proper theatre for your
exploits. Results had shown the wisdom of their counsels. The army had
accomplished nothing, still its skeleton ranks must be filled. A bill
was therefore introduced, increasing the pay of the soldiers from six
to eight dollars per month, and making their persons secure from
arrest for debt, in order to tempt recruits into the service. They
were allowed also to enlist either for five years or for the war.
[Sidenote: Nov. 20.] A clause inserted in this bill, giving minors and
apprentices, over eighteen, permission to enlist without the consent
of their parents and masters, fell like a bomb-shell in the House.
This was striking at the very foundation of social and domestic
life--viz., parental authority--and putting a premium on disobedience
and rebellion. [Sidenote: 1812.] It furnished a new outlet for Mr.
Quincy's wrath, who declared that if Congress dared apply it in New
England the people would resist it, with the laws against kidnapping
and stealing. He said it was odious and atrocious, unequalled, absurd,
and immoral. Mr. Williams replied, that Great Britain allowed
enlistments over sixteen, as did our Government in the Revolutionary
War--nay, that this very clause passed in 1798, which became a law.
[Sidenote: Dec. 3.] Another exciting debate sprung up relative to the
bonds of the merchants for British goods lately imported in
contravention of the non-importation law. This law, it will be
remembered, was passed in March, 1811, in retaliation for the orders
in council, and was to cease with the revocation of those orders.
Before the news of the declaration of war arrived in England they
were revoked, and American owners supposing the non-importation act
would fall with it, immediately took in cargoes of British goods.
These were allowed to depart, as well as others in process of landing,
and provided with licenses to protect them against British cruisers.
Thus a vast amount of merchandise arrived in the various ports of the
United States during the first two or three months of the war. The
non-importation act being still in force, these goods were seized as
forfeited to the Government. Still many of the district judges
surrendered them to the claimants on their giving bonds to the amount
of their value. As under the non-importation law half the value of the
forfeited goods belonged to the informer, Gallatin proposed that, as
in this case there was no informer, that portion should be given to
the owners, and the Government put the other half, amounting to nine
millions, in the public treasury. This proposal was advocated by some
and strenuously opposed by others. [Sidenote: Dec. 30.] After a
vehement debate, extending through several sittings, all the penalties
of the merchants were finally remitted.
Another debate, still more exciting, followed on the army bill. This
bill contained provisions for raising twenty thousand men for one
year, increased bounty enlistments to sixteen dollars, and appointed
an officer to do all the recruiting. [Sidenote: Dec. 27.] Mr.
Williams, chairman of the committee on military affairs, introduced
it with an able speech. After showing that the country demanded such
an augmentation of the army, making the entire regular force 55,000,
and defending the increased bounty and appointment of a special
officer for the recruiting service, he alluded to the disastrous issue
of Hull's campaign. Said he, "there are those, perhaps, who can sneer
at the disasters and misfortunes of the late campaign, and will object
to this bill, saying there is no encouragement to vote additional
forces, seeing that those which have been already raised have been so
idly employed. It becomes us all to be equally faithful to our
country, whether victorious or not; it is in times of discomfiture
that the patriot's resolution and virtues are most needed. It is no
matter by what party names we are distinguished, this is our
country--we are children of the same family, and ought to be brothers
in a common cause. The misfortune which befalls one portion should
sink deep into the breasts of the others also."
[Sidenote: Jan. 5, 1813.]
Mr. Clay congratulated the committee and the nation on the report
that had been made. Mr. Quincy, who saw in every proposition for
replenishing the army, a project for conquering Canada, opposed the
bill. Assuming that to be the object in view, he assailed it with
all that sarcasm and abuse for which he was distinguished. In the
first place, he said, we could not conquer Canada; in the second
place, if we could, it would be a barren triumph. It would not bring
peace nor be of any advantage to the country. He denounced it as
cruel and barbarous, declaring it was not owing to the Government,
that at that moment the bones of the Canadians were not mixed with
the ashes of their habitations. Said he, "Since the invasion of the
buccaneers, there is nothing like this war. We have heard great
lamentations about the disgrace of our arms on the frontier. Why,
sir, the disgrace of our arms on the frontier is terrestrial glory
in comparison with the disgrace of the attempt! The whole atmosphere
rings with the utterance, from the other side of the house, of this
word, glory! glory! What glory? The glory of the tiger which lifts
its jaws all foul and bloody from the bowels of his victim, and
roars for his companions of the forest to come and witness his
prowess and his spoils--the glory of Zenghis Khan, without his
greatness--the glory of Bonaparte." He asked the members if they
supposed the vagabonds who should conquer Canada would, when their
aim was accomplished, heed the orders of Government. No! they would
obey the "choice spirits" placed over them, who in turn would not
consult spinsters and weavers, but take counsel from their leader
what next they shall do. "Remember," said he, "remember, I warn you,
he who plants the American standard on the walls of Quebec, plants
it for himself, and will parcel it out into dukedoms, and
seignorities, and counties for his followers." It was a solace to
him amid all his regrets, that New England was guiltless of this
war, and that she had done her utmost to hurl the wicked authors of
it from their seats. That way of thinking, he said, was not peculiar
to him, but was "the opinion of all the moral sense and nine-tenths
of the intelligence of the section from which he came. Some of those
who are here from that quarter--some of _the household troops_ who
lounge for what they can pick up about the Government-house will say
differently--those who come here and with their families live and
suck upon the heart of the treasury--toad-eaters who live on
eleemosynary, ill-purchased courtesy of the palace, swallow great
men's spittles, get judgships, and wonder at the fine sights, fine
rooms, fine company, and most of all wonder how they themselves got
here--these creatures will tell you, No--that such as I describe are
not the sentiments of the people of New England. Sir, I have
conversed upon the question with men of all ranks, conditions and
parties in Massachusetts, men hanging over the plough and holding
the spade--the twenty, thirty and fifty acre men, and their answers
have uniformly been to the same effect. They have asked simply, What
is the invasion for? Is it for land? We have enough. Is it for
plunder? There is none there. New States? We have more than is good
for us. Territory? If territory, there must be a standing army to
keep it, and there must be another standing army here to watch that.
These are judicious, honest, patriotic, sober men, who when their
country calls, at any wise or real exigency, will start from their
native soils and throw their shields over their liberties, like the
soldiers of Cadmus, yet who have heard the winding of your horn for
the Canadian campaign, with the same indifference they would have
listened to a jews harp or the twanging of a banjo. He declared that
Mr. Madison and his cabinet had been bent on war from the outset,
and their eagerness to come to blows with England evinced the
disposition ascribed to the giant in the children's old play:--
'Fe, faw, fum,
I smell the blood of an Englishman,
Be he dead or be he alive
I will have some.'
He knew there were those who were ready to open on him with the old
stale cry of British connection. It was not egotism to speak of what
belonged to his country. It would ill become a man whose family had
been two centuries settled in the State, and whose interest and
connections were exclusively American, to shrink from his duty for
the yelpings of those bloodhound mongrels who were kept in pay to hunt
down all who opposed the court--a pack of mangy hounds, of recent
importation, their backs still sore with the stripes of European
castigation, and their necks marked with the check collar." Fierce and
vehement, now rising into eloquence, and now descending to the coarse
language of the bar-room, Mr. Quincy dealt his blows on every side--at
one moment coming down on the administration with sweeping charges of
dishonesty and villany, and again rushing fiercely on the solid
phalanx of the war party, assailing them with scoffs and jeers and
taunts, till scorn and rage gathered on their countenances.
Mr. Clay, in his urbane and gentle manner, rose to reply. He took a
review of the two parties. While the administration was endeavoring to
prevent war by negotiations and restrictive measures, the opposition,
he said, was disgusted with the timorous policy pursued, and called
for open, manly war. They declared the administration "could not be
kicked into a war." "War and no restrictions, is their motto, when an
embargo is laid, but the moment war is declared, the cry is
restrictions but no war. They tack with every gale, displaying the
colors of every party and of all nations, steady in only one
unalterable purpose, to steer, if possible, into the haven of power.
The charge of French influence had again and again been made, which
should be met in only one manner--by giving it the lie direct. The
opposition had also amused themselves by heaping every vile epithet
which the English language afforded on Bonaparte. He had been compared
to every monster and beast, from that of the Revelations to the most
insignificant quadruped. He said it reminded him of an obscure lady
who took it into her head to converse on European affairs with an
accomplished French gentleman, and railed on Napoleon, calling him the
curse of mankind, a murderer and monster. The Frenchman listened to
her with patience to the end, and then, in the most affable manner,
replied, 'Madame, it would give my master, the Emperor, infinite pain
if he knew how hardly you thought of him.' Expressing his regret that
he was compelled to take some notice of Mr. Quincy in his remarks, he
defended Jefferson against his attacks, and showed how absurd were all
his statements and scruples respecting the invasion of Canada, by
referring to the part New England took in the capture of Louisburg. He
then alluded to the treasonable attitude assumed by the Federalists,
denounced their hypocrisy in endeavoring to gain the adhesion of the
people to their views by promising peace and commerce. But, said Mr.
Clay, I will quit this unpleasant subject, I will turn from one whom
no sense of decency or propriety could restrain from soiling the
carpet on which he treads, to gentlemen who have not forgotten what is
due to themselves, the place in which we are assembled, nor to those
by whom they are opposed." He then went into a review of the causes
that led to the war, to show that the government had acted with
forbearance and moderation, and at length took up the subject of
impressment. After proving the illegality and oppression of this
right, as claimed and exercised by the English, he said, "there is no
safety to us but in the rule that all who sail under the flag (not
being enemies) are protected by the flag. It is impossible the country
should ever forget the gallant tars who have won for us such splendid
trophies. Let me suppose that the genius of Columbia should visit one
of them in his oppressor's prison, and attempt to reconcile him to his
wretched condition. She would say to him in the language of the
gentlemen on the other side, 'Great Britain intends you no harm; she
did not mean to impress you, but one of her own subjects, having taken
you by mistake; I will remonstrate and try to prevail on her, by
peaceable means, to release you, but I cannot, my son, fight for you.'
If he did not consider this mockery he would address her judgment and
say, 'You owe me my country's protection; I owe you in return,
obedience; I am no British subject, I am a native of old
Massachusetts, where live my aged father, my wife, my children; I have
faithfully discharged my duty, will you refuse to do yours?' Appealing
to her passions, he would continue, 'I lost this eye in fighting under
Truxton with the Insurgente; I got this scar before Tripoli; I broke
this leg on board the Constitution when the Guerriere struck.' If she
remained still unmoved he would break out in the accents of mingled
distress and despair,
'Hard, hard is my fate! once I freedom enjoyed,
Was as happy as happy could be!
Oh! how hard is my fate, how galling these chains!'
I will not imagine the dreadful catastrophe to which he would be
driven by an abandonment of him to his oppressor. It will not be, it
cannot be, that his country will refuse him protection." This
description of a poor sailor, maimed in his country's service,
appealing to that country he had served so well, for protection, and
rejected, cast off, abandoning himself to despair, sketched as it was
with vividness and feeling, and uttered in that touching pathos for
which Clay's rich and flexible voice was remarkable, went home with
thrilling power to each patriotic heart, and tears were seen on the
faces of members in every part of the house.
After reviewing the progress of the war, and the present attitude of
England, and declaring that propositions for peace offered by the
other party were futile, he drew himself to his full height, and
casting his eye around the house, and pitching his voice to the note
of lofty determination, closed with, "An honorable peace can be
attained only by an efficient war. My plan would be to call out the
ample resources of the country, give them a judicious direction,
prosecute the war with the utmost vigor, strike wherever we can reach
the enemy at sea or on land, and negotiate the terms of peace at
Quebec or Halifax. We are told that England is a proud and lofty
nation, that, disdaining to wait for danger meets it half way. Haughty
as she is, we once triumphed over her, and if we do not listen to the
counsels of timidity and despair, we shall again prevail. In such a
cause, with the aid of Providence, we must come out crowned with
success, "_but if we fail, let us fail like men, lash ourselves to our
gallant tars, and expire together in one common struggle, fighting for
'Seaman's rights and Free trade_.'" Before this patriotic burst of
eloquence the harsh and irritating charges and selfish objections of
the opposition disappeared, like the unhealthy vapors of a morass
before the fresh breath of the cool west wind.
The declaration of war consummated a revolution begun long before in
Congress. The affairs of the nation were taken out of the hands of old
and experienced statesmen, and placed in those of young and ardent
men. Henry Clay was but thirty-five; Calhoun, thirty, and Randolph
thirty-nine. Many of less note were also young men, full of hope and
confidence, and jealous of their country's honor. In their first
conflict with the older and more conservative members, they revealed
the dawning genius and statesmanship that afterwards raised them to
such high renown. The Federalists were represented also by men of
great strength of intellect and forcible speakers. Quincy possessed
the elements of a powerful leader, but he at times allowed his
passions to override all propriety and suggestions of prudence.
Vehement and fearless, he moved down on the enemy in gallant style,
but, like Jackson in battle, his hostility for the time lost all
magnanimity, and assumed the character of ferocity. He made the whole
party opposed to him a person, and attacked it with all the malignity,
scorn, invective, and jeers he would one who had grossly abused his
person and assailed his honor. But there was no secresy or trickery in
his movements--his followers and his foes knew where to find him, and
though he often, in his intemperance, violated the rules of courtesy,
and thus exposed himself to retorts that always tell against a
speaker, he still was an ugly opponent to contend with. Full of
energy, inflexible of purpose--aggressive, bold, and untiring--in a
popular cause he would have been resistless. There were men in the
Federalist party at this time capable of carrying even a bad cause if
relieved from external pressure. But the impressment of American
citizens, massacres in the north, and outrages along the sea coast, so
aroused the national indignation, that both words and efforts became
powerless before it. Like the resistless tide, which bears away both
strong and weak, it hushed argument, drowned explanations, and
silenced warnings, as it surged on, breaking down barriers, and
sweeping away defences that seemed impregnable.
One of the most remarkable men in this Congress was John Randolph, of
Roanoke, as he always wrote himself. Possessed of rare endowments, and
of ample wealth, fortune had lavished on him every gift but that of
sex. He was at this time exceedingly fair. Conflicts and rude
jostlings with the world had not yet wrinkled and blackened his
visage, soured his sensitive temper, or driven him into that
misanthropy and those eccentricities which afterwards disfigured his
life. He was six feet high and frail in person, but his brilliant
black eye fairly dazzled the beholder, as he rose to speak, and made
him forget the fragile form before him. His voice was too thin for
public speaking, and when pitched high was shrill and piercing. But
in common conversation it was like an exquisite instrument, on which
the cunning player discoursed strange and bewitching music, and no one
could escape its fascination. His first glance round the hall
attracted silence, and all bent to catch the tones of that musical
feminine voice. As he became excited in his harangue, his eye burned
with increased lustre, while his changing countenance revealed every
thought and feeling before it was uttered. So expressive was it in
transmitting the transitions that passed over the soul and heart of
the speaker, that they scarcely needed the assistance of language.
Sometimes fearfully solemn and again highly excited; he at this time
rarely indulged in that withering sarcasm which afterwards so often
drew blood from his antagonist. With the delicate organization and
sensibilities of a woman, joined to the thought and ambition of a man,
his destiny had led him into scenes that spoiled his temper and erased
some of the most beautiful features of his character. Chivalrous and
fearless, he at first lent his genius to Jefferson's administration,
but shrunk from the awful consequences of war when it approached.
Calhoun, one of the firmest props of the government, was his antipode
in almost every particular. Though young, his face evinced no
enthusiasm--his glistening eye no chivalry. With thin lips, high cheek
bones, rigid, yet not strong lines in his face, an immense head of
hair, his personal appearance would never have arrested the curiosity
of the beholder but for his eye. This was not brilliant and radiant
like Randolph's. It did not light up with valor, nor burn with
indignation, nor melt with pity, but changeless as a piece of
burnished steel, it had a steady, cold glitter, that fascinated for
the time whomsoever it fell upon. Fixed and precise in his attitude,
and moveless in his person, he poured forth his thoughts and views
with a rapidity, yet distinctness, that startled one. Untrammeled at
this time with those abstractions and theories which afterwards
confused his reasoning faculties and gave an irrecoverable twist to
his logic; he brought his cool, clear intellect to the aid of the
administration, and indicated by the power and influence he soon
acquired, his future greatness. No sophistry could escape him--the
stroke of his cimeter cut through all complexity--and when he had done
with his opponent's argument it could not have been recognized as that
which, just before, looked so plausible and consistent.
Two other representatives from the same state were able friends of the
administration. William Lowndes, a young man, and though not a good
speaker, nor prepossessing in his appearance, carried great influence
by mere weight of character, and the consistency and firmness of his
political opinions. He was six feet six inches high, and slender
withal; and when he rose to address the house, his unassuming and
respectful manner commanded attention. Of great integrity, clear
headed and consistent, a proud, bright career seemed opening before
him, but death soon closed it for ever.
Mr. Cheves was chairman of committee of Ways and Means, and exhibited
great ability in that station.
But the pride of the house was the young and graceful speaker, Henry
Clay. Tall, and straight as a young forest tree, he was the embodiment
of the finest qualities of Western character. Possessing none of the
graces and learning of the schools, nor restrained in the freedom of
thought and opinion by the systems and rules, with which they often
fetter the most gifted genius, he poured his whole ardent soul and
gallant heart into the war. The true genius, and final destiny of this
republic, lie west of the Alleghanies. So there, also, will spring up
our noblest American literature. Not shackled by too great reverence
for the old world, educated in a freer life, and growing up under the
true influences of American institutions, man there becomes a freer, a
more unselfish being; his purposes are nobler, and all his instincts
better.
Impelled by pure patriotism, and excited by the wrongs and insults
heaped upon his country, Clay entered into those measures designed to
redeem her honor, and maintain her integrity with a zeal and
solicitude, that soon identified him with them. He thus unconsciously
became a leader; and whether electrifying the house with his appeals,
or in the intervals of the sessions of Congress traversing his state,
and arousing the young men to action, exhibited the highest qualities
of an orator. His stirring call to the sons of Kentucky was like the
winding horn of the huntsman, to which they rallied with ardent
courage and dauntless hearts. We now always associate with Clay, the
scattered white locks and furrowed face, and slow, majestic movements.
But, at this time, not a wrinkle seamed his youthful countenance; and
lithe and active, he moved amid his companions with an elastic tread,
and animated features. His rich and sonorous voice was so flexible,
that it gave him great power in appealing to the passions of men. When
moving to pity, it was soft and pleading as a woman's; but when
rousing to indignation, or to noble and gallant deeds, it rang like
the blast of a bugle. In moments of excitement, his manner became
highly impassioned, his blue eye gleamed with the fire of genius, and
his whole countenance beamed with emotion. Thoughts, images,
illustrations leaped to his lips, and were poured forth with a
prodigality and eloquence, that charmed and led captive all within
reach of his voice. He loved his country well, and sung her wrongs
with a pathos, that even his enemies could not withstand. When he was
disheartened by our first reverses on the northern frontier, he turned
to our gallant navy with a pride and affection, he maintained till his
death. Madison leaned on him throughout this trying struggle, as his
chief prop and stay.
Though the House, rent by the fierce spirit of faction, would often
break through the bounds of decorum and order, he as speaker held the
reins of power with a firm and just hand. With an easy and affable
manner, that attracted every one to him, he yet had a will of iron.
Under all that frankness and familiarity, there was a rock-fast heart,
that never swerved from its purpose. His manner of carrying out his
plans, often misled men respecting the strength of his will. He was
strictly _suaviter in modo fortiter in re_. Clay, Calhoun, Randolph,
and in the next Congress Webster, were striking representatives of the
young country rising rapidly to greatness. Truly, "there were giants
in those days."
It was estimated that the entire revenue for the ensuing year would be
$12,000,000, while the expenses were calculated at $36,000,000. To
make up the $24,000,000 deficit, the President was authorized to sell
$16,000,000 six per cent. stock, continue outstanding the former
$5,000,000 treasury notes, and raise $5,000,000 towards a new loan.
But the more important business was transferred to the next Congress,
which was to meet early in the spring. The two other principal acts
passed this session, was one authorizing the government to occupy
Mobile, and all that part of Florida ceded to the United States, with
Louisiana, and the other giving it power to retaliate for the
twenty-three Irishmen taken from Scott at Quebec, and sent to England
to be tried for treason.
CHAPTER X.
Action between the Chesapeake and Shannon -- Rejoicing in
England over the victory -- The Enterprise captures the
Boxer -- Death of Lieutenant Burrows -- Daring cruise of the
Argus in the English and Irish channels -- Lieutenant
Allen's humanity -- Action with the Pelican -- Death of
Allen -- His character.
[Sidenote: 1813.]
Defeats on land had thus far been compensated by victories at sea, and
to that element we ever turned with pride and confidence. Our
exultation, however, was for a moment checked by the loss of the
Chesapeake, within sight of our shores. This vessel had started on a
cruise in February, under the command of Captain Evans. Unsuccessful
in her attempts to find the enemy, and having captured but four
merchantmen during the whole time of her absence, she returned to
Boston with the character of an "unlucky ship," which she had borne
from the outset, still more confirmed. Captain Lawrence succeeded
Captain Evans in the command of her, and began to prepare for a second
cruise. An English frigate, the Shannon, was lying off the harbor at
the time, and her commander, Captain Broke, sent a challenge to
Lawrence, to meet him in any latitude or longitude. The Chesapeake was
just getting under way when this challenge arrived, and Lawrence
resolved at once to accept it, though reluctantly, from the
disaffected state in which he found his crew. He had joined his vessel
but a few days before; the proper 1st lieutenant lay sick on shore,
and the acting lieutenant was a young man unaccustomed to his
position, while "there was but one other commissioned sea officer in
the ship," two midshipmen acting as third and fourth lieutenants.
Under these circumstances, and with a discontented, complaining crew,
it was evidently unwise to hasten a combat with a ship that had long
been preparing herself for such an encounter, and was, in every way,
in the best possible condition. But Lawrence, brave and ambitious of
renown, knowing, also, that the motives which would prompt him to
avoid a combat would be misconstrued, and having but a short time
before challenged an English vessel in vain, determined to run the
hazard, and on the morning of the 1st of June, stood boldly out to
sea. At four o'clock he overhauled the Shannon, and fired a gun, which
made her heave to. The Chesapeake, now about thirty miles from land,
came down under easy sail, receiving the fire of the enemy as she
approached. Captain Lawrence having determined to lay the vessel
alongside and make a yard-arm to yard-arm fight of it, reserved his
fire until every gun bore, when he delivered a destructive broadside.
The clouds of smoke as they puffed out upon the sea and rolled upward,
thrilled the hearts of the hundreds of spectators that crowned the dim
highlands around Boston harbor. For a few minutes the cannonading was
terrific, but some of the rigging of the Chesapeake being cut to
pieces one of the sails got loose and blew out, which brought the ship
into the wind. Then taking sternway she backed on her enemy, and the
rigging and an anchor becoming entangled, she could not get off. This,
of course, exposed her to a raking fire, which swept her decks.
Captain Lawrence, during the conflict, had received a wound in the
leg, while several of his officers were killed. When he found that his
vessel would inevitably fall aboard that of the enemy, he ordered the
drums to summon the boarders. But a <DW64> bugleman attempting to
perform this duty was so frightened that he could not blow a note, and
verbal orders were distributed. In the mean time, Lawrence fell
mortally wounded. Carried below, his last words were "Don't give up
the ship," a motto which Perry soon after carried emblazoned on his
flag as he passed from his helpless, dismantled ship, through the
enemy's fire, to the Niagara. With his fall ceased all efforts to
carry the Shannon by boarding. The commander of the latter finding
the quarter-deck guns of the Chesapeake abandoned, gave the orders to
board, and the flag which had never yet been struck to anything like
an equal foe, was hauled down. The destruction on board the American
ship after she fell foul of the enemy was frightful. The entire battle
lasted but twelve minutes, and yet in that short time a hundred and
forty-six of her officers and crew were killed or wounded. The loss of
the Shannon was twenty-three killed and fifty-six wounded. This
victory of the British was tarnished by the brutal conduct of
Lieutenant Faulkener, who took command of the prize. The testimony of
the surviving officers proved him unworthy to serve under the gallant
commander who had so nobly fought his ship.
The Americans had become so accustomed to naval victories that they
felt great chagrin at this defeat, while the unexpected triumph,
coming as it did on the top of such successive disasters, was received
with the most extravagant delight in England: the Tower bells were
rung, salvos of artillery fired, and praises innumerable and honors
were lavished on Captain Broke. Our navy never received a greater
compliment than these unwonted demonstrations of joy uttered. The
state of the crew--the accidental blowing out of the sail--the neglect
of officers to board--and a variety of excuses were offered to solace
the American people for this defeat. There was, doubtless, much force
in what was said, but the falling of a mast, or the loss of the wheel,
or any casualty which renders a vessel unmanageable, and gives one or
the other a decided advantage, is always liable to occur; hence,
unbroken success is impossible. Occasional misfortune is a law of
chance.
But during the summer and autumn our other vessels at sea continued to
give a good account of themselves. The three little cruisers, Siren,
Enterprise, and Vixen, were great favorites, for their gallant conduct
in the bay of Tripoli. The latter was captured early in the war by an
English frigate. The Siren did not go to sea till next year, when she
too, after giving a British 74 a chase of eleven hours, was taken. The
Enterprise was kept between Cape Ann and the Bay of Fundy, to chase
off the privateers that vexed our commerce in those waters. She was a
successful cruiser against these smaller vessels, capturing several
and sending them into port. [Sidenote: Sept. 4.] A few days before
Perry's victory, this vessel left the harbor of Portland, and while
sweeping out to sea discovered a strange sail close in shore. The
latter immediately hoisted four British ensigns and stood on after the
Enterprise. Lieutenant Burrows, the commander, kept away, and ordered
a long gun forward to be brought aft and run out of one of the
windows. He had but lately joined the ship, and hence was but little
known by the under officers and men. The latter did not like the looks
of this preparation, especially as he kept carrying on sail. They
feared he had made up his mind to run, and this gun was to be used as
a stern-chaser. From the moment they had seen the British ensign they
were eager to close with the enemy, and the disappointment irritated
them. The seamen on the forecastle stood grouped together, discussing
this strange conduct on the part of their commander for awhile, and
then went to their officer and begged him to go and see about it--to
tell the captain they wanted to fight the British vessel, and they
believed they could whip her. The latter finally went forward and
spoke to the first lieutenant, who told him they need not be troubled,
Mr. Burrows would soon give them fighting enough to do. This was
satisfactory, and they looked cheerful again. The preparations all
being made, and the land sufficiently cleared, Burrows shortened sail
and bore down on the enemy. As the two vessels, approaching
diagonally, came within pistol shot of each other, they delivered
their broadsides, and bore away together. The Enterprise, however,
drew ahead, and Burrows finding himself forward of the enemy's bows,
ordered the helm down, and passing directly across his track, raked
him with his long gun from the cabin window. He then waited for him to
come up on the other quarter, when they again moved off alongside of
each other, firing their broadsides, till at length the main-top-mast
of the English vessel came down. Raking her again with his long gun,
Burrows took up his station on her bows, and poured in a rapid and
destructive fire.
The men serving one of the carronades being sadly reduced in numbers,
and unable to manage their piece, Burrows stepped forward, and seized
hold of the tackle to help them run it out. Placing his feet against
the bulwark to pull with greater force, he was struck in the thigh by
a shot which glanced from the bone and entered his body, inflicting a
mortal, and exceedingly painful wound. He refused, however, to be
carried below, and laid down on deck, resolved, though writhing in
excruciating agony, to encourage his officers and men by his presence
so long as life lasted.
In forty minutes from the commencement of the action the enemy ceased
firing, and hailed to say he had struck. The commanding officer
ordered him to haul down his flag. The latter replied they were nailed
to the mast, and could not be lowered till the firing ceased. It was
then stopped, when an English officer sprang on a gun, and shaking
both fists at the Americans, cried, "No--no," and swore and raved,
gesticulating, in the most ludicrous manner till he was ordered
below. This, together with the awkward manner of lowering colors with
levers and hatchets, drew peals of laughter from the American sailors.
Lieutenant Burrows lived till the sword of the English commander was
placed under his head, when he murmured, "I die contented." This
vessel, which proved to be the Boxer, was terribly cut up, but the
number of killed was never ascertained, as they were thrown overboard
fast as they fell. She had fourteen wounded, while the loss of the
Americans was one killed and thirteen wounded.
After this the Enterprise, under Lieutenant Renshaw, cruised south, in
company with the Rattlesnake, both having many narrow escapes from
British men of war. The former captured, off the coast of Florida, the
British privateer, Mars, of fourteen guns. Soon after she was chased
by a frigate for three days, the latter often being within gunshot.
So hard was the brig pressed, that Lieutenant Renshaw was compelled to
throw his anchors, cables, and all but one of his guns overboard. At
length it fell calm, and the frigate began to hoist out her boats. The
capture of the brig then seemed inevitable, but a light breeze
springing up, bringing her fortunately to windward, her sails filled,
and she swept joyfully away from her formidable antagonist.
Soon after Renshaw was transferred to the Rattlesnake, in which
vessel he was again so hard pressed by a man of war, that he had to
throw over all his guns but two. Afterwards, near the same spot, being
wedged in between a British frigate and the land, he was compelled to
strike his flag.
The Argus, another brig, was launched this year, and dispatched in
June to France, to carry out Mr. Crawford, our newly appointed
Minister to that country. Having accomplished this mission, Lieutenant
Allen, the commander, steered for the coast of England, and cruised
boldly in the chops of the English channel. Here and in the Irish
channel, this daring commander pounced upon British merchantmen while
almost entering their own ports. He was in the midst of the enemy's
cruisers, and the most untiring watchfulness was demanded to avoid
capture. Unable to man his prizes he set them on fire, making the
Irish Channel lurid with the flames of burning vessels, and lighting
up such beacon fires as England never before saw along her coast.
Great astonishment was felt in Great Britain at the daring and success
of this bold marauder, and vessels were sent out to capture him. But
for a long time he eluded their search, leaving only smouldering ships
to tell where he had been. This service was distasteful to Allen, who
was ambitious of distinction, and wished for an antagonist more worthy
of his attention. Determined to combine as much kindness and humanity
with his duty as he could, he allowed no plundering of private
property. All passengers of captured vessels were permitted to go
below, and unwatched, pack up whatever they wished, and to pass
unchallenged. The slightest deviation from this rule, on the part of
his crew, was instantly and severely punished. This humanity, joined
to his daring acts, brought back to the English the days of Robin Hood
and Captain Kidd.
A cruise like this of a single brig in the Irish Channel, could not,
of course, continue long. Even if she could avoid capture, the crew
must in time sink under their constant and fatiguing efforts.
On the thirteenth of August, Allen captured a vessel from Oporto,
loaded with wine. Towards morning he set her on fire, and by the light
of her blazing spars stood away under easy sail. Soon after daylight
he saw a large brig of war bearing down upon him, perfectly covered
with canvas. He immediately took in sail to allow her to close, and
when she came within close range gave her a broadside. As the vessels
continued to approach the firing became more rapid and destructive. In
four minutes Captain Allen was mortally wounded by a round shot,
carrying off his leg. His officers immediately caught him up to carry
him below, but he ordered them back to their posts. In a short time,
however, he fainted from loss of blood and was taken away. Four
minutes after, the first lieutenant, Watson, was struck in the head by
a grape shot, and he too was taken below. There was then but one
lieutenant left, Lieut. H. Allen, who though alone, fought his ship
gallantly. But the rigging was soon so cut up that the vessel became
unmanageable, and the enemy chose his own position. In about a quarter
of an hour Mr. Watson was able to return on deck, when he found the
brig rolling helplessly on the water, a target for the Englishman's
guns. He however determined to get alongside and board, but all his
efforts to do so were abortive, and he was compelled to strike his
colors. His victorious adversary was the Pelican, a brig of war a
fourth larger than the Argus.
Unwilling to believe that this great disparity of force was a
sufficient reason for the defeat, the Americans endeavored to account
for it in other ways. It was said that the sailors succeeded in
smuggling wine from the brig burned a few hours before, and were not
in a condition to fight--others that they were so overcome with
fatigue that they nodded at their guns. Her fire was certainly much
less destructive than that of other American vessels, which one of the
officers on board said was owing to the powder used. Getting short of
ammunition, they had taken some powder from an English vessel bound to
South America. This being placed uppermost in the magazine, was used
in this engagement. It was afterwards ascertained to be condemned
powder, going as usual to supply South American and Mexican armies. In
proof of this, it was said that the Pelican's hull was dented with
shot, that had not force enough to pierce the timbers. The superiority
of the English vessel in size, however, is a sufficient reason,
without resorting to these explanations.[37] If any other was wanted,
it would be found in the early loss of the superior officers. Such a
calamity, at the outset of an engagement, will almost invariably turn
an even scale. One officer cannot manage a ship, and sailors without
leaders never fight well.
[Footnote 37: The Pelican was 485 tons, the Argus 298. The former
threw nearly two hundred pounds more metal than the latter at every
discharge.]
Captain Allen was taken ashore and placed in a hospital. As he was
carried from the ship, he turned his languid eyes on the comrades of
his perils and murmured, "God bless you, my lads; we shall never meet
again." His conduct on the English coast furnishes a striking contrast
to that of Cockburn, along our shores.[38]
[Footnote 38: Capt. Allen was born in Providence in 1784, and entered
the navy as a midshipman when sixteen years of age. His father was an
officer in the Revolution, and served with distinction. Young Allen,
seven years after his appointment, was lieutenant on board the
Chesapeake, when Barron shamefully struck his flag to the Leopard. He
fired the only gun that replied to the British broadside, touching it
off with a coal that he plucked from the fire in the galley. The shot
passed directly through the ward-room of the Leopard. His indignation
at the conduct of Barron overleaped all bounds, and he told him
bluntly, "_Sir, you have disgraced us._" He drew up a letter to the
Secretary of the Navy, demanding a court martial. "Oh," said he, in
writing home, "when I act like this, may I die unpitied and forgotten,
and no tear be shed to my memory." He was a brave and gallant officer,
and distinguished himself in the action between the United States and
Macedonian, and took command of the latter after her surrender. His
death was a great loss to the navy.]
CHAPTER XI.
Cost of transportation to the northern frontier -- English
fleet on our coast -- Chesapeake blockaded -- Blockade of
the whole coast -- Cockburn attacks Frenchtown -- Burns
Havre De Grace -- Attacks Georgetown and Frederickstown --
Arrival of British reinforcements -- Attack on Craney Island
-- Barbarities committed in Hampton -- Excitement caused by
these outrages -- Commodore Hardy blockades the northern
coast -- Torpedoes -- Hostile attitude of Massachusetts --
Remonstrances of its legislature -- Feeling of the people.
[Sidenote: 1813.]
With such a large extent of ocean and lake coast, and so vast and
unprotected western and southern frontiers occupied by hostile
savages, our troops were necessarily distributed over a wide surface.
The northern army alone acted on the offensive--in all other sections
of the country the Republic strove only to preserve its territory
intact. The summer in which Dearborn's army lay inactive at Fort
George, looked gloomy for the nation. Great exertions were being made
to retrieve our errors, and the war in the north was carried on at an
enormous expense. The conveying of provisions and arms for such a
distance on pack-horses, increased immensely the price of every
article. It was said that each cannon, by the time it reached
Sackett's Harbor, cost a thousand dollars, while the transportation
of provisions to the army of Harrison swelled them to such an
exorbitant price, that the amount expended on a small detachment would
now feed a whole army. The cost of building the indifferent vessels we
had on Lake Ontario, was nearly two millions of dollars.
But while these vast expenditures were made for the northern army, and
Harrison was gradually concentrating his troops at Fort Meigs, and
Perry building his little fleet on Lake Erie, soon to send up a shout
that should shake the land, and while the murmuring of the savage
hordes, that stretched from Mackinaw to the Gulf of Mexico, foretold a
bloody day approaching, an ominous cloud was gathering over the
Atlantic sea-coast. English fleets were hovering around our harbors
and threatening our cities and towns with conflagration. The year
before, England could spare but few vessels or troops to carry on the
war. Absorbed in the vast designs of Napoleon, who having wrested from
her nearly all her allies and banded them together under his
standard--Austria, Prussia, Poland, all Germany pressing after his
victorious eagles as they flashed above the waters of the Niemen--was
at that time advancing with a half million of men on the great
northern power. If he should prove successful, England would be
compelled to succumb, or with a still more overwhelming force he
would next precipitate himself upon her shores. But the snow-drifts of
Russia had closed over that vast and gallant host--his allies had
abandoned him, and the rising of the nations around him, in his weak,
exhausted condition, foretold the overthrow that soon sent him forth
an exile from his throne and kingdom. Released from the anxiety that
had hitherto rendered her comparatively indifferent to the war on this
continent, she resolved to mete out to us a chastisement the more
severe since it had been so long withheld. Irritated, too, because we
had endeavored to rob her of her provinces at a moment when she was
the least able to extend protection to them, she did not regard us as
a common enemy, but as one who by his conduct had ceased to merit the
treatment accorded in civilized warfare. The first squadron appeared
in the Chesapeake in February and blockaded it. Soon after another,
entered the Delaware under the command of Beresford, who attempted to
land at Lewistown, but was gallantly repulsed by the militia,
commanded by Colonel Davis. The town was bombarded, and though the
firing was kept up for twenty hours, no impression was made upon it.
In March the whole coast of the United States was declared in a state
of blockade, with the exception of Rhode Island, Massachusetts, and
New Hampshire. It is not known why Connecticut was not also omitted,
but the invidious distinction made between the eastern and the other
states grew out of the well known hostility of the former to the war.
It was intended not only as a reward for their good behavior in the
past, but a guerdon of better things should that hostility assume a
more definite form. This intended compliment to New England was the
greatest insult she ever received. It was a charge of disloyalty--the
offer of a bribe for treason--the proffer of the hand of friendship,
while that same hand was applying the torch to American dwellings and
carrying the horrors of war to the hearth-stone and fireside.
Admiral Cockburn, especially, made his name infamous by his wanton
attacks on farm houses and peaceful citizens, and the license he
allowed to the brutal soldiery, who were guilty of deeds of shame and
violence like those which disgraced the troops of Wellington at
Badajos and St. Sebastian. After amusing himself by these predatory
exercises on peasants, hen roosts, barns, and cattle, he planned the
more important attack on Frenchtown, a village consisting of six
dwellings and two store houses. Taking with him about five hundred
marines, he set out at night, and rousing the terrified inhabitants by
his cannon, landed his imposing force, burned the two store houses,
after taking such of their contents as he needed--committed some petty
depredations, and retired.
The American frigate, Constellation, was blockaded in the bay by this
fleet, but all efforts to take her were repulsed by her brave crew.
[Sidenote: May 3.]
The scene of his next exploits was Havre de Grace, a thriving town,
situated on the Susquehanna, about two miles from the head of the bay.
He set out with his barges by night, and at daylight next morning
awakened the inhabitants with the thunder of cannon and explosion of
rockets in their midst. A scene of consternation and brutality
followed. Frightened women and children ran shrieking through the
streets, pursued by the insults and shouts of the soldiers. The houses
were sacked and then set on fire. The ascending smoke and flames of
the burning dwellings increased the ferocity of the men, and acts were
committed, from mere wantonness, disgraceful both to the soldiers and
their commanders. The work of destruction being completed, the British
force was divided into three bodies--one of which was ordered to
remain as guard, while the other two pierced inland, spoiling and
insulting the farmers, and robbing peaceful travellers. For three days
this gallant corps remained the terror and pest of the surrounding
country, and then re-embarked with their booty, leaving the
inhabitants to return to the ashes of their dwellings. Georgetown and
Frederictown became, in turn, the prey of these marauders, and the
light of burning habitations, and tears of women and children, fleeing
in every direction, kindled into tenfold fury the rage of the
inhabitants. A sympathetic feeling pervaded Congress, and no sooner
did it assemble than Clay, the speaker, descended from the chair, and
demanded an investigation of the charges brought against British
soldiers and officers. These excesses, however, were but the prelude
to greater and more revolting ones. Admiral Warren having arrived in
the bay with reinforcements, and land troops under the command of
General Beckwith, more serious movements were resolved upon. Norfolk
was selected as the first point of attack. This important town was
protected by two forts on either side of the Elizabeth river, between
which the frigate Constellation lay at anchor. Soon after the fleet
moved to the mouth of James river, and began to prepare for an attack
on Craney Island, the first obstacle between it and Norfolk.
Penetrating their design, Captain Tarbell landed a hundred seamen on
the island, to man a fort on the north-west side, while he moved his
gun boats so as to command the other channel. At day dawn on the 22d,
fifty barges loaded with troops were seen pulling swiftly towards the
island, to a point out of reach of the gun boats, but within range of
the batteries on shore. These immediately opened their fire with such
precision, that many of the boats were cut in two and sunk, and the
remainder compelled to retire. An attempt from the mainland was also
repulsed by the Virginia militia, under Colonel Beatty. The enemy
lost in this attack between two and three hundred men, while the
Americans suffered but little. Three days after the repulse at Craney
Island, Admiral Cockburn, assisted by General Beckwith, made a descent
on Hampton, a small fishing town by Hampton roads. The riflemen
stationed there, and the militia, bravely resisted the landing, but
were finally driven back by superior numbers. The place was then
entered and plundered, not merely of its public stores, but private
property. This little fishing town was literally sacked by the British
army of twenty-five hundred men. Private houses were rifled, even the
communion service of the church was carried away, while the women were
subjected to the most degrading insults, and _ravished in open day_!
The American army marched into Mexico over the bodies of their slain
comrades, and were fired upon for a whole day from the roofs of houses
after the city had surrendered, yet no such acts of violence were ever
charged on them as were committed under the sanction of the British
flag in this little peaceful, solitary, and defenceless village. The
authorities of the different towns took up the matter--witnesses were
examined, affidavits made, and the proceedings forwarded to the
British Commander. The charges were denied, but they stand proved to
this day, a lasting stigma on the name of Cockburn. This rear admiral
in the British navy not only allowed such outrages in one instance,
but repeatedly. There was a harmony in his proceedings refuting the
apology of unintentional baseness. His expeditions were those of a
brigand, and he changed civilized warfare into marauding, robbery, and
pillage. The news of these enormities, aggravated as they passed from
mouth to month, spread like wildfire amid the people. Stirring appeals
were heard in every village and town. Calm reflection and reason were
indignantly spurned; woman, manhood, patriotism, all cried aloud for
vengeance, and the war-cry of an aroused and indignant people swelled
like thunder over the land. The leaders of the anti-war faction saw
with consternation this rising sympathy of the masses. It threatened,
for the time, to sweep away their influence entirely. The British
committed a vital error in allowing these excesses, for they
harmonized the hitherto divided feelings of the people, and furnished
the upholders of the war with a new and powerful argument for unity
and energy. The public ear had become accustomed to the tales of
impressment and charges of the invasion of neutral rights. The
atrocities on the north-western frontier affected the west more than
the east, where they were charged rather to the Indians than to the
British Government, and were inflicted on an invading force. But a
system of warfare so abhorrent to humanity, aroused into activity a
spirit which gave tenfold strength to the administration.
While the Chesapeake remained blockaded, Admiral Cockburn, with a
portion of the fleet, moved southward, preceded by the history of his
deeds. The coasts of the Carolinas and Georgia were thrown into a
state of agitation bordering on frenzy. Mrs. Gaston, wife of a member
of Congress, died in convulsions from the terror inspired by this
British Admiral. He, however, effected but little. Landing at
Portsmouth he seized some booty and a few slaves. From the outset he
had attempted to persuade the slaves to rise against their masters,
and actually organized a company of blacks to aid him in his marauding
expeditions.
The squadron blockading the coast north of the Chesapeake was
commanded by Commodore Hardy, the reverse of Cockburn in every quality
that distinguished the latter. He waged no warfare on defenceless
towns, and villages, and women and children. Humane and generous, he
had more cause to complain of the conduct of the excited inhabitants,
than they of his. Although he landed at various places he allowed his
troops to commit no violence.
The American coast, south of Cape Cod, was at length thoroughly
blockaded, so that not only were our ships at home shut in port, but
those endeavoring to enter from without captured, and our whole
coasting trade was cut off, causing the country to feel severely the
miseries of war. The Constellation remained blockaded in the
Chesapeake, while the Macedonian, United States, and sloop Hornet, in
endeavoring to escape from New York by the way of the Sound, were
chased into New London, where they were compelled to lay inactive. In
the mean time, in accordance with an act of Congress, passed in the
winter, allowing half of the value of war ships to those who should
destroy them by other means than armed or commissioned vessels of the
United States, great ingenuity was exhibited in the construction of
torpedoes. Several attempts were made to blow up the British frigates,
but without success. The Plantagenet, however, riding in Lynn Haven
bay, came near falling a victim to one of these missiles, which spread
terror through the British fleet. After several unsuccessful efforts,
Mr. Mix, to whom the torpedo was entrusted, at length succeeded in
getting it near the bows of the vessel, unperceived. [Sidenote: July
24.] The "all's well" of the watch on deck had scarcely pealed over
the water, when it exploded with terrific violence. A red and purple
column suddenly rose fifty feet in the air, and bursting, fell like a
water-spout on deck. The ship rolled heavily in the chasm, and a
general rush was made for the boats, one of which was blown into the
air. Commodore Hardy remonstrated against this mode of warfare, as
contrary to the usages of civilized nations, and it was soon
abandoned. The terror it inspired, however, made him more wary in
approaching the coast. A boat-guard was kept rowing around the ships
all night, and the most extraordinary precautions taken to protect
them from these mysterious engines of destruction.
While our blockaded coast was thus filling Congress with alarm, and
the whole land with gloom and dread, the bold and hostile attitude
which Massachusetts was assuming, both deepened the general
indignation and added to the embarrassments under which the
administration struggled. Owing, doubtless, to the failures which
marked the close of the previous year, the elections in the New
England states during the early spring had terminated very
satisfactorily to the Federalists. Strong was elected Governor of
Massachusetts by a large majority, while both branches of the
Legislature were under the control of the Federalists. In Connecticut
and New Hampshire they had also triumphed, and Vermont, although her
state government and delegation to Congress were Democratic, was still
claimed as Federalist in the popular majority.
On the other side, New York and Pennsylvania spoke loudly for the
Administration, the latter by offering to loan a million of dollars
to the government, as an offset to the efforts of the Federalists to
prevent the loan proposed by government being taken.
[Sidenote: May 20.]
During the summer, acting under a hostile message received from the
governor, the Massachusetts Legislature drew up a remonstrance,
denouncing the war as wrong and unwise, prompted by desire of conquest
and love of France, rather than the wish to maintain the rights of the
people. The report of a committee against the incorporation into the
Union of Louisiana, as the commencement of western annexation,
destined, if not arrested, to destroy the preponderance of the Eastern
states, was also sustained in this remonstrance, which closed with a
solemn appeal to the Searcher of all hearts for the purity of the
motives which prompted it. Quincy in the House, and Otis and Loyd in
the Senate, were the Federalist leaders. Not content with taking this
hostile attitude to the General Government, the Legislature soon after
refused to pass resolutions complimentary to Captain Lawrence for his
gallant conduct in capturing the Peacock, and passed instead, the
following resolution introduced by a preamble, declaring that such
commendations encouraged the continuance of the war. "_Resolved_, as
the sense of the Senate of Massachusetts, that in a war like the
present, waged without justifiable cause, and prosecuted in a manner
showing that conquest and ambition are its real motives, it is not
becoming a moral people to express any approbation of military or
naval exploits, which are not immediately connected with the defence
of our sea-coast and soil." This was not a mere expression of feeling,
but the utterance of a principle acted on from that time to the end of
the war. This proud assumption of state rights and denunciation of the
war when our coasts were blockaded by British cruisers and our
frontiers drenched in blood, met the stern condemnation of the people
throughout the land, and raised a clamor that frightened the authors
of it. Party spirit had made Massachusetts mad, and blinded by her own
narrow views, she wished to wrap herself up in her isolated dignity
and keep forever from the great brotherhood of the Union those western
territories where the hardy settler had to contend not only with the
asperities of nature but a treacherous foe. That West which she then
abjured has since repaid the wrong by pouring into her lap countless
treasures, and furnishing homes for tens of thousands of her sons and
daughters. Allowing the spirit of faction to override the feelings of
nationality, she refused to rejoice in the victories of her country or
sympathize in her defeats. South Carolina has since assumed a similar
hostile attitude to the Union, but it yet remains to be seen whether
she would not sink her private quarrels when the national rights were
struck down and the country wasted by a common foe. As a state, not
only repudiating the authority of the general government and the
sacredness of the Union, but also refusing to stand by the republic in
the hour of adversity and darkness, Massachusetts occupied at that
time a preeminence in our history which it is to be hoped no other
state will ever covet.
CHAPTER XII.
Perry obtains and equips a fleet on Lake Erie -- Puts to sea
-- Kentucky marines -- Description of the battle -- Gallant
bearing of Perry -- Slaughter on the Lawrence -- Perry after
the battle -- Burial of the officers -- Exultation of the
people -- Harrison advances on Malden -- Flight of Proctor
-- Battle of the Thames, and death of Tecumseh.
But while the country, torn with internal strife and wasted by
external foes, looked with sad forebodings on the prospect before it,
there suddenly shot forth over the western wilderness a gleam of
light, like the bright hues of sunset, betokening a fairer to-morrow.
Perry's brilliant victory, followed by the overthrow of Proctor a few
weeks after, thrilled the land from limit to limit. On the frontier,
where we had met with nothing but disgrace, and towards which the
common eye turned with chagrin, we had cancelled a portion of our
shame, and relieved the national bosom of a part of the load that
oppressed it.
After the capture of Forts York and George, by which the river of
Niagara was opened to American navigation, Captain Perry was able to
take some vessels bought for the service from Black Rock into Lake
Erie. The Lake at the time was in the possession of the British fleet,
commanded by Captain Barclay, and Perry ran great hazard in
encountering it before he could reach Presque Isle, now Erie, where
the other vessels to compose his squadron had been built. He, however,
reached this spacious harbor just as the English hove in sight. Having
now collected his whole force he made vigorous preparations to get to
sea. By the first of August he was ready to set sail, but the enemy
lay off the harbor, across the mouth of which extended a bar, that he
was afraid to cross under a heavy fire. To his great delight, however,
the British fleet suddenly disappeared--Captain Barclay not dreaming
that his adversary was ready to go to sea, having gone to the Canada
shore.
Perry was at this time a mere youth, of twenty-seven years of age, but
ardent, chivalrous, and full of energy and resource. From the time he
arrived on the frontier, the winter previous, he had been unceasing in
his efforts to obtain and equip a fleet. Materials had to be brought
from Pittsburgh and Philadelphia, dragged hundreds of miles over bad
roads and across unbridged streams. But after his vessels were ready
for sea, he was destitute of crews. To his repeated and urgent calls
for men, only promises were returned, nor did they arrive till the
English had been able to finish and equip a large vessel, the Detroit,
which gave them a decided preponderance. Perry was exceedingly anxious
to attack the hostile fleet before it received this accession of
strength, but prevented from doing this through want of men, he was at
last compelled to abandon all his efforts, or take his chance with his
motley, untrained crew, in an action where the superiority was
manifest. He boldly resolved on the latter course, and taking
advantage of Barclay's sudden departure, gave orders for the men to
repair immediately on board ship, and dropped with eight of his
squadron down the harbor to the bar. It was Sabbath morning, and young
Perry, impressed with the great issues to himself and his country from
the step he was about to take, sent his boat ashore for a clergyman,
requesting him to hold religious services on board his ship. All the
officers of the squadron were assembled on the deck of the Lawrence,
and listened to an impressive address on the duty they owed their
country. Prayer was then offered for the success of their cause. Young
Perry reverently listening to the voice of prayer, as he is going
forth to battle, and young Macdonough lifting his own in supplication
to God, after his decks are cleared for action, furnish striking and
beautiful examples to naval men.
Next morning the water being smooth, the guns of the Lawrence, the
largest vessel, were taken out, and two scows placed alongside and
filled till they sunk to the water's edge. Pieces of timber were then
run through the forward and after ports of the vessel, and made fast
by blocks to the scows. All being ready, the water was pumped out of
them, and the vessel slowly rose over the bar. She stuck fast,
however, on the top, and the scows had to be sunk again before she
finally floated clear and moved off into deep water. The men worked
all night to get this one brig over. The schooners passed easily and
moored outside. The Lawrence was scarcely once more afloat before the
returning fleet hove in sight. Perry immediately prepared for action.
But Barclay after reconnoitering for half an hour crowded all sail and
disappeared again up the lake.[39] The next day Perry sailed in
pursuit, but after cruising a whole day without finding the enemy,
returned to take in supplies. [Sidenote: Aug. 12.] He was about to
start again, when he received information of the expected approach of
a party of seamen under the command of Captain Elliot. Waiting a day
or two to receive this welcome aid, he set sail for Sandusky, to put
himself in communication with Gen. Harrison and the north-western
army. He then returned to Malden, where the British fleet lay, and
going into Put-in Bay, a haven in its vicinity, waited for the enemy
to come out. [Sidenote: Aug. 25.] Here many of his crew were taken
sick with fever, which at last seized him, together with the three
surgeons of the squadron. He was not able to leave his cabin till the
early part of September, when he received an additional reinforcement
of a hundred volunteers. These troops came from Harrison's army, and
were mostly Kentucky militia and soldiers from the 28th regiment of
infantry, and all volunteers for the approaching battle. The
Kentuckians, most of them, had never seen a square rigged vessel
before, and wandered up and down examining every room and part of the
ship without scruple. Dressed in their fringed linsey-woolsey
hunting-shirts, with their muskets in their hands, they made a novel
marine corps as ever trod the deck of a battle-ship.
[Footnote 39: It was said he had accepted an invitation to dine in a
Canadian town, and expected to be back before the departure of his
enemy.]
[Sidenote: Sept. 10.]
On the morning of the 10th of September, it was announced that the
British fleet was coming out of Malden, and Perry immediately set sail
to meet it. His squadron consisted of three brigs, the Lawrence,
Niagara and Caledonia, the Trippe, a sloop, and five schooners,
carrying in all fifty-four guns. That of the British was composed of
six vessels, mounting sixty-three guns. It was a beautiful morning,
and the light breeze scarcely ruffled the surface of the water as the
two squadrons, with all sails set, slowly approached each other. The
weather-gauge, at first, was with the enemy, but Perry impatient to
close, resolved to waive this advantage, and kept standing on, when
the wind unexpectedly shifted in his favor. Captain Barclay observing
this, immediately hove to, and lying with his topsails aback, waited
the approach of his adversary. With all his canvass out, Perry bore
slowly and steadily down before the wind. The breeze was so light that
he could scarcely make two miles an hour. The shore was lined with
spectators, gazing on the exciting spectacle, and watching with
intense anxiety the movements of the American squadron. Not a cloud
dimmed the clear blue sky over head, and the lake lay like a mirror,
reflecting its beauty and its purity. Perry, in the Lawrence, led the
line.
Taking out the flag which had been previously prepared, and mounting a
gun-slide, he called the crew about him, and said, "My brave lads,
this flag contains the last words of Captain Lawrence. Shall I hoist
it?" "Aye, aye, sir," was the cheerful response. Up went the flag with
a will, and as it swayed to the breeze it was greeted with loud cheers
from the deck. As the rest of the squadron beheld that flag floating
from the mainmast of their commander's vessel, and saw "Don't give up
the ship!" was to be the signal for action, a long, loud cheer rolled
down the line. The excitement spread below, and all the sick that
could move, tumbled up to aid in the approaching combat. Perry then
visited every gun, having a word of encouragement for each captain.
Seeing some of the gallant tars who had served on board the
Constitution, and many of whom now stood with handkerchiefs tied round
their heads, all cleared for action, he said, "Well, boys, are you
ready?" "All ready, your honor," was the quick response. "I need not
say anything to you. _You_ know how to beat those fellows," he added
smilingly, as he passed on.
The wind was so light that it took an hour and a half, after all the
preparations had been made, to reach the hostile squadron. This long
interval of idleness and suspense was harder to bear than the battle
itself. Every man stood silently watching the enemy's vessels, or in
low and earnest tones conversed with each other, leaving requests and
messages to friends in case they fell. Perry gave his last direction,
in the event of his death, to Hambleton--tied weights to his public
papers in order to have them ready to cast overboard if he should be
defeated--read over his wife's letters for the last time, and then
tore them up, so that the enemy should not see those records of the
heart, and turned away, remarking, "_This is the most important day of
my life._" The deep seriousness and silence that had fallen on the
ship, was at last broken by the blast of a bugle that came ringing
over the water from the Detroit, followed by cheers from the whole
British squadron. A single gun, whose shot went skipping past the
Lawrence, first uttered its stern challenge, and in a few minutes all
the long guns of the enemy began to play on the American fleet. Being
a mile and a half distant, Perry could not use his carronades, and he
was exposed to this fire for a half an hour before he could get within
range. Steering straight for the Detroit, a vessel a fourth larger
than his own, he gave orders to have the schooners that lagged behind
close up within half cable's length. Those orders, the last he gave
during the battle, were passed by trumpet from vessel to vessel. The
light wind having nearly died away, the Lawrence suffered severely
before she could get near enough to open with her carronades and she
had scarcely taken her position before the fire of three vessels was
directed upon her. Enveloped in flame and smoke, Perry strove
desperately to maintain his ground till the rest of the fleet could
close, and for two hours sustained without flinching this unequal
contest. The balls crashed incessantly through the sides of the ship,
dismounting the guns and strewing the deck with the dead, until at
length, with "every brace and bow-line shot away," she lay an
unmanageable wreck on the water. But still through the smoke, as it
rent before the heavy broadsides, her colors were seen flying, and
still gleamed forth in the sunlight that glorious motto--"_Don't give
up the ship!_" Calm and unmoved at the slaughter around him and his
own desperate position, Perry gave his orders tranquilly, as though
executing a manoeuvre. Although in his first battle, and unaccustomed
to scenes of carnage, his face gave no token of the emotions that
mastered him. Advancing to assist a sailor whose gun had got out of
order, he saw the poor fellow struck from his side by a twenty-four
pound shot and expire without a groan. His second lieutenant fell at
his feet. Lieutenant Brooks, a gay, dashing officer, of extraordinary
personal beauty, while speaking cheerfully to him, was dashed by a
cannon-ball to the other side of the deck and mangled in the most
frightful manner. His shrieks and imploring cries to Perry to kill him
and end his misery, were heard even above the roar of the guns in
every part of the ship. The dying who strewed the deck would turn
their eyes in mute inquiry upon their youthful commander, as if to be
told they had done their duty. The living, as a sweeping shot rent
huge gaps in the ranks of their companions, looked a moment into his
face to read its expression, and then stepped quietly into the places
left vacant.
Lieutenant Yarnall, with a red handkerchief tied round his head, and
another round his neck, to staunch the blood flowing from two wounds,
his nose swelled to a monstrous size, from a splinter having passed
through it, disfigured and covered with gore, moved amid this terrific
scene the very genius of havoc and carnage. Approaching Perry, he told
him every officer in his division was killed. Others were given him,
but he soon returned with the same dismal tidings. Perry then told him
he must get along by himself, as he had no more to furnish him, and
the gallant man went back alone to his guns. Once only did the shadow
of any emotion pass over the countenance of this intrepid commander.
He had a brother on board, only twelve years old. The little fellow
who had had two balls pass through his hat, and been struck with
splinters, was still standing by the side of his brother, stunned by
the awful cannonading and carnage around him, when he suddenly fell.
For a moment Perry thought he too was gone, but he had only been
knocked down by a hammock, which a cannon ball had hurled against him.
[Illustration: Battle on Lake Erie.]
At length every gun was dismounted but one, still Perry fought with
that till at last it also was knocked from the carriage. Out of the
one hundred men with whom a few hours before he had gone into battle,
only eighteen stood up unwounded. Looking through the smoke he saw the
Niagara, apparently uncrippled, drifting out of the battle. Leaping
into a boat with his young brother, he said to his remaining officer,
"If a victory is to be gained, I will gain it," and standing erect,
told the sailors to give way with a will. The enemy observed the
movement, and immediately directed their fire upon the boat. Oars were
splintered in the rowers' hands by musket balls, and the men
themselves covered with spray from the round shot and grape, that
smote the water on every side. Passing swiftly through the iron storm
he reached the Niagara in safety, and as the survivors of the Lawrence
saw him go up the vessel's side, they gave a hearty cheer. Finding her
sound and whole, Perry backed his maintop sail, and flung out his
signal for close action. From vessel to vessel the answering signals
went up in the sunlight, and three cheers rang over the water. He then
gave his sails to the wind and bore steadily down on the centre of the
enemy's line. Reserving his fire as he advanced, he passed alone
through the hostile fleet, within close pistol range, wrapt in flame
as he swept on. Delivering his broadsides right and left, he spread
horror and death through the decks of the Detroit and Lady Prevost.
Rounding to as he passed the line, he laid his vessel close to two of
the enemy's ships, and poured in his rapid fire. The shrieks that rung
out from the Detroit were heard even above the deafening cannonade,
while the crew of the Lady Prevost, unable to stand the fire, ran
below, leaving their wounded, stunned, and bewildered commander alone
on deck, leaning his face on his hand, and gazing vacantly on the
passing ship. The other American vessels having come up, the action at
once became general. To the spectators from the shore the scene at
this moment was indescribably thrilling. Far out on the calm water lay
a white cloud, from out whose tortured bosom broke incessant flashes
and thunder claps--the loud echoes rolling heavily away over the deep,
and dying amid the silence and solitude of the forest.
An action so close and murderous could not last long, and it was soon
apparent that victory inclined to the Americans, for while the enemy's
fire sensibly slackened, the signal for close action was still flying
from the Niagara, and from every American vessel the answering signal
floated proudly in the wind. In fifteen minutes from the time the
first signal was made the battle was over. A white handkerchief waved
from the taffrail of the Queen Charlotte announced the surrender. The
firing ceased; the smoke slowly cleared away, revealing the two fleets
commingled, shattered, and torn, and strewed with dead. The loss on
each side was a hundred and thirty-five killed and wounded.
Perry having secured the prisoners, returned to the Lawrence, lying a
wreck in the distance, whither she had helplessly drifted. She had
struck her flag before he closed with the Niagara, but it was now
flying again. Not a word was spoken as he went over the vessel's side;
a silent grasp of the hand was the only sign of recognition, for the
deck around was covered with dismembered limbs, and brains, while the
bodies of twenty officers and men lay in ghastly groups before him.
As the sun went down over the still lake his last beams looked on a
mournful spectacle. Those ships stripped of their spars and canvass,
looked as if they had been swept by a hurricane, while desolation
covered their decks. At twilight the seamen who had fallen on board
the American fleet were committed to the deep, and the solemn burial
service of the Episcopal Church read over them.
The uproar of the day had ceased and deep silence rested on the two
squadrons, riding quietly at anchor, broken only by the stifled groans
of the wounded, that were echoed from ship to ship. As Perry sat that
night on the quarter-deck of the Lawrence, conversing with his few
remaining officers, while ever and anon the moans of his brave
comrades below were borne to his ear, he was solemn and subdued. The
exciting scene through which he had safely passed--the heavy load
taken from his heart--the reflection that his own life had been
spared, and the consciousness that his little brother was slumbering
sweetly and unhurt in his hammock beside him, awakened emotions of
gratitude to God, and he gravely remarked, "I believe that my wife's
prayers have saved me."[40]
[Footnote 40: See Mackenzie's Life of Perry.]
It had been a proud day for him, and as he lay that night and thought
what a change a few hours had wrought in his fortunes, feelings of
exultation might well swell his bosom. Such unshaken composure--such
gallant bearing--stern resolution, and steadiness and tenacity of
purpose in a young man of twenty-seven, in his first battle, exhibit a
marvellous strength of character, and one wonders more at him than his
success.
It was a great victory, and as the news spread, bonfires,
illuminations, the firing of cannon and shouts of excited multitudes
announced the joy and exultation of the nation. The gallant bearing of
Perry--his daring passage in an open boat through the enemy's fire to
the Niagara--the motto on his flag--the manner in which he carried his
vessel alone through the enemy's line, and then closed in half pistol
shot--his laconic account of the victory in a letter to the Secretary
of the Navy, "WE HAVE MET THE ENEMY AND THEY ARE OURS"--furnished
endless themes for discussion and eulogy, and he suddenly found
himself in the front rank of heroes.
The day after the battle the funeral of the officers of the two fleets
took place. A little opening on the margin of the bay, a wild and
solitary spot, was selected as the place of interment. It was a
beautiful autumn day, not a breath of air ruffled the surface of the
lake or moved the still forest that fringed that lonely clearing. The
sun shone brightly down on the new-made graves, and not a sound
disturbed the sabbath stillness that rested on forest and lake. The
fallen officers, each in his appropriate uniform, were laid on
platforms made to receive them, and placed with their hands across
their breasts, in the barges. As these were rowed gently away the
boats fell in behind in long procession, and the whole swept slowly
and sadly towards the place of burial. The flags drooped mournfully in
the still air, the dirge to which the oars kept time rose and fell in
solemn strains over the water, while minute guns from the various
vessels blended their impressive harmony with the scene. The day
before had been one of strife and carnage, but those who had closed in
mortal hate, now mourned like a band of brothers for their fallen
leaders, and gathering together around the place of burial, gazed a
last farewell, and firing one volley over the nameless graves, turned
sadly away. There, in that wild spot, with the sullen waves to sing
their perpetual dirge, they slept the sleep of the brave. They had
fought gallantly, and it mattered not to them the victory or defeat,
for they had gone to that still land where human strifes are
forgotten, and the clangor of battle never comes.
This impressive scene occurred off the shore where the massacre of
Raisin was committed, and what a striking contrast does it present to
the day that succeeded the victory of Proctor. By his noble and
generous conduct Perry won the esteem and love of his enemies, while
Proctor by his unfeeling neglect and barbarity received the curse of
all honorable men. The name of one is linked to the spot where he
conquered, with blessings; that of the other with everlasting infamy
and disgrace.
Harrison, after this victory, collected his army of seven thousand
men, and concentrated them at Put-in Bay. Perry's fleet rode
triumphant on the lake, and he offered its service to Harrison. The
latter ordered the regiment of horse, one thousand strong, to proceed
by land to Detroit, while the rest of the army was embarked on board
the vessels and set sail for Malden. [Sidenote: Sept. 13.] Proctor
commanded at the latter place, and hearing of Barclay's defeat and
Harrison's advance, was seized with alarm, and dismantling and blowing
up the fort, and setting on fire the navy yard, barracks and store
houses, and taking with him all the horses and cattle, fled towards
the Thames. The Americans followed in swift and eager pursuit.
Governor Shelby, of Kentucky, though sixty-two years of age, was there
with his brave Kentuckians, a volunteer, shaking his white locks with
the merriest. Perry and Cass also accompanied the army, sharing in the
animation and eagerness of the men. Sending a detachment across the
river to drive out the hostile Indians from Detroit, Harrison, on the
30th, saw with relief the mounted column of Colonel Johnson winding
along the opposite bank, announcing its approach with the stirring
notes of the bugle. Resting one day to complete his preparations, he,
on the 2d of October, resumed the pursuit, and soon, abandoned guns
and shells, destroyed bridges, and houses and vessels on fire,
revealed the haste and rage of the enemy. Proctor, after reaching the
Thames, kept up the river, with the intention of striking the British
posts near the head of Lake Ontario. But Harrison pressed him so
closely, it soon became evident that a battle could not be avoided. On
the 5th, Colonel Johnson, with his mounted Kentuckians, marching two
or three miles in advance, came upon the retreating army drawn up in
order of battle, on the bank of the Thames near the Moravian
settlement. Proctor had taken an admirable position upon a dry strip
of land, flanked by the river on the left and a swamp on the right.
Here he placed his regulars, eight hundred strong, while Tecumseh with
his two thousand Indian allies occupied the eastern margin of the
swamp. Harrison, with his troops jaded out, encamped that night in
front of the enemy. [Sidenote: Oct. 4.] After dark Proctor and
Tecumseh reconnoitred together the American camp, when the latter
advised a night attack. This, Proctor objected to, and strongly urged
a retreat. The haughty savage spurned the proposition, and in the
morning the British general finding he could not escape an engagement,
resolved to give battle where he was. Thinking only of retreat he had
neglected to erect a breastwork or cut a ditch in front of his
position, which would have effectually prevented a cavalry attack. To
ensure the complete success of this blunder, he formed his troops in
open order, thus provoking a charge of horse. [Sidenote: Oct. 5.]
Colonel Johnson, at his earnest request, was allowed to open the
battle with his thousand mounted riflemen. But just as he was about to
order the charge, he discovered that the ground was too cramped to
admit of a rapid and orderly movement of the entire force, and he
therefore divided it into two columns, and putting his brother,
Lieutenant Colonel James Johnson, at the head of the one that was to
advance on the British, he led the other against the Indians. These
two battalions moved slowly forward for a short time parallel to each
other, the infantry following. The column advancing on the British
was checked at the first fire--the horses at the head of it recoiling.
Their riders, however, quickly recovered them, and sending the rowels
home, plunged with a yell of frenzy full on the British line. A few
saddles were emptied, but nothing could stop that astonishing charge.
Those fiery horsemen swept like a whirlwind through the panic-stricken
ranks, and then wheeling, delivered their fire. Nearly five hundred
rifles cracked at once, strewing the ground with men. It was a single
blow, and the battle was over in that part of the field. Scarcely a
minute had elapsed, and almost the entire British force was begging
for quarter. A charge of cavalry with rifles only, was probably a new
thing to those soldiers. Proctor, with forty men and some mounted
Indians, fled at the first onset. His carriage, private papers, even
his sword, were left behind, and goaded by terror he was soon lost in
the distance. He remembered the massacre at Raisin, and knew if those
enraged Kentuckians, whose brothers, fathers and sons he had given up
to the savage, once laid hands on him they would grant him short
shrift. Cruelty and cowardice are often joined together.
The other battalion not finding firm footing for the horses could not
charge, and Johnson seeing that his men were being rapidly picked off,
ordered them to dismount and take to the cover. Tecumseh led his men
gallantly forward, and for a few minutes the conflict was sharp and
bloody. Johnson was wounded in three places, yet stubbornly maintained
his ground. At length Tecumseh fell, when the savages with a loud
whoop, the "death halloo" of their leader, turned and fled. The death
of this remarkable chieftain was worth more than a whole hostile tribe
destroyed, and broke up forever the grand alliance of the Indians with
the British. Not more than twenty-five hundred American troops mingled
in the battle at all; of these but fifty were killed and wounded.
Among the latter was Colonel Johnson, who was borne from the field in
a blanket, with the blood running out at either end. Six hundred
prisoners were taken, a large quantity of stores, ammunition, etc.,
and six pieces of artillery, among which were three captured from the
British during the Revolution, and surrendered by General Hull at
Detroit. The news of this important victory coming so quick on that of
Perry's, filled the nation with increased confidence, and placed a
cheerful countenance once more on the war party. The cloud that had
hung so darkly over the land seemed lifting, and if Chauncey on Lake
Ontario, and Wilkinson on the St. Lawrence, would give equally good
accounts of themselves, the season would close with Canada within our
grasp.
CHAPTER XIII.
Wilkinson takes command of the northern army -- Plan of the
campaign -- Hampton entrusted with the 5th military district
and takes position at Plattsburg -- Quarrel between the two
Generals -- Hampton advances, against orders, into Canada;
is defeated -- Concentration of Wilkinson's army -- Moves
down the St. Lawrence -- Its picturesque aspect -- Harassed
by the enemy -- Battle of Chrystler's field -- Hampton
refuses to join him -- The expedition abandoned and the
armies retire to winter quarters -- Disappointment and
indignation of the war party, and gratification of the
Federalists -- Abandonment of Fort George and burning of
Newark -- Loss of Fort Niagara and burning of Buffalo and
the settlements along the river -- Retaliation -- Gloomy
close of the campaign.
[Sidenote: 1813.]
While Perry and Harrison were thus reclaiming our lost ground on Lake
Erie and in the north-west, Armstrong was preparing to carry out his
favorite plan of a descent on Kingston and Montreal. When he accepted
the post of Secretary of War, he transferred his department from
Washington to Sackett's Harbor, so that he might superintend in person
the progress of the campaign. In April previous, the United States had
been divided into nine military districts, that portion of New York
State north of the Highlands and Vermont, constituting the ninth.[41]
Although Wilkinson had superseded Dearborn, as commander-in-chief of
this district in July, he did not issue his first orders to the army
till the 23d of August. Three days after a council of war was held at
Sackett's Harbor, in which it was estimated that by the 20th of
September the army would consist of nine thousand men, exclusive of
militia. The garrisons at Forts George, Niagara, Oswego and
Burlington, were therefore ordered to rendezvous at Grenadier Island,
near Sackett's Harbor. General Wade Hampton, who had been recalled
from the fifth military district to the northern frontier, encamped
with his army, four thousand strong, at Plattsburg, on Lake Champlain.
The plan finally adopted by the Secretary was, to have Wilkinson drop
down the St. Lawrence, and without stopping to attack the English
posts on the river, form a junction with General Hampton, when the two
armies should march at once on Montreal. These two Generals were both
Revolutionary officers, and consequently too advanced in years to
carry such an expedition through with vigor and activity. Besides, a
hostile feeling separated them, rendering each jealous of the other's
command, which threatened to work the most serious mischief.
Armstrong, however, being the friend of both, thought by acting
himself as commander-in-chief, he could reconcile their differences,
sufficiently to insure harmony of action. Chauncey, in the mean time,
after an action with Yeo, in which both parties claimed the victory,
forced his adversary to take refuge in Burlington Bay. [Sidenote:
Sept. 28.] He then wrote to Wilkinson that the lake was clear of the
enemy, and reported himself ready to transport the troops down the St.
Lawrence.
[Footnote 41: Massachusetts and New Hampshire constituted the first;
Rhode Island and Connecticut the second; New York, south of the
Highlands, and a part of New Jersey, the third; the remaining section
of New Jersey, with Pennsylvania and Delaware, the fourth; Virginia,
south of the Rappahannock, the fifth; Georgia and the two Carolinas,
the sixth; Louisiana, Mississippi and Tennessee, the seventh;
Kentucky, Ohio, Indiana, Michigan, Illinois and Missouri, the eighth.
A tenth was erected during the summer, including Maryland, the
District of Columbia, and that portion of Virginia lying between the
Potomac and Rappahannock rivers.]
The greatest expectations were formed of this expedition. The people
knew nothing of the quarrel between Wilkinson and Hampton, and thought
only of the strength of their united force. The victories of Perry and
Harrison had restored confidence--the tide of misfortune had turned,
and when the junction of the two armies should take place, making in
all nearly twelve thousand men, the fate of Canada, they fondly
believed, would be sealed. No large British force was concentrated on
the frontier, while a garrison of but six hundred held Montreal. The
press, deeming Canada already won, had begun to defend its conquest.
The question was no longer, _how_ to take it, but to reconcile the
nation to its possession.
[Sidenote: Sept. 19.]
While Wilkinson was preparing to fulfill his part of the campaign,
Hampton made a bold push into Canada on his own responsibility.
Advancing from Plattsburg, he marched directly for St. John, but
finding water scarce for his draft cattle, owing to a severe drought,
he moved to the left, and next day arrived at Chateaugay Four Corners,
a few miles from the Canada line. Here he was overtaken by an order
from Armstrong, commanding him to remain where was, until the arrival
of Wilkinson. But jealous of his rival, and wishing to achieve a
victory in which the honor would not be divided, he resolved to take
upon himself the responsibility of advancing alone. Several
detachments of militia had augmented his force of four thousand, and
he deemed himself sufficiently strong to attack Prevost, who he was
told had only about two thousand ill assorted troops under him.
[Sidenote: Oct. 21.] He therefore gave orders to march, and cutting a
road for twenty-four miles through the wilderness, after five days
great toil, reached the British position. Ignorant of its weakness, he
dispatched Colonel Purdy at night by a circuitous route to gain the
enemy's flank and rear and assail his works, while he attacked them in
front. Bewildered by the darkness, and led astray by his guide,
Colonel Purdy wandered through the forest, entirely ignorant of the
whereabouts of the enemy or of his own. General Hampton, however,
supposing that he had succeeded in his attempt, ordered General Izard
to advance with the main body of the army, and as soon as firing was
heard in the rear to commence the attack in front. Izard marched up
his men and a skirmish ensued, when Colonel De Salaberry, the British
commander, who had but a handful of regulars under him, ordered the
bugles, which had been placed at some distance apart on purpose to
represent a large force, to sound the charge. The ruse succeeded
admirably, and a halt was ordered. The bugles brought up the lost
detachment of Purdy, but suddenly assailed by a concealed body of
militia, his command was thrown into disorder and broke and fled.
Disconcerted by the defeat of Purdy, Hampton ordered a retreat,
without making any attempt to carry the British intrenchments. A few
hundred Canadian militia, with a handful of regulars, stopped this
army of more than four thousand men with ten pieces of artillery, so
that it was forced, with a loss of but thirty men killed, wounded and
missing, to retreat twenty-four miles along the road it had cut with
so much labor through the forest. Hampton, defeated by the blasts of a
few bugles, took up his position again at the Four Corners, to wait
further news from Wilkinson's division.
[Illustration: Wilkinson Flotilla Amid the Thousand Isles.]
The latter having concentrated his troops at Grenadier Island,
embarked them again the same day that Hampton advanced, against
orders, towards Montreal. Three hundred boats covering the river for
miles, carried the infantry and artillery, while the cavalry, five
hundred strong, marched along the bank. Beaten about by storms,
drenched with rain, stranded on deceitful shoals, this grand fleet of
batteaux crept so slowly towards the entrance of the St. Lawrence,
that the army, dispirited and disgusted, railed on its commander and
the government alike. They were two weeks in reaching the river.
Wilkinson, who had been recalled from New Orleans, to take charge of
this expedition, was prostrated by the lake fever, which, added to the
infirmities of age, rendered him wholly unfit for the position he
occupied. General Lewis, his second in command, was also sick. The
season was already far advanced--the autumnal storms had set in
earlier than usual--everything conspired to ensure defeat; and around
this wreck of a commander, tossed an army, dispirited, disgusted, and
doomed to disgrace. General Brown led the advance of this army of
invasion, as it started for Montreal, a hundred and eighty miles
distant. Approaching French Creek, eighteen miles below Grenadier
Island, it was attacked by a fleet of boats from Kingston, but
repulsed them with little loss. The news of the invasion, however,
spreading, the British detachment at Kingston, reinforced by the
militia, followed the descending flotilla, harassing it whenever an
opportunity occurred. To a beholder the force seemed adequate to
secure the object contemplated, for the spectacle it presented was
grand and imposing. As the head of that vast fleet came winding around
the bend of the stream and swept out of view below, the long
procession of boats that streamed after seemed to be endless.
Scattered in picturesque groups amid the Thousand Isles, or assailed
with artillery from British forts--now swallowed up in the silent
forest that clothed the banks, and again slowly drifting past the
scattered settlements, or shooting the long and dangerous rapids, it
presented a strange and picturesque appearance. When it reached the
head of the long rapids at Hamilton, twenty miles below Ogdensburg,
Wilkinson ordered General Brown to advance by land and cover the
passage of the boats through the narrow defiles, where the enemy had
established block houses. In the mean time the cavalry had crossed
over to the Canadian side and with fifteen hundred men under General
Boyd, been despatched against the enemy, which was constantly
harassing his rear.
[Sidenote: Nov. 11.]
General Boyd, accompanied by Generals Swartwout and Covington as
volunteers, moved forward in three columns. Colonel Ripley advancing
with the 21st Regiment, drove the enemy's sharp shooters from the
woods, and emerged on an open space, called Chrystler's Field, and
directly in front of two English regiments. Notwithstanding the
disparity of numbers this gallant officer ordered a charge, which was
executed with such firmness that the two regiments retired. Rallying
and making a stand, they were again charged and driven back. General
Covington falling fiercely on the left flank, where the artillery was
posted, forced it to recoil. But at this critical moment, while
bravely leading on his men, he was shot through the body. His fall
disconcerted the brigade, and a shower of grape shot at the same
moment scourging it severely, it retired in confusion. This restored
the combat, and for more than two hours that open field was the scene
of successive and most gallant charges. The front of battle wavered to
and fro, and deeds of personal courage and daring were done that
showed that the troops and younger officers only needed a proper
commander, and they would soon give a report of themselves which would
change the aspect of affairs.
At length the British retired to their camp and the Americans
maintained their position on the shore, so that the flotilla passed
the Saut in safety. This action has never received the praise it
deserves--the disgraceful failure of the campaign having cast a shadow
upon it. The British, though inferior in numbers, had greatly the
advantage in having possession of a stone house in the midst of the
field, from which, as from a citadel, they could keep up a constant
fire, without being injured in return. The conflict was close and
murderous, and the American troops gave there a foretaste of Chippewa
and Lundy's Lane. Nearly one-fifth of the entire force engaged were
killed or wounded; a mortality never exhibited in a drawn battle
without most desperate fighting.
General Wilkinson, who lay sick in his boat, knew nothing of what was
transpiring, except by report. Brown's cannon thundering amid the
rapids below--the dropping fire in the rear of his flotilla, and the
incessant crash of artillery and rattle of musketry in the forest,
blended their echoes around him, augmenting the power of disease, and
increasing that nervous anxiety, which made him long to be away from
such turbulent scenes, amid occupations more befitting his age and
infirmities.
The army, however, still held its course for Montreal. Young Scott,
who had joined the expedition at Ogdensburg, was fifteen miles ahead,
clearing, with a detachment of less than eight hundred men, the river
banks as he went. Montreal was known to be feebly garrisoned, and
Wilkinson had no doubt it would fall an easy conquest. He therefore
sent forward to Hampton to join him at St. Regis, with provisions.
Hampton, in reply, said, that his men could bring no more provisions
than they wanted for their own use, and informed him, in short, that
he should not cooperate with him at all, but make the best of his way
back to Lake Champlain.
On receiving this astounding news, Wilkinson called a council of war,
which reprobated in strong terms the conduct of Hampton, and decided
that in consideration of his failure, and the lateness of the season,
the march should be suspended, and the army retire to winter quarters.
This was carried into effect, and Wilkinson repaired to French Mills,
on Salmon river, for the winter, and Hampton to Plattsburgh. Thus, for
months, an army of twelve thousand men had marched and manoeuvred on
the Canadian frontier without striking a single blow. Confidence in
the success of this campaign had been so great, that its disgraceful
issue fell like a sudden paralysis on the war party, and on the nation
generally. Like Hull's defeat, it was unredeemed by a single glimmer
of light. The mind had nothing to rest upon for momentary relief. The
failure was so complete and total, that the advocates of the war were
struck dumb, and Washington was wrapped in gloom. The Federalists, on
the contrary, were strengthened. Their prognostications had proved
true. The nation had concentrated its strength on Canada for two
years, and yet been unable to make the least impression. A Boston
paper that from the first had denounced the war, said, "Democracy has
rolled herself up in weeds, and laid down for its last wallowing in
the slough of disgrace."
Now lift ye saints your heads on high,
And shout, for your redemption's nigh.[42]
[Footnote 42: Vide Ingersoll.]
The Federalists knew their advantage and prepared to use it, for this
was not a lost battle that might in a few days be retrieved; it was a
lost campaign, and a whole winter must intervene before an opportunity
to redeem it could occur. In that time they hoped to make the
administration a hissing and a bye-word in the land. The war party
looked glum and sullen in view of the long and merciless scourging
which awaited it. Armstrong was loudly censured, while on Wilkinson
and Hampton it poured the whole vials of its wrath. Armstrong was
doubtless too much of a martinet, and could carry through a campaign
on paper much better than practically; still, the one he had proposed
was feasible, and ought to have succeeded. He could not be held
responsible for the insubordination of officers. He however committed
one great error. Aware of the hostile feeling that existed between
Wilkinson and Hampton, he should have remained on the spot and acted
as commander-in-chief, or else if his duties rendered his absence
imperative, accepted the resignation of Wilkinson. Old and sick as the
latter was, no commander could have been more inefficient than he,
while the enmity between him and Hampton was certain to end in
mischief. The junction of the two armies would not have prevented, but
on the contrary increased it. He knew, or ought to have known, they
would not act harmoniously together, and it required no prophet's
vision to foretell the fate of a divided army acting on the enemy's
territory. If he had remained to urge forward the expedition, and sent
home Hampton for disobeying his orders, and compelled the army to form
a junction with that of Wilkinson, no doubt Montreal would have
fallen. But knowing, as he did from the outset, that Hampton would
never harmonize with his enemy--to allow the success of the campaign
to depend on their concerted action, was committing a blunder for
which no apology can be made.
Wilkinson came in for more than his share of public abuse. Sickness
must always cover a multitude of sins. There are very few men whose
will is stronger than disease. The firmest are unstrung by it. Even
Cesar, when prostrated by fever, could say:
"Give me some drink, Titinius,
As a sick girl."
This is especially true of men advanced in years. Age tells heavily
enough on both physical and mental powers in an arduous campaign,
without the additional aid of fever. Wilkinson was perfectly aware of
this, and requested twice to be released from the command. Forced to
retain a position he felt unequal to, his conduct was necessarily
characterized by no vigor; and insubordination, disgraceful quarrels,
and duels, combined to make a sorry chapter in the history of the
expedition. It must be confessed, however, that for some of his
conduct, age and disease are but sorry excuses, and it is pretty
apparent he was in character wholly unfit for the enterprise he had
undertaken. For Hampton there is no apology. His disobedience of
orders in the first place should have been followed by his immediate
withdrawal from the army, while his refusal to do the very thing he
had been sent north to perform, was a crime next to treason. All the
forts we occupied on the frontier had been emptied of their garrisons,
and great expense incurred by the government to carry forward an
expedition, the chief feature in which was the junction and united
advance of the two armies. His resignation saved him from public
disgrace. The withdrawal of our troops from Lake Ontario and Niagara,
together with the suspension of hostilities on the St. Lawrence, was
followed by the capture of all the posts we had been two years in
taking.
When Scott obtained permission to join Wilkinson's army, he left Fort
George in the command of General McClure of the New York militia. The
fort had been put in a complete state of defence by Scott, and was
supposed able to repel any force that would be brought against it.
Vincent, who had abandoned its investment after Proctor's overthrow,
returned when he heard of Wilkinson's retreat. McClure, under the plea
that his militia had left him, and that those volunteers promised
could not be obtained, resolved to abandon the fort without risking a
battle.
[Sidenote: Dec. 10.]
He therefore dismantled it, and then in order to deprive the enemy of
shelter, set fire to the neighboring village of Newark and drove four
hundred women and children forth to the fierce blasts of a northern
winter. The English, who during this war rarely waited for an excuse
to resort to the barbarities of savage warfare, of course retaliated
with tenfold violence.
[Sidenote: Dec. 19.]
Nine days after, Fort Niagara was surprised by a party of British and
Indians, under the command of Colonel Murray, and sixty of the
garrison murdered in cold blood. The manner in which it was taken
created a strong suspicion of treachery somewhere. The British made no
secret of the premeditated attack, and the day before, General McClure
issued a proclamation to the inhabitants of Niagara, Genesee and
Chatauque counties, calling on them to rally to the defence of their
homes and country. To this was appended a postscript, stating, "since
the above was prepared, I have received intelligence from a credible
inhabitant from Canada (who has just escaped from thence) that the
enemy are concentrating all their forces and boats at Fort George, and
have fixed _upon to-morrow night for attacking Fort Niagara_--and
should they succeed they will lay waste our whole frontier." On that
very "morrow night" the attack _did_ take place, and yet the
Commandant, Captain Leonard, was absent, having left during the
evening, without entrusting the command of the post to another. The
picquets were taken by surprise, and the enemy entered by the main
gate, which, it is said, was found open.
It seemed at this time as if the government had carefully selected the
most inefficient men in the nation to command on our frontier, in
order to show what a large stock we had on hand, before those more
capable and deserving could be given a place. General McClure not only
fixed the _time_ of the attack, but declared that the fall of the fort
would be followed by the desolation of the whole frontier, (in both of
which prognostications he proved an admirable prophet,) yet not a man
was sent to reinforce it, no orders were issued to its commander, and
no precautions taken. Had Scott been in his place, fort Niagara would
have enclosed him that night--every door would have been bolted and
barred, and the 27 guns it contained rained death on the assailants
as they approached. McClure was right, the enemy did "lay waste the
frontier." Marching on Lewistown, they burned it to the ground.
Setting fire to every farm-house as they advanced, massacring many of
the inhabitants, and mutilating the corpses, they burned Youngstown,
the Tuscarora Indian village, and Manchester, kindling the whole
frontier into a glow from the light of blazing dwellings. Eleven days
after another party crossed at Grand Island, and burned Black Rock and
Buffalo, leaving scarcely a house standing in the latter place.
[Sidenote: Dec. 30.] At Black Rock they burned three of the schooners
belonging to Perry's gallant fleet. Cruel and merciless as was this
raid, it had a justification, at least in the burning of houses, on
the principles of war. The destruction of Newark was a barbarous act,
and in no way borne out by the orders of government, which authorized
it only on the ground that the defence of the fort rendered it
necessary. To fire a town, turning forth houseless and homeless women
and children, because an attacking enemy might employ it as a shelter
from which to make their approaches: and destroy it on the plea that
it affords merely the shelter of a bivouack, after the position is
abandoned, are totally different acts, nor can they be made similar by
any sophistry. These outrages inflamed the passions of the inhabitants
occupying the frontier to the highest degree. No epithets were too
harsh when speaking of each other, and no retaliation seemed too
severe. This feeling of hostility was still farther exasperated by the
treatment of prisoners of war. The imprisoning of twenty Irishmen,
taken at Queenstown the year before, to be tried as traitors, was no
doubt a stroke of policy on the part of England, and designed to deter
adopted citizens from enlisting in the army. It was announcing
beforehand, that all English, Scotch and Irish taken in battle would
not be regarded as ordinary prisoners of war, but as her own subjects
caught in the act of revolt. Our government could not in any way
recognize this arrogant claim, and twenty-three English prisoners were
placed in close confinement, with the distinct pledge of the
government that they should meet the fate pronounced on the Irishmen.
Prevost, acting under orders, immediately shut up twice the number of
American officers. Madison retorted by imprisoning an equal number of
English officers. Prevost then placed in confinement all the prisoners
of war; Madison did the same. The treatment of these prisoners was
alike only in form, for while we showed all the leniency consistent
with obedience to orders, the English, for the most part, were
haughty, contemptuous, and insulting.
The Creek war commenced this year, and though the Indians were not
subdued, no defeat had sullied the American arms. This, together with
the capture of Detroit, summed up the amount of our successes on land
for the year. York and Fort George were lost to us, while Fort
Niagara, standing on our soil, was in the hands of the enemy. Such,
the administration was compelled to exhibit as the results
accomplished by a regular army of thirty-four thousand men, _six
thousand volunteers_, and the occasional employment of _thirty
thousand militia_. This report following on the heels of the disasters
of the previous year, would have completely broken down the government
but for the exasperated state of the nation, produced by the cruelties
and atrocities of the English. Tenacity of purpose has ever been
characteristic of the nation, and ever will be; disasters make us
sullen and gloomy, but never incline us to submission. Armies may be
beaten, but the nation, never, is a sentiment so grounded and fixed in
the national heart that to question its truth excites only amazement.
To deepen still more the shadows that had closed upon us, Bonaparte,
at this time, was evidently in his last struggle. Although battling
bravely for his throne, and exhibiting in more brilliant light than
ever the splendor of his marvellous genius, yet the "star" that had
led him on was already touching the horizon; and soon as his vast
power should yield and fall, England would give us her undivided
attention, and then our little navy, our pride and solace, would be
swept from the seas.
CHAPTER XIV.
1813--1814.
Winter operations -- Decatur challenges Commodore Hardy to
meet the United States and Macedonian with two of his
frigates -- Wilkinson's second invasion of Canada -- Battle
of la Cole Mill -- Holmes' expedition into Canada --
Romantic character of our border warfare -- Inroad of the
British marines to Saybrook and Brockaway's Ferry.
During the autumn and winter of this year, while Congress was shaken
with conflicting parties, and deeper gloom and embarrassments were
gathering round the administration, reports of conflicts ever and anon
came from the bosom of our northern and southern wildernesses.
Wilkinson was endeavoring to redeem his failures along the St.
Lawrence, and Jackson was leading his gallant little band into the
fastnesses of the Creek nation. Most of the national vessels were
blockaded in our harbors and rivers, but still our bold little
privateers were scouring the ocean in every direction. At this time,
too, a single war vessel might be seen struggling in tempestuous seas
off the stormy cape, on her way to the Pacific ocean to finish in
disaster the most remarkable cruise found in our naval annals.
Decatur, with his squadron, lay blockaded at New London, and it was
said that every attempt to get to sea was thwarted by some disaffected
persons, who burned blue lights at the mouth of the river to give
information of his movements to the enemy. He wrote a letter to Mr.
Jones, the Secretary of the Navy, on the subject, and a proposition
was made in Congress to have it investigated, but it was dismissed as
of trivial importance. Irritated at his inactivity, he challenged the
Endymion and Statira to meet the United States and Macedonian in
single combat, offering to reduce his force till they said it equalled
their own. To this Commodore Hardy at first gave his consent, but
afterwards withdrew it. If the challenge had been accepted, there is
little doubt but that the Chesapeake would have been signally avenged.
At one time Decatur was so confident of a fight, that he addressed his
crew on the subject.
Wilkinson soon after his retirement to winter quarters at French
Mills, on Salmon river, resigned his command to General Izard, and
proceeded to Washington to recruit his health. He here planned a
winter campaign which for hardihood and boldness exceeded all his
previous demonstrations. He proposed to pierce by different routes
with two columns, each two thousand strong, to the St. Pierre, and
sweeping the defenceless cantonments as he advanced, stop and occupy
them or turn with sudden and resistless energy against the Isle Aux
Noix, or go quietly back to his winter quarters again. At the same
time, four thousand men were to cross the St. Lawrence, take Cornwall,
fortify and hold it so as to destroy the communication between the two
provinces. Nay, he proposed at one time to barrack in Kingston. The
secretary, however, distrusting the feasibility of these plans,
ordered him to fall back to Plattsburgh with his troops. Brown, in the
mean time, was directed to take two thousand men and proceed to
Sackett's Harbor, for the defence of our flotilla there, while young
Scott was stationed at Buffalo.
[Sidenote: 1813.]
Matters remained in this state till March, when Wilkinson resolved to
erect a battery at Rouse's Point, and thus keep the enemy from Lake
Champlain. The latter, penetrating the design, concentrated a force
two thousand strong at La Cole Mill, three miles below the point. The
early breaking up of the ice, however, had rendered the project
impracticable. Still, Wilkinson resolved to attack La Cole Mill,
though it does not appear what use he designed to make of the victory
when gained. With four thousand men, and artillery sufficiently heavy,
it was supposed, to demolish the walls of the mill, he set forth. The
main road was blockaded for miles with trees that had been felled
across it. He therefore, after arriving at Odletown, was compelled to
take a narrow winding path only wide enough for a single sleigh, and
which for three miles crept through a dense wood. With a guide who had
been forced into the service to show the way, and who marched on foot
between two dragoons, the advance, led by Major Forsyth and Colonel
Clarke, slowly entered the wintry forest. An eighteen pounder broke
down before it reached the woods, a twelve pounder lagged on the way,
so as to be useless. A twelve pounder and a howitzer were got forward
with great labor, for the wheels sunk into the yielding snow and mud,
and thumped at almost every revolution against the trees that hemmed
in the narrow path. The column was necessarily closely packed, and as
it waded through the snow the fire of the concealed enemy soon opened
upon it. But the two guns, what with lifting and pushing, lumbered
slowly forward, and at length were placed in a position in a clearing
in sight of the mill, which proved to be garrisoned by only two
hundred men. The snow was a foot deep, and the panting troops, though
full of courage and confidence, were brought with difficulty forward.
The woods were so thick that the mill was hidden till directly upon
it, and the only open space where the cannon could play unobstructed
on the walls was so near, that the sharp shooters within the building
could pick off the gunners with fatal rapidity. The first shots told
heavily on the building, but in a short time, of the three officers
who commanded the guns, two were severely wounded, and of the twenty
men who served them, fourteen were dead or disabled. The troops as
they came up were posted so as to prevent the escape of the garrison.
Sortie after sortie was made to take the guns, but always repulsed by
the American troops, who fought gallantly under their intrepid
leaders. Larribee who commanded the howitzer was shot through the
heart, and Macpherson who had charge of the twelve pounder, though cut
by a bullet under the chin, maintained his ground till prostrated by a
frightful wound in the hip. The infantry was of no avail, except to
repel sorties, and stood grouped in the forest waiting till the enemy,
forced by the cannonade to retreat, should uncover themselves. But it
was impossible to serve the guns under the concentrated fire of two
hundred muskets and rifles in such close range. Men dropped in the act
of loading; in one case, after the piece was charged, but a single man
remained to fire it. A portion of the garrison seeing it so
unprotected, rushed forth to seize it. The single man, however, stood
his ground, and as the enemy came, fired his piece. At the same time
the troops in the wood poured in a volley. When the smoke cleared away
but a single man was left standing. The whole column had been shot
down. At length a hundred and forty or fifty having fallen and night
coming on the troops were withdrawn. It was resolved to renew the
attack next morning, but a rain storm set in during the night, turning
the snow into a half fluid mass, and rendering a second approach
impracticable. The chilled and tired army was therefore withdrawn, and
Wilkinson ended at once his invasion of Canada and his military
career. He retired from the army, and younger and more energetic men
were appointed over it, who should lead it to victory. [Sidenote:
1814.] On the 24th of January, Brigadier-Generals Brown and Izard were
promoted to the rank of Major-Generals, and later in the spring took
command on our northern frontier.
While these unsuccessful plans were maturing on the St. Lawrence,
Colonel Butler, commanding at Detroit, dispatched Captain Holmes with
a small detachment into Canada to destroy Fort Talbot, a hundred miles
inland, and what ever other "military establishments might fall in his
way." [Sidenote: Feb. 24.] He had less than two hundred men and but
two cannon. Pushing his way through the forests he found the road when
he reached Point Au Plat, so filled with fallen trees and brushwood
that his guns could not be carried forward. Leaving them therefore
behind, he kept on until he ascertained that his approach was
expected. Seeing that all hopes of a surprise must be abandoned, he
changed his course and marched rapidly against Fort Delaware, on the
Thames, occupied by the British. But when he arrived within fifteen
miles of the place he was informed that his attack was expected, and
that ample preparations had been made to meet it. He immediately fell
back behind Twenty Mile Creek, where he had scarcely taken position,
before the rangers left to protect his rear emerged on a run from the
woods that covered the opposite bank, pushed fiercely by the head of
the enemy's column. He immediately strengthened his position by every
means in his power, and on the following morning was ready for an
attack. Only a small body of the enemy, however, appeared at day
break, and soon after retreated. Holmes at first suspected this to be
a ruse to draw him from his position, but ascertaining from a
reconnaissance that not more than sixty or seventy men composed the
force, he started in pursuit. His first conjecture, however, proved
true, for after marching a few miles he came upon his adversary, well
posted, and expecting him. His great anxiety was now to get back to
his position, and at the same time practice the very deception which
had beguiled him from it. He succeeded admirably, and the British
imagining his retreat to be a hasty and disorderly flight pressed
after, and on coming to the creek resolved at once to attack him.
Crossing the stream they ascended the opposite bank boldly, and
without opposition, till within twenty yards of the top, when they
were met by such a sudden and destructive volley that they broke and
fled. Hiding behind trees they then kept up a harmless fire till
night, when under cover of darkness they effected their retreat with
the loss of nearly a hundred men, or one-third of their force, while
some half dozen killed and wounded covered the loss of the Americans.
This half partisan, half regular warfare, in the midst of our vast
forests, combined much of the picturesque and marvellous. There was
not the pomp of vast armies, nor the splendor of a great battle, but
courage, skill and endurance were required, sufficient to make able
commanders and veteran soldiers. The long and tedious march of a
hundred miles through the snow-filled forest--the solitary block-house
with its small garrison, situated in a lonely clearing, around which
the leafless trees creaked and groaned in the northern blasts--the
bivouack fire gleaming red through the driving storm--the paths of
wild beasts crossing the wilderness in every direction, their cries of
hunger mingling with the muffled sound of half frozen torrents--the
war-cry of the savage and the crack of his rifle at still midnight,
waking up the chilled sleepers to battle and to death--the sudden
onset and the bloody hand-to-hand fight, made up the experience and
history of our border warfare. Far away from the haunts of
civilization, men struggled for the control of an imaginary line, and
many gallant and able officers, fell ingloriously by some Indian
marksman. At far intervals, stretching from the St. Lawrence to
Mackinaw, the faintly heard thunder of cannon amid those vast
solitudes, announced that two nations were battling for untrodden
forest tracts and undisturbed sheets of water. Those tracts are now
covered with towns and cities, and those sheets of water freighted
with commerce. Then it was announced as a great miracle of speed, that
a steamboat made four miles an hour in passing up the Ohio--now the
northern lakes are ploughed with steamers, going at the rate of
eighteen or twenty miles an hour, and wrapped round with railroads,
over which cars are thundering with a velocity that annihilates
distance, and brings into one neighborhood the remotest States.
[Sidenote: April 8.]
An unsuccessful attempt on the part of the British to destroy the
American vessels just launched at Vergennes, and which were to compose
Macdonough's fleet, and a bold inroad of the English marines from the
blockading squadron off New London, in which twenty American vessels
were burned, the men pitching quoits, drinking and playing ball during
the conflagration, till night, when they quietly floated down the
river, constituted the other chief movements that terminated in the
early spring.
CHAPTER XIV.
THIRTEENTH CONGRESS. MAY 27, 1813.
Democratic gain in Congress -- Spirit in which the two
parties met -- Russian mediation offered and accepted, and
commerce opened -- State of the Treasury -- Debate
respecting a reporter's seat -- Direct tax -- Webster's
resolutions -- Governor Chittenden -- Strange conduct of
parties in New Hampshire -- The embargo -- England proposes
peace -- Commissioners appointed -- Army bill -- Webster's
speech upon it -- Sketch of him -- The loan bill -- Defended
by Mr. Eppes -- Sketch of Mr. Pickering, with his speech --
Sketch of John Forsyth, and his speech -- Calhoun --
Grosvenor -- Bill for the support of military establishments
-- Speech of Artemus Ward -- Resolutions of Otis in the
Massachusetts Senate -- Repeal of the embargo -- Calhoun and
Webster -- Strange reversal of their positions -- Strength
of our navy and army.
Soon after the capture of York the Thirteenth Congress assembled. By
the new apportionment made the year previous, a hundred and eighty-two
members had been added to the House of Representatives. One remarkable
man, Randolph, had disappeared from the arena, having been defeated by
Mr. Eppes, son-in-law of Jefferson. As the two great parties came
together they surveyed each other's strength--prepared to close in
combat with the same determination and hostile feeling that had marked
the proceedings of the last session of the Twelfth Congress. In the
accession of members the Federalists had made important gains, chiefly
from New York, so that the House stood one hundred and twelve for the
war and sixty-eight against it, and the Senate twenty-seven to nine.
In the latter, however, the party lines were not so strongly drawn,
and on many questions the Democrats had much less majorities than
their nominal superiority would indicate. Among the new members were
Pickering, who had succeeded Quincey, and Cyrus King, from
Massachusetts, and Daniel Webster, from New Hampshire, Federalists.
Forsyth, of Georgia, M'Lean, of Ohio, Taylor, of New York, and
Findley, of Pennsylvania, were Democrats. Mr. Clay was elected speaker
on the first ballot. The President's message was short, and related
wholly to the war. He informed Congress that an offer of mediation had
been made by the Emperor Alexander, of Russia, on the 8th of March
previous--and accepted, and that Mr. Gallatin, Mr. Bayard, and Mr.
Adams, had been appointed Commissioners under it, to negotiate a peace
with England, and also a treaty with Russia. He expressed the belief
that England would accept the mediation, whether it resulted in any
settlement of difficulties or not.
The receipts into the Treasury during the six months, ending the last
day of March, including sums received on account of Treasury notes and
loans, amounted to $15,412,000, the expenditures to $15,920,000. A
balance, however, was in the Treasury previously, so that there
remained $1,857,000 unexpended. Of the loan of sixteen millions,
authorized in February, one million had been paid in, and formed
[Sidenote: Feb. 18.] part of the receipts mentioned, so that the
remaining $15,000,000, together with $5,000,000 of Treasury notes, and
$9,700,000, the sum expected from customs, sales of public lands,
making in all $29,000,000, constituted the provision for the remaining
nine months of the current year. To avoid the necessity of loans,
which were made at rates injurious to the government, and to give a
more permanent basis to the revenue, additional taxes were
recommended.
The first act of Congress was the passage of a resolution, introduced
by Clay, to refer that part of the message which related to the
barbarous manner in which the enemy waged war to a select committee,
of which Mr. Macon, of Georgia, was chairman. Mr. Eppes was made
chairman of that of Ways and Means, and Calhoun of that on Foreign
Affairs. The gentlemen constituting the latter were Calhoun, Grundy,
Desha, Jackson of Virginia, Ingersoll, Fisk of New York, and Webster.
The extreme sensitiveness of the two parties, and the readiness with
which they seized upon the most trifling matter as a bone of
contention, were strikingly exhibited in some of the earliest
proceedings of Congress. The reporter of the Federal Republican, the
paper which had been mobbed by the Democrats at Baltimore, and was now
published in Georgetown, presented a petition, asking a place to be
assigned him, like that of the other reporters, and stating that the
Speaker had refused to give him one. The implication was, that Mr.
Clay had denied him a place on account of his politics. Mr. Clay said
this was not so, that the true reason was, he had no place to give;
all of those furnished by the House being pre-occupied. This
statement, however, could not satisfy the members, and it was proposed
to make an extra provision for the gentleman. Calhoun was opposed to
the admission of any reporters. Almost the entire day was occupied in
discussing this trifling affair, when such momentous questions asked
the attention of Congress. It even adjourned without coming to a
decision, and not until next day was it disposed of, by rejecting the
prayer of the petitioner.
[Sidenote: June 14.]
Mr. Eppes, from the Committee of Ways and Means, made a report, in
which, after showing that the expenditures for the next year, 1814,
would exceed the revenue by $5,600,000, twelve bills were offered, one
for direct taxation, another establishing the office of Commissioner
of the Revenue, and others laying duties on imported salt, on licenses
to retailers of liquors, on foreign merchandise, carriages, distillers
of liquors, on auction sales of foreign goods and vessels, on sugars
refined in the United States, on bank notes, notes of hand and certain
foreign bills of exchange, and on foreign tonnage.
Mr. Webster then rose and delivered his first speech in the House,
introduced by four resolutions, the purport of which were to inquire
into the time, manner, &c., with the attending circumstances, in which
the document, asserted to be a repeal of the Berlin and Milan decrees,
was communicated to this government. Although these resolutions had
their origin in Federal hostility, and were designed to sustain the
old charge against the administration, of being under French
influence, because it was well aware those decrees had not been
repealed when it declared war against England, yet Webster carefully
avoided implying it in his speech. He felt bound to offer these
resolutions in justice to his constituents. A heated discussion
followed their introduction, but young Webster conducted himself with
great prudence and caution. At home he had made inflammable speeches
against the war, but after he got out of the atmosphere of
Massachusetts, and came in contact with such ardent young patriots as
Clay and Calhoun, his sympathies, doubtless, were moved, and his
patriotism received an impulse which went far to neutralize the views
of Federalism, with which he had been inoculated. The political
opponents of that war having been successively thrown overboard by
the nation since its termination, much effort seems to have been made
by the friends of Webster to omit entirely this portion of his life,
but I have no doubt were it truly and honorably written, it would
exalt his character and enhance his fame. Coming from the very furnace
of Federalism--educated under the influence of men whose opinions he
had been taught to venerate, and who, throwing aside their party hate,
were the wisest statesmen of the land, sent to Washington on purpose
to represent their views, it seems unaccountable that he, a young
aspirant for fame, did not at once plunge into the arena and win
reputation by crossing swords with such men as Clay and Calhoun.
Standing for the first time on the field where political fame was to
be won, and goaded on by attacks upon principles he had been taught to
venerate, he nevertheless carefully stood aloof, and shortly after
retired entirely on leave of absence. How is this strange conduct to
be accounted for in one who ever after never refused to close like a
lion with his foes? With his powers he would soon have been a leader
of the opposition, and yet this soul, full of deep thought and
slumbering fire, looked apparently cold and indifferent on the strife
that was rending the nation asunder. Did not this conduct grow out of
a sense of duty and of patriotism? He could not do less, as a
representative of Federalism, than offer resolutions of inquiry, and
without turning traitor to his constituents, he could not do more for
the administration. Did not that judgment, on whose decisions the
nation afterwards so implicitly relied, tell him even then that his
country was right and his teachers wrong on the great question of war
or no war, and did not that grand heart, which heaved like the
swelling sea when he spoke of the glorious Union, even then revolt at
the disloyal attitude of New England? If this be not true, then his
conduct is wholly inexplicable and contradictory to his after life.
The first session of the Thirteenth Congress continued till August 2d,
when it adjourned to December. In the mean time, a direct tax,
amounting to $3,000,000, apportioned to the eighteen different states,
was laid. A bounty of $25 was voted to privateers for every prisoner
taken, and heavy penalties were placed on the use of British licenses,
and provisions made to raise ten companies for the defence of the sea
coast. The disasters of our northern army, during this autumn,
increased the boldness of the Federalists, and a paper of Boston
openly advocated the proposition for each state to take care of
itself, fight its own battles, and make its own terms. Governor
Chittenden of Vermont, attempted to recall a brigade of militia,
appointed to garrison Burlington, during Hampton's march into Canada,
on the ground it had been unconstitutionally ordered out. The
commander and a part of the brigade refused, when the former was put
under arrest. The Legislature of New Hampshire, in order to get rid of
the democratic judges, appointed by Langdon and Plumer, abolished all
the courts in the state, and constructed an entirely new system, with
new judges. To this high-handed measure the democratic judges refused
to submit, and held court sessions as formerly, side by side with the
new judges. In those counties where the sheriff was democratic, their
decision was sustained by this functionary, confusing and confounding
every thing. By such measures, party spirit was inflamed to the
highest pitch, dividing friends and families and societies. It became
a frenzy, a madness, obliterating, in many parts of New England, all
traces of former urbanity, justice, affection and courtesy. The
appellation of Democrat and Federalist, applied to one or the other,
converted him, in his opponent's eye, into a monster. The charge of
highway robbery, rape or murder would not have been more instantaneous
and direful in its effect. The Boston papers advocated the most
monstrous doctrines, creating great anxiety and solicitude at
Washington. But soon as the New England line was crossed, passing west
and south, the feeling changed. To go from these fierce, debasing
broils, into the harmonious feeling in favor of the war, was like
passing from the mad struggles of a vessel amid the breakers to a
quiet ship moving steadily on her way. The governors of the several
states in their proclamations and messages firmly upheld the
administration, and the legislatures pledged their support.
In the midst of such excitements, oppressed by the failure of
Wilkinson's campaign, and dreading the use which the Federalists would
make of it, Congress, according to adjournment, reassembled.
[Sidenote: Dec. 6.] Mr. Eppes was still continued chairman of the
Committee of Ways and Means. Among the first measures was the
introduction of an embargo act. Madison, in a special message,
strongly recommended it, on the ground that under the present
non-importation act the enemy on our shores and at a distance were
constantly furnished with the supplies they needed. An illegal traffic
was also carried on with foreign ports, not only exporting forbidden
articles, but importing British manufactures. To stop this illicit
trade in future, an act was passed in secret session, laying an
embargo on all the ports of the Union. To prevent evasion, it was
guarded by the most stringent provisions and heavy penalties, so that
the coasting trade suffered severely. Fishermen were compelled to give
bonds that they would not violate it, before they were allowed to
leave port. That portion of it, however, which related to the
importation of woolen, cotton, and spirits, was rejected by the House,
as that prohibiting the release of goods on bonds was rejected by the
Senate.
Soon after, a great excitement was caused in the country by a rumor
that a British schooner, the Bramble, had arrived in Annapolis,
bearing a flag of truce, and despatches of a peaceful nature to our
government. [Sidenote: Jan. 7.] Seven days after, the President
transmitted a message to Congress, informing it of a proposition on
the part of the English government, to have commissioners appointed to
negotiate a peace. This announcement was the signal for the Federalist
papers to indulge in laudations of Great Britain's generosity and
magnanimity. She had taken the first amicable steps, and that, too,
when she was in a condition, owing to Napoleon's sinking fortunes, to
direct her entire power against us. The same vessel brought the news
of the disasters of Leipsic. There was, on the other hand, much
distrust among the Democrats, because the offer of the Russian
mediation had been coldly rejected three several times.
John Quincy Adams, and Henry Clay, and Jonathan Russel and Bayard who
were already abroad, were appointed Commissioners, to whom Gallatin
was soon after added, to proceed to Gottenberg. Russel, after the
negotiations closed, was to remain as minister to Sweden. [Sidenote:
Jan. 19.] Mr. Clay, in an eloquent address, resigned his station as
Speaker of the House, and Mr. Cheves was elected in his place.
[Sidenote: Dec.] One of the most exciting debates during this session
of Congress arose on the introduction of resolutions by the editor of
the Federal Republican, demanding an inquiry respecting a letter
written by Turreau, in 1809, then Minister from France, to the
Secretary of State, said to be withdrawn from the files. The
disappearance of the letter was proof positive that its contents
committed, in some way, the administration. A vehement debate of three
days duration followed. Endless changes were rung on the old charge of
French influence. At length the question was taken, and the
resolutions voted down, and a simple call on the President for
information substituted. This shell which had been so suddenly thrown
into the House, threatening in its explosion to shatter the war party
to fragments, proved a very harmless thing. Turreau, it eventually
turned out, had written a letter of complaint to the Secretary of
State, so overbearing in its tone, so absurd in its complaints, and so
undiplomatic in every respect, that he was requested to withdraw it,
which was done. In such a sensitive and excited state was party
feeling at this time, that the most trivial matters became distorted
and magnified into extraordinary proportions.
The army bill, providing for the filling of the ranks, the enlistment
of men to serve for five years instead of twelve months, and the
re-enlistment of those whose term of service had expired; and another
bill authorizing a new loan of $25,000,000, was the bugle blast
summoning the combatants to battle. Mr. Webster was for the first time
roused. The army bill was evidently designed to provide for a third
campaign against Canada. From the first, almost the entire military
force of the nation had been employed in these futile invasions. The
successive failures, especially the last, gave the opposition great
vantage ground in declaring against the scheme altogether. They
condemned it not only as an aggressive war, and therefore
indefensible, but declared the acquisition of that country worse than
worthless if obtained. The whole project was not only wrong in
principle, but would be evil in its results, if successful.
The clause extending the term of enlistment, and authorizing the
raising of new regiments, making the money bounty $124--fifty of it to
be paid on an enrollment, fifty on mustering, and the remainder at the
close of the war, if living, and if not to go to his heirs, was
assailed with vehement opposition. [Sidenote: Jan. 3, 1814.] Mr.
Webster, who had been cut short in an attack on the administration by
the Speaker, on the ground that no question was before the house, now
rose to speak. Carefully avoiding the asperity which distinguished
his colleagues, he levelled all his force against the embargo act, and
the conquest of Canada. [Sidenote: Jan. 10.] The former he denounced
unjust and unequal in its bearing, and ruinous in its consequences. He
called on the administration to remove it at once, as the first step
towards the acquirement of a just position. He then denounced the
Canadian war, to prosecute which this extraordinary bill was
introduced, whose provisions if carried out would swell the regular
army to sixty-six thousand troops, to say nothing of the power
conferred on the President for calling out the militia for six months
instead of three. Let us, he said, have only force enough on our
frontier to protect it from invasion--let the slaughter of our
yeomanry cease, and the fires along our northern boundary be
extinguished. Already the war had cost nearly half as much as the
entire struggle for independence; and said he, in conclusion, if war
must be, "apply your revenue to the augmentation of your navy. That
navy, in turn, may protect your commerce. Let it no longer be said
that not one ship of force built by your hands since the war, floats
on the ocean. Turn the current of your efforts into the channel which
national sentiment has already worn broad and deep to receive it. A
naval force competent to defend your coast against considerable
armaments, to convoy your trade, and perhaps raise the blockade of
your rivers, is not a chimera. It may be realized. If, then, the war
must continue, go to the ocean. If you are seriously contending for
maritime rights, go to the theatre where alone those rights can be
defended. Thither every indication of your fortune points you. There
the united wishes and exertions of the nation will go with you. Even
our party divisions, acrimonious as they are, cease at the water's
edge. They are lost in attachment to national character, on that
element where that character is made respectable. In protecting naval
interests by naval means, you will arm yourselves with the whole power
of national sentiment, and may command the whole abundance of national
resources. In time you may enable yourselves to redress injuries in
the place where they may be offered, and if need be, to accompany your
own flag throughout the world with the protection of your own cannon."
This speech produced a marked impression on the house. Succeeding as
it did, the resolutions of the Legislature of Massachusetts, refusing
to compliment our naval commanders for their victories, on the ground
that encouragement would be given to the war, it looked like a change
in that quarter. The war was not denounced as it had ever been by the
Federalist leaders--he quarrelled only with the mode of carrying it
on. Nay, it implied that we had wrongs to redress at sea, and thither
our force should be directed. The policy proposed in this speech
should doubtless have been adopted at the commencement of the war, and
might have been wise as late as 1814, but Webster did not propose it
for the purpose of having it acted upon. This fine peroration was
simply a safety-valve to his patriotism. He dared not--he could not
uphold the war, or put his shoulders to any measures designed to carry
it on with vigor. He represented a State opposed to it in principle,
not in mode. Still, the language he used was so different from the
other leading Federalists, that the Democrats, on the whole, did not
wish to complain. Webster at this time was but thirty-one years of
age, and little known except in his own vicinity. This speech,
however, delivered with the fervor and eloquence which distinguished
him, gave clear indications of his future greatness. Though a young
man, he exhibited none of the excitement and eagerness of youth. Calm,
composed, he uttered his thoughts in those ponderous sentences which
ever after characterized his public addresses. Large, well made, his
jet black hair parted from a forehead that lay like a marble slab
above the deep and cavernous eyes; there was a solemnity, and at times
almost a gloom in that extraordinary face, that awakened the interest
of the beholder. There was power in his very glance, and the close
compressed lip revealed a stern and unyielding character. Even at
this age he looked like one apart from his fellows, with inward
communings to which no one was admitted. When excited in debate, that
sombre and solemn face absolutely blazed with fire, and his voice,
which before had sounded sharp and unpleasant, rung like a clarion
through the house. His sentences fell with the weight of Thor's
hammer--indeed, every thing about him was Titanic, giving irresistible
weight to his arguments.
The bill having passed the house, the other authorizing a loan of
$25,000,000 and a reissue of treasury notes to the amount of
$10,000,000, came up. The expenditures for the coming year were
estimated at $45,000,000, to meet which the ordinary means of revenue
were wholly insufficient. A violent and bitter debate arose on its
presentation, which lasted three weeks. Regarded as so much money
appropriated to the conquest of Canada, it met with the determined
hostility of the opponents of the war. Mr. Eppes defended his bill,
and went into a long and statistical account of the revenue and
expenditures of the nation--showed how she could easily, in time of
peace, pay off every dollar she might owe--estimated the value of the
land and produce and capital of the country, and proved, as he deemed
satisfactorily, that the loan combined "all the advantages of safety,
profit, and a command at will of the capital invested." The long
debate upon it had little to do with the bill itself, but swept the
whole range of politics for the last four or five years. The history
of the war was gone over--orders in council, and Berlin and Milan
decrees revived with fresh vigor--the influence of Bonaparte in our
councils, though now struggling for life, was charged anew on the
administration. Personalities were indulged in, and the most absurd
accusations made by men, who on other subjects, exhibited sound
judgment and able statesmanship. Mr. Pitkin spoke a part of two days,
making a frightful exhibit of expenses, and denounced the war in
Canada. Pickering, with his large, powerful frame and Roman features,
not belying the fearless character of the man, came down on the
administration with all the power, backed by the most unquenchable
hatred he was master of. A distinguished man in the Revolution, he had
from that time occupied a prominent place in the political history of
his country. A "Pharisee of the Pharisees" in the Essex Junto, he
cherished all the intense hatred of that branch of the Federalists for
the war and its supporters. Built on a grand scale, yet with a heart
hard as iron towards a foe, fierce and bold, denouncing his old friend
and patron, John Adams, because he did not hate France as cordially as
he thought every good Christian should, having no sympathy with
Washington's quiet and non-committal character, he looked upon
Bonaparte and our war and its supporters, as the most monstrous births
of the age. His indignation at their existence was only exceeded by
his wonder that heaven, in its just wrath, did not quench all
together. Probably the administration had not such a sincere and
honest hater in the whole Federalist ranks. He was an honest man and
possessed of most noble traits, but his feelings obscured his judgment
when speaking of the war, and he gave utterance to the most
extraordinary and absurd assertions. In this speech he wandered over
the whole field--took bold and decided ground--advocated openly the
doctrine of the right of search, as defended by our enemy--declared
that our complaints were unjust--denied the statement respecting the
number of impressed seamen, saying that many Americans served
voluntarily on board of British cruisers--glorified England for her
efforts to overthrow Napoleon, calling her the "world's last hope."
Having thus defined his position so clearly, that there could be no
doubt where he stood, he turned to the Speaker and looking him sternly
in the face through his spectacles, and "swinging his long arm aloft,"
exclaimed, "I stand on a _rock_ from which all Democracy--no, _not all
Democracy and hell to boot_ can move me--the rock of integrity and
truth." Mr. Shelby and Mr. Miller followed in a similar strain, and
Canada, with its disastrous campaigns, was flung so incessantly in the
face of the war party, that it hated the very name. Grundy defended
the bill, and Gaston, of North Carolina, opposed it. Grosvenor
launched forth into a violent harangue, and was so personal and
unparliamentary in his language that he was often called to order.
Very little, however, was said on the merits of the bill. This served
only to open the flood-gates of eloquence, which embracing every topic
of the past and present, deluged for twenty days the floor of
Congress. Langdon Cheves, the Speaker, though opposed to the
restrictive measures of the administration, upheld the war, and
defended the bill in a long and temperate speech. One of the best
speeches elicited by it, was made by John Forsyth. Hitherto he had
taken but little part in the debates of the House, and hence his
brilliant effort took the members by surprise and arrested their
attention. Handsome, graceful, fluent, with a fine voice and
captivating elocution, he came down on the Federalists with sudden and
unexpected power. Their unfounded assertions, unpatriotic sentiments
and personal attacks had at length roused him, and as they had
wandered from the question in their blind warfare, so he passed from
it to repay the blows that had been so unsparingly given. Turning to
the New England delegation, he charged boldly on Massachusetts the
crime of fomenting treason to the State, if not intentionally, yet
practically, by her legislative acts, inflammatory resolutions and
violent complaints of injustice, which were the first steps towards
more open hostility. "I mention them," said he, "not from fear, but to
express my profound contempt for their impotent madness. Fear and
interest hinder the factious spirits from executing their wishes. _If
a leader_ should be found bad and bold enough to try, one consolation
for virtue is left, that those who raise the tempest will be the first
victims of its fury." Calhoun, with his clear logic, demolished the
objections that had been raised. He said they could all be reduced to
two. One was, that the loan could not be had--the other, that the war
was inexpedient. He declared both false, going over the ground he had
been compelled so often to traverse since the commencement of the war.
He took up the question of impressment--declared our war a defensive
one--bore hard upon those who voted against supplies--showed that the
war had liberated us from that slavish fear of England which had
rested like a nightmare on the nation--and started into vigorous
growth home manufactures, destined in the end to render us independent
of foreign products, and furnishing us with ampler means to carry on
any war that might occur in the future.
This debate might have lasted much longer but for a violent harangue
of Grosvenor, full of gross personalities, discreditable to himself
and insulting to the House. It was resolved to put an end to such
disgraceful scenes, and the previous question was moved and carried by
a majority of forty. A similar fierce conflict, however, took place
soon after on the bill for the support of military establishments, in
the ensuing year, and on the motion to repeal the Embargo Act. In a
speech against the former, Artemus Ward opposed not only the invasion
of Canada, and reiterated the old charge of subserviency to France,
but openly and boldly defended England in the course she had taken;
declared that impressment was in accordance with the law of nations,
and that the doctrine "the flag protects all that sails under it" was
untenable and false. He then went gravely into the reasons of the war,
and laid down the following propositions, which he proceeded soberly
to defend:--
"1st. Napoleon had an ascendancy in our councils through the fear or
hopes he inspired.
"2d. The administration wished to destroy commerce, and make an
agricultural and manufacturing people.
"3d. It wished to change the form of our government."
These extraordinary propositions were severally defended, and declared
by himself fully proved. In reply to the charge that the Federalists
were nullifiers, he pronounced it unjust and unfounded, and said that
the Federalists of Massachusetts would "cling to the Union as the rock
of their salvation, and will die in defence of it, _provided they have
an equality of benefits_. But everything has its 'hitherto.' _There is
a point beyond which submission is a crime._ God grant that we may
never arrive at that point." Such language, though guarded, was
significant, and justified the very charges it was designed to rebut.
Coupled with the action of Massachusetts, it furnished ground for the
gravest fears. [Sidenote: Jan. 6.] A motion having been introduced
during the session to the effect that the Attorney-General of the
United States should prosecute Governor Chittenden, of Vermont, for
recalling the militia of the state from Burlington, Otis presented a
resolution to the Massachusetts Senate, declaring that the State was
prepared to sustain, with her whole power, the Governor of Vermont in
support of his constitutional rights. [Sidenote: Jan. 44.] In the mean
time the Legislature voted an address, denouncing the war altogether,
ascribing it to hatred of the friends of Washington's policy, to the
influence of foreigners, to envy and jealousy of the growing
commercial states, and desire for more territory. The Pennsylvania
Legislature, on the other hand, censured the conduct of both
Chittenden and the Massachusetts Legislature, declaring that the
State would support the General Government in meting out justice to
all violators of the Constitution. [Sidenote: Feb. 12.] New Jersey was
still more enraged, and after giving utterance to her contempt and
abhorrence of the "ravings of an infuriated faction, whether issuing
from a legislative body, a maniac governor, or discontented and
ambitious demagogues," "Resolved, that the State was ready to resist
internal insurrection with the same readiness as the invasion of a
foreign foe." Thus the storm of political hate raged both within and
without the halls of Congress, threatening in its fury to send the
waves of civil strife over the already distracted and suffering land.
But there was a large party, composed of the middling classes of New
England, in favor of the war. This, together with the outward pressure
of the entire Union, combined to make the Federalist leaders extremely
cautious in their movements. The farmer was benefitted by the war, for
his produce commanded a higher price in the market, while the
manufacturing interests, which the restrictive acts had forced into
importance, were also advanced, thus creating a new antagonist to the
Federalists. The embargo, however, pressed heavily on a large portion
of the country, calling forth loud denunciations and petitions from
the whole New England coast.
Fortunately for the administration, circumstances soon rendered it
useless. After struggling with almost superhuman courage and endurance
to repel the allies from the soil of France, Napoleon saw them at last
enter Paris in triumph, and demolish with a blow the splendid
structure he had reared with so much skill and labor. With the
overthrow of the French Empire ended the Continental War, and of
course the Orders in Council, the Berlin and Milan Decrees fell at
once to the ground. The grand cause of the restrictive system having
been removed, Madison sent a message to the House of Representatives,
advising a repeal of the Embargo and Non-Importation Act. A bill to
this effect was reported by Mr. Calhoun from the Committee on Foreign
Relations. [Sidenote: Apr. 4.] He spoke at some length on the first
section, embracing the embargo, supported it on the ground of the
recent changes in Europe, resulting from Bonaparte's downfall. Russia,
Sweden, Germany, Denmark, Prussia, and Spain, might now be considered
neutral nations, and by opening our commerce to them, we should in
time, in all probability, attach them to us in common hostility to
England, should she continue her maritime usurpations. This country
had from the first contended for free trade, and consistency required
we should allow it to neutral powers, just as we had claimed it for
ourselves. In short, there was no reason for its continuance, except
the plea of consistency. But he contended that a change of policy
growing out of a change in the circumstances that had originated it,
could not be called inconsistent. Mr. Webster replied to him, saying
that he rejoiced it had fallen to his lot to be present at the funeral
obsequies of the restrictive system. He felt a temperate exultation
that this system, so injurious to the country and powerless in its
effect on foreign nations, was about to be consigned to the tomb of
the Capulets. After ridiculing the whole restrictive system, saying it
was of like faith, to be acted--not deliberated on, and that no saint
in the calendar had been more blindly followed than it had been by its
friends, he went on to show that it was designed, originally, to
cooperate with France. He denounced any system, the continuance of
which depended on the condition of things in Europe. Such policy was
dangerous, exposing us to all the fluctuations and changes that
occurred there. If this universal application of a principle was
unsound and extraordinary in a statesman, what followed was still more
surprising. Speaking of the effect of the system to stimulate
manufactories, he said he wished none reared in a hot-bed. Those
compatible with the interests of the country should be fostered, but
he wished to see no Sheffield or Birmingham in this country. He
descanted largely on the evils of extensive manufactories and populous
towns, and intimated strongly that any protective legislation in
reference to them would be unwise. What complete summersets those two
great men, Webster and Calhoun, and the sections of country they
represented, have made since 1814. Then South Carolina firmly
supported the union against the doctrine of state rights, and Calhoun
reasoned eloquently for manufactories, against Webster, opposed to
them. Years passed by, and Massachusetts, through her Webster, pleaded
nobly, sublimely, for the union, against the nullifying doctrines of
South Carolina, and those two men, standing on the floor of Congress,
fought for the systems they had formerly opposed, and in fierce and
close combat crossed swords each for the cause of the other. Webster
in 1814 condemning measures that forced manufactories into existence,
and afterwards pleading earnestly for a high tariff, and Calhoun at
the same time defending even the embargo on the ground that it
encouraged them, and afterwards fighting sternly against that tariff,
are striking illustrations of the changes and fluctuations of
political life. And yet there may be no inconsistency in all this.
"_Tempora mutantur, et nos mutamur in illis_," is a sound maxim.
Webster, when he charged inconsistency on the administration for
advising the repeal of the embargo act, after the great change in
European affairs, little thought how soon he would be compelled to
shelter himself behind this Latin maxim. In 1814 the interests of New
England were closely allied with free commerce, and her destiny
pointed towards the sea. In a few years her capital was largely
invested in manufactures, and could the tariff have been made a
permanent policy, all her crystal streams and dashing torrents
hurrying from the mountains to the sea, would have been mines of
almost exhaustless wealth. The times being changed, the dictates of
true wisdom required a change of policy. There is no inconsistency so
glaring and injurious as a stubborn adherence to old dogmas or
systems, when events in their progress have exploded both.
Added to the acts of Congress already mentioned, the most important
were those making appropriations for the support of the navy--for the
building and equipment of floating batteries for the defence of the
harbors and rivers of our country. The Yazoo claim was also disposed
of during this session. [Sidenote: April 18, 1814.] After an
ineffectual attempt to introduce a bill for the establishment of a
national bank, and the transaction of some minor business, Congress
adjourned to the last Monday in October.
Our naval force in service in January of this year, independent of the
lake squadrons, gun-boats, etc., for harbor defences, was but seven
frigates, seven sloops-of-war, four brigs, three schooners, and four
other small vessels. The secretary, however, reported in February
three seventy-fours and three forty-fours on the stocks, besides
smaller vessels, which would make thirty-three vessels, large and
small, in actual service or soon to be afloat, while thirty-one were
on the lakes. The army, by law, was increased at this session to
64,759 men, while the militia of the union amounted to 719,449 men.
Added to this, the president was authorized to accept the service of
volunteers to the number of 10,000, their term of service not to
exceed one year.
With such an imposing array of force on paper, with the increased
revenue from the direct tax laid the year before, with a loan of
$25,000,000, and treasury notes amounting to $10,000,000, the
government prepared to enter on a third campaign.
END OF VOL. I.
J. T. HEADLEY'S WORKS.
NAPOLEON AND HIS MARSHALS. By J. T. HEADLEY, 2 vols. 12mo., cloth,
gilt. Illustrated with 12 Portraits, $2.50. 25th Thousand.
WASHINGTON AND HIS GENERALS. By J. T. HEADLEY, 2 vols. 12mo., cloth,
gilt. Illustrated with 16 Portraits, $2.50. 22d Thousand.
THE SACRED MOUNTAINS. By J. T. HEADLEY, Illustrated with 12
engravings, by Burt, with designs by Lossing, 20th Thousand.
Do. do. do., 12mo., cloth, gilt, $1.25.
SACRED SCENES AND CHARACTERS. By J. T. HEADLEY, with 12 Illustrations.
Designed by Darley, 4th Thousand.
Do. do. do., 1 vol. 12mo., cloth, gilt, $1.25.
LETTERS FROM ITALY AND ALPS AND THE RHINE. By J. T HEADLEY, 1 vol.
12mo, cloth. A New Edition. Revised and Enlarged. With a Portrait of
the Author, $1.13. 8th Thousand.
LIFE OF OLIVER CROMWELL. By J. T. HEADLEY, 1 vol. 12mo., cloth, gilt,
with Portrait, $1.25. 6th Thousand.
HEADLEY'S MISCELLANIES. Authorized Edition, 1 vol. 12mo., cloth, $1.
2d Thousand.
ADIRONDACK; OR LIFE IN THE WOODS. By J. T. HEADLEY, with Original
Designs from Gignoux, Ingham, Durand, etc., 1 vol. 12mo., cloth,
$1.25. 4th Thousand.
SKETCHES AND RAMBLES. By J. T. HEADLEY, 1 vol. 12mo., cloth, 75c. 2d
Thousand.
THE IMPERIAL GUARD OF NAPOLEON. From Marengo to Waterloo. By J. T.
HEADLEY, 1 vol. 12mo., with Illustrations, cloth, $1.25. Just
Published.
J. T. HEADLEY'S WORKS--Uniform Edition, 12 vols., in sheep, for
Libraries and District Schools.
"Mr. Headley's peculiarities as an author are universally
known. He is one of the most vigorous and spirit-stirring
writers of the day, especially graphic and powerful in
narratives of exciting events. No one can fail to get from
his descriptions most graphic, vivid, and lasting
impressions of the scenes of which he speaks."--_N. Y.
Courier and Enquirer._
"His descriptions are graphic, his history correct, and his
summing up character scarcely suffers by a comparison with
similar pages in Tacitus."--_N. Y. Evening Post._
"He speaks heartily, earnestly, truthfully; and the warm
heart answers to his voice."--_N. Y. Observer._
"Each one of his Biographies is a grand historical picture,
conveying in a most impressive way, a true idea of the
events of the time."--_Cincinnati Herald._
"Mr. Headley is truly eloquent in his description of
character. He presents to you the strong points of the man
with a clearness that seems to place him before you as an
old acquaintance."--_Cleveland Herald._
"Whatever critics may choose to say, Mr. H. will never lack
readers. The stir and fire of his descriptions will touch a
popular chord. In describing the battle field and the
tumultuous stirring life of the camp, Mr. H. is what Cooper
was upon the Sea."--_N. Y. Evangelist._
LIVING ORATORS OF AMERICA. By Rev. E. L. MAGOON 1 vol. 12mo., with
portraits. Price, $1.25.
THE ORATORS OF THE AMERICAN REVOLUTION. By Rev. E. L. MAGOON. 1 vol.
12mo., with portraits. Price, $1.25.
Mr. Magoon is a decided original. Both his thoughts and his
manner of expressing them, are peculiar and striking.--_N.
Y. Evangelist._
Mr. Magoon, who is a vivid, nervous writer, has thrown a
charm around the character of the men whose history he has
delineated, that will cause the book to be read with unusual
interest.--_Christian Secretary._
These volumes contain exceedingly clear sketches of our
greatest orators; so arranged, contrasted and compared, that
the peculiar powers and excellencies of each are set before
the mind in a strong light.--_Springfield Republican._
Every American will read these works with national pride,
and have his better feelings and sentiments enkindled and
strengthened.--_Western Literary Messenger._
THE WOMEN OF THE AMERICAN REVOLUTION. By Mrs. E. F. ELLET. 3 vols.
12mo., with portraits. Price, $3.50.
The work fills a place in our Revolutionary history that
would scarcely be complete without it; indeed, we consider
it as one of the most valuable contributions that have been
made to the history of our country in a long time.--_Hunt's
Magazine._
We counsel especially the young women of our country to lay
aside their novels, at least until they shall have read "The
Women of the Revolution." Those of them who have souls will
find it replete with interest and instruction.--_N. Y.
Tribune._
The narratives are brief, spirited, and profoundly
interesting; especially as showing how the toils, the
privations and dangers of the war, made themselves felt,
perhaps even more keenly, in the homes than on the
battle-fields of the Revolutionary champions.--_N. Y.
Commercial._
The authoress has succeeded in collecting a large amount of
new and important facts, illustrative of the heroism evinced
in action and suffering, by the women who bore their part in
the Revolution, which have no place in the political
histories of the time, and have been derived almost entirely
from private sources.--_N. Y. Journal of Commerce._
The rich store of information contained in these volumes,
has been procured at the cost of much and laborious
research, from the surviving relatives of the heroines,
scattered through various parts of the Union. Personal
recollections have been recorded, family papers and letters
examined, and the work thus made a faithful and vivid
exhibition of the domestic scenes of the war.--_Charleston
Inquirer._
The conception of the book is at once beautiful and
patriotic, and its execution is worthy of its subject, and
worthy of the reputation of its gifted authoress.--_Albany
Atlas._
These sketches are of thrilling interest, as we gather from
a hasty glance at their pages. The narrative is clear,
concise, and very agreeably written.--_N. B. Mercury._
[Transcriber's notes:
Obvious printer's errors have been corrected. Hyphenation and
accentuation have been standardised, all other inconsistencies are as
in the original. The author's spelling has been maintained.
This book does not have a chapter VI.
Some dates were misprinted in the original (e.g. Jan. 44), they have
been left as it is.]
End of the Project Gutenberg EBook of The Second War with England, Vol. 1 of
2, by Joel Tyler Headley
*** | {
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Dairy Crest cuts 260 jobs at creamery and bottling plant
https://www.bbc.co.uk/news/uk-england-29306822
Image caption The volume of milk supplied in glass bottles has fallen from 94% of the total in 1975 to 4%
Dairy products firm Dairy Crest is to close a creamery in Somerset and bottling dairy in London, with the loss of 260 jobs.
Two hundred people work at the dairy in Hanworth, west London, where milk is put into glass bottles.
The remaining jobs will go at the creamery in Chard, which is due to shut by the end of next year.
Chief executive Mark Allen said the closures were right for the long-term future of the business.
'Environmentally friendly'
Hanworth will remain open for another two years. Its closure is due to reduced demand for milk supplied in glass bottles, with most people opting for milk in plastic bottles.
According to Dairy Crest, the proportion of milk sold in glass bottles has fallen from 94% in 1975 to 4% in 2012.
However, the food producer said plastic containers were now as environmentally friendly as glass.
The creamery in Chard makes a range of alcoholic and retailer-branded creams.
Mr Allen said: "At Hanworth nothing is going to change immediately, but sales of milk in glass bottles are falling and we have to give our employees at Hanworth clarity over the dairy's future.
"We also have to let our milkmen and women know that we are doing all we can to protect their livelihoods."
He added that the firm had tried to make the Chard site "viable for many years" but this had not worked.
Production will be stepped up at its three plastic bottling dairies in Chadwell Heath, Greater London; Foston, Lincolnshire; and Severnside, Bristol; to make up for the loss of production at Hanworth.
A consultation with staff across both sites is now under way.
Hanworth
Dairy Crest Crudgington Creamery closure starts
Dairy Crest closes in Whitland for second time
Dairy Crest sales rise 15% in 'challenging' market
Dairy Crest | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 286 |
Cubalayas, classified as game birds, come from fighting stock. Although more aggressive than the common breed of chicken, they display less aggression than most game birds. Cubalayas do surprisingly well as egg layers and meat producers. They lay four or five medium-sized, tan eggs a week. As a table bird they have a fine grained white meat. Cubalayas can take up to three years to fully mature; however, most can reproduce at six months of age. Cubalayas tolerate both heat and humidity well. Cuba uses Cubalayas for meat and eggs while the US recognizes them primarily as ornamentals.
Cubalayas need to forage. Build a spacious run for your flock and move it often to avoid parasite infestation. Keep roosters apart or the game bird part of their character will display itself with dire consequences. Bred from warm climate fowl, Cubalayas tolerate heat and humidity well. Conversely, they have little tolerance for cold drafty conditions.. If you live in the northern latitudes, insulate and caulk the coop. Americans appreciate the incredible beauty of the Cubalaya and may miss the practical egg laying qualities of the breed. Feed them good layer food and supplement the morning light in the winter months, and they will provide you an egg a day.
Undoubtedly keepers bred Cubalayas to fight. In the mid 19th century breeders in Cuba crossed Asiatic game fowl from the Philippines with European game fowl with the purpose of producing a fighting breed without spurs. They succeeded. In the process they produced a breed with good laying capabilities, fine quality meat, and ornamental splendor. Cubalayas have both a standard and bantam size. The American Livestock Breeds Conservancy lists Cubalayas as endangered. Indeed, few hatcheries offer quality Cubalaya brood in America. They have made a resurgence as a bantam in US exhibition, however. | {
"redpajama_set_name": "RedPajamaC4"
} | 3,125 |
Kaitlin was born in Portland, Oregon and raised in the United States until the age of 12. Then, her perfectly sane family ventured across the world and moved to Auckland, New Zealand.
She loves to experiment with sound to create an atmosphere and tell a story. Her goal, as for many musicians, is to get the music to reflect the lyric, which then bond together to create an image in the listener's mind.
Silhouettes was produced by Simon "Berkfinger" Berckleman (The Temper Trap, Silverchair, Wolfmother) and features Bronte Coluccio (bass) and Petrus Fourie (guitar).
Recommended to the fans of Lorde, Marina and the Diamonds and Oh Land. | {
"redpajama_set_name": "RedPajamaC4"
} | 1,618 |
Q: Scraping data with bs4 I have this line of html:
<td title="Druid"><a href="/pvp/druid"><img src="/images/classes/druid.png" class="img-responsive center" alt="Druid"></a></td>
Using python and beautiful soup,
I'd like to access the the "Druid" from <td title="Druid"> to be stored as a variable.
A: If you want to access the title of the td:
bs4.BeautifulSoup(data).find("td")["title"]
A: To get the attributes of a tag treat it just like a dictionary:
soup.find('td').get('title')
or
soup.find('td')['title']
Note: .get('title', 'some default value') allows you to provide a default value if the key is missing or if omitted is None, while ['title'] will raise a KeyError
Example
from bs4 import BeautifulSoup
html='''<td title="Druid"><a href="/pvp/druid"><img src="/images/classes/druid.png" class="img-responsive center" alt="Druid"></a></td>'''
soup = BeautifulSoup(html)
character = soup.find('td').get('title')
print(character)
Output
Druid
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,535 |
'use strict';
angular
.module('softvApp')
.controller('ModalEditarRefClienteCtrl', function($uibModalInstance, $uibModal, ObjRefCliente, CatalogosFactory, $state, $rootScope, ngNotify){
function UpdateRefPersonal(){
var objtblReferenciasClietes = {
'contrato': vm.IdContrato,
'nombre': vm.NombreRef,
'direccion': vm.DireccionRef,
'email': vm.EmailRef,
'telefono': vm.TelefonoRef,
'id_referencia': vm.IdReferencia,
'op': 1,
'tipo': 'C'
};
CatalogosFactory.UpdatetblReferenciasClietes(objtblReferenciasClietes).then(function(data){
if(data.UpdatetblReferenciasClietesResult == -1){
ngNotify.set('CORRECTO, se guardó la referencia personal.', 'success');
$rootScope.$emit('LoadRefPersonal', vm.IdContrato);
cancel();
}else{
ngNotify.set('ERROR, al guardar la referencia personal.', 'warn');
$rootScope.$emit('LoadRefPersonal', vm.IdContrato);
cancel();
}
});
}
function cancel() {
$uibModalInstance.dismiss('cancel');
}
var vm = this;
vm.IdReferencia = ObjRefCliente.id_referencia;
vm.IdContrato = ObjRefCliente.contrato;
vm.NombreRef = ObjRefCliente.nombre;
vm.TelefonoRef = ObjRefCliente.telefono;
vm.EmailRef = ObjRefCliente.email;
vm.DireccionRef = ObjRefCliente.direccion;
vm.cancel = cancel;
vm.UpdateRefPersonal = UpdateRefPersonal;
}); | {
"redpajama_set_name": "RedPajamaGithub"
} | 8,712 |
\section{Introduction}
\blfootnote{The quote in the title is attributed
to Harry S. Truman~\cite{neustadt1960presidential}, and is used as the
opening quote to chapter 6 in \emph{The Mythical
Man-Month}~\cite{brooks1972mythical}.}
Developers struggle to store passwords securely. Naiakshina~\etal{}
have repeatedly shown that developers do not build in security unless
explicitly asked to do so (and even then typically do so
poorly)~\cite{naiakshina-2017-password,naiakshina-2018-deception,naiakshina-2019-if-you-want}.
In organizations, one can support developers coding securely through
code review, and acceptance testing---but not all developers work in
teams and many work alone on their own
projects~\cite{meyer-2017-characterizing,vanlinden2020schrodinger}.
Developers continue to seek guidance on how to handle passwords. In a survey of
developers' posts on Stack Overflow (a popular developer question and answer
site) Barua~\etal{} found that posts related to authentication and security
(including password storage) and were one of the top 20 topics on the site
and accounted for 2.1\% of all questions~\cite{barua2014developers}.
Furthermore in a survey of just security-focussed posts on Stack Overflow,
Yang~\etal{} found that the most viewed of all security-focussed posts related
to passwords~\cite{yang2016security}, with each post viewed on average 2,731
times. Whilst there are alternatives to passwords~\cite{hardt2012oauth}, many
developers still appear to be working with passwords and implementing password
storage in their apps and software. As well as working with passwords they are
seeking guidance on how to do it \emph{right}.
It is well established that writing a specification before implementing it leads
to code that is of a higher
quality~\cite{boehm1984verifying,parnas1972technique,spolsky2004joel,demarco1979structure,brooks1972mythical,meyer-1992-design-by-contract}.
Since specification writing is beneficial for \emph{quality}, does the act of
writing one also improve developers' security practices? Naiakshina's work
suggests that developers only consider security aspects if explicitly
prompted~\cite{naiakshina-2019-if-you-want}; but if we try to continuously
prompt developers to \emph{work securely} we risk security
fatigue~\cite{furnell2009recognising,parkin2016fatigue}. Since specification is
an established developer practice, this paper seeks to explore whether the act
of writing any form of specification primes developers to program securely: in other words whether giving developers time to make a plan (however formally or informally) leads them to either recalling more about how to store passwords, or to recall that a standard exists and to check.
To test this we recruited 138 developers from an online platform for recruiting
participants for studies, and asked them to write code to store a password in
whatever language they were most comfortable with. Half the developers were
asked to write down a specification---any form of specification from a formal
definition~\cite{lamsweerde2000formal} to a prose
description~\cite{padegs1981system}---of how they would implement this before they
were allowed to write their solution, the rest were allowed to write their
implementation immediately. We scored the security of their implementations
using Naiakshina's end-user password storage
criteria~\cite{naiakshina-2017-password} (Figure~\ref{fig:naiakshina}), which is
itself based on NIST~SP~800-63-3~\cite{nist-800-63-3}, and analyzed their
written justifications of their choices and threats considered.
Specifically, we address the following research questions:
\begin{description}
\item[RQ1] Does specification writing lead to a measurable
improvement in password storage method?
\item[RQ2] What approaches do developers take when implementing
password storage and what do they typically remember and forget?
\item[RQ3] How do developers justify their implementation approach and
what threats do they consider?
\end{description}
\noindent Our key findings are as follows:
\begin{itemize}[leftmargin=*]
\item Developers who were explicitly prompted to write a
specification, stored their passwords \emph{slightly} more securely
than those who were not prompted ($p=0.027$, $r_{rb}=0.209$).
\item Only 38\% of developers remembered to hash passwords, 14\% remembered
to salt them, but other secure password storage practice was largely
absent (Figure~\ref{fig:naiakshina}).
\item Developers think they are storing passwords correctly, but their
scores according to Naiakshina's criteria (Figure~\ref{fig:naiakshina}) do not indicate best practice.
\item If given time to reflect, some developers do realize that there are threats to stored passwords and that their solutions may not be secure.
\end{itemize}
\noindent
Our novel insights are in examining whether specification is a useful tool for priming for security related tasks, and how developers justify the code they write and the threats they consider with respect to the specifications they write. Analyzing the developer's rationale suggests that whilst some developers consider appropriate threats, their knowledge of best practice is out-of-date and that current cryptographic guidelines~\cite{nist-800-63-3}. Providing lists of what developers must do is not working. Instead we must fit the task to the developer and provide usable mechanisms for password storage.
\begin{figure} \centering
\begin{mdframed}\raggedright
\begin{itemize}[leftmargin=*]
\item The end-user password is salted (+1) and hashed (+1).
\item The derived length of the hash is at least 160 bits long (+1).
\item The iteration count for key stretching is at least 1,000 (+0.5) or 10,000(+1) for PBKDF2 and at least $2^{10}$ for bcrypt (+1).
\item A memory-hard hashing function is used (+1).
\item The salt value is generated randomly (+1).
\item The salt is at least 32 bits in length (+1).
\end{itemize}
\end{mdframed}
\caption{Naiakshina's end-user password storage assessment
criteria~\cite{naiakshina-2017-password}, copied verbatim. A score
$\mathbf{\geq 6}$ indicates industrial best practice.}
\label{fig:naiakshina}
\end{figure}
\section{Background and Related Work}
\subsection{Benefits of specification}
The benefits of program specification are well established in both the
academic and engineering communities. Spolsky notes their benefit
saying:
\begin{quote} ``If you don't have a spec, you will always spend
more time and create lower quality code."~\cite{spolsky2004joel}
\end{quote}
Brooks~Jr{.} also notes the benefit of a
specification:
\begin{quote} ``Careful function definition, careful
specification, and the disciplined exorcism of frills of function and
flights of technique all reduce the number of system bugs that have to
be found."~\cite{brooks1972mythical}
\end{quote} Dromey suggested that quality models and requirements
specifications could lead to an improvement in software
quality~\cite{dromey1996cornering}. Haigh and Landwehr have suggested
that by building code to security specifications (drawing analogy to
US \emph{building codes}) we can reduce the vulnerability in software
systems~\cite{haigh2015building,landwehr2017building}.
Polikarpova~\etal{} found that twice as many bugs were found when code
was written with a \emph{strong
specification}~\cite{polikarpova-2013-what-good}. Mohanani~\etal{},
however, found that specifications can lead to developers blindly
following them without considering why the rules
exist~\cite{mohanani2014requirements}.
Our work seeks to demonstrate that the act of writing a specification creates an implicit priming effect that can impact a developer's approach to security.
\subsection{Work on password security}
There is a large body of work surrounding passwords, but a small
subset that addresses how developers perform password storage and
present analysis of the process. Password storage is a feature
generally supported by cryptographic libraries. The usable security
community has studied the developers' interaction with the
cryptographic APIs.
Naiakshina~\etal{} ran the first qualitative usability study to observe how 20
computer science students address the task of password
storage~\cite{naiakshina-2017-password}. They concluded that
participants consider functionality before security. Unless
participants are primed, they do not think the task of password
storage requires a secure solution. On the other hand, participants
who were primed to consider security used various hash functions and
different algorithms to secure their password. For the participants
who were primed, none of their solutions met the academic standards of
the time. Cryptographic frameworks offer password storage as an opt-in
feature. This means the developers needs to understand cryptography to store passwords. 10\% of the non-primed
participants attempted a secure solution for password storage while
70\% of the primed participants attempted a secure solution.
On asking the non-primed
students about the security oversight, they replied that they would
have implemented secure storage if they were writing code for a
commercial product. To address this insight Naiakshina~\etal{} conducted a field study
with freelance developers. Like students, freelance developers do not
consider security for password storage, unless prompted. Both students
and freelance developers have misconceptions about secure password
storage, however interestingly freelance developers show a wider range
of these misconceptions. Freelance developers often stored passwords
with Base64, confusing encoding functions with hash functions, a
misconception they shared with end-users. Naiakshina~\etal{} conclude, that
even when developers believe they are coding for companies they seldom
store the password securely without
prompting~\cite{naiakshina-2019-if-you-want}.
Acar~\etal{} conducted an experiment with GitHub developers to establish if they
are an accurate representation of developers in general for security-based
developer studies. The GitHub developers were asked to perform password storage
securely. The solutions included the storage of plain-text passwords, use of
static salts, use of unsafe hashing algorithms~\cite{acar2017security}. Our
work goes beyond Acar~\etal{}'s and Naiakshina~\etal's work by examining
developer's rationale for their password storage implementations and finds that,
whilst developers aren't storing passwords securely, they \emph{think} they're
following best practices.
Oesch~et~al{.} evaluated 13 popular password managers and their
solutions for handling the 3 main stages of a password's life-cycle;
password generation, storage, and auto-fill. Their evaluation of
password storage showed that developers stored information in plain-text,
left metadata unencrypted, and used insecure
defaults~\cite{oesch2020then}. Our work compliments this by diving deeper into \emph{why} developers do not engage with best practice.
There is a large body of work on
end-user passwords and their security~\cite{shay2010encountering, ur2012helping, ur2015added,
ur2016users, ur2017design, bonneau2012science, egelman2013does,
komanduri2011passwords, weir2010testing}. In contrast our work focuses on developer's approaches to storing passwords.
\subsection{Work on secure programming}
Weir~\etal{} looked at the prevalence of security assurance techniques (including threat assessment and code review) among Android developers~\cite{weir2020needs}. They found that between only 22--30\% of Android developers used these techniques despite a high perceived need for security. We found that $\sim$56\% of developers claimed to write a specification without prompting.
Fischer~\etal{} examined the amount of code copied from Stackoverflow, and its security~\cite{fischer2017stack}. They found that 15\% of Android apps contained vulnerable code copied from Stackoverflow. We found that $\sim$8\% of developers copied from Stackoverflow specifically, but that a further $\sim$12\% copied from other online sources.
Many vulnerabilities arise due to developers misusing cryptographic
libraries.
Nadi~\etal{} performed an empirical investigation into challenges
developers face when using Java cryptographic APIs. Based on the
analysis of 100 Stack Overflow posts, 100 GitHub repositories and a
survey of 48 developers, they found that developers find cryptographic
features such as encryption and digital signatures difficult to
program. they also found that APIs are generally perceived to be too
low-level for developers~\cite{nadi-2016-jumping-through-hoops}.
Egele~\etal{} studied the integration of cryptographic APIs in Android
applications. They found errors in 88\% of the applications. CryptoLint was
introduced as a static analysis tool to find these
errors~\cite{egele-2013-empirical}. Patnaik~\etal{} performed a thematic
analysis of 2491 Stack Overflow posts from developers seeking help with using 7
cryptographic libraries, and found 16 usability
issues~\cite{patnaik2019usability} that could be related to Green and Smith's
earlier work that proposes usability principles for cryptographic APIs. show
that developers find cryptographic APIs challenging to use. We find that as
well as struggling with APIs developers are not clear on what they need to do to
store passwords securely, following current guidelines~\cite{nist-800-63-3}.
\section{Method}
We used a between-subjects design to explore whether the act of
specification writing results in more secure code being produced.
\subsection{Study Design}
To test the effect specification writing had on implementation we designed a
study where developers would implement the part of an app's code for storing
passwords. We chose password storage as a task as it is security relevant,
implementable within a relatively short space of time and is a common task with
plenty of guidance available that most developers would have encountered in
their work.
Our study was implemented as a set of online tasks and questions (to capture
rationale). Developers were randomly assigned a grouping (either
\emph{specification} or \emph{no-specification}) and shown the following
scenario:
\begin{survey}You are working on the backend of an application.
Users create an account on the app, and login before being allowed to
use the program.
The application is complete bar one task: writing the login system
users use to authenticate with the app. You have been tasked with
implementing this part of the app.
You decide to start with storing the users' passwords. Your boss
trusts your judgment when it comes to implementing this feature.
\end{survey}
Developers in the \emph{specification} group were then asked to write
a specification for how the password should be stored.
\begin{survey}You decide to start by writing a specification for
how the password should be stored, and to note down any special
requirements and implementation details. You are provided with a
username and password, and they have been checked to see that they are
valid text.
Describe your specification below.
You can describe your specification using formal notation, informal
notes, a list, mathematical notation or any other method. If you draw
a picture as part of your specification, please say so and say what is
shown.
\end{survey}
Both groups were then asked to implement the password storage using
whichever language they wished. If they used a real programming
language they were asked to note it.
\begin{survey}You start writing the password storage method. You
have been given the password the user wishes to use and you need to
store it so that it can be checked whenever users try and login.
You are given a username and password. Both have been checked to be
valid text (i.e. neither empty nor containing bad characters)
Write code (or pseudocode) to implement the password storage. Your
code doesn't need to be compilable or syntactically correct but should
illustrate your general approach to the implementation.
\end{survey}
Developers in the \emph{no-specification} group were then asked if
they had made some form of specification or plan before starting their
implementation (without being asked to). Those that indicated that
they did, were asked to describe their specification and their results
were added to those of the \emph{specification} group.
Both groups were then asked to provide a rational for their coding
approach in a free text box. They were asked if they considered
\emph{what threats might attack a stored password}, and, whether they
\emph{referred to any standards for password storage} when
implementing the code. Finally, participants were asked whether they
had any formal qualifications in software engineering, or computer
science; and, to rate their knowledge of security and cryptography on
a 5-point Likert scale
and briefly describe their security and development experience.
\subsection{Analysis}
To analyze the data we scored each of their implementations using Naiakshina's
metric~\cite{naiakshina-2017-password} and compared the average score between
different groups using the Mann Whitney $U$ test (a rank-based non-parametric
test to explore if two groups are distinct~\cite{mann1947test}) to test for
significance and to calculate the effect sizes (using the rank-biserial
correlation~\cite{cureton1956rank}). To analyze developer's rationale and
threat models we asked developers to describe them and analyzed them
qualitatively using a grounded theory approach~\cite{Strauss1998,Glaser1967}.
\subsection{Recruitment and Ethics}
Developers were recruited from \emph{Prolific Academic} and were
screened, by Prolific, based on their familiarity with computer
programming. Developers were offered a financial reward for
completing the study of $\pounds${5}, inline
with the \emph{living wage} in our country. All developers who
completed the study were paid for their work.
Ethical approval for the study was sought from and granted by
Bristol University. No personal data was
collected, and demographic data was deleted after coding and
validation. Data is available by request.
\subsection{Limitations and Threats to Validity}
We acknowledge the following limitations and threats to our study:
\begin{itemize}[leftmargin=*]
\item Our developers were recruited by \emph{Prolific Academic} and as such, may not be representative of how developers as a
whole behave. Other studies have also used similar populations for studying passwords and developers~\cite{kelley2012guess,ur2016users,naiakshina-2020-conducting-security-developer-studies}.
\item Developers may not know how to store a password, and may not be
aware that it is a security related task. We mitigate this by
qualitatively analyzing the developers' rationale behind their code.
\item Developers who were not prompted to write a specification,
may opt to write a specification anyway. To correct for this we asked developers not in the specification group if they
wrote a specification, after their implementation. We assume that the
specification produced by the unprompted group is similar to the
prompted group (and we ask them to describe it), but this may not be
the case and some participants may retrospectively write a
specification.
\item We ask the developers about their qualifications and experience,
however all data is self-reported and may not be accurate.
\item We asked developers to implement password storage and 99
developers (72\%) did so. 19 developers (14\%) instead appeared to
write code implementing password authentication (how one would
check if a password was correct) but from which their approach to
password storage could be seen. A further 15 developers (11\%) stored
the password, but did so only checking if the password contained a
suitable range of letters, numbers and symbols, 3 (3\%) approached the
problem by retransmitting their passwords over HTTP\footnote{Three
appeared to have copied the question from:
\url{https://stackoverflow.com/questions/19999417/password-storage-in-code-how-to-make-it-safe}.},
and 1 insisted the passwords be stored \emph{alphabetically}. We include all in our analysis, as they were all conceivably ways a developer may approach storing passwords.
\item Scoring implementations according to Naiakshina's criteria could
introduce subjectivity. To mitigate this, one author scored and then another author independently rescored all the
implementations and calculated Cohen's Kappa (a measure of inter-rater
reliability~\cite{landis1977measurement}). The kappa-value indicates
\emph{almost perfect agreement}
($\kappa=\input{analysis/score_kappa.tex}$)~\cite{landis1977measurement}.
Similarly, our codebooks, whilst grounded in data, were likely influenced by the coder's background and experiences. Using our
codebooks a separate coder independently re-coded the entire dataset. We found
\emph{substantial agreement} ($\kappa=\input{analysis/why_kappa.tex}$)
with our coding for developers' explanations for their implementations
(Table~\ref{tab:whycodebook}) and \emph{almost perfect agreement}
($\kappa=\input{analysis/threat_kappa}$) with our coding for the
threats developers considered.
\item We measure developers' password storage approaches using Naiakshina's
criteria, but this poses a construct validity threat. We chose this metric as
it has been used in prior
work~\cite{naiakshina-2017-password,naiakshina-2019-if-you-want}, and on a
NIST standard for password storage~\cite{nist-800-63-3}. We mitigate this
threat by qualitatively analyzing \emph{why} developers wrote the code they
did as well as their implementations.
\end{itemize}
\section{Quantitative Results}
\begin{table*}\tablestyle
\caption{Distribution of scores for password storage methods by
different groups. Absolute values are given in (parentheses). The
{specification} group consists of two-subgroups: those that we
explicitly prompted for a specification, and those that we did not
prompt but reported writing one unprompted. A score of 6 or more is
considered to be following best practice.}
\input{analysis/scores.tex}
\label{tab:scores}
\end{table*}
\begin{table}\tablestyle \setlength{\tabcolsep}{4pt}
\caption{Comparison between groups using the Mann-Whitney \emph{U}
test.} \input{analysis/mwu.tex}
\label{tab:mwu}
\end{table}
\begin{table}\tablestyle
\caption{Frequency different points in Naiakshina's criteria were
observed compared to the whole population. No answer scored a
half-point for key-stretching. (Absolute values).} \input{analysis/metric.tex}
\label{tab:metric}
\end{table}
\begin{table}\tablestyle \setlength{\tabcolsep}{4pt}
\caption{Co-occurrences of points in Naiakshina's criteria (i.e. 36\%
of all participants who hashed their password also salted their
passwords). (Absolute values).}
\newcommand{\vertically}[1]{\rotatebox{90}{#1}}
\input{analysis/cometric.tex}
\label{tab:cometric}
\end{table}
\begin{table}\tablestyle
\caption{Observations of specific hashing methods used by
developers. Some developers recommended multiple hashing methods.}
\input{analysis/used.tex}
\label{tab:used}
\end{table}
Table~\ref{tab:metric} reports how the teams scored against
Naiakshina's criteria~(Figure~\ref{fig:naiakshina}). In our sample,
only 53 developers (38\%) produced outputs that fulfilled at least one
part of Naiakshina's criteria. The most common criterion fulfilled was
that of hashing data (demonstrated by 38\% of participants who scored
a point, 14\% of overall sample). Just under 20\% of the developers
who scored a point used a random salt or an appropriate hash length
(7\% overall); and the remainder of the points in Naiakshina's
criteria were awarded rarely.
\subsection{RQ1: Do specifications lead to securely stored passwords?}
Developers prompted for a specification ($n=61$) scored better
($\mu=1.03$) than those that were unprompted ($n=77$, $\mu=0.47$)---a
comparison by Mann-Whitney $U$ suggests that
this is a significant difference ($p=0.024$, $U=1947.5$), but with
only a small effect size (rank-biserial
coefficient~\cite{cureton1956rank}, $r_{rb}=0.171$). There remains a
significant difference in performance if we omit the subset of the
unprompted group who reported writing a specification without being asked to---prompted
participants ($n=61$, $\mu=1.03$), in contrast to developers who did
not write a specification ($n=34$, $\mu=0.38$). The two groups are
distinct (Mann-Whitney $U=820$, $p=0.027$) but the effect size remains
small ($r_{rb} = 0.209$). However, a comparison between all
participants who wrote a specification, prompted or not, ($n=104$, $\mu=0.83$) and those
who did not write a specification ($n=34$, $\mu=0.38$) is not statistically significant
($p=0.061$, $U=1495$, $r_{rb}=0.154$).
This could be explained by developers in the \emph{unprompted specification} group (those who were not asked to write a spec but who claimed to have written one anyway) actually writing their spec after their implementation in response to us asking if they had written one beforehand.
This theory is supported by Table~\ref{tab:mwu} where we found no significant difference between
the unprompted specification and the group that claimed not to write a
specification ($p=0.247$).
The distribution of scores is given in
Table~\ref{tab:scores}. 50--70\% of developers did not
store a password in any meaningfully secure way (a score of 0), and no
developer obtained a perfect score (of 7) using Naiakshina's metric,
although two developers did meet the score indicating best practice (a
score of 6; both were in the \emph{prompted specification} group). Of
the 77 developers whom we did not prompt to write a specification 56\%
(43) claimed to write one anyway unprompted; 26\% (36) of developers
reported referring to some kind of standard or guide when writing
their password storage method; 43\% (59) claimed some formal software
engineering qualification.
\begin{finding} Examining the rank-biserial correlation ($r_{rb}$) to
the scores themselves in
Table~\ref{tab:scores}, suggests that whilst forcing developers to
write a specification before coding will lead to more secure password
storage approaches ($p=0.024$), it isn't going to make a huge
difference---developers \emph{might} remember to hash them or to add
salt, but will still leave them stored insecurely.
\end{finding}
\subsection{So what else has an effect?}
If the act of forcing developers to write a specification only has a
small impact on their ability to store passwords securely,
then do we find anything else having an effect?
Participants reported their familiarity with cryptography on a 5-point
Likert scale. There is a small positive relationship between reported
cryptography experience and score (Spearmans
Rho~\cite{spearman1961proof}, $\rho_{s}=0.333$, $p=0.00$), with most
developers reporting that they had \emph{little to no experience}
(107, 78\%) (\emph{No experience}: 44 (32\%), \emph{little
experience}: 63 (46\%), \emph{moderate experience}: 25 (18\%),
\emph{very experienced}: 4 (3\%), \emph{extremely experienced}: 2
(1\%)). This is in contrast to the findings of Hazhirpasand~et~al{.}
who found no significant relationship between developer experience and
their ability to use a cryptography
API~\cite{hazhirpasand2019impact}---though Hazhirpasand~et~al{.} rated
developer experience on the basis of activity on GitHub, as opposed to
a self-reported value. We did not find a significant relationship
between developers who had a formal software engineering qualification
and those who did not ($p=0.061$).
Participants
who reported using a standard to inform their code implementation
scored better than those who used no standard but not significantly~($p=0.135$).
\subsection{RQ2: What did developers do?}
Our observations of hashing and salting rates are broadly inline with what
Naiakshina~\etal{} observed~\cite{naiakshina-2017-password}, where an overall
35\% ($\frac{7}{20}$) of developers hashed passwords and 25\% ($\frac{5}{20}$)
also salted them---however Naiakshina~\etal{}'s study explicitly primed half of
their developers ($\frac{10}{20}$) by asking them to store them security, and
only the primed groups hashed or salted their passwords. In contrast, in our
findings we observe similar rates over all participants.
In our study we asked developers to provide code in any programming
language, including pseudocode. Most developers described their
implementation in these terms using functions called \texttt{hash} and
appending salts, however some gave specific methods for storing their
passwords. Table~\ref{tab:used} shows the specific methods we
encountered for hashing passwords. Many developers recommended hash
functions that were inappropriate for password storage\footnote{They are quick to calculate using little memory, thus making them amenable to cracking, unlike memory hard hashes such as PBKDF2.}---including
MD5, the SHA family, and a substitution cipher. Other developers recommended encryption (which
is unsuitable for password storage~\cite{nist-800-63-3}), or even using base64. Of all the
developers who stored their passwords hashed, 50\% (26) used an
inappropriate hashing method~\cite{nist-800-63-3}, and only 21\% (11) recommended a secure
modern password hash. One developer recommended both a secure and insecure method:
\begin{implementation}[1]
\ldots{}hash password in bcrypt or md5\ldots{}
\end{implementation}
\begin{finding} Only a third of developers wrote code to store their
passwords hashed. 50\% of those developers recommended an insecure
hash function, and only 21\% recommended a secure hash function. The
remaining 29\% did not specify the method---they just `hashed' them.
14\% of developers remembered to salt and hash their passwords. More
comprehensive security (Figure~\ref{fig:naiakshina}) was rare.
\end{finding}
\section{RQ3: Why are developers storing passwords like this?}
\begin{table*}\tablestyle
\caption{Codebook formed from the analysis of developers' explanation of their implementation approach. Quotes are given to illustrate the use of all
codes with relevant passages \hltext{underlined}. Some responses were
assigned more than one code. No more than 3 codes were used to
capture any single response.}
\begin{tabular}{l p{\dimexpr 0.57\linewidth - 2\tabcolsep}r r r}
\toprule
\multicolumn{1}{c}{Code} & \multicolumn{1}{c}{Description} & \multicolumn{1}{c}{Count} & \rotatebox{90}{\stackanchor{Prompted}{Spec}} & \rotatebox{90}{\stackanchor{No}{Spec}} \\
\midrule
Implementation Ease & The developer wrote it like that as the implementation would be \emph{``simple''} & \input{analysis/code-implementation-ease.tex} & \input{analysis/spec-why-implementation-ease.tex} & \input{analysis/nospec-why-implementation-ease.tex}\\
\examplewhy{0}{\hltext{Because it was a simple but quite effective way to store}. To ensure that the data is secure, the function that encrypts the password must be very good.} \\\midrule
Readability & The developer focused on how understandable their code would be to a reader. & \input{analysis/code-readability.tex} & \input{analysis/spec-why-readability.tex} & \input{analysis/nospec-why-readability.tex}\\
\examplewhy{0}{\hltext{I wrote that way because it shows the idea very clearly}. The encryption code is a more difficult question and needs time and ideas to implement a good encryption.} \\\midrule
Na\"\i{}ve & The developer wrote the code in a literal manner without considering the merits of any other approaches. & \input{analysis/code-naive.tex} & \input{analysis/spec-why-naive.tex} & \input{analysis/nospec-why-naive.tex}\\
\examplewhy{0}{Because \hltext{I don't know how to wrote code, so just used a literal approach.}} \\\midrule
Experience & The developer made reference to their experience when describing how they wrote their code. & \input{analysis/code-experience.tex} & \input{analysis/spec-why-experience.tex} & \input{analysis/nospec-why-experience.tex}\\
\examplewhy{3}{\hltext{I'm somewhat experienced in applied security} and I consider the password should be stored securely, considering the worst case possible.} \\\midrule
Replication of previous efforts & The developer said they had done it like this before. & \input{analysis/code-replication.tex} & \input{analysis/spec-why-replication.tex} & \input{analysis/nospec-why-replication.tex}\\
\examplewhy{2}{I wrote code like this \hltext{because it is something I have done before.} I've written a login system for a password manager so recognise that passwords before storage should always be hashed or encrypted to avoid storing them in plain text. I used a struct mainly for storage purposes of this task, but would normally use a database such as SQL to store them, after hashing.}\\
\midrule
Feature justification & The developer justified a specific feature of their implementation (e.g.~ability to send password reminders). & \input{analysis/code-feature-justification.tex} & \input{analysis/spec-why-feature-justification.tex} & \input{analysis/nospec-why-feature-justification.tex}\\
\examplewhy{0}{This is a simple way to code and \hltext{allow for a reminder to the recipient!}} \\\midrule
Method justification & The developer justified the structure of their code. & \input{analysis/code-method-justification.tex} & \input{analysis/spec-why-method-justification.tex} & \input{analysis/nospec-why-method-justification.tex}\\
\examplewhy{0}{I used a utility class. \hltext{This class stores usernames and passwords in a Map data structure}, and then provides functions for user registration and login.} \\\midrule
Acknowledgment of limitations & The developer noted that their code has limitations, and that it doesn't have a certain feature (e.g.~it is insecure). & \input{analysis/code-limitation.tex} & \input{analysis/spec-why-limitation.tex} & \input{analysis/nospec-why-limitation.tex}\\
\examplewhy{3}{It assures the storage of password and allows to recover the password easily \hltext{even if the security is not high.}} \\
\midrule
Perceived best practice & The developer did it this way as this is the correct way to store a password or a standard way in their company. & \input{analysis/code-pbp.tex} & \input{analysis/spec-why-pbp.tex} & \input{analysis/nospec-why-pbp.tex}\\
\examplewhy{4}{this is \hltext{most accepted way} of storing passwords} \\\midrule
Consideration of threats & The developer considered a threat that might attack the code and explicitly attempted to mitigate that threat. & \input{analysis/code-threat.tex} & \input{analysis/spec-why-threat.tex} & \input{analysis/nospec-why-threat.tex}\\
\examplewhy{2}{Hashing passwords is a necessity, \hltext{storing passwords in plain text is a huge security concern:} and should never even be considered.} \\ \midrule
Taken under advisement & Someone told them this was a good way to do it. & \input{analysis/code-advisement.tex} & \input{analysis/spec-why-advisement.tex} & \input{analysis/nospec-why-advisement.tex}\\
\examplewhy{1}{\hltext{my friend who is into cybersecurity told me about this}} \\ \midrule
Only way I know & The developer indicates that this is the only way they knew how to complete the task. & \input{analysis/code-only-way-i-know.tex} & \input{analysis/spec-why-only-way-i-know.tex} & \input{analysis/nospec-why-only-way-i-know.tex}\\
\examplewhy{0}{That was the \hltext{only way i knew} to solve that problem} \\
\bottomrule \\
\end{tabular}
\label{tab:whycodebook}
\end{table*}
\begin{table*}\tablestyle
\caption{Codebook from the analysis of developers' responses to what threats did they consider when storing the passwords. Only developers who indicated that they had considered a threat's responses were analyzed.
Quotes are given to illustrate the use of all
codes with relevant passages \hltext{underlined}. Some responses were
assigned more than one code. No more than 4 codes were used to
capture any single response.}
\begin{tabular}{llrcc}
\toprule
\multicolumn{1}{c}{Code} & \multicolumn{1}{c}{Description} & \multicolumn{1}{c}{Count} & \multicolumn{1}{c}{\rotatebox{90}{\stackanchor{Prompted}{Spec}}} & \multicolumn{1}{c}{\rotatebox{90}{\stackanchor{No}{Spec}}} \\
\midrule
Access & Threat from unauthorized access to the database (e.g. leaks). & \input{analysis/threat-access.tex} & \input{analysis/spec-threat-access.tex} & \input{analysis/nospec-threat-access.tex}\\
\examplewhy{6}{\hltext{Password leaks}} \\\midrule
Cracking & Threat from attacks on stored passwords (e.g. cracking or rainbow tables). & \input{analysis/threat-cracking.tex} & \input{analysis/spec-threat-cracking.tex} & \input{analysis/nospec-threat-cracking.tex}\\
\examplewhy{1}{\hltext{reverse the hash code} but i think that is impossible because is unidirectional} \\\midrule
Hacking & Threat from unspecified threat actors, phishing or social engineering. & \input{analysis/threat-hacking.tex} & \input{analysis/spec-threat-hacking.tex} & \input{analysis/nospec-threat-hacking.tex}\\
\examplewhy{0}{Stealing them by a hacker, \hltext{hacked by an unknown user} to steal information and data} \\\midrule
Programming concerns. & The threat from vulnerabilities in their code (e.g. bugs, SQL injection) & \input{analysis/threat-programming.tex} & \input{analysis/spec-threat-programming.tex} & \input{analysis/nospec-threat-programming.tex}\\
\examplewhy{3}{\hltext{SQL injection}, unauthorized DB access} \\\midrule
Confidentiality & Concerns about making the stored passwords harder to see. & \input{analysis/threat-confidentiality.tex} & \input{analysis/spec-threat-confidentiality.tex} & \input{analysis/nospec-threat-confidentiality.tex}\\
\examplewhy{0}{Someone accessing the content that is not the main user. \hltext{If I used strings the password would be stored in strings until} the Garbage Collector clears it and we cannot control when that happens.} \\\midrule
Malware & Threat from malware, key-loggers or network attacks. & \input{analysis/threat-malware.tex} & \input{analysis/spec-threat-malware.tex} & \input{analysis/nospec-threat-malware.tex}\\
\examplewhy{2}{Someone tracing you with \hltext{keylogger or maybe trojan horse}} \\\midrule
Reflection & Consideration of what they \emph{should} have done and the security of their implementation. & \input{analysis/threat-retrospection.tex} & \input{analysis/spec-threat-retrospection.tex} & \input{analysis/nospec-threat-retrospection.tex} \\
\examplewhy{0}{Since the good is quite simple, \hltext{I am not certain if the storage is secure}.} \\\midrule
Wider-context & Concerns about the wider impact of an insecurely stored password. & \input{analysis/threat-wider.tex} & \input{analysis/spec-threat-wider.tex} & \input{analysis/nospec-threat-wider.tex}\\
\examplewhy{2}{Potential of a database dump, hackers can just login if the passwords were stored in plain text, with hashed passwords they would need to brute force the password. Failure to secure our users passwords \hltext{could lead to them having their accounts on other platforms compromised too} as users tend to reuse passwords.} \\\midrule
Insider-threat & Threats from insiders who might have access to stored passwords. & \input{analysis/threat-insider.tex} & \input{analysis/spec-threat-insider.tex} & \input{analysis/nospec-threat-insider.tex}\\
\examplewhy{4}{The database being accessed by a 3rd party, \hltext{internal threat actors}(excepting those with access to the code for password storage)}\\
\bottomrule \\
\end{tabular}
\label{tab:threatcodebook}
\end{table*}
After implementing their solutions we asked developers why they had
used a particular approach. Two of the authors used a grounded theory
approach~\cite{Strauss1998} to analyze the responses. Two passes were
required to reach the point of theoretical
saturation~\cite{Glaser1967} when no new codes were identified. The
resulting codebook, and illustrative examples of each code, is shown
in Table~\ref{tab:whycodebook}. We also contrasted the distribution
of codes in the \emph{prompted specification} and \emph{no
specification} groups and found them to be broadly similar---with the
\emph{no specification} group being slightly more likely to report
they wrote their code the way they did because the implementation was
easy. Consequently our remaining
analysis of developers explores why they implemented password storage
in the way they did, and is over the entire study group.
We also asked the developers if
they considered any threats when implementing their password storage
solution? Threat modeling is a standard technique when designing for
security~\cite{shostack2014threat} that encourages developers to
consider what defenses are needed to mitigate the potential threats to
a system. 55\% (77)
developers reported considering potential threats when implementing
their password storage solution. Their responses were analyzed by one
author, again using a grounded theory approach~\cite{Strauss1998}.
Two passes were required to reach the point of theoretical
saturation~\cite{Glaser1967} when no new codes were identified. The
resulting codebook, again with illustrative examples of each code, is
shown in Table~\ref{tab:threatcodebook}.
\subsection{You either think you do know, or you know you don't know}
Our analysis of the reasons why developers implemented password
storage in the ways they did reveal two interesting
sub-groups. Several answers appear to indicate that
the developers thought they had stored the passwords properly (the
\emph{experience}, \emph{replication of previous efforts},
\emph{perceived best practice} and \emph{taken under advisement}
codes); whereas others seemed to know that their implementation was
limited and that they didn't know how to do it (the \emph{na\"\i{}ve},
\emph{acknowledgment of limitations} and \emph{only way I know}
codes).
Within the group who thought they knew how to store passwords, developers indicated that they believed their approaches were \emph{best practice}. One developer stored the password directly into a database:
\begin{lstlisting}
INSERT INTO `users` (`username`, `password`) VALUES ('user', PASSWORD('password1'));$\ldots{}$
\end{lstlisting}
They explained this as:
\begin{whyquotation}
``Because that is the best way to store the password''
\end{whyquotation}
\noindent
Yet their solution stores the passwords directly without hashing or salting: they scored 0.
Others stated:
\begin{whyquotation}[4]
``this is most accepted way of storing passwords''
\end{whyquotation}
\begin{whyquotation}[0]
``It's based on corporate best practices''
\end{whyquotation}
\noindent Developers indicated that they knew their answer was correct because they had done similar tasks before calling upon both their experience as well as previously written code:
\begin{whyquotation}[2]
``Because I wrote a user registration system in the past.''
\end{whyquotation}
\begin{whyquotation}[0]
``I'm used to implementing similar login and authentication mechanisms in university projects and the thought process is always the same:\ldots{}''
\end{whyquotation}
\begin{whyquotation}[2]
``I wrote code like this because it is something I have done
before. I've written a login system for a password manager so
recognize that passwords before storage should always be hashed or
encrypted to avoid storing them in plain text.\ldots{}''
\end{whyquotation}
The relevant part of the code based on the login system for the password manager looked like:
\begin{lstlisting}
user.username = std::cin.get();
user.password = hashPassword(std::cin.get());} $\ldots$
void hashPassword(std::string password) {
//Cryptography algorithm to hash password, preferably using a salt }
\end{lstlisting}
It hashed the password with a \emph{cryptography algorithm}. It would \emph{preferably} use salt.
Another developer told us that they had taken advice from someone they considered
knowledgeable about cybersecurity:
\begin{whyquotation}[1]
``my friend who is into cybersecurity told me about this''
\end{whyquotation}
Yet the solution their friend supplied was mostly inadequate, only
showing signs of hashing (with MD5).
\begin{lstlisting}
$\ldots$ string hashpass = MD5(password);
PasswordDatabase.put("login","password");"
\end{lstlisting}
This group of developers appear to believe their answers are correct, and that they are following best practice. They indicate that code similar to what they wrote is in projects they've implemented. Yet despite this, there are many low scores. One developer described their experience as:
\begin{whyquotation}[3]
``I have been working as a software engineer for 8 years and have developed authentication systems for our clients hundreds of times so have come to learn the best practices for doing so.''
\end{whyquotation}
Their score would suggest they have more to learn.
Not all developers seemed to be so confident.
In contrast to the first group, other developers gave explanations that suggest they are aware that they don't know how to store passwords properly, or at least that their code had limitations.
For example one developer stated:
\begin{whyquotation}[1]
``I don't have a lot of knowledge about password storaging\ldots''
\end{whyquotation}
Their implementation hashed the password, suggesting the developer was confused about the distinction between \emph{hashing} and \emph{encryption}:
\begin{lstlisting}
$...$ string encpass = anHashingFunction(password);
myfile << username << endl;
myfile << encpass << endl;
\end{lstlisting}
They scored 1 point using Naiakshina's criteria, for hashing the password.
Another said:
\begin{whyquotation}[1]
``I wrote the code that way since it's the only way I know how to check if the passwords are valid, and the hashing /~storing bit because unhashed passwords are unsafe.
\ldots{}
Other methods could be used to encrypt the password, but I've heard hashing or MD5 hashing is the most common.''
\end{whyquotation}
The following two explanations came from developers who were in the top 10\% of highest scoring implementations, according to Naiakshina's criteria. Both acknowledge the security of their implementations, and that it wasn't perfect:
\begin{whyquotation}[3]
``It assures the storage of password and allows to recover the password easily even if the security is not high.''
\end{whyquotation}
\begin{whyquotation}[4]
``It was the simplest and easiest way I could think
\ldots{}
This way it protects most cases, but of course a more elaborate with more defence lines is needed (and the salt implementations is not very well done, \ldots{}
)''
\end{whyquotation}
This group of developers form a counterpoint to the first group who
think they know how to store passwords: they know they don't know
everything. Whilst directly comparing groups is hard (the codes are
not independent, and emerge from what developers said) a comparison of
average score between them suggests that neither group is storing
passwords more securely (comparison of mean score between the
\emph{think they know} and \emph{know they don't know} groups: $0.79$
vs $0.63$). In short, roughly a third of developers appear to be
overly confident in their knowledge of best practice in our study.
Despite this their answers do indicate that developers are aware that
password storage is an inherently security oriented task. They know they should be storing passwords securely, but plenty of them are overconfident and have misplaced assurance in what they do.
\subsection{On reflection, perhaps you know}
The \emph{acknowledgment of limitations} code from Table~\ref{tab:whycodebook} and the \emph{reflection} code from Table~\ref{tab:threatcodebook} are interesting as they highlight when developers indicated that their implementation was lacking security aspects.
For example, one developer
remembered to use a hash function with a suitable length in their
implementation. When stating which threats they considered they note
that they had forgotten to salt the password (and why that was
necessary).
\begin{whyquotation}[2]
``\ldots
(Thinking about it,
it might have been a good idea to concatenate some constant text at
the end of the password so that whether the user uses the same
password on two different attacked services cannot be determined
simply by checking whether the hashes are identical.)''
\end{whyquotation}
Others, on reflection, realized their
solution was inadequate (with respect to security). Both of the
following developers stored their passwords directly as plain-text
(scoring 0), yet when asked to consider the threats they later seemed to
realize that there were some they should have considered:
\begin{whyquotation}[0]``Unfortunately, I have not considered any
threats, but I know that the password should be
encrypted.''\end{whyquotation}
\begin{whyquotation}[0]``Actually I didn't consider them in the
pseudo-code but I assume there are some threats like brute
hacking''\end{whyquotation}
\noindent One developer stored their password directly,
but when considering threats gave a guide to storing them that would
have scored at least 3:
\begin{whyquotation}[0]``The best security practice is not to store
the password at all (not even encrypted), but to store the salted hash
(with a unique salt per password) of the encrypted
password.''\end{whyquotation}
Whilst we did not prime developers for storing passwords securely as
Naiakshina did~\cite{naiakshina-2019-if-you-want}, we still found that
developers talked about the security of their implementation. Around
half of the developers reported considering threats when implementing
their solutions, and some made reference to those threats when
describing why they'd implemented the code in the way that they did.
The threats described in Table~\ref{tab:threatcodebook} are
reasonable: the reason we hash and salt passwords is to ensure if the
database is \emph{accessed} illegally, that the passwords cannot be
trivially \emph{cracked}. This is hopeful: it suggests developers may
be learning that passwords and security are linked and that they
should store them securely, not \emph{if we want} them
to~\cite{naiakshina-2019-if-you-want}. Developers may not realize it
immediately that passwords should be stored securely, but if given
time to reflect they do seem to make that connection. Even if a
developer doesn't initially realize that password storage is a
security oriented task, by giving them time to reflect (in complement
with time to consider a specification) some developers do realize that
passwords must be stored securely.
\subsection{Google is your friend}
\begin{table}\tablestyle
\caption{Sites apparently referenced by developers.
\input{analysis/sources.tex}
\label{tab:sources}
\end{table}
There is much guidance and advice online about how to store passwords
(on sites such as \emph{Stack Overflow}, for example). When analyzing developers reasons and implementations, we checked for copying from such sites.
We searched online to see if any of the
implementations and pseudocode developers provided appeared online and
found 12 appearing on the \emph{Stack Overflow} developer forum
alongside 15 others appearing on other websites
(Table~\ref{tab:sources}). We found that 27 developers (20\%)
appeared to have copied code from various sites (shown in
Table~\ref{tab:sources}), with the majority having taken code directly
from Stack Overflow. Of these 27, 7 reported using a standard.
The group that used the online source
appeared to score significantly higher than the group whose source was unknown ($\mu=1.19$ vs $\mu=0.60$,
$p=0.017$) though the effect size was relatively small ($U=1155$,
$r_{rb}=0.23$); however when reading the solutions online we noticed that some of the articles developers appeared to have copied from also contained guidance on how to store them near-perfectly (according to Naiakshina's criteria).
One developer justified their answer as:
\begin{whyquotation}[2]
``I wrote the code like this because it is good practice not to store a password in clear.''
\end{whyquotation}
The solution appeared to have been taken from a
\emph{how-to} site which described how to implement password storage
with a variety of hashes and salts, starting with MD5 and ending with
bcrypt and scrypt; however the site went on to describe a solution at
the end of the article that would have scored 6~points (losing the
last point for only using 16 instead of 32~bits for the salt).
Another developer described their implementation as:
\begin{whyquotation}[0]
``The first and foremost way to store passwords in your database is to
have the plain text.\ldots''
\end{whyquotation}
This came from a blog
post~\cite{cox2017password}. The remainder states:
\begin{whyquotation}
``(don't do this)
I can't emphasize strongly enough that you should NEVER, EVER, store passwords in plain text."
\end{whyquotation}
The article does describe how to store
passwords using a hash and a randomly generated salt (3 points); yet again the developer only copied the
insecure counter-example at the start of the article.%
If we want
developers to store passwords correctly then we need to make sure the
code we want them to copy is immediately obvious.
That
developers are copying code from online isn't of itself
worrying---if they copied \emph{the right} solutions we
might see secure password storage. Instead, some developers seem to
be copying online code, using the articles to justify themselves, but
not reading the article all the way through.
\section{Discussion}
\subsection{Do specifications lead to securely stored passwords?}
Writing a specification has a small, but positive, effect on
developers ability to store passwords securely. Yet in saying this,
we avoid the bigger issue that developers seem to really struggle with
implementing password storage correctly. In our study 62\% of
developers failed to hash, salt or add any security mechanism
whatsoever.
Our paper joins an ever-growing body of work demonstrating that
developers are struggling implementing password
storage~\cite{wijayarathna2018johnny,naiakshina-2017-password,naiakshina-2019-if-you-want};
but our work also finds that it isn't \emph{just} that developers
struggle to use cryptography
APIs~\cite{green-2016-developers,patnaik2019usability}; and it isn't
\emph{just} that developers don't know enough about cryptography to
complete the task correctly: developers stated that hashing passwords
with MD5 was best practice (it isn't~\cite{nist-800-63-3}).
Developers would forget about salting and say that's the way that they do
it in their company. They would claim cybersecurity expertise, to
have password storage code in production, as reasons why
their code is secure; as reasons why their code follows best
practice---and yet they fall short. Our paper finds that specification is beneficial ($p=0.024$),
but, equally importantly, it highlights that developers don't know that they're storing
passwords insecurely.
\subsection{Beyond Naiakshina's criteria}
In this study we measured developers' ability to store passwords using
Naiakshina's criteria, as a proxy for the NIST~SP~800-63-3
standard~\cite{nist-800-63-3} which defines current best practice. The criteria
and standard itself is somewhat quiz-like, asking developers to remember
cryptographic techniques like hashing and salting as well as arbitrary lengths and
counts. If developers do not know these requirements then they will not
remember them. so what then do we learn \emph{beyond} the fact that developers do not
seem to recall Naiakshina's criteria?
An ideal specification might have listed the criteria in full as functional
requirements, but it might also have been as simple as:
\emph{``store the password securely, following NIST SP 800-63-3.''};
yet none of the developers in our
study made reference to any standard in their specifications. Developers seemed
to know there was a \emph{best practice} they ought to be following, yet didn't
appear to go look up what it actually was. Whether this
generalizes and developers' recollection of other standards is equally poor is a
topic for future work.
Whilst one good approach to implementing password storage is to do what the
standard says, another equally valid (and arguably better) aproach is to use a
framework and let it do it for you. Web-frameworks, like Django, include
password storage systems (and in Django's case explicitly reference NIST
password
standards~\cite{django-password-management})
and can take care of passwords for developers. Again, developers in our study
did not appear to make use of frameworks like this, so is it that developers are
unaware of these features inside frameworks, or did they choose not to use them?
Perhaps given the seeming recalcitrance towards reading standards, the
resistance towards using frameworks, and the confidence many displayed that they
were in fact following best practice we might conclude that developers are over
confident in their abilities. Why use a library when you can implement it
yourself trivially? Why check the standard when you know already what best
practice is? Developers seem to have learned not to \emph{roll their own
crypto}; perhaps they should also consider avoiding \emph{rolling their own
authentication} in future too?
\subsection{Developers are still not the enemy}
We say that \emph{users and developers are not the
enemy}~\cite{adams1999users,green-2016-developers}---that we must not
blame users or developers when an API or security interface is not
designed for a human to be able to use correctly. Yet when we talk
about password storage we present it as a list diktats that developers
\emph{must} implement to ensure they do the task correctly. As we,
and
others~\cite{wijayarathna2018johnny,naiakshina-2017-password,naiakshina-2019-if-you-want},
have shown developers cannot follow these instructions. Perhaps then,
instead of pointing out that developers can't store passwords and
providing lists on what they \emph{must} do, we should \emph{fit
the task to the human} and provide alternative mechanisms for storing
passwords correctly without having to remember what the current best
practice actually is, or understand the intricacies of various hashing
schemes. Truman said of being the President: \emph{``He'll sit here
and he'll say, ``Do this! Do that!'' And nothing will
happen''}~\cite{neustadt1960presidential}; and a comparison can be
drawn to the security and cryptography communities: we cannot keep
sitting here; saying, \emph{``Hash this! Salt That!''} and pointing at
NIST SP 800-63-3, because Truman was right: \emph{``nothing will
happen''}. We need to find usable mechanisms for password storage.
What might these mechanisms look like? Cryptography libraries, such
as Google's \emph{Tink}~\cite{google-tink}, are attempting to wrap
cryptographic details so that developers can use cryptography without
understanding what a hash really is~\cite{schmieg2020tweet}. There has
been limited usability validation of such
approaches~\cite{mindermann2020fluid}, however, and further work,
documentation, and exemplar code~\cite{patnaik2019usability} is needed
to show whether this approach is effective. Alternatively, some
developers seemed to copy code from online sources---ensuring that
developers can find the trivially find the \emph{right} way to store
passwords and that the \emph{right} code is trivially available may
also help developers without requiring them to understand the
cryptographic details.
Finally, a different solution altogether may be to encourage
developers not to store passwords at all and instead use federated
identity management systems (such as OAuth~\cite{hardt2012oauth}).
Whilst these systems can remove the need for some app developers to
implement cryptography correctly, they come with their own set of
privacy and security \emph{gotchas}~\cite{lodderstedt2020oauth} and
challenges~\cite{sun2012devil}---we should be cautious that by
recommending an alternative to passwords we are not replacing the
challenge of storing a password with the challenge of implementing a
federated authentication system. Work on privacy-preserving federated
identity management has helped to resolve some of the privacy
challenges associated with federated identity
management~\cite{chow2012spice,isaakidis2016unlimitid}, though these
are yet to be widely adopted in practice.
Explicitly prompting developers to write a specification does help
improve the quality of password storage; but developers are still
mostly failing at password storage whilst still believing they are
getting it right. Giving developers time to reflect helps them realize
the limitations of their approach: but until we have
\emph{developer-centered usable} password storage methods, the problem
of poorly stored passwords isn't going away. We can do better than saying \emph{``Do this! Do that!''} and watching nothing happen.
\section{Conclusion}
Does the act of writing a specification (how the code should behave) for a piece
of security sensitive code lead to developers producing more secure code? In a
statistical sense: yes, though the effect is small ($p=0.027$, $r_{rb}=0.209$).
In a broader sense however we show that whilst writing a specification does help
developers remember more of the conditions for secure password storage, leaving
this task to a memory exercise and hoping developers refer to a standard isn't
working.
Future work should examine and empirically evaluate alternative strategies for helping developers complete authentication tasks---whether in the form of usable cryptography libraries, privacy preserving federated identity schemes, or alternative awareness schemes to diktats and standards.
Additionally, whilst this study looked to see if \emph{any} form of specification improved developers ability to store passwords correctly; \emph{specific} approaches (whether that be software building codes~\cite{landwehr2015we-need}, requirements engineering, or formal verification) may yield more promising results. Finally, in this study we saw developers struggling to remember how to do secure password storage, but we may see similar results for other areas where knowledge of what the \emph{right thing to do} is conveyed only through diktats and standards---future work should examine whether this result is general or specific to password storage.
\section*{Acknowledgment}
This research is supported in part by
EPSRC Grant
EP/P011799/2
and the National Cyber Security Centre.
\balance
\bibliographystyle{IEEEtran}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,223 |
Q: Can weighted data be used with the CrossTable function in R? I have attached sample weights to my data using the code below;
s_w <- couple_dta$h_sw /1000000
design <-svydesign(ids =~s_unit + hh, strata =~res , weights = s_w ,data =c_dta)
I had earlier created crosstables with unweighted data using the code;
CrossTable(c_dta$varA, c_dta$varB, prop.c = FALSE ,prop.r = FALSE , prop.chisq = FALSE , format = "SPSS")
The result of CrossTable with unweighted data is something below.
Variable B
Variable A | f | mf | m | Row Total |
---------------------|-----------|-----------|-----------|-----------|
m | n1 | n2 | n3 |n1 +n2+n3 |
|n1/N x 100 | n2/N x 100|n3/N x 100 | |
---------------------|-----------|-----------|-----------|-----------|
mf | n5 | n6 | n7 | n5+n6+n7 |
|n5/N x 100 |n6/N x 100 | n7/N x 100| |
---------------------|-----------|-----------|-----------|-----------|
f | n8 | n9 | n10 |n8+n9+n10 |
|n8/N x 100 |n9/N x 100 |n10/N x 100| |
---------------------|-----------|-----------|-----------|-----------|
Column Total | n1+n5+n8 | n2+n6+n9 |n3+n7+n10 | N |
---------------------|-----------|-----------|-----------|-----------|
Is there a way of incorporating weights to the second data. I have looked at 'prop.table(svytable)' but not sure how to proceed, given that I would also like to display the number of observations in each cell and the corresponding percentage.
Thank you in advance
Edit : I have used the svytable and Crosstable functions to achieve my goal.
table2 <- svytable(~c_dta$VarA + c_dta$wrd_VarB, design=design)
CrossTable(table2 ,prop.c = FALSE ,prop.r = FALSE , prop.chisq = FALSE , format = "SPSS")
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 388 |
Smart, Mercedes-Benz and Porsche as "company car"
Who isn't dreaming of an LR Porsche or a Mercedes-Benz for private use? These dreams come true with LR. More than 5,000 LR Smarts are on the road in Germany. A trend that is sharply on the rise.
The LR car plan with Smart, Mercedes-Benz and Porsche rewards LR partners for successful cooperation and at the same time motivates them to tackle new objectives.
5 tiered car concept from smaller to a luxury sports car.
Over 6500 cars on the roads.
LR is one of the biggest customer of Smart, Mercedes Benz and Porsche. | {
"redpajama_set_name": "RedPajamaC4"
} | 7,044 |
\section{Introduction}
This demo file is intended to serve as a ``starter file''
for IEEE conference papers produced under \LaTeX\ using
IEEEtran.cls version 1.8a and later.
I wish you the best of success.
\hfill mds
\hfill September 17, 2014
\subsection{Subsection Heading Here}
Subsection text here.
\subsubsection{Subsubsection Heading Here}
Subsubsection text here.
\section{Conclusion}
The conclusion goes here.
\ifCLASSOPTIONcompsoc
\section*{Acknowledgments}
\else
\section*{Acknowledgment}
\fi
The authors would like to thank...
\section{Introduction}
Hyperspectral remote sensing images with high spatial and spectral resolution is used to capture the inherent properties of the surface. These hyperspectral images (HSI) contains a huge number of contiguous spectral bands. It spreads over a narrow spectral bandwidth with wealth of information content. These informations are used for characterization, identification and classification of the physical and chemical properties of the land-cover with improved accuracy. The huge spectral bands implies the high dimensional redundant HSI data. This high dimensionality is the major challenge in HSI classification. In order to overcome this challenge, dimensionality reduction (DR) is usually applied to the HSI data. An effective DR method reduces the high dimension data into low dimensional representative features. This DR method improves the classification performance by reducing computational complexity and exploring the intrinsic property of the reduced data features.
In the field of HSI processing, a large number of DR approaches have been developed during past few years. Among them in unsupervised category principal component analysis (PCA) \cite{martinez2001pca} is widely used one. In addition, several supervised DR approaches have also been developed, linear discriminant analysis (LDA) \cite{ye2004optimization} is the most popular classical approach. Among LDA and PCA, LDA uses the labeled information for DR and performs better than PCA in classification task. However, LDA always assumes the data distribution as Gaussian with equal variance and unimodal. Hence, it fails to handle the real HSI data which is heteroscedastic and multimodal in nature. A graph based scaling cut (SC) \cite{zhang2009local}, \cite{zhang2015scaling} method addresses these problem by constructing the pairwise similarity matrix among the samples of the classes.
The graph based SC method basically makes a projection of the data into a lower dimensional space by maximizing the variance of the input data points. Although, the SC method by Zhang \textit{et al.} in \cite{zhang2015scaling} works well for the multimodal hyperspectral data, they are very sensitive in handling the outliers and noise in the dataset. The conventional SC works by computing the dissimilarity matrix among the data samples. This dissimilarity matrix computation is mostly done by calculating the conventional L2-norm between the samples. The square operation in L2-norm criterion magnifies the outliers \cite{ding2006r}, \cite{wang2014fisher}. Therefore, the presence of outliers drift the projection vectors from the desired projection direction. Hence, dimension reduction and classification of hyperspectral data demands robust algorithms that are resistant to possible outliers.
It is found that, the L1-norm based DR method is a robust alternative to handle outliers problem in image classification \cite{wang2014fisher}, \cite{liu2017non}, \cite{ke2005robust}, \cite{kwak2008principal}, \cite{li2010l1}. Kwak \textit{et.al.} \cite{kwak2008principal} computed the covariance matrix using L1-norm and proposed PCA-L1 by greedy strategy. Ke and Kanade, in \cite{ke2005robust}, proposed L1-PCA by using the alternative convex method to solve the projection matrix. Similarly in \cite{wang2014fisher}, Wang \textit{et.al.} proposed LDA-L1 by solving the supervised LDA method using L1-norm maximization in an iterative manner. Li \textit{et.al.} \cite{li2015robust} proposed the 2D version of the LDA (L1-2DLDA) using the L1-norm optimization.
L1-norm based LDA has achieved excellent performance for image classification \cite{wang2014fisher}\cite{li2015robust}. However, our HSI data is heteroscedastic and multimodal. SC has proved its worth \cite{zhang2015scaling} HSI classification. Motivated by these literature, we propose a L1-norm based scaling cut method (L1-SC) for DR and classification of HSI data.
In this work we formulate the SC algorithm into an L1-norm optimization problem by maximizing the ratio of between-class dissimilarity and within-class dissimilarity matrix. Then, we solve this L1-norm optimization problem by using an iterative algorithm to generate a projection matrix. The projected reduced dimension HSI data are further used for classification by using support vector machine (SVM) classifier. We analyze the classification performance by applying it over the spectral information of two real world HSI datasets.
The rest of the paper is organized as follows. In section~\ref{sec:prelimnary}, a brief introduction to the conventional L2-norm based SC method is discussed. We present the proposed L1-SC method including its objective function and algorithmic procedure for its solution in section~\ref{sec:proposed_work}. Then section~\ref{sec:res_analysis} enumerates the experimental results of the proposed L1-SC method over two HSI datasets. Finally, we give the conclusive remarks to our work in section~\ref{sec:conclusn}.
\section{Conventional L2- Norm based Graph Scaling Cut Criterion Revisited} \label{sec:prelimnary}
The purpose of SC is to determine the mapping matrix for projecting the original data into a lower dimension space. The classical LDA method is computed based on the assumption that the data distribution of each class is Gaussian with equal variance. However, the distribution of real world data is more complex than Gaussian. Hence LDA fails when data is heterscedastic and multimodal. The major advantage of the SC over the state-of-art LDA is handling these heteroscedastic and multimodal data. This method eleminates the Gaussian distribution limitation of LDA by constructing the dissimilarity matrix among the data samples.
Let $X =(x_1, x_2, ...,x_n) \in R^{D\times n}$ is the input training dataset, given by $\{x_i,L_i\}|_{i=1}^n$. Here $L_i = \{1,2,...,C\}$ is the class label of the corresponding training data with total $C$ classes and $n$ training data samples. The objective is to determine a projection matrix, that project the input training data of $D$ dimensions into reduced $d$ dimension such that $d << D$. The between-class dissimilarity matrix and the within-class dissimilarity matrix of SC are defined as
\begin{equation}
\begin{split}
S_{B_k}^{SC}\, = \,\sum\limits_{x_i\, \in \,{U_k}} {\sum\limits_{x_j\, \in \,{{\bar U}_k}} {\frac{1}{{{n_k}{n_{\bar{k}}}}}\,({x_i} - {x_j}){{({x_i} - {x_j})}^T}} }\\
S_{W_k}^{SC}\, = \,\sum\limits_{x_i\, \in \,{U_k}} {\sum\limits_{x_j\, \in \,{{U}_k}} {{\frac{1}{{{n_k}{n_k}}}}({x_i} - {x_j}){{({x_i} - {x_j})}^T}} }
\end{split}
\end{equation}
where $U_k$ represents all the samples from $k$th class and $n_k$ is the total number of elements in $U_k$. Similarly, $\bar{U_k}$ represents all the data points that that does not belong to the $k$th class and ${n_{\bar{k}}}$ denotes the total number of elements in $\bar{U_k}$. $S_{B_k}^{SC}$ represents the dissimilarity between $U_k$ class and $\bar{U_k}$, whereas $S_{W_k}^{SC}$ is the dissimilarity matrix within the $U_k$ class. Based on the $S_{W_k}^{SC}$ and $S_{B_k}^{SC}$, the objective function of SC can be written as
\begin{align}\label{eq: scaling_cut}
\begin{aligned}
Scut(W)\, & = \,\frac{{\left| {\sum\limits_{k\, = \,1}^c {{W^T}{S_{B_k}^{SC}}W} } \right|}}{{\left| {\sum\limits_{k\, = \,1}^c {({W^T}{S_{W_k}^{SC}}W\, + {W^T}{S_{B_k}^{SC}}W\,)} } \right|}}\\
& = \,\frac{{\left| {{W^T}{S_{B}^{SC}}W} \right|}}{{\left| {{W^T}{({S_{W}^{SC}} + {S_{B}^{SC}})W}} \right|}}\\
&= \,\frac{{\left| {{W^T}{S_{B}^{SC}}W} \right|}}{{\left| {{W^T}{S_{T}^{SC}}\,W} \right|}}
\end{aligned}
\end{align}
where $S_{B}^{SC}=\sum\limits_{k=1}^C{S_{B_k}^{SC}}$, $S_{W}^{SC}=\sum\limits_{k=1}^C{S_{W_k}^{SC}}$, and $S_{T}^{SC} = (S_{B}^{SC} + S_{W}^{SC})$ is the total dissimilarity matrix and $W$ is the projection matrix. The dissimilarity matrix is scaled according to the size of the class. Hence, this graph cut is termed as scaling cut.
\section{Proposed L1-Norm based Scaling Cut Criterion} \label{sec:proposed_work}
The conventional L2-norm based graph scaling cut criterion basically determines the projection matrix by maximizing the between-class distances, and minimizing the within-class distances to enhance the compactness among the data points. These models characterize the geometric structure of the data by computing the L2-norm. These L2-norm is computed by using square euclidean distance, which is sensitive to outliers and noises \cite{wang2014fisher}, \cite{liu2017non}. These outlier elements drift the projection vectors from the desired projection directions. Hence, it reduces the flexibility of L2-norm based algorithms. To handle this issue, L1-norm based technique is widely used as a robust alternative of conventional L2-norm based technique. Motivated by the idea of L1-norm based modeling, we propose to model the graph based scaling cut criterion by using the L1-norm optimization instead of L2-norm optimization. This L1-norm based SC method is solved by following iterative algorithm
\subsection{L1-norm based Graph Scaling Cut ($L1-SC$)}
Inspired by the existing literatures on L1-norm based method \cite{liu2017non}, \cite{li2015robust}, we propose to maximize the SC criterion using L1-norm rather than L2-norm. The equation (\ref{eq: scaling_cut}) can be simplified to a trace ratio \cite{fukunaga2013introduction} problem, which can further be reduced to the Frobenius norm, given by,
\begin{align}
&W^* = \max_{W^TW = I} \frac{Tr(W^TS_{B}^{SC}W)}{Tr(W^TS_{T}^{SC}W)} \nonumber \\
&= \max_{W^TW = I}\frac{\sum\limits_{\substack{k; x_i \in U_k;\\x_j \in \bar{U}_k}}\frac{1}{n_k n_{\bar{k}}} Tr\Big(W^T({x_i} - {x_j}){{({x_i} - {x_j})}^T}W\Big)}{\sum\limits_{\substack{k; x_i \in U_k;\\x_j \in U_k}} \frac{1}{n_k n_{k}} Tr\Big(W^T({x_i} - {x_j}){{({x_i} - {x_j})}^T}W\Big)} \nonumber \\
&= \max_{W^TW = I}\frac{\sum\limits_{k = 1}^c\sum\limits_{x_i \in U_k}\sum\limits_{x_j \in \bar{U}_k} \frac{1}{n_k n_{\bar{k}}} \left\|W^T({x_i} - {x_j})\right\|_F^2}{\sum\limits_{k = 1}^c\sum\limits_{x_i \in U_k}\sum\limits_{x_j \in U_k} \frac{1}{n_k n_{k}} \left\|W^T({x_i} - {x_j})\right\|_F^2}
\end{align}
As can be observed, the above objective is based on Frobenius norm, which also involves the square operations and in term, it is sensitive to outliers to noise and outliers similar to L2-norm. In order to reduce the sensitivity, we use the objective function in terms of the L1-norm. The proposed model of the objective function for L1-norm SC is defined as,
\begin{align} \label{eq:l1sc_optmiz_prblm}
v_{opt} &= \max_{v^Tv = 1}
\frac{\sum\limits_{k\, = \,1}^c\sum\limits_{x_i \in U_k}\sum\limits_{x_j \in \bar{U}_k} \left\|{{{v^T}\,{\frac{1}{{{n_k}{n_{\bar{k}}}}}\,({x_i} - {x_j})}} } \right\|_1}{\sum\limits_{k\, = \,1}^c \sum\limits_{x_i \in U_k}\sum\limits_{x_j \in {U}_k} \left\| {{{{v^T}\,{\frac{1}{{{n_k}{n_{k}}}}\,({x_i} - {x_j})}}} } \right\|_1} \nonumber \\
&= \max_{v^Tv = 1}
\frac{\sum\limits_{k = 1}^c\sum\limits_{x_i \in U_k}\sum\limits_{x_j \in \bar{U}_k} \frac{1}{{{n_k}{n_{\bar{k}}}}} |{{{v^T}{({x_i} - {x_j})}} }|}{\sum\limits_{k = 1}^c \sum\limits_{x_i \in U_k}\sum\limits_{x_j \in {U}_k} \frac{1}{{{n_k}{n_{k}}}} |{{{{v^T}{({x_i} - {x_j})}}} }|}
\end{align}
The objective of the criterion (\ref{eq:l1sc_optmiz_prblm}) is to find the optimal projection vector $v$ that maximize the ratio of between-class dispersion to the within-class dispersion. These optimized projection vectors are used to construct the optimal projection matrix $ V = \{v_1, v_2, ..., v_d\}$. These projecting vectors are sequentially optimized in $d$ directions.
We derive the following iterative algorithm to find the optimal projection vector $v$ that maximizes the objective function (\ref{eq:l1sc_optmiz_prblm}). The entire algorithmic procedure for L1-SC method is listed below
\subsection{Algorithmic Procedure for L1-SC}
The aforementioned objective function (\ref{eq:l1sc_optmiz_prblm}) involves maximization of L1-norm based optimization problem. We solve this problem by an iterative algorithm to obtain the optimal projection vector $v^*$ of the matrix $V$.
The objective function (\ref{eq:l1sc_optmiz_prblm}) seems similar to the trace ratio formulation of the general graph scaling cut in \cite{zhang2009local} and \cite{zhang2015scaling}.
It is difficult to solve (\ref{eq:l1sc_optmiz_prblm}) by the traditional optimization techniques as both numerator and denominator are constructed by L1-norm maximization and minimization. Inspired by the idea used in \cite{wang2014fisher}, \cite{kwak2008principal}, \cite{li2015robust} and \cite{wang2012l1}, we are using similar L1-norm optimization technique in this work. Thus, we solve the objective function (\ref{eq:l1sc_optmiz_prblm}) to find the optimal projection vector $v^*$ by the iterative technique. The algorithmic procedure of L1-SC is given as follows.
\begin{itemize}
\item[1.] The iteration variable $t$ is set to zero ($t=0$). Then we randomly initialize the $d$ dimensional vector $v(t)$ and normalize it such that ${v(t)}^T{v(t)} = 1$.
\item[2.] Two sign functions are defined to compensate the absolute value operation for the numerator and denominator term of (\ref{eq:l1sc_optmiz_prblm}) . These sign functions are computed as
\begin{equation}\label{eq:sign_func}
\begin{split}
{q_{ij}}(t) = & \,\left\{ {\begin{array}{*{20}{c}}
{1,\,\,\,\,\,\,\mbox{if}\,\,\,\,{v^T}(t)({x_i} - {x_j})\,\, > 0}\\
{ - 1,\,\,\,\,\,\mbox{if}\,\,\,{v^T}(t)({x_i} - {x_j})\, \le 0}
\end{array}} \right.\\
& \mbox{and} \\
{r_{ij}}(t) = & \,\left\{ {\begin{array}{*{20}{c}}
{1,\,\,\,\,\,\,\mbox{if}\,\,\,\,{v^T}(t)({x_i} - {x_j})\,\, > 0}\\
{ - 1,\,\,\,\,\,\mbox{if}\,\,\,{v^T}(t)({x_i} - {x_j})\, \le 0}
\end{array}} \right.
\end{split}
\end{equation}
\item[3.] Use the sign function to compute $p(t)$ and $b(t)$ by the following equation:
\begin{equation}\label{eq:pt_bt}
\begin{split}
p(t) = & \sum\limits_{k = 1}^c \sum\limits_{i = 1}^{{n_k}}{\sum\limits_{j = 1}^{{n_{\bar{k}}}} {{q_{ij}}(t){\frac{1}{{{n_k}{n_{\bar{k}}}}}\,{v^T}(t)({x_i} - {x_j})}} } \\
b(t) = & \sum\limits_{k = 1}^c \sum\limits_{i = 1}^{{n_k}}{\sum\limits_{j = 1}^{{n_k}} {{r_{ij}}(t){\frac{1}{{{n_k}{n_{k}}}}\,{v^T}(t)({x_i} - {x_j})}} } \\
\end{split}
\end{equation}
Then using $p(t)$ and $b(t)$, update $g(v(t))$
\begin{equation} \label{eq:find_g_vt}
g(v(t)) = \frac{p(t)}{{v(t)}^T{p(t)}}-\frac{b(t)}{{v(t)}^T{b(t)}}
\end{equation}
\item[4.] Then update the vector $v(t)$ using $g(v(t))$ by
\begin{equation}\label{eq:update_vt}
v(t+1) = v(t) + \gamma g(v(t))
\end{equation}
where $\gamma$ is the learning rate parameter (a small positive value). Then normalize the $v(t+1)$ and update $t=t+1$. If any denominator in (\ref{eq:find_g_vt}) happen to zero then perturb the $v(t)$ with a small non zero random vector $\Delta v$ and update it by $v(t) = (v(t)+\Delta v)/{||(v(t)+\Delta v)||}$ and start with step-2.
\item[5.] Convergence check: If the $v(t)$ doesn't show significant increment or $||v(t+1)-v(t)|| \le \epsilon$ or total iteration number is greater then maximum given iteration number, then go to step-2 otherwise go to step-6.
\item[6.] Stop iteration and assign $v^* = v(t)$.
\end{itemize}
Above procedure only gives one optimal projection vector. In practical classification problem this one vector is not sufficient for the projection. Hence, It need a projection matrix consists of multiple projection vectors placed in its column space to optimize the objective function. These projection vectors are used to update the input data matrix by
\begin{equation}
X \leftarrow X - {v^*}({v^*}^T)X
\end{equation}
and then the projection matrix $V$ is padded as $V=[V,{v^*}]$.
Using the above procedure, we can form the optimal projection matrix $V$ of size $R^{D \times d}$. The pseudo-code for the complete algorithmic procedure for the projection matrix of L1-SC is listed in Algorithm~$1$
\begin{algorithm} \label{alg:L1_SC}
\SetKwInOut{Input}{Input}
\SetKwInOut{Output}{Output}
\SetKwInOut{Result}{Result}
\Input{The training dataset $ \{x_i, L_i\} _{i = 1}^n \in R^{D \times n}$; \\ $L_i$ is the label of each training data $x_i$; \\ Desired dimensionality is $d$ and $d \ll D$.}
Formulate the L1-norm based objective function in (\ref{eq:l1sc_optmiz_prblm}) to solve the optimization problem.\\
Determine the optimal projection vector $v^*$ by solving the optimization problem (\ref{eq:l1sc_optmiz_prblm}) in Algorithm~2 \\
Update the input data by using $X = X - {v^*}{v^*}^TX$. \\
Pad these optimal projection vectors $v^*$ into the optimal matrix by $V=[V,{v^*}]$. \\
Project the original data into the lower dimensional space $d$ by projection matrix $V$ \\
\Output {Projection matrix $V=\{v_1, v_2, ..., v_d\}$ $\in R^{D \times d}$, consists of $d$ projection vectors
\Result{Projected matrix $Y = {V^T}X$}
\caption{L1-norm based scaling cut algorithm}
\end{algorithm}
\begin{algorithm} \label{alg:projc_mat_L1-SC}
\SetKwInOut{Input}{Input}
\SetKwInOut{Output}{Output}
\SetKwInOut{Result}{Result}
\SetKwProg{For}{For}{}{}
\Input
Number of projection vector $d$ ($d \ll D$); \\ Learning rate parameter $\gamma$; \\ Maximum number of iteration is \textit{itmax}}
Set $t=0$ and Initialize $v(0)$ to a $D$ dimensional random vector such that ${v(0)}^T{v(0)}=1$ \\
Compute the sign function $q_{ij}(t)$ and $r_{ij}(t)$ using (\ref{eq:sign_func}) and set $p(t)$ and $b(t)$ using (\ref{eq:pt_bt})\\
Determine the $g(v(t))$ function using (\ref{eq:find_g_vt}) to update the $v(t)$.\\
Update the $v(t)$ by using (\ref{eq:update_vt}). where $\gamma > 0$ is the learning parameter.\\
Converge if: $||v(t+1)-v(t)|| \le \epsilon$ or $t > itmax$
\Output {Projection vector $v^* = v{(d)}$}
\caption{Computation of projection vector for $v{^*}$}
\end{algorithm}
\section{Experimental Results and Analysis}\label{sec:res_analysis}
In this section we evaluate the performance of the proposed L1-SC method on two HSI datasets\footnote{http://www.ehu.eus/ccwintco/index.php?title=Hyperspectral\_Remote\\\_Sensing\_Scenes}: Salinas $(D=204, C=16)$ and Pavia center $(D=102, C=9)$. Then we compare it with the state-of-art conventional LDA \cite{ye2004optimization}, SC \cite{zhang2015scaling}, LSC \cite{zhang2013semisupervised} and L1-LDA \cite{wang2014fisher}. In conventional L2-norm based methods use PCA as preprocessing but in L1-norm methods we don't use any preprocessing step. In classification stage, we use SVM classifier with linear kernel to identify the robustness of the proposed algorithm.
\begin{figure}[h]
\centering
\subfloat[]{
\label{subfig:Salinas_comp}
\includegraphics[width=0.48\textwidth]{Figures/Salinas_10-50sample_10dims_l1_l2_nw1.png} }
\subfloat[]{
\label{subfig:Pavias_comp}
\includegraphics[width=0.48\textwidth]{Figures/pavia_10-50sample_10dims_l1_l2_nw1.png} }
\caption{ Effects of different number input samples for the methods on overall accuracies on two data sets Salinas (\ref{subfig:Salinas_comp}) and Pavia center (\ref{subfig:Pavias_comp}). From left to right of X-axis shows the overall accuracies with $10, 20, 30, 40$ and $50$ number input data samples for $10$ dimensions.}
\label{fig:salina_pavia_comp}
\end{figure}
\begin{table*}[h]
\centering
\caption{Classification performance of proposed approach compared with other L2-norm and L1-norm based approaches }
\label{tab:Classfcn_L1_l2}
\begin{tabular}{l|c c c|c c c}
\hline
\multicolumn{1}{c|}{Dataset} & \multicolumn{3}{c|}{\textbf{Salinas}} & \multicolumn{3}{c}{\textbf{Pavia Center}} \\ \hline
Methods & Accuracy + stdv & F1-Score & Dims & Accuracy + Stdv & F1-Score & Dims \\ \hline
LDA \cite{ye2004optimization} & $83.14 \pm 1.93$ & $0.8917$ & $35$ & $92.34 \pm 0.64$ & $0.8406$ & $25$ \\
SC \cite{zhang2015scaling} & $81.38 \pm 1.41$ & $0.8558$ & $40$ & $93.61 \pm 0.68$ & $0.8600$ & $25$ \\
LSC \cite{zhang2013semisupervised} & $83.09 \pm 1.88$ & $0.8939$ & $50$ & $93.43 \pm 1.07$ & $0.8587$ & $45$ \\ \hline
L1-LDA \cite{wang2014fisher} & $83.21 \pm 1.85$ & $0.8913$ & $30$ & $93.50 \pm 0.61$ & $0.8542$ & $40$ \\
\textbf{L1-SC} \textbf{(Proposed)} & { $\mathbf{84.01 \pm 1.67}$ } & {$\mathbf{0.8956}$} & {$\mathbf{15}$} & {$\mathbf{94.20 \pm 0.63}$} & {$\mathbf{0.8724}$} & {$\mathbf{10}$} \\ \hline
\end{tabular}
\end{table*}
In these experiments, we randomly select $10$ training samples from each class of the dataset and rest of the samples are used as test dataset. All obtained results are the average of the $5$ iterations. Here we evaluate and analyze the effectiveness of the proposed L1-SC by determining the overall classification accuracy of the SVM classifier on the projected data.
Fig.~\ref{fig:salina_pavia_comp} shows the behavior of different L2-norm and L1-norm based algorithms in terms of overall classification accuracy with respect to varied number of input samples. Here, Fig.~\ref{subfig:Salinas_comp} and Fig.~\ref{subfig:Pavias_comp} shows the overall classification accuracy of Salinas and Pavia dataset for input data size from $10$ to $50$. From this figure, it is clearly observed that the proposed L1-SC method completely outperforms the L2-norm based methods and performs on par with L1-LDA when the input data sample size is less.
\begin{figure}[h]
\centering
\subfloat[]{
\label{subfig:Salinas_Ns_comp}
\includegraphics[width=0.48\textwidth]{Figures/Salinas_10_sample_withNoise.png} }
\subfloat[]{
\label{subfig:Pavias_NS_comp}
\includegraphics[width=0.48\textwidth]{Figures/Pavia_10_sample_withNoise.png} }
\caption{ Illustration of noise robustness of the proposed method with respect to other methods on two data sets Salinas (\ref{subfig:Salinas_Ns_comp}) and Pavia center (\ref{subfig:Pavias_NS_comp}).
\label{fig:salina_pavia_noise_comp}
\end{figure}
To better illustrate the noise robustness feature of the proposed L1-SC method with respect to others, we inject white Gaussian noises of different levels to the raw input HSI data and performed the classification on these data using different approaches. The variance of the noise level is varied from 2\% to 10\% of the variance of the pixel values. As Fig.~\ref{fig:salina_pavia_noise_comp} indicate, the proposed L1-SC method is more robust to noises and achieve better classification accuracies than other methods.
The proposed L1-SC method is compared with other popular L2-norm and L1-norm based methods. The statistics of the highest overall classification accuracy along with corresponding $F1$-score and dimension of the algorithms for Salinas and Pavia center dataset are highlighted in Table~\ref{tab:Classfcn_L1_l2}. Here in Table~\ref{tab:Classfcn_L1_l2}, all the results taken classification accuracy are the average of $5$ runs using $10$ random training samples per class. In order to show the robustness of the algorithm, we have considered the $F1$-score along with the overall classification accuracy as the performance measure \cite{sokolova2009systematic}. Table~\ref{tab:Classfcn_L1_l2} gives the following observations
\begin{itemize}
\item The overall classification accuracy of L1-norm based methods performs better than the other state-of-art L2-norm based methods.
\item The classification results of the proposed L1-SC method outperforms the other L2-norm based methods and L1-LDA for both the datasets with less dimensions.
\item In Salinas dataset, the proposed L1-SC method produces highest accuracy with maximum $F1$-score among other approaches by considering only $15$ dimensions. Similarly in case of Pavia center dataset, it takes only $10$ dimensions. This shows the effectiveness of the algorithm in finding proper projection direction.
\end{itemize}
The above observations clearly explains the robustness of the proposed algorithm in low dimensional feature space.
\section{Conclusion}\label{sec:conclusn}
In this study, we have proposed a novel DR method L1-SC by computing the L1-norm based inter-class and intra-class dispersion. This method determines the projection directions by exploiting the discriminant structure and preserving the geometrical structure of the data. Our method differs from other state-of-art in various ways. For instance, it preserves the intrinsic property as well as the distribution of the data and we believe it handles multimodal and heteroscedastic data with noise and outliers quite well. We examined the performance of our method and other methods over two real world HSI datasets. The promising results of L1-SC on these two datasets demonstrates its noise robustness and efficiency.
\bibliographystyle{IEEEtran}
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\section{Introduction}
Among a number of problems dealt with the surface diffusion, which
occurs either due to thermally activated \cite{PhysA195,Ferrando}
or tunnelling mechanisms \cite{Ferrando,single}, one can single
out the investigation of the frustrated translational mode
(T-mode) of the adsorbate \cite{T-mode-1,T-mode-2}. The T-mode is
known to appear when the adparticle moves between two stable
positions at the surface within one adsorption site (for instance,
between the atop position and the saddle point \cite{single}) due
to interaction with phonons or electronic subsystem of the
substrate. This motion of the adsorbate is being detected during
inelastic helium atom scattering (IHAS) \cite{IHAS-1,IHAS-2} as an
additional peak in the dynamic structure factor
\cite{T-mode-2,Sfactor-1,Sfactor-2}. The vibrational nature of the
T-mode allows to refer this excitation to the external (low
frequency) modes of the adsorbate \cite{exMode-1,exMode-2}, which
are more or less temperature dependent and dispersionless with
homogeneous broadening at low coverages \cite{T-mode-2}.
In the last years the T-mode became a subject of the intensive
studies of both experimentalists and theorists. For instance, in
the recent scanning tunnelling spectroscopy experiments
\cite{Komeda} the excitation of the T-mode in polyatomic molecules
CO/Pd(110) has been explained in terms of the energy transfer from
the C-O stretch mode to the frustrated translational one due to
the anharmonic coupling between normal modes. A certain intrigue
is introduced by the fact that the T-mode is observed even in such
``classical'' systems as CO/Cu(001) and CO/Pt(111)
\cite{Csystems}, though the underlying mechanism of the T-mode
formation is purely quantum mechanical: the transitions between
ground and excited states within a well. This stimulated a
creation of the models based on classical \cite{Csystems} or
quantum \cite{Micha19} Langevin equations, the transition state
theory (TST) \cite{Kramers}, where anharmonicity of the lattice
potential is taken into account, leading to the temperature
induced shift and broadening of the T-mode \cite{T-mode-1}.
At the same time, a theoretical approach for the T-mode
description has been proposed \cite{T-mode-2} from purely quantum
mechanical concepts. This method allows to extrapolate the results
obtained at $T\ne 0$ to the zero temperature limit, yielding
information about the ``adsorbate-substrate'' interaction strength
and vibrational frequency from the IHAS data. Much effort has been
put \cite{T-mode-2} into description of the T-mode temperature
dependence. It is known that unlike diffusion the vibrational
damping is not an activated process \cite{T-mode-2,JCP2}.
Nevertheless, the temperature induced T-peak shifts towards lower
frequencies, and almost linear broadening is observed
\cite{Csystems} for the Na/Cu(001) system in a region between 0 K
and 200 K, while for the CO/Cu(001) and CO/Pt(111) systems the
T-mode is {\it blue}-shifted with temperature. It is believed that
at low temperatures the shape of the T-mode is dominated by a
frictional damping, characterized by the nonadiabatic coupling to
the substrate excitations \cite{T-mode-2}. At high temperatures
the anharmonicity of the static lattice potential plays a dominant
role \cite{T-mode-1}. Summarizing, it could be stated that up to
now there is no unique viewpoint which factors (phonon and/or e-h
excitations, anharmonic contributions, or memory effects) are
predominant in the T-mode development at different temperatures,
couplings and interaction regimes.
Last but not least, one can relate the existence of the T-mode to
multiple jumps of the adsorbate. The onset of multi-\-hops was
associated with an inelastic peak of the dynamic structure factor
at frequency $\omega_{osc}$ of the adparticle oscillations at the
well bottom \cite{PhysA195,SurScience311}. If the T-mode is well
resolved on the dynamic structure factor and not overlapped by the
central quasi-elastic peak, it could be said that thermalization
of the adsorbate velocity has not taken place yet, and multiple
jumps contribute significantly to the diffusion coefficient.
In the present paper we study the conditions of the T-mode
formation, its temperature dependence, and its connection with the
nature of the ``adsorbate--substrate'' interaction. We explore a
two-level model of the light particle coupled non-adiabatically to
the surface phonons \cite{JCP1,PRE2009,PRE2011}. The other kinds
of ``adsorbate--substrate'' interaction, like electronic friction
or nonlinear phonon coupling, will be also considered. The
underbarrier hopping to the nearest adsorption sites is postulated
to be a ``driving force'' of the surface motion of the adsorbate.
We consider non-Markovian effects of the adsorbate motion, dealt
with retarded relaxation of the lattice excitations, to be the
main reason of the T-mode origin. Since this one-particle
excitation is very sensitive to the form of the kinetic kernels,
rigorous numerical evaluation of the T-mode temperature behavior
is carried out without any approximation (e.g., like
Wigner-Weisskopff one \cite{T-mode-2,Micha19}). On the other hand,
both zero temperature and semiclassical limits for the kinetic
kernels are considered in our paper that allows us to obtain the
analytical expressions for the T-mode characteristics at low
``adsorbate--substrate'' coupling.
We perform our analysis in terms of the generalized diffusion
coefficients (which are related to the ``velocity--velocity''
autocorrelation functions) rather than dynamic structure factor.
The latest approach is often complicated due to the overlap of
quasi-elastic and inelastic peaks of the dynamic structure factor
\cite{PhysA195}, while the method of generalized diffusion
coefficients allows one to study the T-mode in more detail, being
focused on the adsorbate motion at the well bottom. We propose a
physical interpretation of the observed temperature induced shift
of the T-mode on the basis of a comparative analysis of two
typical timescales of the system dynamics: a time of decay
$\tau_v$ of the generalized diffusion coefficients and a
correlation time $\tau_{cor}$ of the thermal bath random forces.
The obtained results reveal a close connection between the
direction of the T-mode shift and the nature of the
``adsorbate--substrate'' interaction.
Our paper is organized in the following way. In Sec. II we present
the generalized diffusion coefficient of a light particle derived
by the method of quantum kinetic equations \cite{PRE2009,PRE2011}
on the basis of two-level dissipative model of adparticle coupled
to substrate phonons. In Sec. III we consider different
correlation functions of the thermal bath random forces, which
depend on the nature of the ``adsorbate--substrate'' interaction.
In the next Section we attribute the T-mode of the adsorbate to
the coherent part of the generalized diffusion coefficient and
calculate its temperature dependence numerically at different
values of ohmicity index $n$. A comparison of the obtained results
with the experimental data and the results of similar theoretical
approaches is provided in this Section. In Sec.~V we calculate the
T-mode frequency and width analytically in zero and high
temperature limits for strongly sub-Ohmic (ohmicity index $n=0$),
Ohmic, and the super-Ohmic systems with $n=2$. In Sec. VI,
according to Refs. \cite{PhysA195,SurScience311}, we relate the
T-mode to the onset of multiple jumps of the adsorbate and
generalize the conditions of the multiple hopping to the case of
quantum surface diffusion. In the last Section we discuss briefly
the obtained results and draw final conclusions.
\section{Generalized quantum surface diffusion coefficients}
\setcounter{equation}{0} We consider a light particle, which
performs underbarrier hopping to the nearest adsorption site,
oscillates between ground and excited states within the potential
well, and interacts with the lattice vibrations. Hamiltonian of
the system is chosen as follows ~\cite{JCP1,JCP2} \bea\label{H}
H=H_A+H_{int}+H_B, \eea where the adsorbate is described by the
two-band constituent \bea\label{H_A} H_A\!\!=\!\!\! \sum_{\langle
ss'\rangle}(-t_ 0 a^{\dagger}_{s 0}a_{s' 0}+t_1 a^{\dagger}_{s
1}a_{s' 1})\! +\!\! \sum_s\!\frac{\hbar\Omega}{2}(n_{s 1}-n_{s
0}). \eea Here $s$ denotes the site of the lattice; 0 and 1 are
the ground and excited states within a given well, and $\langle
ss'\rangle$ denotes a sum over the nearest-neighbor sites. The
quantum states within a well are referred to as ``vibrational''
ones with the vibrational frequency $\Omega$. $a^{\dagger}_{s i}$
($a_{s i}$) creates (destroys) a particle on the site $s$ in the
vibrational state $i$; $n_{s i}=a^{\dagger}_{s i}a_{s i}$ is the
number operator for this state, and $n_{s}=n_{s 0}+n_{s 1}$.
Hereafter we will deal with a single adparticle only, hence the
adparticle statistics becomes irrelevant. $t_0$ and $t_1$ are the
nearest-neighbor tunnel\-ling amplitudes in the ground and the
first excited states, respectively, and we expect that $t_1\gg
t_0$.
The coupling to phonons is considered to be local within each
well. Phonons may couple both to the adsorbate density operators
and to the vibrations within a quantum well. The interaction
Hamiltonian is \cite{JCP1}
\bea\nonumber\label{H_int}&&H_{int}=\sum_{s}\!\left\{\! n_
s\sum_q\gamma_{s q}(b_q+b^{\dagger}_q)+(a^{\dagger}_{s 0}a_{s 1}+
a^{\dagger}_{s 1} a_{s 0})\right.
\\
&&\left.\times\sum_q \chi_{s q}(b_q+b^{\dagger}_q)\!\right\}, \eea
where $b^{\dagger}_q$ ($b_q$) creates (destroys) a phonon with a
normal mode frequency $\omega_q$. The strengths $\gamma_{s q}$
($\chi_{s q}$) describe coupling of phonons to the density
(oscillation) modes of the adsorbate. The bandwidths $t_0$, $t_1$
and vibrational frequency $\Omega$ can be evaluated in the
framework of the eigenvector-eigenvalue problem for a periodic
potential, felt by an adsorbate due to the static lattice. The
coupling strengths are expressed via the mean values
$\Gamma=\langle s,i|V_{int}^s|s,j\rangle$ of the lattice
distortion potential $V_{int}^s$ over the localized Wannier states
$|s,j\rangle$ times the phase factor depending on the site number
$s$ and wave-vector $q$ \cite{JCP1}. Likewise, we suppose $\Gamma$
to be the same for different quantum states $ \{i,j\}=\{0,1\}$ and
use the dimensionless coupling parameter \bea\label{Gamma}
G=\frac{\Gamma^2}{M\omega^3_{max}} \eea to characterize the
``adsorbate--substrate'' interaction. Here $\omega_{max}$ stands
for the Debye frequency, and $M$ denotes the mass of the substrate
atom.
The last term in Eq.~(\ref{H}) \bea\label{H_B}
H_B=\sum_q\hbar\omega_q b^{\dagger}_q b_q \eea corresponds to the
phonon bath; longitudinal acoustic phonons only are taken into
account in this model.
Since the tunnelling amplitudes are always much smaller than the
coupling strengths, the interaction part of Hamiltonian
(\ref{H_int}) cannot be considered as a perturbation and has to be
taken into account exactly. The most refined method consists in
performing unitary transformations in order to exclude the linear
over the interaction terms from the system Hamiltonian. In the
unitary transformed Hamiltonian the tunnelling processes can be
considered as those with emmision/adsorption of the vir\-tual
phonons, and the same is true for the vibrational processes.
It is also useful to pass to the hybrid set of states for each
site: \bea\label{a_LR} a_{s {L\atop R}}\equiv \frac{1}{\sqrt
2}(a_{s 0}\pm a_{s 1}),\eea and similarly for the creation
operators. The designation $L$ or $R$ means that a single
adparticle is now localized on the left or right side of the given
well. We will refer to the vibrational transitions with $i\ne j$,
$\{i,j\}=\{L,R\}$, as the end-changing processes, supplying them
afterwards by the subscript (c), and transitions with $i=j$ will
be termed as the end-preserving ones with the corresponding
subscript (p).
Using the method of the reduced density matrix \cite{MorozovBook}
it is possible \cite{JCP2,PRE2009,PRE2011} to obtain the chain of
quantum kinetic equations for diagonal
$f_{s,s}(t)=\sum_{i=L,R}\langle a^{\dagger}_{s i} a_{s
i}\rangle^t_S$ and off-diagonal $f_{s,s'}(t)=\sum_{i=L,R}\langle
a^{\dagger}_{s' i} a_{s i}\rangle^t_S$ one-particle
non-equilibrium distribution functions, where the averaging is
taken with the statistical operator $\rho_S(t)$ of the adsorbate.
These integro-differential equations are linear in $f_{s,s}(t)$,
$f_{s,s'}(t)$ but are non-local in time; hence it is useful to
perform the Laplace transformation $\tilde
f(z)=\int_0^{\infty}\exp(-z t)f(t) dt$. Solving the equations for
the off-diagonal distribution functions and inserting the obtained
results into the equation for the diagonal ones, one can obtain
\cite{PRE2009,PRE2011} an expression for the generalized
(frequency dependent) diffusion coefficient: \bea\label{Dgen}
&&\!\!\!\!\!\!\!\tilde D(z)=\tilde D_{coh}(z)+D_{in}(z)\nonumber
\\
&&\!\!\!\!\!\!\!\!\!\!= \frac{a^2}{4}\!\left[\frac{2
t_{inter}^2/\hbar^2}{z+\tilde{\gamma}_{inter}(z)+\tilde{\gamma}_{intra}(z)+\tilde{\gamma}_{LL}^+(z)}
+\tilde{\gamma}_{inter}(z)\right]. \eea The first term $\tilde
D_{coh}(z)$ in (\ref{Dgen}) describes a coherent contribution to
the generalized diffusion coefficient. It can be interpreted
\cite{JCP2,PRE2009} in terms of a simple model of band-type motion
limited by scattering from the lattice (with interatomic spacing
$a$) at temperatures large relative to the bandwidth $t_{inter}$,
which is narrowed due to polaronic effect. The kinetic kernel
\bea\label{GamInter}
\tilde{\gamma}_{inter}(z)=4\tilde{\gamma}_{LL}(z)+2\tilde{\gamma}_{LR}(z)+2\tilde{\gamma}_{RL}(z)\eea
corresponds to the dissipative intersite motion of the adsorbate
and describes processes, when the adparticle performs random
site-to-site hopping (with or without the change of its quantum
state) owing to the interaction with the bath. The kinetic kernel
$\tilde{\gamma}_{intra}(z)$ in Eq.~(\ref{Dgen}) describes a
dissipative intrasite dynamics, when the adsorbate during its
scattering from the lattice gets enough energy from the bath to be
excited from the ground state to the upper level within the same
adsorption site (the opposite process of particle de-excitation
with a phonon emission is also taken into consideration).
The second term $\tilde{D}_{in}(z)$ in Eq.~(\ref{Dgen}) is an
incoherent contribution to the generalized diffusion coefficient.
This is the result expected from the random walk model for
diffusion with site-to-site hopping rate
$\tilde{\gamma}_{inter}(z)$, describ\-ing processes of the surface
phonon creation/annihilation, when the particle performs a
transition from one Wannier state to another.
The rates $\tilde{\gamma}_{intra}(z)$, $\tilde{\gamma}_{inter}(z)$
can be obtained from the Laplace transformation of the kinetic
kernels \be\label{Gamx} \gamma_x(\tau)=\omega_{max}\lambda_x^2
\mbox{Re}\{\exp[
-(\varphi_x(0)-\varphi_x(\tau))]-\exp[-\varphi_x(0)]\}, \ee
\be\label{GamLLPlus} \gamma_{LL}^+(\tau)\!=\omega_{max}t_{1}^2
\mbox{Re}\{\exp[
-(\varphi_{LL}(0)+\varphi_{LL}(\tau))]-\exp[-\varphi_{LL}(0)]\},\ee
where \bea\label{phi}
\varphi_x(\tau)\!=\!\!\!\int\limits_{0}^1\!\!\frac{J_x(\omega)}{\omega^2}\!\left[\coth\!\left(
\frac{\hbar\omega}{2 k_B T}\!\right)\!\cos(\omega
\tau)-i\sin(\omega \tau) \!\right],\eea and one-particle
parameters $\lambda_x=\{t_1,\Omega\}$ are related to the
corresponding end-changing/end-preserving processes (see also
Table in Ref.~\cite{PRE2009}). The exponential form of the rates
(\ref{Gamx})-(\ref{GamLLPlus}) is a result of averag\-ing of the
lattice time correlation functions \cite{JCP2,PRE2009} over the
bath variables that yields the temperature dependent factor in
Eq.~(\ref{phi}). Hereafter we use dimensionless frequencies in the
units of $\omega_{max}$ and temperatures in the units of
$\hbar\omega_{max}/k_B$.
The ``adsorbate--substrate'' interaction enters the kinetic rates
via spectral weight functions \cite{JCP1,JCP2,PRE2009,PRE2011}
\be\label{Jintra} J(\omega)=\sum\limits_q\chi^2_{s
q}\delta(\omega-\omega_q), \ee \vspace*{-5mm}
\bea\label{Jc}\nonumber
J_{LR}(\omega)\!=\!\!\sum\limits_q\left[(\gamma_{s q}-\gamma_{s'
q})\!+\!(\chi_{s q}+\chi_{s' q})
\right]^2\!\delta(\omega-\omega_q),
\\
\\
\nonumber J_{RL}(\omega)\!=\!\!\sum\limits_q\left[(\gamma_{s
q}-\gamma_{s' q})\!-\!(\chi_{s q}+\chi_{s' q})
\right]^2\!\delta(\omega-\omega_q),
\eea
\bea\label{Jp}\nonumber
J_{LL}(\omega)\!=\!\!\sum\limits_q\left[(\gamma_{s q}-\gamma_{s'
q})\!+\!(\chi_{s q}-\chi_{s' q})
\right]^2\!\delta(\omega-\omega_q),
\\
\\
\nonumber
J_{RR}(\omega)\nonumber\!=\!\!\sum\limits_q\left[(\gamma_{s
q}-\gamma_{s' q})\!-\!(\chi_{s q}-\chi_{s' q})
\right]^2\!\delta(\omega-\omega_q).
\eea
The function (\ref{Jintra}) describes the intrasite dynamics; the
functions (\ref{Jc}) are related to the intersite end-changing
processes, while (\ref{Jp}) are dealt with the intersite
end-preserving processes. The spectral weight function
(\ref{Jintra}) can be considered as site-independent if the system
has a translational symmetry, whereas the functions
(\ref{Jc})-(\ref{Jp}) depend only on the distance $|s-s'|$ between
the nearest neighbor sites $s$ and $s'$ \cite{JCP1,PRE2011}.
The system dynamics is governed by the low frequency behavior of
the spectral weight functions (\ref{Jintra})-(\ref{Jp}). In
Refs.~\cite{JCP1,JCP2,PRE2009,PRE2011} they were chosen to be
scaled as \bea\label{JJc} J_c(\omega)\approx
\Theta(\omega-\omega_0)\Theta(\omega_{max}-\omega)\eta_c\omega^{D-2},
\eea for the end-changing, and \bea\label{JJp}
J_p(\omega)\approx
\Theta(\omega-\omega_0)\Theta(\omega_{max}-\omega)\eta_c\omega^{D},\eea
for the end-preserving processes with $\eta_c=10 G$, $\eta_p=12.5
G$, and $\Theta(x)$ denoting the Heaviside step function.
In Eqs.~(\ref{JJc})-(\ref{JJp}) the power index $D$ equals the
system dimensionality. Thus, for a two-dimensional lattice the
end-changing spectral weight functions are sub-Ohmic, while the
end-preserving ones are super-Ohmic \cite{Leggett}. Such a
behavior is a consequence of the equality of the coupling
strengths $\Gamma$ for all the quantum states. Moreover, the
lattice is assumed to possess a nonzero lowest frequency
$\omega_0$, which is introduced to take into account the finite
size of the system. It not only removes the divergencies
\cite{Leggett}, when the sub-Ohmic spectral functions have the
power index $n = 0$, but also allows one to describe the
adsorbate-induced surface reconstruction \cite{JCP1}, when the
particles become self-trapped due to the overlap of lattice
distortions.
We would like to note that a sharp cut-off of the spectral weight
functions at the Debye frequency $\omega_{max}$ is not a unique
one, and plain exponential \cite{Leggett} or algebraic
\cite{Weiss} cut-offs are also used. However, the obtained results
are found to be rather insensitive to the cut-off form, being
governed above all by the low frequency behavior of $J(\omega)$.
In the next Section we will consider other values of the power
index $n$ in the expressions for spectral weight functions and
discuss their relation to the processes of different physical
nature. Here we would like to emphasize that there is a
one-\-to-\-one correspondence between the low frequency behavior
of $J(\omega)$ and the long-time relaxation of the kinetic kernels
(\ref{Gamx}). It was pointed out in Ref.~\cite{PRE2011} that at
large times we pass from a Gaussian form for $\gamma_x(\tau)$ (for
the sub-Ohmic processes with $n=0$) through exponential relaxation
of kinetic kernels (for the Ohmic processes) to the power law
behavior (in the super-Ohmic case with $n=2$).
To conclude this Section, let us note that at a reasonable
assumption of an infinitesimal value of the tunnel\-ling amplitude
in comparison with vibrational frequency, $t_{1}\ll\hbar\Omega$,
the expression (\ref{Dgen}) for the generalized diffusion
coefficient can be simplified and presented as follows
\bea\label{Dgen1} &&\tilde D(z)\approx \frac{a^2
t_1^2}{2\hbar^2}\left[\frac{\exp(-\varphi_p(0))}{z+\Omega^2\tilde{\gamma}_{c}(z)}
+2\left(\tilde{\gamma}_{c}(z)+\tilde{\gamma}_{p}(z)\right)\right],
\eea where $\tilde{\gamma}_c(z)$ and $\tilde{\gamma}_p(z)$ mean
the Laplace transforms of the end-changing (evaluated with
spectral weight functions (\ref{JJc})) and end-preserving
(evaluated with spectral weight functions (\ref{JJp})) kernels
(\ref{Gamx}) times factor $1/\omega_{max} \lambda_x^2$. A generic
form for the coherent contribution to $\tilde D(z)$ has a
structure similar to Eq.~(\ref{Dgen1}) even if the other kinds of
interaction (like electronic friction and/or anharmonic coupling
to phonon subsystem) are taken into account. In the very general
case, a denominator in the expression for $\tilde D_{coh}(z)$ will
consist of several terms of different physical origin, which
describe the vibrational transitions of the adsorbate within the
well. In Sec.~IV we attribute the T-mode to the coherent part of
the generalized diffusion coefficient, and explore
Eq.~(\ref{Dgen1}) to study in detail its features at different
types of the ``adsorbate--substrate'' interaction.
\section{Correlation functions of the thermal bath random forces}
\setcounter{equation}{0} We can look at the problem of quantum
surface diffusion from another viewpoint. Making use of the
solution of the Heisenberg equations of motion for the external
degrees of freedom \cite{Chaos27} one can derive the so-called
generalized quantum Langevin equation \cite{T-mode-2,Chaos}
\bea\label{GQLE}
M\ddot{q}(t)+M\int\limits_{t_0}^t\gamma(t-\tau)\dot{q}(\tau)d\tau+\frac{d
V(q,t)}{dq}=F_r(t) \eea for the particle with the mass $M$ and a
generalized coordinate $q(t)$ moving within the potential
$V(q,t)$, where the damping kernel $\gamma(t)$ is expressed via
spectral weight function in the following way \bea\label{dkernel}
\gamma(t)=\int\limits_{0}^{\infty}\frac{J(\omega)}{\omega}\cos(\omega
t)d\omega.\eea The mean value of the operator-valued noise
$F_r(t)$ is zero \bea\label{moment1} \langle
F_r(t)\rangle_{bath}=0, \eea whereas the time correlation function
of the thermal bath random forces can be expressed as follows
\bea\label{moment2}\nonumber S_{FF}(t)=\frac{1}{2}\langle
F_r(t)F_r(0)+F_r(0)F_r(t)\rangle_{bath}\\
=\frac{M}{\pi}\int\limits_0^{\infty}\frac{J(\omega)}{\omega}\hbar\omega\coth\left(\frac{\hbar\omega}{2
k_B T}\right)\cos(\omega t)d\omega.\eea In the classical limit it
converts to the non-Markovian Einstein relation
\bea\label{moment2M} S_{FF}^{cl}(t)=M k_B T \gamma(t), \eea where
the average in Eqs.~(\ref{moment1})-(\ref{moment2}) is taken with
respect to a bath density matrix, which contains shifted
oscillators \cite{Chaos}.
The relation (\ref{moment2}) implies that modelling of quantum
dissipation in the system is possible in terms of macroscopic
quantities such as the friction kernel $\gamma(t)$ and temperature
$T$. A class of such systems is by no means restricted to the
``adparticle -- linear Debye phonons'' coup\-ling. One can give
examples of several types of the ``adsorbate-substrate'' coupling,
which are closely related to the low frequency behavior of the
spectral weight functions. They range from the systems with a
flicker noise \cite{SubOhmic,YK} with $J(\omega)\sim\omega^0$
(like the end-changing spectral functions (\ref{JJc})) through the
Ohmic coupling with $J(\omega)\sim\omega^1$, when one takes into
account the electronic friction and/or anharmonic terms in
``adsorbate-substrate'' interaction \cite{MorozovBook,Weiss}, to
the super-Ohmic systems with $J(\omega)\sim\omega^2$, when
coupling to surface Debye phonons is considered
\cite{JCP1,PRE2011} (see also the end-preserving spectral
functions (\ref{JJp})).
At any ohmicity it is useful to introduce the correlation time
$\tau_{cor}$ which defines the decay rate of correlation functions
(\ref{moment2})-(\ref{moment2M}) of the thermal bath random
forces. In other words, at times about $\tau_{cor}$ the excess
energy of the lattice relaxes. For instance, in the systems with
flicker noise, the corresponding time correlation functions
(\ref{moment2M}) have the residual correlations
$\tau_{cor}\sim\omega_0^{-1}$ in damping kernels,
\bea\label{Tcorr0}\gamma(t)\sim-\eta_c Ci(\omega_0 t), \quad
Ci(z)=\int\limits_z^{\infty} dt\frac{\cos t}{t}.\eea The sub-Ohmic
case (\ref{Tcorr0}) with the power index $n=0$ implies an
introduction of the lower limit $\omega_0$ of frequency,
$0<\omega_0\ll\omega_{max}$, which is related to the inverse time
of the experiment duration \cite{YK}, or dealt with the finiteness
of the system size \cite{JCP1,PRE2009,PRE2011} (see also
Eqs.~(\ref{JJc})-(\ref{JJp}) and subsequent explanation).
The Ohmic systems have a white-noise-like behavior $\gamma(t)\sim
\eta_c\delta(t)$, and there are ultra-short range time
correlations in the super-Ohmic case. The super-Ohmic coupling
with the power indexes $n>2$ is beyond our consideration. The
cases of non-integer $n$, which are typical for fractal systems,
will be considered solely for the reason of proper convergence of
the numerical calculations. In particular, in the next Section we
consider the ohmicity indexes $n=\epsilon$, and $n=2-\epsilon$
with $\epsilon\ll 1$. An alternative way is to use the lower bound
cut-off frequency $\omega_0$, as it is done in Sec.~V, where the
analytical expressions for the T-mode features in the
quasi-classical limit are obtained.
There is also another typical time scale of
the system dynamics -- the relaxation time $\tau_v$ of the
velocity autocorrelation functions. This time will be introduced
in the next Section, and along with $\tau_{cor}$ will be used for
explanation of the direction of the temperature induced shift of
the T-mode on the basis of a comparative analysis between
$\tau_{cor}$ and $\tau_v$.
\section{T-mode as a coherent part of the generalized diffusion coefficient}
\setcounter{equation}{0}
As has been already said, the T-mode of
the adsorbate is being detected in IHAS experiments as an
additional (inelastic) peak in the dynamic structure factor. Thus,
to predict theoretically the T-mode features one has to evaluate
the dynamic structure factor \bea\label{Sfactor}\nonumber S({\bf
k},\omega)=\frac{1}{2\pi}\int\limits_{-\infty}^{\infty}
\exp^{-i\omega t}I({\bf k},t)dt
\\
=\frac{1}{2\pi}\int\limits_{-\infty}^{\infty} e^{-i\omega t}
\langle e^{-i{\bf k}\cdot{\bf R}(0)} e^{i{\bf k}\cdot{\bf
R}(t)}\rangle dt, \eea which is nothing but the Fourier transform
of the intermediate scattering function $I({\bf k},t)$. In
Ref.~\cite{T-mode-2} the model of a damped quantum harmonic
oscillator bilinearly coupled to a bath of lattice oscillators has
been proposed. Non-Markovian equations of motion for the
creation/anihilation operators of the adsorbate have been derived,
which have a form of the generalized Langevin equation
(\ref{GQLE}). The dynamic structure factor of the adsorbate has
been found with taking into consideration the memory effects.
Temperature dependences of the frequency of the inelastic peak of
$S({\bf k},\omega)$ and its full width on half maximum (FWHM) have
been studied in detail.
Though an investigation of the T-mode features using the dynamic
structure factor is closely related to scattering experiments,
this approach can sometimes be complicated due to the overlap of
quasi-elastic and inelastic peaks. It happens, for instance
\cite{PhysA195}, in the quasi-continuous regime of adsorbate
motion, at small fric\-tion and high values of $k$, when the
quasi-elastic peak of $S({\bf k},\omega)$, dealt with diffusion of
the adsorbate, becomes low and broad and cannot be well separated
from the inelastic peak at the vibrational frequency $\Omega$. The
inelastic peak also becomes indistinguishable at strong coupling
due to the impossibility of completing coherent oscillations in
the wells.
In such a case, investigation of the T-mode features using the
Fourier transform $\tilde
C_{vv}(\omega)=1/2\pi\,\mbox{Re}\left[\int_{-\infty}^{\infty}e^{i\omega
t}C_{vv}(t) dt \right]$ of the velocity autocorrelation function
$C_{vv}(t)$ looks more promising, being focused on the adsorbate
motion at the bottom of the potential well. For instance, $\tilde
C_{vv}(\omega)$ reveals the adsorbate motion in the potential
wells also in the overdamped regime at high barriers, when, in
spite of large friction, the particle can perform small parts of
oscillations with unthermalized velocity \cite{PhysA195}. On the
other hand, $\tilde C_{vv}(\omega)$ can be easily obtained from
the dynamic structure factor by a simple relation
\cite{SurScience311} \bea\label{CtoS}\tilde
C_{vv}(\omega)=\omega^2\lim_{k\to 0}\frac{S({\bf k},\omega)}{{\bf
k^2}}.\eea
It has been pointed out in our previous papers
\cite{PRE2009,PRE2011} that the generalized diffusion coefficients
are directly related to the velocity autocorrelation function
$C_{vv}(t)$, determined at the adsorption site $s$. We will follow
this rule, having dealt a time-dependent diffusion coefficient
$D(t)$ with $C_{vv}(t)$. Such a definition of the gene\-ralized
diffusion coefficient differs from that used in Ref.~\cite{aging},
where the relation $\bar D(t)=\int_0^t C_{vv}(u)du$ has been
adopted. However, it is much more useful since it allows one to
associate the time of decay of $D(t)$ with the relaxation time
$\tau_v$ of the velocity autocorrelation function. On the other
hand, the zero frequency limit $D_{exp}=\pi\lim_{\omega\to
0}\tilde C_{vv}(\omega)=\int_0^{\infty} D(t)dt$ determines the
experimentally measured diffusion coefficients $D_{exp}$, whose
temperature dependence has been studied quite profoundly
\cite{Ferrando,single}.
In Ref.~\cite{PRE2011} it has been shown that there is a close
relation (at least, within the model proposed) between the
adparticle dynamics at intermediate times $\tau\ll\tau_v$ and
temperature dependence of the diffusion coefficients. Namely, as
the coupling strength increases, the adparticle motion (initially
oscillatory) becomes more and more smooth, indicating that the
temperature behavior of the diffusion coefficients $D_{exp}(T)$
should change from weakly dependent on $T$ to quite a sensitive
function of temperature. The oscillatory behavior of the
generalized diffusion coefficient has been related to the T-mode
onset. In the frequency representation, oscillations of
$C_{vv}(t)$ yield the side wings of $\mbox{Re}[\tilde
C_{vv}(\omega)]$, localized in the vicinity of the vibrational
frequency $\Omega$. The T-mode frequency was found to increase
with temperature (see Fig.~3 in Ref.~\cite{PRE2011}). The
corresponding side peak of $\mbox{Re}[\tilde C_{vv}(\omega)]$
should be {\it blue}-shifted too.
\begin{figure}[htb]
\centerline{\includegraphics[height=0.27\textheight]{ignatyuk1.ps}}
\caption{Frequency dependence of the Fourier
transform of velocity autocorrelation function at Debye
temperature $T_D= \hbar\omega_{max}/k_B$, ohmicity index $n=0$,
and parameters $t_{1}/\hbar\omega_{max}=10^{-5}$,
$\omega_0/\omega_{max}=10^{-4}$, $\eta_c= 10^{-2}$,
$\Omega/\omega_{max}=1/\sqrt{2}$.} \label{Tmode(omega)}
\end{figure}
Thus, there are two peaks of different physical origin in the
Fourier transform $\mbox{Re}[\tilde C_{vv}(\omega)]$ of the
velocity autocorrelation function, presented in
Fig.~\ref{Tmode(omega)}. The central one, localized at $\omega=0$,
is related to the processes of adsorbate site-to-site random
hopping. This peak is determined by the incoherent contribution
\bea\label{Din-t} D_{in}(t)=(a t_{1}/h)^2\mbox{Re}\left[
\gamma_c(t)+\gamma_p(t) \right] \eea to the generalized diffusion
coefficient. In a weak coup\-ling limit, at hight temperatures,
and at large times the end-changing kinetic kernels decay as
\bea\label{PhicApprox}
\gamma_c(\tau)\sim\exp\left[-\eta_c|\ln\omega_0|\left(k_B
T\tau^2+i\tau \right) \right],\eea while the end-preserving ones
decay as \bea\label{PhipApprox1} \gamma_p(\tau)\sim
\Theta(\omega_0^{-1}-t)\left(1/\tau^{2\eta_p k_B
T}-\omega_0^{2\eta_p k_B T}\right).\eea It is seen from
Eqs.~(\ref{PhicApprox})-(\ref{PhipApprox1}) that the relaxation
law of the kinetic kernels changes from the Gaussian behavior for
the sub-Ohmic case with $n=0$ to the truncated long tails for the
super-Ohmic case with $n=2$. It is also easy to show that the
kinetic kernels in the Ohmic regime behave as
\bea\label{PhiOhmicApprox} \gamma_c(\tau)\sim\exp(-\pi\eta_c T
\tau).\eea
In a weak coupling limit and at the vibrational frequency large
enough there is also an additional maximum of $\mbox{Re}[\tilde
C_{vv}(\omega)]$. This peak is determined by the adsorbate
scattering from the substrate atoms \cite{JCP2} and corresponds to
recrossing processes dealt with the adparticle nonmonotonic
dissipative motion \cite{PRE2009,PRE2011}. Hence, a side peak
arises due to the coherent contribution to the generalized surface
diffusion coefficient (\ref{Dgen1}). The expression for frequency
dependence of the T-mode, associated with the above mentioned
maximum of $\mbox{Re}[\tilde C_{vv}(\omega)]$ can be easily
obtained from Eq.~(\ref{Dgen1}), putting $z=-i\omega+0^+$
\bea\label{TmodeGen} \nonumber &&\tilde
C_{vv}^{coh}(\omega)\equiv\mbox{Re}\left[\tilde
D_{coh}(\omega)\right]\\
&&= \frac{a^2 t_{inter}^2}{4\hbar^2} \frac{2 R(\omega)}{\left[
\omega-\Omega^2 I(\omega)\right ]^2+\Omega^4
R(\omega)^2},\\
\nonumber &&
I(\omega)=\int\limits_0^{\infty}\gamma_c(t)\sin(\omega t)dt,\quad
R(\omega)=\int\limits_0^{\infty}\gamma_c(t)\cos(\omega
t)dt. \eea It is seen from Eq.~(\ref{TmodeGen}) that the T-mode
localization in the vicinity of the vibrational frequency $\Omega$
is determined by $I(\omega)$, whereas the T-mode width depends on
$R(\omega)$.
Let us study the time dependence of the coherent contribution to
the generalized diffusion coefficient in more detail. Performing
the inverse Laplace transformation, one can obtain the following
expression: \bea\label{inverseL}\nonumber &&
\!\!\!D_{coh}(t)=\!\mbox{Re}\!\left[ \frac{(a t_{inter})^2}{2\pi
i\hbar^2}\lim_{\epsilon\to
0}\!\!\int\limits_{\epsilon-i\infty}^{\epsilon+i\infty}\!\!
dz\exp(z
t)\frac{1}{z+\Omega^2\tilde{\gamma}_{c}(z)}\right] \\
&&\!\!\!=\left(\frac{a t_{inter}}{\hbar}\right)^2\mbox{Re}\left[
\sum_{i=1}^{\infty}\exp(z_i
t)\frac{1}{1+\Omega^2\tilde{\gamma}'_{c}(z_i)}\right].\eea The
summation in (\ref{inverseL}) in accordance with the residue
theorem runs over all poles $z_i$ of the integrand, which obey the
condition $\mbox{Re} [z_i]<0$. In a general case, the summation is
extended to the infinite number of poles, and the major
contribution comes from terms with maxi\-mal values of
$\mbox{Re}[z_i]$ and weight factors
$[1+\tilde{\gamma}'_c(z_i)]^{-1}$.
The expression for $D_{coh}(t)$ can be even more complicated if
one deals with higher order poles. Indeed, when the temperature
increases, the 2-nd order poles (with rather small weight factors)
appear in the integrand. Even though the high order contributions
to $D_{coh}(t)$ have a form similar to anharmonic corrections to
the velocity autocorrelation function \cite{T-mode-1}, their
physical nature is definitely different. Basically, they are of
non-Markovian origin, while a skewness of the T-mode peak in
Ref.~\cite{T-mode-1} arises due to the anharmonicity of the local
lattice potential.
Just as relaxation times of the incoherent contributions
$D_{in}(t)$ to the generalized diffusion coefficients depend on
the ohmicity of the system (see
Eqs.~(\ref{Din-t})-(\ref{PhiOhmicApprox})), the damping rates
$|\mbox{Re}\,z_i|$ in (\ref{inverseL}) also change over the large
range of values depending on nature of the
``adsorbate--substrate'' interaction. An additional study shows
that at fixed parameters of the model there is a strong
inequality, $\mbox{Max}\{\mbox{Re}[z_i(n=0)]\}\ll
\mbox{Max}\{\mbox{Re}[z_i(n=1)]\}\ll\mbox{Max}\{\mbox{
Re}[z_i(n=2)]\}$, $\mbox{Re}[z_i(n)]<0$, ordering the damping
rates of the coherent term $D_{coh}(t)$ subject to the ohmicity
index $n$.
Turning back to Fig.~\ref{Tmode(omega)}, let us point out that the
T-mode width, which defines the inverse life-time of this
one-particle excitation, can increase for two different reasons.
At fixed temperature the T-peak is broadened when the
``adsorbate--substrate'' coupling increases, and the coherent
motion of the adparticle diminishes. Contrary, one can keep the
coupling fixed and increase the system temperature, ``switching
on'' more and more bath oscillators until their number reaches the
maximum at the Debye temperature $T_D=\hbar\omega_{max}/k_B$. In
such a case not only the T-mode width increases due to higher
dissipation, but also the peak position shifts with temperature.
The temperature dependence of the T-mode frequency and its FWHM
are shown in Figs.~\ref{sub-Ohmic}-\ref{Ohmic}. In the sub- and
super-Ohmic regimes we used the power indexes $n=0.03$ and
$n=1.97$ (which slightly deviate from the corresponding integer
values 0 and 2) to eliminate the lower bound cut-off frequency
$\omega_0$. The others fitting para\-meters (the vibrational
frequency $\Omega$ and the coupling strength $\eta_c$) are chosen
to reproduce the experimental data \cite{T-mode-2}.
It is seen from Fig.~\ref{sub-Ohmic} that in a strong sub-Ohmic
regime the T-mode frequency is {\it blue}-shifted with $T$ up to
temperatures of about $\hbar\Omega/k_B$, where the T-mode
frequency becomes a descending function of temperature.
\begin{figure}[htb]
\centerline{\includegraphics[width=0.25\textwidth]{ignatyuk2.ps}
\includegraphics[width=0.25\textwidth]{ignatyuk3.ps}}
\caption{Left panel: temperature dependence of the
T-mode frequency in the sub-Ohmic regime with $n=0.03$,
dimensionless vibrational frequency $\Omega/\omega_{max}=0.2$ and
coupling constant $\eta_c=0.002$. Right panel: temperature
dependence of the T-mode FWHM at the same parameters.}
\label{sub-Ohmic}
\end{figure}
The T-mode FWHM is found to be a nonlinear function of $T$ at all
temperatures studied. At $k_B T/\hbar\omega_{max}\sim 0.4$ the
T-mode becomes very broad in spite of very small coup\-ling, and
almost disappears from the spectrum function $\mbox{Re}[\tilde
C_{vv}(\omega)]$ (see next Section for analytic estimations).
To explain the T-mode {\it blue}-shift at low-to-moderate
temperatures let us recall that in the sub-Ohmic regime with $n=0$
there are residual correlations of the flicker noise \cite{YK}.
The correlation time $\tau_{cor}$ of the thermal bath random
forces is much larger than the relaxation time $\tau_{v}$ of the
velocity autocorrelation functions (see Eqs.~(\ref{PhicApprox}),
(\ref{inverseL})). Thus, a non-relaxed energy of the lattice is
being delivered to the adparticle increasing its effective
vibrational energy until the inverse process begins at the
temperatures of about $\hbar\Omega/k_B$.
\begin{figure}[htb]
\centerline{\includegraphics[width=0.25\textwidth]{ignatyuk4.ps}
\includegraphics[width=0.25\textwidth]{ignatyuk5.ps}}
\caption{Left panel: temperature dependence of the T-mode
frequency in the super-Ohmic regime with $n=1.97$, dimensionless
vibrational frequency $\Omega/\omega_{max}=0.2$ and coupling
constant $\eta_c=0.166$. Right panel: temperature dependence of
the T-mode FWHM at the same parameters.} \label{super-Ohmic}
\end{figure}
In Fig.~\ref {super-Ohmic} we present the results for the T-mode
tempe\-ra\-tu\-re induced shift and broadening in the strong
super-Ohmic regime. There are ultra-short range time correlations
$\tau_{cor}$ of the thermal bath random forces at super-Ohmic
coupling \cite{Weiss}, and much longer times $\tau_v$ at which the
velocity of the adparticle decays (see Eqs.~(\ref{PhipApprox1}),
(\ref{inverseL})). In such a case the excess energy of the
adsorbate is being transferred to the lattice, yielding a decrease
of the effective vibrational energy of the adparticle with
temperature and, consequently, the {\it red}-shift of the T-mode
frequency. The FWHM of the T-mode accommodates to almost a linear
function of temperature after a short transition regime at low
$T$.
At the Ohmic coupling (see Fig.~\ref{Ohmic}) the T-mode is
slightly {\it blue}-shifted with temperature, and its FWHM is a
linear function of $T$ like in the super-Ohmic case. At the Ohmic
coupling the difference between two typical times $\tau_{cor}$ and
$\tau_v$ is smaller than in the other regimes. As a result, the
T-mode shift is also smaller than in the sub- or super-Ohmic
regimes (at the same values of the parameters of the model), which
will be shown in the next Section. Such a behavior is consistent
with the experimental data of Ref.~\cite{Gadzuk} where the e-h
pair contribution (with a weak Ohmic coupling \cite{MorozovBook})
was found to be almost independent of temperature.
\begin{figure}[htb]
\centerline{\includegraphics[width=0.25\textwidth]{ignatyuk6.ps}
\includegraphics[width=0.25\textwidth]{ignatyuk7.ps}}
\caption{Left panel: temperature dependence of the T-mode
frequency in the Ohmic regime with dimensionless vibrational
frequency $\Omega/\omega_{max}=0.141$ and coupling constant
$\eta_c=0.0066$. Right panel: temperature dependence of the T-mode
FWHM at the same parameters.} \label{Ohmic}
\end{figure}
Summing up this Section, we would like to discuss the difference
between our approach and the one used in Ref.~\cite{T-mode-2} when
studying the temperature behavior of the adsorbate T-mode. In
Ref.~\cite{T-mode-2} two fitting parameters were used, which
characterize the behavior of the spectral weight function
$J_x(\omega)$ times a thermal population factor in the vicinity of
the T-mode frequency. These parameters were found to depend very
weakly on the surface temperature for the three systems studied.
Moreover, the dynamic structure factor itself has been calculated
in the Wigner-Weisskopff approximation \cite{Micha19}. That
introduced an additional inaccuracy in the description of the
system dynamics at intermediate times, when the memory effects
have to be taken into account rigorously \cite{PRE2009,PRE2011}.
Even though in Ref.~\cite{T-mode-2} the quantum model for the
adsorbate motion has been proposed, further calculations were
carried out in the impulsive collision approximation without
reference to the driving Hamiltonian term. The influence of
non-selective measurements (e.g. collisions) on the evolution of
quantum system was considered more precisely in \cite{Zeno}, where
the short- and long-time dynamics of the adsorbate has been
studied in the context of quantum Zeno and anti-Zeno effects,
however, without taking into account the tunnelling-mediated
surface diffusion and memory effects.
In our paper we consider a more general case when the ``driving
force'' is dealt with slow underbarrier site-to-site hopping of
the adsorbate and should be treated on equal footing with other
interaction mechanisms. The interaction term (\ref{H_int}) of
Hamiltonian is not of a bilinear form in creation/annihilation
operators. It takes into account coupling both to density and
oscillation modes of the adsorbate that corresponds to more
realistic systems \cite{Ferrando,JCP1}. Neither a power series
expansion for the spectral weight functions at vibration frequency
$\Omega$ nor any approximation for the kinetic kernels (like the
Wigner-Weisskopff one) are made in our paper. As a result, we
manage to describe the T-mode behavior quite accurately using only
one fitting parameter - the dimensionless coupling constant. It is
shown in the next Section that its value can be extracted from the
residual \cite{T-mode-2} shift and broadening of the T-mode at
zero temperature.
\section{An analytical evaluation of the T-mode temperature dependence}
\setcounter{equation}{0}
Analytical results can be obtained in the
zero temperature and high temperature limits. In the first case, a
thermal population factor from Eq.~(\ref{phi}) is eliminated. On
the other hand, at high temperatures the thermal population factor
can be approximated as $\coth(\hbar\omega/2 k_B T)\approx 2 k_B
T/\hbar\omega$. Then using the long time asymptotics
(\ref{PhicApprox})-(\ref{PhiOhmicApprox}) for the kinetic kernels
instead of the exact expressions (\ref{Gamx}) we can obtain
analytical expressions for the T-mode frequency and FWHM.
\subsection{Zero temperature limit}
In the Ohmic regime and in the weak coupling limit $\eta_c\ll 1$
the following expression for the T-mode frequency is valid
\bea\label{zeroW} \omega_T(0)=\sqrt{\Omega^2- \Delta(0)^2/4}, \eea
that coincides with the expression for the frequency of the damped
harmonic oscillator. The expression (\ref{zeroW}) for the T-mode
localization frequency defines a shift that can be referred to as
the residual one, insofar it is present even at 0 K. The
corresponding residual (or intrinsic) FWHM in the sub- and Ohmic
regimes ($n\le 1$) is scaled as \bea\label{zeroD}
\Delta(0)\sim\eta_c\Omega^n. \eea The damping coefficient (\ref
{zeroD}) is not zero in the $T\to 0$ limit, because the excited
adsorbate can transfer its energy to the lattice, induce
excitations from the zero-point motions of the lattice modes, or
create e-h excitations in the electron distribution.
Let us note that the scaling law (\ref {zeroD}) for the T-mode
FWHM agrees completely with the results of Ref.~\cite{T-mode-2}
obtained in the zero temperature limit. Besides, a practical
significance of such results becomes quite clear: inspect\-ing the
T-mode localization, one can draw a conclusion about the
vibrational frequency $\Omega$ whereas FWHM includes the
information about the ``adsorbate--substrate'' coup\-ling strength
$\eta_c$.
Our model does not admit a straight zero temperature limit in the
super-Ohmic regime because there is no polaron band narrowing in
such a case \cite{JCP1}, and a new derivation of the coherent term
of the generalized diffusion coefficient becomes indispensable.
Nevertheless, the obtained results are quite reliable to be used
for the analysis of the low temperature T-mode features from both
theoretical and experimental viewpoints.
\subsection{High temperature limit}
\subsubsection{Sub-Ohmic regime with $n=0$}
Taking into account the Gaussian form (\ref{PhicApprox}) of the
long time asymptotics for the kinetic kernels and
Eq.~(\ref{TmodeGen}) for the frequency dependence of the T-mode it
is straightforward to obtain the expansion for the T-mode
frequency \bea\label{W_T_0} \omega_T(T)=\Omega+\frac{\eta_c T |\ln
\omega_0|}{\Omega}\left\{1-\frac{5}{2}\frac{\eta_c T |\ln
\omega_0|}{\Omega^2} \right\} \eea as a series in the coupling
strength $\eta_c$. The corresponding FWHM $\Delta(T)$ can be
written down as \bea\label{D_T_0} \Delta(T)=\frac{\Omega^2
\exp(-\Omega^2/4 \eta_c T |\ln\omega_0|)}{2\sqrt{\eta_c T
|\ln\omega_0|}}; \eea it does not admit the $\eta_c$ series
expansion. The T-mode FWHM is found to be a nonlinear function of
temperature, which agrees completely with the results presented in
Fig.~\ref{sub-Ohmic}.
Analyzing the T-mode temperature dependence (\ref{W_T_0}) it is
possible to find the temperature \bea\label{Tstar}
T^*=\frac{\Omega^2}{5\eta_c|\ln\omega_0|}, \eea at which a maximal
shift of the T-mode \bea\label{maxShift0}
\Delta\omega_T(T^*)\equiv\omega_T(T^*)-\Omega=\frac{1}{10} \Omega
\eea takes place. The shift (\ref{maxShift0}) is quite large, and
the T-mode FWHM at this temperature \bea\label{maxD0}
\Delta(T^*)=\sqrt\frac{5}{4}\exp\left(-\frac{5}{4}\right)\Omega\approx\frac{1}{3}\Omega
\eea approaches the vibrational frequency, leading to a rapid
decay of the excitation as it is clearly seen in
Fig.~\ref{sub-Ohmic}.
\subsubsection{Ohmic regime}
Analysis of the T-mode temperature dependence at the Ohmic
coupling shows that at reasonable values of the vibrational
frequency $\Omega$ the T-mode shift
\bea\label{W_T_1}\Delta\omega_T(T)=-\frac{(\pi\eta_c
T)^2}{2\Omega} \eea is smaller than in sub- or super-Ohmic
systems, since the expansion in (\ref{W_T_1}) starts from a
quadratic term in the coupling strength. The FWHM is governed by
the expression \be\label{D_T_1} \Delta(T)\sim\eta_c T\Omega^{n-1},
\ee which is also valid for the super-Ohmic systems with $1<n\le
2$.
It should be stressed that the temperature dependence of the
T-mode frequency (\ref{W_T_1}) differs from the results presented
in Fig.~\ref{Ohmic}. The T-mode is {\it red}-shifted in accordance
with Eq.~(\ref{W_T_1}), whereas the {\it blue}-shift is observed
in Fig.~\ref{Ohmic}. An explanation of this contradiction is quite
simple: we used the exponential form (\ref{PhiOhmicApprox}) of the
kinetic kernel when calculating (\ref{W_T_1}), while at the
numerical evaluation we used the exact expression (\ref{Gamx}),
which up to 5-10\% differs from asymptotic value
(\ref{PhiOhmicApprox}) at short times. This deviation can be
considered negligible when calculating the temperature dependence
of the diffusion coefficients \cite{JCP2,PRE2011}. But it is not
true when one evaluates the temperature dependence of one-particle
excitation of the adsorbate, that once more shows the exceptional
sensitivity of the T-mode behavior to any kind of approximations.
\subsubsection{Super-Ohmic regime with $n=2$}
At the super-Ohmic regime with $n=2$, weak coup\-ling limit
$\eta_c\ll 1$, and moderate vibrational frequencies
$\Omega<\omega_{max}$, the temperature dependence of the T-mode
localization can be presented as \bea\label{W_T_2}
\omega_T(T)=\Omega+\eta_c T\Omega\ln(2\Omega). \eea
It is seen from the last expression that the T-mode is {\it
red}-shifted with temperature up to the vibrational frequencies
$\Omega/\omega_{max}=1/2$, being at the same time a strongly
nonlinear function of $\Omega$. Exact numerical evaluations show
that the $\omega_T(T)$-curve at first reaches a plateau as the
vibrational frequency increases and then becomes a decreasing
function of temperature at $\Omega\sim \omega_{max}/2$.
On the other hand, the T-mode FWHM is very small even at the Debye
temperature \bea\label{D_T_2} \Delta(k_B
T/\hbar\omega_{max}=1)\sim\eta_c\Omega\ll\Omega. \eea Thus, the
T-mode is not broadened too much and should be well defined. It is
also to be pointed out that in the super-Ohmic regime the T-mode
shift is much smaller than that in the sub-Ohmic case, since
$\Omega|\ln\Omega|\ll|\ln\omega_0|/\Omega$.
Summarizing, the analytic investigation of the T-mode behavior
confirms completely the main tendencies observed in
Figs.~\ref{sub-Ohmic}-\ref{Ohmic}. Namely: i) a linear increase of
the T-mode FWHM with temperature in the Ohmic and super-Ohmic
regimes and a non-linear increase of $\Delta(T)$ in the sub-Ohmic
regime; ii) the corresponding {\it red}- or {\it blue}-shifts of
the T-mode location; iii) a considerable T-mode broaden\-ing in
the sub-Ohmic regime even at weak ``adsorbate--substrate''
coupling and a small broadening at $1\le n\le 2$.
Since there is a one-to-one correspondence between the system
ohmicity and the kind of the coupling, one can deduce about a
nature of the ``adsorbate--substrate'' interaction from the
temperature induced shift of the T-mode. When several kinds of the
``adsorbate--substrate'' interaction act simultaneously, the data
obtained could be more complicated than those reported in this
Section. However, such a situation is rather infrequent since
usually the typical relaxation times of different interactions are
separated by several orders of magnitude \cite{Ferrando,T-mode-2},
and it is possible to talk about a single effective interaction.
\section{T-mode and multiple adsorbate hopping}
\setcounter{equation}{0}
Investigation of the adparticle diffusion on the basis of the
Klein-Kramers equation \cite{PhysA195,SurScience311,Kramers}
allows us to look at the problem of T-mode from another viewpoint,
considering this one-particle excitation as a precursor of
multiple or long jumps of the adsorbate. Such a jumping regime
should not be confused with the situation, when at very low
barriers the particle performs a quasi-continuous hopping at
several sites \cite{PhysA195,SurScience311}, and a diffusive stage
of evolution is not reached. One rather has to talk about the
situation when the velocity of the particle, which has localized
at a certain adsorption site $s$, is not thermalized yet, and the
adsorbate jumps to the next nearest neighboring site $s'$ very
soon. Thus, we will use the term ``multiple'' rather than ``long''
hopping of the adsorbate.
In Ref.~\cite{SurScience311} two condi\-tions for the multiple
jumps of the adsorbate at the thermal activated diffusion have
been established, formulated as strong inequalities
\bea\label{condC} \tau_{th}\ll\tau_v,\qquad\tau_{osc}\ll\tau_v
\eea for three typical times of the system dynamics
\bea\label{3timesC} \tau_{osc}=a\sqrt\frac{m}{U},\quad \tau_v\sim
\frac{1}{\eta_c}, \quad \tau_{th}=a\sqrt{\frac{m}{k_B T}}, \eea
where $\tau_{osc}$ means the period of oscillation of the
adparticle with mass $m$ at the bottom of the potential well of
the depth $U$; $\tau_v$ is a relaxation time of the velocity
autocorrelation function, and $\tau_{th}$ denotes the time taken
by the particle to cross over a lattice spacing $a$ with a mean
thermal velocity $v_{th}$.
It is seen from the presented above analysis that the T-mode is
defined by the second inequality of (\ref{condC}). If the system
parameters allow the typical times to obey the first inequality
too, then the multiple jumps can be observed in the system.
Let us suppose that conditions (\ref{condC}) are fulfilled. Then
during both the jump to the nearest neighboring site (left
inequality) and oscillation within a certain adsorption site
(right inequality) the particle does not have enough time to be
thermalized, and the multiple hopping scenario of the diffusion
can be realized. In such a case, the Einstein-Smoluchowski
equation is found to be insufficient \cite{PhysA195,SurScience311}
for the description of the adparticle diffusion, and one has to
use the Klein-Kramers equation for the distribution function,
which depends both on the velocity and on the coordinate of the
adsorbate.
In the case of quantum diffusion the multiple hopping conditions
(\ref{condC}) remain valid too, but the values $\tau_{osc}$ and
$\tau_{th}$ from Eq.~(\ref{3timesC}) should be substituted by the
typical times \bea\label{2timesQ}
\tau_{osc}=\frac{2\pi}{\Omega},\qquad
\tau_{tun}=\frac{2\pi\hbar}{t_{inter}},\qquad\eea where
$\tau_{osc}$ denotes the inverse vibrational frequency, and
$\tau_{tun}$ is a time taken by the particle to perform an
underbarrier hopping to the nearest neighboring site.
It should be pointed out that Refs.~\cite{PhysA195,SurScience311}
were directed mainly to the investigation of inelastic peak of the
dynamic structure factor (or, alternatively, the side peak of
velocity autocorrelation function) at various coupling constants
and barrier heights, and no study of the temperature dependence of
the inelastic peak was performed to attribute it to the T-mode
features.
On the other hand, a generalization of the Klein-Kramers equation
to description of the quantum diffusion (especially in the weak
coupling limit, when there is the energy-diffusion-controlled
regime from the viewpoint of transition state theory
\cite{Kramers}) is an intricate problem, which, up to our
knowledge, has not been solved yet. In Ref.~\cite{PRE2011} we
followed an alternative way, having studied a behavior of the
``velocity--velocity'' time correlation functions, defined on the
adjacent sites, with taking into account the memory effects. It
has been shown that at given parameters of the model the multiple
jumps are absent (the relation $\tau_{tun}\sim\tau_v$ was found to
be valid), but they should appear when the tunnelling amplitude
increases or the coupling strength decreases. The most interesting
question -- about the influence of temperature on the multiple
hopping of adsorbate -- can be answered only after an additional
analysis of the T-mode behavior.
\section{Concluding remarks}
In this paper, we carry out numerical and analytical investigation
of the temperature dependence of the T-mode of adsorbate which
diffuses from one adsorption site to another by a tunnelling
mechanism. The T-mode characteristics (its localization frequency
and width) are known to depend on temperature
\cite{T-mode-1,T-mode-2,PRE2011}. Having adopted a concept that
the T-mode appearance is dealt with memory effects of the
adsorbate motion, we propose an explanation of either ({\it red}
or {\it blue}) temperature induced shifts of the above mentioned
one-particle excitation on the basis of comparative analysis of
two typical timescales: the correlation time $\tau_{cor}$ of the
thermal bath random forces and the relaxation time $\tau_v$ of the
velocity autocorrelation functions.
We show that in the strong sub-Ohmic regime with $n\ll 1$ the
relation $\tau_v\ll\tau_{cor}$ is valid, leading to a {\it
blue}-shift of the T-mode with temperature, since the excess
energy of the lattice is being delivered to the adparticle,
thereby increasing its effective vibrational energy. On the
contrary, in the strong super-Ohmic regime with $n\approx 2$ the
inequality $\tau_v\gg\tau_{cor}$ becomes valid. At the timescales
of about $\tau_{cor}$ the adparticle does not have enough time to
be thermalized and starts to transfer its energy to the lattice,
yielding the observed {\it red}-shift of the T-mode.
We have also analyzed in detail the temperature behavior of the
T-mode width, which changes from a strongly nonlinear function of
$T$ (in the case of strong sub-Ohmic regime with $n\ll 1$) to the
linear dependence in temperature (for Ohmic and super-Ohmic
systems).
The ohmicity type is closely related to the nature of the
``adsorbate--substrate'' interaction: the case with $n=0$
corresponds to the flicker noise, the Ohmic regime is being
realized in the systems with ``electronic'' friction or at the
coupling with nonlinear phonons, while the super-Ohmic case with
$n=2$ corresponds to the linear Debye phonon coupling. Therefore,
one can draw a conclusion about the interaction mechanism from
analysis of the temperature induced shift of the T-mode. On the
other hand, extrapolating the obtained data to the zero
temperature limit, it is possible to evaluate the micro\-scopic
parameters (vibrational frequency $\Omega$ and coupling strength
$\eta_c$), which govern behavior of the ``adsorbate--substrate''
system.
We consider a slow underbarrier site-to-site hopping of the
adparticle to be a ``driving force'' of the surface motion of the
adsorbate. Unlike the impulsive collision approximation
\cite{T-mode-2}, a ``driving term'' (\ref{H_A}) of the Hamiltonian
is treated on equal footing with other interaction mechanisms and
defines a time evolution of the system. Since there is a lack of
data about the T-mode beha\-vior for the case, when the diffusion
is mediated by tunnelling, and the non-Markovian effects play an
important role \cite{Zeno} (or, what is almost the same, when
different regimes of the ohmicity manifest themselves), we believe
that our investigations have a good perspective from a viewpoint
of the study of transition regimes of the adsorbate.
It has to be emphasized that a similar approach should be quite
promising in the case of thermally activated diffusion as well. It
was shown in Ref.~\cite{Pottier} that in non-Ohmic systems with
$0<n<2$, $n\ne 1$, the thermal bath random forces were correlated
as $\langle F_r(t) F_r(0)\rangle\sim\frac{\eta_c k_B T}{t^n}$,
whereas the long time asymptotics of the velocity autocorrelation
functions was scaled as $\langle v(t) v(0)\rangle\sim\frac{\eta_c
k_B T}{m} \frac{1}{t^{2-n}}$. Thus, the relations
$\tau_v\ll\tau_{cor}$ or $\tau_v\gg\tau_{cor}$ remain valid also
at thermally activated diffusion, allowing one to perform a
similar comparative analysis of the typi\-cal timescales and to
study the temperature behavior of the T-mode.
Finally, we relate the T-mode to the onset of the multihops of the
adsorbate. If an eventual temperature induced shift of the T-mode
toward lower frequencies and its broadening are not too large
(quasi- and inelastic peaks of the dynamic structure factor are
well resolved), one can state that there is a portion of multihops
in the system. The computer simulations within the Monte Carlo
wave function formalism \cite{36Ferrando} and direct evaluation of
the ``flux--flux'' time correlation functions \cite{JJ-TCF,Japan}
support this suggestion. Thus, investigation of the T-mode
behavior along with a study of the ``velocity--velocity'' cross
correlation functions can shed more light upon the nature of such
an interesting phenomenon of the adsorbate motion as a diffusion
by the multi-hopping scenario.
\section*{Acknowledgement}
This work was partially supported by the Project ``Models of the
quantum-statistical description of cata\-ly\-tic processes at the
metallic surfaces''(Lviv Polytechnic National University), No.
0110U001091. The author also thanks Dr. A.Moina for the useful
discussions and the assistance in performing of numerical
evaluations.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,299 |
Produced by Mardi Desjardins & the online Distributed
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[Illustration: GRAHAM'S MAGAZINE
1847.
Engraved by W.E. Tucker, Esq.]
GRAHAM'S MAGAZINE.
VOL. XXX. January, 1847. No. 1.
Table of Contents
Fiction, Literature and Articles
The Oath of Marion. A Story of the Revolution.
The Night Watch
Sense and Sympathy
One of the "Upper Ten Thousand," and One of the
People
Musa; or The Pilgrim of Truth
Three Eras of Destiny in the Life of the Painter
Angelica Kauffmann
Sly Love
Game-Birds of America.—No. III.
The Islets of the Gulf
Review of New Books
Poetry and Fashion
Miriam
To the Husband
"Oh Mother of a Mighty Race."
Caius Marius
Love
Solitude
The Past
Hawking
Le Follet
Transcriber's Notes can be found at the end of this eBook.
* * * * *
GRAHAM'S
AMERICAN MONTHLY
MAGAZINE
Of Literature and Art,
EMBELLISHED WITH
MEZZOTINT AND STEEL ENGRAVINGS, MUSIC, ETC.
WILLIAM C. BRYANT, J. FENIMORE COOPER, RICHARD H. DANA, JAMES K. PAULDING,
HENRY W. LONGFELLOW, CHARLES F. HOFFMAN, JOSEPH C. NEAL, J. R. LOWELL.
MRS. LYDIA H. SIGOURNEY, MISS C. M. SEDGWICK, MRS. FRANCES S. OSGOOD,
MRS. EMMA C. EMBURY, MRS. ANN S. STEPHENS, MRS. AMELIA B. WELBY,
MRS. A. M. F. ANNAN, ETC.
PRINCIPAL CONTRIBUTORS.
GEORGE R. GRAHAM, EDITOR.
VOLUME XXX.
PHILADELPHIA:
GEORGE R. GRAHAM & CO. 129 CHESTNUT STREET.
. . . . . .
1847.
* * * * *
CONTENTS
OF THE
THIRTIETH VOLUME.
JANUARY, 1847, TO JUNE, 1847.
Alexandre Dumas' Hamlet. By F. J. GRUND, 142
Abroad and at Home. By F. E. F. 250
A Coquette Conquered. By J. S. WALLACE, 254
A Dream. By FANNY FORESTER, 314
A Chapter on Eating. By FRANCIS J. GRUND, 332
"Boots;" or the Misfortunes of Peter Faber. By JOSEPH C. 325
NEAL,
Frank Beverly. By MARY SPENCER PEASE, 296
Game-Birds of America. No. III. 47
Glimpses of a Soul. By FRANCES S. OSGOOD, 90
Game-Birds of America. No. IV. 118
Game-Birds of America. No. V. 162
Game Birds of America. No. VI. 320
Law and Love. Or Gaining a Case. By ICHABOD JONES, 153
Life in New York. By FRANCES S. OSGOOD, 177
Musa; Or the Pilgrim of Truth. By JAMES K. PAULDING, 28
My Aunt Fabbins's Old Garret. By C. P. CRANCH, 157
Mrs. Bell's Ball. By L. L. 214
Mr. Kerr Mudgeon. Or "You Wont, Wont You?" By JOSEPH C. 246
NEAL,
Margaret's Well. A Tale of the Great Civil War. By HENRY 282
WILLIAM HERBERT,
Old Maids. Or Kate Wilson's Morning Visit. By ENNA 193
DUVAL,
One of the "Upper Ten Thousand," and One of the People. 21
By Mrs. J. C. CAMPBELL,
Sense and Sympathy. By F. E. F. 13
Sly Love. Or Cousin Frank. By Mrs. CAROLINE H. BUTLER, 38
Starting Wrong. By F. E. F. 133
Singleton Snippe. Who Married for a Living. By JOSEPH C. 165
NEAL,
Spectral and Supernatural Appearances. By R. BALMANNO, 361
The Oath of Marion. A Story of the Revolution. By 1, 92, 169
CHARLES J. PETERSON,
The Night Watch. A Tale. 10
Three Eras of Destiny in the Life of the Painter 33
Angelica Kauffmann. By Miss H. B. MACDONALD,
The Islets of the Gulf. Or Rose Budd. By J. FENIMORE 49, 121, 181,
COOPER, 217, 301, 349
Tribulation Trepid. By JOSEPH C. NEAL, 85
The Executioner. By A NEW CONTRIBUTOR, 101
The Young Painter. A Tale. By Mrs. JANE L. SWIFT, 111
Thomas Carlyle and His Works. By HENRY D. THOREAU, 145, 238
The Fields of Stillwater and Saratoga. By N. C. BROOKS, 205
A. M.,
The Loyalist's Daughter. A Tale of the American 265, 337
Revolution. By P. HAMILTON MYERS,
The Irish Match-Maker. A Story of Clare. By J. GERACHTY 274
M'TEAGUE,
The Strawberry-Woman. By T. S. ARTHUR, 345
The Musician. By HENRY COOD WATSON, 372
POETRY.
Ægeus. By WM. H. C. HOSMER, 100
A Prayer. By J. B. 161
Autumn. By JESSE E. DOW, 229
April. 245
Are They Not All Ministering Spirits. By S. DRYDEN 319
PHELPS,
A Prayer. By Mrs. C. E. DA PONTE, 336
Caius Marius. By Mrs. E. J. EAMES, 20
Fanny. By Mrs. MARY SUMNER, 179
Fanny's First Smile. By FRANCES S. OSGOOD, 262
Hawking. By E. M. SIDNEY, 81
Heart Struggles. By Mrs. J. C. CAMPBELL, 176
Love. By J. BAYARD TAYLOR, 27
Lady Jane Grey. By Mrs. E. J. EAMES, 110
Lines. By L. J. CIST, 180
Love Unrequited. By ALICE G. LEE, 228
Lines to a Jews-Harp. By L. B. M., 262
Lines on Visiting Broad Street Hotel. By W. H. C. 344
HOSMER,
Miriam. By KATE DASHWOOD, 9
Midnight Masses. By ARTHUR ALLYN, 132
Morning Invitation. By THE PRIVATE SCHOLAR, 336
Night. By ALICE GREY, 292
"Oh Mother of a Mighty Race." By WM. C. BRYANT, 20
"Oh! that a Little Cot were Mine!" By ROBERT F. GREELY, 120
Pittsburgh. By E. M. SIDNEY, 249
Picture of Tasso. By Mrs. E. J. EAMES, 371
Solitude. By ELIZABETH OAKES SMITH, 27
Sonnets on Receiving a Crown of Ivy from John Keats. By 117
LEIGH HUNT,
Song. By WM. C. BRYANT, 152
Stanzas. By THOMAS FITZGERALD, 237
Sonnet. 279
Settlement of the Genesee. By WILLIAM H. C. HOSMER, 293
Sea-Side Musings. By ADALIZA CUTTER, 313
Sonnet from Petrarch, on the Death of Laura. Translated 331
by ALICE GREY,
To the Husband. By ELLA, 12
The Past. By E. J. E., 37
The Maid of Linden Lane. By T. BUCHANAN READ, 99
The Gleaner. By E. M. SIDNEY, 143
The Midshipman's Farewell. By Mrs. CORNELIA DA PONTE, 152
The Love Dial. By G. W. PATTON, 192
The Brickmaker. By T. BUCHANAN READ, 200
To Mrs. A. T. By Dr. JNO. C. M'CABE, 201
The Oriole's Return. By Miss C. MITCHELL, 213
The Skater's Song. By H. B. T. 216
The Portrait. By KATE DASHWOOD, 237
The Statue in the Snow. By J. B. TAYLOR, 253
The Stolen Child. By THOMAS BUCHANAN READ, 280
To Mrs. P——, of Chestnut Street. 313
The Idiot Boy. By E. P. 330
The Soul's Search. By T. BUCHANAN READ, 348
To Lizzie. By Mrs. M. N. M'DONALD, 348
To Ianthe. By GEO. W. HOBSON, 360
Youthful Love. By ALICE G. LEE, 331
REVIEWS.
History of the Thirty Years' War. By Rev. A. J. 82
Morrison,
The History of Civilization from the Fall of the Roman 82
Empire to the French Revolution. By F. Guizot.
Translated by Wm. Hazlitt,
Stories from the Italian Poets. By Leigh Hunt, 82
The Poetical Works of Thomas Moore, 83
The French Revolution. By Thomas Carlyle, 83
The Life and Correspondence of John Foster. Edited by J. 83
E. Ryland,
The New Timon. A Romance of London, 83
Memoirs of the Life of Addison. By Miss Aiken, 83
Christine, and Other Poems. By T. B. Read, 144
Dealings with the Firm of Domby & Son. By Charles 144
Dickens,
Lives of Donne, Wotton, Hooker, Herbert and Sanders. By 144
Izaak Walton,
Poems. By Ralph Waldo Emerson, 202
The Modern Standard Drama. Edited by Epes Sargent, 202
The Poems of Thomas Campbell, 203
Views A-Foot: or Europe Seen with Knapsack and Staff. By 204
J. Bayard Taylor,
Alderbrook. By Miss Emily Chubbuck, 204
The Prose Writers of America. By Rufus Wilmot Griswold, 263
Songs of the Sea, and other Poems. By Epes Sargent, 263
The Battle of Life. By Charles Dickens, 264
The Countess of Rudolstadt. By George Sand, 264
Cyclopedia of English Literature. Edited by Robert 264
Chambers,
Travels in Peru. By Dr. J. J. Von Tschudi, 264
Ballads and other Poems. By Mary Howitt, 264
The Dog. By William Youatt, 264
The Life of Napoleon Bonaparte. By William Hazlitt, 322
American Comedies. By James K. Paulding and William 322
Irving Paulding,
History of the Roman Republic. By J. Michelet. 322
Translated by Wm. Hazlitt,
Spaniards and their Country. By R. Ford, 323
Hyperion. By H. W. Longfellow, 323
Froissart Ballads. By P. Pendleton Cook, 323
Past and Present. By Thomas Carlyle, 379
The Constitutional History of England from the Accession 379
of Henry VII. to the Death of George II. By Henry
Hallam,
MUSIC.
I've Been upon the Briny Deep. A New Song. Composed by 140
Charles E. Cathrall,
General Taylor's Gallop. Composed and respectfully 260
dedicated to the Ladies of Miss Carpenter's Dancing
Assembly. By A. J. R. Conner
ENGRAVINGS.
The Departure, engraved by J. Sartain, Esq.
Title Page for 1847, designed and engraved by E. Tucker,
Esq.
Paris Fashions, from Le Follet,
Josh Educating a Pig.
The Gleaner, engraved by Rawdon, Wright & Hatch.
Herds of Bisons and Elks, engraved by Rawdon, Wright &
Hatch.
Paris Fashions, from Le Follet.
Saukie and Fox Indians, engraved by Rawdon, Wright &
Hatch.
Falls of the Towalaga, engraved by Smillie.
Paris Fashions, from Le Follet.
Saratoga and Stillwater Battle-Ground, engraved by
Smillie.
Pittsburg, engraved by A. W. Graham.
Paris Fashions, from Le Follet.
Mandan Women, engraved by Rawdon, Wright & Hatch.
Lover's Leap, engraved by Smillie.
Flower, executed by E. Quarré.
The Home-Bird, engraved by A. L. Dick.
Paris Fashions, from Le Follet.
Transcriber's Notes can be found at the end of this eBook.
* * * * *
[Illustration: _PAINTED BY HORACE VERNET._ ENGRAVED BY JOHN
SARTAIN._
DEPARTING FOR THE CHASE.
Engraved expressly for Graham's Magazine.]
* * * * *
GRAHAM'S MAGAZINE.
VOL. XXX. PHILADELPHIA, JANUARY, 1847. NO. 1.
* * * * *
THE OATH OF MARION.
A STORY OF THE REVOLUTION.
BY CHARLES J. PETERSON.
[PRIZE STORY—for which the Premium of $200 was awarded by the Committee.]
CHAPTER I.
Every man knows best how to buckle his own belt.
FALSTAFF.
"Did you get the pass, Macdonald?" said a young man, looking up, as his
servant entered the room of a lodging-house in Charleston, in the latter
part of the year 1780.
"Yes, sir, and the baggage and horses are ready," was the reply of a
stalwart youth, whose dress betokened a condition removed from that of
an ordinary menial, and partaking rather of that of a familiar, though
humble companion. "I think we can give them the slip, sir—Lord! how I
wish for a crack at these fellows! and once with Marion, we'll not long
want an opportunity."
"Be in waiting for me at midnight, then," said the first speaker; and,
as Macdonald retired, he threw himself back again in his chair, and
fixing his eyes on the floor, resigned himself to the abstraction out of
which he had been roused.
Howard Preston, the hero of our story, had just returned from Europe,
where he had been fulfilling the injunctions of his father's will, by a
course of study and travel until his twenty-fourth year. The first great
sorrow of his life had been his parting, at sixteen, with the only child
of his guardian, Kate Mowbray, then a lovely little girl, who for years
had been his pet and playmate. Many were the tears she also shed at the
separation, and faithfully did she promise not to forget her boy lover.
Such childish preferences usually end with youth; but it was not so in
the present instance. With every letter from abroad came a gift for
Kate, which she requited with some trifle worked by her own hands. But
as years elapsed, and Kate approached womanhood, these presents were no
longer returned, and Preston, piqued at what he thought neglect,
gradually came to confine himself, in his letters home, to a cold
inquiry after her health, instead of devoting, as heretofore, two-thirds
of the epistle to her. Yet he never thought of America without also
thinking of Kate; and when he landed at Charleston, a month before our
tale begins, he was wondering into what kind of a woman she had grown
up.
Still his old feeling of pique was uppermost when shown into her
father's magnificent parlor; and this, combined with his astonishment at
seeing a graceful and high bred woman announced as his old playmate,
lent an air of coldness and embarrassment to his greetings. Whether it
was this or some other cause, Kate, who was advancing eagerly, suddenly
checked herself, , and put on all her dignity. The interview, so
inauspiciously begun, was short and formal, and to Preston, at least,
unsatisfactory. He had expected, in spite of their tacit
misunderstanding, that Kate would meet him as rapturously as of old,
forgetting that the child had now become a woman. He overlooked, also,
the effect his own restraint might have produced. Thus he returned to
his lodgings, dissatisfied and angry, half disposed to dislike, yet half
compelled to admire, the beautiful and dazzling creature from whom he
had just parted. The truth was, Preston, though hitherto ignorant of it,
had loved his old playmate from boyhood. This had made him feel her
neglect so acutely, and this had led him secretly to hope that her
welcome on his return would heal the past. No wonder he went home angry,
yet quite as much in love as ever!
Preston and Kate often met after this, but they seemed destined to
misunderstand each other. Kate was really ignorant of the mischief she
had done. She had come down to meet him with a heart full of the
memories of other days, and, if truth must be told, a little nervous and
anxious how he, of whom she had so often thought in secret, would
receive her. His proud demeanor had chilled her. Nor on subsequent
occasions were their interviews more satisfactory. Indeed Kate was
puzzled and vexed at Preston's manner. No one could, at times, be more
interesting; yet no one was so often haughty and disagreeable. Kate
sighed to think how changed he had become; then she was angry at herself
for sighing.
Kate was accordingly as wayward as Preston—and who, indeed, had greater
excuse? Rich and well born, beautiful and high-spirited, she was
positively the reigning belle in Charleston during the whole of that gay
winter. To a complexion delicately fair, and a person of the most
exquisite proportions, she united those graces of mind and manner,
which, in that courtly day, were considered the unerring accompaniments
of high breeding. Report awarded to her numbers of unsuccessful suitors;
but all had tacitly resigned their claims in favor of Major Lindsay, an
English officer of noble blood, between whom and an earldom there was
only a single life. Gay and splendid in person and equipage, the Major
no sooner laid siege to the heart of the heiress, than her less favored
suitors gave over in despair; and what between lounging most of his
mornings away in her parlor, and attending her abroad on all occasions,
he speedily came to have the field nearly altogether to himself.
The arrival of the major anticipated that of Preston about a month, and
when our hero returned, he found his rival almost domesticated at Mr.
Mowbray's house. Jealousy soon revealed to Preston the secret of his own
long hidden love; but it made him heartily hate the major. The two
gentlemen seemed perfectly to understand each other. But the Englishman
knew better than his rival how to suppress his feelings, and accordingly
possessed every advantage over him in superior ease and self-command.
Had Kate wished otherwise, she could not but have given the larger share
of her attention to the graceful, brilliant and composed man of fashion,
rather than to his more irritable and wayward rival, whom a fancied
slight, in word or look, was sufficient to make dumb for a whole
evening. Depend on it, the worst possible use to which a lover can put
himself is to be sulky.
Perhaps it was the enmity he nourished against his more successful
rival; perhaps it was the natural indignation of a frank and noble heart
against oppression; perhaps, which is more natural, it was both
combined, but Preston had not been long at home before he formed the
resolution to take part with his countrymen in the war then going on;
and the sudden appearance of General Marion on the Santee, where he
began a partisan conflict with the invaders, opened to him a favorable
way for carrying out his design, which he only postponed until he could
part from Kate on better terms. He flattered himself that she herself
was secretly on the side of the colonists, for her father had once held
a commission under the provisional government, although since the fall
of Charleston and the apparent conquest of the colony, he, like many
others, had been induced to take a royal protection, and ground his arms
as a neutral.
One morning Preston found Kate alone in her little parlor. It was rare
that she was without visiters, for Major Lindsay, at least, was usually
at her side. Kate wore a pretty morning-dress, and was sewing, her
little tiny foot, that rested on a cushioned stool, peeping provokingly
out beneath the snowy muslin. A woman one admires never looks lovelier
than when occupied in this truly feminine employment; and as Kate made
room for Preston beside her, with her sweetest smile, he thought she had
never seemed half so charming. Lovers can imagine how happy Preston soon
was. He and Kate talked of old times, she busily plying her needle, but
every now and then looking up with animation into his face. His heart
beat quicker, and he longed to tell her how he loved her; it would, I
fear, have set your head or mine, reader, topsy-turvy at once. A dozen
long forgotten incidents were called to mind: how Preston had once
rescued Kate from the river, how they both wept when her old nurse died,
and a score of other things. The color of both heightened, and Preston
felt every instant as if he could snatch the dear girl to his arms. In
the eagerness of conversation, all at once Kate placed her hand
familiarly on his.
"And do you remember," she said, gazing up with sparkling eyes into his
face, "do you remember when the pony ran away with you? Oh! I was half
dead with fright, and screamed lustily. Those were happy days—I wonder
if we are ever as happy as in childhood. I sometimes wish we were back
again on that old lawn." And she sighed.
"Do you, indeed?" said Preston, his whole face lighting up, and he took
her hand by an impulse he could no longer resist.
At that moment the words which would have decided his fate were rising
to Preston's lips, and Kate, as if secretly forewarned, began to tremble
and be confused, when the door was flung open and the servant in a loud
voice announced Major Lindsay.
If any of my readers has ever been interrupted when about to declare
himself, and had to come plump down from rapture to foolishness, he can
imagine Preston's chagrin at the entrance of the visiter. However, he
had tact enough to think of Kate's embarrassment, and as he rose to make
his bow, adroitly placed himself so as to conceal her for a moment, and
allow her time to recover from her confusion. The major gave both
parties, on the instant, a suspicious glance, but his softest smile
immediately succeeded, and with easy assurance taking the seat Preston
had vacated, he glided into a strain of brilliant small talk, such as
would have done honor to any gallant of the day, incomparable at
compliments and snuff-boxes. Preston was angry at this unceremonious
supplanting, but even more angry to see how quickly Kate recovered
herself, and dashed out into the strife of repartee, with a spirit and
ease superior even to the major's. Preston chafed, and thought she might
have been a little less interested. At first he was silent and reserved,
then he began to be uneasy, and once or twice he yielded to his
irritability in words. He cursed his folly for imagining, as he did five
minutes before, that she thought more of him than she did of others. He
fixed his eyes half frowningly, half contemptuously on Kate. She
immediately, he thought with conscious guilt. The next instant she
turned haughtily away and addressed the major. Now, for the first time,
Preston became convinced of the existence of the engagement respecting
which he had heard so much. Burning with mortification, after sitting a
few seconds, during which Kate did not once address him, he arose and
abruptly took his leave.
"She loves him," he exclaimed bitterly. "Dazzled by the glitter of a
coronet, she casts aside her old and tried friend like a worn-out
trinket. Oh! God, was it for this I hastened home? was it for this I
treasured her memory through long years?"
For hours he remained alone, now pacing his chamber with rapid strides,
now burying his face moodily in his hands. He recalled all his various
interviews with Kate, and strove to remember her every word and look:
the result was to curse himself for his egregious folly in fancying for
a moment that she loved him. But after awhile his feelings grew less
exasperated. He reflected on Kate's manner that morning, before the
arrival of Major Lindsay, and hope once more dawned in his bosom.
"I will lose no time," he said, "in learning my fate decisively. I shall
see Kate at her aunt's ball, and her manner there will determine my
suspense. If she is cold and haughty I will understand that she wishes
to rebuke my presumption this morning. In that case, I will trifle here
no longer, but at once join Gen. Marion. Macdonald, my foster-brother,
loves me too well to desert me, but he has been crazy to be gone this
fortnight past. I will order him to get a pass and have every thing
ready in case of the worst, which my heart forebodes."
It was after arriving at this determination, and receiving Macdonald's
message, that Preston gave himself up to his melancholy, nor did he rise
from his desponding position until it was time to dress for Mrs.
Blakeley's ball.
The sound of gay music, the flashing of diamonds and the twinkling of
light forms met his sight as he entered the ball-room; but he had eyes
only for one object: and he soon sought out Kate amid her crowd of
admirers. Never had she looked so transcendently lovely. It is thought a
mark of taste and fashion now-a-days to laugh at the enormous hoops and
powdered hair of our grandmothers: but let us tell you, good reader,
that a belle of the present age, with her deformed tournure and Dutch
amplitude of skirt, though she may create a sort of matter-of-fact
sensation, very suitable perhaps for this money-making generation, never
awakens that deep sentiment of adoration, that respectful, awe-struck,
Sir Charles Grandison feeling, bestowed on the beauty of the last
century, august in silver tissue and high-heeled shoes. The veriest
stickler for modern ease would have given up the point at sight of Kate.
She wore, as was then the custom, a petticoat of rich brocade, a single
yard of which cost more than the twenty ells of lute-string flaunted by
a beauty now. Over this was a robe of white satin, made high on the
shoulders, but opening in front so as partially to reveal the swelling
bust, and expose the richly-gemmed stomacher and glittering petticoat.
The edge of this robe from the neck down was trimmed with a quilling of
blue ribbon, which was also continued around the bottom. The tight
sleeve, with bands like the trimming of the robe, reached to the elbow:
and the deep ruffle of Valenciennes lace which nearly hid the round
white arm, heightened with rare art the beauties it affected to conceal.
Her hair was gathered back from the forehead, richly powdered, and
trimmed coquettishly with blue ribbon. Now, if there be any heretical
repudiator of the past, denying the brilliancy that powder gave a fair
complexion, we wish he would go and look at one of Copley's portraits,
or—what is better!—could have seen Kate then! We trow his mouth would
have watered. We doubt if justice is done to those good old times. Ah!
those were the days of courtly dames and high-bred cavaliers—when the
stately minuet still held sway—when gentlemen bowed reverently over the
hand they scarcely dared to kiss—and when it was the crowning felicity
of a whole evening's devotion to hand a partner to the table by the tips
of the fingers. Now-a-days people bounce through frisky quadrilles,
while gallants tuck the arm of a mistress under their own as cozily as
an old codger does his umbrella.
Preston was advancing toward Kate, when a buzz of admiration announced
that Major Lindsay was about to lead her forth to the minuet. He won
accordingly only a hasty curtsey in reply to his bow. He was meanwhile
subjected to the mortification of hearing from a dozen bystanders the
rumor of Kate's engagement to the major; and one or two officiously
applied to him to confirm the rumor, knowing his intimacy with the
family. When the dance was concluded, which attracted general
admiration, Major Lindsay still remained at Kate's side. Never before
had Preston noticed such meaning and delicate assiduity in his
attentions. Between the incidents of the morning and those of the
evening, no wonder Preston's anger continued unabated. Still he made
several attempts to obtain a moment's _tête-à-tête_ with Kate: but the
crowd of her admirers frustrated this. At length, toward the close of
the ball, he approached her.
"I come to bid you farewell," he said abruptly; "to-morrow I leave
Charleston."
"Leave Charleston!" repeated a dozen voices in dismay. "What shall we do
without you?" Kate alone betrayed neither surprise nor emotion. "Ah!
indeed," was her unconcerned reply.
Preston turned pale with suppressed mortification at this indifference;
mere friendship, he said to himself, demanded some expression of regret
at least. His feelings were not allayed by what followed.
"You're not going to join Marion, are you?" said Major Lindsay, in a
tone of triumphant banter, little imagining how near he was to the
truth. "Has he frightened you by the great oath he has sworn to revenge
his nephew, who was shot for a rebel? I hear he threatens some mighty
deed. Only think of his doing any thing with that brigade of invincible
tatterdemalions—Falstaff's ragged regiment over again!"
"Take care that you are not one of those to pay the penalty of Marion's
oath," retorted Preston, stung by the insolence of his successful rival,
and reckless what he said. "It was a foul deed, and will be terribly
revenged."
Major Lindsay flushed to the brow, and his hand mechanically sought his
sword hilt; but he controlled himself immediately, and said with a
sneer—
"That might be called sedition, only we know you are a man of peace, Mr.
Preston. But he is certainly Marion-bit, is he not?" and he turned to
Kate.
Now Kate felt piqued at this unceremonious leave of her lover, as well
as at his haughty conduct in the morning. She fancied herself trifled
with, and answered cuttingly,
"Never fear Mr. Preston's joining Marion. Our American gentlemen, on
both sides, are but carpet knights of late. They resemble Sancho Panza,
who, good soul, would not stir a step till a rich island was promised
for his share."
Preston tingled in every vein at this speech, which he regarded as aimed
at himself. He bowed sarcastically to Kate, and glanced angrily at Major
Lindsay, as he replied,
"One might almost be tempted to join Marion after this, in order to
raise the reputation of American courage, since just now British bravery
has it dead hollow."
"Oh! pray," said Kate, laughingly, "play the Atlas for the patriots
then. That's a good man: Be the St. George to destroy this British
dragon."
Major Lindsay looked for a moment as if he thought there was more in
this than met the ear; but he contented himself with retorting on
Preston.
"Do, by all means," he said, "and, if you take Bobadil's plan, you may
defeat a whole army yourself. You know he proposed to challenge a single
enemy and slay him by duello: then challenge a second, and slay him:
then a third, and dispose of him also: and so on until the whole army
was annihilated."
Kate, as well as the rest, laughed at this sally. Preston needed but
this to complete his anger and disgust. The field, he saw, was his
rival's, and he was glad when other persons approached and broke up the
colloquy, which, to tell the truth, was growing too personal. But Kate
was piqued and Preston enraged: and as for the major, seeing there was a
quarrel between his rival and mistress, he had striven to widen the
breach.
Preston hurried from the ball-room, and taking time only to change his
dress, repaired to the rendezvous where Macdonald awaited him. Without a
word he flung himself into the saddle, and his companion imitating his
example, they were soon without the city. They had passed the outposts
for some time, when Macdonald, pushing his horse close to Preston's,
opened the conversation.
"We're clear of that confounded town at last, thank Heaven!" he said,
"and I, for one, aint sorry. Them Englishmen are as saucy as princes,
and think nobody has any courage but themselves. But I know one stout
fellow that can snuff a candle with his rifle at two hundred yards, and
before a week we'll have a rap at 'em, for I s'pose you go direct, sir,
to Marion's camp?"
Preston nodded a gloomy assent, for buried in his own thoughts he cared
not to be disturbed. Macdonald saw this, and, defeated in his attempt to
open a conversation, dropped back, but when out of hearing muttered,
"I see how it is. Them women's always getting a man into trouble. For my
part I'll be a bachelor. Marrying's like getting tipsy, very pleasant
except for the after repentance."
CHAPTER II.
Grave men there are by broad Santee,
Grave men with hoary hairs,
Their hearts are all with Marion,
With Marion are their prayers.
BRYANT.
The period of which we write was one that will ever be memorable in the
annals of our country. Never had the fortunes of the patriots been at so
low an ebb in the south, as between the defeat of Gates, at Camden, and
the inroad of Cornwallis into North Carolina. After the fall of
Charleston no time had been lost in overrunning the colony. All
organized resistance being at an end, a proclamation was published,
inviting the citizens to return to his majesty's government, and
stipulating for little more on their part than neutrality. Large
numbers, even of the Whigs, accepted these terms: and had Cornwallis
adhered to his promises, then indeed might liberty have been despaired
of. But the royal leader soon threw off the mask, and required all who
had accepted the protection, as it was called, to declare themselves
openly on the royal side, in the further prosecution of the war. Finding
themselves thus basely deceived, many flew to arms; but such, whenever
captured, were executed as rebels. The fate of Col. Hayne, who was put
to death at Charleston under these circumstances, was but a type of that
of hundreds of lesser note, who perished often without a trial.
The war, meanwhile, was carried on with savage ferocity against the
Whigs. Their plantations were laid waste, their <DW64>s carried off,
their houses given to the flames. The seven vials of wrath were
literally poured out on South Carolina. Instances of cruelty without
number are left on record. One may suffice. An innocent Quaker who took
care of a sentry's musket for a few minutes, while the soldier went on
an errand, was seized for this pretended crime and thrown into prison.
His wife hurried to the jail to see him. She was told to wait a few
minutes and she should be conducted to him. With this brutal jest on
their lips, the royal myrmidons hurried to the man's cell, dragged him
forth and hung him at the jail window: then, returning to his wife, they
led her into the yard, and showed her husband to her quivering in the
agonies of death. But God at last raised up an avenger for these and
other atrocities. Suddenly, in the very heart of the oppressed district,
there arose a defender, bitter, sleepless, unforgiving—seemingly
endowed with miraculous powers of intelligence—whose motions were quick
as lightning—who dealt blows now here, now there, at points least
expected—and who, by a series of rapid and brilliant successes, soon
made his name a terror to the British. Volunteers flocked in crowds to
his standard. His boldness and gallantry filled the colony with
astonishment and rejoicing. Wherever a surprise took place—wherever a
convoy was cut off—wherever a gallant deed was unexpectedly done, men
said that Marion had been there.
Preston had succeeded in raising a troop, for his name was an
influential one in his neighborhood, and he was soon one of Marion's
most trusted adherents. A man who is willing to throw his life away on
every occasion, speedily acquires the reputation of daring and bravery.
The country around the Santee, which was the chief scene of his
exploits, rung with the name of our hero. Nor was his foster-brother,
now a serjeant in Preston's troop, and one of Marion's acutest scouts,
without his share of renown.
Meantime the gay society of Charleston had suffered considerable
diminutions. Many of the royal officers were absent with their commands,
and a large portion of the gentry had retired to their estates. Among
these was Mr. Mowbray, who secretly meditated joining the continental
side again. Kate, too, was absent with her aunt, at the estate of the
latter.
To this place the course of our story now carries us. Mrs. Blakeley's
mansion had heretofore escaped the visitation of war, but within a few
days a detachment under Col. Watson had halted there on its march to
Camden. With him came Major Lindsay, still an eager suitor for Kate. But
scarcely had Col. Watson encamped on the plantation, when a body of
Marion's men, conspicuous among whom was Capt. Preston, made their
appearance, and daily harassed the British officer, by cutting off his
communications, assailing his pickets, and sometimes even beating up his
camp.
One evening Kate was sitting sewing with her aunt in the parlor,
conversing with Col. Watson, and several of his officers, who were their
guests, when the servant came in to light the candles. Old Jacob, as he
was called, filled the office of butler in the family, and was quite a
character. He was a Whig at heart, and cordially disliked his mistress's
compulsory visiters. Having been his deceased master's personal servant,
he had thus acquired a footing of familiarity which allowed him to have
his joke even at the table where he waited. He piqued himself moreover
on what he thought his breeding and fine diction. He was a source of
constant amusement to the British officers, who, however, found him
sometimes their overmatch in repartee.
"Well, Jacob, what news?" said Major Lindsay. "Any more rebels
captured?"
Old Jacob turned, bowed his head profoundly, and showing his teeth in a
broad grin, said—
"Dare is no news yet, sar, dat I know on; but 'spose dare will be some
afore mornin'; for, sartain, Capt. Preston will beat up your quarters as
usual: and den, how de red-coats run!"
Kate looked up archly, yet when she caught the major's eye. That
personage bit his lip, and remarked—
"Never mind Capt. Preston, Jacob: he'll be our prisoner very soon. Has
the flag of truce come back?"
"Oh! yes, sar," said old Jacob, his face radiant with delight. "Habn't
you heard? Dat great news, sar. 'Spose you know Sargent Macdonald?"
"What of him?" said the major, beginning to suspect he was making a
ridiculous figure. "He's a savage. Why he shot Lieut. Torriano yesterday
three hundred yards off."
"Dat he did," said the old butler, waxing grandiloquent, "he hit de
leftenant judgematically, I insure you. But dat is not de news. You
knows Sargent Macdonald sent in word, toder day, dat if his baggage,
took in de sally, was not recorded immediately to him again, he would
kill eight of your men. You know dat? To-day de baggage was sent back,
for dat sargent be de berry debbil, and now he send word dat, since his
baggage be recorded punctiliousy, he will only kill four of your men!"
And the speaker, though too well-bred to laugh at what he considered so
good a joke, grinned from ear to ear.
"The cannibal!" said Lindsay, shrugging his shoulders, "but what can be
expected of the men when their leaders countenance the firing on
pickets."
"Yet you hang them for rebels," said Kate, with spirit.
"They shoot down officers," continued Lindsay, not thinking it advisable
to reply to her palpable hit, "as if this Mr. Marion paid for them at so
much a head. I never saw such unchristian fighting. They are a set of
boors; and cowards at heart, all of them, I'll be sworn."
"Cowards they are not," said Kate, her eyes flashing to hear her
countrymen thus stigmatized. "At least you did not seem to think them
such when Capt. Preston, at the head of his troop, dashed up to your
lines, and challenged you to fight singly, or otherwise. I heard myself
the alarm with which the soldiers cried, 'Here comes Preston again!'"
"He well knew no one would accept his challenge: so his bravado cost him
nothing."
"Go meet him when he comes again, and see whether he meant it for
bravado!" retorted Kate; then, all at once remembering the enthusiasm
into which she had been hurried, she , and resumed her work in
some embarrassment.
Major Lindsay stifled a muttered execration on his American rival, for
he began to fear, from the spirit which Kate had shown, that the
chivalric exploits of Capt. Preston were making a decided impression on
her heart. The desperate daring which the rebel officer had shown within
the last few days, Major Lindsay had attributed, in his own mind, to a
desire on the part of Preston to dazzle his mistress; but Kate's
behavior toward himself had been so flattering, in comparison to that
bestowed on others, that, until this moment, he had consoled himself
that these exploits had been thrown away. He sat, therefore, silent and
moody; and the conversation ceased.
Gradually, one by one, the visiters thinned off and returned to their
quarters, until only Col. Watson and himself were left. The Colonel and
Mrs. Blakeley had sat down to a game of cards in a distant corner of the
apartment. Here was an opportunity to decide his fate. It might be the
last time he would find Kate alone, for the camp was expected to move in
a few days. The occasion was not to be neglected, and, doubtful as he
felt of the issue, he arose, and leaning over her, said, in a low voice,
"I fear, my dear Miss Mowbray, that I offended you by what I said of
Capt. Preston. I forgot, for a moment, that he was an old playmate of
yours. You cannot tell how pained I am that any thing I said should
displease you."
"It matters little—I am not at all displeased," said Kate, keeping her
eyes on her work, her heart beating violently. "Capt. Preston needs no
defender in me, nor asks one. I but spoke generally in behalf of my
countrymen."
Major Lindsay saw her embarrassment, and, misinterpreting the cause,
drew a favorable omen from it.
"You relieve my heart from a load," he said. "I could bear any thing
rather than your displeasure. Indeed you must long have seen how I loved
you. Nay, do not rise from the table. I worship the very ground you
tread on—my life itself is bound up in your smiles—all I have, heart,
fortune, reputation, I lay at your feet—"
He would have continued in the same impassioned strain, but Kate,
summoning up all her self-command, rose with dignity.
"It pains me to hear this, Major Lindsay," she said. "I will be frank.
That you sought my society, I saw, but that you loved me I never
believed."
The face of Major Lindsay flushed, but he controlled his features, and
detained her as she would have moved away.
"Do not bid me despair," he said. "In time I may be allowed to hope. Let
me fancy that my devotion may at last win me this fair hand."
"No time can alter my sentiments," said Kate, coldly.
"I will serve for you as for a second Rachel," and the major still
detained her.
"Nay! I can listen to this no more. You forget yourself!" said Kate,
severely.
At this instant, and before Major Lindsay could reply, Kate saw that her
aunt had finished the game of cards, and was coming toward her. The
major with chagrin turned away. He would have given worlds if the
_tête-à-tête_ could have been protracted, for then he would have
endeavored to discover if Kate really loved Preston, or was indifferent
to all.
"Rejected, by George!" he muttered. "But I must have her, however," he
soliloquized. "She is too lovely, too charming altogether, to be
sacrificed on a provincial—what a sensation she would create at court!
Then she is heiress to one of the best properties in this colony, and
since my cousin has married again, there is no telling how many new
lives may come in between impoverished me and the earldom. By Jove! I
wish this Preston had remained abroad a little longer, or that he would
get knocked over in some skirmish. I wouldn't hesitate to give him his
_coup de grâce_ myself, if I had a chance. But he shan't foil me. I'll
have Kate in spite of him. What a delicious creature she is! What
eyes!—what an arm!"
Major Lindsay met Kate the ensuing day with an unruffled brow and
without embarrassment. If there was any change in his demeanor, it was
perceptible only in the assumption of greater deference toward her than
before. Not Lord Orville himself, the _preux chevalier_ of Evelina,
could have shown more tact and delicacy in bestowing those thousand
little attentions which go so far toward winning the female heart. Kate
was annoyed. She saw that Major Lindsay, in spite of her decided
language, still cherished the hope of winning her favor; but his conduct
was so guarded as to forbid maiden modesty again alluding to the
subject. She could only, therefore, endeavor, by a cold though polite
behavior, to show that her sentiments were unchanged, hoping that in
time he would tire of the pursuit. She little knew the pertinacity and
unscrupulousness of the man with whom she had to deal.
Kate dared not, meanwhile, too closely to examine her own heart. She
could not forget the exquisite pleasure which attended her last
_tête-à-tête_ with Preston, and her bosom thrilled whenever she thought
of what might have been his words if Major Lindsay had not come in. The
subsequent coldness and suspicion of Preston had piqued her, and she had
resolved to punish him for his want of confidence and jealousy, by a
little innocent coquetry with Major Lindsay in the evening. Fatal error!
When she heard of his speedy departure from his own lips, she regretted
for a moment her revenge; but her second feeling was that of anger at
his conduct, and hence her assumed indifference. And yet, after the
lapse of months, she felt herself the aggrieved party. Preston ought not
to have been so jealous. He had no right to be offended at the show of
only ordinary courtesy to a visiter. If he chose to be suspicious and
proud, he ought to be taught better by neglect. He had trifled with her,
else he would have called again, and sought an explanation. But perhaps
he did not love her, perhaps he had meant nothing by his words. She
usually ended her reveries at this point with a sigh, and a haughty
resolution to discard him from her heart. She would love no one who did
not love her.
In a few days Col. Watson left his encampment for Georgetown, where he
arrived, harassed by constant attacks, Major Lindsay accompanying him.
CHAPTER III.
And there was arming in hot haste.
BYRON.
The war meanwhile went on with increased ferocity. The tide of battle,
which at first ran in Marion's favor, had now turned, and his enemies
were everywhere in the ascendant. The army of Greene was in North
Carolina, occupied in watching Cornwallis. Lord Rawdon held Camden with
a strong force. All the other important posts were in the hands of the
British. Marion, for the first time disheartened, talked of retiring
behind the mountains. Armed bodies of Tories, in the mean time,
traversed the country, plundering at will, and hanging, without even the
form of a trial, those of their unfortunate prisoners they had found in
arms.
Mr. Mowbray had long contemplated rising in favor of his country again,
and no time seemed to him so proper as the present, when all others were
becoming disheartened. His daughter he knew to be in safety with her
aunt, who had always maintained a strict neutrality: so there was
nothing to withhold him longer from his purpose. He had accordingly
secretly exerted himself to raise a troop among the young men of his
neighborhood, and his recruiting had been attended with such success,
that their rising only waited the removal of a large body of armed
Tories who had lately infested the vicinity. On the first signal from
Mr. Mowbray, they were to rendezvous at the Hall.
Mowbray Hall was one of those fine old mansions a few of which linger in
South Carolina, fast fading monuments of the departing splendors of her
old provincial nobility. The building stood at the head of a long avenue
of trees, and was a large double house, with an immense hall in the
centre. The outhouses had suffered considerably since the war began, and
many of the fields lay bare and uncultivated; but the mansion itself was
still in a remarkably fine state of preservation, and the architectural
boast of the county.
It was a fine, clear morning when Mr. Mowbray stood on the steps of his
house, to welcome the recruits who, in obedience to his long expected
signal, were on that day to repair to the rendezvous. His feelings, as
one stout yeoman after another rode up, were those of exultation, dashed
a little perhaps with regret for having ever despaired of his country.
"How fortunate that Capt. Ball, with his Tories, has moved up the
river," said his lieutenant, who stood beside him. "We shall have time
to discipline our men, and rally a greater number to our ranks. Our
twenty tall fellows, though brave enough, could scarcely make head
against his hundred troopers. We have a good week before us."
"Very true; and we have assurances of nearly thirty more, provided we
display our banner. Three days of quiet is all I ask. Then, I hope, we
shall be able to give a good account of ourselves even if Ball's Tories
return," said Mr. Mowbray.
"If we are gone when he comes back, my dear sir, he will wreak his
vengeance, I fear, on our homes," said the other, with something of a
sigh.
"I hope you do not think of drawing back," replied Mr. Mowbray. "In this
cause a man must be willing to sacrifice father and mother, house and
land, good repute, and all else he holds dear in the world. God help
us!"
"I am with you till death," said the lieutenant, thinking at that moment
how much more his superior had to lose than himself: and affected by
such heroic and self-sacrificing patriotism.
At this instant a horseman was seen galloping furiously down the avenue,
and as he came onward, he waved his cap as if desirous to call their
attention to something in the road which he had left. Mr. Mowbray looked
in that direction, but a clump of woodland shut out the highway from
sight; however, after a moment's delay, the voice of one of the recruits
called his attention to what seemed a cloud of dust rising above the
tree tops. Almost at the same instant a number of troopers appeared at
the head of the avenue. The approaching horseman now had reached the
lawn.
"We are betrayed," he cried, almost exhausted. "Ball's Tories are
behind, and have chased me for two miles. To arms—to arms!"
The time was too short to allow of barricading the house; but the great
hall was speedily turned into a fortification. The doors at either end
were closed, barred, and further defended by chairs and tables piled
against them; while the entrances into the parlors were closed
effectually in the same way. The great window at the head of the
staircase, and the one at the other extremity of the upper hall were
guarded by a proper force. These dispositions had scarcely been
completed when the Tories galloped up to the lawn, on which they
dismounted with loud shouts, and began instant preparations for the
attack.
When Mr. Mowbray's scanty troop was mustered, it was found to contain
but ten exclusive of himself, for nearly half of the expected recruits
had not yet had time to arrive. It was evident there had been treachery
somewhere among them; for none but those who had enlisted knew of this
rendezvous; and the sudden disappearance of the enemy two days before,
it was now apparent, had been a feint. However, nothing remained but to
sell their lives as dearly as possible.
Mr. Mowbray walked around among his men, and himself saw that every
thing was ready. He exhorted them, in a few words, to do their duty
manfully. His short harangue was brought to a speedy conclusion by a
loud cheer on the part of the assailants, and by a shower of bullets
aimed at the hall window, as they advanced to the attack.
"Fire coolly—and waste no shot!" he said, sternly, himself handling a
musket.
Four men fell at that first discharge; and, mad with rage and shame, the
assailants strove to climb up the pilasters of the hall door; but they
were beaten thence by the butts of the defenders' muskets. The men,
however, who achieved this were severely wounded by the rifles of the
Tories, who, keeping watch, aimed wherever a head appeared. An effort
was now made to break in the hall door. An axe was brought, and, after
several blows, one of the heavy panels gave way. But the moment the wood
fell crashing in, a volley poured through the aperture drove back the
assailants, who, thus foiled at every point, retreated to the cover of
the outhouses, as if to hold a consultation.
The little garrison was now mustered. One of its members had been shot
dead at the great hall window, and several were wounded. The hurts were
bandaged as well as possible, and the stock of ammunition was
distributed more equally. Their slight successes had inspirited the men;
they began now to talk of foiling the enemy; and when notice was again
given of his approach they repaired to their posts with alacrity and
exultation.
The Tories now seemed to have resolved trying a combined attack on all
parts of the house. One party advanced toward the hall door in
front—another made the circuit of the mansion to assail the one in the
rear—and a third remained at one angle, as if contemplating an assault
on the side when the rest should be fully engaged. Mr. Mowbray's heart
forewarned him of the result when he saw these preparations.
"They are breaking into the parlors," exclaimed one of the men, rushing
up the staircase, at the very instant that a new volley was discharged
on the house from the assailants.
Mr. Mowbray listened and heard the dull crash of an axe, followed by the
breaking of glass. The parlor shutters had merely been barred, and the
parlors once gained it was only necessary to break down the doors
leading to the entry, which were comparatively weak, and slightly
barricaded. To desert the hall up stairs would be to seduce the Tories
in front and rear from their cover, and throw open an entrance to them
by the way they had first essayed. It became necessary, therefore, to
divide his already small force, and, leaving a few to maintain the old
positions, defend the threatened door with two or three trusty arms.
"We must sell our lives dearly," he said, as he took his station behind
the door, posting a man on each side.
The enemy was now heard leaping into the parlor, and simultaneously a
general attack began on all sides. The bullets rattled against the wall;
shouts and cries of encouragement rose on both sides. From the quick
firing overhead Mr. Mowbray knew that his men in that quarter were
actively engaged. The axe was now heard against the parlor door before
him, and the frail wood quivered under every blow. Another stroke and
the panel gave way. Instantly the musket of Mr. Mowbray was aimed
through the aperture at the man who wielded the axe, who fell dead at
the explosion. But another promptly seized the instrument, and, posting
himself with more caution at the side of the opening, dealt such
vigorous strokes that the door speedily fell in. As the planks crashed
to the floor there was a general rush on the part of the Tories in the
parlor, toward the aperture.
"Meet them bravely!" shouted Mr. Mowbray. "Strike home, and we drive
them back."
He fired a pistol as he spoke at the foremost assailant; but the Tory
knocked up the weapon, and the ball lodged in the ceiling.
"Hurrah! we have them now," shouted this man, who was their leader.
"Revenge your comrades!"
"Stand fast!" cried Mr. Mowbray, the lion of his nature aroused.
For a few seconds the melee was terrific. Now that the foe had effected
an entrance, the defence of the other posts was no longer necessary, and
the followers of Mr. Mowbray crowded to his assistance. On the other
hand the Tories poured into the parlor, and thence struggled to make
their way into the hall. Inch by inch they fought their road with
overpowering numbers; and inch by inch, with desperate but unavailing
courage, the Whigs gave ground. The clash of swords, the explosion of
pistols, the shouts of either party were mingled in wild disorder with
the oaths and shrieks of the wounded and dying. Swaying to and fro, now
one party, now the other giving ground, the combat raged with increasing
fury. But numbers at last prevailed. When most of his followers had
fallen, Mr. Mowbray, however, still remained, wounded yet erect,
struggling like a noble stag at bay.
"Surrender, and we give quarter!" shouted the Tory leader, who,
throughout the conflict, had seemed desirous rather of taking him
prisoner than slaying him.
Mr. Mowbray thought of his child and faltered: but remembering that the
enemy never showed clemency he said, striking at his adversary,
"Never, so help me God!"
But that moment of indecision sealed his fate. The Tory leader made a
sign to his followers, two of whom rushed in on the old man; and, as he
spoke, his sword was knocked from his hand, and himself overthrown and
bound.
Two days after he was led in triumph into the streets of Georgetown, nor
was it concealed from him that his life had been spared only that he
might expiate his rebellion on the scaffold.
His captor immediately repaired to Major Lindsay's quarters, where he
remained for nearly an hour. When left alone, Major Lindsay exclaimed,
"My information was true, then; he has been caught with arms in his
hands. So far all goes well. That proud beauty is now mine, for she will
marry me to save her father's life."
[_To be continued._
* * * * *
MIRIAM.
BY KATE DASHWOOD.
Oh Harp of Judah! long thy thrilling strain
Hath slumbered 'mid the gloom of centuries—
Save when some master-spirit woke again
Thy silent chords of thousand symphonies.
Not thine, his swelling anthems loudly ringing—
Oh Maid of Judah! with thy prophet-song,
And sounding timbrel's voice, all proudly flinging
Thy warrior-notes Judea's hills among!
Oh voiceless harp! fain would my soul-wrapt ear
Catch some faint echo from thy silent strings.
And, as these trembling fingers half in fear
Sweep o'er thy slumbering chords—lo! there up-springs
Strange spirit-music, tremulous and low
As half-breathed sigh—to fitful silence hushing
Those thrilling strains my unskilled fingers know
Not to control. But hush! again their gushing
Swells like loud battle-peal on fierce blasts rushing.
Night! o'er thy mountains, oh Gilboa! where
The mighty spear of Saul was rent in twain.
And haughty Israel's curse was branded there—
The blood of her first king—dark as the curse of Cain!
Night—on Mount Moriah! o'er his solemn brow
Those sentinels that guard the halls of Heaven
As brightly keep their wakeful vigils now
As when He knelt 'neath their pure beams at even,
And prayed in agony that we might be forgiven.
Moonlight o'er Galilee! the sparkling wave
That bounded as the sunbeams kissed its breast,
Are now all motionless and silent, save
Their low, hushed murmurs where the soft winds rest.
Night o'er lone Samaria! thy dark hill's crest
Fades proudly into gloom. Still linger there
Thy maidens at "The Well" His feet have prest;
Still floats their broken music on the air
At eve, blent with the wave's low murmured prayer.
Thy moon rides slowly o'er thy hills, oh Galilee!
Proud Queen of Heaven! bound to her far-off throne
Behind the Syrian mountains—and thy sea,
Oh lone Tiberias! where of late she shone,
Mirrors the stars upon thy bosom—stars of voiceless Night.
The dark Chaldean, from his cloud-hung tower,
Keeps his lone vigils by thy waning light,
For Israel keepeth Feast of solemn power,[1]
When thy bright beams shall fade at morning hour.
The stern Chaldean turns him from his lore
Where he hath writ the mighty destiny
Those stars revealed. Now seeks he thy dim shore,
Tiberias! the spirit-minstrelsy
Of unborn Ages breathes upon his lyre
In soul-wrapt flame. But hush! the far-off notes
Of timbrel-echoes '<DW41> the hills expire,
As 'twere some seraph's song o'er earth that floats
And fades away in air—when lo! proud Miriam stands
Before him and his prophecy commands.
-----
[1] The "Feast of Tabernacles," which lasted seven days.
THE CHALDEAN'S PROPHECY.
"Daughter of Judah! on thy brow
Thy kingly line is proudly blent
With Israel's faith, and woman's vow—
Now love, now pride—each lineament.
Thine is the faith thy fathers bore—
A heritage despised, contemned—
The fearful curse still lingers o'er
Israel's outcast tribes condemned.
Thine is their faith—but dost thou deem
_Thy soul is with the Nazarene_?"
"False Prophet! had Ben Ezra's ear
But heard thy lying prophecy,
Thou stand'st not, Heaven-daring here,
To mock our Faith thus impiously!
For Israel's Lord is still our God!
And Israel's outcast tribes shall turn
Back to these hills our fathers trod,
And fallen Judah cease to mourn.
False Seer! thy words I heed them not—
Those stars are dim thine eyes have sought."
. . . . . .
Darkness o'er the Eternal City!—gloom
O'er her thousand palaces! and Night,
Deep, solemn Night! broods ever o'er the tomb
Of her vast temples, fallen in their might.
Still to their broken shrines worn pilgrims come—
And 'neath their mighty columns, sunken low,
The fierce Bedouin seeks his midnight home,
And treacherous lurks where footsteps chance to go.
Proud Rome! thy thousand hills are silent now—
Where waved the "Imperial Eagle" o'er their brow.[2]
Yet o'er her mighty temples' fallen shrines
Still sleeps the sunshine 'mid the shadows there;
There many a wearied pilgrim-wanderer finds
A peaceful rest from Life's dark toil and care.
And there awaiteth many a scattered one
Of Israel's people—till the joyful day
Shall see the long "lost tribe of Judah" come
Once more to thy blest land, oh Palestine! for aye,
And here, 'mid fallen Rome, Ben Ezra bides—
_Miriam is not_—earth hath no joy besides.
. . . . . .
America the blest! all proudly to thy shore
Fled Rome's _imperial eagle_! thy fair land
Sleeps e'er 'mid bloom and sunshine; evermore
Thy Freedom's holy cause shall firmly stand.
Our noble sires! their true hearts' incense rose
Here upon God's free altars; _let us keep_
_Their memories holy!_ Room at our shrines for those
Who seek, like them, a rest from bondage deep.
And Miriam! was that prophecy a dream?
_Thy soul—thy faith is with the Nazarene._
-----
[2] The emblem banner of Rome.
* * * * *
THE NIGHT WATCH.
A TALE.
News, fitted to the night.
Black, fearful, comfortless and horrible.
KING JOHN.
On a cold December night, in the winter of 183-, four persons were
assembled in an upper chamber of an old out-house in one of the crooked
streets at the "North End" of Boston. This was in former times the most
fashionable part, the court end, as it were, of the town, and the house
of which I speak had been the residence of one of the old colonial
governors, and bore traces of its former magnificence, now almost
effaced by the ravages of time and neglect.
It was a dark and tempestuous night. The wind howled mournfully through
the narrow streets and around the tall houses of the "North End," and
the few passengers who were abroad wrapped their garments tighter about
them, and hurried to seek shelter from the cutting blast. Within doors
the aspect of things was more cheerful. An old-fashioned wood fire
burned brightly on the hearth; the heavy folds of the crimson curtains
excluded every breath of cold air, and the usual conveniences of comfort
and luxury were distributed through the apartment. The company,
consisting of myself and three female friends, were drawn closely up to
the cheerful blaze, apparently as comfortable as possible. The cause of
our meeting here was this. A neighbor, one Mr. Helger, had died very
suddenly the day before. He had formerly been engaged largely in trade,
but meeting with reverses which soured his disposition, and cast a shade
of gloom over his character, he had withdrawn entirely from the world,
and lived all alone by himself in this large house. We, being neighbors,
had offered our services to watch with the corpse, as was the custom.
The room in which we were had been the apartment of the deceased, and
was fitted up with much taste, and even luxury, but all the rest of the
house was bare and unfurnished, and was said by the neighbors to be
haunted. The corpse was placed in a room just across the entry, so that
we could hear a noise or disturbance if there should be any.
Refreshments had been provided, and we had nothing to do but to make
ourselves comfortable, and amuse ourselves until morning should release
us from our duty.
The time flew by very quickly in pleasant chat, and when, during a lull
of the storm, we heard the neighboring clock on the steeple of the North
church strike the hour of twelve, we were all surprised at the lateness
of the hour.
"'Tis now the very witching time of night,
When church-yards yawn, and hell itself breathes out
Contagion to the world,"
said I; "can't some of you ladies tell a genuine, old-fashioned,
terrific ghost-story for our edification? Surely, Mrs. Johnstone, you
must know one; you always have plenty of interesting stories."
The lady addressed thought a moment in silence, and then replied, "I can
tell you a ghost-story, and what is more, vouch for its reality, for the
incident happened to myself. It was a good many years ago, but it is as
distinctly imprinted on my memory as if it took place yesterday." A
ghost-story, told by one of the actors in it, could not fail to be
interesting; so we drew our chairs nearer the fire, assumed a listening
attitude, and the lady began.
"You must know, in the first place, that I was married at a very early
age, and a year or two after, left my native place, and went with my
husband to live in the interior of Vermont. The country was little
settled at that time, being mostly covered with unbroken forests. I felt
the change of situation very strongly. I had lived all my life in the
midst of a large city, surrounded by a numerous family of brothers and
sisters. We had gone into society a good deal, and had been in the habit
of seeing many people, and engaging in all the amusements of the day. My
present residence was in the midst of dense forests, the next neighbor
lived two miles off, and the nearest town was on the Connecticut, more
than ten miles from our farm. The house stood on one corner of the
clearing, not more than a hundred yards from the woods, through which,
on stormy nights, the winds howled in mournful and sad tones. In winter
the deep snows cut off all communication with the other parts of the
country, and sometimes we did not see a stranger for months. To this
lonely spot I had removed, after having always been accustomed to the
noise and bustle of a city, and it was not strange that it should seem
gloomy to me.
"One day in autumn, in the month of November I think it was, my husband
told me that he was going to take his men and go over to the next town
for some necessary articles, and he was afraid that he should not be
able to get home that night. So away he went, and left me alone in the
house, with the exception of my infant child. I had brought a black
woman with me from home, but the change of situation did not agree with
her. She had been taken ill, and had died about a fortnight before the
time of which I speak. On account of the difficulty of procuring
servants, I had not been able to get another woman to supply her place,
so I was entirely alone.
"After supper I sat by the kitchen fire some time, till at last I
dropped asleep in my chair. I was awakened by the shrill sound of the
tall, old-fashioned clock, striking the hour of ten. The candle had
burned low in its socket, and the expiring embers diffused a faint glow
through the room. I jumped up, rubbed my eyes, and prepared to go to
bed. I took the light and was leaving the room, when somebody knocked at
the outside door of the house. I was a little startled that any one
should knock at the door at that time of night, but presently I thought
that my husband had changed his mind and returned home after all. I went
and opened the door, but nobody was there. I shut the door, rather
surprised, and sat down by the fire.
"To understand my story clearly, you must know the arrangement of the
room in which I was. On one side was the door leading into the open air,
on the opposite side, the doors leading to the parlors, etc. On the
third side of the room was the fireplace, and on the fourth, the door of
a bed-room in which black Charlotte had slept, and where, as I have
said, she died a fortnight before. This door was a little way open. I
went and shut it, and had hardly done so, when the knocking was repeated
with startling distinctness, and a moment after I saw the door of the
bed-room slowly open, and remain ajar. I went again to the door and
looked out, but, as before, I could see no one. I then shut the door of
the bed-room and latched it fast. I began to feel frightened, for I
could find no one who could have knocked at the door, nor could I
account for the mysterious opening of the bed-room door. All the stories
of ghosts and witches that I had ever heard came into my head, and
hundreds of imaginary horrors beside. I made up my mind, however, that
if I should hear the knocking again, I would go into the bed-room and
see if any thing was there. I listened. All was quiet, and I could hear
nothing but the beating of my own heart. A third time the knocking was
repeated, slowly and distinctly, and a third time the haunted door
slowly opened. I seized the candle and rushed in. I looked every where,
but nothing was to be seen. I came out, shut the door behind me, and
then went out into the open air. No one was in sight. There was a storm
coming up, and the wind howled mournfully through the branches of the
tall trees. To my excited fancy every thing looked strangely and
differently from its usual appearance. By the dim light of the waning
moon, which was half obscured by the driving clouds that shrouded her
disk, I fancied I saw something moving in the deep shadow of the trees.
I shuddered and closed the door. I went up stairs and looked at my
child. He lay calmly sleeping in his cradle, and his deep breathing was
the only sound that disturbed the stillness of the house. I felt more
assured after looking at the innocent face of the little boy. I felt
that even if God should permit an evil spirit to work its will for a
time, he would never allow it to harm a thing so holy and innocent as
that little child. I endeavored to calm my mind by the reflection that I
had always treated the dead woman with kindness, and if it was really
her ghost that was haunting the house, it would have no reason to injure
me. But my heart grew sick within me when I heard again—'Knock! knock!
knock!' and saw the door of the haunted room slowly open as before."
Here Mrs. Johnstone stopped talking, and listened intently, as if she
was trying to catch some distant sound.
"I certainly heard it," at length she said. "I hear it now—I certainly
hear a noise as of some one moving in the death-chamber. Let us go in
and see if any thing is there."
So saying she arose, took a candle in her hand, and went across the
entry to the neighboring apartment. Presently she shrieked and ran back
into the room where we were, with her face as pale as death, and said,
in a very excited tone—
"Oh! such a sight as I have seen! The corpse sat upright in his coffin,
and seemed as if trying to speak to me."
"You want to frighten us, Mrs. Johnstone," said I. "First you tell an
awful story about a mysterious knocking, and then, to increase the
effect, you come in and tell us this. I am sorry to say that I don't
believe a word of it."
"It is no time for jesting now, young man," rejoined she. "God forbid
that I should sport with such an awful thing as death. But as true as I
hope for salvation I saw Mr. Helger sitting erect in his coffin, and
such a look as he gave me—it will haunt me till my dying day. But, if
you don't believe me, go and look for yourself."
I hastily seized a candle, and went to the room where the corpse was
laid. The rest of the company followed at a little distance. Just as I
approached the door I thought I heard a step in the inside of the room,
as of one coming to meet me. I said nothing, however, and took hold of
the door-handle to open the door—but to my horror it was grasped on the
inside and violently turned. I seized the door and held it to with all
my strength, while it was pulled strongly against me by whatever
infernal shape was in the room. The women screamed dreadfully and
dropped the lights, which went out, leaving us only the dim light from
the fire in the opposite room. The storm without howled round the old
house with redoubled fury. It was a fearful scene. I felt faint and
sick—my strength gave way—I let go the door. Mr. Helger, in his
grave-clothes, stood in the door-way, deathly pale, his face streaming
with blood, and his features distorted by a ghastly grin. We turned and
ran frantically down stairs, tumbling over each other in our haste.
Just as we were running out of the house we heard Mr. Helger behind us.
We ran up the street all the faster, the women screaming at the top of
their voices. The noise and hubbub at last woke up a watchman, who had
been peaceably slumbering in a sheltered corner. That functionary,
wrathful at being disturbed from his nap, arrested our farther progress
with his hook.
"An' what the divil wud yees be doin' wid yerselves here, the night?"
inquired he, in a decided brogue.
This pertinent question brought me to my senses. I pulled some money
from my pocket, and told the son of Erin to come back with us and he
should be well paid for his services. We went back toward the house, and
there, near the door, we found Mr. Helger, lying exhausted and fainting
on the ground.
We raised him up and carried him back into the house, and put him into
bed; and then I despatched Pat for a physician. He soon returned,
bringing one whom he had roused from his slumbers. The physician took
out his lancet and bled the patient, and, having administered the usual
remedies, I had the satisfaction of hearing him say that he thought it
probable in a few days Mr. Helger would recover, and be as well as ever.
He advised us to remain with him, however, that night, and give him hot
drinks from time to time. I paid the physician and the watchman for
their trouble and dismissed them.
It was understood that Mr. Helger's death had been very sudden, and it
turned out that instead of really dying, he had only fallen into a deep
trance, and on arousing from it had frightened us so dreadfully. We were
all put in excellent spirits by this happy termination of our
adventure—this restoration of the dead to life.
"Supposing you let us hear the rest of your ghost story now, Mrs.
Johnstone," said one of the ladies—"if that awful interruption hasn't
taken away all your desire to finish it."
"Oh, no," replied Mrs. Johnstone, "I will tell you the rest with much
pleasure—perhaps it may turn out as well as our present adventure has.
"I believe I left off where the knocking was again repeated at the door.
Well—the mysterious door again opened, but nobody was there. I felt
desperate. I felt that my reason would give way if I should remain quiet
any longer without doing something, and I determined that, if the
knocking was repeated, I would take my child in my arms and run round
the house, and see if any thing was there which could have produced
these unaccountable sounds. I waited patiently till the knocking was
repeated, and then went out of doors and ran round the house. The
mystery was solved.
"The sheep had come down from the woods, through fear of bears, and were
collected in a crowd behind the house. I stood looking at them, and
presently one raised his fore-leg and knocked against the house. It is
done with the bent joint of the fore-leg, and those who are acquainted
with the habits of sheep know that it produces a sound exactly like the
knocking of a human being at a door. I went back into the house, and in
a few moments I heard the sheep knock, and saw the door open a moment
afterward. The house, built in a hurry, as is usual in a newly settled
country, had not been clap-boarded, so that the jarring of the knock was
easily communicated to the bed-room door, and the latch being worn, it
opened a little way by its own weight, and then remained fixed.
"Thus was the mystery cleared up, and you may conceive what a load was
taken off of my heart. I went to bed and slept soundly till morning,
when the glorious sun with his cheerful beams effectually dispelled all
the phantoms and terrors of the preceding night.
"Next day my husband returned home, and I related to him all the
circumstances of my fright. He praised me for the courage I had shown in
going out to investigate the cause of the sounds, and said that he
thought that few men would have been as brave as I was. And sure enough,
on the very next night, my husband and I were sitting in the parlor,
when suddenly the man-servant, a great strapping fellow, came running
in, as white as a sheet, and cried out,
"'Oh, Lord! we're haunted! we're haunted! Charlotte's ghost has come to
haunt us!'
"'What do you mean, you foolish fellow?' said my husband, 'go back into
the kitchen, and don't let me hear any more such nonsense.'
"He went back again, somewhat abashed, but soon returned, almost
frightened to death.
"'I wouldn't go back into that room again if you'd give me fifty
dollars,' said he; 'it's haunted. There was a dreadful knocking, but
nobody was at the door, and then I saw Charlotte's ghost open the door
of the bed-room. Oh, Lord! what will become of us! what will become of
us!'
"My husband took pity on him, seeing that he was so much alarmed, and
showed him the cause of the phenomena. He was very much ashamed of his
fright, and we heard no more of Charlotte's ghost after that."
Here Mrs. Johnstone finished her story, which we all declared was an
excellent one, and praised not a little the courage she had shown. By
this time the morning had dawned;
"Aurora's harbinger,
At whose approach, ghosts, wandering here and there,
Troop home to churchyards: damned spirits all,
That in cross-ways and floods have burial,
Already to their wormy beds are gone."
* * * * *
TO THE HUSBAND.
Speak kindly to her, little dost thou know
What utter wretchedness, what hopeless wo
Hang on those bitter words—that stern reply—
The cold demeanor and reproving eye;
The death-steel pierces not with keener dart
Than _unkind words_ in woman's _trusting_ heart.
The frailer being by thy side
Is of a finer mould—keener her sense
Of pain—of wrong—greater her love of
Tenderness. How delicately tuned her heart!
Each ruder breath upon its strings complains
In lowest notes of sadness, not _heard_ but
_Felt_. It wears away her life like a deep
Under current, while the fair mirror of
The changeless surface gives not _one sign_
_Of wo_.
ELLA.
* * * * *
SENSE AND SYMPATHY.
BY F. E. F.
CHAPTER I.
Use every man after his desert, and who shall escape whipping.
HAMLET.
"Did you ever hear a man talk so like a fool as Mr. Barton did
yesterday, Sarah?" said Mary Minturn to Miss Gorham. "I declare, I
pitied his wife—did not you?"
"No, certainly not," replied her friend. "Why should I? Mr. Barton does
not talk more like a fool now than he did before his marriage. Fanny
chose him with her eyes or rather ears open, and if she could put up
with his folly then, she may now."
"True enough," answered Mary. "And how she came to fall in love with him
passes my comprehension. I would not have believed it had it not
actually happened."
"Really, Mary," said Sarah laughing, "your sympathies and compassions
often pass my comprehension. Here you are pitying Fanny for having
married a man, who, by your own account, she is in love with."
"No, Sarah," replied Mary, "I am not pitying her for marrying the man
she is in love with, but for being ashamed of the man she loves."
"Ashamed of the man she loves!" repeated Miss Gorham with infinite
contempt. "Now, really, Mary, you had better reserve your compassion for
a more deserving object. If Fanny has married a man she is ashamed of,
she should be ashamed of herself."
"Did you see how painfully she as she caught the glance you gave
me, when he was attempting an account of Dr. H's lecture? I could not
help feeling for her."
"I did not remark it," replied Miss Gorham, "and I have no sympathy for
a woman who has so little feeling or principle, I care not which, as to
marry a man she despises. She probably does not feel for herself, and I
do not know why we should put ourselves to the pain of feeling for her.
I remember the time when Fanny Jones used to laugh at Tom Barton as much
as either you or I."
"So do I," replied Mary. "She little thought then she would ever have
him."
"But finding she could get nobody better, she has thought it as well to
marry him, and that is what you call falling in love, Mary."
"Not at all," rejoined her friend warmly. "But remember it is three
years since Mr. Barton first addressed Fanny, and although she ridiculed
him then, she has become attached to him since. His devotion and
constancy have really won her."
"If then she is in love with him," said Sarah, "she should be satisfied
with him; and if she is not she should not have married him; so arrange
it any way you will, Mary, I do not see that she is deserving of much
pity. If she fancies he has grown wiser during the last three years, so
much the better for her; and if she knows he has not, so much the worse.
Either way I have no sympathy to bestow upon her, Mary."
"Well, I have," replied Mary. "I always pity a sensible person who does
a silly thing. It is laying up themselves such a store of suffering for
the future."
"'Pon my word, Mary, you amuse me," said Sarah, laughing. "Now I might
possibly feel for a fool who was committing a folly, as I would for a
blind man who walked into the fire, but as to wasting my compassion on
those who do such things with their eyes open, is really more than I can
undertake. But then," she continued, half contemptuously, "I have not
your stock of sensibilities to go upon, and consequently, perhaps, do
well to economize mine, or I certainly should exhaust them before they
were called upon for a really deserving object."
"I consider all suffering as deserving pity," replied Mary quietly.
"That is more than I do," returned Sarah with spirit. "Sin and suffering
may go together, but I do not consider them equally deserving of
compassion, or I should go to the jails and work-houses to bestow my
sympathies."
"And if you did," replied Mary, "I believe you would go to the places of
all others where they would be most called forth. I never pass the city
prison without thinking of the many unwritten tragedies it contains.
Could we but know the true history of every heart, and the real anguish
of every crime that have peopled its walls, I believe we should feel
more sorrow than indignation for its unhappy inmates."
"Then," replied Sarah, almost angrily, "I think it is well we do not. If
in your fine sensibilities we are to lose all sense of right and wrong,
I think your 'unwritten tragedies' had better remain 'unwritten' and
unread. They would do infinitely more harm than good. 'Sorrowing for the
unhappy inmates of prisons and work-houses!' Who would imagine you were
talking of jail-birds and vagrants! This is the sickly sentimentality of
the day, and I am sorry to see you falling into it, Mary. Let sin meet
with its due punishment, and crime call forth the righteous indignation
it merits, and then we may hope to see them somewhat diminished."
"That sin meets with its punishment, even in this world, there can be no
doubt, Sarah," said Mary.
"Does it?" said Sarah, with some bitterness. "And roguery is never
successful, nor dishonesty prosperous, I suppose. I think some of our
broken institutions and flourishing directors might tell a different
story! However, that it will be punished in the next," she added, in a
tone that implied she would be much disappointed if it were otherwise,
"is certain, but in this sin and impudence decidedly carry the day. You
have only to look around you to see the truth of what I say."
The discussion, which was growing rather warm, was here fortunately
interrupted by the entrance of Mrs. Eldon, a married sister of Sarah's,
who as usual had much to hear and to say when she had not seen Sarah for
several days, as happened to be the case on the present occasion. A
lively and somewhat satirical description of the dinner at Mrs. Barton's
formed the chief topic of conversation for some time, which highly
amused Mrs. Eldon, and even Mary could not help joining in the laugh,
although she could not always agree with her quick-witted and rather
merciless friend. In fact they seldom did agree, for two more opposite
characters than Mary and Sarah could scarcely be met; and what the bond
of attraction could be that rendered them so intimate, would have
puzzled most people to determine. Sarah was endowed with more than an
ordinary share of sense, but it was that kind of good clear _hard_ sense
that seldom attracts, although it often amuses. Her chief virtue was her
justice, on which she prided herself, and she valued principle, while
she placed little faith on feeling. Sensibility and imagination she
utterly despised.
Mary, on the contrary, was full of quick sympathies and bright theories,
and though often wrong in her premises, was always amiable in her
conclusions.
Notwithstanding that they seldom thought alike on any subject, Sarah
loved Mary, and, moreover, loved to put her down, which, being easily
done, was perhaps a charm in itself; and then she could take liberties
with Mary's good temper, which she could not do with every body's. And
Mary respected Sarah's mind and relied upon her integrity, although she
was somewhat afraid of the severity of her judgments. And besides, they
had grown up together, and had got _used_ to each other, which, after
all, explains more attachments than any theory of sympathies and
associations we have yet met with.
Mrs. Eldon was often amused with the opposite accounts the young friends
gave of the same occurrence, and would frequently say, as she laughed,
"One would really suppose, girls, you had been at different places."
Sarah boasted that she told things just as she saw them, and was very
fond of what she called "the plain English of the case;" while Mary
perhaps arrived quite as nearly at the truth in making some allowance
for human weakness, and in having some compassion for its
inconsistencies.
"Why did you not come to tea last evening, Charlotte?" said Sarah,
addressing Mrs. Eldon. "I kept the table waiting almost an hour for
you."
"My dear child, I was in such a fright and agitation at that time, that
I forgot all about you and your tea-table. Master Georgey escaped from
his nurse, and we could not find him for hours. I was almost wild with
anxiety and alarm."
"Indeed!" exclaimed her sister, with much interest; "and where did you
find him?"
"Nearly a mile and a half from home. I don't know how he managed to
wander so far, for you know he is not quite two years old yet."
"And what did you do to him when you found him?" inquired Miss Gorham.
"Do to him? poor little soul; why I gave him his supper and put him to
bed," replied Mrs. Eldon. "The child was exhausted with crying, besides
being half dead with fright and fatigue."
"You don't mean to say that you did not punish him for his excursion?"
exclaimed Sarah, almost incredulously.
"Punish him! No, certainly not," replied her sister; "but I did what was
much wiser. I had a padlock put upon the gate through which the little
dog made his escape; so it cannot happen again, and that, you know, is
all that is wanted."
But upon that point Sarah did not at all agree with her sister. She
wanted a little summary justice besides, and she said,
"Well, if that is not spoiling children, I do not know what is. And this
is the way you let Georgey disobey with impunity, is it?"
"I am sure even you would have been satisfied if you had seen the state
the poor little fellow was in when he was brought home," replied Mrs.
Eldon. "You would have thought him quite punished enough. She will not
be so hard-hearted by and by, Mary, when she has children of her own,"
continued Mrs. Eldon, smiling.
But Sarah was far from satisfied, and was disposed to contend the point,
when her sister, rising, said,
"It is time for me to be going home. Is there any thing you want, or
that I can do for you?"
"Nothing," replied Sarah.
"Without," said Mary, laughing, "you will give Georgey a whipping as
soon as you get home. Now acknowledge, Sarah, that you would feel better
if Mrs. Eldon would promise to act upon the suggestion."
"I think Georgey would be the better, if I am not," replied Sarah. "It
is of great importance that he learns early that no misdemeanor will be
overlooked."
"When I can prevent the recurrence of a fault, I am satisfied," replied
Mrs. Eldon.
But Sarah was not. She was always for punishing the past, whether it had
reference to the future or not.
Her sister bade her good morning, and Sarah remarking that "Charlotte
would ruin her children if she persisted in her present system," the
subject dropped, and the friends soon after parted.
"Do you think Sarah will ever marry, Mrs. Eldon?" Mary asked one day; to
which she replied,
"No, Mary, I fear she never will. Sarah, from having been placed so
young, I suppose, at the head of my father's house, has acquired an
independence both of manner and temper, that, I think, will prevent her
marrying. With her quick insight into character, and satirical turn of
mind, too, she is not easily interested," and, Mrs. Eldon might have
added, was not interesting; for Sarah was now two-and-twenty, and never
had had a lover, nor any thing that approached to one.
She was not handsome, and had no charm of manner that supplied the
attraction of beauty. It is true she had more mind and information than
usually falls to the lot of women, but though she often amused, she
never won. She was upright, true, sincere, but there was a hardness in
her uprightness, a brusquerie in her truths, and a downrightness in her
sincerity, that rendered them any thing but attractive; and, in fact,
she was not popular, and never had been admired. The few young men who
from time to time visited at her father's house she ridiculed without
mercy, and Mrs. Eldon soon gave up all hope of ever seeing her married.
She consoled herself for the fact by saying that Sarah was one of the
few women to whose happiness it was not necessary, and that though with
her strong mind and active habits she would have made an admirable head
of a family, yet, as it was, she would probably become what is termed a
"society woman," and as such be a most useful member of the community.
And, in fact, she seemed gradually falling into the course her sister
had in her own mind marked out for her. There was so much good sense in
all her views, and so much efficiency in carrying them out, that when
once she fell into the class just indicated, she was found too useful to
be readily relinquished. Nor was the occupation distasteful to her. Her
high sense of duty forbade her living for her own pursuits alone, and
watching over the poor, and correcting the idle, and directing and
dictating generally, suited not less with her tastes than her
principles. It was wonderful how much good she did, and how little
gratitude she got for it. No one detected an impostor as quickly as she
did, and all doubtful and difficult cases were turned over to her
management, and every department that fell to her share was directed
with vigilance and understanding, but at the same time many of her poor
feared, and some of them hated her. She relieved their necessities while
she scolded their recklessness, and most of them, as she turned away,
said with bitterness, "that she was a _hard_ lady," while they blessed
Mary's bonny face when she accompanied her, and never failed to call her
"a sweet spoken young lady," for though she seldom went among them, and
gave little, she listened kindly, and felt for their trials and
distresses. The difference was, that Sarah's charity was that of
principle, Mary's of feeling, and to the latter the poor and ignorant
always respond, while they shrink from the former.
"Sarah," said Mary one day, with some embarrassment, "I have a secret to
tell you."
"A secret," said Sarah, "well, what is it?"
Mary as she answered, "Perhaps it may surprise you, and yet it
seems to me you must half suspect it."
"I am sure I do not know what you mean," replied Sarah, "but if it is a
long story give me that flannel petticoat I was making. There," said
she, threading her needle, "begin, I am ready."
But it did not seem so easy to begin as Sarah supposed, for Mary cleared
her throat and then said with an effort,
"I am going to be married."
"You!" exclaimed Sarah, with extreme surprise. "Why, who to?"
"Oh, Sarah!" said Mary with some disappointment, "how can you ask? To
Frank Ludlow, to be sure."
"To Frank Ludlow!" repeated Sarah.
"Yes; you suspected it before, did you not?"
"Not I, indeed," replied Sarah, so decidedly that Mary saw the surprise
was perfect. "I have noticed that he was attentive to you, but I never
dreamt of your liking him."
"And why not?" asked Mary, not without a little mortification.
"Oh! I don't know," answered Sarah carelessly. Her manner seemed to
imply that she saw nothing in Frank Ludlow to like particularly.
"You are not pleased," said Mary presently, in a low voice. "I hope you
don't dislike Frank, Sarah?"
"Who! I dislike him?" said Sarah, looking up from her sewing with
surprise. "Not at all. I don't care about him either one way or the
other. But that is not the point in question. If you are in love with
him, that is enough, provided," she added with a smile, "you do not
require all your friends to be the same."
Mary smiled faintly as she said, "Oh no!" for there was something in
Sarah's manner that disappointed and chilled her. She made an effort to
say something about her long knowledge of his character and principles,
to which Sarah replied,
"I dare say he is a very nice young man, Mary," while she inwardly
wondered what Mary could see in him, to think him worth all the
sacrifices she must make if she married him.
Mary could say no more. There was something so slighting in the phrase
"nice young man," and it was so evident that Sarah did not think much of
him, that her spirits sunk, and she soon after left her friend, more
dejected than she had been since her engagement had taken place.
Mary soon after married, and Sarah was left more to herself and her
independent ways than ever, and what with her societies and
Sunday-schools, and the many occupations she contrived to make for
herself, time rolled quietly on, and Sarah continued very much
fulfilling the destiny her sister had long since predicted would be her
fate.
"Charlotte," said Mr. Eldon to his wife one day about this time, "what
is Allen doing forever at your father's? It seems to me that I never go
there that I do not meet him."
"I don't know," answered Mrs. Eldon carelessly. "Yet, now that you speak
of it, I remember that he is there a good deal. He is such a quiet,
silent person that one sees him without thinking of him. I wonder what
does take him there. I suppose it is a habit he has fallen into. You
know young men will sometimes visit at a house without any particular
object."
"That may be," replied her husband, "but I do not think it is so in the
present instance. I think Allen admires Sarah."
"Do you?" said his wife with surprise, for the idea of Sarah's exciting
particular admiration was new to her. "I should be sorry for him if it
were so," she added.
"Why so?" inquired Mr. Eldon.
"Because," she replied, "he seems an amiable young man, and I should be
sorry for his disappointment."
"But I am not so sure he will be disappointed," pursued Mr. Eldon.
"My dear husband!" exclaimed Mrs. Eldon almost indignantly, "you surely
do not suppose that Sarah would have a man so inferior to herself as
Allen—he is a gentlemanly, amiable person, but decidedly weak."
"Sarah would not be the first clever woman who has married a fool,"
continued Mr. Eldon.
"But he must be younger than herself," pursued Mrs. Eldon.
"About the same age, I imagine," said her husband. "However, if the idea
has not occurred to you before, look to it now. If I am not much
mistaken, Sarah is interested in him. It would not be a bad match for
her, though certainly not one we would have expected her to make."
And, strange as it may seem, Mr. Eldon's observations had not deceived
him. Weak men generally admire clever women. Not having the capacity to
entertain themselves, they like somebody who can do it for them. Sarah
was now upon the point of doing what she had ridiculed others for all
her life, viz., falling in love with one who was not her equal. She had
often wondered before where the charm, where even the flattery could be,
of the admiration of an inferior. But Sarah had reached her
twenty-seventh year without even exciting that admiration, and
consequently did not understand the charm, and it is wonderful what a
difference the thing's being personal makes in these matters. We often
refuse with the utmost sincerity for our friends somebody who, perhaps,
would be accepted for ourselves. So it proved with Sarah. She would not
have hesitated had Mr. Allen proposed for Mary, but the case was changed
when she found herself the object of his humble and devoted attentions,
her sayings admired, her opinions adopted, her looks watched, as they
had never been admired, adopted, or watched before. Flattery is
certainly bewitching, and few can withstand genuine admiration. But when
they come with the freshness of novelty, and the charm of
unexpectedness, the head must be very sound, or the heart very cold that
can altogether repel them. Sarah had abandoned herself to their
influence before she was aware of it. She did not yield gracefully,
however, nor without a struggle; and she had been engaged several weeks
before she could summon courage to communicate the intelligence to Mrs.
Eldon. It was in vain she repeated to herself that she "had only her own
happiness to consult," and that "she cared not what others said." Her
usual independence almost deserted her, and for the first time in her
life she dreaded a smile, and shrank from hearing "plain English."
"Dear, dear Sarah!" exclaimed Mrs. Ludlow, as she embraced her friend
most affectionately, "how could you keep me so long in the dark? But I
am come to congratulate, and not scold you. And now tell me all about
it;" and the how, and the when, and the where, followed in quick
succession, and was listened to with such animated interest and cordial
sympathy, and all that Mary knew or thought, or had ever heard, that was
favorable to Mr. Allen, was poured forth so kindly, that Sarah's spirits
rose, and, as she parted with her friend, she felt an elasticity and
joyousness of heart that she had not experienced since her engagement.
"Heaven bless her kind nature!" said Sarah, with a degree of enthusiasm
that was unusual to her; "I always feel better after I have been with
her."
Had the same observation ever been made on parting with Sarah? We doubt
it.
CHAPTER II.
It made me laugh to hear Jock skirl in the chimney. "Now," said
I, "you know what hanging is good for." HEART OF MID
LOTHIAN.
"Mr. Allen looks feeble, Sarah," said Mrs. Eldon to her sister, some
time after her marriage—"Is he well?"
"Yes, perfectly," replied Sarah. "Pray don't put it into his head that
he is not, or you will make him more indolent than ever. He wants
exercise, that is all. I wish him to ride on horseback before
breakfast."
"At what hour do you breakfast?" inquired Mrs. Eldon.
"At six," replied her sister.
"At six at this season!" exclaimed Mrs. Eldon. "Why it can scarcely be
light. Does Mr. Allen like such early hours?"
"No," answered Mrs. Allen, laughing, "he would greatly prefer nine, I
believe. But such indolent habits destroy all order and regularity in a
household."
"Now, Mrs. Eldon, I appeal to you," said her brother-in-law,
good-humoredly, "if there is any use in being up at candle-light. I tell
Sarah we have the twenty-four hours before us. I do not see the use of
hurrying so. It appears to me I hardly get asleep before the bell rings
for breakfast."
"The use of early rising," replied Sarah, "is that we need never hurry.
There is time for every thing, and unless the master and mistress are
up, every thing stands still. And, after all, it only depends upon habit
whether we dislike it or not;" and there was something in her tone and
manner that implied it was a habit her husband must acquire.
Now in fact Mr. Allen was not strong; but Sarah, who had never been ill
for an hour, and scarcely knew what it was to be fatigued, had no more
comprehension of the languor of a feeble frame, than she had mercy for a
weak mind, and, consequently, the breakfast bell rang as pitilessly at
break of day, as if Mr. Allen had been endowed with her own "steel and
whalebone constitution." Strong health makes one sometimes unfeeling,
and so it was with Sarah. She thought a good walk or long ride a panacea
for all the ills flesh is heir to, and that if sickness was not sin, it
was what she considered next to it—laziness.
"And now, Sarah," said Mrs. Eldon, "I want a favor of you. I want you to
ask young Brandon and his wife to your party next week."
"Which one?" inquired Mrs. Allen. "I did not know Frank was married, for
I don't suppose you mean the other."
"Yes I do," replied her sister.
"Not the one who was implicated in that affair some years since?"
pursued Mrs. Allen.
"The same," continued Mrs. Eldon. "He was almost a boy when that
happened, and he has quite redeemed himself since. And now that he is
married, his friends wish to make an effort to bring him forward again;
and I promised to ask you to invite him. It will be of service to him to
be seen here."
"Never!" said Sarah, with decision; "I never will countenance any one
who could be guilty of such conduct. I am astonished you could ask it."
"My dear Sarah, remember what a lad he was at the time," urged Mrs.
Eldon.
"He was old enough to know better," replied Mrs. Allen.
"Undoubtedly," resumed her sister—"but, Sarah, if you had a family of
boys growing up around you, as I have, you would learn to look with more
leniency upon their errors."
"If I countenance such young men as Brandon," replied Sarah, "I don't
know what right I should have to look for better things in my own sons.
When society overlooks such acts, we may as well abandon all principle
and order at once."
"As a general rule, I agree with you," returned Mrs. Eldon; "but
situated as we are with regard to the Brandon family, I should wish here
to make an exception. They were my mother's earliest friends, and we are
under many obligations to them."
"Any thing that I could do for them but this, I would do cheerfully,"
replied Sarah.
"But there is nothing else you can do, Sarah," persisted Mrs. Eldon.
"They want nothing else; and it seems to me that friendship is but a
name, if we are not willing to make a sacrifice for our friends."
"Any but that of principle I am willing to make for them," replied Mrs.
Allen, resolutely.
When Sarah took it up as a matter of principle, her sister desisted at
once, as she knew the business to be hopeless. She only sighed, and
hoped Sarah might never know some of the trials of a mother's heart, to
teach her mercy and compassion.
Sarah continued, as a married woman, to be very much what she had been
as a girl, for marriage does not modify the character as much as people
think it does. Her active and energetic nature, which had formerly been
expended on societies and paupers, was now devoted to her household,
husband and children, and all were managed with the same upright
principle and relentless decision which she had ever shown in all her
undertakings.
The attachment between herself and husband was strong, although the
perfect harmony did not always exist between them that might have been
expected, from the sense on her side and the good temper on his.
Mr. Allen, like most weak men, was obstinate, and when he wanted to do a
thing, generally did it, and only showed his consciousness of Sarah's
disapprobation by not telling her of what he had done; and many a time
was she bitterly provoked to find that projects which she had opposed,
and supposed abandoned, had long since been quietly effected. Her heart
was often in a "lime kiln," though perhaps about trifles. Yet upon the
whole she enjoyed as much of happiness, probably, as her nature was
capable of. Her children were pattern children, orderly, correct and
obedient. No act of rebellion had ever been known in the little circle,
but one, and that was in her eldest boy, which had been so severely
punished that it had become a matter of fearful tradition with the rest.
In fact, Sarah was a stern mother, more feared than loved by her
children, yet they were generally looked upon as a "remarkably well
brought up family," and Mrs. Allen received no small praise for her
admirable management of her young flock.
"Who do you think was suspended to-day?" said Charles Eldon, as he threw
down his books on his return from college.
"Who? who?" exclaimed his young brothers and sisters.
"Tom Allen!"
"What, Tommy good-shoes!" exclaimed the children, with shouts of
merriment. "Oh, that is too good! Mamma, only think, Tom Allen is
suspended!"
"Hush, hush, my dear!" said Mrs. Eldon, gravely, "I am sorry to hear
it."
"That is more than I am," said Fanny, in a low voice. "It is the best
news I have heard this many a day. Aunt Sarah made such a fuss when
Lewis got into that scrape, and it was not much after all."
"What has been the matter, my son?" inquired Mrs. Eldon.
"Nothing of much consequence—only Tom has lagged behind the class
almost ever since he has been in it, so now the Puts have suspended him,
and he must take a tutor, and try and pull up."
"To think of one of those pattern children being suspended!" said Frank,
laughing. "It is the best joke I ever heard."
And in spite of all their mother's proper admonitions and grave looks,
the news was matter of perfect jubilee with the young Eldons. Not that
they had positively unkind feelings toward their young cousins, but they
disliked their aunt heartily, and, in short, pattern children always
incur a certain share of unpopularity among juveniles of their own
standing. Free and spirited natures will not brook the superiority which
is often accorded by their elders to the tame and correct inferiority of
such children. Then, too, the sins of the parents are often visited
heavily on their offspring under similar circumstances; and "Aunt
Sarah's lectures," and "the fuss Aunt Sarah made on such and such an
occasion," "and now Aunt Sarah need not make big eyes at Charley any
more," and "let Aunt Allen shut up about Lewis now," and many more such
reminiscences and ejaculations of the kind, broke forth on all sides. In
fact, if the whole truth were known, Mrs. Eldon herself, in spite of her
efforts to maintain the proprieties, did not feel, at the bottom of her
heart, the sorrow for her sister's mortification she assumed. "It will
do her good," she said to herself. "Sarah is too hard upon other
people's children. The thing is not a matter of importance in itself,
but it is enough to show her that her boys are like other boys."
"I thought your sister was wrong when she insisted upon that boy's
taking a collegiate education," remarked Mr. Eldon. "He resembles his
father in mind: that is to say, he has none, and besides, is naturally
indolent. He showed a disposition to enter the counting-house, and he
would have done better there."
"Sarah thinks it great weakness in parents to yield to what she calls
the whims of young people."
"Undoubtedly; but, at the same time, not to study and make allowances
for their natural capacities and dispositions, is equally unwise. Nature
is to be guided, but not controlled."
"You would find it difficult to persuade Sarah that she could not
control all events falling within the sphere of her domestic circle,"
replied Mrs. Eldon.
"Then probably she has a bitter lesson yet to learn," replied Mr.
Eldon—and so the conversation dropped.
The summer coming on, Mrs. Eldon left the city early with her family,
and consequently did not see Mrs. Allen for several months. When she
did, she was much struck with the change in her appearance.
"Are you well, Sarah?" she asked.
"No, I am not," replied Mrs. Allen. "I have heard people talk of being
weak and miserable, but I never knew what they meant before. I saw they
were not really ill, and I thought it was only imagination or indolence.
I now feel that I was wrong. For the first time in my life, I know what
it is to be oppressed with languor. Every thing is a burden to me; and
when I try to rouse myself and shake it off, my limbs refuse to obey my
will."
"My dear sister," said Mrs. Eldon, "don't attempt that. You need
repose—If you overtask yourself now, you may feel the ill effects all
your life."
"That is what my dear, kind husband says," replied Mrs. Allen. "And oh,"
she continued, with much emotion, "you don't know, Charlotte, how my
conscience reproaches me for my former want of consideration—for my
unkindness, in fact, to him. You always told me he was not strong, but I
thought it was only one of your notions, and I laughed at his dislike of
early rising, and had, in short, no sympathy for much that I now am
convinced was bodily indisposition. Formerly, I could not comprehend
what possible good it could do him, _even_ supposing, according to you,
that he was not well, to rise an hour later in the morning. The idea
seemed to me absolutely absurd. And now when I wake so languid, I feel
that an hour's rest is of such infinite importance, and I ask myself,
'Where is the use in getting up?—what matters it whether the household
commences its daily routine an hour earlier or later?' Charlotte, I
sometimes feel that this breaking down of my health is sent as a
punishment, and a lesson to teach me sympathy and mercy for those of a
naturally different constitution from my own."
When Mrs. Eldon repeated this observation of Mrs. Allen's to her
husband, he dryly remarked that, "it was a pity the lesson had not come
earlier."
Pecuniary losses, too, fell heavily upon the Allens about this time. A
public institution failed, in which Mr. Allen had invested much of his
wife's property. It had never been an institution in which she had much
confidence, and when he had consulted her on the subject, she decidedly
objected to the changing certain for what she considered uncertain
property. But Mr. Allen, as we have said, was a weak man, who, when he
had once got a notion in his head, never rested until he had executed
it. He was just sufficiently under his wife's influence to make him
conceal the fact when it was done. If circumstances discovered it, he
would only reply to her remonstrances, which were not always of the
gentlest, "Well, well, it is done now, and there is no use in talking
about it." Sarah was not often to be pacified in that way, and if any
thing could have provoked her more than the facts themselves, it would
have been the quiet, meek, yet obstinate air withal, with which he
listened to her lectures on the subject.
Either Sarah was not the woman she once had been, or the magnitude of
the present offence seemed to stun her into silence, for she bore with
dignity and fortitude what she felt to be a serious misfortune.
What was grief to her, was matter of gossip, however, to the circle of
her immediate acquaintance, and that, too, not always in the most
sympathizing and good-natured spirit.
"Are you not sorry for the Allens?" inquired one of her set. "It is said
they have lost the greater part of their fortune in this company that
has just failed."
The lady thus addressed was one who prided herself on her frankness, and
she answered, with a spirit and promptness that caused the other to
laugh,
"No, I can't say I am. Mrs. Allen has hitherto thought that every body
else's misfortunes were their faults. Let her now bring the matter
home."
The other seemed to enjoy the remark, although hardly daring to say as
much herself, and she only replied, with an affectation of amiability
that her gratified looks denied—
"But it is a hard lesson to learn."
"My dear Mrs. Binney," replied her friend, "we have all of us hard
lessons to learn in our experience through life. But I have no sympathy
for those who _need_ them before they can feel for others."
"She certainly has been rather hard upon those who fell into
misfortune," gently resumed Mrs. Binney.
"_Rather_ hard!" ejaculated the other—"I never shall forget when my
brother failed—" and then came a stored up host of bitter remembrances
and old offences against Mrs. Allen, speeches long forgotten, that had
rankled deep, to rise up in judgment when her turn came to call for
public sympathy and general discussion.
Mr. Allen seemed to escape without either sympathy or animadversion. If
alluded to, he was called "a poor, weak fool," by the men, and "oh, he
is nobody," was all the consideration deigned him by the women. But Mrs.
Allen was canvassed and talked over according to the feelings of the
speakers, as if she were both master and mistress of the establishment.
Mrs. Ludlow, her early friend, was still her friend, and sympathized,
from the bottom of her heart, in all her trials.
Prosperity often seems to mark certain families for its own for
years—but when the tide changes, misfortune frequently clings as
obstinately to those who have hitherto seemed the favorites of fortune.
To most of us, life is as an April day, checkered by clouds and
sunshine; but there are others whose brilliant morning and calm noonday
suddenly darken into clouds and storm. A certain portion of sorrow is
the lot of all, whether it comes drifting through life, or is compassed
within any particular period of existence. Come, however, it must to
all.
Sarah's life had hitherto been blessed above that of most women. But
youth, health and wealth had now passed from her, and her proud, stern
spirit had yet to undergo trials she had never dreamed within the scope
of possibility as falling to her lot. Her eldest boy, the "Tommy
good-shoes" of former days, was now the source of an anguish a mother's
heart alone can know. Forced upon a course of education for which he had
no taste and scarcely any capacity, the four years allotted to
collegiate studies were to him four years of unbroken idleness. The same
easy, docile nature that had made him the "Tommy good-child" of early
years, rendered him still pliant to the influences about him. These,
unhappily, as is generally the case in idleness, were not good. College
suspensions and remonstrances were the commencement of a course of which
little bills soon followed in the wake. When these fell into his
father's hands, they were often paid without a word, for he had learned
to dread, scarce less than the boy, the bitterness of his wife's
indignation when they reached her knowledge.
To his mother's keen reproaches, Tom listened in silence, the same kind
of frightened, meek, obstinate silence with which his father had endured
many a harangue before him. But they did not mend his ways.
Mrs. Eldon had heard from time to time rumors that "Tom Allen was very
wild," but she had thought that "boys will be boys," and her husband
said "young men will be young men," and thus they had both attributed
the rumors they had heard to the indiscretions of a youthful spirit. But
here they were mistaken. Tom's were not the errors of a youthful but of
a weak nature. The influence abroad was bad, and the conduct at home
injudicious. If Mr. Allen's children did not exactly say with the world,
"Oh! he is nobody," they yet felt the fact; while their mother was to
them "the everybody" they feared and looked up to. Consequently, if Tom
got into a scrape there was nothing he so much dreaded as his mother's
hearing of it. There was scarcely any public opprobrium he would not
rather have endured than her anger. In fact, the sort of Coventry in
which he was put, the sad, severe looks that were bestowed upon him at
home were slight inducements to a weak and timid spirit to reveal
difficulties, pour forth confession and implore relief, and thus what
had begun in weakness ended in disgrace.
A debt which, though not large in itself, yet of considerable magnitude
in the eyes of a youth, had been contracted almost unconsciously, and
which he had not courage to avow at home. Harassed, tormented,
terrified, he made use of funds which were not his own, and which his
situation in a counting-house, where he had at last been placed, put
within his reach. Weak, timid and reserved, he neither revealed his
situation, nor asked for aid from either his young companions or natural
friends—but when he found detection could no longer be warded
off—fled.
Public disgrace was the consequence; and the insignificance of the sum
and the magnitude of the offence were alike the theme of general
discussion. Mingled commiseration and blame were bestowed upon the
unhappy parents. People generally love to think that a faulty education
is the root of the evil. Some, therefore, censured the system that had
restricted him in means; others thought a too ample allowance had been
the origin of the sin.
The affair was canvassed in every possible spirit, and though
commiseration could not be refused to the heart-stricken parents, yet
the tone of it was often qualified by the personal sentiments of the
speakers, for it is wondrous how unpopularity will cling to those who
have incurred it, even under calamities which one would suppose were
enough to bury all old griefs.
"I cannot but feel sorry for any mother under such circumstances," had
been said, "but I feel as little for Mrs. Allen as I could feel for any
one so situated. She meets with more sympathy now than she ever would
have given to another."
"Had it been any one else's son but Sarah Allen's," exclaimed another,
"I should have been sorry indeed. But hers is a hard temper. Now,
however, she knows what trials are."
"I am sorry for any one so situated, but if such things will happen, I
had rather it had fallen on Mrs. Allen than on any one else I know."
The Brandons breathed a deeper but silent comment upon the blow that had
fallen on the haughty and unfeeling woman whose early slight they never
had forgiven.
"My early, only friend," cried Mrs. Allen, as she threw herself into
Mary Ludlow's arms, who, ever true to her in sorrow as in joy, was with
her now in her hour of bitterest anguish, "you, you alone feel for one
who did not feel for others. The heart that was hardened by prosperity
deserved to be broken by sorrow." And then the full tide of anguish, and
repentance, and confession, gushed forth with a freedom and humility
that wells up alone from a broken and a contrite heart.
The stern lesson had been taught, and received in a spirit that shows
that where there is Sense, experience must teach Sympathy. The rock had
been smitten, and the waters that gushed forth were pure and
regenerating.
* * * * *
"OH MOTHER OF A MIGHTY RACE."
BY WILLIAM CULLEN BRYANT.
Oh mother of a mighty race,
Yet lovely in thy youthful grace!
The elder dames, thy haughty peers,
Admire and hate thy blooming years.
With words of shame
And taunts of scorn they join thy name.
For on thy cheek the glow is spread
That tints thy morning hills with red;
Thy step—the wild deer's rustling feet
Within thy woods are not more fleet;
Thy hopeful eye
Is bright as thine own sunny sky.
Aye, let them rail—those haughty ones—
While safe thou dwellest with thy sons.
They do not know how loved thou art,
How many a fond and fearless heart
Would rise to throw
Its life between thee and the foe.
They know not, in their hate and pride,
What virtues with thy children bide;
How true, how good, thy graceful maids
Make bright, like flowers, the valley shades;
What generous men
Spring, like thine oaks, by hill and glen.
What cordial welcomes greet the guest
By thy lone rivers of the west;
How faith is kept and truth revered,
And man is loved and God is feared
In woodland homes,
And where the solemn ocean foams.
There's freedom at thy gates, and rest,
For earth's down-trodden and opprest,
A shelter for the hunted head,
For the starved laborer toil and bread—
Power, at thy bounds,
Stops, and calls back his baffled hounds.
Oh fair young mother! on thy brow
Shall sit a nobler grace than now.
Deep in the brightness of thy skies
The thronging years in glory rise,
And, as they fleet,
Drop strength and riches at thy feet.
Thine eye, with every coming hour,
Shall brighten, and thy form shall tower,
And when thy sisters, elder born,
Would brand thy name with words of scorn,
Before thine eye
Upon their lips the taunt shall die.
* * * * *
CAIUS MARIUS.
BY MRS. E. J. EAMES.
"Man—darest thou slay Caius Marius?"
Semblance of him who at three-score-and-ten,
Bleeding and stark, chained in a dungeon lay—
Yet all untamed—whose eye flashed fire as when
The stormy fight he led in war array;
Well might the Cimbrian slave in awe start back,
Oh! fearful Roman, when he met thine eye!
Well might the Gaul, though bold, the courage lack
To consummate thy purposed destiny.
For through the dim and solemn twilight burnt
That eye—in stern and awful grandeur flashing
Its warning light on one who ne'er had learnt
Pale fear till then. Well might his sword fall clashing
At that dread voice—"Man, darest thou slay _me_?"
So didst thou look, and speak, and wert made free!
* * * * *
ONE OF THE "UPPER TEN THOUSAND," AND ONE OF THE PEOPLE.
BY MRS. J. C. CAMPBELL.
CHAPTER I.
At the annual commencement of one of our colleges, the youth who
delivered the valedictory had, by the vigor and beauty of thought
displayed in his address, and by his polished and graceful elocution,
drawn down the applause of the large audience assembled on that
occasion. Not a few eyes were moistened as he bade farewell to the
venerable men under whose care and tuition he had gained the highest
honors, and to the schoolmates with whom he had passed so many happy
hours, and who now, like barques again put forth to sea that had long
been safely moored in one quiet haven, were each to stem alone on life's
great deep.
"He! he! he! that's Bobby Dunning, his father keeps a grocery-store,"
said a foppish-looking stripling who wore the academic gown, as he
pointed with his finger to the speaker on the platform, and at the same
time seated himself beside a young lady in the gallery.
"He! he!" echoed his companion, "I dare say he has weighed many a pound
of sugar in his time. A grocery-store! What queer associates you have at
college, Gus."
"Associates! No indeed, Sophy, when Bob first entered I thought him a
fine, generous fellow, and was just about to ask him to our house, when
I found out who his father was. A lucky escape, by Jupiter! I soon cut
his acquaintance, and made him feel by my cool, contemptuous manner that
the son of a grocer was no fit associate for the son of a gentleman."
Again the young lady tittered, "That's just like you, Gus, you are
always so high spirited."
"So my father says; he often calls me his 'gallant Hotspur,' and laughs
heartily when he hears of my waggish pranks."
Many honors were that day borne away by the ambitious youths who had
late and early sought to win them, but none had been awarded to Gus, or
as he liked best to write himself, Gustavus Adolphus Tremaine.
"Why, Gus, you're a lazy dog," said his father on their return home;
"come, you must do better next time. And so Bob Dunning, the grocer's
son, graduated to-day, and carried away more honors than any of the
other students; rather strange that!"
"There was nothing strange about it, father. Bobby knew he had to get
his living somehow or other, and as Latin and Greek smacked more of
gentility than brown paper and pack-thread, he abandoned the latter, and
took to the former with such avidity, that he has grown thin and pale as
a shadow. A capital village pedagogue Bob will make, to be sure! But
something more manly than poring over musty old books, or flogging
ragged little boys, must be my occupation through life. I say, father,
when does that race come off between Lady Helen and Bluebeard?"
"Next week," answered Mr. Tremaine, who was a member of a jockey
club—"next week. Well remembered, Gus.—I dine with the club to-day,
and this devilish college concern had nearly driven the engagement out
of my head. We are to have splendid arrangements on the race ground for
the accommodation of the ladies—a fine stand erected, covered with an
awning—wines, ices, patés, and I don't know what all. Sarah," turning
to his wife, "I expect you to be there; mind, none of your vapors—and,
Gus, do you bring Sophy Warren; she is a spirited creature, and would
make a capital jockey herself." And with this equivocal compliment to
Miss Sophia Warren, the elder Tremaine left the house.
A tyrant at home, a capital fellow abroad, was Oscar Tremaine. Over his
wife, a mild, gentle creature, he had exercised his authority until she
had become a perfect cipher in her own house; and, unnatural as it may
appear, he had encouraged their son to flout his mother's opinions and
scorn her advice. It was not strange, then, that Mrs. Tremaine had
remained silent while her husband and son were speaking, but now,
looking on the boy with tenderness, she said,
"I regret, my dear Gustavus, that you have not been more successful in
your studies; how happy and how _proud_ I should have been had you
brought home some token of reward, some prize, on which I might have
looked, and said, 'My child has won it!'"
"Fudge! this is all nonsense, mother. What do you know about such
matters? Father has more money than I can ever spend, and why should I
be compelled to mope away my lifetime over the _midnight oil_, as they
call it? I'd rather have a canter on Fancy in the afternoon, and then to
the theatre or opera at night—that is the life for me;" and, humming a
fashionable air, he turned from the room.
His mother gazed after him sorrowfully. "God help thee, my child!—alas!
I fear the worst; God help thee!" she repeated in anguish, and, feeling
how "sharper than a serpent's tooth it is to have a thankless child,"
she bowed her head on her hands, and wept bitterly.
In less than a month after the commencement, Robert Dunning began the
study of the law, and Gustavus Adolphus Tremaine was expelled from
college.
CHAPTER II.
"Confound the fellow! I can't take up a newspaper without having his
name staring me in the face. Eminent lawyer, superior
talents—_superior_—nonsense; I don't believe a word of it. I always
hated him;" and the speaker flung the offending paper on the floor,
apparently unconscious that that very hatred made him blind to the
merits of the man whom he so berated.
"What's the matter now, Gus?—angry again? Was there ever such a man!"
exclaimed an ultra-fashionable lady, who swept into the apartment "with
all her bravery on." "Come, I want you to go with me this morning, to
select a new jewel-case. I saw a superb one the other day for a few
hundred dollars; but it is no matter what it may cost."
"It is a matter, and a serious one, too, Sophia. I told you, six months
ago, we should be ruined by your extravagance, and, by heaven! you must
put a stop to it."
"And I told _you, twelve_ months ago, Mr. Tremaine, that if you did not
quit betting at the race ground and the gambling table, we should
_certainly_ be ruined. You spend thousands, for no earthly good
whatever, while I only make use of hundreds, to purchase things
absolutely necessary for one holding my position in society. Once for
all, let me tell you, Mr. Tremaine, I will have whatever I want;" and,
turning to the piano, the amiable lady ran her fingers over the keys,
with the most provoking indifference.
"Mrs. Tremaine, you are enough to drive a man mad. Do you think I'm a
fool, that I will bear to be treated thus?"
"Oh no, Gussy dear, I should be sorry to suppose such a thing; but you
know the lesson by which I profited was learned in your home. There I
saw how well your father could enact the tyrant, and how your gentle
mother was treated like a slave; and I silently resolved, that from the
hour we were married, I would be mistress in my own house."
"Where is the use of repeating that nonsense continually? I have heard
the same story a dozen times before."
"And shall hear it a dozen times again, or at least as often as I hear
the word _must_ from your lips, Mr. Tremaine. But come, you have not yet
told me why you were so angry when I came in. Let me see," she
continued, taking up the newspaper, "let me see whether this will not
solve the mystery. Ah, now I have it—Robert Dunning, Esq.!"
"Yes, now you have it—that upstart, whom I so hate—to see his name
paraded in this manner before the public, is enough to drive me mad."
"No wonder you hate him, Gus. Only to think of his being retained as
counsel for the heirs of old Latrobe, and gaining the suit by which you
lost one hundred thousand dollars! Now this reminds me of what I heard
yesterday, that Dunning was about to be married to Fanny Austin."
"Nonsense, Sophia, the Austins move in the first circles."
"So they do, my dear, but Fanny has strange ideas, and there is no
knowing what freak she may perform. However, I shall drive there today,
and ask her about it. I ordered the carriage at one—ah! there it
is—will you assist me with my cloak, Mr. Tremaine, or shall I ring for
my maid? Thank you—thank you—I don't know when I shall return."
"And I don't care," muttered her husband as she drove from the door. For
a few moments he stood under the heavy crimson curtains at the window,
looking listlessly in the direction in which the carriage had gone, and
then taking his hat and cane left the house.
Just one little year had passed since Gustavus Tremaine and Sophia
Warren were wedded—but one little year since he had promised to love
and cherish her as his wife, and she had vowed to love and obey him as
her husband, and yet such scenes as the one above related were daily
occurring. The mother of young Tremaine had long since sunk
broken-hearted to her grave, and his father had died in consequence of
injuries received by falling from a staging erected on a race-course.
Shortly before the death of the elder Tremaine, the law-suit had
terminated, by which he lost one hundred thousand dollars, and on the
settlement of his affairs it was found that but a comparatively small
fortune would be possessed by his heir. Sophia Warren, "the capital
jockey," prided herself on her marriage, with being wife to one of the
richest men (that was to be) in the city, and it was a bitter
disappointment when she found her husband's income would not be
one-third of what she had anticipated.
As the union had not been one of affection—where heart and soul unite
in uttering the solemn and holy vows—where "for richer for poorer" is
uttered in all sincerity—as it had not been such a union, but one of
eligibility—a question of mere worldly advantage, no wonder the peevish
word, and the angry retort, were daily widening the breach between a
spendthrift husband and an arrogant wife—no wonder each sought refuge
in the world, from the _ennui_ and the strife that awaited them at
home—no wonder that the wife was recklessly whirling through the giddy
maze of fashion, while the husband was risking health, honor, reputation
on the hazard of a die.
When Mrs. Tremaine reached Mr. Austin's, young Dunning was just leaving
the house, so here was a fine opportunity for bantering Fanny Austin.
"Ah! I've caught you, my dear, and Madam Rumor is likely to speak truth
at last—ha! blushing! well this is confirmation strong—and it is
really true that Mr. Dunning and Miss Austin are engaged."
Too honest-hearted to prevaricate, too delicate-minded not to feel hurt
at the familiar manner in which Mrs. Tremaine alluded to her engagement,
Fanny remained silent, her cheek glowing, and her bright eye proudly
averted from the face of her visiter.
A woman of more delicate feeling than Mrs. Tremaine would have hesitated
on witnessing the embarrassment caused by her remarks, but she had no
such scruples, and continued,
"I contradicted the statement; for it was impossible to believe any
thing so absurd."
Fanny Austin looked up inquiringly, and the glow on her cheek deepened
to crimson as she said,
"Absurd! may I ask your meaning, Mrs. Tremaine?"
"Why, I mean that you would not render yourself so ridiculous in the
eyes of society. _You_ marry Bob Dunning—the son of a grocer—_you_,
who belong to the first families, and who ought to make a most
advantageous match! Why, Fanny dear, no wonder I contradicted it."
"I regret that you took the trouble."
"Oh! it was none at all, and our families had been so long on friendly
terms, that I thought it but right to say you would not throw yourself
away."
"Allow me to ask why you speak in this manner," said Miss Austin, now
fully roused, and recovering her self-possession, "if I should marry Mr.
Dunning, how could I be thought to throw myself away?"
"What a question! Why the man has neither family nor fortune to boast
of, while you have both."
"As far as money is concerned, I grant you I have the advantage; but as
for family, few of us republicans can boast on that score. My
grandmother, and yours too, Mrs. Tremaine, superintended their own
dairies, made butter and cheese with their own hands, and sent them to
market to be sold, nor did I ever hear that the good ladies were ashamed
of their domestic employments. Your father and mine commenced life with
naught save probity and perseverance; they were first clerks, then
junior partners, and at last great capitalists, and we their children
have thus been placed at the head of society."
"I know nothing at all of this nonsensical grandmother story about
butter and cheese. I never heard of such a thing in our family."
"No, I suppose you did not. You have been taught to look on praiseworthy
industry as derogatory to your ideas of gentility; but my father has
always delighted in recurring to those days of boyhood, and he venerates
the memory of his mother, whom he regarded while living as a pattern of
domestic virtue."
"Oh, it is all nonsense talking in this way, Fanny. I wonder what Baron
d'Haut-ton will say when he hears that the lady he wooed so
unsuccessfully has been won by the heir of a man in the 'sugar line?'"
"Pardon me, Mrs. Tremaine, if I say you are forgetting yourself, or at
least that you are presuming too far on your long acquaintance. My
parents have no such ideas as yours, about fortune and family, and with
their approval my heart is proud of its choice—proud, too, that it has
been the chosen of the gifted, the noble-minded Dunning."
"Well, Fanny," persisted Mrs. Tremaine, nothing abashed by the gentle
rebuke which had been given—"well, Fanny, depend upon it you will place
yourself in a false position. The friends who are now eager to court the
society of Miss Austin, will stand aloof when invited to the house of
Mrs. Dunning."
"Friends! did you ever know a true friend do aught that would depreciate
the husband in the eyes of his wife, or lessen the wife in the esteem of
her husband? For such of my so-called friends as would not honor the man
I had chosen, when he was well worthy of their highest regard, I can but
say the sooner we part company the better. It is not the long array of
names upon my visiting list of which I am proud, but the worth of those
who proffer me their friendship."
"Two o'clock!" said Mrs. Tremaine, glancing at the _pendule_ on the
chimney-piece—"two o'clock! Good morning, Miss Austin. How surprised
Tremaine will be to hear that you are really going to marry Bob
Dunning."
And Robert Dunning and Fanny Austin were married—and never was there a
happier home than theirs. The wife watched for her husband's step as the
maiden watches for that of her lover. Daily she met him with smiles,
while her heart throbbed with a love as warm and as pure as that she had
vowed at the altar. And Robert Dunning idolized his wife, and his fine
endowments drew around him a host of admirers and friends, until Fanny's
former acquaintances, including Mrs. Tremaine, contended for the honor
of an invitation to the gifted circle, which weekly met at the house of
Mrs. Dunning.
CHAPTER III.
"So it has come at last—ruin, final, irretrievable ruin—every thing
gone—the very house I'm in mortgaged. Confusion! But I'll not give up
yet—no, not yet! I'll see Browne to-night—what if we should fail? But
that is impossible. Browne has been too long engaged in getting his
living from the dear public to let it scrutinize very closely the
process by which the needful is obtained. If I thought I could win any
thing at play—but I have had such an infernal run of ill luck lately
that there is no chance in that quarter. Well—well! There appears to be
no alternative—and when it is once done, then ho! for England!"
Thus soliloquized Gustavus Tremaine, as he sat at a late hour in the
morning sipping his coffee in his room, for his wife and he had long
ceased to take their meals together. Separate rooms and separate tables
had served to complete the estrangement which caprice and ill temper had
begun, and they now exhibited that pitiable spectacle of a house divided
against itself. And what is more pitiable than to see those who should
mutually encourage and support each other, who should bear one another's
burdens, and in the spirit of blessed charity endure all things, and
hope all things—what is more pitiable than to see them unkind,
self-willed, bandying bitter sarcasms and rude reproaches?
Oh, that the duties, the responsibilities, the self-sacrifices of wedded
life were better understood, their sacred character more fully
appreciated, how would each home become a temple of love, each fireside
an altar, on which was daily laid an offering of all the amenities, all
the sweet charities of social life. How would the child who, in his
early home, had heard none save kind words, had seen none other than
heart-warm deeds, who had been trained to habits of submission, and
taught to yield the gratification of his own wishes for the good or the
pleasure of others, taught to do this even as a child may be taught, in
the meek spirit of the gospel—how would such an one grow up a crown of
glory to the hoary hairs of his parents, and a blessing to society. But,
alas! the spirit of insubordination is rife in the world. The child
spurns the yoke of domestic discipline, sets at naught the counsels of
his father, and hearkens not to the voice of his mother—and the man
disregards the voice of conscience, sets the laws of his country at
defiance, and becomes an outcast and a felon!
It was a cold winter evening, and the heavy clouds were looming up in
broad masses over the troubled sky, while the wind howled through every
cranny, and sent the snow-mist, which began rapidly to descend, into the
faces of the stray pedestrians who were either hardy enough to venture
abroad in search of pleasure, or wretched enough to be obliged from dire
necessity to leave their homes. Mr. Tremaine was among the few who were
braving the fury of the storm. He had left his elegant but cheerless
mansion in the upper part of the city, and sped onward, regardless alike
of wind and snow, to the place of his destination.
It was the haunt of vice, but in no dark alley nor out-of-the-way nook
did it seek to hide itself from public contempt. No—it reared its front
unblushingly in the public thoroughfare—within sound of the
church-going bell—it was fitted up with every luxury; silver and gold,
polished marble, and costly hangings, in lavish profusion, adorned the
place which fostered every malignant and evil passion, and made human
beings, endowed with immortal souls, ripe for deeds of desperation. The
man who robbed his employer, the defaulter, the forger, the destroyer of
female virtue, the murderer, the suicide, each and all of these had been
within its walls—each and all of these had taken their first lessons in
iniquity in that place, so truly and emphatically called a _hell_. And
it was to this place of pollution that Tremaine was hastening. Here he
had staked, and lost, and cursed his ill luck; yet, with the desperate
infatuation of a confirmed gamester, he had staked again and again,
until all was gone. On entering he looked round with a furtive and eager
glance, and, evidently disappointed, sauntered toward a roulette table
round which a crowd was standing.
"Do you play to-night?" The speaker was a tall, slender young man,
scarcely past his minority, but with a wan, sickly countenance, and the
premature stoop of old age. "Do you play to-night?" he repeated.
"I—I believe not," answered Tremaine, again glancing round the room.
"You are a foolish fellow; the fickle goddess may even now be turning
the wheel in your favor. Come," he continued, laughing, "if you have not
been at your banker's to-day, I have, and can accommodate you with a few
hundreds;" and he took a roll of bills from his pocket, and handed them
to Tremaine.
"But when shall I return this, Gladsden?"
"Oh, a fortnight hence will be time enough."
Tremaine turned to the table and staked the money—he won; staked the
whole amount—won again; the third time. "You had better stop now,"
whispered a voice in his ear. He turned, and saw the person for whom, a
short time before, he had been looking so eagerly; but he was elated
with success, and paid no heed to the speaker. The fourth—the fifth
time, he won. Such a run of luck was most extraordinary; he trembled
with excitement, and now determined that he would try but once more,
and, if successful, he might yet retrieve the past.
"Are you mad, Tremaine?—you surely will not risk all?" again whispered
the voice.
"All or nothing. I am fortune's chief favorite to-night. All or
nothing," repeated the gamester, as if communing with himself, "all or
nothing!"
The bystanders looked on earnestly; for a few moments there was a dead
silence—then Tremaine's face became livid, his brow contracted, and his
lips compressed. He had risked all; he had gained—nothing!
"What a fool you have made of yourself!" once more whispered the ominous
voice.
"Not a word, Browne; perhaps it needed this to make me wholly yours,"
replied Tremaine, as he walked through the crowd, which opened to let
him and his companion pass. When in the street, the two walked on for a
time in moody silence, which was first broken by Browne.
"Well, Tremaine, that last was a bad stake of yours, and may cost one of
us the halter."
"Why, I thought you told me there would be no blood spilt?"
"Well, blood _is_ rather ugly looking, I must confess; but if the man
should wake?"
"Did you not say you would have him well drugged?"
"I did, but by the slightest possible chance, I find it cannot be done!"
"How so?"
"You know it was expected that he would sail in the packet from this
port, but I find he has determined on going by the steamer, and will
start to-morrow morning by the Long Island railroad; so that we must do
it now or never."
"Now or never be it, then. I am a ruined man, and ripe for mischief."
Again the two walked on in silence, until they reached a fine looking
house in the vicinity of the Battery. Here Browne applied his key to the
night latch, and in a few moments he and Tremaine had entered one of the
upper rooms and locked the door.
"Where does he sleep?" abruptly inquired Tremaine.
"In the opposite room."
"And you are sure that you can effect an entrance without arousing any
of the boarders?"
"_Sure!_ I wish I was as sure that he would not wake," and Browne smiled
contemptuously. "But you are not growing faint-hearted, eh, Tremaine?
Come, here is something will give you courage, man;" and, taking a
bottle from a side closet, he placed it on the table before them, and
continued—"fifty thousand dollars! I saw him count it over this
afternoon. What fools some men are! Because I flattered him, and
pretended to take an interest in his love affair, he opened his whole
heart, and, what was of far more value, his purse, and displayed its
contents before me. But it grows late, and we must to business.
Remember, when I have secured the money, you are to take it and make
your escape out of the house, while I shall return quietly to bed to
lull suspicion, and to-morrow evening will meet you where we met
to-night. Now do you hold this dark lantern while I open the lock. That
will do—put it in my room again—so—all right; come in a little
farther," continued he, in a low whisper, "we must be cautious—the
money is under his pillow."
Stealthily approaching the bed of the unconscious sleeper, Browne put
his hand softly under the pillow and drew forth a wallet. Thus far they
were successful, but in groping their way out of the room, Browne
stumbled and fell; the noise awoke the sleeping man, and the cries of
"Help!—robbers!—help!" rang through the house. In one moment Browne
was on his feet, in another in his room, where the money was given to
Tremaine, and in the noise and confusion of hastily opening and shutting
doors, the latter escaped.
It is unnecessary to detail the causes which led to the suspicion and
arrest of Browne, and the implication of Tremaine. Suffice it that on
the following evening, when entering the place in which he had appointed
to meet his accomplice and divide the booty, Tremaine was taken into
custody, and the money found in his possession.
Sophia was dressing for the opera. It was the first night on which she
had laid aside the mourning worn for the loss of her parents, and,
determined on appearing in a style of almost regal magnificence, she had
placed a circlet of jewels on her brow, and a diamond bracelet was seen
flashing on her arm amid the rich lace of a demi-sleeve as she reached
out her hand to receive a note brought in by the servant. On opening it
her agitation was extreme, and, hastily dismissing her attendants, she
read over word by word the news of her husband's crime, and subsequent
imprisonment.
And now was she tortured by conflicting emotions. She had never believed
that her husband's affairs were in the ruinous state in which he had
represented them to be—but she could no longer doubt. Crime had been
committed—disgrace had fallen upon them—and then came the thought,
"Have not I helped to goad him on to ruin?" and pity for him brought a
momentary forgetfulness of self—the woman was not wholly dead within
her!
The next day the hateful news was bruited abroad that Tremaine, the
dashing Tremaine, was imprisoned for robbery! His fashionable friends
wisely shook their heads, and raised their hands, and uttered sundry
exclamations. But they stood aloof—not one offered to go forward as
bail for the unfortunate man. Not one of Mrs. Tremaine's gay lady
visiters went to speak a word to the humbled woman as she sat writhing
under her disgrace. But we forget—there was _one_! Fanny Dunning, like
a ministering angel, strove to soothe and comfort her, promised that her
husband would do his utmost to aid Mr. Tremaine, and, when the mortgage
on the house was foreclosed, took the weeping Sophia to her own home and
was to her as a sister.
CHAPTER IV.
It was not in human nature to forget the repeated slights and insults
with which Tremaine had sought to wound the feelings of his old
school-mate; but it was in human nature to imitate the divine exemplar,
to forgive injuries, and to return good for evil, and Robert Dunning
promised Sophia that he would do all in his power to effect the
liberation of her husband. For this purpose it became necessary that he
should visit Tremaine in prison. But the culprit obstinately refused to
see him, until at length, finding the time draw near when he would be
publicly arraigned at the bar, he consented to his admittance. Dunning
gave him to understand that he must know the facts of the case, at the
same time assuring him that he would plead his cause with pleasure, and
that there was no doubt of his acquittal.
"The thing can be easily managed," said Tremaine, doggedly—"I intend to
plead an alibi."
Dunning started.
"Is this necessary, Mr. Tremaine? I thought the charge could not be
proven against you?"
"Nor can it, if you are the expert lawyer you are said to be."
"Mr. Tremaine, let us understand each other. Is it important that you
should plead an alibi?"
"It is."
"Then I regret that I cannot undertake your cause. I was still under the
impression that you were innocent."
"And who dares say I am not? Did you, sir, come here to entrap me in my
words? Who will dare say I am not innocent, when the most famous lawyer
in town shall have proven that I was far from here on the night of the
robbery?"
The last words were said in a sneering and almost contemptuous manner.
"I must repeat my regret that I cannot undertake your cause, while at
the same time I assure you that I shall be silent as to what has
transpired between us."
"Puppy!" exclaimed Tremaine, thoroughly enraged. "Who asked you to
undertake it? Who asked you to come and thrust yourself upon me?
Puppy—plebeian! did I seek advice or assistance from you?"
"Mr. Tremaine," replied Dunning, with a calm and gentlemanly
dignity—"Mr. Tremaine, it is vain talking in this manner. I came to you
in the spirit of kindness—but my errand has been a fruitless one."
Before Tremaine had time to reply the door was opened by the keeper, and
Dunning passed out of the cell.
It was with a heavy heart Fanny heard from her husband that he could not
undertake to plead for the accused, and, gently as she could, she broke
the sad news to Sophia. Browne and Tremaine were tried, convicted and
sentenced to the State prison. And now the hand which had sinfully
lavished thousands—the hand that had been kept so daintily white and
soft—the hand of the "son of a gentleman" was roughly manacled, and
linked to the brown, hard, weather-beaten hand of a fellow convict. He
who had been the pampered heir of luxury was now to be the partaker of
coarse fare—the daily companion of all that was base and vile—and the
nightly dweller in the lone dark cell of a prison. He, the once
flattered, courted and caressed, was to pass shamefully from the haunts
of his fellow-man, and, after a few exclamations of wonder and reproach,
was finally to be forgotten.
But there was one secretly at work, one who had been spurned, one whose
noble hand had been flung aside with contempt—and that one was now
busily employed in writing petitions, in traveling to and fro, and doing
all in his power to obtain the liberation of the man who had ever
treated him with insult and scorn. At length he was successful, and
Tremaine was pardoned on condition of his leaving the State. But for
Browne, who had been recognized as an old offender, there were no
attempts made to procure his release.
It was with mingled feelings of shame and defiance that Tremaine
ungraciously received the assurance of his freedom from the mouth of
Dunning; for, the better to avoid observation, the latter went himself
for the prisoner, brought him from his convict cell, and conveyed him to
the warm hospitalities of a happy home, where he was received by Mrs.
Dunning with that refined delicacy and unobtrusive kindness which soon
placed him comparatively at ease in their society.
A strange and embarrassed meeting was that of Tremaine and his wife.
Sophia's first impulse was to break out into invective against him who
had thus brought disgrace and ruin, not only upon himself, but upon her.
Better feelings, however, prevailed, for she had learned many a lesson
of late, and had already begun to catch the kind and forgiving spirit of
those with whom she dwelt; so, after a few moments' hesitation, a few
moments' struggle between pride, anger and womanly tenderness, she drew
near to her husband, laid her head upon his bosom, and sobbed in very
grief and sorrow of heart. "Sophia!" "Tremaine!" were the only words
uttered during that first outburst of anguish. But soon the fountain of
thought was unsealed, when, instead of taunts and mutual upbraidings,
the bitter lessons learned in the school of adversity made them
self-accusing, and willing to excuse each other.
But little time was given to make arrangements for the departure of
Tremaine, who had determined not only on leaving the State, but the
country. Mr. and Mrs. Dunning wished Sophia to remain with them, at
least until her husband had procured some situation which might afford
him a competent support. But Sophia would not listen to this—she would
go with him—"she could do many things," she said, "to aid him." Fanny
Dunning smiled, but she knew that Sophia was right in thus fulfilling
her wifely duties, and both herself and her husband prepared every thing
necessary for the comfort of the voyagers.
It was a bright morning in May, when these true and tried friends
accompanied Tremaine and his wife in the noble ship which bore them down
the bay, and with many a warm tear and repeated blessing wished them a
prosperous voyage to England, and returned to the city.
And now we cannot better conclude their story than by giving an extract
from a letter, written some time after the occurrence of the events
already related, by Mr. Tremaine to his friend _Judge_ Dunning.
"I must congratulate you, my dear Dunning, on your elevation to the
bench; but I must not allow myself to utter all the praises that are
swelling at my heart, nor does it require words to convey to you my
respect, my esteem, my gratitude, and my love—ay, my love—for I do
love you as a brother.
"Sophy bids me haste and tell you our good fortune—softly, dear wife, I
will do so in a moment or two. You may perhaps recollect, my dear
friend, that I wrote you how difficult it was for me to procure
employment on my first arrival in Liverpool, and that this was mainly
owing to my total ignorance of any kind of business. Indeed, had it not
been for the few valuables belonging to my wife, which she cheerfully
parted with, and had it not been for her kind and encouraging words, I
should have yielded to despair. You know, too, my dear Dunning, that,
glad to do any thing in honesty, I at last obtained a situation as clerk
in a grocery store.
"How often has my cheek burned with shame, at the recollection of my
silly contempt for trades-people, when I was worse than idling away my
time at college? How often has my heart smote me when I thought of my
conduct toward you, my noble-minded, my best earthly friend? But why
repeat all this? You have long since forgiven me, and yet I never can
forgive myself. And now for my good fortune. My employer has enlarged
his business and taken me into partnership, so that I am in a fair way
of being once more a rich man, (and may I not add a wiser one?) and your
little namesake here, Robert Dunning, who is standing at my knee, is in
an equally fair way of remaining what he now is—_the son of a grocer_.
Heaven grant that he may in every thing resemble the man to whom his
father once used the words as a term of reproach. This is now my highest
earthly ambition for my boy, and I pray that my own lessons in the
school of adversity may enable me to teach him to place a juster
estimate on the empty distinctions of society, and to learn how true are
the words of the poet—
"Honor and shame from no condition rise;
Act well thy part, there all the honor lies."
* * * * *
LOVE.
BY J. BAYARD TAYLOR.
A fading, fleeting dream!
That blinds awhile with bright and dazzling ray,
Until the heart is wildered by its beam,
And wanders from its lofty path away,
While meteors wild like holy planets gleam,
To tempt our steps astray!
A creature of the brain!
Whom poets painted with a hue divine—
That, bright embodied in their thrilling strain,
Makes the soul drunken, as with mental wine,
While the heart bows in longing and in pain
Before its mystic shrine!
The shadow of a bliss!
That flies the spirit hastening to enjoy—
That seems to come from fairer climes than this,
To throw its spells around the dreaming boy,
But steals his quiet with its siren-kiss,
And robs his soul of joy!
Is this that power unknown
That rules the world with curbless, boundless sway,
Binding the lowest cot and loftiest throne
In golden fetters, which resist decay,
And breathing o'er each cold and rugged zone
The balminess of May?
No! By the soul's high trust
On Him whose mandate bade the planets move!
Who, kind and merciful, though sternly just,
Gave unto man that loftiest boon of love,
To bless the spirit till his form is dust,
Then soar with it above!
'Tis no delusive spell,
Binding the fond heart in its shadowy hall;
But 'neath its power the purer feelings swell,
Till man forgets his thraldom and his fall,
And bliss, that slumbers in the spirit's cell,
Wakes at its magic call.
Where'er its light has been,
But for a moment, twilight will remain;
Before whose ray, the night-born thoughts of sin
Cease from their torture of the maddened brain.
The spirit, deepest fallen, it can win
To better thoughts again!
'Tis for the young a star,
Beckoning the spirit to the future on—
Shining with pure and steady ray afar,
The herald of a yet unbroken dawn,
Where every fetter that has power to bar
In its warm glow is gone!
Who ne'er hath oped his heart
To that dove-messenger on life's dark sea,
Binds down his soul, in cold, mistaken art,
When vainly hoping he has made it free!
In earth's great family he takes no part—
He has not learned _to be_!
Who longs to feel its glow,
And nurtures every spark unto him given,
Has instincts of the rapture he shall know
When from its thralling dust the soul is riven.
He breathes, so long it blesses him below,
The native air of Heaven!
* * * * *
SOLITUDE.
BY ELIZABETH OAKES SMITH.
Oh! what a solitude doth mind create!
A solitude of deep and holy thought—
Alone with that Ideal good and great,
Which never yet companionship hath sought;
E'en as the eagle, when he highest soars,
Leaves the dim earth and shadows all behind—
Alone, the thunder-cloud around him roars,
And the reft pinion flutters in the wind—
Alone, he soars where higher regions sleep,
And the calm ether knows nor storm nor cloud—
And thus the soul its heavenward way must keep,
Despite the tempest raging long and loud;
Alone, to God bear up its earthly weight
Of human hope and fear, nor feel all desolate.
* * * * *
MUSA; OR THE PILGRIM OF TRUTH.
BY JAMES K. PAULDING, AUTHOR OF "THE DUTCHMAN'S FIRESIDE," ETC.
In the famous city of Bagdad there lived a rich merchant, named
Abdallah, of whose numerous offspring the youngest alone survived in the
person of Musa, an ingenuous and sprightly youth, in whom all the hopes
and affections of the father were centered. He often pondered on the
course of life to which he should direct the attention of his beloved
son, and at length consulted the sage dervise Motalleb, celebrated for
his learning, wisdom and virtue above all the inhabitants of that
renowned city, where the Kaliph Haroun Al Raschid once reigned amid the
splendors of oriental magnificence. Motalleb answered in few words,
after the manner of wise men, "Thy son will be rich without the labor of
acquiring wealth. Make him good, and, for that purpose, let him be
taught to distinguish what is true from what is false; for I say unto
thee, O Abdallah! that the knowledge and the love of Truth is the
foundation of all virtue."
At the earnest solicitation of Abdallah, the dervise consented to
superintend the education of his son, and Musa was accordingly committed
to his care. His first lesson was never to depart from the truth,
whatever might be the danger or temptation. This was continually
repeated, until one day Musa, with all the simplicity of youth, asked,
"What is Truth?"
"Truth," replied the dervise, "is that which is confirmed by the
evidence of the senses, or sanctioned by the assent of the
understanding. What thou seest, hearest, and feelest, thou mayst be
certain is true; and what is sustained by thy reason, or understanding,
though it may not be true, thou mayest assert, and believe, without
being guilty of falsehood."
Musa pondered on these definitions until his young and tender intellect
became involved in a maze of mystery; and the next time Motalleb
repeated his daily injunction, he again asked, "What is truth?" "Have I
not already told thee?" replied Motalleb. "True," answered the other,
"but I confess I cannot comprehend what I heard. I may believe what is
not true, and if I assert it to be the truth, surely I speak falsely?"
"But," replied the dervise, "thou wouldst not commit a crime, since it
is the wilful violation of Truth that constitutes the guilt."
Just at that moment a great crowd passed, with loud shouting and tumult,
outside the garden where Musa received his instructions, and, with the
curiosity natural to youth, he climbed up the wall to see what caused
the uproar. "What seest thou, my son?" asked the dervise. "I see a man
with his hands tied behind him, followed by an enraged multitude,
pulling his beard, spitting in his face, and beating him with staves and
stones, while he is staggering toward the river. What means all this, O
wise Motalleb?" "Allah be praised!" cried Motalleb, who had been tempted
by these details to look over the wall, "Allah be praised! it is the
recreant Mussulman, who, incited by the spirit of darkness, the other
day renounced the Koran and the true Prophet, for the Bible and the
false prophets of the Christian dogs. He is going to suffer the penalty
of his crime by being impaled alive."
Musa fell into a profound reverie, from whence suddenly rousing himself,
he asked, "If the follower of Mahomet is convinced by the evidence of
his senses, or the dictates of his reason, that the religion of the
Christian dogs is the true faith, is he guilty of a crime in forsaking
that which he believes to be false?" "But," rejoined Motalleb, "he is
deceived by the angel of darkness, or more probably only affects to
believe in his accursed creed." "Methinks, then," said Musa, with
perfect simplicity, "that he must be a great fool either to suffer
himself to be deceived, or to sacrifice his life for that in which he
does not believe." "But if his belief in the creed of the Christian dogs
should be serious, what then, my son?" asked Motalleb. "Then," replied
Musa, "he ought not to die, for you have often told me, that what is
sanctioned by our reason may be adopted without being guilty of
falsehood or committing a crime."
Motalleb hereupon fell into a long dissertation, involving various nice
distinctions between wilful and involuntary errors of opinion, owing, in
a great measure, sometimes to the influence of early education, habits
and example; sometimes to the seduction of the passions, and at others
to the weakness or perverseness of the understanding. When he thought he
had made the subject quite clear to the comprehension of his pupil, the
latter, after reflecting a few moments, asked him how he could
distinguish those opinions which were adopted through the influence of
education, passion, habit and example, from those derived from the
convictions of pure impartial reason. "That is impossible," said
Motalleb; "Allah alone can see into the human heart, and detect the
secret springs by which it is directed." "It seems to me, then," said
the youth, doubtingly, "that to Allah alone should be left the
punishment of errors of opinion, since none other can know whether they
are wilful or involuntary. But," continued he, after another pause of
deep reflection, "surely there must be some standard of truth, equally
invariable and universal, to which mankind may appeal, instead of
sacrificing each other, as this poor man is about to be, for a
difference of opinion." "Thou art right, my son, there is such a
standard. Thou shalt study the Koran, for that is the fountain of truth,
the only exposition of the wisdom of Allah himself."
Motalleb placed the Koran in the hands of his pupil, who studied it with
equal ardor and intelligence, the dervise having, by his repeated
exhortations, inspired him with a fervent admiration of truth, as well
as a longing desire to obtain its possession. But there were many
portions of the book which neither corresponded with the evidence of his
senses nor the dictates of his reason. When he read that the Prophet
had, according to his own assertions, ascended to the seventh heaven in
company with the angel Gabriel, on the back of a white camel, and
advanced alone so near the throne of the Almighty as to be touched on
the shoulder by his hand; and that he had, in less than the tenth part
of a single night, thus performed a journey of at least a thousand
years—these and other miraculous tales confounded his understanding,
and contradicted not only the lessons of past experience, but the
evidences of his senses. He tried to believe, but found it impossible;
and when his preceptor, after allowing him sufficient time to study the
great work of the Prophet, asked him whether he had not at length drank
at the pure fountain of truth, he frankly expressed his doubts as to the
miraculous journey. The dervise stroked his long beard, and frowned
indignantly. "What!" cried he, "dost thou disbelieve the revelations of
the Prophet himself?"
"I am compelled to do so," replied Musa, "since they neither accord with
the evidence of my senses nor are confirmed by the assent of my reason."
Motalleb grew angry, and cried out with a loud voice, "What hath the
evidence of the senses or the assent of reason to do with that which is
beyond the reach of the senses or the comprehension of reason? Know,
foolish youth, that these things are miracles, and that neither the
understanding nor the reason of mortals can comprehend them. Dost thou
doubt the testimony of him who communed with angels, and was inspired by
Allah himself?"
"I am neither learned nor wise as thou art, O! Motalleb," answered Musa,
bowing his head, and touching his forehead reverently, "but it seemeth
to me that thy words do not exactly accord with the definition of truth
which was one of my earliest lessons, and which thou hast repeated to me
every day. Thou didst tell me that truth was the evidence of the senses,
confirmed by the assent of the understanding. Now thou sayest otherwise,
and I am to believe what neither my reason can comprehend, nor my senses
realize as possible, because it contradicts all my experience."
"Thy reason! thy experience!" answered Motalleb, contemptuously. "Thy
beard is not yet grown; thou hast as yet read little and seen nothing.
When thou hast mastered all the learning of Arabia, and traversed the
distant regions of the earth, thou mayest then found thy belief on the
evidence of thy senses, the dictates of reason, and the results of
experience. Go thy ways, my son. Thou art already too wise for me, since
thou doubtest the miracles of the Prophet." Saying this, he dismissed
his pupil, who bent his way homeward, thoughtful and depressed.
Abdallah received him with his usual affection, and being told of the
dismissal of Musa by his preceptor, straightway went forth and purchased
great store of costly manuscripts, containing all the learning, science
and philosophy of the East, together with many translations from the
Grecian sages and poets. To these Musa applied himself with such zeal
and perseverance for several years, that he at length possessed himself
of all the wisdom they contained. Every step, however, that he proceeded
in his search after truth, only seemed to render its existence more
doubtful. Scarcely any two of those illustrious wise men agreed in their
religious, moral or political opinions, and he counted among the
philosophers upwards of three hundred different definitions of the
_summum bonum_—that is, the great constituent of human happiness.
"Strange," thought Musa; "surely that which leads to happiness can be
only the truth; and yet, in this most important of all concerns, these
sages almost invariably dissent from each other. I will henceforth see
with my own eyes, instead of those of others. Surely truth must exist
somewhere in this world. I will traverse the earth, according to the
advice of Motalleb, until I find it, or perish in the search."
At this moment he heard a loud cry at the door which opened toward the
street, and going hastily forth, encountered four slaves bringing in the
body of his father, who had been suddenly smitten by the angel of death,
while drinking from a cool fountain in one of the public gardens of the
city. Musa fell on the body and wept, and mourned a long while with all
the depth and sincerity of filial love. But when time had assuaged his
sorrows, he recalled to mind the anxious wishes of his parent, that he
should seek and find out the truth; and being now rich, and his own
master, he resolved to set out on his pilgrimage without delay. Placing
the management of his affairs in the hands of a discreet friend of his
father, he one morning, just at the dawning of day, mounted his Arabian
steed, and turned his back on the once splendid capital of the Kaliphs.
In the course of twenty years, Musa visited a great portion of the
habitable globe, with the exception of the new world, which was not then
discovered. He sojourned among the Persians, whom he found almost
equally divided between the worshippers of fire and the followers of the
sect of Ali, abhorred by all the faithful. Each believed in the truth of
their faith, and were ready to die in its defence. He then joined a
caravan of merchants, and bent his way toward Hindostan, where, having
safely arrived, he quitted his companions, and pursued his journey
alone. The first thing that attracted his attention was a party of young
people of both sexes bathing promiscuously together, who seemed to be
utterly unconscious of any impropriety, and laughed and gamboled with
all the hilarity of innocence. To a disciple of Mahomet, accustomed to
the jealous seclusion of females, the spectacle was revolting in the
extreme, and he turned away in bitter disgust, exclaiming against such a
violation not only of decency, but the law of the Prophet.
Proceeding onward, he observed several persons with a piece of fine
muslin or gauze before the mouth, and others walking slowly, with
brooms, carefully brushing away the dust before they ventured to take a
step forward. On inquiring the reason, he was told that the former
method was adopted lest they might accidentally swallow some insect, and
the latter to prevent their treading on some living thing, and thus
depriving it of life—a crime which subjected them to severe penance and
mortification, as being against one of the fundamental principles of
their faith. On hearing this, Musa pursued his way laughing, though a
grave Mussulman; and, having crossed a river, encountered a person
uttering the most horrid execrations against an evil spirit, who, it
seems, had, in the shape of a dragon or serpent, raised a great thunder
storm, which laid waste his fields and destroyed his crop of rice.
"Head of Mahomet!" said Musa, "what a set of ignorant barbarians are
these! There is no use in seeking for truth among them. I will visit
their wise men, and hear what they have got to say for themselves."
Learning, on inquiry, that the sect or caste of the Brahmins were
considered the most wise and enlightened of all the people of Hindostan,
he sought and obtained the society of some of the chief bonzes, under
the character of a traveler in search of the truth. From these he
learned, with no little surprise, that their religion was a perfect
mystery, confined altogether to the priests, and that so far from
wishing to make proselytes of strangers, none could be admitted among
them but by hereditary succession. "Strange," thought Musa, "that people
should be so selfish. If they believe their faith the only true one, it
is cruel to keep it from the knowledge of others."
Passing away from these exclusives, he came to a temple, where he beheld
a number of persons undergoing a variety of the most extraordinary
tortures, to which they were voluntarily submitting. Some of these had
held up one arm in the same position till it became fixed and
inflexible, and so remained during the rest of their lives. Others had
clenched their fists with such force, and kept them thus so long, that
the nails had grown through the palms, and projected from the back of
the hand. Others had turned their faces over one shoulder, until they
were irrevocably fixed in that direction. Others were suspended, by iron
hooks fixed in the shoulder-blade, to a beam which turned round with
great velocity on a pivot at the top of a long pole, while the penitent
sometimes sung a song, or blew a trumpet, as he whirled around, to the
great admiration of the spectators. On inquiring the meaning of all
this, he was told that they were celebrating their religious rites, and
exemplifying the sincerity of their devotion.
Musa turned away from this exhibition with mingled feelings of pity and
contempt, and pursued his way pondering on the strange diversities of
human opinion, most especially on subjects involving not only the
temporal but eternal welfare of mankind.
"All cannot be true," exclaimed he, "and yet one must be the truth. I
will not be discouraged, but continue my pilgrimage until I find the
fountain of truth, or become involved in endless, inextricable doubt,
and believe nothing."
Continuing his journey, he entered the great empire of China, where he
found three hundred millions of people, divided into the followers of
Loo Tsee, Fokè, and Confucius, or Confutsee, each equally convinced of
the truth of their creed, and each equally despising the others. Thence
he proceeded to Japan, where he arrived at the period of celebrating a
great religious festival, and saw them trampling the cross under foot,
and sacrificing human beings to a great idol, which resembled neither
beast, bird, fish, nor man, but exhibited a monstrous combination of the
deformities of almost every species of animal.
It would be tedious to follow him throughout his various peregrinations
through Asia and Africa. Suffice it to say, that he everywhere
encountered the strangest diversities of manners, habits, opinions and
modes of faith, and every day became more hopeless of gaining the object
of his weary pilgrimage. The course of his wanderings at length brought
him to Cairo in Egypt, where he accidentally fell into the company of a
learned European traveler, who had visited the country to unravel the
mystery of the pyramids, and decipher hieroglyphics. On learning from
Musa the object of his journeyings, he turned up his nose somewhat
scornfully and exclaimed—
"Pooh! what is the use of seeking for Truth among the barbarians of the
East? You should visit enlightened Europe, the seat of learning,
philosophy and true religion. I have completed the purposes which
brought me hither, and am about to return home, where, I flatter myself,
I shall prove to the satisfaction of all reasonable people that the
whole tribe of travelers who preceded me are no better than a parcel of
ignorant blockheads. You shall accompany me to Europe, where alone is to
be found true religion and true philosophy."
Musa caught at the proposal. They embarked together in a vessel destined
for Marseilles, where in good time they arrived without accident. On the
night of his first sojourn in that city he was suddenly roused from a
sweet sleep by a series of heart-rending shrieks and groans, mingled
with loud imprecations and shouts of triumph, that seemed to come from
all quarters of the city. Starting from his bed, he ran to the window,
where he beheld bodies of armed ruffians raging through the streets,
massacring men, women and children without mercy, breaking open the
houses, tearing forth their wretched inmates, whom they slaughtered with
every species of barbarous ingenuity, and committing their bodies to the
flames of their consuming habitations. While shivering at this
exhibition of barbarity, and meditating an escape from its horrors, he
was interrupted by his friend, and addressed him in a voice trembling
with apprehension,
"In the name of the Prophet!" cried he, "what does all this mean? Is the
city become a prey to banditti or hostile barbarians, who spare neither
sex nor age, and riot in blood and fire?"
"It is nothing," answered the other, coolly. "They are only punishing
the heretics for not believing in the Pope."
"And is that the name of your God?" asked Musa, with perfect simplicity.
"No—he is only his vicar on earth."
"But do not these poor people believe in your Bible, which you have told
me is the great volume of Truth, and in that Supreme Being who you say
is the only true God?"
"Yes—but they deny the supremacy of the Pope, and deserve to be
punished with fire and sword."
"Then the Pope must be greater than your God," said Musa.
His friend turned away with a gesture of impatient contempt, and
muttered something of which he could only distinguish the
words—"Ignorant barbarians!"
At dawn of day he left the city in disgust, but wherever he came he
found the country smoking with the blood of helpless innocence and
unresisting weakness, and was told by the priests in tones of triumph
that in one night all the heretics of the kingdom had been exterminated.
He asked then what these poor people had done, whether they were thieves
and robbers, traitors or rebels, that they should be cut down in one
single night without discrimination and without mercy. But all the
answer he received was—
"They deny the supremacy of the Pope!"
"Strange!" thought Musa. "But I am among true believers and enlightened
philosophers, and no doubt shall find the Truth at last."
He, however, determined to leave the country as soon as possible, and
bending his course to the seaside, embarked in a vessel destined for
England, but which was driven by stress of weather into a port of
Ireland. Here he found every thing in confusion. People were setting
fire to the churches, pulling down stately abbeys and convents, and
driving their inmates before them with every species of violence and of
opprobrium.
"Who are these people?" asked he—"and what have they done—most
especially those poor women and children, whom I see fleeing from their
pursuers, pale with affright, and crying out in despair?"
"They are heretics and believe in the Pope," was the cool reply.
"That is very strange," said Musa—"I am just from a land where they
were massacring men, women and children because they did not believe in
the Pope. How is this?"
"We are only retaliating their persecutions. When they had the upper
hand they oppressed us, and it is but just that they should suffer in
turn."
"But does not your religion inculcate forgiveness of enemies?"
Before Musa could receive a reply, an aged, bald-headed friar ran
tottering past, with a nun holding by his hand, and pursued by several
people who seemed half mad with hate and eagerness, and assailed them
with missiles of every kind. His companion joined the throng, and left
him without an answer. He inquired of another what the old man, and
especially the poor woman, had done to merit such unworthy treatment,
and was told that one was a friar of the Order of Mercy, and the other a
Sister of Charity.
"And what are their occupations?" inquired Musa.
"One is employed in the redemption of captives among the infidels—the
other passes her life attending the bedside of the sick, relieving their
wants, administering to their comfort, without fee or reward, and
devoting herself to charity and devotion. But they both believe in the
Pope, and that is the great original sin."
"Head of the Prophet!" exclaimed Musa—"and yet you persecute these
people! Surely that cannot be the true religion which deals thus with
the votaries of mercy and charity."
The man, instead of answering, stooped down and seizing a stone, threw
it at Musa with such good aim that it grazed his turban, and began
crying out—"A <DW7>!—A <DW7>!" whereupon Musa made the best of his
way to the ship, where he sought shelter from an angry crowd that was
shouting and shrieking in his rear. He continued his journey through
England, Spain, Holland, Germany, Switzerland and Italy, and wherever he
went perceived such strange diversities and contrasts in the standard of
morals and religion, that in despair he at length resolved to return
home, having come to the conclusion that there was no such thing as
truth in this world. With this intention he arrived at Rome, on his way
to Venice, whence it was his purpose to embark for Smyrna, and thence to
proceed by land through Asia Minor to Constantinople, on his way to
Bagdad. At Rome he saw the Pope, a feeble, decrepit old man, who had, in
order to give more imposing dignity to the ceremony, consented to
preside at the burning of a heretic, who was convicted before the
Inquisition of having pulled off his hat and made a bow to the statue of
Hercules and the Centaurs. The poor victim, who was an ignorant peasant,
solemnly declared that he mistook Hercules for a saint; but all would
not do. He perished at the stake, after which Te Deum was sung, and high
mass celebrated throughout the ancient capital of the world.
Sickened and disgusted with Europe, he embarked for Smyrna, and crossing
Mount Sipylus on his way to Constantinople, was benighted and lost his
way. He wandered about amid the deep recesses, until at length he
descried a light at a distance, which, on approaching, was found to
proceed from a cave, where Musa beheld an aged man, with a long white
beard, reading by the light of a lamp. So deeply was he engaged, that
the lost traveler entered the cave and stood beside him ere he was aware
of his presence. He was not, however, in the least startled when he
perceived the stranger, but courteously requesting him to be seated,
closed the manuscript volume in which he had been reading, and kindly
inquired into his wants and desires.
Musa related to the old man how he had lost his way in returning
homeward, after an absence of twenty years, and requested his
hospitality. The old man assured him he was welcome, and having provided
a frugal repast of milk, dates and bread, they sat and conversed
together, making mutual inquiries of each other. The aged hermit
informed his guest that he was of the sect of the Maronites, and had
many years ago sought refuge from the persecutions of his fellow
Christians in this spot, where he could alone enjoy liberty of
conscience. "But thou," continued he, "hast just informed me that thou
art returning home after twenty years of travel. Thou must have gathered
vast stores of wisdom and many truths during thy long pilgrimage."
"I did indeed set forth in search of the truth," replied Musa, "but am
returning only more in doubt than before. I have sought for some
standard of manners, morals and religion, by which all mankind might
regulate their opinions and conduct, for such a standard can be only the
truth."
"And didst thou find it?" asked the hermit, smiling.
"Alas! no, venerable father," replied Musa. "I found no two nations
agreeing in one or the other. A river, a mountain, or even an imaginary
line of separation, not only produced a contrast in all these, but a
bitter feeling of hostility, the parent of broils and bloodshed, seeming
to proceed from mere differences in opinion, of which a great portion
knew neither the grounds of their belief nor the source of their
convictions. Even in matters involving their eternal welfare, I found no
standard of truth, for millions differ with millions on the subject, and
shed each other's blood for a diversity in creeds which are alike
derived from the great book in which they all believe."
"And to what conclusion has all this travel, study and experience
brought thee at last?" asked the hermit.
"I scarcely dare tell thee, O! venerable father. But if I have formed a
decided opinion on any one thing, it is that there is no such virtue as
truth on earth, and no Supreme Being in Heaven, since there are so many
different opinions with regard to one, and so many modes of worshiping
the other. Surely where such diversities exist, it is the height of
presumption for men to persecute each other for not believing alike.
"But," asked the hermit, "amid these endless varieties of faith, didst
thou ever encounter, in all thy pilgrimage, a people who believed not in
a Supreme Being, either by himself or his ministers, presiding over the
government of the universe?"
Musa reflected awhile, and then answered, "No; however different might
be their faith, in their modes of manifesting it, I do not recollect
ever to have found a people, civilized or barbarous, where I could not
distinctly perceive, even among the darkest clouds of ignorance, a
recognition, more or less distinct, of a Supreme Intelligence, in some
shape or other. Even where they worshiped beasts or idols, I thought I
could always trace their devotion, step by step, to a Supreme Being."
"Then," said the old man, "thou mightest have found in thy long search,
hadst thou made a wise use of thine experience, at least one great
truth, of more importance to the welfare of mankind than all the
conclusions of learning and philosophy. Instead of drawing, from the
various modes in which religion manifests itself, the conclusion that
there is no God, thou shouldst have gathered, from the universal belief
of all mankind, that there is assuredly such a Being, since neither the
most wise nor the most ignorant deny his existence.
"This is one great truth thou mightest have learned in thy twenty years
of travel. A second, scarcely less important, at least to the temporal
happiness of mankind, is, that since almost all nations and communities
differ in a greater or lesser degree in their modes of worship, and
there is no earthly standard to which all are willing to submit, it
becomes us short-sighted, erring beings, instead of persecuting each
other by fire, sword and defamation, to be tolerant of that which we
call error of opinion in morals or religion. However we may differ in
the modes by which these are manifested, we may be assured that though
we may be mistaken in abstract points of faith or morality, still there
is one great universal truth which all may comprehend, namely—that
charity for human errors must be the bounden duty of all, since without
such charity on the part of the Most High, the gates of Heaven would be
forever closed against his sinful creatures."
Musa remained several days in the cave of the hermit, during which time
the old man often repeated the lesson he had given, and then bent his
way toward Bagdad, which he reached without any adventure. Here he
passed the remainder of his life in practising the precepts of the wise
hermit of Mount Sipylus. He became the friend of the ignorant, the
benefactor of the needy; nor did he ever inquire, ere he relieved them,
to what sect they belonged, or pamper the pride of superior wisdom by
despising their inferiority. And when, after many years of happy repose
and wide-spread benevolence, he was smitten by the angel of death, he
died in the full conviction that he had found the truth, and that it
consisted in reverence for the Creator of the world, and charity toward
all his creatures—charity not only for their wants, but their errors
and opinions.
* * * * *
THREE ERAS OF DESTINY
IN THE LIFE OF THE PAINTER ANGELICA KAUFFMANN.
BY MISS H. B. MACDONALD.
PART I.
There is perhaps no scenery in the world so ravishingly beautiful as
that offered by those vast plains of northern Italy situated at the base
of the Rhætian Alps. A champaign elaborately tilled, and laid out into
those regular divisions of meadow, corn-field, and vineyard, which make
so much of the beauty of cultivated landscape; groves and belts of trees
so disposed as to be productive of the highest effect; classic looking
villas, villages and towns, with their surrounding orchards and
pleasure-grounds; bright rivers winding their way through all this
beauty till they lose themselves in those magic lakes, which, with their
green banks kissed by the waters, and bordered on every winding
promontory and inlet by belts of overshadowing trees, reflect the sunset
splendors of the Alps, and seem, in every rainbow grotto and crystal
palace mirrored in their lucid depths, meet homes for those genii of the
waters with which a graceful superstition peoples their enchanted
caverns. All these, with the back ground of gigantic mountains, pile on
pile, that seem to raise a barrier from earth to heaven between this
Paradise and a ruder world beyond, fill us with the idea of wandering
amid some remnant of the scenery of the Golden Age, where of old, as the
fables tell, the primeval deities used to dwell with a purer humanity,
and in a younger and lovelier earth.
From a village situated at a considerable elevation on the surface of
the <DW72>s into which these smiling plains incline themselves as they
approach the mountains, one bright spring evening, a troop of young
girls might have been seen issuing, apparently as if broken loose from
school, so joyous were their gestures, so wild their mirth, as with the
vivacious grace belonging to the children of the South they bounded over
the grass, some gliding in imitation of the motions of a dance, some
skipping, some chasing others with the speed of the wind, till at a call
from one, "to the water—to the water!" echoed by a dozen voices, they
descended a hollow leading to the bed of the bright Ticino, and in a few
moments were plunging and gliding in the stream.
One of them, apparently between fourteen and fifteen years of age,
instead of following the example of her companions, had, in the
excitement attending this operation, slipped away unperceived, and
wandering listlessly along the windings of the river soon found herself
out of hearing and sight. Proceeding on her way, and picking up a pebble
or a flower just as it suited her, and stopping to observe every
effective point of view in the landscape, with a narrowness of
observation and sense of its beauty uncommon in one so young, she came
to a ravine leading up from the side of the stream, which she ascended,
till arriving on a high point that overlooked the channel of the river,
she witnessed one of the most superb sunsets that ever gladdened an
enthusiast's eye. Amidst an array of purple clouds, fringed with silver,
the sun was descending, gold , behind a peak of Mount Rosa, and
suffusing the surrounding Alpine masses with a dim violet vapor. At her
feet, and flowing in a direction opposite to the eye, was the river, now
transformed into a stream of rich ruddy amber, with its sloping and
picturesque banks and wooded islands, that diversified its brilliance
with emerald shadows, taking its way in a hundred windings, whose
succession she could trace, curve beyond curve, as it clove its course
through the opening hills—far away, till, in the termination of the
vista, gleamed the shining roofs of the Pania, with the white spire of
its cathedral seeming to lose itself in the gold of the evening sky. To
the left, immediately at the foot of the eminence where she stood, was
the little white village, with its orchards and trim vineyards, and,
beyond, those vast <DW72>s on which the mountains lose themselves in the
Italian plains. To the right, arose perpendicularly from the river a
wall of sparkling granite rocks, now of the deepest vermilion in the
alchemy of evening; and behind, towered grandly into the sky those white
wildernesses of Julian Alps, receiving from their brethren, the
Rhætians, the reflections of the opposite sunset in a thousand tints of
lingering rose.
A singular effect was produced on the girl by the contemplation of this
scene. Her bosom heaved, her cheeks flushed, her eyes filled with tears.
"Oh! for the voice of a poet," said she, speaking to herself, "to
celebrate these splendors in some immortal song! Or the hand of a
painter, to retain them in undying hues, for a joy to the worshipers of
beauty forever. Alas! they are fading—they shall soon be lost to the
universe; and there is none here who, with the power of inhaling them
into his spirit as I, hath the happier gift of reproducing them in some
diviner form. Alas! I am weak, with no power but to _feel_; as when
gazing on some noble statue—some magic scene—some surpassing human
form—an irrepressible emotion seizes me, which, when I would invest
with expression, my heart dies away in utter impotence!"
Ah! innocent soul, thou didst not then know that the first power of an
artist is to _feel_; that in his susceptibility for emotion lie his
strength and the spirit of his calling; and that the achievement of the
painter, the poet, or the sculptor, is but the expression of that
emotion which our common language is too weak to supply, and only
acquired, like any other language, through practice and experience. The
girl who mused thus was very beautiful, now rendered more so by the
freshness and vivacity of her extreme youth. Long tresses of chestnut
hair, braided across her temples and slightly twisted up behind, were
then suffered to fall in ringlets over her neck. Her complexion was
brilliantly fair, with that rather deep carmine tinge on cheek and lip
common to the Teutonic race, on the confines of whose clime she was
born; while her slender figure and regular features betrayed the
vicinage of classic Italy. But the most remarkable feature were the
eyes; they were large and of the deepest black, in whose serious,
melting, intellectual expression we could read all the soul of Angelica
Kauffmann.
Throwing herself on the grass, she gave way to a delicious reverie on
the enchantments of the scene, which the twilight, the fading colors and
the silence soon deepened into a sort of dream. She thought herself in
the midst of a vast temple, whose dome expanded into the skyey concave
above her head, lamp-lighted with its thousand stars. Its area, whose
termination on any side she could not descry, seemed to extend into an
interminable space, lost amid a wilderness of surrounding columns. By
degrees she became aware of the presence of groups of majestic statues,
that seemed, by some enchantment, one after another to strike her view,
like the scenery of a diorama. Watching them attentively, she saw that
though raised on pedestals, in the attitudes and repose of statuary,
they were endowed with all the features of animated life, but a life
more than human—it seemed immortal, divine; and she recognized in these
forms the presence of that gifted and glorious company enshrined in the
temple of the immortal heart of man. Amidst the group in whose immediate
vicinity she found herself, stood "Rafaelle the Divine," with that
countenance of his so expressive of the spirit of the sainted religion
whose attributes he has embodied in glorious painting, and his
melancholy eyes filled with the presentiment of his early death. Angelo,
grand and majestic like his own Moses, and a brow worthy of the
conception of that great St. Peter's—the temple of the Christian world.
Murillo, glorifying in his aspect the stolid simplicity of that humble
life whence he drew his origin, and the delineation of which he made
peculiarly the subject of his design. Carracci, with that forsaken look
when the child of genius, like, alas! too many of his calling, lay down
to die of a broken heart. Titian, beautiful as his own Apollos—and many
more. But among these her attention was directed in surprise to a
conspicuous pedestal, deficient of its statue, whereon was engraven in
large letters, on the granite of its base, the name of "Angelica
Kauffmann." Looking up at the same moment to the vast sky-blue dome
above her head, she saw blazing directly over the vacant pedestal a
large, bright, solitary star, that lighted the whole temple with its
radiance. After a long riveted gaze toward it, she became slowly
sensible of looking on the true sky, from which the sunset and the
twilight had now quite faded, abandoning it to the deep cobalt blue of
the approaching darkness. The statues had vanished; the pillars had
resolved themselves into the surrounding trees of the landscape; and,
instead of the temple, were the familiar features of the scenery, though
now almost lost in the darkness, she had gazed upon before falling into
slumber. Every thing had vanished except that bright, solitary star,
which, though now restored to complete consciousness, she continued to
gaze upon with eyes riveted by wonder and delight. Familiar with the
geography of the heavenly world, she was wholly unable to account to
herself for the appearance of this particular star, which differed in
position and lustre from any of the heavenly bodies she had hitherto
been familiar with. It was evidently some new comer, and the girl
thought to herself of those presiding stars that were of old said to
arise over the destinies of the great ones of the earth, and
dreamed—who can tell in that hour—wild dreams to herself of future
glory and renown.[3]
-----
[3] This seemingly supernatural orb was probably one of those since
classed under the catalogue of "Variable Stars," which disappear for
stated periods, and then become visible again, to blaze for a short time
with extraordinary lustre.
PART II.
There were preparations for a festival in the halls of the "Royal
Academy" of London. A distinguished foreign member of the profession was
expected to be present, and the first individual not a native on whom
the fellowship of the Academy had hitherto been conferred. The king and
royal family had promised the honor of their attendance, and the prize
medals of the exhibition were to be presented, of which the eminent
foreign artist alluded to had carried off the first. The saloons were
gorgeously lighted. All the pictures of the exhibition had been removed
from the walls, except those few favored masterpieces obtaining the
award of the prizes—and one surpassing work of art that hung by itself
at the head of the principal saloon, with a delicate wreath of laurel
suspended above it, betokening it the first in honor as in place. It
consisted of two figures, of which the most conspicuous was that of a
shrinking, prostrate female, expressing the highest ideal of loveliness
and grace, joined to utter abandonment, contrition and shame; appearing
as if the whole soul had imbued itself through every muscle and
lineament of the frame, for the delineation of these emotions, that none
could mistake that model of penitential sorrow, afterward so celebrated
as "The Weeping Magdalene." The face was completely buried in her hands,
but so far from the absence of this most essential tablet of female
beauty being felt as a defect, it was rather an adjunct to the effect,
inasmuch as it left to the imagination's heightening conception the
modeling of a countenance meet for such a form, and such magic tones of
color—burning with blushes—we know it from the roseate tint that
almost seemed reflected from it along the pearly edges of the
enshrouding hands—and drowned in tears, that fell like liquid diamonds
over the snow of the Redeemer's feet. The accompanying figure was
somewhat inferior, yet it expressed that union of majesty and sweetness
joined to godlike compassion, in as great a degree as human art has ever
been able to embody in its ideas of the Divine man. On the side of the
hall opposite the picture was erected a pavilion, emblazoned with the
royal arms of England, and surmounted by a crown, under which George the
Third had just seated himself, habited in his usual dress of a marshal's
uniform, with the rather vulgar, squat figure of his queen, the German
Charlotte, surrounded by their _suite_, who gazed, with curious though
certainly not very connoisseur like eyes, occasionally through their
opera glasses at the divine picture suspended in front of them on the
opposite wall.
The Academicians had severally arrived in their badges; there were
gentlemen in the splendid Windsor uniform—officers glittering in
epaulettes and gold lace—collars and grand crosses of
knighthood—ladies in coronets and plumes. The music played, and the
festival was begun. The _élite_ of England's ennobled by birth and
ennobled by mind were there, and mingled in conversation—some in
animated groups round the pictures and statuary—some promenading the
halls, when suddenly the buzz of conversation ceased, and an expression
of eagerness pervaded the assembly, greater than that which had greeted
the entrance of royalty itself, and there entered through the yielding
crowds, conducted by a gentlemanly looking person in the badge of the
Academy, a young slender girl—a child indeed no more, but still
retaining the chestnut ringlets and glorious black eyes of Angelica
Kauffmann. Conducting the young Academician, and the first woman ever
invested with such a distinction, toward the pavilion, Sir Joshua
Reynolds presented her to their majesties; when the peasant girl of the
Alps, as she knelt before them, told that high-born and high-bred throng
of a grace derived from the sense of the beautiful in the soul, and
which the atmosphere of a court could neither add to nor bestow. Raising
her hastily, George the Third, after a few words addressed to her, and
graciously made in German by his queen, conducted her, leaning on his
arm, through the saloons, rendering her the envied of all the envious.
"Such amiable condescension! But his majesty has such a passion for
foreigners—beside his patronage of the Fine Arts—quite indeed
auspicious of their restoration to the age."
"It is whispered," said another, "that she has been commanded to paint
the royal family."
"By no means," interposed a gentleman in plain clothes. "My information
came from an individual who had it from a high quarter, that such a
report is incorrect. I understood that this honor was in contemplation
for the signora, but no positive orders have been yet issued on the
subject."
It is to be doubted whether the object of these remarks was so highly
sensible of these distinctions as a refined education would have taught
her; and we have even a suspicion that she might have gone so far as to
wish to escape from the gracious condescension of the conversation with
which George honored her, as promenading round the hall she found
herself obliged to stand _answer_ to the abrupt and sometimes ridiculous
questions originating in the royal mind, after the catechumenical method
of conversation then in vogue in intercourse with majesty.
But higher honors awaited the young artist. Sir Joshua Reynolds, then
President of the Academy, having mounted the chair, proceeded to descant
upon the excellencies of the several productions distinguished by the
Society's prizes—but there was one, he said, which he could not pass
over without some more especial notice.
"Need I direct attention," said he, "to that noble work at the head of
the hall, whose magic beauties, as they shine from the canvas, have
enchained the admiration of the most distinguished connoisseurs, and
evidence stronger reasons for the decision we have come to in its favor
than any words of mine could adduce. Although the age and sex of the
artist invested the work with an interest in our eyes it would not
otherwise perhaps so strongly possess, we would not for a moment have it
supposed that they exercised the smallest influence upon our suffrages.
We adore beauty, womanhood and youth, but we adore Art more, and have
too high a sense of its dignity to permit any extrinsic consideration,
however fascinating to the imagination, to divert us from our undivided
homage toward it. It is to the solid excellence of the work itself—the
new principles which it involves—principles, for the acquirement of
which, I am not ashamed to say that I myself, as well as many others
grown old in honors as in years, are not unwilling to descend into the
character of pupilage—and not the less that we sit at the feet of a
genius and a woman. While awarding in this direction the highest
distinction, we can speak for our brethren of Art that have come forward
in competition for the honors of this day, that they will feel satisfied
in withdrawing into an inferior place before her who, from a distant
land, chose to throw her merits upon our judgment, and her talents into
the service of the British nation. Therefore I bestow the First Prize of
the Institution upon the 'Weeping Magdalene,' property of the Academy,
and executed by the Signora Angelica Kauffman, of the Grisons, whom I
have great pleasure in investing with the medal."
So saying, the President descended, and presented to Angelica, who stood
up to receive him, a massive gold medal and chain. There was neither
bashfulness nor awkwardness in her demeanor as she stood up amid that
vast assembly, whose shouts and plaudits now shook the building to its
foundation—only a vivid blush passed over her face as she gazed round
the assembly for a moment with an almost bewildered look; but it seemed
of some higher emotion than vanity—as if the consciousness and the
exultation of genius—the satisfaction of having achieved something for
Art—the experienced realization of the hopes and the labors of
years—and the knowledge of having won for herself a place among the
Immortals, and in the sympathies of her race, which is, perhaps, the
principal ingredient in a woman's passion for fame—were all crowded
into the emotion which gave it birth. The simplicity of her appearance
contrasted strangely with the splendor of her reputation—young looking
for her years, which then amounted to no more than twenty-two, her
dress, too, plain and unadorned, and as much after the modest form of
the antique as conformity with modern usage would allow without the
charge of being particular or fantastic—no less added to this effect,
contrasted, as it was, with the gauds and superfluity of hoop and
head-dress then in vogue; her arms were bare nearly to the shoulder—and
her hair, confined by a bandeau of pearls made to imitate a pointed
coronet, was braided over her temples, and twisted up into a loose knot
behind, as in times long ago, from which a few rich tresses escaping,
fell over a neck possessing the contour and graceful set of an antique
statue.
Fatigued and excited, she was glad to escape from the glare of the rooms
into an adjoining balcony, to cool her eyes in the dim gleam of the
stars—in all moments of excitement or passion, still the same bright,
unchanging stars, ever ready to tranquilize us with thoughts of that
world where passion and excitement cannot enter. A young man, who had
watched her unceasingly all the evening with a deeper interest in his
glance than mere curiosity, followed her hastily and in a moment was by
her side. She did not attempt to conceal her pleasure at his appearance.
"Where have you been, Alexander?" she said; "I often looked for you, but
could not recognize yours among the bewildering crowd of faces that
swarm in these busy halls."
"And you thought of me, amid honors and applause, and the caresses of
the enlightened, and the smiles of a king!—but oh! Angelica, they may
give you praise, they may give you wealth; they may elevate you to a
lofty place in the world's view, where thy beauty and thy worth being
recognized, may command the homage of the great and good; they may
appoint you to a high rank among the hierarchy of genius that minister
in the temple of fame—but I, only I, love thee! Poor in circumstances,
poor in dignity, with no other advantage to offer you but a heart rich
in affection, I have chosen this moment to lay it at your feet, in
homage to a nobleness which, if my thought mistakes not, knows how to
esteem such above all other gifts the world else can bestow." And with
many more impassioned words and adoring glances did he woo her, she
responding in tones and looks as endearing as his own. Just then, in the
midst of her triumphs of art, honors, and of love, she looked up toward
the heavens, and saw shining above her that bright, still, solitary
star—the same that had risen above the fantasies of her childhood, when
she dreamed amid the sunny hills of Italy, far away! Many a strange
experience, many a scene had passed before her since it first met her
gaze; and now they all seemed to be crowded, as bestirred from her
memory, into one moment of review. Her progress from the child to the
woman—the strange intervening changes—the same, as she felt herself,
yet not the same;—the vistas of fame opened to her with the first
appearance of that star—her early struggles, and the space between, to
the exulting consciousness of the pinnacle where she now stood, loftier
than even her visions had conceived.
"The star triumphs!" thought she; "I am not superstitious," she
continued, aloud, "but, Alexander, I have seen that orb _once_ before,
and feel as if I should see it but _once_ again. With every hour of joy
does there not mingle a pang?—that telling of the dark reverse, which,
in this unstable scene, must sooner or later await the most fortunate."
"Hush! dear Angelica," said her lover, laying his finger on her lips;
"to-night let us only think of being happy."
"You are right," replied she, and, seizing his arm, they were soon
mingling and jesting with the crowds of the saloon.
PART III.
It had been a day of clouds and heavy rain, and now the night was
closing over a dreary and scantily furnished apartment in one of those
ruined palaces of Florence, which, like so many objects in Italy, are
invested with the romantic prestige of grandeur passed away. A single
rushlight threw into view the dilapidated marble walls, on which were
the tattered remains of what might once have been gorgeous tapestry, and
a large oriel window, in whose immediate vicinity stood a mean
uncurtained bed, where lay a woman apparently dying. A single female,
sitting near her to administer such assistance as she needed, and a
cold, indifferent looking man, who had his chair drawn up in an opposite
corner of the room, and evidently stationed there more from duty or
necessity than any feeling of interest, were the sole occupants beside.
Low murmuring sounds broke from the lips of the dying woman. She was
talking incessantly, as in that thronging of indistinct, though perhaps
not undelightful images that often flit across the brain of the
departing, her thoughts seemed to be wandering over many varied scenes,
and her consciousness of existence to be quickened as it was about to be
closed forever. Her speech was of flowers and of sunshine, and of every
thing fullest of life. Distant, happy years seemed to be restored to
her, for her imagination transported her back to the era of her
childhood, and she talked of wandering in old familiar places with her
companions, many of them dead and gone—for by some subtle process of
association, those of them mainly seemed present to her visions—and of
"bounding," as she said, "fast, fast" after something she could not
detain. "Let me rest!" she would murmur, "I am breathless with
running—let me rest!" The passionless placidity of the countenance was
in strange contrast with this—and the helplessness of the limbs, which,
cold and nearly motionless, began to assume the semblance of that clay
to which they were fast returning. Suddenly she opened her eyes,
restored to the full consciousness of her situation. The eyes—those
mirrors of the soul which neither time nor sorrow can rob of their
magic, as long as they are the reflection of that which is
immortal—were all that told of Angelica Kauffmann—and the long
chestnut hair, which, though now hard and icy to the touch, still clung
round her temples with some of the old luxuriance of those days when she
dreamed inspired visions by the Alpine streams, or shone, the star of
genius, in metropolitan saloons. For the rest, her features were faded
and pale, their classic outline vanished in the hollows of time and the
sharpness of death—haggard, too, but bearing that pathetic expression
which told it might be the result more of suffering than years. And that
cold, almost repulsive looking man!—can he be the same who knelt beside
her beneath the stars and talked of unperishing love? Yes, such is life!
In those worldly reverses which are too often the doom of the mentally
gifted, poverty and neglect arrived—years of indifference followed, the
character of the lover soon merging into that of the selfish and
somewhat exacting husband—and now it had come to this. Calling him
toward her, he took her proffered hand with a look of cold compassion.
"I have been dreaming strangely to-night, Alexander," said she, "and
have the strangest sensations, as if all past life were passing in
review before me, and its experiences crowded into a few fleeting
hours—circumstances which I had believed long since forgotten, and
feelings which I had thought to have outlived or crushed into oblivion.
Yet there is none that return to me with a more vivid consciousness than
my old feeling for you; and even now I seem to leap back over long,
weary years of coldness, indifference, and estrangement, and the sad
imprints with which they have dimmed your features, and to see you stand
before me, ardent and beautiful as when I dreamed that Heaven had no
brighter reflection than the fondness of your eyes. You will pardon
this," said she, on perceiving that such sympathies moved him not; "I
have no wish to recall you to the past, nor too late to revive an
extinguished affection, which can so seldom be brought into review
without pain—far less with a thought of reproach for any, except for
myself. It is but to testify to you in parting, that with the life I
have led, happy as it was before I knew you—spent amid dreams of
beauty, and the caresses of a family that sympathized with the delights
of my calling, and were proud of my fame, honored as it afterward became
when my achievements as an artist, extolled in every country in Europe,
drew me forth from my retreat to receive that brief and brilliant
homage, less intoxicating to me on the score of my individual self, than
as a tribute to the success of that art to which I had consecrated the
energies of my existence—yet there is no part of it I would willingly
live over again but the early, too brief moments spent near you—no part
of it than this I more fervently hold to my heart, as the true gold
hoarded from what else appears, in this hour whose solemnity dispels all
illusions, the dross and scum of existence. Does not this prove that
love is immortal? And now a thought has struck me, that that sweet,
bright blossoming which, alas! for us yielded so little fruit, may yet
offer a harvest to be reaped in some other world. Will you think of
this, Alexander?—let us part forgiving each other—our next meeting
will be happier—and brighter!"
She turned her eyes toward the window, which had been thrown open to
admit the cool air of the evening, for the wind had died away, and the
heavens were clear—and there, conspicuous amongst its fiery brethren,
shone that bright, still, solitary star—still fair and tranquil, when
life with all its excitements and hopes was passing away, as when
shining above the passion of her young life. It spoke to her of the
glory of other worlds contrasted with the vapidity of this, which she
had weighed in the balance and found wanting—a high and unchangeable
emblem of that _which is above us_ amid all the storms, treacherous
calms, and exulting yet bewildering spring-tides of life—the star of
her destiny, indeed, if it pointed to Heaven as the haven where her
hopes should at last find rest! Her soul passed away in that gaze; they
could not tell the exact moment when, but by the dull fixture of the
eye, and the dead weight of the hand which lay in his, Alexander knew
that he gazed upon the dead.
That oracle spoke truth, which told there is nothing stable in the
universe but Heaven and Love!
* * * * *
THE PAST.
In her strange, shadowy coronet she weareth
The faded jewels of an earlier time;
An ancient sceptre in her hand she beareth—
The purple of her robe is past its prime.
Through her thin silvery locks still dimly shineth
The flower-wreath woven by pale mem'ry's fingers.
Her heart is withered—yet it strangely shineth
In its lone urn, a light that fitful lingers.
With her low, muffled voice of mystery,
She reads old legends from Time's mouldering pages;
She telleth the present the recorded hist'ry,
And change perpetual of by-gone ages.
Her pilgrim feet still seek the haunted sod
Once ours, but _now_ by naught but memory's footsteps trod.
E. J. E.
* * * * *
SLY LOVE.
OR COUSIN FRANK.
BY MRS. CAROLINE H. BUTLER.
CHAPTER I.
HUSBAND AND WIFE.
Back and forth, up and down—creak, creak, creak, strides Mr. Hazleton.
From the back parlor to the front, from the front to the back—his head
down, his lips firmly compressed, his arms crossed behind his back,
while, by the knitting of his brows and the occasional jerk he gives his
head, it is very easy to see that the mind of Mr. Hazleton is crossed
also.
And how perfectly unconscious sits the lady in black satin upon the
sofa! With what a nonchalant air she beats the time with her foot, upon
the little _brioche_, to the air she is humming. The spirit of the
storm—yet herself how calm! Nothing vexes an angry man more, perhaps,
than indifference to his anger. Mrs. Hazleton knew her advantage, and
she also knew she was idolized, as young and pretty wives are apt to be,
whose husbands, like poor Mrs. ——, are a "score of years too old."
Pretty sure, therefore, of carrying her point in the matter under
debate, she highly enjoyed this unwonted ebullition of anger in her
usually placid husband. By degrees the features of Mr. Hazleton
softened—his step became slower and lighter, and then approaching the
sofa, he said, in a tone which was evidently meant to be conciliatory,
"Come, come, this is all very foolish. I think I know your goodness of
heart too well, my dear Anna, to believe you serious, or that you will
receive so ungraciously the child of my only sister."
"Mr. Hazleton, I tell you again," replied the lady, carelessly playing
with her eye-glass, "you are demanding a most unheard-of thing! Were she
only coming here for a few days, to see the _lions_ and be off to the
woods again, I assure you I would be the most attentive chaperone. I
would escort her from one end of the city to the other with the greatest
pleasure, and load her off with ribbons, gew-gaws, and the latest novel,
when the joyful moment came for my release. But a fixture for the
winter—and that, too, my dear Julia's first winter—O, heavens!"
Something very like an oath whistled through the teeth of Mr. Hazleton.
"Madam—Mrs. Hazleton—let me tell you I consider your remark as
reflecting upon myself. No relative of mine, madam, can ever disgrace
either yourself or your daughter, in any society."
"Indeed!" was the cool reply.
"And I insist upon your treating my niece, Alice Churchill, not only
with politeness, but with kindness—and your daughter also must be
schooled to meet her as her equal."
"Her equal, indeed!" and now the ire of Mrs. Hazleton was fast kindling
to a flame. "Her equal! I would ask you, Mr. Hazleton, if the Ninnybrain
blood flows in her veins?—the Ninnybrains, Mr. Hazleton, one of whom
was maid of honor to a queen—another—"
"Pish!" interrupted Mr. Hazleton, "and confound all the Ninnybrains!"
"Confound the Ninnybrains! Very pretty, really—yes, so much for
marrying beneath me! Confound all the Ninnybrains, I think you said!"
"Yes, and I repeat, confound them all! What have they to do with my poor
little Alice?"
It was now Mrs. Hazleton's turn to sail majestically from room to room,
muttering,
"_Hem!_ very pretty treatment—very pretty, indeed!"
While her husband, throwing himself into the seat she had just occupied
upon the sofa, very coolly knocked his heels upon the unfortunate
footstool. At length the lady paused in her walk, and turning to her
husband, said,
"My dear," (and when Mrs. Hazleton said "my dear," it was no idle word,)
"I think you misjudge my motives entirely for what I have said. It is
only for the good of your dear niece, for of course she must be very
dear to you, and no doubt she is a very sweet girl, that I have raised
any objections to her becoming a member of our happy family—no doubt,
my love, she would prove a great acquisition—but—_hem_—but I think I
have heard you say your sister, our sister Churchill, was in rather
limited circumstances, and has been obliged to use great economy in
bringing up her family. Now I ask you, my dear, if—if—we should not be
doing wrong, very wrong, to vitiate the simple, happy tastes of Alice,
and render dull and uncongenial the home of contentment in which she has
ever so peacefully dwelt? This surely would be the case were we to
introduce her into the gay world. So perfectly unsophisticated as she
is, she would the more easily be led astray by the frivolities of
fashionable life. Would it not be better for her, then, better for her
dear mother, that this visit should not take place?"
"No, I tell you no!—she shall come, she shall go everywhere, she shall
see every thing the city has to boast."
"That can easily be done, love, in a few days," replied the plausible
lady. "Some pleasant morning you can go with her to the Museum, and
Girard College, and the Water-Works. When I spoke of her going out, I
meant to parties—"
"And I mean to parties, and to theatres, and concerts, and—"
"You are absurd, Mr. Hazleton!"
"Go on!"
"You have no regard for my feelings!"
"Go on."
"You would willingly mortify me, and embarrass my sweet Julia, by
linking her in companionship with this uncultivated hoyden!"
"Go on."
"And also ruin the girl!"
"What next?"
"No, let me tell you, Mr. Hazleton, it must not, shall not be. Julia
shall not be put to the blush continually for the solecisms this niece
of yours will commit upon the rules of etiquette!"
"Little dear!"
"And, and—and, Mr. Hazleton—Lord, I wish I had never married!" and
Mrs. Hazleton burst into tears.
Mr. Hazleton walked out.
CHAPTER II.
A BACHELOR IN CUPID'S NET.
In blessed bachelorhood had passed sixty years of Mr. Hazleton's life.
With no one's whims but his own to nurse—no one to scold but his tailor
and washerwoman, their flight had left little trace save in the silver
threads with which Time weaves experience—linking the what has been to
the what is and what will be. It is true, in early life he had wooed but
not won, and it might be from disgust at the willful blindness of the
lady of his love, he from that moment looked coldly upon the whole
sex—blind to their beauty—deaf to their voices, and invulnerable to
all their witchery, "charmed they never so wisely."
But, alas! the work of years may be shattered in a moment! Hard as the
heart of Mr. Hazleton had become, it melted like the frost of an autumn
morning under the sunny beams of Mrs. Ketchim's eyes! It was at
Saratoga, that great hunting-ground of Cupid, that Mr. Hazleton first
encountered the glances of the pretty widow. Whether that lady was in
truth on a matrimonial chase cannot be definitely stated. Yet one thing
is certain, no sooner did she meet with this rich, hard-hearted old
bachelor than she determined to forget her departed Ketchim, and catch
him—thus nobly avenging in her own person the slights her sex had
received. What could not a fair and handsome widow accomplish with
"sparkling black e'en and a bonnie sweet man!" Mr. Hazleton was lost.
The age of the widow was an enigma which no one but herself could solve.
She did acknowledge she was _too_ young—she did also own to the
interesting fact that one sweet child called her "mother." "Ah, a little
golden-haired cherub, of some four or five summers!" thought our lover.
What, then, was the surprise of Mr. Hazleton when, a few weeks after
their marriage, a tall, beautiful girl of seventeen rushed into the
parlor, and, giving him a hearty kiss, called him "papa!"
He had abjured spectacles, using only the eyes of love, but he now for a
moment involuntarily resumed them, and gazed long and inquiringly at his
charming wife. He was satisfied. Mrs. Hazleton smiled as sweetly, and
looked just as young and bewitching as she had appeared to him
before—so he returned the filial salute of his _daughter_ with a
paternal embrace, and unlocked another chamber of his heart to receive
her.
Some months passed pleasantly on, and the honey-moon waxed not old. The
so long time bachelor almost wept with sorrow over those lost years
spent alone, and blessed the hour which had harbingered his present
happiness. By degrees a little, a very little difference of opinion
began to display itself—but insensibly gathering strength from frequent
recurrence. Most generally, however, the husband yielded, and harmony
was restored.
Julia was a lively, good-hearted girl—her faults more the result of her
mother's mismanagement than her own willfulness. In fact, it was Julia
herself who first suggested the invitation which Alice Churchill
received from her uncle.
"Dear me, papa, how dull it is! Pray have not you any relations?" she
inquired one evening, when they were left _tête-à-tête_.
This was rather a posing question, for indeed Mr. Hazleton could hardly
remember whether he had any or not.
"No sisters, or nieces?" continued Julia.
"Or nice young nephews?" added Mr. Hazleton.
"Yes, papa—a cousin would be so delightful!" and here Julia sighed and
looked sad. Why she sighed the reader shall know bye and bye.
This careless remark of Julia aroused a train of long banished
reflections in the mind of Mr. Hazleton. Early associations came
thronging upon him, vividly calling up the image of his only sister, as
tearfully and patiently she had turned from his reproaches at their last
meeting, to follow the fortunes of him she loved. Ere Mr. Hazleton
sought his pillow, the letter to his long neglected sister was written,
and not even the possession of the late Mrs. Ketchim had made his heart
so light as this simple act of duty and kindness.
Mrs. Hazleton had many weak points, but there were two upon which she
was peculiarly sensitive. The first, viz.—her family. The Ninnybrains
could trace a pedigree almost as far back as Adam—a sprig of nobility,
too, had once engrafted itself upon the family tree, which important
item had been handed down from generation to generation, and Mrs.
Hazleton never lost an opportunity of proclaiming her noble lineage,
while at the same time she indulged an almost slavish fear of deviating
from the code of gentility, in _her_ acceptation of the term. Her second
tangible weakness was an affectation of juvenility. The idea of growing
old gracefully was preposterous. Although she saw the seams and creases
of Time's fingers on other faces, she would not see them on her own, and
while all the world were growing old around her, she resolved to set the
gray-beard at defiance.
Mrs. Hazleton loved her daughter as much as she was capable of loving,
yet she could not forgive her for the very contradictory evidence she
brought against her youthfulness—could not pardon her for stepping
forth from the nursery a tall, grown up girl, instead of quietly
contenting herself with pantalettes and pinafores. The widow felt there
must be a rapid race, or her daughter would reach the goal of Hymen
before her—hence her conquest of Mr. Hazleton. Her own purpose
attained, she then generously resolved to give Julia a chance, who,
nothing loth, was summoned from a country boarding-school to catch a
husband as quick as possible. To be sure this latter clause was not
expressed in so many words—it was the ultimatum of the mother alone. As
for Julia, she thought only of escaping from the odious Mrs. Rulem—of
new dresses, theatres, and dancing till two o'clock in the morning. For
once, then, Mrs. Hazleton concluded to assume maternity gracefully, and
to matronize her daughter with all the dignity of the Ninnybrain school.
She was exceedingly annoyed, therefore, when she found her plans might
all be defeated by the arrival of Alice Churchill. No way could she
reconcile herself to this unavoidable evil. If handsome and engaging,
she would only be in the way of her daughter's advancement—if awkward
and ugly, a constant source of mortification. Every device of which she
was mistress was put in practice to thwart the expected visit, but that
she did not accomplish her object has already been shown.
CHAPTER III.
THE ARRIVAL.
Alice Churchill was none of those fragile beauties whose step is too
light to bend "a hare-bell 'neath its tread"—whose eyes are compared to
those of the gazelle, or to violets and dew-drops—with cheeks like the
blush rose, and lips vieing with sea-corals, contrasted by teeth of
pearls! No such wealth of beauty had Alice, but she was a very sweet
girl notwithstanding—just pretty enough to escape being called plain,
and yet plain enough to escape being spoiled for her prettiness. Mrs.
Churchill was a widow of very moderate fortune, living in a retired
village of Pennsylvania, more than fifty miles from any town of note,
and which even in the year '45, (happy little village!) could boast of
neither steam-boat nor railroad. It was here she had removed with her
husband soon after their marriage, and here for a few brief years their
happiness had been unclouded—until the shadow of death resting on that
happy home severed all earthly ties. Peaceful now in the quiet
grave-yard is the sleep of the husband and father.
Seventeen summers of Alice's life had passed away—not all cloudless,
but happily—for she was kind and affectionate—in making others happy
she was herself so—indeed, as I said before, although she had no wealth
of beauty, Alice was rich in goodness and purity of heart. Mrs.
Churchill had offended her family by marrying a poor man, and there had
been little or no intercourse since that period. When, therefore, she
received a letter from her brother, not only affectionate, but
accompanied also by a kind invitation for her daughter Alice to pass a
few months in Philadelphia, it is difficult to say whether joy or
surprise preponderated. Anxious alone to promote the happiness of Alice,
Mrs. Churchill, sacrificing her own feelings at parting with her child,
hesitated not to accept the offer. Little did Alice know of the world,
except from books. Books had been her only companions, and, under her
mother's judicious selection, these best of friends had wrought a silent
influence over her mind, preparing her to meet the realities of life,
its pleasures and its trials also, with rationality.
Such, then, was Alice Churchill, the innocent cause of the matrimonial
_fracas_ illustrated in a preceding chapter.
The boat touched the wharf, and the motley crowd which had been watching
her approach, noisily sprang on her deck. "Have a cab, miss?" "Cab,
sir?" "Take your baggage, ma'am?" "Have a carriage?" Poor Alice shrank
back into the farthest corner of the ladies' cabin, perfectly bewildered
with the noise and confusion. At length she heard her own name called,
and, stepping forward, she was the next moment in the arms of her uncle.
Mr. Hazleton embraced her affectionately, and then, gazing long and
earnestly upon her, exclaimed, as he wiped a tear from his eye—
"Yes, you do look like your dear mother!"
But this was no time for sentiment, especially as the stewardess,
anxious herself to be on shore, already began to bustle about
preparatory to the next trip—so, after attending to the baggage, they
left the boat, and were soon rattling through the streets at the mercy
of an independent cabman who "_had another job_."
Who that has passed through the streets of a great city for the first
time cannot imagine the feelings of our simple country-girl, as she
found herself thus borne amid the busy throng—the side-walks crowded
with people hurrying to and from their business—the gaily ornamented
windows—elegantly dressed ladies—beggars—squeaking
hand-organs—dancing monkeys—the cry of the fish-man, mingling with the
noisy bell of the charcoal-vender—carriages clashing rapidly
past—omnibuses rattling heavily along—dust, din, smoke—no wonder the
poor girl rejoiced when the cab stopped at her uncle's dwelling, and she
found herself safe within its walls.
"My dear love, let me have the pleasure of introducing you to my niece,"
said Mr. Hazleton, advancing with the blushing Alice on his arm.
Mrs. Hazleton coldly raised her eyes from the book on which they had
been pertinaciously fixed, and with a slight bow and a formal "How do
you do, Miss Churchill!" as coldly dropped them again.
Not so Julia, who, in spite of the lessons her ma'ma had been teaching
her for the last half hour, could not see this young, blushing stranger
so repulsed—she therefore rushed forward, exclaiming—
"O papa, do stand away, and let me greet my new cousin."
"_Julia!_ my dear!" emphasized Mrs. Hazleton.
"Now, my dear Alice—that's your name, is it not? Mine is Julia—Julia
Ketchim—horrible! don't you think so? Now you must not wonder at
ma'ma—she is a great reader—she has got hold of Carlyle—but she is
very glad to see you—so are we all—but that's her way. Come, sit
down—or would you prefer to go to your room?"
"Julia, I am surprised!" and Mrs. Hazleton rang the bell.
A servant entered.
"Show Miss Churchill her apartment."
"O no, ma'ma, I am going with Alice."
"Nancy, attend Miss Churchill. Julia, I want you—_Julia!—Julia!_" and
with pouting lips and a very flushed face Julia was forced to obey, but
not until she had whispered to Alice, who, almost terrified, was
following the servant maid:
"Never mind ma'ma, dear—she is great upon etiquette—she is a
Ninnybrain you know."
There was an attempt at a Caudle lecture after Alice had left, but to
her dismay Mrs. Hazleton found her influence, like the honey-moon,
rapidly on the wane! When Alice again appeared in the drawing-room
escorted by Julia, who, in spite of ma'ma, had contrived to slip away to
her apartment, Mrs. Hazleton for the first time allowed her eyes to
dwell searchingly upon the person of her unwelcome guest. To her
inexpressible relief she found Miss Churchill presented that happy
medium of which she had never dreamed, viz. that although her
countenance was pleasing, yet she was by no means handsome enough to
cause her one moment's fear on the score of rivalship—while her natural
ease of manner at once removed her from that awkward simplicity she had
expected to find in an unskilled country girl. The effect of her
scrutiny, therefore, was so satisfactory that Mrs. Hazleton with a
pretty, girlish air instantly embraced her, and trusted she would feel
herself as much at home as under her own dear mother's roof. Although
somewhat surprised, Alice did not doubt the sincerity of her welcome,
and grateful for her kindness, returned her aunt's embrace. Mr. Hazleton
gave his wife a smile of approbation, while Julia whispered:
"There, I told you so—O that odious Carlyle—I knew ma'ma would be glad
to see you when she had put down her book."
At the close of the evening, after the girls had retired, Mrs. Hazleton
affirmed that really Miss Churchill was quite passable, and that if her
manners only had a little of the Ninnybrain air—as, for instance,
Julia's or her own—one would hardly suspect that she had never been
accustomed to good society! Upon which wondrous conclusion of his lady,
Mr. Hazleton shrugged his shoulders and went to bed.
CHAPTER IV.
COUSIN FRANK
Alice and Julia were soon good friends—and by degrees Alice became the
confidante of a little episode in the life of her cousin which she
feared might bear heavily upon her future happiness, unless her
affections were as the wind-kissed lakelet—disturbed only on the
surface—the heart-depths unmoved.
At first Julia only spoke of "Cousin Frank" as being such a "dear, merry
soul," "so pleasant," "so kind"—she next admitted that she loved him
"dearly, very dearly," indeed she did—and that he loved her just as
well, poor fellow!—and finally, blushing like a rose, she acknowledged
that both hand and heart were pledged to "dear Cousin Frank!"
But did ma'ma know any thing about it? Not she indeed! A pretty fuss she
would make to find out she loved Frank—a poor midshipman in the navy,
that had not even a drop of the Ninnybrain blood to compensate for want
of fortune! No indeed! But they had vowed to be faithful, and that was
enough—Cousin Frank was too proud to say a word to ma'ma until he had
won laurels as well as money—poor fellow! and so Julia cried one moment
and laughed the next.
It appeared they had become acquainted at the house of a mutual relative
in the village where Julia had been placed at school by her youthful
mother. Cousins are without doubt a very dangerous allotment of the
human family, as it proved in this case, for Frank Reeve came near
losing his examination before the navy-board, while Julia, instead of
treasuring up the wisdom of Mrs. Rulem, was filling her little brain
with love, and such nonsense—just as naughty girls will sometimes do
for their cousins!
Mrs. Hazleton would indeed have made a fuss had she known of this. Far
different views had she for her daughter, and she would have spurned the
poor midshipman's love as most presumptuous.
It was now the joyous season of the holydays—when happiness and mirth,
pleasure and folly trip hand in hand, gladdening this _once a year_ the
beggar and the bondman, and sweeping triumphantly through the halls of
wealth and fashion. Parties and balls followed each other in rapid
succession, and on the topmost wave of this tumultuous sea giddily
floated Mrs. Hazleton. How the money fled from the well-lined pockets of
Mr. Hazleton into the hands of tradesmen and milliners—smooth hard
dollars, and soft silky scraps of paper exchanged for rings and
bracelets, that the dress of both mother and daughter might be all as
fine as money could purchase or fashion form. Alice seldom accompanied
her aunt and cousin into these gay scenes. A short essay in fashionable
life sufficed for her quiet tastes and habits, and she preferred
therefore remaining at home with her uncle, who was no less pleased to
have her do so, as with her he could talk over the scenes of his early
life, and he loved too to listen to her own artless details of mother
and home. Nor was Mrs. Hazleton sorry for Alice's decision. She was
often surprised to find that her modest pretty face, and her unaffected
manners, attracted nearly or quite as much attention as the brilliant
charms of Julia, so that on the whole she rather countenanced her
remaining _tête-à-tête_ with her uncle. "O you dear, quiet little soul,"
she would often say, "you must marry a country parson, and knit
stockings."
One evening, Mrs. Hazleton came home from a large party in high spirits.
She had marked her future son-in-law, and Julia had now only to bring
down the game! Full, therefore, was she of the praises of young Herman
Wallace. He was not only very rich, very handsome, very graceful, but of
an ancient Scottish family—could trace his descent even from the great
hero, Sir William Wallace—at least Mrs. Pryout had said so.
"But, ma'ma," interposed Julia, "he is the stiffest, coldest mortal—a
beautiful petrifaction of man! When at last you got an opportunity to
introduce me,"—and Julia, sly girl, remembered how blind she had been
to many winks and nods and "wreathed smiles" of managing ma'ma,—"he
looked down upon me with those great black eyes—oh, so cold and
disdainful—he might just suit you, Alice, but as for me—"
"Nonsense!" interrupted Mrs. Hazleton, "he did no such thing. I tell you
what first drew my particular attention to _him_, was his very evident
admiration of _you_!"
"Indeed, ma'ma!"
"Yes, indeed, silly child. I overheard him asking who that very
beautiful girl was in blue and silver—"
"O, ma'ma!"
"I don't wonder he asked, however, for you did look sweetly. It was when
you were waltzing with young Langden, and as you floated so sylph-like
around the room, I could not help thinking of a portrait I once saw
of—"
"A Ninnybrain, ma'ma?"
Mr. Hazleton burst into a hearty laugh, in which the saucy girl as
heartily joined, and even Alice could not refrain a smile. Mrs. Hazleton
was evidently disconcerted, but too well pleased with her plans to be
angry.
"You will see him again to-morrow evening, love," she continued, "and I
think you will alter your opinion."
"By the way, Alice, you promised to go to Mrs. Dashwood's grand party,"
cried Julia; "so you will be able to judge of ma'ma's prodigy;" and
then, as they left the room, she whispered, "Talk of _Herman Wallace_,
indeed! I would not give one of dear Frank's heart-glances for all his
frozen lordly looks!"
CHAPTER V.
MRS. DASHWOOD'S PARTY.
The toilet of the fair Julia, for this eventful evening, was made under
the tasteful eye of Mrs. Hazleton herself, who wished her daughter to
look her loveliest—to eclipse all other stars in that brilliant galaxy
of youth and beauty. Next, the adornment of her own person was her chief
care—upon Alice she bestowed not a thought. Julia would fain have had
the dress of her friend as beautiful as her own, but this Alice rejected
as unsuitable, and made her appearance in the dressing-room of her aunt
in a simple white muslin, her only ornaments a set of corals, the gift
of her uncle. Mrs. Hazleton enrobed in crimson velvet, and Julia
radiantly lovely in white satin and blonde, offered a striking contrast
to the unpretending Alice.
"Well, child, you really look quite well—don't she, love?" was the
careless remark of Mrs. Hazleton, "but only see what a rich color Julia
has!—I think I never saw her look so perfectly lovely—quite mature,
don't you think so?—more like me! Why what have you got on?—white
muslin over a _plain cambric_! Mercy, had you not a silk skirt? Julia's
tunic is magnificent—I paid one hundred dollars for the lace at Levy's.
Corals are too warm, child—but they will do very well for you—they
won't be noticed. Come here, Julia, and let Alice examine the chasteness
of that beautiful aquamarine bracelet—now the ruby—and look at her
pin, Alice, is it not superb!"
But a brighter jewel was in the breast of Alice—_a heart free from
envy_!
And now over the tessellated floor fair and lovely forms are
gliding—music pours its enchanting strains, and voices scarcely less
sweet float on the perfumed air—jewels flash, feathers wave—there are
smiles on the brow of beauty, soft speeches on the lips of manhood.
But why, amid this joyous scene, is the brow of Mrs. Hazleton clouded?
Admiration can find no higher aim than the charms of Julia; nor does her
own ear drink in unwelcome the flatterer's whisper—yet still the cloud
is there. Would you know the reason? Herman Wallace makes not one of the
festive throng. She is almost angry with Julia for being so carelessly
happy—with Alice for her composure. Suddenly her eye brightens. Ah, the
game's in view! And in a few moments Mrs. Hazleton, now all smiles,
presses on to the gay circle of which Wallace seems to be the
attraction. She soon fastened upon him, and led him off triumphant to
the spot where she had a moment before seen Julia—but Julia was gone,
and Alice alone remained, quietly viewing the scene before her. Mrs.
Hazleton, however, took not the slightest notice of her, but continued a
ceaseless strain in the ears of Wallace. Did not Mr. Wallace like
waltzing? Mr. Wallace did not. The polka? Decidedly not. Was Mr. Wallace
fond of music? Not in a crowded room.
Mr. Wallace now turned his eye upon Alice. Could Mrs. Hazleton tell him
who that interesting looking girl was?
"O, a niece of my husband's—poor child! You know, my dear sir, every
family cannot look back upon a pedigree like yours—like mine, I was
going to say—a very good sort of girl, though, but poor, and all that
sort of thing."
Yet the descendant of a "noble pedigree" asked for an introduction to
that "good sort of a girl," which, with a very ill grace, was granted.
Julia now joined them, and a lively conversation ensued, which Mrs.
Hazleton with great chagrin saw interrupted. The fair hand of Julia was
claimed for a dance, and away she tripped. Mrs. Hazleton, too, soon
followed, to bring her back the earliest moment, leaving Alice and
Wallace alone.
There was a pause of a few moments, when, with some embarrassment,
Wallace said,
"The interest I feel, Miss Churchill, in a very dear friend, must be my
apology for what I am about to say. He is a noble, generous fellow, but
I fear has recklessly given his affections where they are but too
lightly prized. You look surprised, Miss Churchill—I allude to Francis
Reeve. I think you can be no stranger to the relationship existing
between him and Miss Ketchim."
"I have frequently heard Julia speak of her cousin, Mr. Reeve," replied
Alice.
"And no more! Has she never told you they stand in a far nearer light
than mere cousins?"
"I will be candid with you, Mr. Wallace. Julia has confessed to me her
affection for your friend."
"Her affection! Then you think she does love him?"
"Most sincerely."
"Is it possible! And has she a heart—she who seems to be the mere sport
and puppet of fashion!" exclaimed Wallace.
"Indeed she has, and a warm one, too," replied Alice. "You must not
judge of her as you now see her—that she is very volatile I
acknowledge, but most affectionate and sincere."
"I rejoice to hear you say so," answered Wallace. "You know not, Miss
Churchill, the ardor of my friend's attachment. True love is always
jealous—and you surely then cannot blame poor Frank, when, on his
return from a long voyage, he hears of her only as the gayest among the
gay, receiving with apparent pleasure the flatterer's insidious
praises!"
"She is not alone to blame, Mr. Wallace. Believe me, with all her
seeming indifference, she is worthy the love of your friend," said
Alice.
"I surely can no longer doubt her worth when I find her so ably
defended, and by so amiable a champion," answered Wallace, bowing. "May
I then ask you to deliver her this note, with which poor Frank, in an
agony of jealous doubts, has entrusted me?"
Ere Alice could reply Mrs. Hazleton and Julia joined them. What could
have brought such a glow to the cheek of Alice? thought her aunt—and
Wallace, too, how animated! whose eyes were bent on the plain
country-girl with an expression of admiration which caused the heart of
this worldly woman to swell with envy and mortification. But dressing
her countenance in well-feigned smiles, she exclaimed—
"Really, you seem to be having a very interesting discussion—I have
been watching you some time. Come, I am dying to know what it is—and
here is Julia, too, all curiosity."
Wallace made some cool reply to Mrs. Hazleton, and then, turning to the
latter, began conversing with her so entirely different from his former
manner, that she was astonished. He was no longer the "petrifaction" she
had pronounced him, but animated and agreeable. She little thought how
much she was indebted to the praises of Alice for this change. Mrs.
Hazleton noticed this also, and her jealous fears subsided. The deer is
wounded at last! was her exulting conclusion.
That may be, my good madam—but the shaft may have sped from another
source, nevertheless!
"Do come into my room," said Julia to Alice, upon their return from Mrs.
Dashwood's party. "For mercy's sake! let me get away from that Scotch
bag-pipe ma'ma is ever sounding! One would think she was in love with
Herman Wallace herself—but I'm sure I am not—though, just as plain as
looks can speak, she tells him, 'Here she is—you may have her for the
asking.' If this is Ninnybrain dignity, I beg to be excused from sharing
it. I wonder what poor Frank would say? But how happy you look,
Alice—what is the matter? After all, I believe poor ma'ma's trouble has
all been thrown away.
'Yet marked I where the bolt of Cupid fell—
It fell upon a little western flower.'
Ah, ah! Alice—now confess—has not this descendant of heroes been
saying tender things to you?"
"He has, indeed, talked of love!" said Alice, laughing.
"Oh, excellent!" cried the giddy girl, clapping her hands.
"But alas for your theory, you were the object," continued Alice.
"_Me?_"
"Yes, you—and one other—and that other was—can't you guess?"
"No, Ally dear, you talk in enigmas."
"Which perhaps this may solve," and kissing her blushing cheek, Alice
placed the note in her hand.
Julia screamed with surprise and pleasure, as she recognized the beloved
handwriting. When she looked up her friend had left the room.
There was a light tap at the door of Alice's chamber, and Julia entering
threw herself upon her neck, covered with tears and blushes.
"Oh, my dear Alice, he has come! Frank is here—in this city! How happy
I am—and—and, oh dear, what shall I do? He wishes to come and see me!
Ma'ma will be so angry—I dare not—what shall I do? Dear Alice, do tell
me."
Alice advised her to accede unhesitatingly to the wishes of her lover,
urging her no longer to have any concealment from her mother. Perhaps,
after all, her fears were groundless, and she might sanction her choice.
In any event, this clandestine intercourse must not continue, and Alice,
"severe in youthful beauty," endeavored to point out the great fault she
would be committing against her parent by allowing it to proceed
further. Julia was overcome by the serious manner in which Alice spoke.
She had never before allowed herself to reflect upon her error in its
true light—her mother's anger had been her only fear—but she now
resolved to break the subject at once to her mother, and ask forgiveness
for her fault.
CHAPTER VI.
COUSIN FRANK AGAIN.
Breakfast was over—Mr. Hazleton gone to his office—Alice to pen a
letter to her mother—and Julia was left alone with Mrs. Hazleton. It
was no light errand upon which she was bent, and gladly would she have
followed her cousin from the room—but an encouraging smile from Alice
re-assured her. Yet how to open the dreaded subject? Several times she
essayed to speak, but the words died upon her lips. Meanwhile Mrs.
Hazleton, in a most voluble strain, was planning characters and dresses
for a fancy ball. So far as Julia herself was concerned, the Scottish
Chiefs were chosen for the field of display—deciding she should go as
Helen Mar, and she was now trying to fix upon some character calculated
to set forth her own charms to the best advantage.
"What do you think of Die Vernon?" said she turning to Julia—"or would
Flora McIvor suit my style better—perhaps Mary, Queen of Scots, or—but
what is the matter with you? How stupid you are! Why don't you speak? I
declare I believe you will get to be as dull as Alice Churchill. What
ails you?"
"Nothing, ma'ma—I—I only—"
"Only what? do speak!" cried Mrs. Hazleton, impatiently.
"I only wanted to tell you that—that Frank Reeve is in town," stammered
poor Julia.
"And pray who is Frank Reeve, to call such a blush to your cheek?"
"Why, dear me, ma'ma, you know Cousin Frank Reeve!"
"No, I don't know Cousin Frank Reeve!" exclaimed Mrs. Hazleton, turning
very red—"neither do I wish to know him."
"Why, ma'ma, he is so pleasant—so delightful!"
"_Is he?_ Well, Miss Julia, that is no reason why I should know him, or
you either—and, let me tell you, if you have any ridiculous, childish
_penchant_ for 'Cousin Frank,' you had better banish it at once!" and
Mrs. Hazleton looked very knowing.
"Ma'ma, I—I don't understand you."
"O yes you do. I have said enough—so no more of Frank Reeve. Now tell
me if you can what were the colors of the _Vich-ian Vohr_ plaid—Alice
knows I dare say—go and ask her." And glad of an excuse to leave the
room, Julia quickly withdrew.
Mrs. Hazleton spoke the truth—she did not know Cousin Frank, though the
nephew of the departed Ketchim. She had never seen him—but she had
heard of moonlight walks and tender billet-doux. In her widowhood, so
long as Julia was out of the way, she cared little which most occupied
her time—books or a lover. The case was now altered. She had a higher
object to be accomplished, to which the plighted affections of her
daughter must be made to yield—what did she care for the affections!
Poor Julia's eyes were swollen with weeping—her head ached intolerably,
but her heart ached worse. There was a ring at the door—she listened—O
happiness! ma'ma was out—and there was Cousin Frank! What could Julia
do! What _did_ she do but rush down stairs and burst into a fresh flood
of tears on Cousin Frank's shoulders! Very improper, was it not?
However, we will not stop to argue the matter now, but rather adopt Jack
Easy's system—finish the story first and have the argument afterward!
As interesting as our pair of lovers undoubtedly were to themselves, a
third party might not form the same opinion. We will not intrude,
therefore, but content ourselves with marking the result of this
interview, which was that Julia from that hour appeared in excellent
spirits, quite delighting ma'ma with her praises of Herman Wallace, and
never once mentioning the name of Cousin Frank again—simply amusing
herself when alone with kissing mysteriously folded billets, and penning
little rose- notes—surely there was no harm in that!
In the meanwhile Wallace had become a constant visiter. Although Alice
was generally in the room upon these occasions, Mrs. Hazleton had no
longer any fears. Wallace to be sure was very polite and
agreeable—brought her books—sometimes reading a favorite passage—of
course, why should he not? and so Mrs. Hazleton herself began to treat
her with more attention—but with Julia he would chat in a low voice in
snug window seats, or remote corners, while she in turn seemed to lend a
willing ear—blushing, smiling, and evidently very happy. "Ah, there
certainly must be some understanding between them!" thought the
delighted Mrs. Hazleton.
CHAPTER VII.
MASQUERADING.
Mrs. Hazleton resolved to give a party which should eclipse in splendor
all those to which the gay season had given rise, and Mr. Hazleton,
willing to gratify her, had placed both his purse and time at her
command. For once every thing went favorably—the presiding Fates were
all on the side of Mrs. Hazleton. Taste and elegance marked the
upholsterer's high finish—the rooms were flooded with that soft, mellow
light which throws so becoming a shade o'er the cheek of beauty—music
was to lend its charms—and the luxuries of every clime were gathered on
the refreshment tables, mingled with all those tasteful little devices
which the skill of the confectioner can compound. So far well, and Mrs.
Hazleton, bowing to herself as she took a last survey in her mirror,
pronounced the image superb!
Mr. Wallace had begged permission to bring a friend—certainly, any
friend of his would be most welcome. The rooms were already rapidly
filling, when trembling and blushing Julia saw Mr. Wallace approaching,
and with him—_Cousin Frank_! And how handsome the fellow looked, too,
and what a joyous, happy glance met hers!
"Allow me to present my friend, Mr. Francis—" the rest was somewhat
unintelligible—and Mrs. Hazleton most gracefully bent to the modest
salute of the stranger, and then turned to introduce her daughter also.
It certainly was praiseworthy in Julia not to know cousin Frank, as her
mother had so positively forbidden; so she merely bowed, and that, too,
in the stiffest manner, which bow was as stiffly returned, and then
immediately turning from her, Mr. Francis began an animated conversation
with her mother. It is true that, in the course of the evening, he very
formally invited Miss Julia to dance, who, with a toss of her pretty
head, gave him her hand to lead her off—and that no sooner were they
free from the vicinity of Mrs. Hazleton, than they both laughed right
merrily, and said a great many things which must have been interesting
to themselves, to judge from their looks; nay, more than this, instead
of joining the dancers as they had proposed, they strolled off into the
conservatory!
Mrs. Hazleton seemed blessed this evening with wonderful ubiquity of
vision. She could not only look to the wants of her numerous guests, and
see that each one was placed in his or her peculiar sphere for
display—that the feet of the merry dancers stayed not for music—that
the waiters were all in the quiet performance of their duties; but also
that the actors in her private play of "_Manœuvering_" should not fail
in the favorite parts she had allotted them. Thus when she suddenly came
upon Herman Wallace and Alice evidently much engrossed by some
interesting topic, and discovered the fact that the latter had never
looked so well as on this evening, how adroitly she contrived to
separate them by despatching Alice upon some trifling commission to
another part of the room, and then, with a bland smile, requesting
Wallace to go in search of her dear Julia! In a few moments, however,
Julia appeared, leaning on the arm of Frank, who, by his graceful
compliments, soon restored her good humor; nay, so well did he top his
part in a play of his own, that, although Mrs. Hazleton's eyes were
almost blasted by seeing Wallace leading that odious Alice Churchill to
the dance, while Julia herself was disengaged, she yet had not courage
to break away from his flattering speeches.
"How very much your sister resembles you!" said Frank, recovering from a
sudden fit of absence, during which his eyes had been watching the
movements of Julia.
"My sister!" cried Mrs. Hazleton, blushing and laughing, "my
_sister_!—my daughter you mean."
"Daughter! good heavens!" and here Cousin Frank gave a tragedy
start—"you don't mean to say that lady is your _daughter_! O, no, it
cannot be—the resemblance is certainly striking—the same expressive
eyes, the same noble brow, the full red lip, and luxuriant hair the
same—but your daughter—it cannot be!"
Mrs. Hazleton, however, was obliged to own the "soft impeachment," while
she mentally wished she had not visited Saratoga, or that she had
allowed some other of the sex to avenge the sisterhood on Mrs. Hazleton,
for here indeed was a prize which might else have been hers!
CHAPTER VIII.
UNMASKING!
A few mornings after the party, both Wallace and Francis had a long and
confidential interview with Mr. Hazleton, which resulted in the penning
of a letter by the former to Mrs. Churchill, not, however, without the
consent of the blushing Alice. Mr. Hazleton then went in search of his
wife, whom he found absorbed in reflections which, could he have read
her heart's frivolous page, he would have found not at all flattering to
himself.
"Ah, my dear Anna, I have news for you! Who would have thought young
Wallace so much in love!"
"Ha! why what is it, Mr. Hazleton?" demanded his lady, eagerly.
"Why that he has this morning proposed."
"Indeed! and to _you_—I should have thought—but no matter, I am truly
rejoiced at the dear girl's good fortune—however, I think it would have
been more proper if Wallace had spoken to me first."
"I don't think so, my dear," said Mr. Hazleton.
"No, I dare say not," replied the lady, evidently piqued; "it is to be
sure a mark of respect to your—your years."
"On the contrary, I think it a mark of respect to Mrs. Churchill."
"_Mrs. Churchill!_" exclaimed Mrs. Hazleton, "what has Mrs. Churchill to
do with Herman Wallace's proposals for my daughter?"
"Nothing at all—but a great deal to do with his proposals for her own."
"What! _Alice Churchill!_ You don't mean to say that Herman Wallace has
made proposals of marriage to _her_!"
"Certainly I do—and I have given my consent with all my heart, and I
doubt not, from my representations, her mother will also give hers."
"He is a villain!" exclaimed Mrs. Hazleton. "Have all his devoted
attentions come to this? My poor Julia! has he been trifling with her
affections merely for his own amusement—and has he now the audacity to
offer his hand to another!"
"I thought you were aware, my dear," said Mr. Hazleton, mildly, "that
the affections of Julia were already given to a very deserving nephew of
yours."
"Ridiculous, Mr. Hazleton! I should like to see Julia disposing of her
affections without my consent. Pray, where did you hear this nonsense?"
"From Julia herself," answered Mr. Hazleton. "She would have made a
confidante of you, Anna, but you would not listen to her. She has
acknowledged to me, therefore, her long attachment for Frank Reeve, and
has requested me to intercede with you to sanction their engagement."
"That I will never do," cried Mrs. Hazleton, in a towering passion.
"What!—consent to her marrying a poor midshipman? No, never!"
"But he will rise—he will be promoted."
"No matter if he is—he shall never marry Julia Ketchim!"
"She loves him, my dear, sincerely," interposed Mr. Hazleton. "It has
been an attachment since childhood—would you break her heart?"
"Yes, I would—before I would consent to her becoming his wife."
"But, my dear, will you not see your nephew, and let him plead his own
cause? Do, my dear, reflect upon the consequences of what you are now
doing."
"No, Mr. Hazleton—I tell you I will not see him, and I have already
forbidden Julia. If it had not been for him, and for the artful
machinations of your niece, I might have seen Julia properly
allied—rank with rank."
Mr. Hazleton could swallow a great deal, and he therefore swallowed
this, though with something of a take-physic face. He then resumed:
"Since such, then, is your firm decision, I feel more free to inform you
that the friend of Mr. Wallace, Mr.——"
"Francis."
"The same—has also requested permission to pay his addresses to Julia."
"Ah, indeed!" and now Mrs. Hazleton began to look pleased again.
"He is an old friend of Wallace," continued Mr. Hazleton—"is of a good
family—has great expectations, I am told—and, for my own part, I see
no reasonable objection against encouraging his addresses—that is, if
Julia herself can be persuaded."
"I shall take care of that, Mr. Hazleton. Thank Heaven! the Ninnybrains
are no such obstinate people as some other people I _could_ name. None
of _my_ family ever married against the wishes of their friends, as some
other people's friends have done! Julia will receive Mr. Francis—I
shall command her to do so."
And as Julia had made up her mind to be henceforth very dutiful to
ma'ma, she promised, like a good girl, to transfer all her affections
from Cousin Frank to Mr. Francis, and most submissively and demurely
consented to receive his visits.
The wooing sped rapidly, and the happy day was already appointed for
their nuptials, when Julia took an unaccountable freak in her head that
she could not be married unless Cousin Frank was present at the
ceremony! Mrs. Hazleton ridiculed—Julia insisted—and finally Mrs.
Hazleton concluded to do the amiable, and wrote:
"DEAR NEPHEW—
"I hear you have been in town some weeks. Am surprised you have
not paid your respects to your aunt and cousin. Julia will be
married to-morrow morning at half-past eleven. Shall be happy to
see you.
"Your affectionate aunt,
"ANNA HAZLETON."
"TO MR. FRANCIS REEVE."
How brightly dawned the morning—how lovely looked the fair young
bride—how happy the bridegroom, dear reader mine, determine in your own
mind. Every one seemed particularly happy, but no one more so than Mr.
Hazleton—although several times, with a very grave face, he demanded of
the blushing bride if _Cousin Frank had not come yet_?
Alice, whose return home had only been postponed that she might be
present at her friend's wedding, stood by the side of Julia, while
Wallace performed the same pleasing office for his friend.
And now the priest has blessed them. Mrs. Hazleton has gracefully folded
her daughter to her bosom, and turned her cheek modestly to the salute
of her son-in-law. The carriage whirls to the door—tender adieus are
interchanged, and with a "blush on her cheek and a tear in her eye,"
Julia is borne off by the exulting bridegroom!
As the carriage rolled from the door, Mrs. Hazleton sank down on the
sofa, and folded her hands, and threw up her beautiful eyes
complacently, exclaiming—
"Thank Heaven! my duty to Julia is done—she is off my hands! She has
certainly made a most eligible match—as Lady Lackwit, who married into
the Ninnybrain family in the reign of George the Second,
observed——how, a letter for me?—where did you get it, John?"
"The postman just brought it, ma'am."
Mrs. Hazleton broke the seal and read:
"DEAR AUNT—
"Your invitation to Julia's wedding was received—was accepted.
And you did not know me, dear aunt—nay, you would not know me!
You could trust your daughter's happiness to a stranger, but not
to one whom she has known and loved from childhood! The fond
hopes of years you could recklessly destroy, uncaring for the
anguish you might inflict—or of your daughter's peace of
mind—wrecked perhaps forever! All this you could do. But to
assure you that your child's happiness will be safe in the hands
of your _chosen_ son-in-law, I gratefully acknowledge myself
that happy person!
"Your affectionate _nephew_ and _son_,
"FRANCIS REEVE."
"P. S.—Julia sends her dutiful love."
* * * * *
GAME-BIRDS OF AMERICA.—NO. III.
[Illustration]
COMMON DUCK OR MALLARD.
The common wild duck is the one which is usually meant when the word
duck is used without any other qualification, and it is the species
which is most frequently seen in the markets. They breed in all parts of
the country, from Pennsylvania north as far as the inland woody
districts of the fur countries, and it is met with everywhere in Europe,
up to Spitzbergen. As a bird of passage it is seen in every part of the
United States, always showing more activity in the night than in the
day; its conduct even in a domesticated state presenting evidences of
noisy watchfulness in the evening and at dawn. Its food is small fish,
fry snails, aquatic insects and plants, and all kinds of seeds and
grain. In England, ducks are very highly esteemed, and many expedients
are resorted to by the fowlers who supply the London markets with this
kind of food. Some account of their operations may prove interesting as
well as instructive. The chief method employed in capturing them is the
decoy, and instances have been known of eight hundred pounds being
cleared in one year by a single decoy on the Essex coast. These decoys
consist, in the first place, of an expanse of water which is called the
pond, and which is placed in the shelter of reeds, and generally
speaking also of bushes. The banks of the pond are left clear for some
little way, so that the birds may rest upon land, and, in short, this
portion of the contrivance is made as tempting as possible, as much of
the success depends upon this requisite. But though the ducks resort to
the pond in vast numbers, and pass the day in an inactive state, yet
still great skill, or at all events practice, is required in examining
the pond, because they are exceedingly watchful, take wing on the least
alarm, and do not readily settle. The sense of smelling is remarkably
acute in these birds, as one might naturally suppose from the margins of
their bills being so copiously supplied with nerves. In consequence of
this, when it becomes necessary to approach them on the windward, it is
usual to carry a bit of burning turf, the acid smoke of which
counteracts the smell of the carrier, which would be sufficient to alarm
the birds except for this precaution. The inland extremity of the pond
is formed into pipes or funnel-shaped channels which narrow gradually,
and have at the end a permanent net placed upon hoops. This net forms
the trap in which the birds are taken, often in vast numbers at one
time. In order that the decoy may be worked in all weathers, it is
necessary that there should be one to suit each of the prevailing winds.
We need not go farther into the details of this mode of bird catching.
The ducks are enticed by tame ones, which are trained to the purpose.
These birds begin to be taken in October, and the taking continues, by
law, only until the following February. Beside these decoys, there are,
in the places where ducks are numerous, many of the country people who
shoot them, and these are called _Punt Shooters_ or _Punt Gunners_—in
the creeks and openings of the streams, in the lower part of the Thames
estuary, and, as they ply night and day, according as the tide answers,
their labor is very severe and hazardous. This occupation once led a
fowler into singular distress. It happened in the day-time. Mounted on
his mud pattens (flat, square pieces of board, tied to the foot, to
avoid sinking in the ooze) he was traversing one of these oozy plains in
search of ducks, and being intent only on his game, suddenly found the
water, which had been accelerated by some peculiar circumstance
affecting the tide, had made an alarming progress around him, and he
found himself completely encircled. In this desperate situation, an idea
struck him as the only hope of safety. He retired to that part which
seemed the highest from its being yet uncovered by water, and striking
the barrel of his long gun deep in the ooze, he resolved to hold fast by
it, as well as for a support as a security against the waves, and to
wait the ebbing of the tide. He had reason to believe a common tide
would not have flowed above his waist; but, in the midst of his
reasoning on the subject, the water reached him. It rippled over his
feet, it gained his knees, his waist, button after button was swallowed
up, until at length it advanced over his shoulders. Fortunately for
himself, he preserved his courage and hope—he held fast by his anchor,
and with his eye looked anxiously about in search of some boat which
might accidentally be passing. None appeared. A head upon the surface of
the water, and that sometimes covered by a wave, was no object to be
descried from the land at the distance of half a league; nor could he
make any sounds of distress that could be heard so far. He finally
concluded that his destruction was inevitable. Just now a new object
attracted his attention. He thought he saw the topmost button of his
coat begin to appear. No mariner, floating on a wreck, could behold
succor approach with greater transport than he felt at this transient
view of the button; but the fluctuation of the water was such, and the
turn of the tide so slow, that it was yet some time before he dared
venture to assure himself that the button was yet fairly above the level
of the flood. At length, a second button appearing at intervals, his
sensations may rather be imagined than described, and his joy gave him
spirits and resolution to hold on four or five hours longer, until the
waters had fully retired.
One of the most tender and delicately flavored of the ducks which find
their way into our markets is the Shoveller, (_Anas Clypeata_). The
Shoveller is a very handsome bird, though its bill is disproportionally
large, and very peculiar in shape—it is about three inches in length,
of a black color, widened toward the extremity; and the fibres along the
margin are so much produced that the bill has the appearance of being
surrounded all along the gape with a fringe of hairs. The form of the
bill is well adapted to the habit of the animal, which is that of
picking up very small animal matters in the shallows and runs of the
rivers, and as these fibrous appendages are very sensitive, they enable
it to detect with great nicety all substances that are edible. The
Shoveller is an inland bird, and somewhat discursive. It is found, we
believe with very little difference of appearance, as well in the
Eastern continent as in our own; but, so far as is known, it is a bird
of the northern hemisphere, and is not met with in any part of the
south. On the continent of Europe it is pretty abundant, and it breeds
in the marshes of the middle latitudes; but in Britain it is not common,
even in the fens, and, in our own country, it is much more migratory
than in the eastern continent. This, however, does not establish a
difference in the birds themselves, but may readily be accounted for in
the difference of the two countries. The American summer is more dry
than the European, and the American marshes in the middle latitudes
partake of this drought; or, if they do not, they are covered with
pumpers and other evergreens, so that they do not answer well for the
summer resort of dabbling birds. The northern latitudes of America,
again, are remarkably well adapted on account of their flatness, the
abundance of water, the high temperature, and the corresponding great
production of small animals. Yet, in respect of latitude, the climate to
which the shoveller moves northward during the American summer is not
more northerly than those in which it breeds in central Europe,
although, from the different character of the seasons, it ranges more in
the one country than in the other. In all countries where it is known,
this bird forms its nest in the tallest and thickest tufts of rushes and
other aquatic herbage, and generally also in places which are not
accessible by man, or indeed by any of the land mammalia. The nest is
rudely formed of withered grass, collected in considerable quantity, and
the female is a close sitter. The young Shovellers have to find their
food in the water, and therefore they have the feet and the bill in a
tolerably complete state when they come out of the shell, whereas the
organs of flight are then in a rudimental state; and they continue so
much longer than they do in birds which are obliged to make use of the
wing at an early stage of their existence. This slow production of the
organs of flying is general among birds which seek their food upon the
ground, whether in the shallow waters, the marshes, the fields, or the
uplands; but all of them are better provided for the use of their bills
and feet than birds of more early flight. Thus we see how well these
creatures are adapted to the places in which they reside, and to which
they are of course drawn by this very adaptation. The Shoveller is thus
accurately described by Nuttall. The head, adjoining half of the neck,
medial stripe to the interscapulars; the whole back, interior scapulars
and primaries, umber brown; sides of the head, the neck and crest,
glossed with duck green; the rump and tail coverts, above and below,
with blackish green; lower half of the neck, the breast, shoulders,
shorter scapulars, ends of the greater wing coverts and sides of the
rump, white; longer scapulars, striped with pale blue, white and
blackish brown; lesser coverts, pale blue; speculum or wing-spot,
brilliant grass green, broadly bordered above and narrowly edged below
with white, bounded interiorly with greenish black; belly and flanks,
deep orange brown, the latter waved posteriorly with black; bill, black;
legs, orange.
* * * * *
THE ISLETS OF THE GULF;
OR, ROSE BUDD.
Ay, now I am in Arden; the more fool
I; when I was at home I was in a better place; but
Travelers must be content. AS YOU LIKE IT.
BY THE AUTHOR OF "PILOT," "RED ROVER," "TWO ADMIRALS," "WING-AND-WING,"
"MILES WALLINGFORD," ETC.
[Entered, according to the Act of Congress, in the year 1846, by
J. Fenimore Cooper, in the Clerk's Office of the District Court
of the United States, for the Northern District of New York.]
_Pros._ Why, that's my spirit!
But was not this nigh shore?
_Ariel._ Close by, my master.
_Pros._ But are they, Ariel, safe?
_Ariel._ Not a hair perished. TEMPEST.
"D'ye hear there, Mr. Mulford?" called out Capt. Stephen Spike, of the
half-rigged brigantine Swash, or Molly Swash, as was her registered
name, to his mate—"we shall be dropping out as soon as the tide makes,
and I intend to get through the Gate, at least, on the next flood.
Waiting for a wind in port is lubberly seamanship, for he that wants one
should go outside and look for it."
This call was uttered from a wharf of the renowned city of Manhattan, to
one who was in the trunk-cabin of a clipper-looking craft, of the name
mentioned, and on the deck of which not a soul was visible. Nor was the
wharf, though one of those wooden piers that line the arm of the sea
that is called the East River, such a spot as ordinarily presents itself
to the mind of the reader, or listener, when an allusion is made to a
wharf of that town which it is the fashion of the times to call the
_Commercial_ Emporium of America—as if there might very well be an
_emporium_ of any other character. The wharf in question had not a
single vessel of any sort lying at, or indeed very near it, with the
exception of the Molly Swash. As it actually stood on the eastern side
of the town, it is scarcely necessary to say that such a wharf could
only be found high up, and at a considerable distance from the usual
haunts of commerce. The brig lay more than a mile above the Hook
(Corlaer's, of course, is meant—not Sandy Hook) and quite near to the
old Alms-House—far above the ship-yards, in fact. It was a solitary
place for a vessel, in the midst of a crowd. The grum, top-chain voice
of Captain Spike had nothing there to mingle with, or interrupt its
harsh tones, and it instantly brought on deck Harry Mulford, the mate in
question, apparently eager to receive his orders.
"Did you hail, Captain Spike?" called out the mate, a tight, well-grown,
straight-built, handsome sailor-lad of two or three-and-twenty—one full
of health, strength and manliness.
"Hail! If you call straining a man's throat until he's hoarse, hailing,
I believe I did. I flatter myself there is not a man north of Hatteras
that can make himself heard further in a gale of wind than a certain
gentleman who is to be found within a foot of the spot where I stand.
Yet, sir, I've been hailing the Swash these five minutes, and thankful
am I to find some one at last who is on board to answer me."
"What are your orders, Capt. Spike?"
"To see all clear for a start as soon as the flood makes. I shall go
through the Gate on the next young flood, and I hope you'll have all the
hands aboard in time. I see two or three of them up at that Dutch
beer-house, this moment, and can tell 'em, in plain language, if they
come here with their beer aboard _them_, they'll have to go ashore
again."
"You have an uncommonly sober crew, Capt. Spike," answered the young
man, with great calmness. "During the whole time I have been with them,
I have not seen a man among them the least in the wind."
"Well, I hope it will turn out that I've an uncommonly sober mate in the
bargain. Drunkenness I abominate, Mr. Mulford, and I can tell you, short
metre, that I will not stand it."
"May I inquire if you ever saw me, the least in the world, under the
influence of liquor, Capt. Spike?" _demanded_ the mate, rather than
asked, with a very fixed meaning in his manner.
"I keep no log-book of trifles, Mr. Mulford, and cannot say. No man is
the worse for bowsing out his jib when off duty, though a drunkard's a
thing I despise. Well, well—remember, sir, that the Molly Swash casts
off on the young flood, and that Rose Budd and the good lady, her aunt,
take passage in her, this v'y'ge."
"Is it possible that you have persuaded them into that, at last!"
exclaimed the handsome mate.
"Persuaded! It takes no great persuasion, sir, to get the ladies to try
their luck in that brig. Lady Washington herself, if she was alive and
disposed to a sea-v'y'ge, might be glad of the chance. We've a ladies'
cabin, you know, and it's suitable that it should have some one to
occupy it. Old Mrs. Budd is a sensible woman, and takes time by the
forelock. Rose is ailin'—pulmonary, they call it, I believe, and her
aunt wishes to try the sea for her constitution—"
"Rose Budd has no more of a pulmonary constitution than I have myself,"
interrupted the mate.
"Well, that's as people fancy. You must know, Mr. Mulford, they've got
all sorts of diseases now-a-days, and all sorts of cures for 'em. One
sort of a cure for consumption is what they tarm the Hyder-Ally—"
"I think you must mean hydropathy, sir—"
"Well, it's something of the sort, no matter what—but cold water is at
the bottom of it, and they _do_ say it's a good remedy. Now Rose's aunt
thinks if cold water is what is wanted, there is no place where it can
be so plenty as out on the ocean. Sea-air is good, too, and by taking a
v'y'ge her niece will get both requisites together, and cheap."
"Does Rose Budd think herself consumptive, Capt. Spike?" asked Mulford,
with interest.
"Not she—you know it will never do to alarm a pulmonary, so Mrs. Budd
has held her tongue carefully on the subject before the young woman.
Rose fancies that her _aunt_ is out of sorts, and that the v'y'ge is
tried on her account—but the aunt, the cunning thing, knows all about
it."
Mulford almost nauseated the expression of his commander's countenance
while Spike uttered the last words. At no time was that countenance very
inviting, the features being coarse and vulgar, while the color of the
entire face was of an ambiguous red, in which liquor and the seasons
would seem to be blended in very equal quantities. Such a countenance,
lighted up by a gleam of successful management, not to say with hopes
and wishes that it will hardly do to dwell on, could not but be
revolting to a youth of Harry Mulford's generous feelings, and most of
all to one who entertained the sentiments which he was quite conscious
of entertaining for Rose Budd. The young man made no reply, but turned
his face toward the water, in order to conceal the expression of disgust
that he was sensible must be strongly depicted on it.
The river, as the well known arm of the sea in which the Swash was lying
is erroneously termed, was just at that moment unusually clear of craft,
and not a sail, larger than that of a boat, was to be seen between the
end of Blackwell's Island and Corlaer's Hook, a distance of about a
league. This stagnation in the movement of the port, at that particular
point, was owing to the state of wind and tide. Of the first, there was
little more than a southerly air, while the last was about two-thirds
ebb. Nearly every thing that was expected on that tide, coast-wise, and
by the way of the Sound, had already arrived, and nothing could go
eastward, with that light breeze and under canvas, until the flood made.
Of course it was different with the steamers, who were paddling about
like so many ducks, steering in all directions, though mostly crossing
and re-crossing at the ferries. Just as Mulford turned away from his
commander, however, a large vessel of that class shoved her bows into
the view, doubling the Hook, and going eastward. The first glance at
this vessel sufficed to drive even Rose Budd momentarily out of the
minds of both master and mate, and to give a new current to their
thoughts. Spike had been on the point of walking up the wharf but he now
so far changed his purpose as actually to jump on board the brig and
spring up alongside of his mate, on the taffrail, in order to get a
better look at the steamer. Mulford, who loathed so much in his
commander, was actually glad of this, Spike's rare merit as a seaman
forming a sort of attraction that held him, as it might be against his
own will, bound to his service.
"What will they do next, Harry?" exclaimed the master, his manner and
voice actually humanized, in air and sound at least, by this unexpected
view of something new in his calling—"What _will_ they do next?"
"I see no wheels, sir, nor any movement in the water astern, as if she
were a propeller," returned the young man.
"She's an out-of-the-way sort of a hussy! She's a man-of-war, too—one
of Uncle Sam's new efforts."
"That can hardly be, sir. Uncle Sam has but three steamers, of any size
or force, now the Missouri is burned, and yonder is one of them, lying
at the Navy Yard, while another is, or was lately, laid up at Boston.
The third is in the Gulf. This must be an entirely new vessel, if she
belong to Uncle Sam."
"New! She's as new as a Governor, and they tell me they've got so now
that they choose five or six of _them_, up at Albany, every fall. That
craft is sea-going, Mr. Mulford, as any one can tell at a glance. She's
none of your passenger-hoys."
"That's plain enough, sir—and she's armed. Perhaps she's English, and
they've brought her here into this open spot to try some new machinery.
Ay, ay! she's about to set her ensign to the navy men at the yard, and
we shall see to whom she belongs."
A long, low, expressive whistle from Spike succeeded this remark, the
colors of the steamer going up to the end of a gaff on the sternmost of
her schooner-rigged masts, just as Mulford ceased speaking. There was
just air enough, aided by the steamer's motion, to open the bunting, and
let the spectators see the design. There were the stars and stripes, as
usual, but the last ran perpendicularly, instead of in a horizontal
direction.
"Revenue, by George!" exclaimed the master, as soon as his breath was
exhausted in the whistle. "Who would have believed they could have
screwed themselves up to doing such a thing in that bloody service?"
"I now remember to have heard that Uncle Sam was building some large
steamers for the revenue service, and, if I mistake not, with some new
invention to get along with, that is neither wheel nor propeller. This
must be one of these new craft, brought out here, into open water, just
to try her, sir."
"You're right, sir, you're right. As to the natur' of the beast, you see
her buntin', and no honest man can want more. If there's any thing I
_do_ hate, it is that flag, with its unnat'ral stripes, up and down,
instead of running in the true old way. I _have_ heard a lawyer say,
that the revenue flag of this country is onconstitutional, and that a
vessel carrying it on the high seas might be sent in for piracy."
Although Harry Mulford was neither Puffendorf nor Grotius, he had too
much common sense, and too little prejudice in favor of even his own
vocation, to swallow such a theory, had fifty Cherry-Street lawyers
sworn to its justice. A smile crossed his fine, firm-looking mouth, and
something very like a reflection of that smile, if smiles _can_ be
reflected in one's own countenance, gleamed in his fine, large, dark
eye.
"It would be somewhat singular, Capt. Spike," he said, "if a vessel
belonging to any nation should be seized as a pirate. The fact that she
is national in character would clear her."
"Then let her carry a national flag, and be d—d to her," answered Spike
fiercely. "I can show you law for what I say, Mr. Mulford. The American
flag has its stripes fore and aft by law, and this chap carries his
stripes parpendic'lar. If I commanded a cruiser, and fell in with one of
these up and down gentry, blast me if I wouldn't just send him into
port, and try the question in the old Alms-House."
Mulford probably did not think it worth while to argue the point any
further, understanding the dogmatism and stolidity of his commander too
well to deem it necessary. He preferred to turn to the consideration of
the qualities of the steamer in sight, a subject on which, as seamen,
they might better sympathise.
"That's a droll-looking revenue cutter, after all, Capt. Spike," he
said—"a craft better fitted to go in a fleet, as a look-out vessel,
than to chase a smuggler in-shore."
"And no goer in the bargain! I do not see how she gets along, for she
keeps all snug under water; but, unless she can travel faster than she
does just now, the Molly Swash would soon lend her the Mother Carey's
Chickens of her own wake to amuse her."
"She has the tide against her, just here, sir; no doubt she would do
better in still water."
Spike muttered something between his teeth, and jumped down on deck,
seemingly dismissing the subject of the revenue entirely from his mind.
His old, coarse, authoritative manner returned, and he again spoke to
his mate about Rose Budd, her aunt, the "ladies' cabin," the "young
flood," and "casting off," as soon as the last made. Mulford listened
respectfully, though with a manifest distaste for the instructions he
was receiving. He knew his man, and a feeling of dark distrust came over
him, as he listened to his orders concerning the famous accommodations
he intended to give to Rose Budd and that "capital old lady, her aunt;"
his opinion of "the immense deal of good sea-air and a v'y'ge would do
Rose," and how "comfortable they both would be on board the Molly
Swash."
"I honor and respect Mrs. Budd, as my captain's lady, you see, Mr.
Mulford, and intend to treat her accordin'ly. She knows it—and Rose
knows it—and they both declare they'd rather sail with me, since sail
they must, than with any other ship-master out of America."
"You sailed once with Capt. Budd yourself, I think I have heard you say,
sir?"
"The old fellow brought me up. I was with him from my tenth to my
twentieth year, and then broke adrift to see fashions. We all do that,
you know, Mr. Mulford, when we are young and ambitious, and my turn came
as well as another's."
"Capt. Budd must have been a good deal older than his wife, sir, if
_you_ sailed with him when a boy," Mulford observed a little drily.
"Yes; I own to forty-eight, though no one would think me more than five
or six-and-thirty, to look at me. There was a great difference between
old Dick Budd and his wife, as you say, he being about fifty when he
married, and she less than twenty. Fifty is a good age for matrimony, in
a man, Mulford; as is twenty in a young woman."
"Rose Budd is not yet nineteen, I have heard her say," returned the
mate, with emphasis.
"Youngish, I will own, but that's a fault a liberal-minded man can
overlook. Every day, too, will lessen it. Well, look to the cabins, and
see all clear for a start. Josh will be down presently with a cart-load
of stores, and you'll take 'em aboard without delay."
As Spike uttered this order, his foot was on the plank-sheer of the
bulwarks, in the act of passing to the wharf again. On reaching the
shore, he turned and looked intently at the revenue steamer, and his
lips moved, as if he were secretly uttering maledictions on her. We say
maledictions, as the expression of his fierce, ill-favored countenance
too plainly showed that they could not be blessings. As for Mulford,
there was still something on his mind, and he followed to the gangway
ladder and ascended it, waiting for a moment, when the mind of his
commander might be less occupied, to speak. The opportunity soon
occurred, Spike having satisfied himself with the second look at the
steamer.
"I hope you don't mean to sail again without a second mate, Capt.
Spike?" he said.
"I do, though, I can tell you. I hate Dickies—they are always in the
way, and the captain has to keep just as much of a watch with one as
without one."
"That will depend on his quality. You and I have both been Dickies in
our time, sir; and my time was not long ago."
"Ay—ay—I know all about it—but you didn't stick to it long enough to
get spoiled. I would have no man aboard the Swash who made more than two
v'y'ges as second officer. As I want no spies aboard my craft, I'll try
it once more without a Dicky."
Saying this in a sufficiently positive manner, Capt. Stephen Spike
rolled up the wharf, much as a ship goes off before the wind, now
inclining to the right, and then again to the left. The gait of the man
would have proclaimed him a sea-dog, to any one acquainted with that
animal, as far as he could be seen. The short squab figure, the arms
bent nearly at right angles at the elbow, and working like two fins with
each roll of the body, the stumpy, solid legs, with the feet looking in
the line of his course and kept wide apart, would all have contributed
to the making up of such an opinion. Accustomed as he was to this
beautiful sight, Harry Mulford kept his eyes riveted on the retiring
person of his commander, until it disappeared behind a pile of lumber,
waddling always in the direction of the more thickly peopled parts of
the town. Then he turned and gazed at the steamer, which, by this time,
had fairly passed the brig, and seemed to be actually bound through the
Gate. That steamer was certainly a noble-looking craft, but our young
man fancied she struggled along through the water heavily. She might be
quick at need, but she did not promise as much by her present rate of
moving. Still, she was a noble-looking craft, and, as Mulford descended
to the deck again, he almost regretted he did not belong to her; or, at
least, to any thing but the Molly Swash.
Two hours produced a sensible change in and around that brigantine. Her
people had all come back to duty, and what was very remarkable among
seafaring folk, sober to a man. But, as has been said, Spike was a
temperance man, as respects all under his orders at least, if not
strictly so in practice himself. The crew of the Swash was large for a
half-rigged brig of only two hundred tons, but, as her spars were very
square, and all her gear as well as her mould seemed constructed for
speed, it was probable more hands than common were necessary to work her
with facility and expedition. After all, there were not many persons to
be enumerated among the "people of the Molly Swash," as they called
themselves; not more than a dozen, including those aft, as well as those
forward. A peculiar feature of this crew, however, was the circumstance
that they were all middle-aged men, with the exception of the mate, and
all thorough-bred sea-dogs. Even Josh, the cabin-boy, as he was called,
was an old, wrinkled, gray-headed <DW64>, of near sixty. If the crew
wanted a little in the elasticity of youth, it possessed the steadiness
and experience of their time of life, every man appearing to know
exactly what to do, and when to do it. This, indeed, composed their
great merit; an advantage that Spike well knew how to appreciate.
The stores had been brought alongside of the brig in a cart, and were
already stowed in their places. Josh had brushed and swept, until the
ladies' cabin could be made no neater. This ladies' cabin was a small
apartment beneath a trunk, which was, ingeniously enough, separated from
the main cabin by pantries and double doors. The arrangement was
unusual, and Spike had several times hinted that there was a history
connected with that cabin; though what the history was Mulford never
could induce him to relate. The latter knew that the brig had been used
for a forced trade on the Spanish Main, and had heard something of her
deeds in bringing off specie, and proscribed persons, at different
epochs in the revolutions of that part of the world, and he had always
understood that her present commander and owner had sailed in her, as
mate, for many years before he had risen to his present station. Now,
all was regular in the way of records, bills of sale, and other
documents; Stephen Spike appearing in both the capacities just named.
The register proved that the brig had been built as far back as the last
English war, as a private cruiser, but recent and extensive repairs had
made her "better than new," as her owner insisted, and there was no
question as to her sea-worthiness. It is true the insurance offices blew
upon her, and would have nothing to do with a craft that had seen her
two score years and ten; but this gave none who belonged to her any
concern, inasmuch as they could scarcely have been underwritten in their
trade, let the age of the vessel be what it might. It was enough for
them that the brig was safe, and exceedingly fast, insurances never
saving the lives of the people, whatever else might be their advantages.
With Mulford it was an additional recommendation, that the Swash was
usually thought to be of uncommonly just proportions.
By half past two, P. M., every thing was ready for getting the
brigantine under way. Her foretopsail—or fore_taw_sail, as Spike called
it—was loose, the fasts were singled, and a spring had been carried to
a post in the wharf that was well forward of the starboard bow, and the
brig's head turned to the southwest, or down stream, and consequently
facing the young flood. Nothing seemed to connect the vessel with the
land but a broad gangway plank, to which Mulford had attached
life-lines, with more care than it is usual to meet with on board of
vessels employed in short voyages. The men stood about the decks with
their arms thrust into the bosoms of their shirts, and the whole picture
was one of silent, and possibly of somewhat uneasy expectation. Nothing
was said, however; Mulford walking the quarter-deck alone, occasionally
looking up the still little tenanted streets of that quarter of the
suburbs, as if to search for a carriage. As for the revenue-steamer, she
had long before gone through the southern passage of Blackwell's,
steering for the Gate.
"Dat's dem, Mr. Mulford," Josh at length cried, from the look-out he had
taken in a stern-port, where he could see over the low bulwarks of the
vessel. "Yes, dat's dem, sir. I know dat old gray horse dat carries his
head so low and sorrowful like, as a horse has a right to do dat has to
drag a cab about dis big town. My eye! what a horse it is, sir!"
Josh was right, not only as to the gray horse that carried his head
"sorrowful like," but as to the cab and its contents. The vehicle was
soon on the wharf, and in its door soon appeared the short, sturdy
figure of Capt. Spike, backing out, much as a bear descends a tree. On
top of the vehicle were several light articles of female appliances, in
the shape of bandboxes, bags, &c., the trunks having previously arrived
in a cart. Well might that over-driven gray horse appear sorrowful, and
travel with a lowered head. The cab, when it gave up its contents,
discovered a load of no less than four persons besides the driver, all
of weight, and of dimensions in proportion, with the exception of the
pretty and youthful Rose Budd. Even she was plump, and of a well-rounded
person; though still light and slender. But her aunt was a fair picture
of a ship-master's widow; solid, comfortable and buxom. Neither was she
old, nor ugly. On the contrary, her years did not exceed forty, and
being well preserved, in consequence of never having been a mother, she
might even have passed for thirty-five. The great objection to her
appearance was the somewhat indefinite character of her shape, which
seemed to blend too many of its charms into one. The fourth person, in
the fare, was Biddy Noon, the Irish servant and _factotum_ of Mrs. Budd,
who was a pock-marked, red-faced, and red-armed single woman, about her
mistress's own age and weight, though less stout to the eye.
Of Rose we shall not stop to say much here. Her deep-blue eye, which was
equally spirited and gentle, if one can use such contradictory terms,
seemed alive with interest and curiosity, running over the brig, the
wharf, the arm of the sea, the two islands, and all near her, including
the Alms-House, with such a devouring rapidity as might be expected in a
town-bred girl, who was setting out on her travels for the first time.
Let us be understood; we say town-bred, because such was the fact; for
Rose Budd had been both born and educated in Manhattan, though we are
far from wishing to be understood that she was either very-well born, or
highly educated. Her station in life may be inferred from that of her
aunt, and her education from her station. Of the two, the last was,
perhaps, a trifle the highest.
We have said that the fine blue eye of Rose passed swiftly over the
various objects near her, as she alighted from the cab, and it naturally
took in the form of Harry Mulford, as he stood in the gangway, offering
his arm to aid her aunt and herself in passing the brig's side. A smile
of recognition was exchanged between the young people, as their eyes
met, and the color, which formed so bright a charm in Rose's sweet face,
deepened, in a way to prove that that color spoke with a tongue and
eloquence of its own. Nor was Mulford's cheek mute on the occasion,
though he helped the hesitating, half-doubting, half-bold girl along the
plank with a steady hand and rigid muscles. As for the aunt, as a
captain's widow, she had not felt it necessary to betray any
extraordinary emotions in ascending the plank, unless, indeed, it might
be those of delight on finding her foot once more on the deck of a
vessel!
Something of the same feeling governed Biddy, too, for, as Mulford
civilly extended his hand to her also, she exclaimed—
"No fear of me, Mr. Mate—I came from Ireland by wather, and knows all
about ships and brigs, I do. If you could have seen the times we had,
and the saas we crossed, you'd not think it nadeful to say much to the
likes iv me."
Spike had tact enough to understand he would be out of his element in
assisting females along that plank, and he was busy in sending what he
called "the old lady's dunnage" on board, and in discharging the cabman.
As soon as this was done, he sprang into the main-channels, and thence,
_viâ_ the bulwarks, on deck, ordering the plank to be hauled aboard. A
solitary laborer was paid a quarter to throw off the fasts from the
ring-bolts and posts, and every thing was instantly in motion to cast
the brig loose. Work went on as if the vessel were in haste, and it
consequently went on with activity. Spike bestirred himself giving his
orders in a way to denote he had been long accustomed to exercise
authority on the deck of a vessel, and knew his calling to its minutiæ.
The only ostensible difference between his deportment to-day and on any
ordinary occasion, perhaps, was in the circumstance that he now seemed
anxious to get clear of the wharf and that in a way which might have
attracted notice in any suspicious and attentive observer. It is
possible that such a one was not very distant, and that Spike was aware
of his presence, for a respectable-looking, well-dressed, middle-aged
man _had_ come down one of the adjacent streets, to a spot within a
hundred yards of the wharf and stood silently watching the movements of
the brig, as he leaned against a fence. The want of houses in that
quarter enabled any person to see this stranger from the deck of the
Swash, but no one on board her seemed to regard him at all, unless it
might be the master.
"Come, bear a hand, my hearty, and toss that bow-fast clear," cried the
captain, whose impatience to be off seemed to increase as the time to do
so approached nearer and nearer. "Off with it, at once, and let her go."
The man on the wharf threw the turns of the hawser clear of the post,
and the Swash was released forward. A smaller line, for a spring, had
been run some distance along the wharves, ahead of the vessel, and
brought in aft. Her people clapped on this, and gave way to their craft,
which, being comparatively light, was easily moved, and was very
manageable. As this was done, the distant spectator who had been leaning
on the fence, moved toward the wharf with a step a little quicker than
common. Almost at the same instant, a short, stout, sailor-like looking
little person, waddled down the nearest street, seeming to be in
somewhat of a hurry, and presently he joined the other stranger, and
appeared to enter into conversation with him; pointing toward the Swash,
as he did so. All this time, both continued to advance toward the wharf.
In the meanwhile, Spike and his people were not idle. The tide did not
run very strong near the wharves and in the sort of a bight in which the
vessel had lain, but, such as it was, it soon took the brig on her inner
bow, and began to cast her head off shore. The people at the spring
pulled away with all their force, and got sufficient motion on their
vessel to overcome the tide, and to give the rudder an influence. The
latter was put hard a-starboard, and helped to cast the brig's head to
the southward.
Down to this moment, the only sail that was loose on board the Swash,
was the fore-topsail, as mentioned. This still hung in the gear, but a
hand had been sent aloft to overhaul the buntlines and clew-lines, and
men were also at the sheets. In a minute the sail was ready for
hoisting. The Swash carried a wapper of a fore-and-aft mainsail, and,
what is more, it was fitted with a standing gaff, for appearance in
port. At sea, Spike knew better than to trust to this arrangement, but
in fine weather, and close in with the land, he found it convenient to
have this sail haul out and brail like a ship's spanker. As the gaff was
now aloft, it was only necessary to let go the brails to loosen this
broad sheet of canvas, and to clap on the out-hauler, to set it. This
was probably the reason why the brig was so unceremoniously cast into
the stream, without showing more of her cloth. The jib and flying-jibs,
however, did at that moment drop beneath their booms, ready for
hoisting.
Such was the state of things as the two strangers came first upon the
wharf. Spike was on the taffrail, overhauling the main-sheet, and
Mulford was near him, casting the fore-topsail braces from the pins,
preparatory to clapping on the halyards.
"I say, Mr. Mulford," asked the captain, "did you ever see either of
them chaps afore? These jokers on the wharf I mean."
"Not to my recollection, sir," answered the mate, looking over the
taffrail to examine the parties. "The little one is a burster! The
funniest looking little fat old fellow I've seen in many a day."
"Ay, ay, them fat little bursters, as you call 'em, are sometimes full
of the devil. I don't like either of the chaps, and am right glad we are
well cast, before they got here."
"I do not think either would be likely to do us much harm, Capt. Spike."
"There's no knowing, sir. The biggest fellow looks as if he might lug
out a silver oar at any moment."
"I believe the silver oar is no longer used, in this country at least,"
answered Mulford, smiling. "And if it were, what have we to fear from
it? I fancy the brig has paid her reckoning."
"She don't owe a cent, nor ever shall for twenty-four hours after the
bill is made out, while I own _her_. They call me ready-money Stephen,
round among the ship-chandlers and caulkers. But I don't like them
chaps, and what I don't relish I never swallow, you know."
"They'll hardly try to get aboard us, sir; you see we are quite clear of
the wharf, and the mainsail will take now, if we set it."
Spike ordered the mate to clap on the out-hauler, and spread that broad
sheet of canvas at once to the little breeze there was. This was almost
immediately done, when the sail filled, and began to be felt on the
movement of the vessel. Still, that movement was very slow, the wind
being so light, and the _vis inertiæ_ of so large a body remaining to be
overcome. The brig receded from the wharf, almost in a line at right
angles to its face, inch by inch, as it might be, dropping slowly up
with the tide at the same time. Mulford now passed forward to set the
jibs, and to get the topsail on the craft, leaving Spike on the
taffrail, keenly eyeing the strangers, who, by this time, had got down
nearly to the end of the wharf, at the berth so lately occupied by the
Swash. That the captain was uneasy was evident enough, that feeling
being exhibited in his countenance, blended with a malignant ferocity.
"Has that brig any pilot?" asked the larger and better-looking of the
two strangers.
"What's that to you, friend?" demanded Spike, in return. "Have you a
Hell-Gate branch?"
"I may have one, or I may not. It is not usual for so large a craft to
run the Gate without a pilot."
"Oh! my gentleman's below, brushing up his logarithms. We shall have him
on deck to take his departure before long, when I'll let him know your
kind inquiries after his health."
The man on the wharf seemed to be familiar with this sort of sea-wit,
and he made no answer, but continued that close scrutiny of the brig, by
turning his eyes in all directions, now looking below, and now aloft,
which had in truth occasioned Spike's principal cause for uneasiness.
"Is not that Capt. Stephen Spike, of the brigantine Molly Swash?" called
out the little, dumpling-looking person, in a cracked, dwarfish sort of
a voice, that was admirably adapted to his appearance. Our captain
fairly started; turned full toward the speaker; regarded him intently
for a moment, and gulped the words he was about to utter, like one
confounded. As he gazed, however, at little dumpy, examining his
bow-legs, red broad cheeks, and coarse snub nose, he seemed to regain
his self-command, as if satisfied the dead had not really returned to
life.
"Are you acquainted with the gentleman you have named?" he asked, by way
of answer. "You speak of him like one who ought to know him."
[Illustration: Josh educating a Pig
Philadelphia 1847]
"A body is apt to know a shipmate. Stephen Spike and I sailed together
twenty years since, and I hope to live to sail with him again."
"_You_ sail with Stephen Spike? when and where, may I ask, and in what
v'y'ge, pray?"
"The last time was twenty years since. Have you forgotten little Jack
Tier, Capt. Spike?"
Spike looked astonished, and well he might, for he had supposed Jack to
be dead fully fifteen years. Time and hard service had greatly altered
him, but the general resemblance in figure, stature, and waddle,
certainly remained. Notwithstanding, the Jack Tier Spike remembered was
quite a different person from this Jack Tier. That Jack had worn his
intensely black hair clubbed and curled, whereas this Jack had cut his
locks into short bristles, which time had turned into an intense gray.
That Jack was short and thick, but he was flat and square; whereas this
Jack was just as short, a good deal thicker, and as round as a dumpling.
In one thing, however, the likeness still remained perfect. Both Jacks
chewed tobacco, to a degree that became a distinct feature in their
appearance.
Spike had many reasons for wishing Jack Tier were not resuscitated in
this extraordinary manner, and some for being glad to see him. The
fellow had once been largely in his confidence, and knew more than was
quite safe for any one to remember but himself while he might be of
great use to him in his future operations. It is always convenient to
have one at your elbow who thoroughly understands you, and Spike would
have lowered a boat and sent it to the wharf to bring Jack off, were it
not for the gentleman who was so inquisitive about pilots. Under the
circumstances, he determined to forego the advantages of Jack's
presence, reserving the right to hunt him up on his return.
The reader will readily enough comprehend that the Molly Swash was not
absolutely standing still while the dialogue related was going on, and
the thoughts we have recorded were passing through her master's mind. On
the contrary, she was not only in motion, but that motion was gradually
increasing, and by the time all was said that has been related, it had
become necessary for those who spoke to raise their voices to an
inconvenient pitch in order to be heard. This circumstance alone would
soon have put an end to the conversation, had not Spike's pausing to
reflect brought about the same result, as mentioned.
In the mean time, Mulford had got the canvas spread. Forward, the Swash
showed all the cloth of a full-rigged brig, even to royals and flying
gib; while aft, her masts was the raking, tall, naked pole of an
American schooner. There was a taut top-mast, too, to which a
gaff-topsail was set, and the gear proved that she could also show, at
need, a staysail in this part of her, if necessary. As the Gate was
before them, however, the people had set none but the plain, manageable
canvas.
The Molly Swash kept close on a wind, luffing athwart the broad reach
she was in, until far enough to weather Blackwell's, when she edged off
to her course, and went through the southern passage. Although the wind
remained light, and a little baffling, the brig was so easily impelled,
and was so very handy, that there was no difficulty in keeping her
perfectly in command. The tide, too, was fast increasing in strength and
velocity, and the movement from this cause alone was getting to be
sufficiently rapid.
As for the passengers, of whom we have lost sight in order to get the
brig under way, they were now on deck again. At first, they had all gone
below, under the care of Josh, a somewhat rough groom of the chambers,
to take possession of their apartment, a sufficiently neat, and
exceedingly comfortable cabin, supplied with every thing that could be
wanted at sea, and, what was more, lined on two of its sides with
state-rooms. It is true, all these apartments were small, and the
state-rooms were very low, but no fault could be found with their
neatness and general arrangements, when it was recollected that one was
on board a vessel.
"Here ebbery t'ing heart can wish," said Josh, exultingly, who, being an
old-school black, did not disdain to use some of the old-school dialect
of his caste. "Yes, ladies, ebbery t'ing. Let Capt. Spike alone for dat!
He won'erful at accommodation! Not a bed-bug aft—know better dan come
here; jest like de people, in dat respects, and keep deir place forrard.
You nebber see a pig come on the quarter-deck, nudder."
"You must maintain excellent discipline, Josh," cried Rose, in one of
the sweetest voices in the world, which was easily attuned to
merriment—"and we are delighted to learn what you tell us. How do you
manage to keep up these distinctions, and make such creatures know their
places so well?"
"Nuttin easier, if you begins right, miss. As for de pig, I teach dem
wid scaldin' water. Whenever I sees a pig come aft, I gets a little
water from de copper, and just scald him wid it. You can't t'ink, miss,
how dat mend his manners, and make him squeel fuss, and t'ink arter. In
that fashion I soon gets de ole ones in good trainin', and den I has no
more trouble with dem as comes fresh aboard; for de ole hog tell de
young one, and 'em won'erful cunnin', and know how to take care of
'emself."
Rose Budd's sweet eyes were full of fun and expectation, and she could
no more repress her laugh than youth and spirits can always be discreet.
"Yes, with the pigs," she cried, "that might do very well; but how is it
with those—other creatures?"
"Rosy, dear," interrupted the aunt, "I wish you would say no more about
such shocking things. It's enough for us that Capt. Spike has ordered
them all to stay forward among the men, which is always done on board
well disciplined vessels. I've heard your uncle say, a hundred times,
that the quarter-deck was sacred, and that might be enough to keep such
animals off it."
It was barely necessary to look at Mrs. Budd in the face to get a very
accurate general notion of her character. She was one of those inane,
uncultivated beings, who seem to be protected by a benevolent Providence
in their pilgrimage on earth, for they do not seem to possess the power
to protect themselves. Her very countenance expressed imbecility and
mental dependence, credulity and a love of gossip. Notwithstanding these
radical weaknesses, the good woman had some of the better instincts of
her sex, and was never guilty of any thing that could properly convey
reproach. She was no monitress for Rose, however, the niece much oftener
influencing the aunt than the aunt influencing the niece. The latter had
been fortunate in having had an excellent instructress, who, though
incapable of teaching her much in the way of accomplishments, had
imparted a great deal that was respectable and useful. Rose had
character, and strong character, too, as the course of our narrative
will show; but her worthy aunt was a pure picture of as much mental
imbecility as at all comported with the privileges of self-government.
The conversation about "those other creatures" was effectually checked
by Mrs. Budd's horror of the "animals," and Josh was called on deck so
shortly after as to prevent its being renewed. The females staid below a
few minutes, to take possession, and then they re-appeared on deck, to
gaze at the horrors of the Hell-Gate passage. Rose was all eyes, wonder
and admiration of every thing she saw. This was actually the first time
she had ever been on the water, in any sort of craft, though born and
brought up in sight of one of the most thronged havens in the world. But
there must be a beginning to every thing, and this was Rose Budd's
beginning on the water. It is true the brigantine was a very beautiful,
as well as an exceedingly swift vessel, but all this was lost on Rose,
who would have admired a horse-jockey bound to the West Indies, in this
the incipient state of her nautical knowledge. Perhaps the exquisite
neatness that Mulford maintained about every thing that came under his
care, and that included every thing on deck, or above board, and about
which neatness Spike occasionally muttered an oath, as so much senseless
trouble, contributed somewhat to Rose's pleasure; but her admiration
would scarcely have been less with anything that had sails, and seemed
to move through the water with a power approaching that of volition.
It was very different with Mrs. Budd. She, good woman, had actually made
one voyage with her late husband, and she fancied that she knew all
about a vessel. It was her delight to talk on nautical subjects, and
never did she really feel her great superiority over her niece, so very
unequivocally, as when the subject of the ocean was introduced, about
which she did know something, and touching which Rose was profoundly
ignorant, or as ignorant as a girl of lively imagination could remain
with the information gleaned from others.
"I am not surprised you are astonished at the sight of the vessel,
Rosy," observed the self-complacent aunt at one of her niece's
exclamations of admiration. "A vessel is a very wonderful thing, and we
are told what extr'orny beings they are that 'go down to the sea in
ships.' But you are to know this is not a ship at all, but only a
half-jigger rigged, which is altogether a different thing."
"Was my uncle's vessel, The Rose In Bloom, then, very different from the
Swash?"
"Very different, indeed, child! Why, The Rose In Bloom was a
full-jiggered ship, and had twelve masts—and this is only a
half-jiggered brig, and has but two masts. See, you may count
them—one—two!"
Harry Mulford was coiling away a top-gallant-brace, directly in front of
Mrs. Budd and Rose, and, at hearing this account of the wonderful
equipment of The Rose In Bloom, he suddenly looked up, with a lurking
expression about his eye that the niece very well comprehended, while he
exclaimed, without much reflection, under the impulse of surprise—
"Twelve masts! Did I understand you to say, ma'am, that Capt. Budd's
ship had twelve masts?"
"Yes, sir, _twelve_! and I can tell you all their names, for I learnt
them by heart—it appearing to me proper that a ship-master's wife
should know the names of all the masts in her husband's vessel. Do you
wish to hear their names, Mr. Mulford?"
Harry Mulford would have enjoyed this conversation to the top of his
bent, had it not been for Rose. She well knew her aunt's general
weakness of intellect, and especially its weakness on this particular
subject, but she would suffer no one to manifest contempt for either, if
in her power to prevent it. It is seldom one so young, so mirthful, so
ingenuous and innocent in the expression of her countenance, assumed so
significant and rebuking a frown as did pretty Rose Budd when she heard
the mate's involuntary exclamation about the "twelve masts." Harry, who
was not easily checked by his equals, or any of his own sex, submitted
to that rebuking frown with the meekness of a child, and stammered out,
in answer to the well-meaning, but weak-minded widow's question—
"If you please, Mrs. Budd—just as you please, ma'am—only twelve is a
good many masts—" Rose frowned again—"that is—more than I'm used to
seeing—that's all."
"I dare say, Mr. Mulford—for you sail in only a half-jigger; but Capt.
Budd always sailed in a full-jigger—and _his_ full-jiggered ship had
just twelve masts, and, to prove it to you, I'll give you the
names—first, then, there were the fore, main, and mizzen masts—"
"Yes—yes—ma'am," stammered Harry, who wished the twelve masts and The
Rose In Bloom at the bottom of the ocean, since her owner's niece still
continued to look coldly displeased—"that's right, I can swear!"
"Very true, sir, and you'll find I am right as to all the rest. Then,
there were the fore, main, and mizzen top-masts—they make six, if I can
count, Mr. Mulford?"
"Ah!" exclaimed the mate, laughing, in spite of Rose's frowns, as the
manner in which the old sea-dog had quizzed his wife became apparent to
him. "I see how it is—you are quite right, ma'am—I dare say The Rose
In Bloom had all these masts, and some to spare."
"Yes, sir—I knew you would be satisfied. The fore, main and mizzen
top-gallant-masts make nine—and the fore, main and mizzen royals make
just twelve. Oh, I'm never wrong in any thing about a vessel, especially
if she is a full-jiggered ship."
Mulford had some difficulty in restraining his smiles each time the
full-jigger was mentioned, but Rose's expression of countenance kept him
in excellent order—and she, innocent creature, saw nothing ridiculous
in the term, though the twelve masts had given her a little alarm.
Delighted that the old lady had got through her enumeration of the spars
with so much success, Rose cried, in the exuberance of her spirits—
"Well, aunty, for my part, I find a half-jigger vessel so very, very
beautiful, that I do not know how I should behave were I to go on board
a _full_-jigger."
Mulford turned abruptly away, the circumstance of Rose's making herself
ridiculous giving him sudden pain, though he could have laughed at her
aunt by the hour.
"Ah, my dear, that is on account of your youth and inexperience—but you
will learn better in time. I was just so, myself when I was of your age,
and thought the fore-rafters were as handsome as the squared-jiggers,
but soon after I married Capt. Budd I felt the necessity of knowing more
than I did about ships, and I got him to teach me. He didn't like the
business, at first, and pretended I would never learn; but, at last, it
came all at once like, and then he used to be delighted to hear me 'talk
ship,' as he called it. I've known him laugh, with his cronies, as if
ready to die, at my expertness in sea-terms, for half an hour
together—and then he would swear—that was the worst fault your uncle
had, Rosy—he _would_ swear, sometimes, in a way that frightened me, I
do declare!"
"But he never swore at you, aunty?"
"I can't say that he did exactly do that, but he would swear all round
me, even if he didn't actually touch me, when things went wrong—but it
would have done your heart good to hear him laugh! He had a most
excellent heart, just like your own, Rosy dear; but, for that matter,
all the Budds have excellent hearts, and one of the commonest ways your
uncle had of showing it was to laugh, particularly when we were together
and talking. Oh, he used to delight in hearing me converse, especially
about vessels, and never failed to get me at it when he had company. I
see his good-natured, excellent-hearted countenance at this moment, with
the tears running down his fat, manly cheeks, as he shook his very sides
with laughter. I may live a hundred years, Rosy, before I meet again
with your uncle's equal."
This was a subject that invariably silenced Rose. She remembered her
uncle, herself, and remembered his affectionate manner of laughing at
her aunt, and she always wished the latter to get through her eulogiums
on her married happiness, as soon as possible, whenever the subject was
introduced.
All this time the Molly Swash kept in motion. Spike never took a pilot
when he could avoid it, and his mind was too much occupied with his
duty, in that critical navigation, to share at all in the conversation
of his passengers, though he did endeavor to make himself agreeable to
Rose, by an occasional remark, when a favorable opportunity offered. As
soon as he had worked his brig over into the south or weather passage of
Blackwell's, however, there remained little for him to do, until she had
drifted through it, a distance of a mile or more, and this gave him
leisure to do the honors. He pointed out the castellated edifice on
Blackwell's as the new penitentiary, and the hamlet of villas, on the
other shore, as Ravenswood, though there is neither wood nor ravens to
authorize the name. But the "Sunswick," which satisfied the Delafields
and Gibbses of the olden time, and which distinguished their lofty halls
and broad lawns, was not elegant enough for the cockney tastes of these
later days, so "wood" must be made to usurp the place of cherries and
apples, and "ravens" that of gulls, in order to satisfy its cravings.
But all this was lost on Spike. He remembered the shore as it had been
twenty years before, and he saw what it was now, but little did he care
for the change. On the whole, he rather preferred the Grecian Temples,
over which the ravens would have been compelled to fly, had there been
any ravens in that neighborhood, to the old fashioned and highly
respectable residence that once alone occupied the spot. The point he
did understand, however, and on the merits of which he had something to
say, was a little farther ahead. That, too, had been re-christened—the
Hallet's Cove of the mariner being converted into Astoria—not that
bloody-minded place at the mouth of the Oregon, which has come so near
bringing us to blows with our "ancestors in England," as the worthy
denizens of that quarter choose to consider themselves still, if one can
judge by their language. This Astoria was a very different place, and is
one of the many suburban villages that are shooting up, like mushrooms,
in a night, around the great _Commercial_ Emporium. This spot Spike
understood perfectly, and it was not likely that he should pass it
without communicating a portion of his knowledge to Rose.
"There, Miss Rose," he said, with a didactic sort of air, pointing with
his short, thick finger at the little bay which was just opening to
their view; "there's as neat a cove as a craft need bring up in. That
_used to be_ a capital place to lie in, to wait for a wind to pass the
Gate; but it has got to be most too public for my taste. I'm rural, I
tell Mulford, and love to get in out-of-the-way berths with my brig,
where she can see salt-meadows, and smell the clover. You never catch me
down in any of the crowded slips, around the markets, or any where in
that part of the town, for I _do_ love country air. That's Hallet's
Cove, Miss Rose, and a pretty anchorage it would be for us, if the wind
and tide didn't sarve to take us through the Gate."
"Are we near the Gate, Capt. Spike?" asked Rose, the fine bloom on her
cheek lessening a little, under the apprehension that formidable name is
apt to awaken in the breasts of the inexperienced.
"Half a mile, or so. It begins just at the other end of this island on
our larboard hand, and will be all over in about another half mile, or
so. It's no such bad place, a'ter all, is Hell-Gate, to them that's used
to it. I call myself a pilot in Hell-Gate, though I _have_ no branch."
"I wish, Capt. Spike, I could teach you to give that place its proper
and polite name. We call it Whirl-Gate altogether now," said the relict.
"Well, that's new to me," cried Spike. "I _have_ heard some
chicken-mouthed folk say _Hurl_-Gate, but this is the first time I ever
heard it called Whirl-Gate—they'll get it to Whirlagig-Gate next. I
don't think that my old commander, Capt. Budd called the passage any
thing but honest, up and down Hell-Gate."
"That he did—that he did—and all my arguments and reading could not
teach him any better. I proved to him that it was Whirl-Gate, as any one
can see that it ought to be. It is full of Whirlpools, they say, and
that shows what Nature meant the name to be."
"But, aunty," put in Rose, half reluctantly, half anxious to speak,
"what has _gate_ to do with whirlpools? You will remember it is called a
gate—the gate to that wicked place I suppose is meant."
"Rose, you amaze me! How can _you_, a young woman of only nineteen,
stand up for so vulgar a name as Hell-Gate?"
"Do you think it as vulgar as Hurl-Gate, aunty? To me it always seems
the most vulgar to be straining at gnats."
"Yes," said Spike, sentimentally, "I'm quite of Miss Rose's way of
thinking—straining at gnats is very ill-manners, especially at table. I
once knew a man who strained in this way, until I thought he would have
choked, though it was with a fly to be sure; but gnats are nothing but
small flies, you know, Miss Rose. Yes, I'm quite of your way of
thinking, Miss Rose; it _is_ very vulgar to be straining at gnats and
flies, more particularly at table. But you'll find no flies or gnats
aboard here, to be straining at, or brushing away, or to annoy you.
Stand by there, my hearties, and see all clear to run through Hell-Gate.
Don't let me catch _you_ straining at any thing, though it should be the
fin of a whale!"
The people forward looked at each other, as they listened to this novel
admonition, though they called out the customary "ay, ay, sir," as they
went to the sheets, braces and bowlines. To them the passage of no
Hell-Gate conveyed the idea of any particular terror, and with the one
they were about to enter, they were much too familiar to care any thing
about it.
The brig was now floating fast, with the tide, up abreast of the east
end of Blackwell's, and in two or three more minutes she would be fairly
in the Gate. Spike was aft, where he could command a view of every thing
forward, and Mulford stood on the quarter-deck, to look after the
head-braces. An old and trustworthy seaman, who acted as a sort of
boatswain, had the charge on the forecastle, and was to tend the sheets
and tack. His name was Rove.
"See all clear," called out Spike. "D'ye hear there, for'ard! I shall
make a half-board in the Gate, if the wind favor us, and the tide prove
strong enough to hawse us to wind'ard sufficiently to clear the pot—so
mind your—"
The captain breaking off in the middle of this harangue, Mulford turned
his head, in order to see what might be the matter. There was Spike,
leveling a spy-glass at a boat that was pulling swiftly out of the north
channel, and shooting like an arrow directly athwart the brig's bows
into the main passage of the Gate. He stepped to the captain's elbow.
"Just take a look at them chaps, Mr. Mulford," said Spike, handing his
mate the glass.
"They seem in a hurry," answered Harry, as he adjusted the glass to his
eye, "and will go through the Gate in less time than it will take to
mention the circumstance."
"What do you make of them, sir?"
"The little man who called himself Jack Tier is in the stern-sheets of
the boat, for one," answered Mulford.
"And the other, Harry—what do you make of the other?"
"It seems to be the chap who hailed to know if we had a pilot. He means
to board us at Riker's Island, and make us pay pilotage, whether we want
his services or not."
"Blast him and his pilotage too! Give me the glass"—taking another long
look at the boat, which by this time was glancing, rather than pulling,
nearly at right angles across his bows. "I want no such pilot aboard
here, Mr. Mulford. Take another look at him—here, you can see him, away
on our weather bow, already."
Mulford did take another look at him, and this time his examination was
longer and more scrutinising than before.
"It is not easy to cover him with the glass," observed the young
man—"the boat seems fairly to fly."
"We're forereaching too near the Hog's Back, Capt. Spike," roared the
boatswain, from forward.
"Ready about—hard a-lee," shouted Spike. "Let all fly, for'ard—help
her round, boys, all you can, and wait for no orders! Bestir
yourselves—bestir yourselves."
It was time the crew should be in earnest. While Spike's attention had
been thus diverted by the boat, the brig had got into the strongest of
the current, which, by setting her fast to windward, had trebled the
power of the air, and this was shooting her over toward one of the
greatest dangers of the passage on a flood tide. As everybody bestirred
themselves, however, she was got round and filled on the opposite tack,
just in time to clear the rocks. Spike breathed again, but his head was
still full of the boat. The danger he had just escaped as Scylla met him
as Charybdis. The boatswain again roared to go about. The order was
given as the vessel began to pitch in a heavy swell. At the next instant
she rolled until the water came on deck, whirled with her stern down the
tide, and her bows rose as if she were about to leap out of water. The
Swash had hit the Pot Rock.
PART II.
_Watch._ If we know him to be a thief, shall we not lay hands on
him?
_Dogb._ Truly, by your office, you may; but I think they that
touch pitch will be defiled: the most peaceable way for you, if
you do take a thief, is, to let him show himself what he is, and
steal out of your company.
MUCH ADO ABOUT NOTHING.
We left the brigantine of Capt. Spike in a very critical situation, and
the master himself in great confusion of mind. A thorough seaman, this
accident would never have happened, but for the sudden appearance of the
boat and its passengers; one of whom appeared to be a source of great
uneasiness to him. As might be expected, the circumstance of striking a
place as dangerous as the Pot Rock in Hell-Gate, produced a great
sensation on board the vessel. This sensation betrayed itself in various
ways, and according to the characters, habits, and native firmness of
the parties. As for the ship-master's relict, she seized hold of the
main-mast, and screamed so loud and perseveringly, as to cause the
sensation to extend itself into the adjacent and thriving village of
Astoria, where it was distinctly heard by divers of those who dwelt near
the water. Biddy Noon had her share in this clamor, lying down on the
deck in order to prevent rolling over, and possibly to scream more at
her leisure, while Rose had sufficient self-command to be silent, though
her cheeks lost their color.
Nor was there any thing extraordinary in females betraying this alarm,
when one remembers the somewhat astounding signs of danger by which
these persons were surrounded. There is always something imposing in the
swift movement of a considerable body of water. When this movement is
aided by whirlpools and the other similar accessories of an interrupted
current, it frequently becomes startling, more especially to those who
happen to be on the element itself. This is peculiarly the case with the
Pot Rock, where, not only does the water roll and roar as if agitated by
a mighty wind, but where it even breaks, the foam seeming to glance up
stream, in the rapid succession of wave to wave. Had the Swash remained
in her terrific berth more than a second or two, she would have proved
what is termed a "total loss;" but she did not. Happily the Pot Rock
lies so low, that it is not apt to fetch up any thing of a light draught
of water; and the brigantine's fore-foot had just settled on its summit,
long enough to cause the vessel to whirl round and make her obeisance to
the place, when a succeeding swell lifted her clear, and away she went
down stream, rolling as if scudding in a gale, and, for a moment, under
no command whatever. There lay another danger ahead, or it would be
better to say astern, for the brig was drifting stern foremost, and that
was in an eddy under a bluff, which bluff lies at an angle in the reach,
where it is no uncommon thing for craft to be cast ashore, after they
have passed all the more imposing and more visible dangers above. It was
in escaping this danger, and in recovering the command of his vessel,
that Spike now manifested the sort of stuff of which he was really made,
in emergencies of this sort. The yards were all sharp up when the
accident occurred, and springing to the lee-braces, just as a man winks
when his eye is menaced, he seized the weather fore-brace with his own
hands, and began to round in the yard, shouting out to the man at the
wheel to "port his helm" at the same time. Some of the people flew to
his assistance, and the yards were not only squared, but braced a little
up on the other tack, in much less time than we have taken to relate the
evolution. Mulford attended to the main-sheet, and succeeded in getting
the boom out in the right direction. Although the wind was in truth very
light, the velocity of the drift filled the canvas, and taking the
arrow-like current on her lee bow, the Swash, like a frantic steed that
is alarmed with the wreck made by his own madness, came under command,
and sheered out into the stream again, where she could drift clear of
the apprehended danger astern.
"Sound the pumps," called out Spike to Mulford, the instant he saw he
had regained his seat in the saddle. Harry sprang amidships to obey, and
the eye of every mariner in that vessel was on the young man, as, in the
midst of a death-like silence, he performed this all-important duty. It
was like the physician's feeling the pulse of his patient before he
pronounces on the degree of his danger.
"Well, sir?" cried out Spike, impatiently, as the rod re-appeared.
"All right, sir," answered Harry, cheerfully—"the well is nearly
empty."
"Hold on a moment longer, and give the water time to find its way
amidships, if there be any."
The mate remained perched up on the pump, in order to comply, while
Spike and his people, who now breathed more freely again, improved the
leisure to brace up and haul aft, to the new course.
"Biddy," said Mrs. Budd, considerately, during this pause in the
incidents, "you needn't scream any longer. The danger seems to be past,
and you may get up off the deck now. See, I have let go of the mast. The
pumps have been sounded, and are found tight."
Biddy, like an obedient and respectful servant, did as directed, quite
satisfied if the pumps were tight. It was some little time, to be sure,
before she was perfectly certain whether she were alive or not—but,
once certain of this circumstance, her alarm very sensibly abated, and
she became reasonable. As for Mulford, he dropped the sounding rod
again, and had the same cheering report to make.
"The brig is tight as a bottle, sir."
"So much the better," answered Spike. "I never had such a whirl in her
before in my life, and I thought she was going to stop and pass the
night there. That's the very spot on which 'The Hussar' frigate was
wrecked."
"So I have heard, sir. But she drew so much water that she hit slap
against the rock, and started a butt. We merely touched on its top, with
our fore-foot, and slid off."
This was the simple explanation of the Swash's escape, and every body
being now well assured that no harm had been done, things fell into
their old and regular train again. As for Spike, his gallantry,
notwithstanding, was upset for some hours, and glad enough was he when
he saw all three of his passengers quit the deck to go below. Mrs.
Budd's spirits had been so much agitated that she told Rose she would go
down into the cabin and rest a few minutes on its sofa. We say sofa, for
that article of furniture, now-a-days, is far more common in vessels
than it was thirty years ago in the dwellings of the country.
"There, Mulford," growled Spike, pointing ahead of the brig, to an
object on the water that was about half a mile ahead of them, "there's
that bloody boat—d'ye see? I should like of all things to give it the
slip. There's a chap in that boat I don't like."
"I don't see how that can be very well done, sir, unless we anchor,
repass the gate at the turn of the tide, and go to sea by the way of
Sandy Hook."
"That will never do. I've no wish to be parading the brig before the
town. You see, Mulford, nothing can be more innocent and proper than the
Molly Swash, as you know from having sailed in her these twelvemonths.
You'll give her that character, I'll be sworn?"
"I know no harm of her, Capt. Spike, and hope I never shall."
"No, sir—you know no harm of her, nor does any one else. A nursing
infant is not more innocent than the Molly Swash, or could have a
clearer character, if nothing but truth was said of her. But the world
is so much given to lying, that one of the old saints, of whom we read
in the good book, such as Calvin and John Rogers, would be vilified if
he lived in these times. Then, it must be owned, Mr. Mulford, whatever
may be the raal innocence of the brig, she has a most desperate wicked
look."
"Why, yes, sir—it must be owned she is what we sailors call a
wicked-looking craft. But some of Uncle Sam's cruisers have that
appearance also."
"I know it—I know it, sir, and think nothing of looks myself. Men are
often deceived in me, by _my_ looks, which have none of your long-shore
softness about 'em, perhaps; but my mother used to say I was one of the
most tender-hearted boys she had ever heard spoken of—like one of the
babes in the woods, as it might be. But mankind go so much by
appearances, that I do not like to trust the brig too much afore their
eyes. Now, should we be seen in the lower bay, waiting for a wind, or
for the ebb tide to make, to carry us over the bar, ten to one but some
philotropic or other would be off with a complaint to the District
Attorney, that we looked like a slaver, and have us all fetched up to be
tried for our lives as pirates. No, no—I like to keep the brig in
out-of-the-way places, where she can give no offence to your 'tropics,
whether they be philos, or of any other sort."
"Well, sir, we are to the eastward of the Gate, and all's safe. That
boat cannot bring us up."
"You forget, Mr. Mulford, the revenue craft that steamed up, on the ebb.
That vessel must be off Sands' Point by this time, and _she_ may hear
something to our disparagement from the feller in the boat, and take it
into her smoky head to walk us back to town. I wish we were well to the
eastward of that steamer! But there's no use in lamentations. If there
is really any danger, it's some distance ahead yet, thank Heaven!"
"You have no fears of the man who calls himself Jack Tier, Capt. Spike?"
"None in the world. That feller, as I remember him, was a little
bustlin' chap that I kept in the cabin, as a sort of steward's mate.
There was neither good nor harm in him, to the best of my recollection.
But Josh can tell us all about him—just give Josh a call."
The best thing in the known history of Spike was the fact that his
steward had sailed with him for more than twenty years. Where he had
picked up Josh no one could say, but Josh and himself, and neither chose
to be very communicative on the subject. But Josh had certainly been
with him as long as he had sailed the Swash, and that was from a time
actually anterior to the birth of Mulford. The mate soon had the <DW64>
in the council.
"I say, Josh," asked Spike, "do you happen to remember such a hand
aboard here as one Jack Tier?"
"Lor' bless you, yes, sir—'members he as well as I do the pea-soup that
was burnt, and which you t'rowed all over him to scald him for
punishment."
"I've had to do that so often, to one careless fellow or other, that the
circumstance doesn't recall the man. I remember him, but not as clear as
I could wish. How long did he sail with us?"
"Sebberal v'y'ge, sir, and got left ashore down on the Main, one night,
when 'e boat war obliged to shove off in a hurry. Yes, 'members little
Jack, right well I does."
"Did you see the man that spoke us from the wharf, and hailed for this
very Jack Tier?"
"I see'd a man, sir, dat was won'erful Jack Tier built like, sir; but I
didn't hear the conwersation, habbin' the ladies to 'tend to. But Jack
was oncommon short in his floor timbers, sir, and had no length of keel
at all. His beam was won'erful for his length, altogedder—what you call
jolly-boat or bum-boat build, and was only good afore 'e wind, Capt.
Spike."
"Was he good for any thing aboard ship, Josh? Worth heaving-to for,
should he try to get aboard of us again?"
"Why, sir, can't say much for him in dat fashion. Jack _was_ handy in
the cabin, and capital feller to carry soup from the galley, aft. You
see, sir, he was so low-rigged that the brig's lurchin' and pitchin'
couldn't get him off his pins, and he stood up like a church in the
heaviest wea'der. Yes, sir, Jack was right good for _dat_."
Spike mused a moment—then he rolled the tobacco over in his mouth, and
added, in the way a man speaks when his mind is made up—
"Ay, ay!—I see into the fellow. He'll make a handy lady's maid, and we
want such a chap, just now. It's better to have an old friend aboard,
than to be pickin' up strangers, 'long shore. So, should this Jack Tier
come off to us, from any of the islands or points ahead, Mr. Mulford,
you'll round to and take him aboard. As for the steamer, if she will
only pass out into the Sound, where there's room, it shall go hard with
us but I get to the eastward of her, without speaking. On the other
hand, should she anchor this side of the Fort, I'll not attempt to pass
her. There is deep water inside of most of the islands, I know, and
we'll try and dodge her in that way, if no better offer. I've no more
reason than another craft, to fear a government vessel; but the sight of
one of them makes me oncomfortable—that's all."
Mulford shrugged his shoulders, and remained silent, perceiving that his
commander was not disposed to pursue the subject any further. In the
mean time, the brig had passed beyond the influence of the bluff, and
was beginning to feel a stronger breeze, that was coming down the wide
opening of Flushing Bay. As the tide still continued strong in her
favor, and her motion through the water was getting to be four or five
knots, there was every prospect of her soon reaching Whitestone, the
point where the tides meet, and where it would become necessary to
anchor; unless, indeed, the wind, which was now getting to the southward
and eastward, should come round more to the south. All this Spike and
his mate discussed together, while the people were clearing the decks,
and making the preparations that are customary on board a vessel before
she gets into rough water.
By this time, it was ascertained that the brig had received no damage by
her salute of the Pot Rock, and every trace of uneasiness on that
account was removed. But Spike kept harping on the boat, and "the
pilot-looking chap who was in her." As they passed Riker's Island, all
hands expected a boat would put off with a pilot, or to demand pilotage;
but none came, and the Swash now seemed released from all her present
dangers, unless some might still be connected with the revenue steamer.
To <DW44> her advance, however, the wind came out a smart working breeze
from the southward and eastward, compelling her to make "long legs and
short ones" on her way towards Whitestone.
"This is beating the wind, Rosy dear," said Mrs. Budd, complacently, she
and her niece having returned to the deck a few minutes after this
change had taken place. "Your respected uncle did a great deal of this
in his time, and was very successful in it. I have heard him say, that
in one of his voyages between Liverpool and New York, he beat the wind
by a whole fortnight, every body talking of it in the insurance offices
as if it was a miracle."
"Ay, ay, Madam Budd," put in Spike, "I'll answer for that. They're
desperate talkers in and about them there insurance offices in Wall
street. Great gossips be they, and they think they know every thing.
Now, just because this brig is a little old or so, and was built for a
privateer in the last war, they'd refuse to rate her as even B, No. 2,
and my blessing on 'em."
"Yes, B, No. 2, that's just what your dear uncle used to call me,
Rosy—his charming B, No. 2, or Betsy, No. 2; particularly when he was
in a loving mood. Captain Spike, did you ever beat the wind in a long
voyage?"
"I can't say I ever did, Mrs. Budd," answered Spike, looking grimly
around, to ascertain if any one dared to smile at his passenger's
mistake; "especially for so long a pull as from New York to Liverpool."
"Then your uncle used to boast of the Rose In Bloom's wearing and
attacking. She would attack any thing that came in her way, no matter
who, and, as for wearing, I think he once told me she _would_ wear just
what she had a mind to, like any human being."
Rose was a little mystified, but she looked vexed at the same time, as
if she distrusted all was not right.
"I remember all my sea education," continued the unsuspecting widow, "as
if it had been learnt yesterday. Beating the wind and attacking ship, my
poor Mr. Budd used to say, were nice manœuvres, and required most of his
tactics, especially in heavy weather. Did you know, Rosy dear, that
sailors weigh the weather, and know when it is heavy and when it is
light?"
"I did not, aunt; nor do I understand now how it can very well be done."
"Oh! child, before you have been at sea a week, you will learn so many
things that are new, and get so many ideas of which you never had any
notion before, that you'll not be the same person. My captain had an
instrument he called a thermometer, and with that he used to weigh the
weather, and then he would write down in the log-book 'to-day, heavy
weather, or to-morrow, light weather,' just as it happened, and that
helped him mightily along in his voyages."
"Mrs. Budd has merely mistaken the name of the instrument—the
'barometer' is what she wished to say," put in Mulford, opportunely.
Rose looked grateful, as well as relieved. Though profoundly ignorant on
these subjects herself she had always suspected her aunt's knowledge. It
was, consequently, grateful to her to ascertain that, in this instance,
the old lady's mistake had been so trifling.
"Well, it may have been the barometer, for I know he had them both,"
resumed the aunt. "Barometer, or thermometer, it don't make any great
difference; or quadrant, or sextant. They are all instruments, and
sometimes he used one, and sometimes another. Sailors take on board the
sun, too, and have an instrument for that, as well as one to weigh the
weather with. Sometimes they take on board the stars, and the moon, and
'fill their ships with the heavenly bodies,' as I've heard my dear
husband say, again and again! But the most curious thing at sea, as all
sailors tell me, is crossing the line, and I do hope we shall cross the
line, Rosy, that you and I may see it."
"What is the line, aunty, and how do vessels cross it?"
"The line, my dear, is a place in the ocean where the earth is divided
into two parts, one part being called the North Pole, and the other part
the South Pole. Neptune lives near this line, and he allows no vessel to
go out of one pole into the other, without paying it a visit. Never!
never!—he would as soon think of living on dry land, as think of
letting even a canoe pass, without visiting it."
"Do you suppose there is such a being, really, as Neptune, aunty?"
"To be sure I do; he is king of the sea. Why shouldn't there be? The sea
must have a king, as well as the land."
"The sea may be a republic, aunty, like this country; then, no king is
necessary. I have always supposed Neptune to be an imaginary being."
"Oh! that's impossible—the sea is no republic; there are but two
republics, America and Texas. I've heard that the sea is a highway, it
is true—the 'highway of nations,' I believe it is called, and that must
mean something particular. But my poor Mr. Budd always told me that
Neptune was king of the seas, and _he_ was always so accurate, you might
depend on every thing he said. Why, he called his last Newfoundland dog
Neptune, and do you think, Rosy, that your dear uncle would call his dog
after an imaginary being?—and he a man to beat the wind, and attack
ship, and take the sun, moon and stars aboard! No, no, child; fanciful
folk may see imaginary beings, but solid folk see solid beings."
Even Spike was dumfounded at this, and there is no knowing what he might
have said, had not an old sea-dog, who had just come out of the
fore-topmast cross-trees, come aft, and, hitching up his trowsers with
one hand while he touched his hat with the other, said, with immovable
gravity,
"The revenue-steamer has brought up just under the Fort, Capt. Spike."
"How do you know that, Bill?" demanded the captain, with a rapidity that
showed how completely Mrs. Budd and all her absurdities were momentarily
forgotten.
"I was up on the fore-topgallant yard, sir, a bit ago, just to look to
the strap of the jewel-block, which wants some sarvice on it, and I
see'd her over the land, blowin' off steam and takin' in her kites.
Afore I got out of the cross-trees, she was head to wind under bare
poles, and if she hadn't anchored, she was about to do so. I'm sartain
'twas she, sir, and that she was about to bring up."
Spike gave a long, low whistle, after his fashion, and he walked away
from the females, with the air of a man who wanted room to think in.
Half a minute later, he called out—
"Stand by to shorten sail, boys. Man fore-clew-garnets, flying jib
down-haul, topgallant sheets, and gaff-topsail gear. In with 'em all, my
lads—in with every thing, with a will."
An order to deal with the canvas in any way, on board ship, immediately
commands the whole attention of all whose duty it is to attend to such
matters, and there was an end of all discourse while the Swash was
shortening sail. Every body understood, too, that it was to gain time,
and prevent the brig from reaching Throg's Neck sooner than was
desirable.
"Keep the brig off," called out Spike, "and let her ware—we're too busy
to tack just now."
The man at the wheel knew very well what was wanted, and he put his helm
up, instead of putting it down, as he might have done without this
injunction. As this change brought the brig before the wind, and Spike
was in no hurry to luff up on the other tack, the Swash soon ran over a
mile of the distance she had already made, putting her back that much on
her way to the Neck. It is out of our power to say what the people of
the different craft in sight thought of all this, but an opportunity
soon offered of putting them on a wrong scent. A large coasting
schooner, carrying every thing that would draw on a wind, came sweeping
under the stern of the Swash, and hailed.
"Has any thing happened, on board that brig?" demanded her master.
"Man overboard," answered Spike—"you havn't seen his hat, have you?"
"No—no," came back, just as the schooner, in her onward course, swept
beyond the reach of the voice. Her people collected together, and one or
two ran up the rigging a short distance, stretching their necks, on the
lookout for the "poor fellow," but they were soon called down to "'bout
ship." In less than five minutes, another vessel, a rakish coasting
sloop, came within hail.
"Didn't that brig strike the Pot Rock, in passing the Gate?" demanded
her captain.
"Ay, ay!—and a devil of a rap she got, too."
This satisfied _him_; there being nothing remarkable in a vessel's
acting strangely that had hit the Pot Rock, in passing Hell-Gate.
"I think we may get in our mainsail on the strength of this, Mr.
Mulford," said Spike. "There can be nothing oncommon in a craft's
shortening sail, that has a man overboard, and which has hit the Pot
Rock. I wonder I never thought of all this before."
"Here is a skiff trying to get alongside of us, Capt. Spike," called out
the boatswain.
"Skiff be d——d! I want no skiff here."
"The man that called himself Jack Tier is in her, sir."
"The d——l he is!" cried Spike, springing over to the opposite side of
the deck to take a look for himself. To his infinite satisfaction he
perceived that Tier was alone in the skiff, with the exception of a
<DW64>, who pulled its sculls, and that this was a very different boat
from that which had glanced through Hell-Gate, like an arrow darting
from its bow.
"Luff, and shake your topsail," called out Spike. "Get a rope there to
throw to this skiff."
The orders were obeyed, and Jack Tier, with his clothes-bag, was soon on
the deck of the Swash. As for the skiff and the <DW64>, they were cast
adrift the instant the latter had received his quarter. The meeting
between Spike and his quondam steward's mate was a little remarkable.
Each stood looking intently at the other, as if to note the changes
which time had made. We cannot say that Spike's hard, red, selfish
countenance betrayed any great feeling, though such was not the case
with Jack Tier's. The last, a lymphatic, puffy sort of a person at the
best, seemed really a little touched, and he either actually brushed a
tear from his eye, or he affected so to do.
"So, you are my old shipmate, Jack Tier, are ye?" exclaimed Spike, in a
half-patronizing, half-hesitating way—"and you want to try the old
craft ag'in. Give us a leaf of your log, and let me know where you have
been this many a day, and what you have been about. Keep the brig off,
Mr. Mulford. We are in no particular hurry to reach Throg's, you'll
remember, sir."
Tier gave an account of his proceedings, which could have no interest
with the reader. His narrative was any thing but very clear, and it was
delivered in a cracked, octave sort of a voice, such as little dapper
people not unfrequently enjoy—tones between those of a man and a boy.
The substance of the whole story was this. Tier had been left ashore, as
sometimes happens to sailors, and, by necessary connection, was left to
shift for himself. After making some vain endeavors to rejoin his brig,
he had shipped in one vessel after another, until he accidentally found
himself in the port of New York, at the same time as the Swash. He
know'd he never should be truly happy ag'in until he could once more get
aboard the old hussy, and had hurried up to the wharf, where he
understood the brig was lying. As he came in sight, he saw she was about
to cast off, and, dropping his clothes-bag, he had made the best of his
way to the wharf, where the conversation passed that has been related.
"The gentleman on the wharf was about to take boat, to go through the
Gate," concluded Tier, "and so I begs a passage of him. He was
good-natured enough to wait until I could find my bag, and as soon
a'terwards as the men could get their grog we shoved off. The Molly was
just getting in behind Blackwell's as we left the wharf, and, having
four good oars, and the shortest road, we come out into the Gate just
ahead on you. My eye! what a place that is to go through in a boat, and
on a strong flood! The gentleman, who watched the brig as a cat watches
a mouse, says you struck on the Pot, as he called it, but I says, 'no,'
for the Molly Swash was never know'd to hit rock or shoal in my time
aboard her."
"And where did you quit that gentleman, and what has become of him?"
asked Spike.
"He put me ashore on that point above us, where I see'd a <DW65> with
his skiff, who I thought would be willin' to 'arn his quarter by giving
me a cast along side. So here I am, and a long pull I've had to get
here."
As this was said, Jack removed his hat and wiped his brow with a
handkerchief, which, if it had never seen better days, had doubtless
been cleaner. After this, he looked about him, with an air not entirely
free from exultation.
This conversation had taken place in the gangway, a somewhat public
place, and Spike beckoned to his recruit to walk aft, where he might be
questioned without being overheard.
"What became of the gentleman in the boat, as you call him?" demanded
Spike.
"He pulled ahead, seeming to be in a hurry."
"Do you know who he was?"
"Not a bit of it. I never saw the man before, and he didn't tell me his
business, sir."
"Had he any thing like a silver oar about him?"
"I saw nothing of the sort, Capt. Spike, and knows nothing consarning
him."
"What sort of a boat was he in, and where did he get it?"
"Well, as to the boat, sir, I _can_ say a word, seein' it was so much to
my mind, and pulled so wonderful smart. It was a light ship's yawl, with
four oars, and came round the Hook just a'ter you had got the brig's
head round to the eastward. You must have seen it, I should think,
though it kept close in with the wharves, as if it wished to be snug."
"Then the gentleman, as you call him, expected _that_ very boat to come
and take him off?"
"I suppose so, sir, because it _did_ come and take him off. That's all I
knows about it."
"Had you no jaw with the gentleman? You wasn't mum the whole time you
was in the boat with him?"
"Not a bit of it, sir. Silence and I doesn't agree together long, so we
talked most of the time."
"And what did the stranger say of the brig?"
"Lord, sir, he catechised me like as if I had been a child at
Sunday-school. He asked me how long I had sailed in her; what ports we'd
visited, and what trade we'd been in. You can't think the sight of
questions he put, and how cur'ous he was for the answers."
"And what did you tell him in your answers? You said nothin' about our
call down on the Spanish Main, the time you were left ashore, I hope,
Jack?"
"Not I, sir. I played him off surprisin'ly. He got nothin' to count upon
out of me. Though I _do_ owe the Molly Swash a grudge, I'm not goin' to
betray her."
"You owe the Molly Swash a grudge! Have I taken an enemy on board her,
then?"
Jack started, and seemed sorry he had said so much; while Spike eyed him
keenly. But the answer set all right. It was not given, however, without
a moment for recollection.
"Oh, you knows what I mean, sir. I owe the old hussy a grudge for having
desarted me like; but it's only a love quarrel atween us. The old Molly
will never come to harm by my means."
"I hope not, Jack. The man that wrongs the craft he sails in can never
be a true-hearted sailor. Stick by your ship in all weathers is my rule,
and a good rule it is to go by. But what did you tell the stranger?"
"Oh! I told him I'd been six v'y'ges in the brig. The first was to
Madagascar—"
"The d—l you did! Was he soft enough to believe that?"
"That's more than I know, sir. I can only tell you what I _said_; I
don't pretend to know how much he _believed_."
"Heave ahead—what next?"
"Then I told him we went to Kamschatka for gold-dust and ivory."
"Whe-e-e-w! What did the man say to that?"
"Why, he smiled a bit, and a'ter that he seemed more curious than ever
to hear all about it. I told him my third v'y'ge was to Canton, with a
cargo of broom-corn, where we took in salmon and dun-fish for home.
A'ter that we went to Norway with ice, and brought back silks and money.
Our next run was to the Havana, with salt and 'nips—"
"'Nips! what the devil be they?"
"Turnips, you knows, sir. We always calls 'em 'nips in cargo. At the
Havana I told him we took in leather and jerked beef, and came home. Oh!
he got nothin' from me, Capt. Spike, that'll ever do the brig a morsel
of harm!"
"I am glad of that, Jack. You must know enough of the seas to understand
that a close mouth is sometimes better for a vessel than a clean bill of
health. Was there nothing said about the revenue-steamer?"
"Now you name her, sir, I believe there was—ay, ay, sir, the gentleman
_did_ say, if the steamer fetched up to the westward of the Fort, that
he should overhaul her without difficulty, on this flood."
"That'll do, Jack; that'll do, my honest fellow. Go below, and tell Josh
to take you into the cabin again, as steward's mate. You're rather too
Dutch built, in your old age, to do much aloft."
One can hardly say whether Jack received this remark as complimentary,
or not. He looked a little glum, for a man may be as round as a barrel,
and wish to be thought genteel and slender; but he went below, in quest
of Josh, without making any reply.
The succeeding movements of Spike appeared to be much influenced by what
he had just heard. He kept the brig under short canvas for near two
hours, sheering about in the same place, taking care to tell every thing
which spoke him that he had lost a man overboard. In this way, not only
the tide, but the day itself, was nearly spent. About the time the
former began to lose its strength, however, the fore-course and the
main-sail were got on the brigantine, with the intention of working her
up toward Whitestone, where the tides meet, and near which the
revenue-steamer was known to be anchored. We say near, though it was, in
fact, a mile or two more to the eastward, and close to the extremity of
the Point.
Notwithstanding these demonstrations of a wish to work to windward,
Spike was really in no hurry. He had made up his mind to pass the
steamer in the dark, if possible, and the night promised to favor him;
but, in order to do this, it might be necessary not to come in sight of
her at all; or, at least, not until the obscurity should in some measure
conceal his rig and character. In consequence of this plan, the Swash
made no great progress, even after she had got sail on her, on her old
course. The wind lessened, too, after the sun went down, though it still
hung to the eastward, or nearly ahead. As the tide gradually lost its
force, moreover, the set to windward became less and less, until it
finally disappeared altogether.
There is necessarily a short reach in this passage, where it is always
slack water, so far as current is concerned. This is precisely where the
tides meet, or, as has been intimated, at Whitestone, which is somewhat
more than a mile to the westward of Throgmorton's Neck, near the point
of which stands Fort Schuyler, one of the works recently erected for the
defence of New York. Off the pitch of the point, nearly mid-channel, had
the steamer anchored, a fact of which Spike had made certain, by going
aloft himself, and reconnoitering her over the land, before it had got
to be too dark to do so. He entertained no manner of doubt that this
vessel was in waiting for him, and he well knew there was good reason
for it; but he would not return and attempt the passage to sea by way of
Sandy Hook. His manner of regarding the whole matter was cool and
judicious. The distance to the Hook was too great to be made in such
short nights ere the return of day, and he had no manner of doubt he was
watched for in that direction, as well as in this. Then he was
particularly unwilling to show his craft at all in front of the town,
even in the night. Moreover, he had ways of his own for effecting his
purposes, and this was the very spot and time to put them in execution.
While these things were floating in his mind, Mrs. Budd and her handsome
niece were making preparations for passing the night, aided by Biddy
Noon. The old lady was factotum, or factota, as it might be most
classical to call her, though we are entirely without authorities on the
subject, and was just as self-complacent and ambitious of seawomanship
below decks, as she had been above board. The effect, however, gave
Spike great satisfaction, since it kept her out of sight, and left him
more at liberty to carry out his own plans. About nine, however, the
good woman came on deck, intending to take a look at the weather, like a
skilful marineress as she was, before she turned in. Not a little was
she astonished at what she then and there beheld, as she whispered to
Rose and Biddy, both of whom stuck close to her side, feeling the want
of good pilotage, no doubt, in strange waters.
The Molly Swash was still under her canvas, though very little sufficed
for her present purposes. She was directly off Whitestone, and was
making easy stretches across the passage, or river, as it is called,
having nothing set but her huge fore-and-aft mainsail and the jib. Under
this sail she worked like a top, and Spike sometimes fancied she
traveled too fast for his purposes, the night air having thickened the
canvas as usual, until it "held the wind as a bottle holds water." There
was nothing in this, however, to attract the particular attention of the
ship-master's widow, a sail, more or less, being connected with
observation much too critical for her schooling, nice as the last had
been. She was surprised to find the men stripping the brig forward, and
converting her into a schooner. Nor was this done in a loose and
slovenly manner, under favor of the obscurity. On the contrary, it was
so well executed that it might have deceived even a seaman under a
noon-day sun, provided the vessel were a mile or two distant. The manner
in which the metamorphosis was made was as follows. The studding-sail
booms had been taken off the topsail yard, in order to shorten it to the
eye, and the yard itself was swayed up about half mast, to give it the
appearance of a schooner's fore-yard. The brig's real lower yard was
lowered on the bulwarks, while her royal yard was sent down altogether,
and the topgallant-mast was lowered until the heel rested on the topsail
yard, all of which, in the night, gave the gear forward very much the
appearance of that of a fore-topsail schooner, instead of that of a half
rigged brig, as the craft really was. As the vessel carried a try-sail
on her foremast, it answered very well, in the dark, to represent a
schooner's foresail. Several other little dispositions of this nature
were made, about which it might weary the uninitiated to read, but which
will readily suggest themselves to the mind of a sailor.
These alterations were far advanced when the females re-appeared on
deck. They at once attracted their attention, and the captain's widow
felt the imperative necessity, as connected with her professional
character, of proving the same. She soon found Spike, who was bustling
around the deck, now looking around to see that his brig was kept in the
channel, now and then issuing an order to complete her disguise.
"Captain Spike, what _can_ be the meaning of all these changes? The
tamper of your vessel is so much altered that I declare I should not
have known her!"
"Is it, by George! Then, she is just in the state I want her to be in."
"But why have you done it—and what does it all mean?"
"Oh, Molly's going to bed for the night, and she's only undressing
herself—that's all."
"Yes, Rosy dear, Captain Spike is right. I remember that my poor Mr.
Budd used to talk about the Rose In Bloom having her clothes on, and her
clothes off, just as if she was a born woman! But don't you mean to
navigate at all in the night, Captain Spike? Or will the brig navigate
without sails?"
"That's it—she's just as good in the dark, under one sort of canvas, as
under another. So, Mr. Mulford, we'll take a reef in that mainsail; it
will bring it nearer to the size of our new foresail, and seem more
ship-shape and Brister fashion—then I think she'll do, as the night is
getting to be rather darkish."
"Captain Spike," said the boatswain, who had been sent to look-out for
that particular change—"the brig begins to feel the new tide, and sets
to windward."
"Let her go, then—now is as good a time as another. We've got to run
the gantlet, and the sooner it is done the better."
As the moment seemed propitious, not only Mulford, but all the people,
heard this order with satisfaction. The night was star-light, though not
very clear at that. Objects on the water, however, were more visible
than those on the land, while those on the last could be seen well
enough, even from the brig, though in confused and somewhat shapeless
piles. When the Swash was brought close by the wind, she had just got
into the last reach of the "river," or that which runs parallel with The
Neck for near a mile, doubling where the Sound expands itself,
gradually, to a breadth of many leagues. Still the navigation at the
entrance of this end of the Sound was intricate and somewhat dangerous,
rendering it indispensable for a vessel of any size to make a crooked
course. The wind stood at south-east, and was very scant to lay through
the reach with, while the tide was so slack as barely to possess a
visible current at that place. The steamer lay directly off the Point,
mid-channel, as mentioned, showing lights, to mark her position to any
thing which might be passing in or out. The great thing was to get by
her without exciting her suspicion. As all on board, the females
excepted, knew what their captain was at, the attempt was made amid an
anxious and profound silence; or, if any one spoke at all, it was only
to give an order in a low tone, or its answer in a simple monosyllable.
Although her aunt assured her that every thing which had been done
already, and which was now doing, was quite in rule, the quick-eyed and
quick-witted Rose noted these unusual proceedings, and had an opinion of
her own on the subject. Spike had gone forward, and posted himself on
the weather-side of the forecastle, where he could get the clearest look
ahead, and there he remained most of the time, leaving Mulford on the
quarter-deck, to work the vessel. Perceiving this, she managed to get
near the mate, without attracting her aunt's attention, and at the same
time out of ear-shot.
"Why is every body so still and seemingly so anxious, Harry Mulford?"
she asked, speaking in a low tone herself as if desirous of conforming
to a common necessity. "Is there any new danger here? I thought the Gate
had been passed altogether, some hours ago?"
"So it has. D'ye see that large dark mass on the water, off the Point,
which seems almost as huge as the Fort, with lights above it? That is a
revenue steamer which came out of York a few hours before us. We wish to
get past her without being troubled by any of her questions."
"And what do any in this brig care about her questions? They can be
answered, surely."
"Ay, ay, Rose—they _may_ be answered, as you say, but the answers
sometimes are unsatisfactory. Capt. Spike, for some reason or other, is
uneasy, and would rather not have any thing to say to her. He has the
greatest aversion to speaking the smallest craft when on a coast."
"And that's the reason he has undressed his Molly, as he calls her, that
he might not be known."
Mulford turned his head quickly toward his companion, as if surprised by
her quickness of apprehension, but he had too just a sense of his duty
to make any reply. Instead of pursuing the discourse, he adroitly
contrived to change it, by pointing out to Rose the manner in which they
were getting on, which seemed to be very successfully.
Although the Swash was under much reduced canvas, she glided along with
great ease and with considerable rapidity of motion. The heavy night air
kept her canvas distended, and the weatherly set of the tide, trifling
as it yet was, pressed her up against the breeze, so as to turn all to
account. It was apparent enough, by the manner in which objects on the
land were passed, that the crisis was fast approaching. Rose rejoined
her aunt, in order to await the result, in nearly breathless
expectation. At that moment, she would have given the world to be safe
on shore. This wish was not the consequence of any constitutional
timidity, for Rose was much the reverse from timid, but it was the fruit
of a newly awakened and painful, though still vague, suspicion. Happy,
thrice happy was it for one of her naturally confiding and guileless
nature, that distrust was thus opportunely awakened, for she was without
a guardian competent to advise and guide her youth, as circumstances
required.
The brig was not long in reaching the passage that opened to the Sound.
It is probable she did this so much the sooner because Spike kept her a
little off the wind, with a view of not passing too near the steamer. At
this point, the direction of the passage changes at nearly a right
angle, the revenue-steamer lying on a line with the Neck, and leaving a
sort of bay, in the angle, for the Swash to enter. The land was somewhat
low in all directions but one, and that was by drawing a straight line
from the Point, through the steamer, to the Long Island shore. On the
latter, and in that quarter, rose a bluff of considerable elevation,
with deep water quite near it; and, under the shadows of that bluff,
Spike intended to perform his nicest evolutions. He saw that the revenue
vessel had let her fires go down, and that she was entirely without
steam. Under canvas, he had no doubt of beating her hand over hand,
could he once fairly get to windward, and then she was at anchor, and
would lose some time in getting under way, should she even commence a
pursuit. It was all important, therefore, to gain as much to windward as
possible, before the people of the government vessel took the alarm.
There can be no doubt that the alterations made on board the Swash
served her a very good turn on this occasion. Although the night could
not be called positively dark, there was sufficient obscurity to render
her hull confused and indistinct at any distance, and this so much the
more when seen from the steamer outside, or between her and the land.
All this Spike very well understood, and largely calculated on. In
effect he was not deceived; the look-outs on board the revenue vessel
could trace little of the vessel that was approaching beyond the spars
and sails which rose above the shores, and these seemed to be the spars
and sails of a common fore-topsail schooner. As this was not the sort of
craft for which they were on the watch, no suspicion was awakened, nor
did any reports go from the quarter-deck to the cabin. The steamer had
her quarter watches, and officers of the deck, like a vessel of war, the
discipline of which was fairly enough imitated, but even a man-of-war
may be overreached on an occasion.
Spike was only great in a crisis, and then merely as a seaman. He
understood his calling to its minutiæ, and he understood the Molly Swash
better than he understood any other craft that floated. For more than
twenty years had he sailed her, and the careful parent does not better
understand the humors of the child, than he understood exactly what
might be expected from his brig. His satisfaction sensibly increased,
therefore, as she stole along the land, toward the angle mentioned,
without a sound audible but the gentle gurgling of the water, stirred by
the stem, and which sounded like the ripple of the gentlest wave, as it
washes the shingle of some placid beach.
As the brig drew nearer to the bluff, the latter brought the wind more
ahead, as respected the desired course. This was unfavorable, but it did
not disconcert her watchful commander.
"Let her come round, Mr. Mulford," said this pilot-captain, in a low
voice—"we are as near in as we ought to go."
The helm was put down, the head sheets started, and away into the wind
shot the Molly Swash, forereaching famously in stays, and, of course,
gaining so much on her true course. In a minute she was round, and
filled on the other tack. Spike was now so near the land, that he could
perceive the tide was beginning to aid him, and that his weatherly set
was getting to be considerable. Delighted at this, he walked aft, and
told Mulford to go about again as soon as the vessel had sufficient way
to make sure of her in stays. The mate inquired if he did not think the
revenue people might suspect something, unless they stood further out
toward mid-channel, but Spike reminded him that they would be apt to
think the schooner was working up under the southern shore because the
ebb first made there. This reason satisfied Mulford, and, as soon as
they were half way between the bluff and the steamer, the Swash was
again tacked, with her head to the former. This manœuvre was executed
when the brig was about two hundred yards from the steamer, a distance
that was sufficient to preserve, under all the circumstances, the
disguise she had assumed.
"They do not suspect us, Harry!" whispered Spike to his mate. "We shall
get to windward of 'em, as sartain as the breeze stands. That boatin'
gentleman might as well have staid at home, as for any good his hurry
done him or his employers!"
"Whom do you suppose him to be, Capt. Spike?"
"Who?—a feller that lives by his own wicked deeds. No matter who he is.
An informer, perhaps. At any rate, he is not the man to outwit the Molly
Swash, and her old, stupid, foolish master and owner, Stephen Spike.
Luff, Mr. Mulford, luff. Now's the time to make the most of your
leg—luff her up and shake her. She is setting to windward fast, the ebb
is sucking along that bluff like a boy at a molasses hogshead. All she
can drift on this tack is clear gain; there is no hurry, so long as they
are asleep aboard the steamer. That's it—make a half-board at once, but
take care and not come round. As soon as we are fairly clear of the
bluff, and open the bay that makes up behind it, we shall get the wind
more to the southward, and have a fine long leg for the next stretch."
Of course Mulford obeyed, throwing the brig up into the wind, and
allowing her to set to windward, but filling again on the same tack, as
ordered. This, of course, delayed her progress toward the land, and
protracted the agony, but it carried the vessel in the direction she
most wished to go, while it kept her not only end on to the steamer, but
in a line with the bluff, and consequently in the position most
favorable to conceal her true character. Presently, the bay mentioned,
which was several miles deep, opened darkly toward the south, and the
wind came directly out of it, or more to the southward. At this moment
the Swash was near a quarter of a mile from the steamer, and all that
distance dead to windward of her, as the breeze came out of the bay.
Spike tacked his vessel himself now, and got her head up so high that
she brought the steamer on her lee quarter, and looked away toward the
island which lies northwardly from the Point, and quite near to which
all vessels of any draught of water are compelled to pass, even with the
fairest winds.
"Shake the reef out of the mainsail, Mr. Mulford," said Spike, when the
Swash was fairly in motion again on this advantageous tack. "We shall
pass well to windward of the steamer, and may as well begin to open our
cloth again."
"Is it not a little too soon, sir?" Mulford ventured to remonstrate;
"the reef is a large one, and will make a great difference in the size
of the sail."
"They'll not see it at this distance. No, no, sir, shake out the reef,
and sway away on the topgallant-mast rope; I'm for bringing the Molly
Swash into her old shape again, and make her look handsome once more."
"Do you dress the brig, as well as undress her, o'nights, Capt. Spike?"
inquired the ship-master's relict, a little puzzled with this fickleness
of purpose. "I do not believe my poor Mr. Budd ever did that."
"Fashions change, madam, with the times—ay, ay, sir—shake out the
reef, and sway away on that mast-rope, boys, as soon as you have manned
it. We'll convert our schooner into a brig again."
As these orders were obeyed, of course, a general bustle now took place.
Mulford soon had the reef out, and the sail distended to the utmost,
while the topgallant-mast was soon up and fidded. The next thing was to
sway upon the fore-yard, and get that into its place. The people were
busied at this duty, when a hoarse hail came across the water on the
heavy night air.
"Brig ahoy!" was the call.
"Sway upon that fore-yard," said Spike, unmoved by this summons—"start
it, start it at once."
"The steamer hails us, sir," said the mate.
"Not she. She is hailing a brig; we are a schooner yet."
A moment of active exertion succeeded, during which the foreyard went
into its place. Then came a second hail.
"Schooner, ahoy!" was the summons this time.
"The steamer hails us again, Capt. Spike."
"The devil a bit. We're a brig now, and she hails a schooner. Come,
boys, bestir yourselves, and get the canvas on Molly for'ard. Loose the
fore-course before you quit the yard there, then up aloft and loosen
every thing you can find."
All was done as ordered, and done rapidly, as is ever the case on board
a well ordered vessel when there is occasion for exertion. That occasion
now appeared to exist in earnest, for while the men were sheeting home
the topsail a flash of light illuminated the scene, when the roar of a
gun came booming across the water, succeeded by the very distinct
whistling of its shot. We regret that the relict of the late Capt. Budd
did not behave exactly as became a ship-master's widow, under fire.
Instead of remaining silent and passive, even while frightened, as was
the case with Rose, she screamed quite as loud as she had previously
done that very day in Hell-Gate. It appeared to Spike, indeed, that
practice was making her perfect; and, as for Biddy, the spirit of
emulation became so powerful in her bosom, that, if any thing, she
actually outshrieked her mistress. Hearing this, the widow made a second
effort, and fairly recovered the ground some might have fancied she had
lost.
"Oh! Captain Spike," exclaimed the agitated widow, "do not—do not, if
you love me, do not let them fire again!"
"How am I to help it!" asked the captain, a good deal to the point,
though he overlooked the essential fact, that, by heaving-to, and
waiting for the steamer's boat to board him, he might have prevented a
second shot, as completely as if he had the ordering of the whole
affair. No second shot was fired, however. As it afterward appeared, the
screams of Mrs. Budd and Biddy were heard on board the steamer, the
captain of which, naturally enough, supposing that the slaughter must be
terrible where such cries had arisen, was satisfied with the mischief he
had already done, and directed his people to secure their gun and go to
the capstan-bars, in order to help lift the anchor. In a word, the
revenue vessel was getting under way, man-of-war fashion, which means
somewhat expeditiously.
Spike understood the sounds that reached him, among which was the call
of the boatswain, and he bestirred himself accordingly. Experienced as
he was in chases and all sorts of nautical artifices, he very well knew
that his situation was sufficiently critical. It would have been so,
with a steamer at his heels, in the open ocean; but, situated as he was,
he was compelled to steer but one course, and to accept the wind on that
course as it might offer. If he varied at all in his direction it was
only in a trifling way, though he did make some of these variations.
Every moment was now precious, however, and he endeavored to improve the
time to the utmost. He knew that he could greatly outsail the revenue
vessel, under canvas, and some time would be necessary to enable her to
get up her steam; half an hour at the very least. On that half hour,
then, depended the fate of the Molly Swash.
"Send the booms on the yards, and set stun'sails at once, Mr. Mulford,"
said Spike, the instant the more regular canvas was spread forward.
"This wind will be free enough for all but the lower stun'sail, and we
must drive the brig on."
"Are we not looking up too high, Capt. Spike? The Stepping-Stones are
ahead of us, sir."
"I know that very well, Mulford. But it's nearly high water, and the
brig's in light trim, and we may rub and go. By making a short cut here,
we shall gain a full mile on the steamer; that mile may save us."
"Do you really think it possible to get away from that craft, which can
always make a fair wind of it, in these narrow waters, Capt. Spike?"
"One don't know, sir. Nothin' is done without tryin', and by tryin' more
is often done than was hoped for. I have a scheme in my head, and
Providence may favor me in bringing it about."
Providence! The religionist quarrels with the philosopher if the latter
happen to remove this interposition of a higher power, even so
triflingly as by the intervention of secondary agencies, while the
biggest rascal dignifies even his success by such phrases as
Providential aid! But it is not surprising men should misunderstand
terms, when they make such sad confusion in the acts which these terms
are merely meant to represent. Spike had his Providence as well as a
priest, and we dare say he often counted on its succor, with quite as
rational grounds of dependence as many of the pharisees who are
constantly exclaiming, "The Temple of the Lord, the Temple of the Lord
are these."
Sail was made on board the Swash with great rapidity, and the brig made
a bold push at the Stepping-Stones. Spike was a capital pilot. He
insisted if he could once gain sight of the spar that was moored on
those rocks for a buoy, he should run with great confidence. The two
lights were of great assistance, of course, but the revenue vessel could
see these lights as well as the brig, and _she_, doubtless, had an
excellent pilot on board. By the time the studding-sails were set on
board the Swash, the steamer was aweigh, and her long line of peculiar
sails became visible. Unfortunately for men who were in a hurry, she lay
so much within the bluff as to get the wind scant, and her commander
thought it necessary to make a stretch over to the southern shore,
before he attempted to lay his course. When he was ready to tack, an
operation of some time with a vessel of her great length, the Swash was
barely visible in the obscurity, gliding off upon a slack bowline, at a
rate which nothing but the damp night air, the ballast-trim of the
vessel, united to her excellent sailing qualities, could have produced
with so light a breeze.
The first half hour took the Swash completely out of sight of the
steamer. In that time, in truth, by actual superiority in sailing, by
her greater state of preparation, and by the distance saved by a bold
navigation, she had gained fully a league on her pursuer. But, while the
steamer had lost sight of the Swash, the latter kept the former in view,
and that by means of a signal that was very portentous. She saw the
light of the steamer's chimneys, and could form some opinion of her
distance and position.
It was about eleven o'clock when the Swash passed the light at Sands'
Point, close in with the land. The wind stood much as it had been. If
there was a change at all, it was half a point more to the southward,
and it was a little fresher. Such as it was, Spike saw he was getting,
in that smooth water, quite eight knots out of his craft, and he made
his calculations thereon. As yet, and possibly for half an hour longer,
he was gaining, and might hope to continue to gain on the steamer. Then
her turn would come. Though no great traveler, it was not to be expected
that, favored by smooth water and the breeze, her speed would be less
than ten knots, while there was no hope of increasing his own without an
increase of the wind. He might be five miles in advance, or six at the
most; these six miles would be overcome in three hours of steaming, to a
dead certainty, and they might possibly be overcome much sooner. It was
obviously necessary to resort to some other experiment than that of dead
sailing, if an escape was to be effected.
The Sound was now several miles in width, and Spike, at first, proposed
to his mate, to keep off dead before the wind, and by crossing over to
the north shore, let the steamer pass ahead, and continue a bootless
chase to the eastward. Several vessels, however, were visible in the
middle of the passage, at distances varying from one to three miles, and
Mulford pointed out the hopelessness of attempting to cross the sheet of
open water, and expect to go unseen by the watchful eyes of the revenue
people.
"What you say is true enough, Mr. Mulford," answered Spike, after a
moment of profound reflection, "and every foot that they come nearer,
the less will be our chance. But here is Hempstead Harbor a few leagues
ahead; if we can reach _that_ before the blackguards close we may do
well enough. It is a deep bay, and has high land to darken the view. I
don't think the brig could be seen at midnight by any thing outside, if
she was once fairly up that water a mile or two."
"That is our chance, sir!" exclaimed Mulford cheerfully. "Ay, ay, I know
the spot, and every thing is favorable—try that, Capt. Spike; I'll
answer for it that we go clear."
Spike did try it. For a considerable time longer he stood on, keeping as
close to the land as he thought it safe to run, and carrying every thing
that would draw. But the steamer was on his heels, evidently gaining
fast. Her chimneys gave out flames, and there was every sign that her
people were in earnest. To those on board the Swash these flames seemed
to draw nearer each instant, as indeed was the fact, and just as the
breeze came fresher out of the opening in the hills, or the low
mountains, which surround the place of refuge in which they designed to
enter, Mulford announced that by aid of the night-glass he could
distinguish both sails and hull of their pursuer. Spike took a look, and
throwing down the instrument, in a way to endanger it, he ordered the
studding-sails taken in. The men went aloft like cats, and worked as if
they could stand in air. In a minute or two the Swash was under what
Mrs. Budd might have called her "attacking" canvas, and was close by the
wind, looking on a good leg well up the harbor. The brig seemed to be
conscious of the emergency, and glided ahead at capital speed. In five
minutes she had shut in the flaming chimneys of the steamer. In five
minutes more Spike tacked, to keep under the western side of the harbor,
and out of sight as long as possible, and because he thought the breeze
drew down fresher where he was than more out in the bay.
All now depended on the single fact whether the brig had been seen from
the steamer or not, before she hauled into the bay. If seen, she had
probably been watched; if not seen, there were strong grounds for hoping
that she might still escape. About a quarter of an hour after Spike
hauled up, the burning chimneys came again into view. The brig was then
half a league within the bay, with a fine dark back-ground of hills to
throw her into shadow. Spike ordered every thing taken in but the
trysail, under which the brig was left to set slowly over toward the
western side of the harbor. He now rubbed his hands with delight, and
pointed out to Mulford the circumstance that the steamer kept on her
course directly athwart the harbor's mouth! Had she seen the Swash no
doubt she would have turned into the bay also. Nevertheless, an anxious
ten minutes succeeded, during which the revenue vessel steamed fairly
past, and shut in her flaming chimneys again by the eastern headlands of
the estuary.
PART III.
The western wave was all a flame,
The day was well nigh done,
Almost upon the western wave
Rested the broad bright sun;
When that strange ship drove suddenly
Betwixt us and the sun.
THE ANCIENT MARINER.
At that hour, on the succeeding morning, when the light of day is just
beginning to chase away the shadows of night, the Molly Swash became
visible within the gloom of the high land which surrounds so much of the
bay of Hempstead, under easy sail, backing and filling, in order to keep
within her hiding place, until a look could be had at the state of
things without. Half an hour later, she was so near the entrance of the
estuary, as to enable the look-outs aloft to ascertain that the coast
was clear, when Spike ordered the helm to be put up, and the brig to be
kept away to her course. At this precise moment, Rose appeared on deck,
refreshed by the sleep of a quiet night, and with cheeks tinged with a
color even more delicate than that which was now glowing in the eastern
sky, and which was almost as brilliant.
"We stopped in this bit of a harbor for the night, Miss Rose, that is
all;" said Spike, observing that his fair passenger was looking about
her, in some little surprise, at finding the vessel so near the land,
and seemingly so much out of her proper position. "Yes, we always do
that, when we first start on a v'y'ge, and before the brig gets use to
traveling—don't we, Mr. Mulford?"
Mr. Mulford, who knew how hopeless was the attempt to mystify Rose, as
one might mystify her credulous and weak-minded aunt, and who had no
disposition to deal any way but fairly by the beautiful, and in one
sense now helpless young creature before him, did not see fit to make
any reply. Offend Spike he did not dare to do, more especially under
present circumstances; and mislead Rose he would not do. He affected not
to hear the question, therefore, but issuing an order about the
head-sails, he walked forward as if to see it executed. Rose herself was
not under as much restraint as the young mate.
"It is convenient, Capt. Spike," she coolly answered for Mulford, "to
have stopping places for vessels that are wearied, and I remember the
time when my uncle used to tell me of such matters, very much in the
same vein; but, it was before I was twelve years old."
Spike hemmed, and he looked a little foolish, but Clench, the boatswain,
coming aft to say something to him in confidence, just at that moment,
he was enabled to avoid the awkwardness of attempting to explain. This
man Clench, or Clinch, as the name was pronounced, was deep in the
captain's secrets; far more so than was his mate, and would have been
filling Mulford's station at that very time, had he not been hopelessly
ignorant of navigation. On the present occasion, his business was to
point out to the captain, two or three lines of smoke, that were visible
above the water of the Sound, in the eastern board; one of which he was
apprehensive might turn out to be the smoke of the revenue craft, from
which they had so recently escaped.
"Steamers are no rarities in Long Island Sound, Clench," observed the
captain, leveling his glass at the most suspected of the smokes. "That
must be a Providence, or Stonington chap, coming west with the Boston
train."
"Either of _them_ would have been further west, by this time, Capt.
Spike," returned the doubting, but watchful boatswain. "It's a large
smoke, and I fear it is the revenue fellow coming back, after having had
a look well to the eastward, and satisfying himself that we are not to
be had in that quarter."
Spike growled out his assent to the possibility of such a conjecture,
and promised vigilance. This satisfied his subordinate for the moment,
and he walked forward, or to the place where he belonged. In the mean
time, the widow came on deck, smiling, and snuffing the salt air, and
ready to be delighted with any thing that was maritime.
"Good morning, Capt. Spike," she cried—"are we in the offing, yet—you
know I desired to be told when we are in the offing, for I intend to
write a letter to my poor Mr. Budd's sister, Mrs. Sprague, as soon as we
get to the offing."
"What is the offing, aunt?" enquired the handsome niece.
"Why _you_ have hardly been at sea long enough to understand me, child,
should I attempt to explain. The offing, however, is the place where the
last letters are always written to the owners, and to friends ashore.
The term comes, I suppose, from the circumstance that the vessel is
about to be off, and it is natural to think of those we leave behind, at
such a moment. I intend to write to your aunt Sprague, my dear, the
instant I hear we are in the offing; and what is more, I intend to make
you my amanuensis."
"But how will the letter be sent, aunty?—I have no more objections to
writing than any one else, but I do not see how the letter is to be
sent. Really, the sea _is_ a curious region, with its stopping places
for the night, and its offings to write letters at!"
"Yes, it's all as you say, Rose—a most remarkable region is the sea!
You'll admire it, as I admire it, when you come to know it better; and
as your poor uncle admired it, and as Capt. Spike admires it, too. As
for the letters, they can be sent ashore by the pilot, as letters are
always sent."
"But, aunty, there _is_ no pilot in the Swash—for Capt. Spike refused
to take one on board."
"Rose!—you don't understand what you are talking about! No vessel ever
yet sailed without a pilot, if indeed any _can_. It's opposed to the
law, not to have a pilot; and now I remember to have heard your dear
uncle say it wasn't a voyage if a vessel didn't take away a pilot."
"But if they take them away, aunty, how can they send the letters ashore
by them?"
"Poh! poh! child; you don't know what you're saying; but you'll overlook
it, I hope, Capt. Spike, for Rose is quick, and will soon learn to know
better. As if letters couldn't be sent ashore by the pilot, though he
was a hundred thousand miles from land! But, Capt. Spike, you must let
me know when we are about to get off the Sound, for I know that the
pilot is always sent ashore with his letters, before the vessel gets off
the Sound."
"Yes, yes," returned the captain, a little mystified by the widow,
though he knew her so well, and understood her so well—"you shall know,
ma'am, when we get off soundings, for I suppose that is what you mean."
"What is the difference? Off the Sound, or off the soundings, of course,
must mean the same thing. But, Rosy, we will go below and write to your
aunt at once, for I see a light-house yonder, and light-houses are
always put just off the soundings."
Rose, who always suspected her aunt's nautical talk, though she did not
know how to correct it, and was not sorry to put an end to it, now, by
going below, and spreading her own writing materials, in readiness to
write, as the other dictated. Biddy Noon was present, sewing on some of
her own finery.
"Now write, as I tell you, Rose," commenced the widow—
"My dear sister Sprague—Here we are, at last, just off the soundings,
with light-houses all round us, and so many capes and islands in sight,
that it does seem as if the vessel never _could_ find its way through
them all. Some of these islands must be the West Indies"—
"Aunty, that can _never_ be!" exclaimed Rose—"we left New York only
yesterday."
"What of that? Had it been old times, I grant you several days might be
necessary to get a sight of the West Indies, but, now, when a letter can
be written to a friend in Boston and an answer received in half an hour,
it requires no such time to go to the West Indies. Besides, what other
islands are there in this part of the world?—they can't be England—"
"No—no"—said Rose, at once seeing it would be preferable to admit they
were the West Indies; so the letter went on:—
"Some of these islands must be the West Indies, and it is high time we
saw some of them, for we are nearly off the Sound, and the light-houses
are getting to be quite numerous. I think we have already seen four
since we left the wharf. But, my dear sister Sprague, you will be
delighted to hear how much better Rose's health is already becoming—"
"My health, aunty! Why, I never knew an ill day in my life!"
"Don't tell me that, my darling; I know too well what all these
deceptive appearances of health amount to. I would not alarm you for the
world, Rosy dear, but a careful parent—and I'm your parent in
affection, if not by nature—but a careful parent's eye is not to be
deceived. I know you _look_ well, but you are ill, my child; though,
Heaven be praised, the sea air and hydropathy are already doing you a
monstrous deal of good."
As Mrs. Budd concluded, she wiped her eyes, and appeared really glad
that her niece had a less consumptive look than when she embarked. Rose
sat, gazing at her aunt, in mute astonishment. She knew how much and
truly she was beloved, and that induced her to be more tolerant of her
connection's foibles than even duty demanded. Feeling was blended with
her respect, but it was almost too much for her, to learn that this
long, and, in some respects painful voyage, was undertaken on her
account, and without the smallest necessity for it. The vexation,
however, would have been largely increased, but for certain free
communications that had occasionally occurred between her and the
handsome mate, since the moment of her coming on board the brig. Rose
knew that Harry Mulford loved her, too, for he had told her as much with
a seaman's frankness; and, though she had never let him know that his
partiality was returned, her woman's heart was fast inclining toward
him, with all her sex's tenderness. This made the mistake of her aunt
_tolerable_, though Rose was exceedingly vexed it should ever have
occurred.
"Why, my dearest aunt," she cried, "they told me it was on _your_
account that this voyage was undertaken!"
"I know they did, poor, dear Rosy, and that was in order not to alarm
you. Some persons of delicate constitutions—"
"But my constitution is not in the least delicate, aunt; on the
contrary, it is as good as possible; a blessing for which, I trust, I am
truly grateful. I did not know but you might be suffering, though you do
look so well, for they all agreed in telling me you had need of a
sea-voyage."
"I, a subject for hydropathy! Why, child, water is no more necessary to
me, than it is to a cat."
"But going to sea, aunty, is not hydropathy—"
"Don't say that, Rosy; do not say that, my dear. It is hydropathy on a
large scale, as Capt. Spike says, and when he gets us into blue water,
he has promised that you shall have all the benefits of the treatment."
Rose was silent and thoughtful; after which she spoke quickly, like one
to whom an important thought had suddenly occurred.
"And Capt. Spike, then, was consulted in my case?" she asked.
"He was, my dear, and you have every reason to be grateful to him. He
was the first to discover a change in your appearance, and to suggest a
sea voyage. Marine Hydropathy, he said, he was sure would get you up
again; for Capt. Spike thinks your constitution good at the bottom,
though the high color you have proves too high a state of habitual
excitement."
"Was Dr. Monson consulted at all, aunt?"
"Not at all. You know the doctors are all against hydropathy, and
mesmerism, and the magnetic telegraph, and every thing that is new; so
we thought it best not to consult him."
"And my aunt Sprague?"
"Yes, _she_ was consulted after every thing was settled, and when I knew
her notions could not undo what had been already done. But she is a
seaman's widow, as well as myself, and has a great notion of the virtue
of sea air."
"Then it would seem that Dr. Spike was the principal adviser in my
case!"
"I own that he was, Rosy dear. Capt. Spike was brought up by your uncle,
who has often told me what a thorough seaman he was. 'There's Spike,
now,' he said to me one day, 'he can almost make his brig talk'—this
very brig, too, your uncle meant, Rosy, and of course one of the best
vessels in the world, to take hydropathy in."
"Yes, aunty," returned Rose, playing with the pen, while her air proved
how little her mind was in her words. "Well, what shall I say next to my
aunt Sprague?"
"Rose's health is already becoming _confirmed_," resumed the widow, who
thought it best to encourage her niece by as strong terms as she could
employ, "and I shall extol hydropathy to the skies, as long as I live.
As soon as we reach our port of destination, my dear sister Sprague, I
shall write you a line to let you know it, by the magnetic telegraph—"
"But there is no magnetic telegraph on the sea, aunty," interrupted
Rose, looking up from the paper, with her clear, serene, blue eyes,
expressing even _her_ surprise, at this touch of the relict's ignorance.
"Don't tell me _that_, Rosy child, when every body says the sparks will
fly round the whole earth, just as soon as they will fly from New York
to Philadelphia."
"But they must have something to fly on, aunty; and the ocean will not
sustain wires, or posts."
"Well, there is no need of being so particular; if there is no
telegraph, the letter must come by mail. You can say telegraph, here,
and when your aunt gets the letter, the post-mark will tell her how it
came. It looks better to talk about telegraphic communications, child."
Rose resumed her pen, and wrote at her aunt's dictation, as
follows:—"By the magnetic telegraph, when I hope to be able to tell you
that our dear Rose is well. As yet, we both enjoy the ocean exceedingly;
but when we get off the Sound, into blue water, and have sent the pilot
ashore, or discharged him, I ought to say, which puts me in mind of
telling you that a cannon was discharged at us only last night, and that
the ball whistled so near me, that I heard it as plain as ever you heard
Rose's piano."
"Had I not better first tell my aunt Sprague what is to be done when the
pilot is discharged?"
"No; tell her about the cannon that was discharged, first, and about the
ball that I heard. I had almost forgot that adventure, which was a very
remarkable one, was it not Biddy?"
"Indeed, Missus, and it was! and Miss Rose might put in the letter how
we both screamed at that cannon, and might have been heard as plainly,
every bit of it, as the ball."
"Say nothing on the subject, Rose, or we shall never hear the last of
it. So, darling, you may conclude in your own way, for I believe I have
told your aunt all that comes to mind."
Rose did as desired, finishing the epistle in a very few words, for,
rightly enough, she had taken it into her head there was no pilot to be
discharged, and consequently that the letter would never be sent. Her
short, but frequent conferences with Mulford were fast opening her eyes,
not to say her heart, and she was beginning to see Capt. Spike in his
true character, which was that of a great scoundrel. It is true, that
the mate had not long judged his commander quite so harshly; but had
rather seen his beautiful brig and her rare qualities, in her owner and
commander, than the man himself; but jealousy had quickened his
observation of late, and Stephen Spike had lost ground sensibly with
Harry Mulford, within the last week. Two or three times before, the
young man had thought of seeking another berth, on account of certain
distrusts of Spike's occupations; but he was poor, and so long as he
remained in the Swash, Harry's opportunities of meeting Rose were
greatly increased. This circumstance, indeed, was the secret of his
still being in the "Molly," as Spike usually called his craft; the last
voyage having excited suspicions that were rather of a delicate nature.
Then the young man really loved the brig, which, if she could not be
literally made to talk, could be made to do almost every thing else. A
vessel, and a small vessel, too, is rather contracted as to space, but
those who wish to converse can contrive to speak together often, even in
such narrow limits. Such had been the fact with Rose Budd and the
handsome mate. Twenty times since they sailed, short as that time was,
had Mulford contrived to get so near to Rose, as to talk with her,
unheard by others. It is true, that he seldom ventured to do this, so
long as the captain was in sight, but Spike was often below, and
opportunities were constantly occurring. It was in the course of these
frequent but brief conversations, that Harry had made certain dark hints
touching the character of his commander, and the known recklessness of
his proceedings. Rose had taken the alarm, and fully comprehending her
aunt's mental imbecility, her situation was already giving her great
uneasiness. She had some undefined hopes from the revenue steamer,
though, strangely enough as it appeared to her, her youngest and most
approved suitor betrayed a strong desire to escape from that craft, at
the very moment he was expressing his apprehensions on account of her
presence in the brig. This contradiction arose from a certain _esprit de
corps_, which seldom fails, more or less, to identify the mariner with
his ship.
But the writing was finished, and the letter sealed with wax, Mrs. Budd
being quite as particular in that ceremony as Lord Nelson, when the
females again repaired on deck. They found Spike and his mate sweeping
the eastern part of the sound, with their glasses, with a view to look
out for enemies; or, what to them, just then, was much the same thing,
government craft. In this occupation, Rose was a little vexed to see
that Mulford was almost as much interested as Spike himself, the love of
his vessel seemingly overcoming his love for her, if not his love of the
right—she knew of no reason, however, why the captain should dread any
other vessel, and felt sufficiently provoked to question him a little on
the subject, if it were only to let him see that the niece was not as
completely his dupe as the aunt. She had not been on deck five minutes,
therefore, during which time several expressions had escaped the two
sailors touching their apprehensions of vessels seen in the distance,
ere she commenced her inquiries.
"And why should we fear meeting with other vessels?" Rose plainly
demanded—"here in Long Island Sound, and within the power of the laws
of the country?"
"Fear!" exclaimed Spike, a little startled, and a good deal surprised at
this straight-forward question—"Fear, Miss Rose! You do not think we
are afraid, though there are many reasons why we do not wish to be
spoken by certain craft that are hovering about. In the first place, you
know it is war time—I suppose you know, Madam Budd, that America is at
war with Mexico?"
"Certainly," answered the widow, with dignity—"and that is a sufficient
reason, Rose, why one vessel should chase, and another should run. If
you had heard your poor uncle relate, as I have done, all his chasings
and runnings away, in the war times, child, you would understand these
things better. Why, I've heard your uncle say that, in some of his long
voyages, he has run thousands and thousands of miles, with sails set on
both sides, and all over his ship!"
"Yes, aunty, and so have I, but that was 'running before the wind,' as
he used to call it."
"I s'pose, however, Miss Rose," put in Spike, who saw that the niece
would soon get the better of the aunt;—"I s'pose, Miss Rose, that
you'll acknowledge that America is at war with Mexico?"
"I am sorry to say that such is the fact, but I remember to have heard
you say, yourself, Capt. Spike, when my aunt was induced to undertake
this voyage, that you did not consider there was the smallest danger
from any Mexicans."
"Yes, you did, Capt. Spike," added the aunt—"you did say there was no
danger from Mexicans."
"Nor is there a bit, Madam Budd, if Miss Rose, and your honored self
will only hear me. There is no danger, because the brig has the heels of
any thing Mexico can send to sea. She has sold her steamers, and, as for
any thing else under her flag, I would not care a straw."
"The steamer from which we ran, last evening, and which actually fired
off a cannon at us, was not Mexican, but American," said Rose, with a
pointed manner that put Spike to his trumps.
"Oh! that steamer—" he stammered—"that was a race—only a race, Miss
Rose, and I wouldn't let her come near me, for the world. I should never
hear the last of it, in the insurance offices, and on 'change, did I let
_her_ overhaul us. You see, Miss Rose—you see, Madam Budd—" Spike ever
found it most convenient to address his mystifying discourse to the
aunt, in preference to addressing it to the niece—"You see, Madam Budd,
the master of that craft and I are old cronies—sailed together when
boys, and set great store by each other. We met only last evening, just
a'ter I had left your own agreeable mansion, Madam Budd, and says he,
'Spike, when do you sail?' 'To-morrow's flood, Jones,' says I—his name
is Jones;—Peter Jones, and as good a fellow as ever lived. 'Do you go
by the Hook, or by Hell-Gate—'"
"Hurl-Gate, Capt. Spike, if you please—or Whirl-Gate, which some people
think is the true sound; but the other way of saying it is awful."
"Well, the captain, my old master, always called it Hell-Gate, and I
learned the trick from him—"
"I know he did, and so do all sailors; but genteel people, now-a-days,
say nothing but Hurl-Gate, or Whirl-Gate."
Rose smiled at this, as did Mulford; but neither said any thing, the
subject having once before been up between them. As for ourselves, we
are still so old fashioned as to say, and write, Hell-Gate, and intend
so to do, in spite of all the Yankees that have yet passed through it,
or who ever shall pass through it, and that is saying a great deal. We
do not like changing names to suit their uneasy spirits.
"Call the place Hurl-Gate, and go on with your story," said the widow,
complacently.
"Yes, Madam Budd—'Do you go by the Hook, or by Whirl-Gate?' said Jones.
'By Whirl-a-Gig-Gate,' says I. 'Well,' says he, 'I shall go through the
Gate myself, in the course of the morning. We may meet somewhere to the
eastward, and, if we do, I'll bet you a beaver,' says he, 'that I show
you my stern.' 'Agreed,' says I, and we shook hands upon it. That's the
whole history of our giving the steamer the slip, last night, and of my
not wishing to let her speak me."
"But you went into a bay, and let her go past you," said Rose, coolly
enough as to manner, but with great point as to substance. "Was not that
a singular way of winning a race?"
"It does seem so, Miss Rose, but it's all plain enough, when understood.
I found that steam was too much for sails, and I stood up into the bay
to let them run past us, in hopes they would never find out the trick. I
care as little for a hat, as any man, but I do care a good deal about
having it reported on 'change that the Molly was beat, by even a
steamer."
This ended the discourse, for the moment, Clench again having something
to say to his captain in private.
"How much of that explanation am I to believe, and how much disbelieve?"
asked Rose, the instant she was left alone with Harry. "If it be all
invention, it was a ready and ingenious story."
"No part of it is true. He no more expected that the steamer would pass
through Hell-Gate, than I expected it myself. There was no bet, or race,
therefore; but it was our wish to avoid Uncle Sam's cruiser, that was
all."
"And why should _you_ wish any such thing?"
"On my honor, I can give you no better reason, so far as I am concerned,
than the fact that, wishing to keep clear of her, I do not like to be
overhauled. Nor can I tell you why Spike is so much in earnest in
holding the revenue vessel at arm's length; I know he dislikes all such
craft, as a matter of course, but I can see no particular reason for it
just now. A more innocent cargo was never struck into a vessel's hold."
"What is it?"
"Flour; and no great matter of that. The brig is not half full, being
just in beautiful ballast trim, as if ready for a race. I can see no
sufficient reason, beyond native antipathy, why Capt. Spike should wish
to avoid any craft, for it is humbug his dread of a Mexican, and least
of all, here in Long Island Sound. All that story about Jones is a tub
for whales."
"Thank you for the allusion; my aunt and myself being the whales."
"You know I do mean—_can_ mean nothing, Rose, that is disrespectful to
either yourself or your aunt."
Rose looked up, and she looked pleased. Then she mused in silence, for
some time, when she again spoke.
"Why have you remained another voyage, with such a man, Harry?" she
asked, earnestly.
"Because, as his first officer, I have had access to your house, when I
could not have had it otherwise; and because I have apprehended that he
might persuade Mrs. Budd, as he had boasted to me it was his intention
to do, to make this voyage."
Rose now looked grateful; and deeply grateful did she feel, and had
reason to feel. Harry had concealed no portion of his history from her.
Like herself, he was a ship-master's son, but one better educated and
better connected than was customary for the class. His father had paid a
good deal of attention to the youth's early years, but had made a seaman
of him, out of choice. The father had lost his all, however, with his
life, in a ship-wreck, and Harry was thrown upon his own resources, at
the early age of twenty. He had made one or two voyages as a second
mate, when chance threw him in Spike's way, who, pleased with some
evidences of coolness and skill, that he had shown in a foreign port, on
the occasion of another loss, took him as his first officer; in which
situation he had remained ever since, partly from choice and partly from
necessity. On the other hand, Rose had a fortune; by no means a large
one, but several thousands in possession, from her own father, and as
many more in reversion from her uncle. It was this money, taken in
connection with the credulous imbecility of the aunt, that had awakened
the cupidity, and excited the hopes of Spike. After a life of lawless
adventures, one that had been chequered by every shade of luck, he found
himself growing old, with his brig growing old with him, and little left
beside his vessel and the sort of half cargo that was in her hold. Want
of means, indeed, was the reason that the flour barrels were not more
numerous.
Rose heard Mulford's explanation favorably, as indeed she heard most of
that which came from him, but did not renew the discourse, Spike's
conference with the boatswain just then terminating. The captain now
came aft, and began to speak of the performances of his vessel in a way
to show that he took great pride in them.
"We are traveling at the rate of ten knots, Madam Budd," he said
exultingly, "and that will take us clear of the land, before night shuts
in ag'in. Montauk is a good place for an offing; I ask for no better."
"Shall we then have _two_ offings, this voyage, Capt. Spike?" asked
Rose, a little sarcastically. "If we are in the offing now, and are to
be in the offing when we reach Montauk, there must be two such places."
"Rosy, dear, you amaze me!" put in the aunt. "There is no offing until
the pilot is discharged, and when he's discharged there is nothing but
offing. It's all offing. On the Sound, is the first great change that
befalls a vessel as she goes to sea; then, comes the offing; next the
pilot is discharged—then—then—what comes next, Capt. Spike?"
"Then the vessel takes her departure—an old navigator like yourself,
Madam Budd, ought not to forget the departure."
"Quite true, sir. The departure is a very important portion of a
seaman's life. Often, and often have I heard my poor, dear Mr. Budd talk
about his departures. His departures, and his offings and his—"
"Land-falls," added Spike, perceiving that the ship-master's relict was
a little at fault.
"Thank you, sir; the hint is quite welcome. His land-falls, also, were
often in his mouth."
"What is a land-fall, aunty?" enquired Rose—"It appears a strange term
to be used by one who lives on the water."
"Oh! there is no end to the curiosities of sailors! A 'land-fall,' my
dear, means a ship-wreck of course. To fall on the land, and a very
unpleasant fall it is, when a vessel should keep on the water. I've
heard of dreadful land-falls in my day, in which hundreds of souls have
been swept into eternity, in an instant."
"Yes; yes, Madam Budd—there are such accidents truly, and serious
things be they to encounter," answered Spike, hemming a little to clear
his throat, as was much his practice whenever the widow ran into any
unusually extravagant blunder; "yes, serious things to encounter. But
the land-fall that I mean is a different sort of thing; being, as you
well know, what we say when we come in _sight_ of land a'ter a v'y'ge;
or, meaning the land we may happen first to see. The departure is the
beginning of our calculation when we lose sight of the last cape or
head-land, and the land-fall closes it, by letting us know where we are,
at the other end of our journey, as you probably remember."
"Is there not such a thing as clearing out in navigation?" asked Rose
quickly, willing to cover a little confusion that was manifest in her
aunt's manner.
"Not exactly in navigation, Miss Rose, but clearing out, with honest
folk, ought to come first and navigation a'terwards. Clearing out means
going through the Custom House, accordin' to law."
"And the Molly Swash has cleared out, I hope?"
"Sartain—a more lawful clearance was never given in Wall Street; it's
for Key West and a market. I did think of making it Havana and a market,
but port-charges are lightest at Key West."
"Then Key West is the place to which we are bound?"
"It ought to be, agreeable to papers; though vessels sometimes miss the
ports for which they clear."
Rose put no more questions, and her aunt being conscious that she had
not appeared to advantage in the affair of the "land-fall," was also
disposed to be silent. Spike and Mulford had their attention drawn to
the vessel, and the conversation dropped.
The reader can readily suppose that the Molly Swash had not been
standing still all this time. So far from this, she was running "down
Sound," with the wind on her quarter, or at south-west, making great
head-way, as she was close under the south shore, or on the island side
of the water she was in. The vessel had no other motion than that of her
speed, and the females escaped every thing like sea-sickness, for the
time being. This enabled them to attend to making certain arrangements
necessary to their comforts below, previously to getting into rough
water. In acquitting herself of this task, Rose received much useful
advice from Josh, though his new assistant, Jack Tier, turned out to be
a prize indeed, in the cabins. The first was only a steward; but the
last proved himself not only a handy person of his calling, but one full
of resources; a genius, in his way. Josh soon became so sensible of his
own inferiority, in contributing to the comforts of females, that he
yielded the entire management of the "ladies' cabin," as a little place
that might have been ten feet square, was called, to his
uncouth-looking, but really expert deputy. Jack waddled about below, as
if born and brought up in such a place, and seemed every way fitted for
his office. In height, and in build generally, there was a surprising
conformity between the widow and the steward's deputy, a circumstance
which might induce one to think they must often have been in each
other's way, in a space so small; though, in point of fact, Jack never
ran foul of any one. He seemed to avoid this inconvenience, by a species
of nautical instinct.
Towards the turn of the day, Rose had every thing arranged, and was
surprised to find how much room she had made for her aunt and herself,
by means of Jack's hints, and how much more comfortable it was possible
to be, in that small cabin, than she had, at first, supposed.
After dinner, Spike took his siesta. He slept in a little state-room
that stood on the starboard side of the quarter-deck, quite aft; as
Mulford did in one on the larboard. These two state-rooms were fixtures;
but a light deck over-head, which connected them, shipped and unshipped,
forming a shelter for the man at the wheel, when in its place, as well
as for the officer of the watch, should he see fit to use it, in bad
weather. This sort of cuddy, Spike termed his "coach-house."
The captain had no sooner gone into his state-room, and closed its
window, movements that were understood by Mulford, than the latter took
occasion to intimate to Rose, by means of Jack Tier, the state of things
on deck, when the young man was favored with the young lady's company.
"He has turned in for his afternoon's nap, and will sleep for just one
hour, blow high, or blow low," said the mate, placing himself at Rose's
side on the trunk, which formed the usual seat for those who could
presume to take the liberty of sitting down on the quarter-deck. "It's a
habit with him, and we can count on it, with perfect security."
"His doing so, now, is a sign that he has no immediate fears of the
revenue steamer?"
"The coast is quite clear of her. We have taken good looks at every
smoke, but can see nothing that appears like our late companion. She has
doubtless gone to the eastward, on duty, and merely chased us, on her
road."
"But _why_ should she chase us, at all?"
"Because we ran. Let a dog run, or a man run, or a cat run, ten to one
but something starts in chase. It is human nature, I believe, to give
chase; though I will admit there was something suspicious about that
steamer's movements—her anchoring off the Fort, for instance. But let
her go, for the present; are you getting things right, and to your mind,
below decks?"
"Very much so. The cabin is small, and the two state-rooms the merest
drawers that ever were used, but, by putting every thing in its place,
we have made sufficient room, and no doubt shall be comfortable."
"I am sorry you did not call on me for assistance. The mate has a
prescriptive right to help stow away."
"We made out without your services," returned Rose, slightly
blushing—"Jack Tier, as he is called, Josh's assistant, is a very
useful person, and has been our adviser and manager. I want no better,
for such services."
"He is a queer fellow, all round. Take him altogether, I hardly ever saw
so droll a being! As thick as he's long, with a waddle like a duck, a
voice that is cracked, hair like bristles, and knee high, the man might
make a fortune as a show. Tom Thumb is scarcely a greater curiosity."
"He is singular in 'build,' as you call it," returned Rose, laughing,
"but, I can assure you, that he is a most excellent fellow in his
way—worth a dozen of Josh. Do you know, Harry, that I suspect he has
strong feelings towards Capt. Spike; though whether of like or dislike,
friendship or enmity, I am at a loss to say."
"And why do you think that he has any feeling, at all? I have heard
Spike say, he left the fellow ashore, somewhere down on the Spanish
Main, or in the Islands, quite twenty years since, but a sailor would
scarce carry a grudge so long a time, for such a thing as that."
"I do not know—but feeling there is, and much of it, too; though,
whether hostile, or friendly, I will not undertake to say."
"I'll look to the chap, now you tell me this. It is a little odd, the
manner in which he got on board us, taken in connection with the company
he was in, and a discovery may be made. Here he is, however, and, as I
keep the keys of the magazine, he can do us no great harm, unless he
scuttles the brig."
"Magazine! Is there such a thing here?"
"To be sure there is, and ammunition enough in it, to keep eight
carronades in lively conversation for a couple of hours."
"A carronade is what you call a gun, is it not?"
"A piece of a one—being somewhat short, like your friend Jack Tier, who
is shaped a good deal like a carronade."
Rose smiled—nay, half laughed, for Harry's pleasantries almost took the
character of wit in her eyes, but she did not the less pursue her
inquiries.
"Guns! And where are they, if they be on this vessel?"
"Do not use such a lubberly expression, my dear Rose, if you respect
your father's profession. _On_ a vessel is a new fangled Americanism,
that is neither fish, flesh, nor red-herring, as we sailors say—neither
English nor Greek."
"What should I say, then? My wish is not to parade sea-talk, but to use
it correctly, when I use it at all."
"The expression is hardly 'sea-talk,' as you call it, but every-day
English—that is when rightly used. On a vessel is no more English, than
it is nautical—no sailor ever used such an expression."
"Tell me what I ought to say, and you will find me a willing, if not an
apt scholar. I am certain of having often read it, in the newspapers,
and that quite lately."
"I'll answer for that, and it's another proof of its being wrong. _In_ a
vessel is as correct as _in_ a coach, and _on_ a vessel as wrong as can
be; but you can say _on board_ a vessel, though not 'on a vessel!' Not
on the 'boards of a vessel,' as Mrs. Budd has it."
"Mr. Mulford!"
"I beg a thousand pardons, Rose, and will offend no more—though she
does make some very queer mistakes!"
"My aunt thinks it an honor to my uncle's memory to be able to use the
language of his professional life, and if she do sometimes make mistakes
that are absurd, it is with a motive so respectable that no sailor
should deride them."
"I am rebuked for ever. Mrs. Budd may call the anchor a silver spoon,
hereafter, without my even smiling. But, if the aunt has this kind
remembrance of a seaman's life, why cannot the niece think equally well
of it."
"Perhaps she does," returned Rose, smiling again—"seeing all its
attractions through the claims of Capt. Spike."
"I think half the danger from him gone, now that you seem so much on
your guard. What an odious piece of deception, to persuade Mrs. Budd
that you were fast falling into a decline!"
"One so odious that I shall surely quit the brig at the first port we
enter, or even in the first suitable vessel that we may speak."
"And Mrs. Budd—could you persuade her to such a course?"
"You scarce know us, Harry Mulford. My aunt commands, when there is no
serious duty to perform, but we change places, when there is. I can
persuade her to any thing that is right, in ten minutes."
"You might persuade a world!" cried Harry, with strong admiration
expressed in his countenance; after which he began to converse with
Rose, on a subject so interesting to themselves that we do not think it
prudent to relate any more of the discourse, forgetting all about the
guns.
About four o'clock, of a fine summer's afternoon, the Swash went through
the Race, on the best of the ebb, and with a staggering south-west wind.
Her movement by the land, just at that point, could not have been less
than at the rate of fifteen miles in the hour. Spike was in high
spirits, for his brig had got on famously that day, and there was
nothing in sight to the eastward. He made no doubt, as he had told his
mate, that the steamer had gone into the Vineyard Sound, and that she
was bound over the shoals.
"They want to make political capital, out of her," he added, using one
of the slang phrases that the "business habits" of the American people
are so fast, and so rapidly incorporating with the common language of
the country—"They want to make political capital out of her, Harry, and
must show her off to the Boston folk, who are full of notions. Well, let
them turn her to as much account in that way, as they please, so long as
they keep her clear of the Molly. Your sarvant, Madam Budd"—addressing
the widow, who just at that moment came on deck—"a fine a'ternoon, and
likely to be a clear night to run off the coast in."
"Clear nights are desirable, and most of all at sea, Capt. Spike,"
returned the relict, in her best, complacent, manner, "whether it be to
run _off_ a coast, or to run _on_ a coast. In either case, a clear
night, or a bright moon must be useful."
Capt. Spike rolled his tobacco over in his mouth, and cast a furtive
glance at the mate, but he did not presume to hazard any further
manifestations of his disposition to laugh.
"Yes, Madam Budd," he answered, "it is quite as you say, and I am only
surprised where you have picked up so much of what I call useful
nautical knowledge."
"We live and learn, sir. You will recollect that this is not my first
voyage, having made one before, and that I passed a happy, happy, thirty
years in the society of my poor, dear husband, Rose's uncle. One must
have been dull, indeed, not to have picked up, from such a companion,
much of a calling that was so dear to him, and the particulars of which
were so very dear to him. He actually gave me lessons in the 'sea
dialect,' as he called it, which probably is the true reason I am so
accurate and general in my acquisitions."
"Yes, Madam Budd—yes—hem—you are—yes, you are wonderful in that way.
We shall soon get an offing, now, Madam Budd—yes, soon get an offing,
now."
"And take in our departure, Capt. Spike—" added the widow with a very
intelligent smile.
"Yes, take our departure. Montauk is yonder, just coming in sight; only
some three hours' run from this spot. When we get there, the open ocean
will lie before us, and give me the open sea, and I'll not call the king
my uncle."
"Was he your uncle, Capt. Spike?"
"Only in a philanthropic way, Madam Budd. Yes, let us get a good offing,
and a rapping to'gallant breeze, and I do not think I should care much
for two of Uncle Sam's new-fashioned revenue craft, one on each side of
me."
"How delightful do I find such conversation, Rose! It's as much like
your poor, dear uncle's, as one pea is like another. 'Yes,' he used to
say, too, 'let me only have one on each side of me, and a wrapper round
the topgallant sail to hold the breeze, and I'd not call the king my
uncle.' Now I think of it, _he_ used to talk about the king as his
uncle, too."
"It was all talk, aunty. He had no uncle, and what is more, he had no
king."
"That's quite true, Miss Rose," rejoined Spike, attempting a bow, which
ended in a sort of a jerk. "It is not very becoming in us republicans to
be talking of kings, but a habit is a habit. Our forefathers had kings,
and we drop into their ways without thinking of what we are doing.
Fore-topgallant yard, there?"
"Sir."
"Keep a bright look-out, ahead. Let me know the instant you make any
thing in the neighborhood of Montauk."
"Ay, ay, sir."
"As I was saying, Madam Budd, we seamen drop into our forefather's ways.
Now, when I was a youngster, I remember, one day, that we fell in with a
ketch—you know, Miss Rose, what a ketch is, I suppose?"
"I have not the least notion of it, sir."
"Rosy, you amaze me!" exclaimed the aunt—"and you a ship-master's
niece, and a ship-master's daughter! A catch is a trick that sailors
have, when they quiz landsmen."
"Yes, Madam Budd, yes; we have them sort of catches, too, but I now mean
the vessel with a peculiar rig, which we call a ketch, you know."
"Is it the full-jigger, or the half-jigger sort, that you mean?"
Spike could hardly stand this, and he had to hail the top-gallant-yard
again, in order to keep the command of his muscles, for he saw by the
pretty frown that was gathering on the brow of Rose, that she was
regarding the matter a little seriously. Luckily, the answer of the man
on the yard diverted the mind of the widow from the subject, and
prevented the necessity of any reply.
"There's a light, of course sir, on Montauk, is there not, Capt. Spike?"
demanded the seaman who was aloft.
"To be sure there is—every head-land, here-abouts, has its light; and
some have two."
"Ay, ay, sir—it's that which puzzles me; I think I see one light-house,
and I'm not certain but I see two."
"If there is any thing like a second, it must be a sail. Montauk has but
one light."
Mulford sprang into the fore-rigging, and in a minute was on the yard.
He soon came down and reported the light-house in sight, with the
afternoon's sun shining on it, but no sail near.
"My poor, dear Mr. Budd used to tell a story of his being cast away on a
light-house, in the East Indies," put in the relict, as soon as the mate
had ended his report, "which always affected me. It seems there were
three ships of them together, in an awful tempest directly off the
land—"
"That was comfortable any how," cried Spike;—"if it must blow hard, let
it come off the land, say I."
"Yes, sir, it was directly off the land, as my poor husband always said,
which made it so much the worse you must know, Rosy, though Capt.
Spike's gallant spirit would rather encounter danger than not. It blew
what they call a Hyson, in the Chinese seas—"
"A what, aunty?—Hyson is the name of a tea, you know."
"A Hyson, I'm pretty sure it was, and I suppose the wind is named after
the tea, or the tea after the wind."
"The ladies do get in a gale, sometimes, over their tea," said Spike
gallantly. "But I rather think Madam Budd must mean a Typhoon."
"That's it—a Typhoon, or a Hyson—there is not much difference between
them, you see. Well, it blew a Typhoon, and they are always mortal to
somebody. This my poor Mr. Budd well knew, and he had set his
chronometer for that Typhoon—"
"Excuse me aunty, it was the barometer that he was watching—the
chronometer was his watch."
"So it was—his watch on deck _was_ his chronometer, I declare. I _am_
forgetting a part of my education. Do you know the use of a chronometer,
now, Rose? You have seen your uncle's often, but do you know how he used
it?"
"Not in the least, aunty. My uncle often tried to explain it, but I
never could understand him."
"It must have been, then, because Capt. Budd did not try to make himself
comprehended," said Mulford, "for I feel certain nothing would be easier
than to make _you_ understand the uses of the chronometer."
"I should like to learn it from _you_, Mr. Mulford," answered the
charming girl, with an emphasis so slight on the 'you,' that no one
observed it but the mate, but which was clear enough to him, and caused
every nerve to thrill.
"I can attempt it," answered the young man, "if it be agreeable to Mrs.
Budd, who would probably like to hear it, herself."
"Certainly, Mr. Mulford, though I fancy you can say little on such a
subject, that I have not often heard, already, from my poor, dear, Mr.
Budd."
This was not very encouraging, truly, but Rose continuing to look
interested, the mate proceeded.
"The use of the chronometer is to ascertain the longitude," said Harry,
"and the manner of doing it, is simply this: A chronometer is nothing
more nor less, than a watch made with more care than usual, so as to
keep the most accurate time. They are of all sizes, from that of a
clock, down to this which I wear in my fob, and which is a watch in size
and appearance. Now, the nautical almanacs are all calculated to some
particular meridian—"
"Yes," interrupted the relict, "Mr. Budd had a great deal to say about
meridians."
"That of London, or Greenwich, being the meridian used by those who use
the English Almanacs, and those of Paris or St. Petersburgh, by the
French and Russians. Each of these places has an observatory, and
chronometers that are kept carefully regulated, the year round. Every
chronometer is set by the regulator of the particular observatory or
place to which the almanac used is calculated."
"How wonderfully like my poor, dear Mr. Budd, all this is, Rosy!
Meridians, and calculated and almanacs! I could almost think I heard
your uncle entertaining me with one of his nautical discussions, I
declare!"
"Now the sun rises earlier in places east, than in places west of us."
"It rises earlier in the summer, but later in the winter, every where,
Mr. Mulford."
"Yes, my dear Madam, but the sun rises earlier every day, in London,
than it does in New York."
"That is impossible," said the widow, dogmatically—"Why should not the
sun rise at the same time in England and America?"
"Because England is east of America, aunty. The sun does not move, you
know, but only appears to us to move, because the earth turns round from
west to east, which causes those who are farthest east to see it the
first. That is what Mr. Mulford means."
"Rose has explained it perfectly well," continued the mate. "Now the
earth is divided into 360 degrees, and the day is divided into 24 hours.
If 360 be divided by 24, the quotient will be 15. It follows, that for
each fifteen degrees of longitude, there is a difference of just one
hour in the rising of the sun, all over the earth, where it rises at
all. New York is near five times 15 degrees west of Greenwich, and the
sun consequently rises five hours later at New York than at London."
"There _must_ be a mistake in this, Rosy," said the relict in a tone of
desperate resignation, in which the desire to break out in dissent, was
struggling oddly enough, with an assumed dignity of deportment. "I've
always heard that the people of London are some of the latest in the
world. Then I've been in London, and know that the sun rises in New
York, in December, a good deal earlier than it does in London, by the
clock—yes, by the clock."
"True enough, by the clock, Mrs. Budd, for London is more than ten
degrees north of New York, and the farther north you go, the later the
sun rises in winter, and the earlier in summer."
The relict merely shrugged her shoulders, as much as to say that she
knew no such thing; but Rose, who had been well taught, raised her
serene eyes to her aunt's face, and mildly said—
"All true, aunty, and that is owing to the fact that the earth is
smaller at each end, than in the middle."
"Fiddle faddle with your middles and ends, Rose—I've been in London,
dear, and know that the sun rises later there than in New York, in the
month of December, and that I know by the clock, I tell you."
"The reason of which is," resumed Mulford, "because the clocks of each
place keep the time of that place. Now, it is different with the
chronometers, they are set in the observatory of Greenwich, and keep the
time of Greenwich. This watch chronometer was set there, only six months
since, and this time, as you see is near nine o'clock, when in truth it
is only about four o'clock, here, where we are."
"I wonder you keep such a watch, Mr. Mulford!"
"I keep it," returned the mate smiling, "because I know it to keep good
time. It has the Greenwich time; and, as your watch has the New York
time, by comparing them together, it is quite easy to find the longitude
of New York."
"Do you, then, keep watches to compare with your chronometers?" asked
Rose, with interest.
"Certainly not, as that would require a watch for every separate part of
the ocean, and then we should only get known longitudes. It would be
impracticable, and load a ship with nothing but watches. What we do, is
this: We set our chronometers at Greenwich, and thus keep the Greenwich
true time, wherever we go. The greatest attention is paid to the
chronometers, to see that they receive no injuries, and usually there
are two, and often more of them, to compare one with another, in order
to see that they go well. When in the middle of the ocean, for instance,
we find the true time of day at that spot, by ascertaining the height of
the sun. This we do by means of our quadrants, or sextants; for, as the
sun is always in the zenith at twelve o'clock, nothing is easier than to
do this, when the sun can be seen, and an arc of the heavens measured.
At the instant the height of the sun is ascertained by one observer, he
calls to another, who notes the time on the chronometer. The difference
in these two times, or that of the chronometer and that of the sun,
gives the distance in degrees and minutes, between the longitude of
Greenwich and that of the place on the ocean, where the observer is; and
that gives him his longitude. If the difference is three hours and
twenty minutes, in time, the distance from Greenwich is fifty degrees of
longitude, because the sun rises there three hours and twenty minutes
sooner in London, than in the fiftieth degree of west longitude."
"A watch is a watch, Rosy," put in the aunt, doggedly—"and time is
time.—When it's four o'clock at our house, it's four o'clock at your
aunt Sprague's, and it's so all over the world. The world may turn
round—I'll not deny it, for your uncle often said as much as _that_,
but it cannot turn in the way Mr. Mulford says, or we should all fall
off it, at night, when it was bottom upwards. No, sir, no; you've
started wrong. My poor, dear, late Mr. Budd always admitted that the
world turned round, as the books say; but, when I suggested to him the
difficulty of keeping things in their places, with the earth upside
down, he acknowledged candidly—for he was all candor, I must say that
for him—and owned that he had made a discovery, by means of his
barometer, which showed that the world did not turn round, in the way
you describe, or by rolling over, but by whirling about as one turns in
a dance. You must remember your uncle's telling me this, Rose?"
Rose did remember her uncle's telling her aunt this, as well as a great
many other similar prodigies. Capt. Budd had married his silly wife, on
account of her pretty face, and when the novelty of that was over, he
often amused himself by inventing all sorts of absurdities, to amuse
both her and himself. Among other things, Rose well remembered his
quieting her aunt's scruples about falling off the earth, by laying down
the theory that the world did not "roll over," but "whirl round." But
Rose did not answer the question.
"Objects are kept in their places on the earth, by means of attraction,"
Mulford ventured to say, with a great deal of humility of manner. "I
believe it is thought there is no up or down, except as we go from, or
towards the earth; and that would make the position of the last a matter
of indifference, as respects objects keeping on it."
"Attractions are great advantages, I will own, sir, especially to our
sex. I think it will be acknowledged there has been no want of them in
our family, any more than there has been of sense and information.
Sense, and information, we pride ourselves on; attractions being gifts
from God, we try to think less of them. But all the attractions in the
world could not keep Rosy, here, from falling off the earth, did it ever
come bottom upwards. And, mercy on me, where would she fall to!"
Mulford saw that argument was useless, and he confined his remarks,
during the rest of the conversation, to showing Rose the manner in which
the longitude of a place might be ascertained, with the aid of the
chronometer, and by means of observations to get the true time of day,
at the particular place itself. Rose was so quick witted, and already so
well instructed, as easily to comprehend the principles; the details
being matters of no great moment to one of her sex and habits. But Mrs.
Budd remained antagonist to the last. She obstinately maintained that
twelve o'clock was twelve o'clock; or, if there _was_ any difference,
"London hours were notoriously later, than those of New York."
Against such assertions, arguments were obviously useless, and Mulford,
perceiving that Rose began to fidget, had sufficient tact to change the
conversation altogether.
And still the Molly Swash kept in swift motion. Montauk was, by this
time, abeam, and the little brigantine began to rise and fall, on the
long swells of the Atlantic, which now opened before her, in one vast
sheet of green and rolling waters. On her right, lay the termination of
Long Island; a low, rocky cape, with its light, and a few fields in
tillage, for the uses of those who tended it. It was the "land's end" of
New York, while the island that was heaving up out of the sea, at a
distance of about twenty miles to the eastward, was the property of
Rhode Island, being called Blok Island. Between the two, the Swash
shaped her course for the ocean.
Spike had betrayed uneasiness, as his brig came up with Montauk; but the
coast seemed clear, with not even a distant sail in sight, and he came
aft rubbing his hands with delight, speaking cheerfully.
"All right, Mr. Mulford," he cried—"every thing ship-shape and
brister-fashion—not even a smack fishing here-away, which is a little
remarkable. Ha!—what are you staring at, over the quarter, there?"
"Look here, sir, directly in the wake of the setting sun, which we are
now opening from the land—is not that a sail?"
"Sail! Impossible, sir. What should a sail be doing in there, so near
Montauk—no man ever saw a sail there, in his life. It's a spot in the
sun, Madam Budd, that my mate has got a glimpse at, and, sailor-like, he
mistakes it for a sail! Ha—ha—ha—yes, Harry, it's a spot in the sun."
"It is a spot _on_ the sun, as you say, but it's a spot made by a
vessel—and here is a boat pulling towards her, might and main; going
from the light, as if carrying news."
It was no longer possible for Spike's hopes to deceive him. There was a
vessel sure enough, though, when first seen, it was so directly in a
line with the fiery orb of the setting sun, as to escape common
observation. As the brig went foaming on towards the ocean, however, the
black speck was soon brought out of the range of the orb of day, and
Spike's glass was instantly leveled at it.
"Just as one might expect, Mr. Mulford," cried the captain, lowering his
glass, and looking aloft to see what could be done to help his craft
along; "a bloody revenue cutter, as I'm a wicked sinner! There she lies,
sir, within musket shot of the shore, hid behind the point, as it might
be in waiting for us, with her head to the southward, her helm hard
down, topsail aback, and foresail brailed; as wicked looking a thing as
Free Trade and Sailor's Rights ever ran from. My life on it, sir, she's
been put in that precise spot, in waiting, for the Molly to arrive. You
see, as we stand on, it places her as handsomely to windward of us, as
the heart of man could desire."
"It _is_ a revenue cutter, sir; now she's out of the sun's wake, that is
plain enough. And that is her boat, which has been sent to the light to
keep a lookout for us. Well, sir; she's to windward, but we have every
thing set for our course, and as we are fairly abeam, she must be a
great traveler to overhaul us."
"I thought these bloody cutters were all down in the Gulf," growled the
captain, casting his eyes aloft, again, to see that every thing drew.
"I'm sure the newspapers have mentioned as many as twenty that are down
there, and here is one, lying behind Montauk, like a snake in the
grass!"
"At any rate, by the time he gets his boat up, we shall get the start of
him—ay; there he fills and falls off, to go and meet her. He'll soon be
after us, Capt. Spike, at racing speed."
Every thing occurred as those two mariners had foreseen. The revenue
cutter, one of the usual fore-topsail schooners that are employed in
that service, up and down the coast, had no sooner hoisted up her boat,
than she made sail, a little off the wind, on a line to close with the
Swash. As for the brig, she had hauled up to an easy bowline, as she
came round Montauk, and was now standing off south south-east, still
having the wind at south-west. The weatherly position of the cutter
enabled her to steer rather more than one point freer. At the
commencement of this chase, the vessels were about a mile and a half
apart, a distance too great to enable the cutter to render the light
guns she carried available, and it was obvious from the first, that
every thing depended on speed. And speed it was, truly; both vessels
fairly flying; the Molly Swash having at last met with something very
like her match. Half an hour satisfied both Spike and Mulford that, by
giving the cutter the advantage of one point in a freer wind, that she
would certainly get along side of them, and the alternative was to keep
off.
"A starn chase is a long chase, all the world over," cried Spike—"edge
away, sir; edge away, sir, and bring the cutter well on our quarter."
This order was obeyed, but to the surprise of those in the Swash, the
cutter did not exactly follow, though she kept off a little more. Her
object seemed to be to maintain her weatherly position, and in this
manner, the two vessels ran on, for an hour longer, until the Swash had
made most of the distance between Montauk and Blok Island. Objects were
even becoming dimly visible on the last, and the light on the point was
just becoming visible, a lone star above a waste of desert, the sun
having been down now fully a quarter of an hour, and twilight beginning
to draw the curtain of night over the waters.
"A craft under Blok," shouted the look-out, that was still kept aloft as
a necessary precaution.
"What sort of a craft?" demanded Spike, fiercely; for the very mention
of a sail, at that moment, aroused all his ire. "Arn't you making a
frigate out of an apple orchard?"
"It's the steamer, sir. I can now see her smoke. She's just clearing the
land, on the south side of the island, and seems to be coming round to
meet us."
A long, low, eloquent whistle from the captain, succeeded this
announcement. The man aloft was right. It _was_ the steamer, sure
enough; and she had been lying hid behind Blok Island, exactly as her
consort had been placed behind Montauk, in waiting for their chase to
arrive. The result was to put the Molly Swash in exceeding jeopardy, and
the reason why the cutter kept so well to windward, was fully explained.
To pass out to sea between these two craft was hopeless. There remained
but a single alternative from capture, by one or by the other, and that
Spike adopted instantly. He kept his brig dead away, setting
studding-sails on both sides. This change of course brought the cutter
nearly aft, or somewhat on the other quarter, and laid the brig's head
in a direction to carry her close to the northern coast of the island.
But the principal advantage was gained over the steamer, which could not
keep off, without first standing a mile or two, or even more, to the
westward, in order to clear the land. This was so much clear gain to the
Swash, which was running off at racing speed, on a northeast course,
while her most dangerous enemy was still heading to the westward. As for
the cutter, she kept away; but, it was soon apparent that the brig had
the heels of her, dead before the wind.
Darkness now began to close around the three vessels; the brig and the
schooner soon becoming visible to each other principally by means of
their night-glasses; though the steamer's position could be easily
distinguished by means of her flaming chimney. This latter vessel stood
to the westward for a quarter of an hour, when her commander appeared to
become suddenly conscious of the ground he was losing, and he wore short
round, and went off before the wind, under steam and canvas; intending
to meet the chase off the northern side of the island. The very person
who had hailed the Swash, as she was leaving the wharf, who had passed
her in Hell-Gate, with Jack Tier in his boat, and who had joined her off
Throgmorton's, was now on her deck, urging her commander, by every
consideration, not to let the brig escape. It was at his suggestion that
the course was changed. Nervous, and eager to seize the brig, he
prevailed on the commander of the steamer to change his course. Had he
done no more than this, all might have been well; but, so exaggerated
were his notions of the Swash's sailing, that, instead of suffering the
steamer to keep close along the eastern side of the island, he persuaded
her commander of the necessity of standing off, a long distance to the
northward and eastward, with a view to get ahead of the chase. This was
not bad advice, were there any certainty that Spike would stand on, of
which, however, he had no intention.
The night set in dark and cloudy, and, the instant that Spike saw, by
means of the flaming chimney, that the steamer had wore, and was going
to the eastward of Blok, his plan was laid. Calling to Mulford, he
communicated it to him, and glad to find that his intelligent mate was
of his own way of thinking. The necessary orders were given,
accordingly, and every thing was got ready for its execution.
In the meantime, the two revenue craft were much in earnest. The
schooner was one of the fastest in the service, and had been placed
under Montauk, as described, in the confident expectation of her being
able to compete with even the Molly Swash successfully; more especially
if brought upon a bowline. Her commander watched the receding form of
the brig with the closest attention, until it was entirely swallowed up
in the darkness, under the land, towards which he then sheered himself,
in order to prevent the Swash from hauling up, and turning to windward,
close in under the shadow of the island. Against this manœuvre, however,
the cutter had now taken an effectual precaution, and her people were
satisfied that escape in that way was impossible.
On the other hand, the steamer was doing very well. Driven by the
breeze, and propelled by her wheels, away she went, edging further and
further from the island, as the person from the Custom House succeeded,
as it might be, inch by inch, in persuading the captain of the necessity
of his so doing. At length a sail was dimly seen ahead, and then no
doubt was entertained that the brig had got to the northward and
eastward of them. Half an hour brought the steamer along side of this
sail, which turned out to be a brig, that had come over the shoals, and
was beating into the ocean, on her way to one of the southern ports. Her
captain said there had nothing passed to the eastward.
Round went the steamer, and in went all her canvas. Ten minutes later
the look-out saw a sail to the westward, standing before the wind. Odd
as it might seem, the steamer's people now fancied they were sure of the
Swash. There she was, coming directly for them, with square yards! The
distance was short, or a vessel could not have been seen by that light,
and the two craft were soon near each other. A gun was actually cleared
on board the steamer, ere it was ascertained that the stranger was the
schooner! It was now midnight, and nothing was in sight but the coasting
brig. Reluctantly, the revenue people gave the matter up; the Molly
Swash having again eluded them, though by means unknown.
[_To be continued._
* * * * *
HAWKING.
BY E. M. SIDNEY.
Up and away, for the day is bright,
With the falconers shouting cheerily!
Look at the gos-hawk's eye of light,
As he plumes his pinions merrily!
He sees the heron, and quick he starts,
Wheeling to heaven so cheerily!
Now, like a thunderbolt down he darts
Away, away right merrily!
* * * * *
REVIEW OF NEW BOOKS.
_History of the Thirty Years' War. Translated from the German of
Frederick Schiller. By the Rev. A. J. W. Morrison, M. A. New
York: Harper & Brothers. 1 vol. 12mo._
In the opinion of Carlyle this is the best philosophical history that
Germany has produced. The Harpers have reprinted it in the cheap and
elegant series of valuable books, entitled their "New Miscellany." The
volume presents a graphic and exceedingly interesting view of one of the
most terrible and devastating wars with which Europe was ever cursed. It
represents the struggle of the Protestant States against the overgrown
power of Austria, and the various motives, religious and devilish, which
animated the parties during the contest. The skill and bravery of the
commanders engaged in the war, give a personal as well as general
interest to the narrative. On the one side we have Gustavus Adolphus,
Count Thorn, Mansfield, Bernard of Weimar, Banner, Torstensohn, on the
other Wallenstein, Tilly, Piccolimini, Pappenheim, and Hatzfeld.
Gustavus Adolphus and Wallenstein are, of course, the leading objects of
interest. In reading this history the mind becomes so accustomed to the
devastation of provinces, the murder of peasants, and horrible outrages
on all the decencies and sanctities of life,—that fire, famine and
slaughter become mere commonplaces and matters of course. We read, at
last, the most terrible accounts of wretchedness and cruelty, with
hardly a shudder. Schiller, in summing up the various evils of this war,
a war which devastated whole provinces, reduced towns and cities to
ashes, "smothered the glimmering sparks of civilization in Germany, and
threw back the improving manners of the country into their pristine
barbarity and wildness," still finds consolation in the thought that
from this fearful war Europe came forth free and independent. "In it she
first learned to recognize herself as a community of nations; and this
intercommunion of States, which originated in the thirty years' war,
would alone be sufficient to reconcile the philosopher to its horrors."
There is, in truth, some consolation in the idea that a soul of goodness
abides in things evil,—that men, mad with passion or drunk with
fanaticism, cannot hack each other to pieces, without having their blind
fury directed by a higher power to a good result.
* * * * *
_The History of Civilization from the Fall of the Roman Empire
to the French Revolution. By F. Guizot. Translated by William
Hazlitt. New York: D. Appleton & Co. 4 vols. 12mo._
No person can have watched the course of the prominent American
publishers of the United States, without observing a manifest
improvement, within the last three or four years, in the character of
the books they reprint, and the style of their execution. The house of
Appleton & Co. have been especially distinguished for the intrinsic
value, and the cheapness and elegance, of their publications. Their
mercantile daring, in hazarding capital on books which were not
considered, until lately, profitable speculations, deserves the highest
praise. The present edition of Guizot's admirable work on Civilization,
is one of their most important additions to the stock of works,
combining great learning and profound thought, with some of the most
charming qualities of style. The first portion of the present
publication, on the General History of Civilization in Europe, is well
known; but the other three volumes, containing Guizot's lectures on the
History of Civilization in France, have been but lately translated.
Guizot is probably the greatest historian that France has produced, in
the combination of those qualities which go to make up a genius for
history. He yields to none in the research which collects facts, the
understanding which analyses and arranges them, and the imagination
which represents them as realities, and endows them with substantial
life and meaning. To all these advantages, he adds a beautiful
clearness, vigor and brilliancy of style, in narrating the progress of
events and setting forth their laws and principles. The present history
is at once popular and profound. It is calculated to delight and
instruct the common reader as well as the student. We cordially
recommend it to all, as a book containing a vast amount of erudition and
thought, devoted to the illustration of a subject in which everybody has
an interest, and calculated to improve the literary taste of the reader,
as well as to inform and enlarge his understanding.
* * * * *
_Stories from the Italian Poets. By Leigh Hunt. New York: Wiley
& Putnam. 1 vol. 12mo._
This is one of the most entertaining volumes of the season. It contains
a summary in prose of Dante's Divine Comedy, and various stories from
the poems of Pulci, Boiardo, Ariosto and Tasso, with occasional passages
versified, and some interesting critical notices of the lives and genius
of the poets. In the criticisms Hunt evinces a knowledge of his authors,
founded on a long acquaintance with them, and a keen enjoyment of their
excellencies. The account of the Divine Comedy is the best, for the
general mind, which we have yet seen in English, and is calculated to
give delight to thousands, to whom Cary's translation would be a bore.
The stories from Pulci are exquisite for their mirthful beauty. The
tales from Boiardo, Ariosto and Tasso, will introduce the common novel
reader into a new world of beauty, heroism and romance. The passages of
grandeur and sublimity, of pathos and sweetness,—the images both
delicate and magnificent, with which the volume abounds,—make its
circulation in this country a thing devoutly to be wished. It will
enable the reader to obtain some idea of the splendor and opulence of
the Italian mind, in all which enchants the senses and thrills the
imagination.
Hunt's critical notices and occasional comments are very characteristic.
His style has the same sweetness and felicity which constitute the charm
of his other essays; and is dotted over with those little impertinences
of personal opinion, from which nothing that he writes is wholly free.
His remarks on Dante throw more light upon his own character than that
of his subject. From the very constitution of his mind he revolts at all
infliction of suffering, even for sin. He would have ice-creams in
Pandemonium. He is inexpressibly shocked at Dante's severity and spleen,
and speaks many a fair word for the poor rascals whom the austere
Florentine has consigned to perdition. His comments on the remorseless
severity of the punishments in Hell,—his indignation that Cato should
be placed in Purgatory while his wife, Marcia, sojourns in the pit,—his
exceptions to some of the persons placed on high seats in heaven,—are
often exquisitely amusing. It requires a man like Hunt to criticise a
man like Dante.
* * * * *
_The Poetical Works of Thomas Moore. New York: D. Appleton & Co.
1 vol. 8vo._
This is a splendid edition of one of the most popular of English poets.
It has ten fine steel embellishments, and its general execution places
it very nearly on a level with the English edition. As a specimen of
American typography it is very honorable to the enterprising publishers.
It is the only complete edition of Moore ever published in this country,
being reprinted from the London collection, lately edited by the poet
himself, and containing his autobiographical prefaces and illustrations.
In these the poet very pleasantly prattles about his own life and works,
and is exhibited as the most graceful of egotists. The volume contains
an immense number of brilliant verses, ranging in subject from the
romantic poem to the political squib. Without depth of passion,
elevation of sentiment, or grandeur of imagination, the poems of Moore
still evince a quickness of sensibility, an opulence of fancy, and a
brilliancy of wit, which have made them among the most popular works
produced within the present century. His poems are lit up with an
incessant shower of sparkling fancies. Almost everything he has written
is full of glitter and point—his sentiment as well as his satire. His
songs are often epigrams of feeling. Though, as a poet, he can hardly
stand by the side of Wordsworth, Shelley, Coleridge, or Byron, in the
greatest qualities of the bard, yet no one can glance over the present
volume without being impressed with the brilliant genius of its author,
and fascinated with the stores of wit, fancy, learning and sentiment,
which glisten and gleam on every page.
* * * * *
_The French Revolution. A History. By Thomas Carlyle. Newly
Revised by the Author, with Index. New York: Wiley & Putnam. 3
Parts. 12mo._
This is Carlyle's grandest work—a prose epic on the great event of
modern history. In our narrow limits we cannot hope to do any thing like
justice, to the imagination, fancy, learning, humor, pathos, sublimity,
characterization, with which the volumes abound. In spite of some
obstinate faults, in spite of much false and pernicious doctrine, in
spite of the style, no work ever written on the French Revolution equals
this in the clearness with which it represents the causes of that
revolution, in the vividness with which it brings up its different
events in magnificent pictures, speaking directly to the eye, and in the
grandeur of its delineations of the principal actors in the drama. The
portraits of Mirabeau, Danton, Robespierre, are masterpieces. Every page
glows with vital life. The words are all alive with meaning. They paint
objects so distinctly that we become observers of the scenes to which
they relate. Carlyle, in truth, is a master of expression as
distinguished from mere fluency. He selects the "inevitable best word,"
or compounds it, with an unmistakable tact and sureness. If to his other
great qualities he joined calmness, comprehension, mental honesty, the
present work would be almost perfect. Viewing it with an eye to all its
faults, it must be pronounced a work of great genius and power.
* * * * *
_The Life and Correspondence of John Foster. Edited by J. E.
Ryland. New York: Wiley & Putnam. 2 vols. 12mo._
Foster is well known as the author of a volume of essays, laden with
weighty thought and acute observations on character and life. The
present volume, containing his letters and journals from his earliest to
his latest years, is one of great value, not merely to his own sect, the
Baptists, but to all who can appreciate originality of character and
thought. Foster was a hard, determined, patient thinker, gifted with
much imagination, and impressing on every thing he wrote the invincible
honesty of his character. His correspondence reveals to us the inmost
recesses of his mind and disposition, and constitutes a kind of
psychological autobiography, replete with materials of interest and
instruction. The separate thoughts scattered over these volumes would
alone be sufficient to reward abundantly the trouble of its perusal. One
of the strongest peculiarities of genius, Foster says in one place, "is
the power of lighting its own fire." Of a soft and pensive evening, he
remarks—"It is as if the soul of Eloisa pervaded all the air."
Shakspeare, he observes, had perceptions of every kind; "he could think
every way. His mind might be compared to that monster the prophet saw in
his vision, which _had eyes all over_." Again he says—"Lord Chatham did
not _reason_; he struck, as by intuition, directly on the _results_ of
reasoning; as a cannon-shot strikes the mark without your seeing its
course through the air as it moves towards its object." When shown a
piece of ornamental worsted-work, with a great deal of red in it, he
said "it was red with the blood of murdered time." The volumes are full
of thoughts and observations equally striking and pointed.
* * * * *
_The New Timon. A Romance of London. Philadelphia: Carey & Hart.
1 vol. 12mo._
This poem has excited no inconsiderable interest in London. It is
reprinted from the third English edition. Bulwer has been mentioned as
the probable author, but this must be a mistake, unless Bulwer has
essentially changed his literary opinions. Wordsworth, Keats and
Tennyson, each of whom the author of "Pelham" has warmly praised, the
author of "Timon" most ignorantly and pertly ridicules. The poem, it
must be admitted, has much merit. It is written in a vigorous style,
contains numerous passages of flashing description, much keen
portraiture of prominent English politicians, and many beautiful scenes
of pathos and passion. The pith and nerve of the verse, the
half-misanthropic, half-romantic tone of the sentiment, the frequent
allusion to contemporary events and persons, and the bitter sharpness of
the satire on social evils,—often remind the reader of Byron. The work
evidences a brilliant and restless intellect, ill at ease with the
manners and institutions of society, scornful, dogmatic and perverse,
but quite felicitous in running keen observations into the moulds of
fancy and wit. Kinglake, the author of Eothen, might have written it.
The author's character is a composite, made up of Diogenes and
Alcibiades.
* * * * *
_Memoirs of the Life of Addison. By Miss Aiken. Philadelphia:
Carey & Hart. 1 vol. 12mo._
The publishers of this volume have started a "Library for the People,"
of which the Life of Addison constitutes No. 5. It makes a volume of
about 300 pages, elegantly printed. The price is only fifty cents, or
_one-fourteenth_ of the cost of the English edition. All the mistakes of
the English edition, so acutely pointed out by Macaulay, have been
corrected in the American reprint. The work is well written, and
introduces us to a most interesting period of English literature and
history. The correspondence of Addison confers great value upon the
work. Most of the letters were never before printed. The beautiful
character of the subject, joined to the immense influence which his
writings have exerted on English letters and manners, give to the
details of his virtuous and well-spent life a peculiar interest and
charm. A volume which introduces us so completely to Addison, and
strengthens that affectionate companionship with him, which his works
may have commenced, cannot fail to be popular.
* * * * *
_The Poetry of Wit and Humor. Selected from the English Poets.
With an Illustrative Essay, and Critical Comments. By Leigh
Hunt. 1 vol. 12mo._
The matter of this book will ensure its success. It contains extracts
from Chaucer, Shakspeare, Ben Jonson, Beaumont and Fletcher, Suckling,
Dryden, Pope, Goldsmith and Wolcot, with running comments on the authors
and on particular passages of the poems. The essay on Wit and Humor,
though it does not exhaust the topic, is ingenious, and pleasantly
illustrated. We do not think that in the case of a few of the authors,
Hunt has hit upon the happiest selections. Few, for example, would
obtain an idea of the comic genius of Fletcher from the specimens quoted
in the volume. The task, however, was a difficult one to perform; and
the editor, in compiling an entertaining volume, has done all that
perhaps could be expected, in the limited space to which he was
confined.
* * * * *
_The Island Bride, and other Poems. By James F. Colman. Boston:
Wm. D. Ticknor & Co. 1 vol. 12mo._
The most superficial glance over this volume would convince even the
supercilious critic, that the author is destined to take a high rank
among American poets. "The Island Bride" contains nine Cantos of
Spenserian verse, finished in diction, poetical in feeling, and replete
with thought, fancy and imagination. It is one of the very few long
poems in American literature, which more than repay perusal. The other
pieces are of much merit, and bear unmistakable marks of power. The most
surprising quality manifested in the volume, is perhaps the correct
taste which is everywhere observable throughout its pages. It seems the
work of a veteran in composition, rather than the first volume of a
youthful poet. We should be pleased, had we time, to make it the subject
of a more extended notice; but at present, we can do little more than
cordially commend it to the notice of our readers.
* * * * *
_Classical Antiquities, a Compendium of Roman and Grecian
Antiquities, with a Sketch of Ancient Mythology. By Joseph
Salkeld. New York: Harper & Brothers. 1 vol. 12mo._
The object of this volume is a good one, and it will be found eminently
useful. To read modern books understandingly, some knowledge of the
religion, government and manners and customs of the Greeks and Romans,
is indispensable, from the multitude of allusions to them throughout
every department of modern literature. In addition to this, the subject
of Classical Antiquities is sufficiently interesting of itself, to
justify the reading of a much larger book than the present. The "way of
life" among two nations, which have once held a vast dominion on earth,
by virtue of their power and policy, and still hold even a vaster
dominion over the mind by virtue of their literature, must be
interesting to every reflective and curious mind.
* * * * *
_Rationale of Crime, and its Appropriate Treatment; being a
Treatise on Criminal Jurisprudence considered in relation to
Cerebral Organization. By M. B. Sampson. With Notes and
Illustrations by E. W. Farnham. New York: D. Appleton & Co. 1
vol. 12mo._
The character of this volume is indicated by its title. It is the
application of the principles of phrenology to the phenomena of crime.
The notions of the author are illustrated by a number of portraits of
criminals and other persons, the shape of whose heads are said to
indicate the bent of their characters. The book is readable, even to
unbelievers in the science of bumps. Phrenology, however, to all intents
and purposes, is an exploded system; and thieves and murderers cannot,
at this day, save themselves from punishment, by exhibiting in
extenuation of their crime, the most gigantic organs of acquisitiveness
and destructiveness.
* * * * *
_Notes on the Northwest and Valley of the Upper Mississippi. By
Wm. J. A. Bradford. New York: Wiley & Putnam. 1 vol. 12mo._
A work like this has long been wanted. The large mass of readers are
singularly deficient in accurate knowledge respecting the great region
of which it treats. Mr. Bradford has interesting chapters on the
physical geography, history, topography, pursuits, health, geology,
botany, monuments, and aboriginal inhabitants of the Northwest. Under
this name he includes the country between Lakes Superior and Michigan,
east,—the Illinois and Missouri Rivers, and the Northern Boundary of
the United States,—including Iowa and Wisconsin, part of Michigan
northwest of the Straits of Mackinaw, and Northern Illinois and
Missouri.
* * * * *
_Poetry and Truth from my Life. From the German of Goethe. By
Parke Godwin. New York: Wiley & Putnam. 2 Parts, 12mo._
It is singular that this is the first good English translation of the
celebrated work of Goethe on his own life. As a record of the external
influences and internal experiences, which went to form the character of
Germany's master-intellect, it is one of the most important works of the
age. Carlyle, in referring to it, well says—"what would we give for
such an autobiography of Shakspeare, of Milton, even of Pope or Swift?"
The publishers have included it in their series of "Choice Books"—an
enterprise which they have successfully extended to eighty numbers,
without any evidence of exhausting their materials.
* * * * *
_Something for Every-Body: Gleaned in the Old Purchase, from
Fields often Reaped. By Robert Carlton. New York: D. Appleton &
Co. 1 vol. 12mo._
This book well bears out its title. It is a collection of anecdotes,
personal adventures, and hits upon popular errors. The author is a
shrewd observer of life and character, and has an eye for the tendencies
of popular movements. There is much sense and humor in his remarks on
the various moral reforms of the day. He is "a gentleman of the old
school," and perhaps does not always do complete justice to the objects
of his sarcasm or indignation; but he well probes their weak points.
* * * * *
_Sartor Resartus: the Life and Opinions of Herr Teufelsdröckh.
In Three Books. New York: Wiley & Putnam. 1 vol. 12mo._
This edition of Carlyle's celebrated work on the philosophy of clothes,
is revised by the author; and Wiley & Putnam are authorized by him, to
"print and vend the same in the United States." The book, itself, with
all its wildness of style, is one of the most fascinating works of the
century—full of splendid imagination, deep thought, and humorous
insight into life, character and manners. Its wealth of pictorial
expression, would alone entitle it to a high rank among works of
imagination. The present edition is altogether the best and most elegant
ever published in the United States.
* * * * *
_Experimental Researches on the Food of Animals, and the
Fattening of Cattle; with Remarks on the Food of Man. By Robert
Dundas Thomson, M. D. New York: D. Appleton & Co. 1 vol. 12mo._
This work presents the results of an extensive series of original
experiments, undertaken by order of the British government. It is full
of matter important at once to the practical agriculturist and the
scientific physiologist. The publishers have issued it in a cheap form,
so as to bring it within the reach of the humblest means. The author is
evidently a patient man of science, who may be relied upon as a close
observer of facts, and strict reasoner from them. No farmer can well
dispense with the book.
* * * * *
[Illustration:
LE FOLLET
Boulevart S^{t.} Martin, 61.
_Coiffure de_ Normandin, _passage Choiseul, 19—Chapeaux de M^{me}._
Baudry, _r. Richlieu 87;_
_Toilettes de M^{me}._ Ferrière Pennona, _r. Mondovi, 1—plumes de M^{me}._
Tilman, _rue Minars, 5;_
_Dentelles de_ Violard, _r. de Choiseul, 2^{bis}—Mouchoirs de_ L. Chapron
& Dubois, _r. de la Paix, 7;_
_Essences & flacons de_ Guerlain, _r. de la Paix, 11—Chaussures de_
Hoffmann, _r. du Dauphin, 9_.
Graham's Magazine.]
* * * * *
Transcriber's Notes:
Table of Contents has been added for reader convenience. Archaic
spellings and hyphenation have been retained. Punctuation has been
corrected without note. Other errors have been corrected as noted below.
For illustrations, some caption text may be missing or incomplete due to
condition of the originals available for preparation of the eBook.
page iv, by Charles E. Cathrall, 149 ==> by Charles E. Cathrall, 140
page iv, Fox and Saukie Indians, ==> Saukie and Fox Indians,
page 5, a suprise took place ==> a surprise took place
page 21, like barks again put ==> like barques again put
page 28, thou seeest, hearest, ==> thou seest, hearest,
page 30, the streets, massacreing ==> the streets, massacring
page 31, supremay of the Pope! ==> supremacy of the Pope!
page 31, they were massacreing men, ==> they were massacring men,
page 46, your neice, I might ==> your niece, I might
page 51, with a manifest distate ==> with a manifest distaste
page 54, this arrangment, but in ==> this arrangement, but in
page 55, was a taunt top-mast, ==> was a taut top-mast,
page 60, would be villified ==> would be vilified
page 144, Firm of Domby & Son ==> Firm of Dombey & Son
Le Follet, _Chapeau de M^{me}._ Baudry ==> _Chapeaux de M^{me}._ Baudry
[End of Graham's Magazine, Vol. XXX, No. 1, January 1847, George Rex
Graham, Editor]
End of the Project Gutenberg EBook of Graham's Magazine, Vol. XXX, No. 1,
January 1847, by Various
*** | {
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Termites Foretell Climate Change in Africa's Savannas
Termite Mound in Tanzania
The Carnegie Institution's Department of Global Ecology has mapped over 40,000 termite mounds across the African savanna. Why would they do this? It turns out that termites are exceptionally sensitive to heat and moisture in the soil. By mapping where the termites choose to place their mounds, the insects are providing an indicator of climate change across regions.
Palo Alto, CA—Using sophisticated airborne imaging and structural analysis, scientists at the Carnegie Institution's Department of Global Ecology mapped more than 40,000 termite mounds over 192 square miles in the African savanna. They found that their size and distribution is linked to vegetation and landscape patterns associated with annual rainfall. The results reveal how the savanna terrain has evolved and show how termite mounds can be used to predict ecological shifts from climate change. The research is published in the September 7, 2010, advanced online edition of Nature Communications.
"By understanding the patterns of the vegetation and termite mounds over different moisture zones, we can project how the landscape might change with climate change," explained co-author Greg Asner at Carnegie. "Warming is expected to increase the variability of future precipitation in African savannas."
The technique will be used to track future changes in climate. From the smallest of creatures, empirical data to help forecast what larger creatures can expect to face.
LABELS: CLIMATE CHANGE, ENVIRONMENT, FAUNA, GLOBAL WARMING, SCIENCE | {
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Q: Why can a static member function only be declared static inside the class definition and not also in its own definition? While implementing a class for creating/updating boxes on the screen, I wanted to add a static member function that makes sure no currently visible boxes overlap (taking its information from a static pointer array to all currently visible boxes)
My initial code had the following structure:
class Box
{
public:
// ...
static void arrangeOverlappingBoxes();
};
static void Box::arrangeOverlappingBoxes()
{
// ...
}
I was quite surprised that this generated an error C2724: 'static' should not be used on member functions defined at file scope.
With some trial, google and error, I figured out that my function definition should lose the keyword static, i.e. it should be
void Box::arrangeOverlappingBoxes()
{
// ...
}
Yet I have no clue what the rationale behind this could be. It appears to be so asymetric and confusing to have a different function header for its declaration in the class definition and its own definition. Is there any reason for this?
A: Your class definition (in the header file) will provide the function with whatever propreties are necessary :
*
*static
*inlined
*virtual
Considering that every further object will look at your class definition using the .h then it makes sense that these properties to be defined there.
Furthermore, each function from the class will mentain it's property in the derived classes (for example you need to declare the destructor virtual only in your base class, every subsequent inheritance will take the destructor as virtual).
It makes no sense to redeclare these properties in your implementation body .
Having to declare function proprieties in both .h and .cpp files would actually lead to allot of problems.
Imagine this scenario : you declare a function as virtual in a .h file, and as static in the .cpp file. What will the compiler make that function ? virtual or static ? (or more likely a compile error , but the compiler error will just urge you to match in your .cpp file the declaration in the header. You cannot overload a function according to "static" or "virtual").
| {
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} | 14 |
Shannondale – jednostka osadnicza w Stanach Zjednoczonych, w stanie Wirginia Zachodnia, w hrabstwie Jefferson.
CDP w stanie Wirginia Zachodnia | {
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Q: I can't reach the table's td tag I can't grab table's td tag. I'm trying to first td property and second for value. This is the website:
https://www.mecsumai.com/bkn-summary/?bid=16076001&bg1=026937&bg2=dce8e2&wdt=100%25&aln=center&newid=06076001
My foreach codes are hare:
$allTables = $DOMParser->getElementsByTagName('table');
foreach ($allTables as $table) {
foreach ($table->getElementsByTagName('tr') as $tr) {
$tds = $tr->getElementsByTagName('td');
if ($tds->length == 2) {
$property = trim($tds->item(0)->nodeValue);
$value = trim($tds->item(1)->nodeValue);
switch ($property) {
case '販売価額':
$changeForMyDB['price'] = $value;
break;
case '所在地':
$changeForMyDB['address'] = $value;
break;
case '総戸数':
$changeForMyDB['hows_old'] = $value;
break;
case '間取り':
$changeForMyDB['rooms'] = $value;
break;
case '建物竣工':
$changeForMyDB['old'] = $value;
break;
case '入居(予定)日':
$changeForMyDB['entery'] = $value;
break;
case 'バルコニー面積':
$changeForMyDB['balcon_m2'] = $value;
break;
case '管理会社':
$changeForMyDB['company_name'] = $value;
break;
case '物件名':
$changeForMyDB['name'] = $value;
break;
case '専有面積':
$changeForMyDB['extend'] = $value;
break;
default:
# code...
break;
}
}
}
}
Estates::insertGetId($changeForMyDB);
$this->line('DATA saved.');
}
}
}
I updated codes and getting no errors but still can't get the data.
What am I doing wrong here?
Any idea? Thank you!
A: You can't access DOMNodeList directly as an array, but you have an equivalent method of accessing Nodes. I also added some lazy checks to make sure the tr has at least two elements corresponding to the property and value:
$dom = DOMDocument::loadHTMLFile("https://www.mecsumai.com/bkn-summary/?bid=16076001&bg1=026937&bg2=dce8e2&wdt=100%25&aln=center&newid=06076001");
$allTables = $dom->getElementsByTagName('table');
foreach ($allTables as $table){
foreach ($table->getElementsByTagName('tr') as $tr){
$tds = $tr->getElementsByTagName('td');
if ($tds->length == 2) {
$property = trim($tds->item(0)->nodeValue);
$value = trim($tds->item(1)->nodeValue);
$d[$property] = $value;
}
}
if (isset($d)) {
echo "Keys: " . count($d) . "\n";
unset ($d);
}
}
Output:
Keys: 31
Keys: 27
Keys: 30
| {
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} | 1,315 |
{"url":"http:\/\/physics.stackexchange.com\/questions\/56151\/when-does-hbar-rightarrow-0-provide-a-valid-transition-from-quantum-to-class","text":"# When does $\\hbar \\rightarrow 0$ provide a valid transition from quantum to classcial mechanics? When and why does it fail?\n\nLets look at the transition amplitude $U(x_{b},x_{a})$ for a free particle between two points $x_{a}$ and $x_{b}$ in the Feynman path integral formulation\n\n\u2022 $U(x_{b},x_{a}) = \\int_{x_{a}}^{x_{b}} \\mathcal{D} x e^{\\frac{i}{\\hbar}S}$\n\n($S$ is the classical action). It is often said that one gets classical mechanics in the limit $\\hbar \\rightarrow 0$. Then only the classical action is contributing, since the terms with non-classical $S$ cancel each other out because of the heavily oscillating phase. This sounds reasonable.\n\nBut when we look at the Heisenberg equation of motion for an operator $A$\n\n\u2022 $\\frac{dA}{dt} = \\frac{1}{i \\hbar} [A,H]$\n\nthe limit $\\hbar \\rightarrow 0$ does not make any sense (in my opinion) and does not reproduce classical mechanics. Basically, the whole procedure of canonical quantization does not make sense:\n\n\u2022 $\\{\\cdots,\\cdots\\} \\rightarrow \\frac{1}{i \\hbar} [\\cdots,\\cdots]$\n\nI don't understand, when $\\hbar \\rightarrow 0$ gives a reasonable result and when not. The question was hinted at here: Classical limit of quantum mechanics. But the discussion was only dealing with one particular example of this transition. Does anyone has more general knowledge about the limit $\\hbar \\rightarrow 0$?\n\n-\nHave a look at this entry by Lubos Motl motls.blogspot.com\/2011\/11\/\u2026 . If one uses the poisson brackets formulation of mechanics one gets back the classical poisson brackets as h-->0 ,and hence to classical mechanics in the Poisson bracket formulation. Also page 416 of Goldstein's second eddition \"classical mechanics\", chapter 9-7 . \u2013\u00a0 anna v Mar 7 '13 at 6:57\nPossible duplicates: physics.stackexchange.com\/q\/17651\/2451 , physics.stackexchange.com\/q\/32112\/2451 and links therein. \u2013\u00a0 Qmechanic Oct 15 '13 at 17:24\n\nThe theory of deformation quantization provides a framework in which the quantum to classical transition can be carried out and understood.\n\nAccording to this theory, for (practically any) quantum system, one can find (may be nonuniquely) a Poisson manifold $\\mathcal{M}$ (phase space) equipped with an associative product called the \"star product\" such that the quantum observables are represented by smooth functions on $\\mathcal{M}$ and the quantum operator product is given by the star product.\n\nFurthermore, the star product of two functions has a formal power series in $\\hbar$\n\n$f\\star g = \\sum_{k=0}^{\\infty} \\hbar^k B_k(f,g)$\n\nSuch that:\n\n$B_0(f,g) = fg$\n\n$B_1(f,g)-B_1(g, f) = \\{f,g\\}$, (Poisson bracket)\n\nThus we obtain:\n\n$f\\star g - g\\star f = \\hbar\\{f,g\\} + \\sum_{k=2}^{\\infty} \\hbar^k (B_k(f,g)-B_k(g,f))$\n\nPlease notice that according to the deformation Philosophy, the quantum observables are just functions on the phase space just as the classical observables and all the quantum noncommutativity is provided by the star product. Thus if we define $\\hat{f} = \\frac{\\hbar}{i} f$, we get the required classical limit.\n\nIt should be emphasized that this procedure can be carried out even for quantum systems defined by matrix algebras for example an appropriate phase for spin iis the two-sphere $S^2$, please, see the following article by Moreno and Ortega-Navarro. Morover,\n\nKontsevich in his seminal work provided a constructive method to construct this star product on every finite dimensional Poisson manifold, Please see the following Wikipedia page.\n\nIt is also worthwhile to mention that there are efforts to generalize the deformation construction to field theories and incorporate renormalization into it, please see the following work by Dito.\n\n-\nThank you! This is surely an interesting approach. It is hard for me, though, to understand the physical significance of this mathematical structure. Is there any physical justification for the introduction of the $\\star$-product or was it invented to make the limit $\\hbar \\rightarrow \\infty$ work? \u2013\u00a0 stankowait Mar 8 '13 at 1:22\n@stankowait Quantum mechanical amplitudes can be represented by expectations of products of operators. Thus, the star product allows to compute physical amplitudes. It is true that for elementary systems, other quantiation methods are more suitable. However, there are some systems such as moduli spaces and certain infinte dimensional phase spaces of physical interest, where deformation quantization is may be the only available quantization method. \u2013\u00a0 David Bar Moshe Mar 9 '13 at 5:37\n@stankowait cont. Please, see the following lecture by Daniel Sternheimer on the current status of deformation quantization: guests.mpim-bonn.mpg.de\/deform\/dsMPIMaugust08.pdf \u2013\u00a0 David Bar Moshe Mar 9 '13 at 5:39\n\nIn the operator language of quantum mechanics one does not (blindly) perform the limit $\\hbar \\rightarrow 0$ in the equations of motion (the schr\u00f6dinger equation), but expand the states as powerseries in $\\hbar$. In first order: $\\psi(x) = a(x) e^{S(x)}$. If you insert this expression in the schr\u00f6dinger equation you get (in first order) the classical Hamilton-Jacobi equation. See for example: http:\/\/en.wikipedia.org\/wiki\/WKB_approximation#Application_to_Schr.C3.B6dinger_equation or Bates, Weinstein: Lectures on the geometry of quantization for an geometric interpretation\n\n-\n\nThis sounds reasonable.\n\nMy rather rough understanding is that, (if there is a classical action for the transition,) in the limit it is only the neighbourhood of the classical action that is contributing. The contribution of the classical action itself maintains to have measure $0$ relative to the contribution of the neighbourhood, even when taking the limit (wherein that neighbourhood goes to \"size\" or \"spread\" $0$.)\n\nIf there isn't a classical action for the transition, then the whole thing fails anyway.\n\n-","date":"2014-09-19 01:47:57","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8613060116767883, \"perplexity\": 460.7145304156928}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2014-41\/segments\/1410657129431.12\/warc\/CC-MAIN-20140914011209-00268-ip-10-196-40-205.us-west-1.compute.internal.warc.gz\"}"} | null | null |
\section{Introduction}
In \cite{MR696688}, Jones initiated the study of modern subfactor theory. Given a finite index $II_{1}$ subfactor $A_{0} \subset A_{1}$, one computes its standard invariant: two towers $(A_{0}' \cap A_{j}: j \geq 0)$ and $(A_{1}' \cap A_{j}: j \geq 1)$ of finite dimensional von Neumann algebras \cite{MR696688}. The standard invariant has been axiomatized by Ocneanu's paragroups \cite{MR996454}, Popa's $\lambda-$lattices \cite{MR1334479}, and Jones' subfactor planar algebras \cite{ArXiv:1007.1158}. Popa showed that given a standard invariant $\mathcal{P}$, we can reconstruct a $II_{1}$ subfactor $A_{0} \subset A_{1}$ whose standard invariant is $\mathcal{P}$ \cite{MR1334479}. Guionnet, Jones, and Shlyakhtenko \cite{MR2732052} give a planar-algebraic proof of the above result. Moreover, if $\mathcal{P}$ is finite depth with loop paramater $\delta > 1$, they showed that $A_{k}$, the $k^{th}$ factor in the Jones tower, is isomorphic to $L(\mathbb{F}(1 + 2\delta^{-2k}(\delta - 1)I))$ where $I$ is the global index of $\mathcal{P}$ \cite{MR2807103}. Kodiyalam and Sunder also obtained this formula when $\mathcal{P}$ is depth 2 \cite{MR2574313, MR2557729}. In this paper, we prove the following theorem:
\begin{thm*}
If $\mathcal{P}$ is infinite depth, then every factor in the construction of \cite{MR2732052} is isomorphic to $L(\mathbb{F}_{\infty})$.
\end{thm*}
Using this theorem, we recover a diagrammatic proof of a result of Popa and Shlyakhtenko for $\mathcal{P}$ infinite depth \cite{MR2051399}:
\begin{cor*}
Every infinite depth subfactor planar algebra is the standard invariant of $\mathcal{N} \subset \mathcal{M}$ where $\mathcal{N}, \mathcal{M} \cong L(\mathbb{F}_{\infty})$.
\end{cor*}
\subsection{Outline of the proof}
To prove the above theorem, we will bootstrap the proof from \cite{MR2807103} of the finite-depth case to the infinite-depth case using standard embedding tricks.
\paragraph {The GJS Construction:}
We will recall the construction of Guionnet, Jones and Shlyakhtenko. For more details, see \cite{MR2732052} and \cite{MR2807103}. Let $\mathcal{P} = (\mathcal{P}_{n}^{\pm})_{n \geq 0}$ be a subfactor planar algebra with loop parameter $\delta > 1$ (see \cite{ArXiv:1007.1158} for the definition of a subfactor planar algebra). Set $Gr_{k}(\mathcal{P}^{+})= \bigoplus_{n \geq 0} \mathcal{P}_{k,n}^{+}$ where $\mathcal{P}^{+}_{k,n} = \mathcal{P}^{+}_{k+n}$ and an element of $\mathcal{P}^{+}_{k,n}$ is represented as
$$
\begin{tikzpicture}
\draw (-.5, -.5) -- (-.5, .5) -- (.5, .5) -- (.5, -.5) -- (-.5, -.5);
\draw (-1, -1) -- (-1, 1) -- (1, 1) -- (1, -1) -- (-1, -1);
\draw[ultra thick] (0, 1) -- (0, .5);
\draw[ultra thick] (1, 0) -- (.5, 0);
\draw[ultra thick] (-1, 0) -- (-.5, 0);
\node at (0, 0) {$x$};
\node at (-.75, .25) {$k$};
\node at (.75, .25) {$k$};
\node at (.30, .75) {$2n$};
\node at (-.5, .6) {*};
\node at (-1, 1.1) {*};
\end{tikzpicture}
$$
where the * is always in an unshaded region and a thick string with a $j$ next to it denotes $j$ parallel strings. If $x \in \mathcal{P}_{n+k}^{+}$ and $y \in \mathcal{P}_{m + k}^{+}$ then define a multiplication $\wedge_{k}$ by
$$
x \wedge_{k} y =
\begin{tikzpicture} [baseline = 0 cm]
\draw (-1.5, -.5) -- (-1.5, .5) -- (-.5, .5) -- (-.5, -.5) -- (-1.5, -.5);
\draw[ultra thick] (-1, 1) -- (-1, .5);
\draw[ultra thick] (0, 0) -- (-.5, 0);
\draw[ultra thick] (-2, 0) -- (-1.5, 0);
\node at (-1, 0) {$x$};
\node at (-1.75, .25) {$k$};
\node at (-.7, .75) {$2n$};
\node at (-1.5, .6) {*};
\draw (.5, -.5) -- (.5, .5) -- (1.5, .5) -- (1.5, -.5) -- (.5, -.5);
\draw[ultra thick] (1, 1) -- (1, .5);
\draw[ultra thick] (2, 0) -- (1.5, 0);
\draw[ultra thick] (0, 0) -- (.5, 0);
\node at (1, 0) {$y$};
\node at (1.75, .25) {$k$};
\node at (1.30, .75) {$2m$};
\node at (.5, .6) {*};
\draw (-2, -1) -- (2,-1)--(2,1)--(-2, 1)--(-2, -1);
\node at (-2, 1.1) {*};
\end{tikzpicture}
$$
which is an element in $\mathcal{P}_{k, m + n}^{+}$. One can endow $Gr_{k}(\mathcal{P}^{+})$ with the following trace: if $x \in \mathcal{P}^{+}_{k, n}$ then
$$
\tr(x) = \delta^{-k} \cdot \begin{tikzpicture}[baseline=.5cm]
\draw (.5,.5) --(-.5,.5) -- (-.5,-.5) -- (.5,-.5) -- (.5, .5) ;
\draw (.7,2)--(-.7,2)--(-.7,1)--(.7, 1)--(.7,2);
\draw[ultra thick] (-.5, 0) arc (90:270: .5cm) -- (.5, -1) arc(-90:90: .5cm);
\draw[ultra thick] (0, .5) -- (0, 1);
\node at (0, 0) {$x$};
\node at (-.5, .6) {*};
\node at (-.7, 2.1) {*};
\node at (0, 1.5) {$\sum TL$};
\node at (0, -.75) {$k$}; \end{tikzpicture}
$$
where $\sum TL$ denotes the sum of all Temperely-Lieb diagrams, i.e. all planar pairings of the $2n$ strings on top of $x$. This trace is positive definite, and one can form the von Neumann algebra $A_{k}$ which is the strong closure of $Gr_{k}(\mathcal{P}^{+})$ acting on $L^{2}(Gr_{k}(\mathcal{P}^{+}))$ by left multiplication (under $\wedge_{k}$). It is shown that $A_{k}$ is a $II_{1}$ factor. Moreover one can view $x \in A_{k}$ as an element in $A_{k+1}$ as follows:
$$
\begin{tikzpicture} [baseline = 0 cm]
\draw (-.5, -.5) -- (-.5, .5) -- (.5, .5) -- (.5, -.5) -- (-.5, -.5);
\draw[ultra thick] (0, 1) -- (0, .5);
\draw[ultra thick] (1, 0) -- (.5, 0);
\draw[ultra thick] (-1, 0) -- (-.5, 0);
\node at (0, 0) {$x$};
\node at (-.75, .25) {$k$};
\node at (.75, .25) {$k$};
\node at (-.5, .6) {*};
\node at (-1, 1.1) {*};
\draw[thick] (-1, -1) -- (-1, 1) -- (1, 1) -- (1, -1) -- (-1, -1);
\draw (-1, -.65) -- (1, -.65);
\end{tikzpicture} \, .
$$
With this identification, $A_{k}$ is a von Neumann subalgebra of $A_{k+1}$ and $A_{0} \subset A_{1} \subset \cdots \subset A_{k} \subset \cdots$ is a Jones tower of $II_{1}$ factors with standard invariant $\mathcal{P}^{+}$.
To identify the isomorphism type of the $A_{k}$, we look at the semi-finite algebra $$V_{+} = \bigoplus_{k + l + m \textrm{ even }} \mathcal{P}^{+}_{k,l,m}$$ where $\mathcal{P}^{+}_{k,l,m} = \mathcal{P}^{+}_{\frac{k + l + m}{2}}$ and is spanned by boxes of the form
$$
\begin{tikzpicture} [baseline = 0 cm]
\draw (-.5, -.5) -- (-.5, .5) -- (.5, .5) -- (.5, -.5) -- (-.5, -.5);
\draw[ultra thick] (0, 1) -- (0, .5);
\draw[ultra thick] (1, 0) -- (.5, 0);
\draw[ultra thick] (-1, 0) -- (-.5, 0);
\node at (0, 0) {$x$};
\node at (-.75, .25) {$k$};
\node at (.75, .25) {$l$};
\node at (.25, .75) {$m$};
\node at (-.5, -.7) {*};
\end{tikzpicture} \, .
$$
The element $x$ above is identified with the following element of $\mathcal{P}_{k+2p, l+2q, m}^{+}$:
\begin{equation}
\label{r}
\delta^{-(p+q)/2} \begin{tikzpicture}[baseline = -.5cm]
\draw (-.5, -.5) -- (-.5, .5) -- (.5, .5) -- (.5, -.5) -- (-.5, -.5);
\draw[ultra thick] (0, 1) -- (0, .5);
\draw[ultra thick] (1, 0) -- (.5, 0);
\draw[ultra thick] (-1, 0) -- (-.5, 0);
\draw[thick] (-1,1)--(-1,-2)--(1, -2)--(1,1)--(-1,1);
\draw (-1, -.5) arc(90:-90 : .2cm);
\draw (-1, -1.5) arc(90:-90 : .2cm);
\draw (1, -0.5) arc(90:270 : .2cm);
\draw (1, -1.5) arc(90:270 : .2cm);
\node at (0, 0) {$x$};
\node at (-.75, .25) {$k$};
\node at (.75, .25) {$l$};
\node at (.25, .75) {$m$};
\node at (-1, -2.2) {*};
\node at (-.85, -1.1) {\vdots};
\node at (.85, -1.1) {\vdots};
\node at (-.7, -1.1) {$p$};
\node at (.7, -1.1) {$q$};
\node at (-.5, -.7) {*};
\end{tikzpicture}
\end{equation}
where there are $p$ cups on the left and $q$ cups on the right. Under these identifications, $V_{+}$ completes to a semifinite von Neumann algebra, $\mathcal{M}_{+}$ where the multiplication is given by
$$
\left(\begin{tikzpicture} [baseline = 0cm]
\draw (-.5, -.5) -- (-.5, .5) -- (.5, .5) -- (.5, -.5) -- (-.5, -.5);
\draw[ultra thick] (0, 1) -- (0, .5);
\draw[ultra thick] (1, 0) -- (.5, 0);
\draw[ultra thick] (-1, 0) -- (-.5, 0);
\node at (0, 0) {$x$};
\node at (-.75, .25) {$k$};
\node at (.75, .25) {$l$};
\node at (.25, .75) {$m$};
\node at (-.5, -.7) {*};
\end{tikzpicture}\right) \cdot \left(\begin{tikzpicture}[baseline = 0cm]
\draw (-.5, -.5) -- (-.5, .5) -- (.5, .5) -- (.5, -.5) -- (-.5, -.5);
\draw[ultra thick] (0, 1) -- (0, .5);
\draw[ultra thick] (1, 0) -- (.5, 0);
\draw[ultra thick] (-1, 0) -- (-.5, 0);
\node at (0, 0) {$y$};
\node at (-.75, .25) {$k'$};
\node at (.75, .25) {$l'$};
\node at (.25, .75) {$m'$};
\node at (-.5, -.7) {*};
\end{tikzpicture}\right) = \delta_{l, k'} \begin{tikzpicture}[baseline = 0cm]
\draw (-1.5, -.5) -- (-1.5, .5) -- (-.5, .5) -- (-.5, -.5) -- (-1.5, -.5);
\draw[ultra thick] (-1, 1) -- (-1, .5);
\draw[ultra thick] (0, 0) -- (-.5, 0);
\draw[ultra thick] (-2, 0) -- (-1.5, 0);
\node at (-1, 0) {$x$};
\node at (-1.75, .25) {$k$};
\node at (-.7, .75) {$n$};
\node at (-1.5, -.7) {*};
\draw (.5, -.5) -- (.5, .5) -- (1.5, .5) -- (1.5, -.5) -- (.5, -.5);
\draw[ultra thick] (1, 1) -- (1, .5);
\draw[ultra thick] (2, 0) -- (1.5, 0);
\draw[ultra thick] (0, 0) -- (.5, 0);
\node at (1, 0) {$y$};
\node at (1.75, .25) {$l'$};
\node at (1.30, .75) {$m'$};
\node at (0, .3) {$l$};
\node at (.5, -.7) {*};
\draw (-2, -1) -- (2,-1)--(2,1)--(-2, 1)--(-2, -1);
\node at (-2, -1.2) {*};
\end{tikzpicture}
$$
where we have assumed that we have added enough cups as in diagram \eqref{r} so that $l$ and $k'$ are either the same or differ by 1. The trace on $\mathcal{M}_{+}$ is given by
$$
\Tr(x) = \begin{tikzpicture}[baseline=.5cm]
\draw (.5,.5) --(-.5,.5) -- (-.5,-.5) -- (.5,-.5) -- (.5, .5) ;
\draw (.7,2)--(-.7,2)--(-.7,1)--(.7, 1)--(.7,2);
\draw[ultra thick] (-.5, 0) arc (90:270: .5cm) -- (.5, -1) arc(-90:90: .5cm);
\draw[ultra thick] (0, .5) -- (0, 1);
\node at (0, 0) {$x$};
\node at (-.5, -.7) {*};
\node at (-.7, 2.1) {*};
\node at (0, 1.5) {$\sum TL$};
\node at (0, -.75) {$k$}; \end{tikzpicture}
$$
provided that the number of strings on the left and right of $x$ have the same parity and is zero otherwise. It is easy to check that the identification in diagram \eqref{r} respects both the trace and multiplication.
The algebras $A_{2k}$ above are a compression of $\mathcal{M}_{+}$ by the projection $p_{2k}^{+}$ where for general $n$,
$$
p_{n}^{+} = \begin{tikzpicture}[baseline = 0cm]
\draw[thick] (-.5, -.5) -- (-.5, .5) -- (.5, .5) -- (.5, -.5) -- (-.5, -.5);
\draw[ultra thick] (-.5, 0) -- (.5, 0);
\node at (0, .2) {$n$};
\node at (-.5, -.7) {*};
\end{tikzpicture}
$$
Similarly, we can consider a semifinite von Neumann algebra $\mathcal{M}_{-}$ generated by the $\mathcal{P}_{n}^{-}$'s (where the * is in a \emph{shaded} region and on the bottom of the box), and if we define projections $p_{n}^{-}$, then $A_{2k+1}$ is the compression of $\mathcal{M}_{-}$ by $p_{2k+1}^{-}$.
A diagrammatic argument shows that $\mathcal{M}_{+}$ is generated by
$$
\mathcal{A}_{+} = \displaystyle \left(\bigcup_{k, \ell} \mathcal{P}^{+}_{k, \ell, 0}\right)^{''} \textrm{ and } X = \textrm{s}-\lim_{k \rightarrow \infty} \begin{tikzpicture}[baseline = 0cm]
\draw[thick] (-.7, -.7) -- (-.7, .7) -- (.7, .7) -- (.7, -.7) -- (-.7, -.7);
\draw (-.7, .4)--(0, .4) arc(-90:0 : .3cm);
\draw[ultra thick] (-.7, 0) -- (.7, 0);
\node at (0, -.3) {$2k$};
\node at (-.7, -.9) {*};
\node at (-.7, -.9) {*};
\end{tikzpicture}
+
\begin{tikzpicture} [baseline = 0cm]
\draw[thick] (-.7, -.7) -- (-.7, .7) -- (.7, .7) -- (.7, -.7) -- (-.7, -.7);
\draw (.7, .4)--(0, .4) arc(-90:-180 : .3cm);
\draw[ultra thick] (-.7, 0) -- (.7, 0);
\node at (0, -.3) {$2k$};
\node at (-.7, -.9) {*};
\end{tikzpicture}
$$
where the limit above is in the strong operator topology. This element is an $\mathcal{A}_{+}$-valued semicircular element in the sense of \cite{MR1704661} and is used in the calculation of the isomorphism class of the algebras $A_{k}$
\paragraph{The finite depth case:} Let $\Gamma$ denote the principal graph of $\mathcal{P}$ with edge set $E(\Gamma)$ and initial vertex *. Let $\ell^{\infty}(\Gamma)$ as the von Neumann algebra of bounded functions on the vertices of $\Gamma$ and endow $\ell^{\infty}(\Gamma)$ with a trace $\tr$ such that $\tr(p_{v}) = \mu_{v}$, where $p_{v}$ is the delta function at $v$ and $\mu_{v}$ is the entry corresponding to a fixed Perron-Frobenius eigenvector for $\Gamma$ with $\mu_* = 1$. From \cite{MR2807103}, $A_{0} = p_{*}\mathcal{M}(\Gamma)p_{*}$ where $\mathcal{M}(\Gamma)$ is the von Neumann algebra generated by $(\ell^{\infty}(\Gamma), \tr)$ and $\ell^{\infty}(\Gamma)$-valued semicircular elements $\{X_{e}: e \in E(\Gamma)\}$ which are compressions of $X$ by partial isometries in $\mathcal{A}_{+}$ and are free with amalgamation over $\ell^{\infty}(\Gamma)$. Each $X_{e}$ is supported under $p_{v} + p_{w}$, where $e$ connects $v$ and $w$, and we have $X_{e} = p_{v}X_{e}p_{w} + p_{w}X_{e}p_{v}$. Assuming that $\mu_v \geq \mu_w$, the scalar-valued distribution of $X_{e}^{2}$ in $(p_v + p_w)\mathcal{M}(\Gamma)(p_v + p_w)$ is free-Poisson with an atom of size $\frac{\mu_v - \mu_w}{\mu_v + \mu_w}$ at 0. Therefore,
$$
vN(\ell^{\infty}(\Gamma), X_{e}) = L(\mathbb{Z}) \otimes M_{2}(\mathbb{C}) \oplus \mathbb{C} \oplus \ell^{\infty}(\Gamma \setminus \{v, w\})
$$
with $p_w = (1\otimes e_{1,1})\oplus 0\oplus 0$ and $p_v = (1\otimes e_{2,2})\oplus 1\oplus 0$, where $\{e_{i,j}: 1 \leq i,j \leq 2\}$ is a system of matrix units for $M_{2}(\mathbb{C})$. If $\Gamma$ is finite, Dykema's formulas for computing certain amalgamated free products \cite{MR1201693, MR2765550} show that $\mathcal{M}(\Gamma)$ is an interpolated free group factor and the compression formula gives the result for $A_{0}$. Since $A_{2n}$ is a $\delta^{2n}-$amplification of $A_{0}$, the result holds for $A_{2n}$. The factor $A_{1}$ is a compression of $M(\Gamma^{*})$ with $\Gamma^{*}$ the dual principal graph of $\mathcal{P}$. Applying the same analysis to $\Gamma^{*}$ gives the formula for the $A_{2n+1}$'s.
\paragraph{The infinite depth case:}
We similarly define $\mathcal{M}(\Gamma)$ for an arbitrary connected, loopless (not necessarily bipartite) graph $\Gamma$. If $\Gamma$ is finite, we show that $\mathcal{M}(\Gamma) \cong L(\mathbb{F}_{t}) \oplus A$ where $A$ is finite-dimensional and abelian ($A$ can possibly be $\{0\}$). Furthermore, if $p_{\Gamma}$ is the identity of $L(\mathbb{F}_{t})$ and $\Gamma'$ is a finite graph containing $\Gamma$, then the inclusion $p_{\Gamma}\mathcal{M}(\Gamma)p_{\Gamma} \rightarrow p_{\Gamma}\mathcal{M}(\Gamma')p_{\Gamma}$ is a standard embedding of interpolated free group factors (see Definition \ref{defn:Dyk} and Remark \ref{rem:Dyk} below). Therefore, if $\mathcal{P}$ is infinite depth with principal graph $\Gamma$, we write $\Gamma$ as an increasing union of finite graphs $\Gamma_{k}$ where $\Gamma_{k}$ is $\Gamma$ truncated at depth $k$. Since standard embeddings are preserved by cut-downs, the inclusion $p_{*}\mathcal{M}(\Gamma_{k})p_{*} \rightarrow p_{*}\mathcal{M}(\Gamma_{k+1})p_{*}$ is a standard embedding. As $A_{0}$ is the inductive limit of the $p_{*}\mathcal{M}(\Gamma_{k})p_{*}$'s, it is an interpolated free group factor where the parameter is the limit of the parameters for the $p_{*}\mathcal{M}(\Gamma_{k})p_{*}$'s, which is $\infty$. Since the factors $A_{2k}$ are amplifications of $A_{0}$, $A_{2k} \cong L(\mathbb{F}_{\infty})$. Applying the same analysis to $\Gamma^{*}$ (the dual principal graph of $\mathcal{P}$) shows that $A_{2k+1} \cong L(\mathbb{F}_{\infty})$.
\paragraph{Organization:} Section \ref{sec:preliminaries} covers some preliminary material on interpolated free group factors, free dimension, and standard embeddings. Section \ref{sec:VNGraph} introduces $\mathcal{M}(\Gamma)$ and establishes both its structure and how it includes into $\mathcal{M}(\Gamma')$ for $\Gamma$ a subgraph of $\Gamma'$. Section \ref{sec:GJSInfinite} provides the proof that the factors $A_{k}$ above are all isomorphic to $L(\mathbb{F}_{\infty})$.
\paragraph{Acknowledgements:} The author would like to thank Arnaud Brothier, Vaughan Jones, David Penneys, and Dimitri Shlyakhtenko for their conversations and encouragement. The author was supported by NSF Grant DMS-0856316 and DOD-DARPA grants HR0011-11-1-0001 and HR0011-12-1-0009.
\section{Preliminaries}\label{sec:preliminaries}
Dykema \cite{MR1256179} and R\u{a}dulescu \cite{MR1258909} independently developed interpolated free group factors $L(\mathbb{F}_{t})$ for $1 < t \leq \infty$. These coincide with the usual free group factors when $t \in \mathbb{N} \cup \{\infty\}$ and they satisfy
$$
L(\mathbb{F}_{t})*L(\mathbb{F}_{s}) = L(\mathbb{F}_{s+t}) \textrm{ and } L(\mathbb{F}_{t})_{\gamma} = L(\mathbb{F}(1 + \gamma^{-2}(t-1))),
$$
where $M_{\gamma}$ is the $\gamma-$amplification of the $II_{1}$ factor $M$. It is known that either the interpolated free group factors are all isomorphic or they are pairwise non-isomorphic \cite{MR1256179, MR1258909}.
\begin{nota} \label{nota:vNA} Throughout this paper, we will be concerned with finite von Neumann algebras $(\mathcal{M}, tr)$ which can be written in the form
$$
\mathcal{M} = \overset{p_{0}}{\underset{\gamma_{0}}{\mathcal{M}_{0}}} \oplus \bigoplus_{j \in J} \overset{p_{j}}{\underset{\gamma_{j}}{L(\mathbb{F}_{t_{j}})}} \oplus \bigoplus_{k \in K} \overset{q_{k}}{\underset{\alpha_{k}}{M_{n_{k}}}}
$$
where $\mathcal{M}_{0}$ is a diffuse hyperfinite von Neumann algebra, $L(\mathbb{F}_{t_{j}})$ is an interpolated free group factor with parameter $t_{j}$, $M_{n_{k}}$ is the algebra of $n_{k} \times n_{k}$ matrices over the scalars, and the sets $J$ and $K$ are at most finite and countably infinite respectively. We use $p_{j}$ to denote the projection in $L(\mathbb{F}_{t_{j}})$ corresponding to the identity of $L(\mathbb{F}_{t_{j}})$ and $q_{k}$ to denote a minimal projection in $M_{n_{k}}$. The projections $p_{j}$ and $q_{k}$ have traces $\gamma_{j}$ and $\alpha_{k}$ respectively. Let $p_{0}$ be the identity in $\mathcal{M}_{0}$ with trace $\gamma_{0}$. We write $\overset{p,q}{M_{2}}$ to mean $M_{2}$ with a choice of minimal orthogonal projections $p$ and $q$. \end{nota}
If the interpolated free group factors turn out to be non-isomorphic, it is desirable to be able to calculate which interpolated free group factors appear in amalgamated free products. To help facilitate this calculation, Dykema defined the notion of free dimension. In general, one has
$$
\fdim(\mathcal{M}_{1} \underset{D}* \mathcal{M}_{2}) = \fdim(\mathcal{M}_{1}) + \fdim(\mathcal{M}_{2}) - \fdim(D)
$$
whenever $\mathcal{M}_{1}$ and $\mathcal{M}_{2}$ are of the form of Notation \ref{nota:vNA} and $D$ is finite dimensional \cite{MR1201693, MR1363079,MR2765550,arXiv:1110.5597v1}. In general, for the algebra $\mathcal{M}$ in Notation \ref{nota:vNA}, we have $$\fdim(\mathcal{M}) = 1 + \sum_{j \in J}\gamma_{j}^{2}(t_{j} - 1) - \sum_{k \in K}\alpha_{k}^{2}.$$
Notice that this includes the special case $\fdim(L(\mathbb{F}_{t})) = t$.
Of course if the interpolated free group factors are isomorphic, then the free dimension is not well defined; however, the only purpose of the free dimension is to determine the parameter of interpolated free group factors which show up in amalgamated free products. Therefore all the lemmas below will remain valid if all references to free dimension are removed.
Of critical importance will be the notion of a \emph{standard embedding} of interpolated free group factors \cite{MR1201693}. This is a generalization of a mapping $\mathbb{F}_{n} \rightarrow \mathbb{F}_{m}$ for $m > n$ sending the $n$ generators of $\mathbb{F}_{n}$ onto $n$ of the $m$ generators for $\mathbb{F}_{m}$.
\begin{defn} \label{defn:Dyk}
Let $1 < r < s$ and $\phi : L(\mathbb{F}_{r}) \rightarrow L(\mathbb{F}_{s})$ be a von Neumann algebra homomorphism. We say that $\phi$ is a standard embedding if there exist nonempty sets $S \subset S'$, a family of projections $\{p_{s'}: s' \in S'\}$ with $p_{s'} \in R$ (the hyperfinite $II_{1}$ factor), a free family $\{X^{s'}: s' \in S'\}$ of semicircular elements which are also free from $R$, and isomorphisms
$$
\alpha: L(\mathbb{F}_{r}) \rightarrow (R \cup \{p_{s}X^{s}p_{s}\}_{s \in S})'' \textrm{ and } \beta : L(\mathbb{F}_{s}) \rightarrow (R \cup \{p_{s'}X^{s'}p_{s'}\}_{s' \in S'})''
$$
such that $\phi = \beta^{-1} \circ \iota \circ \alpha$ where $\iota: (R \cup \{p_{s}X^{s}p_{s}\}_{s \in S})'' \rightarrow (R \cup \{p_{s'}X^{s'}p_{s'}\}_{s' \in S'})''$ is the canonical inclusion. We will write $A \overset{s.e.}{\hookrightarrow} B$ to mean that the inclusion of $A$ into $B$ is a standard embedding.
\end{defn}
\begin{rem} \label{rem:Dyk} Dykema in \cite{MR1201693} and \cite{MR1363079} shows the following useful properties of standard embeddings which we will use extensively in this paper.
\begin{itemize}
\item[(1)] If $A$ is an interpolated free group factor, the canonical inclusion $A \rightarrow A * \mathcal{M}$ is a standard embedding whenever $\mathcal{M}$ is of the form in Notation \ref{nota:vNA}.
\item[(2)] A composite of standard embeddings is a standard embedding.
\item[(3)] If $A_{n} = L(\mathbb{F}_{s_{n}})$ with $s_{n} < s_{n+1}$ for all $n$ and $\phi_{n}: A_{n} \overset{s.e.}{\hookrightarrow} A_{n+1}$, then the inductive limit of the $A_{n}$ with respect to the $\phi_{n}$ is $L(\mathbb{F}_{s})$ where $s = \displaystyle \lim_{n \rightarrow \infty}s_{n}$.
\item[(4)] If $t > s$ then $\phi: L(\mathbb{F}_{s}) \overset{s.e.}{\hookrightarrow} L(\mathbb{F}_{t})$ if and only if for any nonzero projection $p \in L(\mathbb{F}_{s})$, $\phi|_{pL(\mathbb{F}_{s})p}: pL(\mathbb{F}_{s})p \overset{s.e.}{\hookrightarrow} \phi(p)L(\mathbb{F}_{t})\phi(p)$.
\end{itemize}
\end{rem}
Our work will rely heavily on the following two lemmas.
\begin{lem} [\cite{arXiv:1110.5597v1}] \label{lem:DR1}
Let $\mathcal{N} = (\overset{p}{M_{n}(\mathbb{C})} \oplus B) \underset{D}{*} C$ and $\mathcal{M} = (M_{n}(\mathbb{C}) \otimes A \oplus B) \underset{D}{*} C$ where $A$, $B$ and $C$ are finite von Neumann algebras and $D$ is a finite dimensional abelian von Neumann algebra. Let $E$ be the trace-preserving conditional expectation of $\mathcal{M}$ onto $D$. Assume $p$ lies under a minimal projection in $D$ and $E|_{M_{n}(\mathbb{C}) \otimes A} = E|_{M_{n}(\mathbb{C})} \otimes tr_{A}$. Then $p\mathcal{M} p = p\mathcal{N} p * A$ and the central support of $p$ in $\mathcal{M}$ is the same as that in $\mathcal{N}$.
\end{lem}
\begin{lem} [\cite{arXiv:1110.5597v1}] \label{lem:DR2}
Let $\mathcal{N} = (\overset{p}{\underset{\gamma}{M_{m}(\mathbb{C})}} \oplus \overset{q}{\underset{\gamma}{M_{n-m}(\mathbb{C})}} \oplus B) \underset{D}{*} C$ and $\mathcal{M} = (\underset{\gamma}{M_{n}(\mathbb{C})} \oplus B) \underset{D}{*} C$ with $B$, $C$, $D$ as in Lemma \ref{lem:DR1}. Assume $p$ and $q$ sit under minimal projections in $D$ and $p$ is equivalent to $q$ in $\mathcal{N}$. Then $p\mathcal{M} p = p\mathcal{N} p * L(\mathbb{Z})$ and the central support of $p$ in $\mathcal{M}$ is the same as that in $\mathcal{N}$.
\end{lem}
Note that if $A$, $B$ and $C$ are in the form in Notation \ref{nota:vNA}, and if $\mathcal{N}$ is an interpolated free group factor, then the proofs of the above lemmas in \cite{arXiv:1110.5597v1} show that $p\mathcal{N} p \rightarrow p\mathcal{M} p$ of Lemmas \ref{lem:DR1} and \ref{lem:DR2} are standard embeddings. This implies $\mathcal{N} \overset{s.e.}{\hookrightarrow} \mathcal{M}$ by Remark \ref{rem:Dyk}.
\section{A von Neumann algebra associated to a finite connected graph}\label{sec:VNGraph}
Let $\Gamma$ be a connected, loopless finite graph with edge set $E(\Gamma)$ and vertex set $V(\Gamma)$. Assume further that each vertex $v \in V(\Gamma)$ is weighted by a real constant $\gamma_{v} > 0$ with $\sum_{v \in \Gamma} \gamma_{v} = 1$ (the weighting does \emph{not} have to be the Perron-Frobenius weighting). Consider the abelian von Neumann algebra $\ell^{\infty}(\Gamma)$. Let $p_{v}$ be the indicator function on the vertex $v$ and its trace will be $\gamma_{v}$. We construct a finite von Neumann algebra associated to $\Gamma$ (also see \cite{MR2772347}).
\begin{defn}\label{defn:vNGraph}
Let $\Gamma$ be as above, $e$ be an edge in $\Gamma$ connecting the vertices $v$ and $w$, and assume $\gamma_{v} \geq \gamma_{w}$. Define
$$
\mathcal{A}_{e} = \underset{2\gamma_{w}}{M_{2}(\mathbb{C}) \otimes L(\mathbb{Z})} \oplus \CC_{\gamma_{v} - \gamma_{w}}^{p^{e}_{v}} \oplus \ell^{\infty}(\Gamma \setminus \{v, w\})
$$
where the trace on $M_{2} \otimes L(\mathbb{Z})$ is $\tr_{M_{2}} \otimes \tr_{L(\mathbb{Z})}$. $\mathcal{A}_{e}$ includes $\ell^{\infty}(\Gamma)$ by setting \begin{align*}p_{w} &= 1 \otimes e_{1, 1} \oplus 0 \oplus 0 \textrm{ and } \\ p_{v} &= 1 \otimes e_{2, 2} \oplus 1 \oplus 0.\end{align*} Therefore, the trace preserving conditional expectation $E_{e}: \mathcal{A}_{e} \rightarrow \ell^{\infty}(\Gamma)$ has the property $E_{e}|_{M_{2} \otimes L(Z)} = E_{e}|_{M_{2}} \otimes \tr|_{L(\mathbb{Z})}$. We define $\mathcal{M}(\Gamma)$, the von Neumann algebra associated to $\Gamma$, by $$
\mathcal{M}(\Gamma) = \underset{{\ell^{\infty}(\Gamma)}}{*} (\mathcal{A}_{e}, E_{e})_{e \in E(\Gamma)}.
$$
\end{defn}
\begin{rem} If $\Gamma$ is an infinite graph with a weighting that is not $\ell^{1}$, then we can still define $M(\Gamma)$ as in \ref{defn:vNGraph} although it will be a semifinite algebra. Given $e \in E(\Gamma)$ connecting vertices $v$ and $w$, the compressed algebra $(p_{v} + p_{w})\mathcal{A}_{e}(p_{v} + p_{w})$ is still finite, and if $E_{e}: \mathcal{A}_{e} \rightarrow \ell^{\infty}(\Gamma)$ is the (tracial-weight) preserving conditional expectation, then $E_{e}$ is clearly normal on $(p_{v} + p_{w})\mathcal{A}_{e}(p_{v} + p_{w})$ and is the identity on $(1 - p_{v} - p_{w})\mathcal{A}_{e}(1 - p_{v} - p_{w})$. Therefore one can take the algebraic free product $Q$ of $(\mathcal{A}_{e})_{e\in E(\Gamma)}$ with amalgamation over $\ell^{\infty}(\Gamma)$ and represent it on $L^{2}(Q, Tr \circ \underset{\ell^{\infty}(\Gamma)}{*}E_{e})$ to obtain $\mathcal{M}(\Gamma)$.
\end{rem}
\begin{defn} \label{defn:H2} Let $v, w \in V(\Gamma)$ We write $v \sim w$ if $v$ and $w$ are connected by at least 1 edge in $\Gamma$ and denote $n_{v, w}$ be the number of edges joining $v$ and $w$. We set $\alpha^{\Gamma}_{v} = \sum_{w\sim v} n_{v, w}\gamma_{w}$, and define $B(\Gamma) = \{ v \in V(\Gamma) : \gamma_{v} > \alpha^{\Gamma}_{v}\}$. \end{defn}
For the rest of this section, we assume $\Gamma$ is finite. We show that $\mathcal{M}(\Gamma)$ is the direct sum of an interpolated free group factor and a finite dimensional abelian algebra. More precisely, we prove the following theorem:
\begin{thm} \label{thm:H1}
Let $\Gamma$ and $\Gamma'$ be connected, finite, loopless, and weighted graphs with at least 2 edges. Then $\mathcal{M}(\Gamma) \cong \overset{p^{\Gamma}}{L(\mathbb{F}_{t_{\Gamma}})} \oplus \underset{{v \in B(\Gamma)}}{\bigoplus} \overset{r_{v}^{\Gamma}}{\underset{\gamma_{v} - \alpha^{\Gamma}_{v}}{\mathbb{C}}}$ where $r_{v}^{\Gamma} \leq p_{v}$ and $t_{\Gamma}$ is such that this algebra has the appropriate free dimension. Furthermore, if $\Gamma$ is a subgraph of $\Gamma'$, then $p^{\Gamma}\mathcal{M}(\Gamma)p^{\Gamma} \overset{s.e.}{\hookrightarrow} p^{\Gamma}\mathcal{M}(\Gamma')p^{\Gamma}$.
\end{thm}
Notice that since we are assuming that all vertices have positive weight, it follows that $p_{v}p^{\Gamma}\neq 0$ for all $v \in \Gamma$. We prove Theorem \ref{thm:H1} in a series of lemmas.
\begin{lem} \label{lem:H1}
Let $\Gamma$ be a finite, connected, weighted, loopless graph with 2 edges. Then $M(\Gamma)$ is of the form in Theorem \ref{thm:H1}.
\end{lem}
\begin{proof}
Set $D = \ell^{\infty}(\Gamma)$. There are two overlying cases to consider. One where $\Gamma$ has 2 vertices and the other where $\Gamma$ has 3 vertices.
\emph{\underline{Case 1}}: Assume that $\Gamma$ has 2 vertices $v, w$ and 2 edges $e_{1}$ and $e_{2}$ connecting $v$ and $w$ and without loss of generality assume $\gamma_{v} \geq \gamma_{w}$. We obtain the desired formula for $\mathcal{M}(\Gamma)$ by examining the following sequence of inclusions:
\begin{align*}
\mathcal{N}_{0} &= \left(\overset{p_{w}}{\underset{\gamma_{w}}{\mathbb{C} }}\oplus \overset{p_{v}^{I}}{\underset{\gamma_{w}}{\mathbb{C}}} \oplus \underset{\gamma_{v} - \gamma_{w}}{\mathbb{C}}\right) \underset{D}* \left(\overset{p_{w}}{\underset{\gamma_{w}}{\mathbb{C} }}\oplus \overset{q_{v}^{I}}{\underset{\gamma_{w}}{\mathbb{C}}} \oplus \underset{\gamma_{v} - \gamma_{w}}{\mathbb{C}}\right)\\
\cap&\\
\mathcal{N}_{1} &= \left(\overset{p_{w}, p_{v}^{I}}{\underset{\gamma_{w}}{M_{2}}} \oplus \underset{\gamma_{v} - \gamma_{w}}{\mathbb{C}}\right) \underset{D}{*} \left(\overset{p_{w}}{\underset{\gamma_{w}}{\mathbb{C} }}\oplus \overset{q_{v}^{I}}{\underset{\gamma_{w}}{\mathbb{C}}} \oplus \underset{\gamma_{v} - \gamma_{w}}{\mathbb{C}}\right)\\
\cap&\\
\mathcal{N}_{2} &= \left(\overset{p_{w}, p_{v}^{I}}{\underset{\gamma_{w}}{M_{2}}} \oplus \underset{\gamma_{v} - \gamma_{w}}{\mathbb{C}}\right) \underset{D}{*} \left(\overset{p_{w}, q_{v}^{I}}{\underset{\gamma_{w}}{M_{2}}} \oplus \underset{\gamma_{v} - \gamma_{w}}{\mathbb{C}}\right)\\
\cap&\\
\mathcal{N}_{3} &= \left(\underset{2\gamma_{w}}{M_{2} \otimes L(\mathbb{Z})} \oplus \underset{\gamma_{v} - \gamma_{w}}{\mathbb{C}}\right) \underset{D}{*} \left(\overset{p_{w}}{\underset{\gamma_{w}}{M_{2}}} \oplus \underset{\gamma_{v} - \gamma_{w}}{\mathbb{C}}\right)\\
\cap&\\
\mathcal{M}(\Gamma) &= \left(\underset{2\gamma_{w}}{M_{2} \otimes L(\mathbb{Z})} \oplus \underset{\gamma_{v} - \gamma_{w}}{\mathbb{C}}\right) \underset{D}{*} \left(\underset{2\gamma_{w}}{M_{2} \otimes L(\mathbb{Z})} \oplus \underset{\gamma_{v} - \gamma_{w}}{\mathbb{C}}\right),
\end{align*}
where $p_{v}$ decomposes as $(1 \otimes e_{2, 2}) \oplus 1$ in $\mathcal{A}_{e_{1}}$ and $\mathcal{A}_{e_{2}}$ with $p_{v}^{I} = 1 \otimes e_{2,2}$ in $\mathcal{A}_{e_{1}}$ and $q_{v}^{I} = 1 \otimes e_{2,2}$ in $\mathcal{A}_{e_{2}}$. From Lemma \ref{lem:DR1} and \cite{MR1201693}, we see that
$$
p_{v}\mathcal{N}_{0}p_{v} = \overset{p_{v}^{I}}{\underset{\frac{\gamma_{w}}{\gamma{v}}}{\mathbb{C}}} \oplus \underset{\frac{\gamma_{v} - \gamma_{w}}{\gamma{v}}}{\mathbb{C}}*\overset{q_{v}^{I}}{\underset{\frac{\gamma_{w}}{\gamma{v}}}{\mathbb{C}}} \oplus \underset{\frac{\gamma_{v} - \gamma_{w}}{\gamma{v}}}{\mathbb{C}} = \begin{cases} \underset{2\frac{\gamma_{v} - \gamma_{w}}{\gamma_{v}}}{M_{2} \otimes L(\mathbb{Z})} \oplus \overset{p_{v}^{I} \wedge q_{v}^{I}}{\underset{\frac{2\gamma_{w} - \gamma_{v}}{\gamma_{v}}}{\mathbb{C}}} & \textrm{if } 2\gamma_{w} \geq\gamma_{v}\\ \underset{\frac{2\gamma_{w}}{\gamma_{v}}}{M_{2} \otimes L(\mathbb{Z})} \oplus \overset{(p_{v} - p_{v}^{I})\wedge(p_{v} - q_{v}^{I})}{\underset{\frac{\gamma_{v} - 2\gamma_{w}}{\gamma_{v}}}{\mathbb{C}}} & \textrm{if }\gamma_{v} > 2\gamma_{w} \end{cases}
$$
where in the first algebra, the identity element copy of $\mathbb{C}$ is $p_{v}^{I} \wedge q_{v}^{I}$ and and in the second algebra, the identity of the copy of $\mathbb{C}$ is orthogonal to both $p_{v}^{I}$ and $q_{v}^{I}$.
\emph{\underline{Case 1a}}: Assume $2\gamma_{w} \geq \gamma_{v}$. As $p_{v}\wedge q_{v}$ is minimal and central in $\mathcal{N}_{0}$, we see that
$$
\mathcal{N}_{1} = \underset{3(\gamma_{v} - \gamma_{w})}{M_{3}\otimes L(\mathbb{Z})} \oplus \underset{2\gamma_{w} - \gamma_{v}}{\overset{p_{v}^{I} \wedge q_{v}^{I}}{M_{2}}}.
$$
By \cite{MR1201693}, the projections $p_{v}^{I}$ and $q_{v}^{I}$ are equivalent in $\mathcal{N}_{0}$, so it follows that $p_{w}$ is equivalent to $q_{v}^{I}$ in $\mathcal{N}_{1}$. Therefore by Lemma \ref{lem:DR2},
$$
p_{w}\mathcal{N}_{2}p_{w} = p_{w}\mathcal{N}_{1}p_{w} * L(\mathbb{Z}) = (\underset{\frac{\gamma_{v} - \gamma_{w}}{\gamma_{w}}}{L(\mathbb{Z})} \oplus \underset{\frac{2\gamma_{w} - \gamma_{v}}{\gamma_{w}}}{\mathbb{C}}) * L(\mathbb{Z}),
$$
which is an interpolated free group factor $L(\mathbb{F}_{t})$ \cite{MR1201693}. As the central support of $p_{w}$ in $\mathcal{N}_{2}$ is 1, it follows that $\mathcal{N}_{2}$ is also an interpolated free group factor $L(\mathbb{F}_{t_{1}})$. To finish up this case, we write
\begin{align*}
\mathcal{N}_{2} \subset \mathcal{N}_{3} &= \left(\underset{2\gamma_{w}}{M_{2} \otimes L(\mathbb{Z})} \oplus \underset{\gamma_{v} - \gamma_{w}}{\mathbb{C}}\right) \underset{D}{*} \left(\overset{p_{w}}{\underset{\gamma_{w}}{M_{2}}} \oplus \underset{\gamma_{v} - \gamma_{w}}{\mathbb{C}}\right) \textrm{ and }\\
\mathcal{N}_{3} \subset \mathcal{M}(\Gamma) &= \left(\underset{2\gamma_{w}}{M_{2} \otimes L(\mathbb{Z})} \oplus \underset{\gamma_{v} - \gamma_{w}}{\mathbb{C}}\right) \underset{D}{*} \left(\underset{2\gamma_{w}}{M_{2} \otimes L(\mathbb{Z})} \oplus \underset{\gamma_{v} - \gamma_{w}}{\mathbb{C}}\right),
\end{align*}
and use Lemma \ref{lem:DR1} twice, as well as the amplification formula for interpolated free group factors to obtain that $\mathcal{M}(\Gamma)$ is an interpolated free group factor.
\emph{\underline{Case 1b}}: The case $\gamma_{v} > 2\gamma_{w}$ for $\mathcal{N}_{0}$ is treated exactly the same as the first with only the caveat that the central support of $p_{w}$ in $\mathcal{N}_{1}$ is a projection of trace $3\gamma_{w}$, so $\mathcal{N}_{1}$, and thus $\mathcal{N}_{2}$, $\mathcal{N}_{3}$, and $\mathcal{M}(\Gamma)$, have a minimal central projection of trace $\gamma_{v} - 2\gamma_{w}$.\\
\emph{\underline{Case 2}}: Next we consider the case where $\Gamma$ has 3 vertices $v_{1}$, $v_{2}$, and $v_{3}$ with weights $\gamma_{1}$, $\gamma_{2}$, and $\gamma_{3}$ respectively, where $v_{2}$ is connected to $v_{1}$ by $e_{1}$ and to $v_{3}$ by $e_{2}$. There are two sub-cases to consider. The first is when $\gamma_{2} \geq \gamma_{1} \geq \gamma_{3}$, and the second is when $\gamma_{1} > \gamma_{2}$ and $\gamma_{1} \geq \gamma_{3}$.
\emph{\underline{Case 2a}}: We examine the following sequence of inclusions:
\begin{align*}
\mathcal{N}_{0} &= \left(\overset{p_{v_{1}}}{\underset{\gamma_{1}}{\mathbb{C}}} \oplus \overset{p^{I}_{2}}{\underset{\gamma_{1}}{\mathbb{C}}} \oplus \overset{p^{II}_{2}}{\underset{\gamma_{2} - \gamma_{1}}{\mathbb{C}}} \oplus \overset{p_{v_{3}}}{\underset{\gamma_{3}}{\mathbb{C}}}\right) \underset{D}{*} \left(\overset{p_{v_{1}}}{\underset{\gamma_{1}}{\mathbb{C}}} \oplus \overset{q^{I}_{2}}{\underset{\gamma_{2} - \gamma_{3}}{\mathbb{C}}} \oplus \overset{q^{II}_{2}}{\underset{\gamma_{3}}{\mathbb{C}}} \oplus \overset{p_{v_{3}}}{\underset{\gamma_{3}}{\mathbb{C}}}\right)\\
\cap& \\
\mathcal{N}_{1} &= \left(\overset{p_{v_{1}}, p_{2}^{I}}{\underset{\gamma_{1}}{M_{2}}} \oplus \overset{p_{2}^{II}}{\underset{\gamma_{2} - \gamma_{1}}{\mathbb{C}}} \oplus \overset{p_{v_{3}}}{\underset{\gamma_{3}}{\mathbb{C}}}\right) \underset{D}{*} \left(\overset{p_{v_{1}}}{\underset{\gamma_{1}}{\mathbb{C}}} \oplus \overset{q_{2}^{I}}{\underset{\gamma_{2} - \gamma_{3}}{\mathbb{C}}} \oplus \overset{q_{2}^{II},p_{v_{3}}}{\underset{\gamma_{3}}{M_{2}}}\right)\\
\cap &\\
\mathcal{N}_{2} &= \left(\underset{2\gamma_{1}}{M_{2}\otimes L(\mathbb{Z})} \oplus \overset{p_{2}^{II}}{\underset{\gamma_{2} - \gamma_{1}}{\mathbb{C}}} \oplus \overset{p_{v_{3}}}{\underset{\gamma_{3}}{\mathbb{C}}}\right) \underset{D}{*} \left(\overset{p_{v_{1}}}{\underset{\gamma_{1}}{\mathbb{C}}} \oplus \overset{q_{2}^{I}}{\underset{\gamma_{2} - \gamma_{3}}{\mathbb{C}}} \oplus \overset{q_{2}^{II}, p_{v_{3}}}{\underset{\gamma_{3}}{M_{2}}}\right)\\
\cap &\\
\mathcal{M}(\Gamma) &= \left(\underset{\gamma_{1}}{M_{2}\otimes L(\mathbb{Z})} \oplus \overset{p_{2}^{II}}{\underset{\gamma_{2} - \gamma_{1}}{\mathbb{C}}} \oplus \overset{p_{v_{3}}}{\underset{\gamma_{3}}{\mathbb{C}}}\right) \underset{D}{*} \left(\overset{p_{v_{1}}}{\underset{\gamma_{1}}{\mathbb{C}}} \oplus \overset{q_{2}^{I}}{\underset{\gamma_{2} - \gamma_{3}}{\mathbb{C}}} \oplus \underset{2\gamma_{3}}{M_{2}\otimes L(\mathbb{Z})}\right),
\end{align*}
where $p_{v_{2}}$ decomposes as $1 \otimes e_{22} \oplus 1 \oplus 0$ in $\mathcal{A}_{e_{1}}$ and $0 \oplus 1 \oplus 1 \otimes e_{1, 1}$ in $\mathcal{A}_{e_{2}}$. We set $p_{2}^{I}$ and $p_{2}^{II}$ as the summands of $p_{v_{2}}$ supported in the diffuse and atomic parts of $\mathcal{A}_{e_{1}}$ respectively and $q_{2}^{I}$ and $q_{2}^{II}$ as the summands of $p_{v_{2}}$ supported in the atomic and diffuse parts of $\mathcal{A}_{e_{2}}$ respectively. As above,
$$
p_{v_{2}}\mathcal{N}_{0}p_{v_{2}} = \overset{p^{I}_{2}}{\underset{\frac{\gamma_{1}}{\gamma_{2}}}{\mathbb{C}}} \oplus \overset{p^{II}_{2}}{\underset{\frac{\gamma_{2} - \gamma_{1}}{\gamma_{2}}}{\mathbb{C}}} * \overset{q^{I}_{2}}{\underset{\frac{\gamma_{2} - \gamma_{3}}{\gamma_{2}}}{\mathbb{C}}} \oplus \overset{q^{II}_{2}}{\underset{\frac{\gamma_{3}}{\gamma_{2}}}{\mathbb{C}}} = \begin{cases} \underset{2\frac{\gamma_{2} - \gamma_{1}}{\gamma_{2}}}{M_{2} \otimes L(\mathbb{Z})} \oplus \overset{p_{2}^{I} \wedge q_{2}^{I}}{\underset{\frac{\gamma_{1} - \gamma_{3}}{\gamma_{2}}}{\mathbb{C}}} \oplus \overset{p_{2}^{I} \wedge q_{2}^{II}}{\underset{\frac{\gamma_{1} - \gamma_{2} + \gamma_{3}}{\gamma_{2}}}{\mathbb{C}}} & \textrm{ if } \gamma_{2} \leq \gamma_{1} + \gamma_{3} \\ \underset{2\frac{\gamma_{3}}{\gamma_{2}}}{M_{2} \otimes L(\mathbb{Z})} \oplus \overset{p_{2}^{I} \wedge q_{2}^{I}}{\underset{\frac{\gamma_{1} - \gamma_{3}}{\gamma_{2}}}{\mathbb{C}}} \oplus \overset{p_{2}^{II} \wedge q_{2}^{I}}{\underset{\frac{\gamma_{2} - \gamma_{1} - \gamma_{3}}{\gamma_{2}}}{\mathbb{C}}} & \textrm{ if } \gamma_{2} > \gamma_{1} + \gamma_{3} \end{cases}.
$$
\emph{\underline{Case 2a(i)}}: Assume $\gamma_{2} \leq \gamma_{1} + \gamma_{3}$. Since the two new matrix units in $\mathcal{N}_{1}$ introduce equivalences between $p_{v_{1}}$ and $p_{2}^{I}$ and between $q_{2}^{II}$ and $p_{v_{3}}$ respectively, we see that $\mathcal{N}_{1}$ has the same number of summands as $p_{v_{2}}\mathcal{N}_{0}p_{v_{2}}$, but with suitable amplifications. Explicitly, we find that
$$
\mathcal{N}_{1} = \underset{4(\gamma_{2} - \gamma_{1})}{M_{4}\otimes L(\mathbb{Z})} \oplus \overset{p_{2}^{I}\wedge q_{2}^{I}}{\underset{\gamma_{1} - \gamma_{3}}{M_{2}}} \oplus \overset{p_{2}^{I} \wedge q_{2}^{II}}{\underset{\gamma_{1} + \gamma_{3} - \gamma_{2}}{M_{3}}}
$$
where the central support of $p_{v_{1}}$ is the identity. By applying Lemma \ref{lem:DR1} and applying the same reasoning as case 1,
we see that $\mathcal{N}_{2}$ is an interpolated free group factor. Applying Lemma \ref{lem:DR1} again shows that $\mathcal{M}(\Gamma)$ is an interpolated free group factor.
\emph{\underline{Case 2a(ii)}}: Assume $\gamma_{2} > \gamma_{1} + \gamma_{3}$. This case is treated in the same way as above except that in $\mathcal{N}_{1}$, $q_{2}^{I} \wedge p_{2}^{II}$ with trace $\gamma_{2} - \gamma_{3} - \gamma_{1}$ is minimal and central, so it is minimal and central in $\mathcal{M}(\Gamma)$.
\emph{\underline{Case 2b}}: Now let $\gamma_{1}$ be the largest weight. First assume $\gamma_{3} \geq \gamma_{2}$. We consider the algebra
$$
\mathcal{N}_{1} = \left(\overset{p_{1}^{I}}{\underset{\gamma_{1} - \gamma_{2}}{\mathbb{C}}} \oplus \overset{p_{v_{2}}}{\underset{\gamma_{2}}{M_{2}}} \oplus \overset{p_{v_{3}}}{\underset{\gamma_{3}}{\mathbb{C}}}\right) \underset{D}{*} \left(\overset{p_{v_{1}}}{\underset{\gamma_{1}}{\mathbb{C}}} \oplus \overset{p_{v_{2}}}{\underset{\gamma_{2}}{M_{2}}} \oplus \overset{p_{3}^{I}}{\underset{\gamma_{3} - \gamma_{2}}{\mathbb{C}}}\right),
$$
where the projections orthogonal to $p_{v_{2}}$ in each copy of $M_{2}$ sit under $p_{i}$ and $p_{i}^{I} \leq p_{v_{i}}$ for $i = 1$ or 3. It follows that $\mathcal{N}_{1} = \overset{p_{1}^{I}}{\underset{\gamma_{1} - \gamma_{2}}{\mathbb{C}}} \oplus \overset{p_{v_{2}}}{\underset{\gamma_{2}}{M_{3}}} \oplus \overset{p_{3}^{I}}{\underset{\gamma_{3} - \gamma_{2}}{\mathbb{C}}}$, so tensoring each copy of $M_{2}$ with $L(\mathbb{Z})$ and using the standard arguments as above show that
$$
\mathcal{M}(\Gamma) = \overset{p_{1}^{I}}{\underset{\gamma_{1} - \gamma_{2}}{\mathbb{C}}} \oplus \underset{3\gamma_{2}}{L(\mathbb{F}_{t})} \oplus \overset{p_{3}^{I}}{\underset{\gamma_{3} - \gamma_{2}}{\mathbb{C}}}.
$$
Finally, if $\gamma_{2} > \gamma_{3}$ then we consider
$$
\mathcal{N}_{1} = \left(\overset{p_{1}^{I}}{\underset{\gamma_{1} - \gamma_{2}}{\mathbb{C}}} \oplus \overset{p_{v_{2}}}{\underset{\gamma_{2}}{M_{2}}} \oplus \overset{p_{v_{3}}}{\underset{\gamma_{3}}{\mathbb{C}}}\right) \underset{D}{*} \left(\overset{p_{v_{1}}}{\underset{\gamma_{1}}{\mathbb{C}}} \oplus \overset{p_{2}^{I}}{\underset{\gamma_{2} - \gamma_{3}}{\mathbb{C}}} \oplus \overset{p_{v_{3}}}{\underset{\gamma_{3}}{M_{2}}}\right) = \overset{p_{1}^{I}}{\underset{\gamma_{1} - \gamma_{2}}{\mathbb{C}}} \oplus \underset{\gamma_{3}}{M_{3}} \oplus \underset{\gamma_{2} - \gamma_{3}}{M_{2}},
$$
where the central support of $p_{v_{2}}$ is $1 - p_{1}^{I}$. Therefore, tensoring each copy of $M_{2}$ with $L(\mathbb{Z})$ gives $\mathcal{M}(\Gamma) = \overset{p_{1}^{I}}{\underset{\gamma_{1} - \gamma_{2}}{\mathbb{C}}} \oplus \underset{2\gamma_{2} + \gamma_{3}}{L(\mathbb{F}_{t})}$ as desired.
\end{proof}
We now inductively assume that for some $\Gamma$, $\mathcal{M}(\Gamma)$ has the form as described in Theorem \ref{thm:H1}.\\
\begin{lem} \label{lem:H2}
Suppose $\Gamma'$ is a graph obtained from $\Gamma$ by adding an edge $e$ connecting two vertices $v$ and $w$ of $\Gamma$ (so that in particular $\Gamma$ and $\Gamma'$ have the same underlying set of vertices with the same weighting). Assume that
$$
\mathcal{M}(\Gamma) = \overset{p^{\Gamma}}{L(\mathbb{F}_{t_{\Gamma}})} \oplus \underset{{v \in B(\Gamma)}}{\bigoplus} \overset{r_{v}^{\Gamma}}{\underset{\gamma_{v} - \alpha^{\Gamma}_{v}}{\mathbb{C}}}
$$
as in Theorem \ref{thm:H1}. Then
$$
\mathcal{M}(\Gamma') = \overset{p^{\Gamma'}}{L(\mathbb{F}_{t_{\Gamma'}})} \oplus \underset{{v \in B(\Gamma')}}{\bigoplus} \overset{r_{v}^{\Gamma'}}{\underset{\gamma_{v} - \alpha^{\Gamma'}_{v}}{\mathbb{C}}}
$$
where $p^{\Gamma} \leq p^{\Gamma'}$, $r_{v}^{\Gamma'} \leq r_{v}^{\Gamma}$, and $p^{\Gamma}\mathcal{M}(\Gamma)p^{\Gamma} \overset{s.e.}{\hookrightarrow} p_{\Gamma}\mathcal{M}(\Gamma')p_{\Gamma}$.
\end{lem}
\begin{proof}
We use the convention that if the term $\overset{p}{\underset{\alpha}{\mathbb{C}}}$ appears where $\alpha \leq 0$ then this term is identically zero. All parts of the proof below are valid if this modification is made.
Set $D = \ell^{\infty}(\Gamma') = \ell^{\infty}(\Gamma)$ and let the new edge $e$ connect $v$ to $w$ with $\gamma_{v} \geq \gamma_{w}$. We examine the following sequence of inclusions:
\begin{align*}
\mathcal{M}(\Gamma) \subset \mathcal{N}_{1} &= \mathcal{M}(\Gamma) \underset{D}{*} \left(\overset{p_{w}}{\underset{\gamma_{w}}{\mathbb{C}}} \oplus \left(\bigoplus_{k=1}^{n} \overset{p_{v, k}}{\underset{\gamma_{w}/n}{\mathbb{C}}} \oplus \overset{p_{v}^{I}}{\underset{\gamma_{v} - \gamma_{w}}{\mathbb{C}}}\right) \oplus \ell^{\infty}(\Gamma \setminus \{v, w\})\right)\\
\cap &\\
\mathcal{N}_{2} &= \mathcal{M}(\Gamma) \underset{D}{*} \left(\bigoplus_{k=1}^{n} \overset{p_{w, k}}{\underset{\gamma_{w}/n}{\mathbb{C}}} \oplus \left(\bigoplus_{k=1}^{n} \overset{p_{v, k}}{\underset{\gamma_{w}/n}{\mathbb{C}}} \oplus \overset{p_{v}^{I}}{\underset{\gamma_{v} - \gamma_{w}}{\mathbb{C}}}\right) \oplus \ell^{\infty}(\Gamma \setminus \{v, w\})\right)\\
\cap &\\
\mathcal{N}_{3} &= \mathcal{M}(\Gamma) \underset{D}{*} \left(\bigoplus_{k=1}^{n}\overset{p_{w, k}, p_{v, k}}{\underset{\gamma_{w}/n}{M_{2}}} \oplus \overset{p_{v}^{I}}{\underset{\gamma_{v} - \gamma_{w}}{\mathbb{C}}} \oplus \ell^{\infty}(\Gamma \setminus \{v, w\})\right)\\
\cap &\\
\mathcal{M}(\Gamma') &= \mathcal{M}(\Gamma) \underset{D}{*} \left(L(\mathbb{Z}) \otimes M_{2} \oplus \overset{p_{v}^{I}}{\underset{\gamma_{v} - \gamma_{w}}{\mathbb{C}}} \oplus \ell^{\infty}(\Gamma \setminus \{v, w\})\right).
\end{align*}
The projections $p_{w, k}$ are an orthogonal family with trace $\gamma_{w}/n$ in $\mathcal{A}_{e}$ whose sum is $p_{w}$. The projection $p_{v}$ decomposes as $\sum_{k=1}^{n}p_{v, k} + p_{v}^{I}$ with $p_{v}^{I}$ supported in the atomic part of $\mathcal{A}_{e}$ and the $p_{v, k}$ are an orthogonal family of projections with trace $\gamma_{w}/n$ supported in the diffuse part of $\mathcal{A}_{e}$. The positive integer $n$ is chosen large enough such that $\frac{1}{n} + \frac{\gamma_{w} - \alpha^{\Gamma}_{w}}{\gamma_{w}} < 1$ and $\frac{\gamma_{w}}{n\gamma_{v}} + \frac{\gamma_{v} - \alpha^{\Gamma}_{v}}{\gamma_{v}} < 1$. From the induction hypothesis,
$$
p_{v}\mathcal{M}(\Gamma)p_{v} = \overset{p^{\Gamma}_{v}}{L(\mathbb{F}_{t_{v}})} \oplus \overset{r_{v}^{\Gamma}}{\underset{\frac{\gamma_{v} - \alpha_{v}}{\gamma_{v}}}{\mathbb{C}}}, \textrm{ and }p_{w}\mathcal{M}(\Gamma)p_{w} = \overset{p^{\Gamma}_{w}}{L(\mathbb{F}_{t_{w}})} \oplus \overset{r_{w}^{\Gamma}}{\underset{\frac{\gamma_{w} - \alpha_{w}}{\gamma_{w}}}{\mathbb{C}}},
$$
with $p^{\Gamma}_{u} = p^{\Gamma}p_{u}$ for any vertex $u$. From Lemma \ref{lem:DR1},
$$
p_{v}\mathcal{N}_{1}p_{v} = \left(\overset{p^{\Gamma}_{v}}{L(\mathbb{F}_{t_{v}})} \oplus \overset{r_{v}^{\Gamma}}{\underset{\frac{\gamma_{v} - \alpha^{\Gamma}_{v}}{\gamma_{v}}}{\mathbb{C}}}\right) * \left(\bigoplus_{k=1}^{n} \overset{p_{v, k}}{\underset{\frac{\gamma_{w}}{n\gamma_{v}}}{\mathbb{C}}} \oplus \overset{p_{v}^{I}}{\underset{\frac{\gamma_{v} - \gamma_{w}}{\gamma_{v}}}{\mathbb{C}}}\right) = L(\mathbb{F}_{t_{v,1}}) \oplus \overset{p_{v}^{I}\wedge r_{v}^{\Gamma}}{\underset{\frac{\gamma_{v} - \alpha^{\Gamma'}_{v}}{\gamma_{v}}}{\mathbb{C}}}.
$$
Lemma \ref{lem:DR1} applied to the inclusion
$$
\left(\overset{p^{\Gamma}_{v}}{\mathbb{C}} \oplus \overset{r_{v}^{\Gamma}}{\underset{\frac{\gamma_{v} - \alpha_{v}}{\gamma_{v}}}{\mathbb{C}}}\right) * \left(\bigoplus_{k=1}^{n} \overset{p_{v, k}}{\underset{\frac{\gamma_{w}}{n\gamma_{v}}}{\mathbb{C}}} \oplus \overset{p_{v}^{I}}{\underset{\frac{\gamma_{v} - \gamma_{w}}{\gamma_{v}}}{\mathbb{C}}}\right) \rightarrow \left(\overset{p^{\Gamma}_{v}}{L(\mathbb{F}_{t_{v}})} \oplus \overset{r_{v}^{\Gamma}}{\underset{\frac{\gamma_{v} - \alpha_{v}}{\gamma_{v}}}{\mathbb{C}}}\right) * \left(\bigoplus_{k=1}^{n} \overset{p_{v, k}}{\underset{\frac{\gamma_{w}}{n\gamma_{v}}}{\mathbb{C}}} \oplus \overset{p_{v}^{I}}{\underset{\frac{\gamma_{v} - \gamma_{w}}{\gamma_{v}}}{\mathbb{C}}}\right),
$$
shows that the inclusion $\displaystyle L(\mathbb{F}_{t_{v}}) = p^{\Gamma}_{v}\mathcal{M}(\Gamma)p^{\Gamma}_{v} \rightarrow p^{\Gamma}_{v}\mathcal{N}_{1}p^{\Gamma}_{v}$
is equivalent to the canonical inclusion
$$
L(\mathbb{F}_{t_{v}}) \rightarrow L(\mathbb{F}_{t_{v}}) * p^{\Gamma}_{v}\left[\left(\overset{p'_{v}}{\mathbb{C}} \oplus \underset{\frac{\gamma_{v} - \alpha_{v}}{\gamma_{v}}}{\mathbb{C}}\right) * \left( \bigoplus_{k=1}^{n} \overset{p_{v, k}}{\underset{\frac{\gamma_{w}}{n\gamma_{v}}}{\mathbb{C}}} \oplus \overset{p_{v}^{I}}{\underset{\frac{\gamma_{v} - \gamma_{w}}{\gamma_{v}}}{\mathbb{C}}}\right)\right]p^{\Gamma}_{v}
$$
so $p^{\Gamma}_{v}\mathcal{M}(\Gamma)p^{\Gamma}_{v}\overset{s.e.}{\hookrightarrow} p^{\Gamma}_{v}\mathcal{N}_{1}p^{\Gamma}_{v}$. From Remark \ref{rem:Dyk}, $p^{\Gamma}\mathcal{M}(\Gamma)p^{\Gamma} \overset{s.e.}{\hookrightarrow} p^{\Gamma}\mathcal{N}_{1}p^{\Gamma}$ as well.
By Lemma \ref{lem:DR1} we have
$$
p_{w}\mathcal{N}_{2}p_{w} = L(\mathbb{Z}/n\mathbb{Z}) * p_{w}\mathcal{N}_{1}p_{w} = L(\mathbb{Z}/n\mathbb{Z}) * \left(\overset{p_{w}^{\mathcal{N}_{1}}}{L(\mathbb{F}_{t_{w}})} \oplus \overset{r_{w}^{\mathcal{N}_{1}}}{\underset{\gamma_{w}}{\mathbb{C}}}\right),
$$
where $p_{w}^{\mathcal{N}_{1}} = p_{w}p^{\mathcal{N}_{1}}$ with $p^{\mathcal{N}_{1}}$ the central support of $p_{\Gamma}$ in $\mathcal{N}_{1}$ (note $p_{w}^{\mathcal{N}_{1}} \geq p_{w}^{\Gamma}$ so $r_{w}^{\mathcal{N}_{1}} \leq r_{w}^{\Gamma}$ which implies $\delta_{w} \leq \gamma_{w} - \alpha^{\Gamma}_{w}$). From these observations, it follows that $p_{w}\mathcal{N}_{2}p_{w}$ is an interpolated free group factor (since $n$ was chosen such that $\frac{\gamma_{w}}{n\gamma_{v}} + \frac{\gamma_{v} - \alpha_{v}}{\gamma_{v}} < 1$) and the arguments used in the inclusion $\mathcal{M}(\Gamma) \rightarrow \mathcal{N}_{1}$ imply $p_{w}^{\mathcal{N}_{1}}\mathcal{N}_{1}p_{w}^{\mathcal{N}_{1}} \overset{s.e.}{\hookrightarrow} p_{w}^{\mathcal{N}_{1}}\mathcal{N}_{2}p_{w}^{\mathcal{N}_{1}}$. Therefore $p_{w}^{\Gamma}\mathcal{N}_{1}p_{w}^{\Gamma} \overset{s.e.}{\hookrightarrow} p_{w}^{\Gamma}\mathcal{N}_{2}p_{w}^{\Gamma}$ so $p^{\Gamma}\mathcal{N}_{1}p^{\Gamma} \overset{s.e.}{\hookrightarrow} p^{\Gamma}\mathcal{N}_{2}p^{\Gamma}$. Also, observe that since the projections $p_{v, k}$ and $p_{w, k}$ lie in the interpolated free group factor summand of $\mathcal{N}_{2}$, they are equivalent in $\mathcal{N}_{2}$. We now define algebras $\mathcal{N}_{2, j}$ for $j = 0,...,n$ so that
$$
\mathcal{N}_{2} = \mathcal{N}_{2, 0} \subset \mathcal{N}_{2, 1} \subset \mathcal{N}_{2, 2} \subset \cdots \subset \mathcal{N}_{2, n} = \mathcal{N}_{3} \textrm{ where }
$$ $$
\mathcal{N}_{2, j} = \left(\bigoplus_{k=j+1}^{n} \overset{p_{w, k}}{\underset{\gamma_{w}/n}{\mathbb{C}}} \oplus \bigoplus_{k=1}^{j} \overset{p_{w, k}, p_{v, k}}{\underset{\gamma_{w}/n}{M_{2}}} \oplus \bigoplus_{k=j+1}^{n}\overset{p_{v, k}}{\underset{\gamma_{w}/n}{\mathbb{C}}} \oplus \overset{p_{v}^{I}}{\underset{\gamma_{v} - \gamma_{w}}{\mathbb{C}}} \oplus \ell^{\infty}(\Gamma \setminus \{v, w\})\right) \underset{D}{*} \mathcal{M}(\Gamma).
$$
Let $p^{\mathcal{N}_{2}}$ be the central support of $p_\Gamma$ in $\mathcal{N}_{2}$. Applying Lemma \ref{lem:DR2} to the inclusion
$$
p_{w, j+1}\mathcal{N}_{2, j}p_{w, j+1} \rightarrow p_{w, j+1}\mathcal{N}_{2,j+1}p_{w, j+1} = p_{w, j+1}\mathcal{N}_{2, j}p_{w, j+1} * L(\mathbb{Z})
$$
shows that this inclusion is a standard embedding, so it follows from Remark \ref{rem:Dyk} that $p^{\mathcal{N}_{2}}\mathcal{N}_{2, j}p^{\mathcal{N}_{2}} \overset{s.e.}{\hookrightarrow} p^{\mathcal{N}_{2}}\mathcal{N}_{2, j+1}p^{\mathcal{N}_{2}}$, implying $p^{\Gamma}\mathcal{N}_{2, j}p^{\Gamma} \overset{s.e.}{\hookrightarrow} p^{\Gamma}\mathcal{N}_{2, j+1}p^{\Gamma}$ for all $j$. Inductively,
$$
\mathcal{N}_{3} = \left(\overset{p^{\mathcal{N}_{2}}}{L(\mathbb{F}_{t_{3}})} \oplus \overset{p_{v}^{I}\wedge r_{v}^{\Gamma}}{\underset{\gamma_{v} - \alpha_{v}^{\Gamma'}}{\mathbb{C}}} \bigoplus_{u \in L(\Gamma)\setminus\{v, w\}} \underset{\gamma_{u} - \alpha^{\Gamma'}_{u}}{\overset{r^{\Gamma}_{u}}{\mathbb{C}}}\right)
$$
and $p^{\Gamma}\mathcal{N}_{2}p^{\Gamma} \overset{s.e.}{\hookrightarrow} p^{\Gamma}\mathcal{N}_{3}p^{\Gamma}$. To finish, we look at the sequence of algebras
$$
\mathcal{N}_{3} = \mathcal{N}_{3, 0} \subset \mathcal{N}_{3, 1} \subset ... \subset \mathcal{N}_{3, n} = \mathcal{M}(\Gamma') \textrm{ where }
$$ $$\mathcal{N}_{3, j} = \left(\bigoplus_{k=1}^{j} \overset{p_{w, k} + q_{w, k}}{M_{2} \otimes L(\mathbb{Z})} \oplus \bigoplus_{k=j+1}^{n} \overset{p_{w, k}, p_{v, k}}{M_{2}} \oplus \overset{p_{v}^{I}}{\underset{\gamma_{v} - \gamma_{w}}{\mathbb{C}}} \bigoplus \ell^{\infty}(\Gamma \setminus \{v, w\})\right) \underset{D}{*} \mathcal{M}(\Gamma).
$$
Lemma \ref{lem:DR1} implies that the inclusion
$$
p_{w, j+1}\mathcal{N}_{3, j}p_{w, j+1} \rightarrow p_{w, j+1}\mathcal{N}_{3, j+1}p_{w, j+1} = p_{w, j+1}\mathcal{N}_{3, j}p_{w, j+1} * L(\mathbb{Z})
$$
is a standard embedding, so by Remark \ref{rem:Dyk}, $p^{\mathcal{N}_{2}}\mathcal{N}_{3, j}p^{\mathcal{N}_{2}} \overset{s.e.}{\hookrightarrow} p^{\mathcal{N}_{2}}\mathcal{N}_{3, j+1}p^{\mathcal{N}_{2}}$ and thus $p^{\Gamma}\mathcal{N}_{3, j}p^{\Gamma} \overset{s.e.}{\hookrightarrow} p^{\Gamma}\mathcal{N}_{3, j+1}p^{\Gamma}$. Therefore the inclusion $p^{\Gamma}\mathcal{N}_{3}p^{\Gamma} \rightarrow p^{\Gamma}\mathcal{M}(\Gamma')p^{\Gamma}$ is standard since it is a composite of standard embeddings. This implies $\mathcal{M}(\Gamma')$ has the desired formula and $p^{\Gamma}\mathcal{M}(\Gamma)p^{\Gamma} \overset{s.e.}{\hookrightarrow} p^{\Gamma}\mathcal{M}(\Gamma')p^{\Gamma}$.\end{proof}
We again assume that $\mathcal{M}(\Gamma)$ is in the form of Theorem \ref{thm:H1}.
\begin{lem} \label{lem:H3}
Let $\Gamma'$ be a weighted graph obtained from $\Gamma$ by adding a vertex $v$ and an edge $e$ connecting $v$ to $w \in V(\Gamma)$ woth weighting $\gamma_{v}$, and assume $\mathcal{M}(\Gamma) = \overset{p^{\Gamma}}{L(\mathbb{F}_{t_{\Gamma}})} \oplus \underset{{v \in B(\Gamma)}}{\bigoplus} \overset{r_{v}^{\Gamma}}{\underset{\gamma_{v} - \alpha^{\Gamma}_{v}}{\mathbb{C}}}$ with notation as in Theorem \ref{thm:H1}. Then
$$
\mathcal{M}(\Gamma') = \overset{p^{\Gamma'}}{L(\mathbb{F}_{t_{\Gamma'}})} \oplus \underset{{u \in B(\Gamma')}}{\bigoplus} \overset{r_{u}^{\Gamma'}}{\underset{\gamma_{u} - \alpha^{\Gamma'}_{u}}{\mathbb{C}}}
$$ where $p^{\Gamma} \leq p^{\Gamma'}$, $r_{u}^{\Gamma'} \leq r_{u}^{\Gamma}$ for all $u$, and $p_{\Gamma}\mathcal{M}(\Gamma)p_{\Gamma} \overset{s.e.}{\hookrightarrow} p_{\Gamma}\mathcal{M}(\Gamma')p_{\Gamma}$.
\end{lem}
Notice that the natural inclusion $\mathcal{M}(\Gamma) \rightarrow \mathcal{M}(\Gamma')$ is not unital, but the compressed inclusion $p_{\Gamma}\mathcal{M}(\Gamma)p_{\Gamma} \rightarrow p_{\Gamma}\mathcal{M}(\Gamma')p_{\Gamma}$ is.
\begin{proof}
Just as in the proof of Lemma \ref{lem:H2}, if the term $\overset{p}{\underset{\alpha}{\mathbb{C}}}$ appears where $\alpha \leq 0$ then this term is identically zero.
Set $D = \ell^{\infty}(\Gamma')$. We rescale all of the weights on $\Gamma$ such that all of the weights on $\Gamma'$ sum to 1. We have 2 cases: when $\gamma_{v} > \gamma_{w}$ and when $\gamma_{w} \geq \gamma_{v}$.
\emph{\underline{Case 1, $\gamma_{v} > \gamma_{w}$}}: We look at the following sequence of inclusions:
\begin{align*}\mathcal{M}(\Gamma) \oplus \overset{p_{v}}{\underset{\gamma_{v}}{\mathbb{C}}} \subset \mathcal{N}_{1} &= \left(\mathcal{M}(\Gamma) \oplus \overset{p_{v}}{\underset{\gamma_{v}}{\mathbb{C}}}\right) \underset{D}{*} \left(\ell^{\infty}(\Gamma' \setminus \{v, w\}) \oplus \bigoplus_{k=1}^{n} \overset{p_{w, k}}{\underset{\gamma_{w}/n}{\mathbb{C}}} \oplus \left(\bigoplus_{k=1}^{n} \overset{p_{v, k}}{\underset{\gamma_{w}/n}{\mathbb{C}}} \oplus \overset{p_{v}^{I}}{\underset{\gamma_{v} - \gamma_{w}}{\mathbb{C}}}\right)\right)\\
\cap &\\
\mathcal{N}_{2} &= \left(\mathcal{M}(\Gamma) \oplus \overset{p_{v}}{\underset{\gamma_{v}}{\mathbb{C}}}\right) \underset{D}{*} \left(\ell^{\infty}(\Gamma' \setminus \{v, w\}) \oplus \bigoplus_{k=1}^{n}\overset{p_{w, k}, p_{v, k}}{\underset{\gamma_{w}/n}{M_{2}}} \oplus \overset{p_{v}^{I}}{\underset{\gamma_{v} - \gamma_{w}}{\mathbb{C}}}\right)\\
\cap &\\
\mathcal{M}(\Gamma') &= \left(\mathcal{M}(\Gamma) \oplus \overset{p_{v}}{\underset{\gamma_{v}}{\mathbb{C}}}\right) \underset{D}{*} \left(\ell^{\infty}(\Gamma' \setminus \{v, w\}) \oplus \underset{2\gamma_{w}}{L(\mathbb{Z}) \otimes M_{2}} \oplus \overset{p_{v}^{I}}{\underset{\gamma_{v} - \gamma_{w}}{\mathbb{C}}}\right).
\end{align*}
The projections $p_{w, k}$ are an orthogonal family with trace $\gamma_{w}/n$ in $\mathcal{A}_{e}$ whose sum is $p_{w}$. In $\mathcal{A}_{e}$, $p_{v}$ decomposes as $\sum_{k=1}^{n}p_{v, k} + p_{v}^{I}$ with $p_{v}^{I}$ supported in the atomic part of $\mathcal{A}_{e}$, and the $p_{v, k}$ are an orthogonal family of projections with trace $\gamma_{w}/n$ supported in the diffuse part of $\mathcal{A}_{e}$.
By the inductive hypothesis,
$$
p_{w}\mathcal{M}(\Gamma)p_{w} = \overset{p^{\Gamma}_{w}}{\underset{\frac{\alpha^{\Gamma}_{w}}{\gamma_{w}}}{L(\mathbb{F}_{t_{w}})}} \oplus \overset{r_{w}^{\Gamma}}{\underset{\frac{\gamma_{w} - \alpha^{\Gamma}_{w}}{\gamma_{w}}}{\mathbb{C}}},
$$
with $p_{w}^{\Gamma} = p_{w}p^{\Gamma}$. We choose $n$ large enough such that $\frac{1}{n} + \frac{\gamma_{w} - \alpha_{w}}{\gamma_{w}} < 1$, i.e., so that $p_{w}\mathcal{M}(\Gamma)p_{w} * L(\mathbb{Z} / n\mathbb{Z})$ is an interpolated free group factor.
From Lemma \ref{lem:DR1},
$$
p_{w}\mathcal{N}_{1}p_{w} = p_{w}\mathcal{M}(\Gamma)p_{w} * \left(\bigoplus_{k=1}^{n} \overset{p_{w, k}}{\underset{1/n}{\mathbb{C}}}\right) = \left(\overset{p'_{w}}{\underset{\frac{\alpha_{w}}{\gamma_{w}}}{L(\mathbb{F}_{t_{w}})}} \oplus \underset{\frac{\gamma_{w} - \alpha_{w}}{\gamma_{w}}}{\mathbb{C}}\right) * \left(\bigoplus_{k=1}^{n} \overset{p_{w, k}}{\underset{1/n}{\mathbb{C}}}\right),
$$
so it is an interpolated free group factor, and applying Lemma $\ref{lem:DR1}$ again, we see that
$$
p^{\Gamma}_{w}\mathcal{N}_{1}p^{\Gamma}_{w} = p^{\Gamma}_{w}\mathcal{M}(\Gamma)p^{\Gamma}_{w} * p^{\Gamma}_{w}\left[\left(\overset{p^{\Gamma}_{w}}{\underset{\frac{\alpha_{w}}{\gamma_{w}}}{\mathbb{C}}} \oplus \overset{r_{w}^{\Gamma}}{\underset{\frac{\gamma_{w} - \alpha_{w}}{\gamma_{w}}}{\mathbb{C}}}\right) * \left(\bigoplus_{k=1}^{n} \overset{p_{w, k}}{\underset{1/n}{\mathbb{C}}}\right)\right]p^{\Gamma}_{w}
$$
with the inclusion $p^{\Gamma}_{w}\mathcal{M}(\Gamma)p^{\Gamma}_{w} \rightarrow p'_{w}\mathcal{N}_{1}p'_{w}$ the canonical one. Therefore $\displaystyle p^{\Gamma}_{w}\mathcal{M}(\Gamma)p^{\Gamma}_{w} \overset{s.e.}{\hookrightarrow} p^{\Gamma}_{w}\mathcal{N}_{1}p^{\Gamma}_{w}$, so it follows that $p^{\Gamma}\mathcal{M}(\Gamma)p^{\Gamma} \overset{s.e.}{\hookrightarrow} p^{\Gamma}\mathcal{N}_{1}p^{\Gamma}$ as well. It is clear that $p_{v}^{I}$ will be a minimal central projection in $\mathcal{N}_{2}$, and since the projections $p_{v, k}$ lie under the minimal projection $p_{v} \in \mathcal{M}(\Gamma) \oplus \overset{p_{v}}{\underset{\gamma_{v}}{\mathbb{C}}}$, it follows that
$$
\mathcal{N}_{2} = L(\mathbb{F}_{t_{2}}) \oplus \overset{p_{v}^{I}}{\underset{\gamma_{v} - \gamma_{w}}{\mathbb{C}}} \oplus \bigoplus_{u \in B(\Gamma)\setminus\{w\}} \underset{\gamma_{u} - \alpha^{\Gamma}_{u}}{\overset{r^{\Gamma}_{u}}{\mathbb{C}}},
$$
where $L(\mathbb{F}_{t_{2}})$ is an amplification of $p^{\Gamma}\mathcal{N}_{1}p^{\Gamma}$. Hence $p^{\Gamma}\mathcal{N}_{1}p^{\Gamma} = p^{\Gamma}\mathcal{N}_{2}p^{\Gamma}$. As a final step, we tensor each copy of $M_{2}$ with $L(\mathbb{Z})$ to obtain $\mathcal{M}(\Gamma')$ and apply Lemma \ref{lem:DR1} and Remark \ref{rem:Dyk} $n$ times as in the proof of Lemma \ref{lem:H2} to conclude that
$$
\mathcal{M}(\Gamma') = L(\mathbb{F}_{t_{3}}) \oplus \overset{p_{v}^{I}}{\underset{\gamma_{v} - \gamma_{w}}{\mathbb{C}}} \oplus \bigoplus_{u \in B(\Gamma)\setminus\{w\}} \underset{\gamma_{u} - \alpha^{\Gamma'}_{u}}{\overset{r^{\Gamma}_{u}}{\mathbb{C}}}
$$
and $p^{\Gamma}\mathcal{N}_{2}p^{\Gamma} \overset{s.e.}{\hookrightarrow} p^{\Gamma}\mathcal{M}(\Gamma')p^{\Gamma}$. Therefore $p^{\Gamma}\mathcal{M}(\Gamma)p^{\Gamma} \overset{s.e.}{\hookrightarrow} p^{\Gamma}\mathcal{M}(\Gamma')p^{\Gamma}$ and $\mathcal{M}(\Gamma')$ has the desired form.
\emph{\underline{Case 2, $\gamma_{w} \geq \gamma_{v}$}}: We look at a sequence of inclusions similar to those in the previous case:
\begin{align*}
\mathcal{M}(\Gamma) \oplus \overset{p_{v}}{\underset{\gamma_{v}}{\mathbb{C}}} \subset \mathcal{N}_{1} &= \left(\mathcal{M}(\Gamma) \oplus \overset{p_{v}}{\underset{\gamma_{v}}{\mathbb{C}}}\right) \underset{D}{*} \left(\ell^{\infty}(\Gamma' \setminus \{v, w\}) \oplus \left(\bigoplus_{k=1}^{n} \overset{p_{w, k}}{\underset{\gamma_{v}/n}{\mathbb{C}}} \oplus \overset{p_{w}^{I}}{\underset{\gamma_{w} - \gamma_{v}}{\mathbb{C}}}\right) \oplus \bigoplus_{k=1}^{n} \overset{p_{v, k}}{\underset{\gamma_{v}/n}{\mathbb{C}}}\right)\\
\cap &\\
\mathcal{N}_{2} &= \left(\mathcal{M}(\Gamma) \oplus \overset{p_{v}}{\underset{\gamma_{v}}{\mathbb{C}}}\right) \underset{D}{*} \left(\ell^{\infty}(\Gamma' \setminus \{v, w\})\oplus \bigoplus_{k=1}^{n} \overset{p_{w, k}, p_{v, k}}{\underset{\gamma_{v}/n}{M_{2}}} \oplus \overset{p_{w}^{I}}{\underset{\gamma_{w} - \gamma_{v}}{\mathbb{C}}}\right)\\
\cap &\\
\mathcal{M}(\Gamma') &= \left(\mathcal{M}(\Gamma) \oplus \overset{p_{v}}{\underset{\gamma_{v}}{\mathbb{C}}}\right) \underset{D}{*} \left(\ell^{\infty}(\Gamma' \setminus \{v, w\})\oplus \underset{2\gamma_{v}}{L(\mathbb{Z})\otimes M_{2}} \oplus \overset{p_{w}^{I}}{\underset{\gamma_{w} - \gamma_{v}}{\mathbb{C}}}\right).
\end{align*}
The projections $p_{v, k}$ are an orthogonal family with trace $\gamma_{v}/n$ in $\mathcal{A}_{e}$ whose sum is $p_{v}$. In $\mathcal{A}_{e}$, $p_{w}$ decomposes as $\sum_{k=1}^{n}p_{w, k} + p_{w}^{I}$ where $p_{w}^{I}$ is supported in the atomic part of $\mathcal{A}_{e}$, and the $p_{w, k}$ are an orthogonal family of projections with trace $\gamma_{v}/n$ supported in the diffuse part of $\mathcal{A}_{e}$. We choose $n$ large enough so that $\frac{\gamma_{w} - \alpha_{w}}{\gamma_{w}} + \frac{\gamma_{v}}{n\gamma_{w}} < 1$. Observe by the condition on $n$ that $p_{w}\mathcal{N}_{1}p_{w} = \overset{p^{\mathcal{N}_{1}}_{w}}{L(\mathbb{F}_{t'_{1}})} \oplus \underset{\gamma_{w} - \alpha_{w} - \gamma_{v}}{\mathbb{C}}$ where the copy of $\mathbb{C}$ is orthogonal to each $p_{w, k}$. Therefore as in the proof of Lemma \ref{lem:H2} $p_{\Gamma}\mathcal{M}(\Gamma)p_{\Gamma} \overset{s.e.}{\hookrightarrow} p_{\Gamma}\mathcal{N}_{1}p_\Gamma$. We next look at
$$
\mathcal{N}_{1} \subset \mathcal{N}_{2} = \left(\mathcal{M}(\Gamma) \oplus \overset{p_{v}}{\underset{\gamma_{v}}{\mathbb{C}}}\right) \underset{D}{*} \left(\ell^{\infty}(\Gamma' \setminus \{v, w\})\oplus \bigoplus_{k=1}^{n} \overset{p_{w, k}, p_{v, k}}{\underset{\gamma_{v}/n}{M_{2}}} \oplus \overset{p_{v}^{I}}{\underset{\gamma_{w} - \gamma_{v}}{\mathbb{C}}}\right).
$$
Since the $p_{v,k}$ lie under the minimal central projection $p_{v} \in \mathcal{M}(\Gamma) \oplus \overset{p_{v}}{\underset{\gamma_{v}}{\mathbb{C}}}$, the arguments above imply
$$
\mathcal{N}_{2} = L(\mathbb{F}_{t_{2}}) \oplus \underset{\gamma_{w} - \gamma_{v} - \alpha_{w}}{\mathbb{C}} \oplus \bigoplus_{u \in L(\Gamma)\setminus\{w\}} \underset{\gamma_{u} - \alpha_{u}}{\overset{r^{\Gamma}_{u}}{\mathbb{C}}}
$$
and $p^{\Gamma}\mathcal{N}_{1}p^{\Gamma} = p^{\Gamma}\mathcal{N}_{2}p^{\Gamma}$. To finish, we tensor each copy of $M_{2}$ with $L(\mathbb{Z})$ and apply Lemma \ref{lem:DR1} and Remark \ref{rem:Dyk} $n$ times as in the end of the proof of Lemma \ref{lem:H2} to obtain
$$
\mathcal{M}(\Gamma') = L(\mathbb{F}_{t_{3}}) \oplus \underset{\gamma_{w} - \gamma_{v} - \alpha_{w}}{\mathbb{C}} \oplus \bigoplus_{u \in L(\Gamma)\setminus\{w\}} \underset{\gamma_{u} - \alpha_{u}}{\overset{r^{\Gamma}_{u}}{\mathbb{C}}}
$$
with the inclusion $p^{\Gamma}\mathcal{M}(\Gamma)p^{\Gamma} \rightarrow p^{\Gamma}\mathcal{M}(\Gamma')p^{\Gamma}$ standard. \end{proof}
\begin{proof}[Proof of Theorem \ref{thm:H1}]
Note that if $\Gamma'$ and $\Gamma$ are connected, loopless, finite graphs, then $\Gamma'$ can be constructed form $\Gamma$ by considering the steps in Lemmas $\ref{lem:H2}$ and $\ref{lem:H3}$. Therefore, we can deduce Theorem $\ref{thm:H1}$ by observing that the composite of standard embeddings is a standard embedding and that standard embeddings are preserved by cut-downs by projections. \end{proof}
\section{The GJS construction in infinite depth} \label{sec:GJSInfinite}
Recall that the vertices on a principal graph for $A_{0} \subset A_{1}$ represent isomophism classes of irreducible $A_{0}-A_{0}$ and $A_{0}-A_{1}$ subbimodules of tensor products of $X = _{A_{0}}L^{2}(A_{1})_{A_{1}}$ and its dual, $X^{*} = _{A_{1}}L^{2}(A_{1})_{A_{0}}$. Assume $\Gamma$ is the principal graph for an infinite-depth subfactor. If $*$ is the depth-0 vertex of $\Gamma$, then the factor $A_{0}$ as in the introduction is isomorphic to $p_{*}\mathcal{M}(\Gamma)p_{*}$. $\mathcal{M}(\Gamma)$ is now a semifinite algebra where the weighting $\gamma$ on $\ell^{\infty}(\Gamma)$ corresponds to the bimodule dimension obtained by identifying each vertex with an irreducible bimodule as above. Under this identification, $\gamma_* = 1$ and $\delta\cdot\gamma_{v} = \sum_{w \sim v}n_{v, w}\gamma_{w}$ where $\delta = [A_{1}:A_{0}]^{1/2}$. To circumvent the difficulty of dealing with a semifinite algebra, we realize that $A_{0}$ is an inductive limit of the algebras $p_{*}\mathcal{M}(\Gamma_{k})p_{*}$ where $\Gamma_{k}$ is $\Gamma$ truncated at depth $k$. To aid our computation of the isomorphism class of $A_{0}$, we have the following lemma, whose proof is a routine calculation and is identical to that in $\cite{MR2807103}$.
\begin{lem} \label{lem:GJS2}
The free dimension of $\mathcal{M}(\Gamma_{k})$ is
$$
1 + \frac{1}{\Tr(F_{k})^{2}}\left( -\sum_{v \in \Gamma_{k}} \gamma_{v}^{2} + \sum_{v \in \Gamma_{k}}\sum_{w\sim v} n_{v, w}\gamma_{v}\gamma_{w}\right)
$$ where $w \sim v$ means $w$ is connected to $v$ in $\Gamma_{k}$, $F_{k} = \sum_{u \in \Gamma_{k}} p_{u}$, and $\Tr$ is the trace on the semifinite algebra $\mathcal{M}(\Gamma)$.
\end{lem}
\begin{thm} \label{thm:H2}
Let $\mathcal{P}$ be an infinite depth subfactor planar algebra. Then the factor $A_{0}$ in the construction of \cite{MR2732052} is isomorphic to $L(\mathbb{F}_{\infty})$.
\end{thm}
\begin{proof}
For a given $k$, we write
$$
\mathcal{M}(\Gamma_{k}) = \overset{p_{k}}{\underset{\underset{w \not\in B(\Gamma_{k})}{\sum\gamma_{w}} + \underset{v \in B(\Gamma_{k})}{\sum \alpha^{\Gamma_{k}}_{v}}}{L(\mathbb{F}_{t_{k}})}} \oplus \bigoplus_{v \in B(\Gamma_{k})} \overset{p^{\Gamma_{k}}_{v}}{\underset{\gamma_{v} - \alpha^{\Gamma_{k}}_{v}}{\mathbb{C}}}.
$$
The free dimension of this algebra is
$$
1 + (t_{k}-1)\left(\frac{\sum_{w \not\in B(\Gamma_{k})}\gamma_{w} + \sum_{v \in B(\Gamma_{k})}\gamma_{v}}{\Tr(F_{k})}\right)^{2} - \frac{\sum_{v\in B(\Gamma_{k})}(\gamma_{v} - \alpha^{\Gamma_{k}}_{v})^{2}}{\Tr(F_{k})^{2}},
$$
so by Lemma \ref{lem:GJS2}, we have the equation
$$
(t_{k}-1)\left(\sum_{w \not\in B(\Gamma_{k})}\gamma_{w} + \sum_{v \in B(\Gamma_{k})}\alpha^{\Gamma_{k}}_{v}\right)^{2} = \sum_{u \in \Gamma_{k}}\sum_{w\sim u} n_{u, w}\gamma_{u}\gamma_{w} -\sum_{u \in \Gamma_{k}}\gamma_{u}^{2} + \sum_{v\in B(\Gamma_{k})}(\gamma_{v} - \alpha^{\Gamma_{k}}_{v})^{2}.
$$
Observe that in $\Gamma_{k}$, the vertices up to depth $k-1$ are connected to all of their neighbors in $\Gamma$, so by the Perron-Frobenius condition and the fact that $\delta > 1$, none of these vertices are in $B(\Gamma_{k})$. If we let $B'(\Gamma_{k})$ be the vertices $v$ at depth $k$ with $\gamma_{v} \leq \sum_{w\sim v}n_{v, w}\gamma_{w}$, then the right hand side of the above equality becomes
\begin{align*}
(\delta - 1)\sum_{v \in \Gamma_{k-2}}\gamma_{v}^{2} &+ \sum_{v \in \Gamma_{k-1}\setminus\Gamma_{k-2}}\gamma_{v} \left(-\gamma_{v} + \sum_{\substack{ w\not\in B(\Gamma_{k}) \\ w \sim{v}}} n_{v, w}\gamma_{w} + \sum_{\substack{w \in B(\Gamma_{k}) \\ w \sim v}} \alpha^{\Gamma_{k}}_{w} \right) \\ &+ \sum_{v \in B'(\Gamma_{k})} \gamma_{v}\left(-\gamma_{v} + \sum_{w \sim v}n_{v,w}\gamma_{w}\right)
\end{align*}
where we have used $\alpha^{\Gamma_{k}}_{v} = \sum_{w\sim v}n_{v, w}\gamma_{w}$. This quantity majorizes $(\delta - 1)\sum_{v \in \Gamma_{k-2}}\gamma_{v}^{2}$. Since the bimodule dimensions of any irreducible sumbimodule of $(X \otimes _{A_{1}} X^{*})^{\otimes_{A_{0}}^{n}}$ and $(X \otimes _{A_{1}} X^{*})^{\otimes_{A_{0}}^{n}} \otimes_{A_{0}} X$ are bounded below by 1, $\gamma_{v} \geq 1$ for all $v \in \Gamma$ so we conclude that
$$
(t_{k}-1)\left(\sum_{w \not\in L(\Gamma_{k})}\gamma_{w} + \sum_{v \in L(\Gamma_{k})}\alpha^{\Gamma_{k}}_{v}\right)^{2} \rightarrow \infty
$$
as $k \rightarrow \infty$. From the amplification formula, $p_{*}\mathcal{M}(\Gamma_{k})p_{*} = L(\mathbb{F}_{t'_{k}})$ where
$$
t'_{k} = 1 + (t_{k}-1)\left(\sum_{w \not\in L(\Gamma_{k})}\gamma_{w} + \sum_{v \in L(\Gamma_{k})}\alpha^{\Gamma_{k}}_{v}\right)^{2}.
$$ Hence $p_{\Gamma_{k}}\mathcal{M}(\Gamma_{k})p_{\Gamma_{k}} \overset{s.e.}{\hookrightarrow} p_{\Gamma_{k}}\mathcal{M}(\Gamma_{k+1})p_{\Gamma_{k}}$ so by Remark \ref{rem:Dyk}, $p_{*}\mathcal{M}(\Gamma_{k})p_{*} \overset{s.e.}{\hookrightarrow} p_{*}\mathcal{M}(\Gamma_{k+1})p_{*}$. As $p_{*}\mathcal{M}(\Gamma)p_{*}$ is the inductive limit of the $p_{*}\mathcal{M}(\Gamma_{k})p_{*}$, it follows that $p_{*}\mathcal{M}(\Gamma)p_{*} = L(\mathbb{F}_{t})$ where $t = \lim t'_{k} = \infty$. \end{proof}
\begin{cor} The factors $A_{k}$ are isomorphic to $L(\mathbb{F}_{\infty})$.
\end{cor}
\begin{proof} If $k$ is even, then $A_{k}$ is an amplification of $A_{0}$ so it follows for $A_{k}$. If $k$ is odd, then $A_{k}$ are cut-downs of $\mathcal{M}(\Gamma')$ with $\Gamma'$ the dual principal graph of $\mathcal{P}$. Applying the same analysis as in Theorem \ref{thm:H2} shows that $A_{k} \cong L(F_{\infty})$. \end{proof}
\bibliographystyle{amsalpha}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,170 |
phillygl24
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About phillygl24
Favorite Twisted Plot
phillygl24 posted a topic in Your Favorites
What movie did you see that you thought you had figured out but by the time the credits were rolling you realized you were duped! Alfred Hitchcock is the king of this devise. (Take Vertigo or Suspicion.) I can also think of some recent films, Fight Club and The Usual Suspects. Can you think of some more?
Your Favorite Movie Lines
phillygl24 replied to a topic in Your Favorites
I just thought of another one. "I do wish we could chat longer, but I'm having an old friend for dinner." Hannibal Lecter
From "The Little Foxes" Regina (annoyed) to her servant: "Cal, the grits is cold. Take it back." Cal: "Yes'm." (He grabs the plate then runs quickly toward the kitchen) "The grits didn't hold the heat! The grits didn't hold the heat!"
Over-Rated Movies
phillygl24 replied to a topic in General Discussions
Sorry for previous typos Ditto regarding Citizen Kane's retirement.
I have to agree about that "Titanic" and The English Patient" are over-rated. I hated "The English Patient." "Titanic" was ok the first time I saw it, but I've grown to hate it because of the hype. Speaking of over-rated, two words...Leonardo DiCaprio. Who said they didn't like "Close Encounters?" In my opinion, that was when they knew how to make sci-fi suspense movies. Actually, "Close Encounters" is one of my favorites.
Great Stairway Scenes
phillygl24 replied to path40a's topic in Your Favorites
What about James Stewart in "It's a Wonderful Life." Throughout the movie he curses the old wobbly knob at the bottom of the staircase. Then at the end of the film he grabs the knob right off the railing and just starts telling it how great it is. Then of course there's the rest of the film with Stewart and his family standing at the top of the stairs watching wonderful things flooding through the door. Also, "Suspicion," the scene with Carey Grant creeping stealthily up the stairs with a glass of milk that is or is not poisoned.
Catcher In The Rye
phillygl24 replied to czahuran's topic in Information, Please!
czahuran, have you seen Igby Goes Down, the 2002 movie staring Kieran Culkin? His character is very similar to Holden. I think that's one reason I enjoyed the movie so much.
Favorite restraunt scene
phillygl24 replied to slappy3500's topic in Your Favorites
Great topic! My choice has to be THE GODFATHER. That restraunt scene sent chills down my spine, Michael Corleone defending his family's honor in an act of retribution that sent his life into a spiral. Yeah...pretty powerful.
Re: Best Directors
phillygl24 replied to phillygl24's topic in General Discussions
Yes Bansi, Frank Darabont definitely proved himself with THE SHAWSHANK REDEMPTION. That movie had a perfect rhythm to the plot. What about Jon Avnet? He directed Fried Green Tomatoes and is working on SKY CAPTAIN, a movie someone mentioned wanting to see in another post.
phillygl24 replied to birchkitty5554's topic in Your Favorites
Snap out of it! Yeah, Moonstruck was pretty good. The Lady Eve. I can't believe someone said that. I saw that when I was a kid, and loved it. It was the first Stanwyck movie I saw. The next time I saw her she was playing a cold, calculating broad and I was shocked! These were all good movies, but the formula for the best romantic comedy is to add some Sinatra to the mix. By the way, did anyone say Sleepless in Seattle? Tisc, tisc.
Things We Would Never Know Without The Movies PART 2
phillygl24 replied to ladymirabelle45's topic in General Discussions
ladymirabelle, very funny! I'm not sure if anyone has said these already, but here goes some general observations. If you do not believe in friendly alien lifeforms until they arrive on the planet you are usually the villain. If you do believe in them, you are the only brilliant person on Earth. If you are a woman smoker you are usually trouble. If you are a male smoker you are usually trouble and could possibly be the hero. If you are the only man in the film who does not smoke you are a dunce.
phillygl24 posted a topic in General Discussions
I love the extra information tucked into DVDs. Did you know in one of the most memorable scenes in movie history while Ilsa prepares to board the plane that will take her away from Casablanca and Rick Blaine forever. . . off in the distance you see mechanics making their final adjustments on the plane. Because the creators could not afford full-scale equipment, they used a model plane only a few feet high. After the model was created, the director decided that in order to maintain a sense of realism mechanics had to be added to the scene. So how did they accomplish this without the
Alfred Hitchcock. Enough said.
phillygl24 replied to phillygl24's topic in Your Favorites
If I'm not his number one fan, I am probably up there. I even got a kick out of HIGH ANXIETY, which poked fun at his films. Two moments that had me laughing the most were the tributes to PSYCHO and THE BIRDS. (the shower scene and the pigeons in the park) I like his cameo in ROPE. It's been a while since I saw it, but I seem to remember the entire movie took place in real time in an apartment. At one point someone looks out the window and sees Hitchcock walking.
There is only one Alfred Hitchcock. His combination of humor, and horror is at times unsettling and always enjoyable Well, that's my opinion, anyway. What do you think of this master of suspense? What was his best cameo appearance?
A perfectly executed film can be magical. Which modern directors do you think have the skills of the greats--John Ford, Victor Fleming, Howard Hawks, etc.? I recently saw LOST IN TRANSLATION. Most of my friends said it was slow. I liked it a lot. Sofia Coppola uses an understated approach to create classic movie moments. Then there are the Coen brothers. Whether delving into a new feel for film noir or screwball comedy this director/producer team understands film making. Who would be on your list? | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,737 |
Q: Pass argument as member of a python dictionary I have 2 python files 1 where only dictionary is saved
Example :
Dic.py
A={"1":{"a":1}, "2":{"b":2}}
And calldic.py
import dic
def todo(Value,Index):
Data=dic.Value(Index)
Print(Data)
As in the above code I am trying to pass argument as member of the dic.py file.
Can anyone please help me resolve this or correct me where I am wrong.
Thanks in advance
A: If what I infer from your question is correct, this should work (assuming Value="A"):
variable_name = Value
attr = getattr(dic, variable_name)
data = attr.get(index)
or
data = attr[index]
Convert index to string before if you are passing index as an integer:
index = str(index)
Edit: As mentioned in the comment, you can use the dict attribute on modules/classes as well.
data = dic.__dict__[value][index]
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,769 |
Has it been almost two months since I posted here?
Why yes. Yes it has.
I blame the hive of scum and villany that is the Evil Former Employer in which I — somehow, don't ask me how — have become the project manager for my merry little band.
In either case, still up to my elbows in that mess which...is no fun.
I keep telling myself "this will be worth it in the end...this will be worth it in the end...this will be worth it in the end..."
So, what's new with all of you? | {
"redpajama_set_name": "RedPajamaC4"
} | 8,014 |
Q: UITextField will not autoresize when editing a UITableViewCell I am working on a table under iOS, I added a couple of cells, and each cell has one UITextField added as a subview. An excerpt:
UITextField *t = [[UITextField alloc] initWithFrame:CGRectMake(20.0, 5.0, 220.0, 20.0)];
// here I set properties for t ...
t.autoresizingMask = UIViewAutoresizingFlexibleLeftMargin | UIViewAutoresizingFlexibleWidth;
[cell addSubview:t];
cell.autoresizeSubviews = YES;
// if needed, I set the UIImageView for the cell
if (...) {
cell.imageView.image = [UIImage imageNamed:@"myimage.png"];
t.frame = CGRectOffset(text.frame, 33, 0);
}
[t release];
What happens? When I enter the editing mode for the tabel, I'd expect that each cell will resize to make the red minus sign visible, and that the UITextField will move to right to remain aligned to the cell itself, as the other components. But this do not happen.
Also, I tried to change the autoresizingMask param using various combinations of UIViewAutoresizingFlexibleLeftMargin, UIViewAutoresizingFlexibleRightMargin and UIViewAutoresizingFlexibleWidth, but without success.
Am I doing something wrong here? Should I change the way I add the text field as a subview?
Thank you!
A: add your views to the contentView of the cell:
[cell.contentView addSubview:t];
| {
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} | 1,684 |
Q: WPF - Accessing Parent DataContext I have my WPF project set up as follows
In my MainWindow I have some tabs. A SearchJob tab and an Edit Job tab, the tabs display their own respective user controls
They all have their own ViewModels as their DataContext
MainWindow - MainWindowVM
SearchJobs - SearchJobsVM
EditJob - EditJobVM
After I search for jobs I get a grid back that is bound to an ObservableCollection of Job objects
When I double click the results grid I want to make the Edit tab visible passing it's view model the id of the row I double clicked on
I also want to make some of the tabs in my MainWindow invisible. The tabs are bound to Visibility properties in my MainWindowVM
I am able to get the id of the row I double clicked on
My question is that from the SearchJobsVm I need to access bot the MainWindowVM to set the Visibility properties and also access the EditJobVM to set the ID
How do I access the DataContext (the view models) of the MainWindowVM and EditJobVM from SearcvhJobVM?
In Mainwindow I set the DataContext like so:-
<Window.DataContext>
<vm:MainWindowViewModel />
</Window.DataContext>
and the user controls are added in the xaml like so
<TabItem Header="Search">
<Grid Background="#FFE5E5E5">
<uc:SearchJobView></uc:SearchJobView>
</Grid>
</TabItem>
My DataContext for SearchJobView is set like:-
<UserControl.DataContext>
<vm:SearchJobViewModel/>
</UserControl.DataContext>
My DataContext for EditJobView is set like:-
<UserControl.DataContext>
<vm:JobViewModel/>
</UserControl.DataContext>
A: the simple way would be that the MainVM hold both instances of your SearchJobsVM and EditJobVM. now the MainVM can simply handle all stuff.
eg the SearchJobVM expose an event for your doubleclick stuff. the MainVM subscribe to this event and give the Id from the eventargs to the EditJobVM and set the current workspace to the EditJobVM.
EDIT. i would use DataTemplates for your child vms and a contentPresenter in the MainView. but you can also use a TabControl and set Visibility
<DataTemplate DataType="{x:Type local:EditJobVM}">
<uc:EditJobUsercontrol/>
</DataTemplate>
MainView
<ContentPresenter Content="{Biinding 'Workspace}"/>
MainVM
public object WorkSpace {get;set;}
this.Workspace = this._myInstanceOfEditJobVM; //now the EditJobView is shown in the contentpresenter
| {
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Q: How to capture session values when session time out in ASP.Net MVC 5 in global.asax file I want to access a value which is in session, when the session times out in my ASP.Net MVC 5 application. So, below is what I did.
<system.web>
<sessionState timeout="3"></sessionState>
</system.web>
I added a value in session variable
System.Web.HttpContext.Current.Session["Val"] = myVal;
Now I want to access it when the session ends. So in global.asax I wrote below code.
public void Session_OnEnd()
{
if (System.Web.HttpContext.Current.Session["Val"] != null) // EXCEPTION
{
int TenantSessionId = (int)System.Web.HttpContext.Current.Session["Val"];
}
}
But after time out (3 minutes) I get exception as NULL REFERENCE in Session_OnEnd() Method. Kindly guide me. Have I missed something here? I just want to access the session variable. Or is it not possible to capture the session value just before the session is about to time out?
Kindly note that I am setting session variable when user logs in. So the setting up of session variable code is not in "Session_start". Just wanted to put out this information. But I am sure that the value is properly set in the session when the session_end() is getting called as per my code flow.
| {
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} | 6,055 |
UN: Ban Abusive Bangladesh Unit from Peacekeeping
Bangladesh's democracy erodes amid tilt to China
For the US, the question is how to be aggressive enough to keep some democratic alleys open for the future.
Curtesy: FridayTimes
As far as I could tell, most Bangladeshi leaders were not particularly upset that their country did not get invited to the Summit on Democracy held by US President Joe Biden the last week of December. But they were outraged by the sanctions the US placed, just after that summit, on seven of the leaders of the Rapid Action Battalion (RAB), Bangladesh's version of an elite paramilitary police force which is responsible for numerous disappearances and/or deaths of dissidents and government opponents over the past decade or longer. The predations of the RAB have been the subject of numerous reports by international human rights agencies such as Human Rights Watch and Amnesty International, as well as annually recorded in the US State Department's Annual Human Rights Report on Bangladesh.
While these various reports are probably not read by the bulk of the Bangladesh population, they circulate widely through the intellectual community and the media. There is no secret to the long record of human rights abuses by RAB. Yes, there is some ambiguity about the support that the RAB received from the US, some other Western governments, as well as India, when it was created in 2004 as a counter-terrorist force. Terrorism in South Asia was high on the list of issues the West was concerned about. In other parts of the region, particularly in Pakistan and Afghanistan, terrorism was leading to insurgencies menacing political and social stability. But this was short lived in Bangladesh. While some argue that the RAB was needed then, looking back the threat looks illusory; but it certainly was attractive to Western allies.
Looking back at history from another angle, however, puts a very different light on the development of the RAB. Most readers know the history of Bangladesh's slow but inexorable politically clear deliberate drift toward authoritarianism. I, and others, have described it in these pages often. Starting in 2008, when the Awami League (AL) was elected with a large majority, after the 2007-8 military interregnum (a turn back toward democracy, many of us thought), the AL has steered a careful and cautious but unerring course away from democracy. In that first term, Prime Minister Sheikh Hasina's main objective was to get rid of the Caretaker Amendment (which she had demanded a decade earlier), which would have ensured reasonably free and fair elections. When the opposition boycotted the next election because of the removal of that amendment, the AL with no restraints left on cheating, marched to an even greater victory. And the most recent election was a farce that made Bangladesh a de facto one-party state, a state that seemed not only to identify with authoritarians, but which resembled one in almost all ways, especially in its repression of opponents, of the media, and of any sign of dissent.
Clearly this is the reason that the RAB was useful to the government from 2008 onward, despite the opprobrium it brought on Bangladesh from Human Rights agencies and advocates. Being created as an anti-terrorist organization, unofficially licensed to use the violent tactics of terrorism against putative terrorists, it became instead a violent terrorist unit against those citizens of Bangladesh which are marked as opponents of the government and described therefore as "terrorists." The RAB became the main muscle of a state authoritarian in all respects except its self-identification.
And, of course, the outside world that Bangladesh has been dealing with has also changed in radical ways. I wasn't involved personally of course, but I assume the sequence of US involvement went something like this: the US, which had focused on terrorism when the RAB was created, supported it against critics like the human rights agencies early on, because it thought the RAB was useful as an anti-terrorism tool, then took to reforming it to explain to Congress why it was still defending it (many "training" programs which its leaders obviously just winked at), to forceful diplomatic demarches and threats but no action to stop it from the many excesses, to nonchalance (Trump Administration).
Biden said at the beginning of his administration that he would make democracy and human rights at the center of his foreign policy. It took the Administration a while to get around to it. The long wait may have been the terrible shape in which Trump left the State Department. And the continuing trouble the Biden Administration is having getting high-level echelon (political) appointees confirmed because of Republican tactics in the Senate. Though things appear to have speeded up somewhat, there remain a large number of officers, mostly those who are professional diplomats, awaiting Ambassadorial Assistant Secretary confirmation. The new Ambassador to Bangladesh has just been confirmed and will arrive at post next month. And, by the way, a new Ambassador to Pakistan has finally been named, but not confirmed yet. I believe there hasn't been a regular (nominated and confirmed) Ambassador to Pakistan since 2018. That's how badly the Trump Administration screwed things up at the State Department.
As to Bangladesh, I assume that readers are interested in two questions: one, will these sanctions, and perhaps more (this may not be over yet, as I will explain below), make any difference in whether Bangladesh continues its political direction towards one-party authoritarianism; and two, will it turn US-Bangladesh relations into a hostile relationship? I suspect the answer to both questions is, not really.
I think Sheikh Hasina is far too close to her lifetime objective— which to me has appeared for some years now to be the perpetual rule of Bangladesh by the family of the 'Father of the Nation.' Every decision she has made along the way from 2008 until now points to that obsession, from the deification of Mujib, to the final destruction of the major opposition party, to the establishment by means different from Mujib of a one-party state. This does not mean that I think that Bangladesh will remain forever an autocracy under her and her family. I suspect, however, that she has locked down the nation so successfully that fear reigns among potential rivals for power, and the instruments of repression are so efficient that no opposition can form while she is still in power. But whether this efficient mechanism of repression will hold together when she departs the scene is quite another question. I doubt that it can, as it seems to have no ideology except self-aggrandizement, which is a self-destructive ideology once the sole ideologue is gone.
And will the US-Bangladesh relationship deteriorate into serious hostility? In this case, hostility does not mean violence, because the US is not interested enough in Bangladesh to resort to violence, even if Sheikh sold her country's soul to China. But she would not do that, as she wants Chinese money (don't we all?), but not enough to undercut her own obsession with perpetual family rule. For the US, the question is how to be aggressive enough to keep some democratic alleys open for the future and save as many lives as possible for a viable opposition when the time comes for that to be relevant to the country's future.
One document which gives me an idea for a future US political strategy is a quite brilliant paper, done for the Carnegie Endowment for International Peace by my friend Ali Riaz, entitled "How Bangladesh's Digital Security Act is Creating a Culture of Fear." I draw in this paragraph from Ali's article. The act is relatively new, having pulled together by the government in 2018 several previous acts which were already draconian in their censorship of dissent or criticism of the government. Thus, it turned out to limit speech even more that the predecessor laws had by "giving law enforcement agencies the power to arrest anyone, search any premises, and seize any equipment without a warrant, requiring only suspicion that a crime had been committed using social media." Furthermore, "it allows the government to order the removal and blocking [of] any information or data on the internet that it deems necessary, thereby providing broad scope to silence those critical of its policies or data on human rights violations." In the three years since its promulgation, more than 1,500 cases have been filed under this law. Over 25 per cent of these concerned journalists; 30 per cent were politicians (clearly opposition). Of course, there are many others which are not documented.
The US has a serious interest in keeping Bangladesh out of Chinese clutches, which must temper its enthusiasm for its revived promotion of democracy there, but I believe it will be the other main, if not the main item on the agenda.
BANGLADESH: In pursuit of a one-party state? | {
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{"url":"https:\/\/www.physicsforums.com\/threads\/estimating-head-loss-from-pipe-slope.998087\/page-2","text":"# Estimating head loss from pipe slope?\n\n444 feet vertical, 126 gpm, 1kw? Double check your numbers.\nYes check your numbers, I think you are off by a factor of ten.\n\nruss_watters\nMentor\nYes check your numbers, I think you are off by a factor of ten.\nWhere are you guys seeing 1kW? I see 5 kW in post #19. That seems reasonable based on 50% extraction efficiency.\n\nWhere are you guys seeing 1kW?\n\nFor the given conditions (126 gpm and 444 feet) I get ~10.5 kW. As @russ_watters alludes, the this would be a maximum theoretical value with real-world considerably less.\n\nruss_watters\n256bits\nGold Member\nPer Bernoulli, they are all the same.\nThanks for answering, but it was mainly for @morrobay to think about in response to his question.\n\nruss_watters\n256bits\nGold Member\nCase 4 converts gravitational potential energy into kinetic energy by allowing the water to accelerate through open air\nCase 4 adds a vertical pipe. You are referencing case 1.\nSince they are all gravity fed, the energy of the water is the same at the end of the 444 drop in elevation, barring, as I said, any friction loss in the pipes., which in the real world would have to be taken into account.\nYour penstock could be of either .\nA free falling column of water would be difficult to control onto the turbine buckets.\n\nBeware of overpressure at the turbine end. Be especially aware of what will happen if you try to turn off the flow too fast. With 2689 feet of penstock the inertia is very big and rapid shut off will destroy all your equipment. You may even need a surge pipe with a blow-out diaphragm to protect against overpressure.\n\nThis is a good point, but I'm a bit confused about how a surge tank would be made. If I'm understanding correctly, the surge tank would need to be located at the bottom of the pipeline, and would need to be higher than the head, in order to prevent water from coming out during normal operation. In other words, if I have 444 feet of head, then my surge pipe would need to be greater than 444 feet tall. Would that even work? It seems like the 444 ft of head pressure in the surge tank would prevent it from rapidly absorbing pressure spikes. I must be missing something .\n\nPerhaps a simpler option in this case would simply be to install a pressure relief valve?\n\nAre you serious about the dimensions? 10\" diameter and 2689 feet, 444 feet vertical, 126 gpm, 1kw? Double check your numbers. What is the total mass of water in the pipe? What is the velocity of the water?\n\nNot sure where you got 1 kw from. Some of my earlier calculations were a little bit off, but I think my current numbers below are good. I'm seeing about 10 kw power available, of which the turbine will probably capture about 80%.\n\nOne thing I notice is that the water PSI is now 176 which exceeds the 150 PSI limit for PVC (and that's without taking into account pressure surges). Therefore, I would either need to use a steel pipe, or shorten the pipeline to stay safely below 150 PSI. During actualy construction, I would need to be careful to measure the PSI and see how close reality is to theory.\n\n Resource\u200b \u200b Head(f)\u200b 444.32520\u200b Stream velocity(ft\/sec)\u200b 1.00000\u200b Stream cross section(in^2)\u200b 45.00000\u200b Flow(gpm)\u200b 140.25971\u200b \u200b \u200b Pipeline\u200b \u200b Pipe Length(f)\u200b 2,689.60000\u200b Pipe Diameter(inch)\u200b 10.00000\u200b Pipe cross section(inch^2)\u200b 78.53982\u200b Pipe Absolute Roughness (in)\u200b 0.00006\u200b Pipe volume (gal)\u200b 43,894.17240\u200b \u200b \u200b Constants\u200b \u200b Fluid density(lb\/f^3)\u200b 62.40000\u200b Fluid viscocity\u200b 1.10000\u200b \u200b \u200b Intermediate calculations\u200b \u200b Re\u200b 40,307.88717\u200b F (Darcy friction factor)\u200b 0.02183\u200b \u200b \u200b Results\u200b \u200b Head Loss(f)\u200b 35.91983\u200b Effective Head(f)\u200b 408.40537\u200b Water PSI\u200b 176.83952\u200b Water velocity through pipe (ft\/sec)\u200b 0.57262\u200b Total pipe travel time (min)\u200b 78.28398\u200b Max power (kw)\u200b 10.79508\u200b Gallons per kwh\u200b 779.57561\u200b Rain barrels per kwh\u200b 15.59151\u200b\n\nLast edited:\nJust to be pedantic, you should know that in general pipe inside diameter is not the same as the nominal pipe size. Pipe comes in \"schedules\" which are different wall thicknesses. 10-inch pipe has an outer diameter of 10.750 inches. Normal or standard is schedule 40; for 10-inch sch 40 pipe the ID is 10.02 inch, transverse area is 78.86 in^2. So in this case you can get away with using 10 inch ID in your calculations.\n\nI have never seen PVC in anything but schedule 40. You can look at the pipe manufacturer's website to see what they supply; they usually have useful tables of \"Pipe Data\" showing the dimensions for the various schedules in each nominal size. There is some ASME specification that defines the dimensions.\n\nanorlunda\nStaff Emeritus\nIf you have 176 psi working pressure, the burst pressure should be on the order of 800 psi. Then pressure relief valves and\/or burst diaphragms should try to limit the pressure to 400 psi.\n\nThat much 10 inch steel pipe, I couldn't find the price, but at least several hundred thousand dollars.\n\nI see 10-inch sch 40 PVC online at about $13 per foot, so there's$35,000. Plus 150 pipe couplings, glue, supports, etc... The turbine, the controls, wiring back up to the house...\n\nour neighbor who owns property next to the road wasn't willing to give us 5 ft of easement onto a tiny corner of their 200+ acre property that we needed for the power line clearance region.\nMaybe you can resume negotiations with the neighbor. Grid power at about 20 cents a kW-hr is a bargain.\n\nanorlunda\nStaff Emeritus\nI see 10-inch sch 40 PVC online at about $13 per foot, so there's$35,000\nFar too small pressure rating. He needs steel pipe.\n\nEdit: Something like in this picture. My guess is that the picture shows something like a 10 inch pipe with 10 inches of insulating jacket. But it's hard to get accurate size from the picture. Just laying bare pipe on the ground would cause dents and dents become weak points.\n\nyahastu\nFar too small pressure rating. He needs steel pipe.\n\nNo argument there.\n\nMaybe the OP can live with reduced power, then they could locate the turbine higher on the hill, reducing turbine inlet pressure and pipe length.\n\nAs interesting as the hydro project is, it will be costly and require work and to maintain.\n\nFar too small pressure rating. He needs steel pipe.\n\nPSI is approximately 0.433 times head (ft). Therefore, if PVC can sustain up to 140 psi working pressure, then I can use PVC for the first 140\/0.433 = 323 feet of head (a bit longer actually, due to head loss). That would be approximately 80% of the length of the pipeline. Then I only have to use steel for the bottom 20%.\n\nHere I can find 10\" PVC for about $12\/ft: https:\/\/pvcpipesupplies.com\/10-x-20-schedule-40-pvc-pipe-h0401000pw200b.html I have not searched around to find prices on steel pipe yet, but this looks promising.. https:\/\/www.alibaba.com\/product-det...ferlist.topad_creative.d_title.1c0616c3k7evwI Maybe you can resume negotiations with the neighbor. Grid power at about 20 cents a kW-hr is a bargain. Even if I got the easement, it was going to cost$70k for the electric hookup. I can actually build a pipeline to give me free energy for less!\n\nLast edited:\nWell it sure is interesting!\n\nI don't know what kind of permitting is required for an installation like that. Have you checked your creeks for snail darters?\n\nI work in a heavily regulated industry so part of my job is being able to come up with an endless stream of objections, reasons why plans \/ ideas will not work. We need to think of all that stuff ahead of time. Sorry if I come off as a wet blanket. I just can't help it\n\nruss_watters\nI don't know what kind of permitting is required for an installation like that.\n\nYeah, I have begun the less fun process of investigating the various pathways for permitting such a project. There are a few different ways...and eligibility depends a lot on the system design. It's much easier to get it permitted if I do it as a Run of River project (ie, no dam, and no upstream storage allowed)...which is another reason why large diameter pipes are preferred!\n\nJust walked around to scope out some new spots today, took some more flow rate measurements. I have concluded that my method of measurement, which consists of dropping a styrofoam ball into the water and timing how long it takes to travel, is a really terrible way of estimating average stream velocity. So many eddies, currents, the surface moves differently than the undertow...yeah. I'm going to need to find a more accurate way to do that, but I don't want to shell out the cash for this thing...\nhttps:\/\/rickly.com\/usgs-type-aa-current-meter\/\n\nHere's the proposed pipeline path:\n\nAnd some new numbers. A little bit lower than before, because I decided to change my pipeline path to try to optimize more reliable and streams, rather than to maximize peak power output.\n\n Resource\u200b \u200b Head(f)\u200b 312.25928\u200b Stream velocity(ft\/sec)\u200b 1.00000\u200b Stream cross section(in^2)\u200b 45.00000\u200b Flow(gpm)\u200b 140.25971\u200b \u200b \u200b Pipeline\u200b \u200b Pipe Length(f)\u200b 4089.832\u200b Pipe Diameter(inch)\u200b 10.00000\u200b Pipe cross section(inch^2)\u200b 78.53982\u200b Pipe Absolute Roughness (in)\u200b 0.00006\u200b Pipe volume (gal)\u200b 66,745.90679\u200b \u200b \u200b Constants\u200b \u200b Fluid density(lb\/f^3)\u200b 62.40000\u200b Fluid viscocity\u200b 1.10000\u200b \u200b \u200b Intermediate calculations\u200b \u200b Re\u200b 40,307.88717\u200b F (Darcy friction factor)\u200b 0.02183\u200b \u200b \u200b Results\u200b \u200b Head Loss(f)\u200b 54.62005\u200b Effective Head(f)\u200b 257.63923\u200b Water PSI\u200b 111.55779\u200b Water velocity through pipe (ft\/sec)\u200b 0.57262\u200b Total pipe travel time (min)\u200b 119.03939\u200b Max power (kw)\u200b 6.80999\u200b Gallons per kwh\u200b 1,235.77010\u200b Rain barrels per kwh\u200b 24.71540\u200b Pipeline fill time (hours)\u200b 7.93123\u200b\n\njrmichler\nMentor\nThere is something wrong with your calculations. The lowest flow rate in my copy of Cameron Hydraulic Data for 10 inch Schedule 40 steel pipe is 180 GPM, where the head loss is 0.022 feet per 100 feet, so the total friction head loss is ##0.022 * 40.89 = 0.9 feet##. The head loss that you are getting at 140 GPM is very close to the head loss of 4 inch pipe at that flow rate. Your system just got a lot more affordable.\n\nStyrofoam balls do not work well for measuring stream flow velocity. Much better is a piece of wood, preferably one that is wet enough to float low in the water. If you want even more accurate measurements, use a weir: https:\/\/www.openchannelflow.com\/weirs. The weir can be a simple piece of plywood jammed into the streambed, with sand and gravel shoveled up against it to hold it in place. Search weir flow measurement calculation to find how to calculate flow rates. They work much better than trying to estimate flow from stream bed size and velocity.\n\nThere is something wrong with your calculations.\nI think @jrmichler is right. For 10-inch sch 40 pipe, I get v=0.5707 ft\/sec, Re=44,000, and f=0.022. L\/D = 4900. Then head loss is ~0.55 ft.\n\n@jrmichler @gmax137\n\nHmm...I'm having difficulty finding out the source of the discrepancy. I would like to know if the fundamental equations I'm using or wrong, or if I'm just misapplying them or what.\n\nI am using the exact equations from here:\n\nI first entered the values used in the example on the above website:\nQ (gpm) = 400 gpm\nL (ft) = 100\nd (inch) = 4.026\nepisolon(in) = 0.0018\n\nUsing those numbers, I get:\nRe = 285,524.45468 (pretty close to what they got but not exact)\nf = 0.01809 (again close)\n\nFor the final head loss calculatation (hL), it looks like their arithmetic is incorrect:\nhttps:\/\/www.wolframalpha.com\/input\/?i==0.0311*0.018*100*400^2\/4.026^3\n\nIe, using their own numbers, they should be value of 137.9 feet for head loss, rather than 8.46.\n\nHowever, it looks like the units are inconsistent in their equation. L is given in feet, d is given in inches...so maybe there is a units conversion error?\n\nThe units are all wrapped up into the leading 0.0311 factor. These can be tedious to unravel. My Crane book shows this with the d^5 not d^3 (shown in your link), that explains maybe why you're getting values much higher.\n\nCrane 410: h = 0.03111 f L Q^2\/d^5\n\nL in feet\nd in inches\nQ in gpm\n\nI think the d^5 is correct and the d^3 is a typo\n\nyahastu\nyeah the velocity is flow\/area and area is ~d^2\n\nso the v^2 gives you d^4\n\nand the L\/d gives you \"another\" d, so you have d^5\n\nso you see a small change in design diameter gives a big change in head loss (d to the 5th power). so doubling the diameter will reduce the loss by a factor of 2^5 = 32. This is not perfectly true since the diameter comes into the friction factor via the Reynolds number. But for turbulent flow it makes a small effect.\n\nNice, thanks for spotting that @gmax137!\n\nStyrofoam balls do not work well for measuring stream flow velocity. Much better is a piece of wood, preferably one that is wet enough to float low in the water. If you want even more accurate measurements, use a weir: https:\/\/www.openchannelflow.com\/weirs. The weir can be a simple piece of plywood jammed into the streambed, with sand and gravel shoveled up against it to hold it in place. Search weir flow measurement calculation to find how to calculate flow rates. They work much better than trying to estimate flow from stream bed size and velocity.\n\nThanks for the suggestion :) I constructed a couple simple weirs yesterday. I opted for a V-shaped design, since I read that it provides a more accurate flow measurement than other profiles. Here is a pic installed:\n\nInstalling the weir was a bit challenging due to the conditions, because the ground is frozen and the only dirt I had available to pack around it was loose rocks and gravel from the streambed. Unfortunately I was not able to stop all the flow from going underneath and around the sides of the weir in my initial attempt. I think I managed to capture somewhere in the range of 50% to 90% of the flow.\n\nI measured the head over the V-notch to be 1.5\" and 2\" respectively at two different streams, which implies much lower flow rates on the order of 7-13 gpm...less than 10 times what I had estimated before using the velocity method. As a result, I'm now estimating 400 to 800 watts per stream, so that is certainly disappointing, but it's still a decent amount of energy...ie, more energy than consume in our current house on avg. However, it won't be enough to run the proposed heating system (geothermal heat pump) and charge EVs that we need. Fortunately this does not kill the project, because there is a near inifinite supply of water at the bottom of the hill, so it just means that I may need to rely more on using solar power to pump water up to the top into the pipeline in order to maintain higher rates of flow.\n\nAs for pipe diameter, it's awesome that head loss is so much lower than I originally thought. Even a 2\" pipe would be sufficient for this native flow rate. However, since the plan is to use the hydro for retrieval of pumped storage energy, I really need to size the pipe based on the max power that I would want to deliver. It looks like, if I want my max hydro power to be able to ramp up to about 20 kw, then I should have at least a 8\" pipe. I still might want to boost that up to 10\" for the extra storage capacity in the pipe, if I cannot get the permit for a dam.\n\njrmichler\nanorlunda\nStaff Emeritus\nHow much volume at the top of the hill do you have to store pumped water? That too may become a permitting issue.","date":"2021-06-13 14:08:02","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.27430814504623413, \"perplexity\": 2005.1811083424384}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-25\/segments\/1623487608856.6\/warc\/CC-MAIN-20210613131257-20210613161257-00600.warc.gz\"}"} | null | null |
Q: How do I set default text for description field on the enter bug page? Description will need to change on update of one of the custom fields I have done this using javascript for the edit bug page, where I used a change of the bug status to modify the default text. This was done by calling a javascript function onchange of the bug status.
I am now trying to do a similar operation on the enter bug page, but I need the default text to change based on the issue type. As this is a custom field it does not show up in the template files, so I cant (that I am aware of) use the onchange in the select tag for the issue type drop down menu. Is there another way of using the onchange feature to call a javascript function?
Thanks
A: The way that I have accomplished something similar is to modify field.html.tmpl which is where the HTML for the custom fields is rendered. You would find the place in the code where it is rendering your field (e.g. [% CASE [constants.FIELD_TYPE_SINGLE_SELECT). Then you could add in your own code to include an onchange handler as appropriate for your particular situation.
Something like this (note: Bugzilla 3.2.3):
[% CASE [ constants.FIELD_TYPE_SINGLE_SELECT
constants.FIELD_TYPE_MULTI_SELECT ] %]
<select id="[% field.name FILTER html %]"
name="[% field.name FILTER html %]"
[% IF field.type == constants.FIELD_TYPE_MULTI_SELECT %]
[% SET field_size = 5 %]
[% IF field.legal_values.size < 5 %]
[% SET field_size = field.legal_values.size %]
[% END %]
size="[% field_size FILTER html %]" multiple="multiple"
[% END %]
[%# BEGIN ADDED CODE %]
[% IF field.name == 'cf_mycustomissuetypefield' %]
onchange="javascript:updateDescription()"
[% END %]
[%# END ADDED CODE %]
>
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,568 |
package org.semanticweb.elk.reasoner.saturation.rules;
import org.semanticweb.elk.reasoner.saturation.rules.backwardlinks.BackwardLinkChainFromBackwardLinkRule;
import org.semanticweb.elk.reasoner.saturation.rules.backwardlinks.ContradictionOverBackwardLinkRule;
import org.semanticweb.elk.reasoner.saturation.rules.backwardlinks.SubsumerBackwardLinkRule;
import org.semanticweb.elk.reasoner.saturation.rules.contextinit.OwlThingContextInitRule;
import org.semanticweb.elk.reasoner.saturation.rules.contextinit.RootContextInitializationRule;
import org.semanticweb.elk.reasoner.saturation.rules.contradiction.ContradictionPropagationRule;
import org.semanticweb.elk.reasoner.saturation.rules.disjointsubsumer.ContradictionCompositionRule;
import org.semanticweb.elk.reasoner.saturation.rules.forwardlink.BackwardLinkFromForwardLinkRule;
import org.semanticweb.elk.reasoner.saturation.rules.forwardlink.NonReflexiveBackwardLinkCompositionRule;
import org.semanticweb.elk.reasoner.saturation.rules.forwardlink.ReflexiveBackwardLinkCompositionRule;
import org.semanticweb.elk.reasoner.saturation.rules.propagations.SubsumerPropagationRule;
import org.semanticweb.elk.reasoner.saturation.rules.subcontextinit.PropagationInitializationRule;
import org.semanticweb.elk.reasoner.saturation.rules.subsumers.ComposedFromDecomposedSubsumerRule;
import org.semanticweb.elk.reasoner.saturation.rules.subsumers.ContradictionFromNegationRule;
import org.semanticweb.elk.reasoner.saturation.rules.subsumers.ContradictionFromOwlNothingRule;
import org.semanticweb.elk.reasoner.saturation.rules.subsumers.DisjointSubsumerFromMemberRule;
import org.semanticweb.elk.reasoner.saturation.rules.subsumers.EquivalentClassFirstFromSecondRule;
import org.semanticweb.elk.reasoner.saturation.rules.subsumers.EquivalentClassSecondFromFirstRule;
import org.semanticweb.elk.reasoner.saturation.rules.subsumers.IndexedClassDecompositionRule;
import org.semanticweb.elk.reasoner.saturation.rules.subsumers.IndexedClassFromDefinitionRule;
import org.semanticweb.elk.reasoner.saturation.rules.subsumers.IndexedObjectComplementOfDecomposition;
import org.semanticweb.elk.reasoner.saturation.rules.subsumers.IndexedObjectHasSelfDecomposition;
import org.semanticweb.elk.reasoner.saturation.rules.subsumers.IndexedObjectIntersectionOfDecomposition;
import org.semanticweb.elk.reasoner.saturation.rules.subsumers.IndexedObjectSomeValuesFromDecomposition;
import org.semanticweb.elk.reasoner.saturation.rules.subsumers.ObjectIntersectionFromFirstConjunctRule;
import org.semanticweb.elk.reasoner.saturation.rules.subsumers.ObjectIntersectionFromSecondConjunctRule;
import org.semanticweb.elk.reasoner.saturation.rules.subsumers.ObjectUnionFromDisjunctRule;
import org.semanticweb.elk.reasoner.saturation.rules.subsumers.PropagationFromExistentialFillerRule;
import org.semanticweb.elk.reasoner.saturation.rules.subsumers.SuperClassFromSubClassRule;
import org.semanticweb.elk.util.logging.statistics.AbstractStatistics;
import org.semanticweb.elk.util.logging.statistics.StatisticsPrinter;
import org.slf4j.Logger;
/**
* The object that is used to measure the number of applied rules and time spent
* inside rules.
*
* @author "Yevgeny Kazakov"
*
*/
public class RuleStatistics extends AbstractStatistics {
// TODO: limit access
public final RuleCounter ruleCounter = new RuleCounter();
public final RuleApplicationTimer ruleTimer = new RuleApplicationTimer();
public synchronized void add(RuleStatistics stats) {
super.add(stats);
ruleCounter.add(stats.ruleCounter);
ruleTimer.add(stats.ruleTimer);
}
public long getTotalRuleAppCount() {
return ruleCounter.getTotalRuleAppCount();
}
public double getTotalRuleTime() {
return getNumberOfMeasurements() == 0 ? 0 : 1d
* ruleTimer.getTotalRuleAppTime() / getNumberOfMeasurements();
}
public void print(Logger logger) {
if (!logger.isDebugEnabled() || !measurementsTaken())
return;
if (ruleCounter.getTotalRuleAppCount() == 0)
return;
StatisticsPrinter printer = new StatisticsPrinter(logger,
"%{RULES:}s %,{count}d [%,{time}d ms]", "TOTAL RULES",
ruleCounter.getTotalRuleAppCount(),
ruleTimer.getTotalRuleAppTime());
// TODO: sort in a better order
printer.printHeader();
print(printer, BackwardLinkChainFromBackwardLinkRule.NAME,
ruleCounter.countBackwardLinkChainFromBackwardLinkRule,
ruleTimer.timeBackwardLinkChainFromBackwardLinkRule);
print(printer, BackwardLinkFromForwardLinkRule.NAME,
ruleCounter.countBackwardLinkFromForwardLinkRule,
ruleTimer.timeBackwardLinkFromForwardLinkRule);
print(printer, NonReflexiveBackwardLinkCompositionRule.NAME,
ruleCounter.countNonReflexiveBackwardLinkCompositionRule,
ruleTimer.timeNonReflexiveBackwardLinkCompositionRule);
print(printer, ComposedFromDecomposedSubsumerRule.NAME,
ruleCounter.countComposedFromDecomposedSubsumerRule,
ruleTimer.timeComposedFromDecomposedSubsumerRule);
print(printer, ContradictionCompositionRule.NAME,
ruleCounter.countContradictionCompositionRule,
ruleTimer.timeContradictionCompositionRule);
print(printer, ContradictionFromNegationRule.NAME,
ruleCounter.countContradictionFromNegationRule,
ruleTimer.timeContradictionFromNegationRule);
print(printer, ContradictionFromOwlNothingRule.NAME,
ruleCounter.countContradictionFromOwlNothingRule,
ruleTimer.timeContradictionFromOwlNothingRule);
print(printer, ContradictionOverBackwardLinkRule.NAME,
ruleCounter.countContradictionOverBackwardLinkRule,
ruleTimer.timeContradictionOverBackwardLinkRule);
print(printer, ContradictionPropagationRule.NAME,
ruleCounter.countContradictionPropagationRule,
ruleTimer.timeContradictionPropagationRule);
print(printer, DisjointSubsumerFromMemberRule.NAME,
ruleCounter.countDisjointSubsumerFromMemberRule,
ruleTimer.timeDisjointSubsumerFromMemberRule);
print(printer, IndexedClassDecompositionRule.NAME,
ruleCounter.countIndexedClassDecompositionRule,
ruleTimer.timeIndexedClassDecompositionRule);
print(printer, IndexedObjectComplementOfDecomposition.NAME,
ruleCounter.countIndexedObjectComplementOfDecomposition,
ruleTimer.timeIndexedObjectComplementOfDecomposition);
print(printer, IndexedObjectIntersectionOfDecomposition.NAME,
ruleCounter.countIndexedObjectIntersectionOfDecomposition,
ruleTimer.timeIndexedObjectIntersectionOfDecomposition);
print(printer, IndexedObjectSomeValuesFromDecomposition.NAME,
ruleCounter.countIndexedObjectSomeValuesFromDecomposition,
ruleTimer.timeIndexedObjectSomeValuesFromDecomposition);
print(printer, IndexedObjectHasSelfDecomposition.NAME,
ruleCounter.countIndexedObjectHasSelfDecomposition,
ruleTimer.timeIndexedObjectHasSelfDecomposition);
print(printer, SubsumerPropagationRule.NAME,
ruleCounter.countSubsumerPropagationRule,
ruleTimer.timeSubsumerPropagationRule);
print(printer, ObjectIntersectionFromFirstConjunctRule.NAME,
ruleCounter.countObjectIntersectionFromFirstConjunctRule,
ruleTimer.timeObjectIntersectionFromFirstConjunctRule);
print(printer, ObjectIntersectionFromSecondConjunctRule.NAME,
ruleCounter.countObjectIntersectionFromSecondConjunctRule,
ruleTimer.timeObjectIntersectionFromSecondConjunctRule);
print(printer, ObjectUnionFromDisjunctRule.NAME,
ruleCounter.countObjectUnionFromDisjunctRule,
ruleTimer.timeObjectUnionFromDisjunctRule);
print(printer, OwlThingContextInitRule.NAME,
ruleCounter.countOwlThingContextInitRule,
ruleTimer.timeOwlThingContextInitRule);
print(printer, PropagationFromExistentialFillerRule.NAME,
ruleCounter.countPropagationFromExistentialFillerRule,
ruleTimer.timePropagationFromExistentialFillerRule);
print(printer, RootContextInitializationRule.NAME,
ruleCounter.countRootContextInitializationRule,
ruleTimer.timeRootContextInitializationRule);
print(printer, SubsumerBackwardLinkRule.NAME,
ruleCounter.countSubsumerBackwardLinkRule,
ruleTimer.timeSubsumerBackwardLinkRule);
print(printer, SuperClassFromSubClassRule.NAME,
ruleCounter.countSuperClassFromSubClassRule,
ruleTimer.timeSuperClassFromSubClassRule);
print(printer, EquivalentClassFirstFromSecondRule.NAME,
ruleCounter.countEquivalentClassFirstFromSecondRule,
ruleTimer.timeEquivalentClassFirstFromSecondRule);
print(printer, EquivalentClassSecondFromFirstRule.NAME,
ruleCounter.countEquivalentClassSecondFromFirstRule,
ruleTimer.timeEquivalentClassSecondFromFirstRule);
print(printer, IndexedClassFromDefinitionRule.NAME,
ruleCounter.countIndexedClassFromDefinitionRule,
ruleTimer.timeIndexedClassFromDefinitionRule);
print(printer, ReflexiveBackwardLinkCompositionRule.NAME,
ruleCounter.countReflexiveBackwardLinkCompositionRule,
ruleTimer.timeReflexiveBackwardLinkCompositionRule);
print(printer, PropagationInitializationRule.NAME,
ruleCounter.countPropagationInitializationRule,
ruleTimer.timePropagationInitializationRule);
printer.printSeparator();
print(printer, "TOTAL RULES:", ruleCounter.getTotalRuleAppCount(),
ruleTimer.getTotalRuleAppTime());
printer.printSeparator();
}
void print(StatisticsPrinter printer, String name, long count, long time) {
if (count == 0)
return;
printer.print(name, count, time / getNumberOfMeasurements());
}
/**
* Reset all timers to zero.
*/
@Override
public void reset() {
super.reset();
ruleCounter.reset();
ruleTimer.reset();
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,234 |
<?php
namespace metatron;
require_once 'common.php';
class EditionsResponse extends Response {
/**
* @var Edition[]
*/
protected $editions = array();
/**
* @var Edition
*/
protected $requestedEdition;
public function loadFromJson($jsonDoc)
{
$response = json_decode($jsonDoc, true);
$requestedId = null;
// Find our requested edition id, if set
if(isset($response['requested']['identifier']))
{
$requestedId = $response['requested']['identifier'];
}
// Set the services used in response
if(isset($response['service']))
{
$this->services = $response['service'];
}
// Set the filters used in response
if(isset($response['filters']))
{
$this->filters = $response['filters'];
}
if(isset($response['editions']))
{
foreach($response['editions'] as $editionArray)
{
$edition = new Edition($this->client);
$edition->loadFromArray($editionArray);
$this->editions[] = $edition;
if($requestedId && isset($edition->identifier) && $requestedId === $edition->identifier)
{
$this->requestedEdition = &$edition;
}
}
}
$this->total = count($this->editions);
$this->limit = $this->total;
}
/**
* @return \metatron\Edition[]
*/
public function getEditions()
{
return $this->editions;
}
/**
* @return \metatron\Edition
*/
public function getRequestedEdition()
{
return $this->requestedEdition;
}
} | {
"redpajama_set_name": "RedPajamaGithub"
} | 8,710 |
\section{Introduction}
Quantum computing and quantum information have been well-known to be highly
developing fields in which a number of disciplines such as quantum mechanics,
mathematics, communication, information, statistics, control, optimization,
etc.\ are crossing over (see \cite{NC} for their history, for example).
In this paper, a pair of interesting mathematical objects having different origins
meet together both of which are described on the quantum state space (QSS),
the space of regular density matrices of an arbitrarily fixed degree:
One is the extended averaged Hebbian learning equation (EAHLE) on the QSS
\cite{UY1} originating from one of the Hebbian synaptic-neuron learning
models and the other is the e-geodesics arising naturally from quantum
information geometry.
\par
In order to describe the motive of this paper, a brief history of the series of
the author's works \cite{UY1,UHI,UY2,U} is given below. As a departure point
of the series of the author's works, Grover's quantum search algorithm \cite{G}
is worth touched on, which is well-known to be one of the milestones on the
road of quantum computation \cite{NC}: For a large number, say $N=2^n$,
of randomly sorted data, the complexity of Grover's algorithm is of
$O(\sqrt{N})$, which is lower than the theoretical boundary, $O(N)$, of any
non-quantum searches. On Grover's algorithm, Miyake and Wadati \cite{MW}
made a pioneering geometric study saying that the search sequence is on a
geodesic on the $2^{n+1}-1$ dimensional unit sphere, $S^{2^{n+1}-1}$, of
$n$-qubit states and that the projection of the search sequence on the complex
projective space ${\bf C}P^{2^{n}-1}$ is also on a geodesic. Motivated by
Miyake and Wadati \cite{MW}, the author made a geometric study, with Hino
and Ishiwatari, on a Grover-type search for an ordered tuple of multi-qubits
\cite{UHI}: As a rigorous analogue to the projection applied to Grover's search
sequence, a projection map from the space of ordered tuples to the space of
density matrices is constructed. Further, the projection map thus obtained
is shown to equip the space of regular density matrices with the SLD-Fisher metric,
so that the projection proceeded in \cite{UHI} is a new geometric realization
of the quantum state space (QSS).
\par
A geometric study analogous to \cite{MW} about the projection of the Grover-type
search on the QSS was however deferred to \cite{U} because of another new
interest in the gradient system on the QSS associated with the negative
von-Neumann entropy. It is shown in \cite{UHI} that the gradient system of
interest is understood to be a very natural extension of the gradient system
associated with the negative Shannon entropy on a classical statistical manifold
which is studied by Nakamura \cite{N2}.
This result encourages the author to seek other noted dynamical systems which are
extendable on the QSS. Among the systems displayed in the series of papers
\cite{N1,N2,N3} by Nakamura on integrable systems, the author and Yuya succeed
to extend in \cite{UY1} the averaged Hebbian learning equation (AHLE)
which describes the Hebbian synaptic-neuron learning model proposed by Oja
\cite{N1,Oja}. The dynamical system thus extended on the QSS from the AHLE is
the EAHLE dealt with in this paper. A continuous-time limit of Karmarkar's
projective scaling algorithm of non-constraint \cite{N3,Karmarkar} is also shown
by the author and Yuya to be extendable on the QSS \cite{UY2}.
\par
After the papers \cite{UY1,UY2} by the author and Yuya, the deferred task for a
geometric study of the projection of the Grover-type search sequence for an ordered
tuple of multi-qubits is made successfully by the author \cite{U}: The projection of
the Grover-type search sequence on the QSS is shown to be on an m-geodesic,
an autoparallel curve with respect to the mixture-type parallel transport \cite{Hayashi},
on the QSS. This result strongly encourages the author to seek other dynamical systems
whose trajectories realize geodesics on the QSS.
\par
The aim of this paper is to study the extended averaged Hebbian learning equation
(EAHLE) constructed in \cite{UY1} from a quantum-information-geometric point of
view: All the trajectories of the EAHLE are shown to be the e-geodesics, the
autoparallel curves with respect to the exponential-type parallel transport
\cite{Hayashi}, on the QSS which are known to play an important role not only in
quantum information geometry but also in quantum estimation. In what follows,
the organization of this paper is outlined.
\par
At the beginning of the outline, it should be remarked that the pair of sections,
Section~2 and Section~3, among five sections in this paper are mostly for
reviews of the QSS, the EAHLE and the e-geodesics, which are done according to
the author's previous papers \cite{UY1,UHI,U} and the literature \cite{Hayashi}
by Hayashi on quantum information. Although the review part seems to occupy
rather large part of this paper, it is indispensable because
a similarity between looks of the EAHLE and of the tangent vector along the
e-geodesics play a key role to reach to the main theorem of this paper.
\par
In Section~2, the QSS is introduced together with the symmetric logarithmic
derivative (SLD) and the SLD-Fisher metric on that.
The SLD works not only in the definition of the SLD-Fisher metric
endowed with the QSS but also in that of the exponential-type parallel
transport dealt with in Sec.~3. Section~3 is devoted to reviewing
the extended averaged Hebbian learning equation (EAHLE) and the
e-geodesics on the QSS. The EAHLE is reviewed in subsection~3.1 together with
the way how the EAHLE comes from its origin, the AHLE. In subsection~3.2,
the e-geodesics on the QSS are defined to be the autoparallel curves with respect
to the exponential-type parallel transport. In Section~4, the main theorem of this
paper is proved, which shows that all the trajectories of the EAHLE are the
e-geodesics on the QSS. An explicit representation of solution of the AHLE is derived
as an outcome of the main theorem. Section~5 is for conclusion.
\section{The QSS}
In this section, we set up the quantum state space (QSS) as the space
of regular density matrices endowed with the SLD-Fisher metric,
following \cite{UY1,UHI,UY2}. The literature \cite{Hayashi} by Hayashi is worth
cited to have a general framework on quantum information geometry including
the QSS, in which the QSS is referred to as \lq the space of quantum
states'.
\par
Let $Q_n$ be the set of $n \times n$ regular density matrices, namely, the set
of $n \times n$ positive-definite Hermitean matrices with unit trace.
On denoting by $M(n)$ the set of all the $n \times n$ complex matrices,
$Q_n$ is defined to be the set
\begin{align}
\label{def-Q}
&
Q_n =
\left\{
\rho \in M(n) \, \left\vert \, \rho:\mbox{positive definite}, \,
\rho^{\dagger}=\rho , \, \mbox{Tr} \, \rho =1 \,
\right. \right\}
,
\end{align}
where ${}^{\dagger}$ stands for the Hermitean conjugate operation and
$\mbox{Tr}$ for the trace of matrices. The tangent space, denoted by
$T_{\rho}Q_n$, of $Q_n$ at $\rho \in Q_n$ then takes the form
\begin{align}
\label{def-tangent}
&
T_{\rho}Q_n =
\left\{
X \in M(n) \, \left\vert \, X^{\dagger}=X , \, \mbox{Tr} \, X =0 \,
\right. \right\}
,
\end{align}
which is equipped with the ${\bf R}$-vector space structure.
\par
As a natural quantum-information-geometric structure of $Q_n$,
the SLD-Fisher metric is endowed with $Q_n$ in what follows.
For the endowment, we need to introduce the symmetric logarithmic
derivative (SLD) on tangent vectors.
The SLD, denoted by $L_{\rho}(X)$, on $X \in T_{\rho}Q_n$ is
the $n \times n$ matrix determined uniquely by the equation
\begin{align}
\label{def-SLD}
&
X
=
\frac{1}{2} \left\{ \, \rho L_{\rho}(X) + L_{\rho}(X) \, \rho \right\}
\quad
(X \in T_{\rho}Q_n ) .
\end{align}
It follows from (\ref{def-SLD}) that the SLD satisfies
\begin{align}
\label{SLD-Hermitean}
&
\left( L_{\rho}(X) \right)^{\dagger}
=
L_{\rho}(X)
\quad
(X \in T_{\rho}Q_n ).
\end{align}
\par
The matrix-element display of the SLD given in \cite{UY1,UHI,UY2} is
of great help also in this paper, which is utilized to prove our main theorem
in Sec.4. Let $\rho \in Q_n$ be written in the form
\begin{align}
\label{diag-rho}
&
\rho
=
h \, \mathrm{diag} \,
\left( \theta_1 , \theta_2 \cdots , \theta_n \right)
\, h^{\dagger}
\quad
(h \in U(n)),
\end{align}
where $\mathrm{diag} \, ( \theta_1 , \theta_2 \cdots , \theta_n)$
denotes the $n \times n$ diagonal matrix whose $j$-th diagonal
entry is $\theta_j$ ($j=1,2,\cdots,n$) and $U(n)$ stands for the group
of $n \times n$ unitary matrices.
The symbol \lq $\mathrm{diag}$' indicates the diagonal matrices
henceforce. On expressing $X \in T_{\rho}Q_n$ as
\begin{align}
\label{X}
&
X=h \widetilde{X} h^{\dagger}
\end{align}
with $h \in U(n)$ of (\ref{diag-rho}),
the $(j,k)$-entry of $h^{\dagger} L_{\rho}(X) h$ ($X \in T_{\rho}Q_n$)
is calculated to be
\begin{align}
\label{alt-SLD}
&
\left( h^{\dagger} L_{\rho}(X) h \right)_{jk}
=
\left( \frac{2}{\theta_j + \theta_k} \right) \widetilde{X}_{jk}
\quad
(j,k=1,2, \cdots ,n).
\end{align}
Equations (\ref{def-SLD})-(\ref{alt-SLD}) are put together to
show the following lemma on the SLD.
\begin{lemma}
\label{lemma_SLD}
The symmetric logarithmic derivative (SLD), $L_{\rho}$, is a one-to-one and
onto ${\bf R}$-linear map from $T_{\rho}Q_n$ to
\begin{align}
\label{SLD-Q_n}
&
L_{\rho}(T_{\rho} Q_n)
=
\left\{
\Xi \in M(n) \, \left\vert \, \, \Xi^{\dagger}=\Xi , \,
\mathrm{Tr}\, (\rho \Xi + \Xi \rho) =0 \right.
\right\}
\quad
(\rho \in Q_n) .
\end{align}
Under (\ref{diag-rho}) and
\begin{align}
\label{Xi}
&
\Xi = h \widetilde{\Xi} h^{\dagger} \in L_{\rho}(T_{\rho}Q_n) ,
\end{align}
the inverse, denoted by $L_{\rho}^{-1}$, of the SLD
is given to satisfy
\begin{align}
\label{inv-SLD}
&
\left( h^{\dagger} L_{\rho}^{-1}(\Xi) h \right)_{jk}
=
\left( \frac{\theta_j+\theta_k}{2} \right) \widetilde{\Xi}_{jk}
\quad (j,k=1,2,\cdots ,n).
\end{align}
\end{lemma}
\par
In terms of the SLD, the SLD-Fisher metric $\langle \cdot , \cdot \rangle$
is defined by
\begin{align}
\label{def-Fisher}
&
\langle X , \, X^{\prime} \rangle_{\rho}
=
\mathrm{Tr}\, \left( X^{\dagger} L_{\rho}(X^{\prime}) \right)
\quad
(X, X^{\prime} \in T_{\rho}Q_n)
\end{align}
(see Hayashi \cite{Hayashi}). On using (\ref{def-SLD}) and
(\ref{SLD-Hermitean}), the SLD-Fisher metric is brought into
the form
\begin{align}
\label{SLD-Fisher}
&
\langle X , \, X^{\prime} \rangle_{\rho}
=
\frac{1}{2} \,
\mathrm{Tr}\,
\left(
\rho
\left( L_{\rho}(X) L_{\rho}(X^{\prime})
+ L_{\rho}(X^{\prime}) L_{\rho}(X) \right)
\right)
\quad
(X, X^{\prime} \in T_{\rho}Q_n)
\end{align}
\cite{UY1,UHI,UY2,U}. Furthermore, with the matrix-element displays,
(\ref{diag-rho})-(\ref{alt-SLD}), and
\begin{align}
\label{X'}
&
X^{\prime}=h \widetilde{X}^{\prime} h^{\dagger},
\end{align}
the SLD-Fisher metric is expressed to be
\begin{align}
\label{alt-Fisher}
&
\langle X , X^{\prime} \rangle_{\rho}
=
\sum_{j,k=1}^{n}
\left( \frac{2}{\theta_j+\theta_k} \right) \,
\overline{\widetilde{X}}_{jk} \widetilde{X}_{jk}^{\prime}
\end{align}
\cite{UY1,UHI,UY2,U}. Equation (\ref{alt-Fisher}) works effectively
to derive a useful formula to the gradient equation on the QSS
\cite{UY1,UHI,UY2}.
The Riemannian manifold $Q_n$ endowed with the SLD-Fisher metric
$\langle \cdot , \cdot \rangle$ is what we are referring to as the quantum
state space.
\section{The EAHLE and the e-geodesics}
In this section, the extended averaged Hebbian learning equation (EAHLE)
and the e-geodesics are introduced according to \cite{UY2} for the EAHLE
and to \cite{Hayashi} for the e-geodesics.
\subsection{The EAHLE}
The extended averaged Hebbian learning equation (EAHLE) is
organized by the present author and Yuya \cite{UY2} who are
inspired by Nakamura's paper \cite{N1} on the averaged Hebbian learning
equation (AHLE). According to \cite{UY2}, the EAHLE
is the first order differential equation
\begin{align}
\label{EAHLE}
&
\frac{d\rho}{dt}
=
\rho \, C + C \rho -2 \, \mathrm{Tr}\, (C\rho) \, \rho
\end{align}
on the QSS. The $C$ on the rhs of (\ref{EAHLE}) is the real diagonal matrix
\begin{align}
\label{C}
&
C= \mathrm{diag} \, \left( c_1, c_2, \cdots , c_n \right)
\end{align}
of degree $n$, whose diagonal entries stand for the eigenvalues
of the autocorrelation matrix of the stationary stochastic process
governing the Hebbian learning process \cite{N1,Oja,Hebb}.
\par
The reason for referring to Eq.\ (\ref{EAHLE}) as the \lq extended'
averaged Hebbian learning equation is given in what follows.
Let $w=(w_j)_{j=1,2,\cdots ,n}$ be the variables on $t$
expressing the coupling strengths of neurons obtained through an
appropriate change of the independent variable to have $t$.
The first-order differential equation
\begin{align}
\label{AHLE}
&
\frac{dw} {dt}
=
Cw - \left( w^T C w \right) \, w
\quad
\end{align}
on the $n-1$ dimensional sphere
\begin{align}
\label{sphere}
&
S^{n-1}
=
\left\{ w = (w_1,w_2, \cdots ,w_n)^T \in {\bf R}^n
\, \left\vert \,
w^T w =1 \right.
\right\}
\end{align}
with unit radius describes Oja's rule \cite{Oja} on the Hebbian learning process
of synaptic neurons \cite{Hebb}, where $C$ is the diagonal matrix given by
(\ref{C}). In (\ref{AHLE}), the $C$ is understood again to be the diagonalization
of the autocorrelation matrix of the governing stationary stochastic process
of neurons. The differential equation (\ref{AHLE}) is what we are referring
to as the averaged Hebbian learning equation (AHLE).
\par
If we restrict Eq.\ (\ref{AHLE}) on each of the open subsets,
\begin{align}
\nonumber
&
S^{n-1}_{\sigma}
=
\left\{
w \in S^{n-1} \, \left\vert \, \sigma_j w_j >0, \, j=1,2,\cdots ,n
\right. \right\}
\\
\label{S_sigma}
&
\quad
\left(
\sigma=(\sigma_j), \, \sigma_j =\pm 1 , \, j=1,2,\cdots ,n
\right)
,
\end{align}
of $S^{n-1}$, it is brought into the first-order differential equation
\begin{align}
\label{AHLE-D}
&
\frac{ d\theta_j} {dt}
=
2c_j \theta_j - 2 \left( \sum_{k=1}^{n} c_j \theta_j \right) \, \theta_j
\quad
(j=1,2,\cdots,n) ,
\end{align}
on the submanifold
\begin{align}
\label{D_n}
&
D_n
=
\left\{
\Theta \in Q_n \, \left\vert \,
\Theta = \mathrm{diag} \, (\theta_1,\theta_2, \cdots , \theta_n) \,
\right.
\right\}
\end{align}
of $Q_n$ through the map
\begin{align}
\nonumber
&
p_{n,\sigma} (w) =
\mathrm{diag} \left( w_1^2, w_2^2,\cdots , w_n^2 \right)
\\
\label{p_n_sigma}
&
\quad
\left(
w \in S^{n-1}_{\sigma}, \,
\sigma=(\sigma_j), \, \sigma_j =\pm 1 , \, j=1,2,\cdots ,n
\right)
\end{align}
from $S^{n-1}_{\sigma}$ to $D_n$ \cite{UY1}.
The $\theta_j$'s in (\ref{AHLE-D}) and (\ref{D_n}) are subject to the
constraints
\begin{align}
\label{theta-constraints}
&
\theta_j > 0 \,\, (j=1,2,\cdots n)
\quad \mbox{and} \quad
\sum_{j=1}^{n} \theta_j =1 .
\end{align}
We note here that Eq.\ (\ref{AHLE-D}) is the same form
as the Toda lattice written in Moser's form \cite{N1,Moser,MZ}.
\par
Since every mapping $p_{n,\sigma}$ defined by (\ref{p_n_sigma}) is
a diffeomorphism with the inverse
\begin{align}
\nonumber
&
p_{n,\sigma}^{-1} (\Theta)
=
\left(
\sigma_1 \sqrt{\theta_1}, \sigma_2 \sqrt{\theta_2},
\cdots , \sigma_n \sqrt{\theta_n}
\right)
\\
\label{p_n_sigma_inv}
&
\quad
\left(
\Theta \in D_n, \,
\sigma=(\sigma_j), \, \sigma_j =\pm 1 , \, j=1,2,\cdots ,n
\right)
,
\end{align}
we can understand that the differential equation (\ref{AHLE-D})
on $D_n$ is a \lq copy' of the AHLE restricted on each $S^n_{\sigma}$
and vice versa \cite{UY1}.
\par
We are at the final stage to account for the naming of the EAHLE.
To complete the account, we show that the differential equation
(\ref{AHLE-D}) on $D_n$ is the restriction of the EAHLE, (\ref{EAHLE}),
on $D_n$. In fact, the substitution of $\Theta \in D_n$ for $\rho$ in (\ref{EAHLE})
yields the \lq copy', (\ref{AHLE-D}), of the AHLE.
In a summary, we have the following lemma \cite{UY1,N1}.
\begin{lemma}
\label{AHLE-EAHLE}
The restriction of the averaged Hebbian learning equation (AHLE) on each
$S^{n-1}_{\sigma}$ is equivalent,
up to the diffeomorphisms given by (\ref{p_n_sigma}),
to Eq.\ (\ref{AHLE-D}) which describes not only the restriction of the extended
averaged Hebbian learning equation (EAHLE) on $D_n$ but also the Toda lattice
in Moser's form \cite{N1,Moser,MZ}.
\end{lemma}
\subsection{The e-geodesics on the QSS}
To those who are not familiar with differential geometry,
a geodesic connecting a given pair of points would be thought of
as the shortest-distance path between the given points. For example,
in the Euclidean plane, a typical model space
for school-geometry, we are taught that the straight-line segment
connecting a given pair of points is the geodesic between them.
In differential geometry, however, the notion of length or distance,
is unnecessary in defining geodesics:
What is needed in the definition of geodesics is the idea of
parallel transports, namely, the idea
for comparing tangent vectors at a certain point
with those at another point. Once a parallel transport is fixed,
the geodesics are defined to be the autoparallel curves with respect
to that parallel transport.
For an intuitive description of geodesics and parallel transports,
the literature \cite{Nakahara} by Nakahara is worth cited.
\par
Let us start with the definition
of the exponential-type (e-) parallel transport.
According to Hayashi \cite{Hayashi},
the e-parallel transport from $T_{\rho_1}Q_n$ to
$T_{\rho_2}Q_n$ is the ${\bf R}$-linear map
$\tau_{\rho_1,\rho_2}: T_{\rho_1}Q_n \rightarrow T_{\rho_2}Q_n$
subject to
\begin{align}
\label{parallel}
&
L_{\rho_2}(\tau_{\rho_1,\rho_2}(X))
=
L_{\rho_1}(X)- \mathrm{Tr}\, \left( \rho_2 \, L_{\rho_1}(X) \right)
\quad
(X \in T_{\rho_1}Q_n) ,
\end{align}
where $L_{\rho_1}$ and $L_{\rho_2}$ denote the SLD defined
by (\ref{def-SLD}) with $\rho =\rho_1$ and $\rho=\rho_2$, respectively.
Combining the defining equation (\ref{def-SLD}) for the SLD
with Eq.\ (\ref{parallel}), we can obtain a more direct form,
\begin{align}
\label{alt-parallel}
&
\tau_{\rho_1,\rho_2}(X)
=
\frac{1}{2}\left\{ \rho_2 L_{\rho_1}(X) + L_{\rho_1}(X) \rho_2 \right\}
-
\mathrm{Tr}\, \left( \rho_2 \, L_{\rho_1}(X) \right) \rho_2
\quad
(X \in T_{\rho_1}Q_n) ,
\end{align}
of the e-parallel transport. The e-parallel transport satisfies, of course,
the postulate of parallel transports (see Guggenheimer \cite{Gugg},
for example), but we do not get it into detail here.
\begin{definition}
\label{def-e-parallel}
Tangent vectors $X_1 \in T_{\rho}Q_n$ and $X_2 \in T_{\rho_2} Q_n$
are e-parallel if they are parallel with respect to the e-parallel transport;
namely, $X_1$ and $X_2$ are e-parallel if they satisfy
\begin{align}
\label{def-para}
&
X_2 = \tau_{\rho_1,\rho_2}(X_1) ,
\end{align}
where $\tau_{\rho_1, \rho_2}$ is the e-parallel transport given by
(\ref{alt-parallel}).
\end{definition}
\par
Once we fix a parallel transport, we can consider the geodesics
as the autoparallel curves to that parallel transport \cite{Nakahara,Gugg}.
In view of Definition \ref{def-e-parallel},
we can define the e-geodesics as follows \cite{Hayashi}.
\begin{definition}
\label{def-e-geod}
A smooth curve $\rho (t)$ ($0 \leq t \leq {}^{\exists}T$)
on the QSS is an e-geodesic if it satisfies
\begin{align}
\nonumber
\frac{d \rho}{dt}(t)
&= \tau_{\rho (0) , \, \rho (t)} \left( \frac{d \rho}{dt}(0) \right)
\\
\nonumber
&=
\frac{1}{2}
\left\{ \rho (t) L_{\rho (0) } \left( \frac{d\rho}{dt}(0) \right)
+ L_{\rho (0) } \left( \frac{d\rho}{dt}(0) \right) \rho (t) \right\}
\\
\label{autoparallel}
& \quad \qquad
-\mathrm{Tr}\, \left(
L_{\rho (0)} \left( \frac{d\rho}{dt}(0)) \right) \rho (t)
\right) \rho (t)
\qquad
(0 \leq t \leq T) ,
\end{align}
where $\tau_{\rho (0) , \, \rho (t)}$ is the e-parallel transport
from $T_{\rho(0)}Q_n$ to $T_{\rho (t)}Q_n$ given by (\ref{alt-parallel})
with $\rho (0)$ and $\rho (t)$ in place of $\rho_1$ and $\rho_2$, respectively.
\end{definition}
Equation (\ref{autoparallel}) for the autoparallelism with respect to
the e-parallel transport (\ref{alt-parallel}) must not be understood to be
a first-order differential equation on the QSS because of the appearance
of the initial tangent vector $(d\rho /dt)(0)$ in the rhs of (\ref{autoparallel})
that never takes place in first-order differential equations.
Hence the expression (\ref{autoparallel}) of the e-geodesics does not
contradict the second-order-differential-equation form taught in theory
of geodesics. According to Hayashi \cite{Hayashi}, the e-geodesic admits
the explicit representation below.
\begin{lemma}
\label{e-geod-exp}
The e-geodesic $\rho^{e} \left( t; \rho^{(0)} , X^{(0)} \right)$ with the initial conditions,
\begin{align}
\label{init-pos}
&
\rho^{e} \left( 0;\rho^{(0)}, X^{(0)} \right) = \rho^{(0)} \in Q_n
\\
\intertext{and}
&
\label{init-tan}
\frac{d\rho^{e}}{dt} \left( 0; \rho^{(0)},X^{(0)} \right)
= X^{(0)} \in T_{\rho^{(0)}} Q_n ,
\end{align}
takes the form
\begin{align}
\nonumber
\rho^{e} \left( t; \rho^{(0)}, X^{(0)} \right)
=
&
\left\{
\mathrm{Tr}\, \left( e^{\frac{t}{2}L_{\rho^{(0)}}(X^{(0)})} \rho^{(0)} \, e^{\frac{t}{2}L_{\rho^{(0)}}(X^{(0)})} \right)
\right\}^{-1}
\\
\label{e-geod}
&
\quad
\times
e^{\frac{t}{2}L_{\rho^{(0)}}(X^{(0)})} \rho^{(0)} \, e^{\frac{t}{2}L_{\rho^{(0)}}(X^{(0)})}
\end{align}
for $0 \leq t < \infty$, where $L_{\rho^{(0)}} \left( X^{(0)} \right)$
is the SLD, defined by (\ref{def-SLD}), on $X^{(0)} \in T_{\rho^{(0)}}Q_n$.
\end{lemma}
A direct differentiation of (\ref{e-geod}) by $t$ clearly shows that
$\rho^{e} (t;\rho^{(0)} , X^{(0)} )$ satisfies Eq.\ (\ref{autoparallel})
of the autoparallelism. Namely, we have
\begin{align}
\nonumber
&
\frac{d \rho^{e}}{dt} \left( t; \rho^{(0)},X^{(0)} \right)
\\
\nonumber
=
&
\frac{1}{2}
\left\{
\rho^{e} \left( t;\rho^{(0)},X^{(0)} \right)
L_{\rho^{(0)}} \left( X^{(0)} \right)
+
L_{\rho^{(0)}} \left( X^{(0)} \right)
\rho^{e} \left( t;\rho^{(0)}, X^{(0)} \right)
\right\}
\\
\label{e-geod-diff}
&
\quad
-\mathrm{Tr}\, \left(
L_{\rho^{(0)}}\left( X^{(0)} \right) \rho^{e} \left (t;\rho^{(0)},X^{(0)} \right) \right)
\, \rho^{e} \left( t;\rho^{(0)},X^{(0)} \right) .
\end{align}
We see that Eq.\ (\ref{e-geod-diff})
for any fixed e-geodesic looks quite similar to the EAHLE (\ref{EAHLE})
and therefore we may expect that every trajectory of
the EAHLE can be realized as an e-geodesic.
\section{The EAHLE trajectories as the e-geodesics}
Now that we have found the similarity of the EAHLE (\ref{EAHLE})
and Eq.\ (\ref{e-geod-diff}) for the e-geodesics, we show that
the trajectories of the EAHLE are the e-geodesics below.
Further, as an outcome of Theorem~\ref{main}, an explicit representation
of solution of the AHLE is derived from the representation (\ref{e-geod})
of the e-geodesics.
\par
On comparing very naively Eq.\ (\ref{EAHLE}) with
Eq.\ (\ref{e-geod-diff}), one might come to choose
$L_{\rho^{(0)} }( X^{(0)} )$ in (\ref{e-geod-diff}) to be equal to
$C$ in (\ref{EAHLE}).
However, this choice fails because the diagonal matrix $C$ never
belongs to $L_{\rho^{(0)}} (T_{\rho^{(0)}}Q_n )$
(see (\ref{SLD-Q_n}) with $\rho^{(0)}$ in place of $\rho$).
By choosing $L_{\rho^{(0)}}(X^{(0)})$ in (\ref{e-geod-diff}) suitably,
we have the following theorem to characterize all the trajectories
of the EAHLE as the e-geodesics.
\par
\begin{theorem}[Main Theorem]
\label{main}
For any fixed $\rho^{(0)} \in Q_n$,
let $\rho^{h} (t; \rho^{(0)})$ denote the trajectory of the EAHLE
subject to the initial condition
\begin{eqnarray}
\label{init-EAHLE}
\rho^h (0;\rho^{(0)})=\rho^{(0)} ,
\end{eqnarray}
and let $\rho^{e} (t; \rho^{(0)}, X^{(C)})$ denote
the e-geodesic $\rho^{e} (t; \rho^{(0)}, X^{(C)})$ subject to the initial conditions
\begin{align}
\label{init-e-geod-pos}
&
\rho^{e} (0; \rho^{(0)}, X^{(C)}) = \rho^{(0)}
\\
\intertext{and}
\label{init-e-geod-tan}
&
\frac{d\rho^{e}}{dt} (0; \rho^{(0)}, X^{(C)}) = X^{(C)}
\\
\intertext{with}
\label{XC}
&
X^{(C)}
=
\rho^{(0)} C + C \rho^{(0)} - 2\mathrm{Tr}\,(C \rho^{(0)}) \rho^{(0)} .
\end{align}
Then, for $t \geq 0$,
the trajectory $\rho^{h} (t; \rho^{(0)})$ of the EAHLE coincides with
the e-geodesic $\rho^{e} (t; \rho^{(0)}, X^{(C)})$.
\end{theorem}
\par\noindent
{\bf Proof}
\quad
From (\ref{init-EAHLE}) and (\ref{init-e-geod-pos}),
we easily confirm that $\rho^{h} (t; \rho^{(0)} )$ and
$\rho^{e} (t;\rho^{(0)}, X^{(C)})$ share $\rho^{(0)}$ as the initial point.
As a necessary condition for
$
\rho^{e} (t; \rho^{(0)} , X^{(C)}) = \rho^{h} (t; \rho^{(0)} )
$
,
we pose the coincidence
\begin{align}
\label{init-tan-coincidence}
&
\frac{d\rho^{e}}{dt}(0; \rho^{(0)} , X^{(C)})
=
\frac{d\rho^{h}}{dt}(0; \rho^{(0)} )
\end{align}
of the initial tangent vectors,
which is equivalent to the pair of equations, (\ref{init-e-geod-tan}) and (\ref{XC}).
Hence, what we have to show here is that the pair,
(\ref{init-e-geod-tan}) and (\ref{XC}), is also a sufficient condition for
$
\rho^{e} (t; \rho^{(0)} , X^{(C)}) = \rho^{h} (t; \rho^{(0)} )
$
.
Through the proof, we often apply the abbreviation $\rho^e$ to
$\rho^e(t:\rho^{(0)} , X^{(C)} )$.
The core part of the proof is given in what follows in a straightforward
calculation form with the notation
\begin{align}
\label{init-diag}
&
h^{\dagger} \rho^{(0)} h
=
\Theta^{(0)}
=
\mathrm{diag} \, (\theta^{(0)}_1 , \theta^{(0)}_2 , \cdots , \theta^{(0)}_n)
\quad
(h \in U(n))
\\
\intertext{and}
\label{notation}
&
\widetilde{X}^{(C)} = h^{\dagger} X^{(C)} h , \quad
\widetilde{L}^{(0)} = h^{\dagger} L_{\rho^{(0)}}(X^{(C)}) h , \quad
\widetilde{C} = h^{\dagger} C h , \quad
R= h^{\dagger} \rho^e h .
\end{align}
\noindent
We note here that $\widetilde{C}$ and $R$ are non-diagonal in general
and that $R$ is of unit trace.
With the notation given above,
the matrix-element display of $\widetilde{X}^{(C)}$ takes the form
\begin{align}
\nonumber
\widetilde{X} ^{(C)} _{jk}
&=
\left(
h^{\dagger} \{ \rho^{(0)} C + C \rho^{(0)} - 2\, \mathrm{Tr}\, (C\rho^{(0)}) \rho^{(0)} \}h
\right)_{jk}
\\
\nonumber
&=
\left(
\Theta^{(0)} \widetilde{C} + \widetilde{C} \Theta^{(0)}
-
2\, \mathrm{Tr}\, (\widetilde{C} \Theta^{(0)} ) \Theta^{(0)} \right)_{jk}
\\
\label{X^C_jk}
&=
\theta^{(0)} _j \widetilde{C}_{jk} + \widetilde{C}_{jk} \theta^{(0)} _k
- 2 \, \mathrm{Tr}\, (\widetilde{C} \Theta^{(0)} ) \delta_{jk} \theta^{(0)} _k
\quad
(j,k=1,2,\cdots,n) ,
\end{align}
where the symbol $\delta_{jk}$ indicates Kronecker's delta
($j,k=1,2,\cdots ,n$).
Equation (\ref{X^C_jk}) is combined with (\ref{alt-SLD}) to yield
the matrix-element display
\begin{align}
\label{tilde-L_jk}
\widetilde{L}^{(0)} _{jk}
=
2 \widetilde{C}_{jk}
-
\left(
\frac{4}{\theta^{(0)} _j + \theta^{(0)} _k}
\right)
\,
\mathrm{Tr}\, \left( \widetilde{C} \Theta^{(0)} \right) \delta_{jk} \theta^{(0)} _k
\quad
(j,k=1,2,\cdots,n)
\end{align}
for $\widetilde{L}^{(0)}$.
\par
We are now in a position to calculate the rhs of (\ref{e-geod-diff})
with $X^{(0)} = X^{(C)}$ and (\ref{XC}).
Putting Eqs.\ (\ref{init-diag}), (\ref{notation}) and (\ref{tilde-L_jk})
together with the abbreviation $\rho^e$ for $\rho^{e} (t; \rho^{(0)}, X^{(C)})$,
we have
\begin{align}
\nonumber
&
\left(
h^{\dagger}
\left\{
\frac{1}{2}
\left(
\rho^e L_{\rho^{(0)}} \left( X^{(C)} \right) + L_{\rho^{(0)}}\left( X^{(C)} \right) \rho^e
\right)
- \mathrm{Tr}\, \left( L_{\rho^{(0)}}(X^{(C)}) \rho^e \right) \rho^e
\right\} h
\right)_{jk}
\\
\nonumber
=
&
\left(
\frac{1}{2}
\left(
R \widetilde{L}^{(0)} + \widetilde{L}^{(0)} R
\right)
- \mathrm{Tr}\, \left( \widetilde{L}^{(0)} R \right) R
\right)_{jk}
\\
\nonumber
=
&
\frac{1}{2} \sum_{m=1}^n
\left\{
\left( R_{jm} \widetilde{L}^{(0)} _{mk} + \widetilde{L}^{(0)} _{jm} R_{mk} \right)
- 2 \mathrm{Tr}\, (\widetilde{L}^{(0)} R) R_{jk} \right\}
\\
\nonumber
=
&
\sum_{m=1}^n
R_{jm}
\left\{
\widetilde{C}_{mk} - \left( \frac{2 }{\theta^{(0)}_m + \theta^{(0)}_k} \right)
\mathrm{Tr}\, \left( \widetilde{C}\Theta^{(0)} \right) \delta_{mk} \theta^{(0)}_k
\right\}
\\
\nonumber
&
\qquad
-
\sum_{m=1}^n
\left\{
\widetilde{C}_{jm} - \left( \frac{2}{\theta^{(0)}_j + \theta^{(0)}_m} \right)
\mathrm{Tr}\, \left( \widetilde{C}\Theta^{(0)} \right) \delta_{jm} \theta^{(0)}_m \right\}
R_{mk}
\\
\nonumber
&
\qquad \qquad
-
2
\left[
\sum_{m,l=1}^{n}
\left\{
\widetilde{C}_{lm}
- \left( \frac{2}{\theta^{(0)}_l + \theta^{(0)}_m} \right) \mathrm{Tr}\, \left( \widetilde{C}\Theta^{(0)} \right)
\delta_{lm} \theta^{(0)}_m \right\} R_{ml}
\right]
R_{jk}
\\
\noalign{\bigskip}
\nonumber
=
&
\sum_{m=1}^{n}
\left( R_{jm}\widetilde{C}_{mk} + \widetilde{C}_{jm}R_{mk} \right)
-2 \mathrm{Tr}\, \left( \widetilde{C}\Theta^{(0)} \right) R_{jk}
\\
\nonumber
&
\qquad
-2 \left( \sum_{m,l=1}^n \widetilde{C}_{lm}R_{ml} \right) R_{jk}
+ 2 \mathrm{Tr}\, \left( \widetilde{C}\Theta^{(0)} \right) \left( \sum_{m=1}^n R_{mm} \right) R_{jk}
\\
\nonumber
=
&
\left( R \widetilde{C} + \widetilde{C}R \right)_{jk} - 2 \mathrm{Tr}\, \left( \widetilde{C}R \right) R_{jk}
\\
\label{rhs-e-geod-diff}
=
&
\left(
h^{\dagger}
\left\{ \rho^e C + \rho^e C - 2\mathrm{Tr}\, (C\rho^e) \rho^e \right\}
h
\right)_{jk} .
\end{align}
Equation (\ref{rhs-e-geod-diff}) is put together with
Eq.\ (\ref{e-geod-diff}) to show that $\rho^e(t:\rho^{(0)} , X^{(C)} )$
satisfies the equation
\begin{align}
\nonumber
\frac{d\rho^{e}}{dt}(t:\rho^{(0)} , X^{(C)} )
=
&
\rho^{e} \left( t:\rho^{(0)} , X^{(C)} \right) C
+
C \rho^{e} \left( t:\rho^{(0)} , X^{(C)} \right)
\\
\label{e-geod-EAHLE}
&
\quad
-2\mathrm{Tr}\, (C \rho^e(t:\rho^{(0)} , X^{(C)} )) \rho^e(t:\rho^{(0)} , X^{(C)} ) .
\end{align}
which turns out to be the same as Eq.\ (\ref{EAHLE}) with
$\rho^{e} (t;\rho^{(0)},X^{(C)})$ in place of $\rho$. Put in another way,
the e-geodesic $\rho^{e} (t;\rho^{(0)}, X^{(C)})$ satisfies the
EAHLE (\ref{EAHLE}) with the initial condition $\rho (0)=\rho^{(0)}$
and accordingly $\rho^{e} (t;\rho^{(0)}, X^{(C)})$ coincides with
$\rho^{h} (t;\rho^{(0)})$.
This completes the proof.
\par\medskip
Combining Lemma~\ref{AHLE-EAHLE}, Lemma~\ref{e-geod-exp} and
Theorem~\ref{main} together, we can give an explicit representation of
solution of the averaged Hebbian learning equation (AHLE) from
the representation, (\ref{e-geod}), of the e-geodesics.
Although it is pointed out in Nakamura \cite{N1} that the representation
of solution of the AHLE is available from that of the Toda lattice in Moser's
form \cite{Moser,MZ} (see also Lemma~\ref{AHLE-EAHLE}),
we are to present the same one as in \cite{N1} because our derivation
process below is new.
\par
On recalling Lemma~\ref{AHLE-EAHLE}, the representation of solution
of the AHLE can be given by calculating explicitly the Eq.\ (\ref{e-geod})
with the initial conditions,
\begin{align}
\label{init-diag-pos}
&
\rho^{e} (0) = \rho^{(0)} = \Theta^{(0)}
= \mathrm{diag} \,
\left(\theta^{(0)}_1 , \theta^{(0)}_2 , \cdots , \theta^{(0)}_n \right) \in D_n \subset Q_n
\\
\intertext{and}
\label{init-diag-velocity}
&
\frac{d\rho^{e}}{dt}(0)
=
X^{(0)}
=
\Xi^{(C)}
=
\mathrm{diag} \, \left( \xi^{(0)}_1 , \xi^{(0)}_2 , \cdots , \xi^{(0)}_n \right) \in T_{\Theta^{(0)}}D_n
\subset T_{\Theta^{(0)}}Q_n
\\
\intertext{with}
\label{xiz}
&
\xi^{(0)}_j
=
2c_j \theta^{(0)}_j -2 \mathrm{Tr} \, \left( C\Theta^{(0)} \right) \, \theta^{(0)}_j
\qquad
(j=1,2,\cdots,n),
\end{align}
where $C$ is the diagonal matrix governing both the EAHLE (\ref{EAHLE})
and the AHLE (\ref{AHLE}).
Under (\ref{init-diag-pos})-(\ref{xiz}), the SLD of $\Xi^{(C)}$ and its exponential
are calculated to be
\begin{align}
\label{SLD-Xc-diag}
&
L_{\Theta^{(0)}}\left( \Xi^{(C)} \right)
=
\mathrm{diag} \,
\left(
\frac{\xi^{(0)}_1}{\theta^{(0)}_1}, \frac{\xi^{(0)}_2}{\theta^{(0)}_2}, \cdots ,
\frac{\xi^{(0)}_n}{\theta^{(0)}_n}
\right)
=
2C- 2 \mathrm{Tr} \, \left( C\Theta^{(0)} \right) I
\\
\intertext{and}
&
\label{exp-Thetaz}
e^{\frac{t}{2}L_{\Theta^{(0)}} \left( \Xi^{(C)} \right)}
=
e^{-t \, \mathrm{Tr} \, \left( C\Theta^{(0)} \right)} \,
\mathrm{diag} \,
\left(
e^{tc_1}, e^{tc_2}, \cdots , e^{tc_n}
\right) .
\end{align}
Hence it follows from Lemma~\ref{e-geod-exp} and Theorem~\ref{main}
that the trajectory on $D_n$, denoted by $\Theta^h (t)$,
of the EAHLE with the initial condition (\ref{init-diag-pos}) takes the form
\begin{align}
\label{EAHLE-diag-1}
&
\Theta^h (t)
=
\mathrm{diag} \, \left( \theta^h_1(t), \theta^h_2(t), \cdots , \theta^h_n(t) \right)
\\
\intertext{with}
&
\label{EAHLE-diag-2}
\theta^h_j (t)
=
\left( \sum_{k=1}^n e^{2tc_k}\theta^{(0)}_k \right)^{-1}
e^{2tc_1}\theta^{(0)}_j
\quad
(j=1,2,\cdots,n) .
\end{align}
We note here that Eqs.\ (\ref{EAHLE-diag-1})
and (\ref{EAHLE-diag-2}) reproduce the solution of the Toda lattice
in Moser's form \cite{Moser,MZ} in view of Lemma~\ref{AHLE-EAHLE}.
Applying the map $p_{n,\sigma}^{-1}$ defined by
(\ref{p_n_sigma_inv}) to $\Theta^h (t)$, we have
\begin{align}
\nonumber
w_{\sigma}^h(t)
&=
p_{n,\sigma}^{-1}(\Theta^h(t))
\\
\nonumber
&
=
\left( \sum_{k=1}^n e^{2tc_k} \theta^{(0)}_k \right)^{-1/2}
\left(
e^{tc_1}\sigma_1 \sqrt{\theta^{(0)}_1},
e^{tc_2}\sigma_2 \sqrt{\theta^{(0)}_2},
\cdots ,
e^{tc_n}\sigma_n \sqrt{\theta^{(0)}_n}
\right)^T
\\
\label{inv-Theta}
& \qquad
\left( \sigma=(\sigma_j), \, \sigma_j =\pm 1 , \, j=1,2,\cdots ,n \right)
\end{align}
which realizes the solutions of the AHLE on the open-dense subset
$\cup_{\sigma} S^{n-1}_{\sigma}$ of $S^{n-1}$
(see (\ref{S_sigma}) for $S^{n-1}_{\sigma}$).
Thus we have the following corollary to Theorem~\ref{main}.
\begin{corollary}
\label{AHLE-sol}
The solution of the averaged Hebbian learning equation (\ref{AHLE}) subject
to the initial condition $w(0)=(w^{(0)}_1,w^{(0)}_2,\cdots,w^{(0)}_n)^T \in S^{n-1}$
is given by
\begin{align}
\label{wh1}
&
w^h(t)=
\left( \sum_{k=1}^n e^{2tc_k} \left( w^{(0)}_k \right)^2 \right)^{-1/2}
\left(
e^{tc_1}w^{(0)}_1, e^{tc_2}w^{(0)}_j, \cdots , e^{tc_n}w^{(0)}_n
\right)^T .
\end{align}
\end{corollary}
\section{Conclusions}
We show in Theorem~\ref{main}
that all the trajectories of the extended averaged
Hebbian learning equation (EAHLE) on the QSS are the e-geodesics
on the QSS. As a direct application of Theorem~\ref{main},
the explicit representation, (\ref{wh1}), of solution of the averaged
Hebbian learning equation (AHLE), the departure equation
of the EAHLE, is derived from the representation, (\ref{e-geod}),
of the e-geodesics.
Although the expression (\ref{wh1}) is known already to be
available from the Toda lattice in Moser's form due to the
equivalence between the AHLE and the Moser's form \cite{N1},
our derivation in Sec.4 is worth given because it is made from a novel
point of view, a quantum-information-geometric point of view.
\par
We would like to offer a remark on Theorem~\ref{main} from a
geometric-mechanics point of view: In view of the gradient-system
structure of the EAHLE revealed in Uwano and Yuya \cite{UY1},
Theorem~\ref{main} is understood to provide a gradient system
whose trajectories are the e-geodesics. Further, since the e-geodesics
are known to play an important role in quantum estimation \cite{Hayashi},
the EAHLE is expected to be a new candidate of gradient
systems dealt with in Braunstein \cite{Br} for quantum estimation.
Another remark is offered from an integrable-systems point of view:
The EAHLE would be looked on as an extended Toda lattice in Moser's form:
This view is supported from the coincidence given in Lemma~\ref{AHLE-EAHLE}
between the EAHLE restricted on $D_n$ and the Moser's form.
\par
On closing this paper, the author would like to make the following conjecture
on the e-geodesics which do not satisfy the initial conditions,
(\ref{init-e-geod-tan}) and (\ref{XC}), attached to the initial tangent vector.
\par\medskip\noindent
{\bf Conjecture}\,\,
{\it
All the e-geodesics on the QSS are realized as the EAHLE
trajectories up to the adjoint $SU(n)$ actions on the QSS and
the affine transformations of time.
}
\par\medskip\noindent
The conjecture will be investigated soon together with the dynamics on
the QSS described by the EAHLE.
\par\bigskip\noindent
{\bf Acknowlegement}\,\,
The author thanks Professor Yoshimasa Nakamura
at Kyoto University for his valuable remark on the paper \cite{N1}
and his suggestion to include our derivation of the AHLE solution
(Corollary~\ref{AHLE-sol}) in the present paper.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 7,684 |
WWDC 2012 Highlights
Written by Geoff Bender on June 12, 2012
The year's Apple Worldwide Developer's Conference (WWDC) kicked off in San Francisco on Monday. As usual, Apple introduced some new hardware and software to whet the appetites of both consumers and developers alike. Aside from announcing a new design for the MacBook Pro with a lovely new retina display and the re-introduction of the upcoming version of the Mac desktop operating system OS X Mountain Lion, Apple (predictably) announced the next version of its mobile operating system, iOS 6. Ever since the first iPhone was released back in 2007, Apple has used the WWDC as an opportunity to introduce new operating systems for its mobile devices. This year's conference was no exception. Over 200 new features are expected in iOS 6. Below is not only an overview of the highlights from the event, but what these announcements mean for iOS developers.
iOS Adoption Rate
Scott Forstall, Apple's senior vice president of iOS software, began his presentation by showing a pie chart of the iOS adoption rate by users of various platforms. iOS 5 has a higher than 80% adoption rate, which is quite high compared to users of other platforms. As a developer I am always concerned with how many users are still running older versions of the iOS operating system. This iOS adoption rate can greatly affect development decisions. For instance, as old methods become deprecated and new features continue to emerge, I try to integrate these features into my apps. Seeing such a high rate of adoption means I can rest assured knowing that I can reach a majority of my target audience if I keep my apps current with the latest technologies.
Siri Enhancements
Siri was introduced in iOS 5 as a voice-controlled personal assistant for iPhone 4S users. With iOS 6, this feature will now be compatible with the iPad 3. While developers cannot currently access Siri capability from their apps, an interesting feature in iOS 6 is the ability to launch apps by voice command. This seems to be a built-in feature and shouldn't require any changes to an application by a developer. Forstall also briefly mentioned a new "eyes free" feature that Apple is working on with automobile manufacturers. This feature would allow integration of Siri into steering wheel controls, allowing drivers to use the assistant without having to touch or look at the device. This feature would be great for launching apps or getting audible information, but it remains to be seen how Siri might access certain features within an app once it has been launched. Perhaps in the future Apple will give developers access to a Siri API so we will be able to interact with our apps by voice command. So far nothing of this sort has been announced.
iOS 5 introduced Twitter integration. This meant developers had access to a new API that allowed them to easily access Twitter account data and post tweets from within an app using action sheets. This greatly simplified the process of adding social media integration into applications. With iOS 6, Apple does the same thing with Facebook, which has been a highly requested feature. Now developers can access Facebook account information from the system settings and use this account information to post Facebook updates from within their applications. The process uses the same action sheets that Twitter uses. iOS 6 allows Facebook users to post from the notifications page, have their contacts appear in the Contacts app, and sync their events and birthdays in the Calendar app. There is no word yet on whether developers will be able to access shared Facebook contact and event data for use in their own apps. Still, the simple ability to contextually post to Facebook from within your own app is a big deal to a lot of developers and potential clients. According to Apple, the addition of Twitter to iOS 5 tripled the amount of twitter usage. We can expect this integration to do the same, if not more, for Facebook.
Mobile Safari
Many new features will be available in the mobile version of Safari. Most don't affect developers directly, but one feature was listed that may apply. Users will now be able to upload pictures and video from their mobile device to web pages directly in Safari without leaving the app. If you're a mobile web developer, this may be of interest to you since it required workarounds in the past that were difficult enough to cause native development consideration. This capability appears to be built into iOS 6 and may not require anything more than a file upload field in your mobile web application. When the user clicks the file upload field, a popover shows your camera roll so you can choose a file for upload. Another interesting feature is something called Smart Banners. If a user goes to a mobile version of your website and you have a native app, you can alert them to the fact that you have a native app available with a banner at the top of your mobile web site. This banner would replace the intrusive alert message that we've all grown accustomed to. The banner would have a link to your app on the app store, and if your native app is already installed on the device, the user can click the banner to automatically switch over to it. In addition, the web app communicates with the native app so the user will immediately pick up where they left off after the switch.
The Passbook App
Apple is introducing a new app in iOS 6 called Passbook. It acts as a central repository for all sorts of passes including movie tickets, boarding passes, store cards with balances and store coupons. If you develop these sorts of applications (think mobile payments at coffee shops or electronic airline boarding passes) you will be able to store items in the Passbook app and take advantage of time and location-based services. If a user arrives at an airport or walks near a coffee shop, an alert will appear on the user's lock screen. By swiping the alert, the user will be taken to the appropriate pass in the Passbook for immediate use. Information such as account balances and boarding times can also be updated in real-time through the Passbook app.
Apple has completely redone maps within iOS 6. Google maps are gone and everything is being done in-house with new cartography and worldwide coverage. Apple has ingested 100 million business listings worldwide and is working hard to make meaningful local searches available globally. Search results have new detail views with Yelp integration for reviews. New 3D views, flyover views and free turn-by-turn navigation are now options in the maps application. However, to use these more advanced features you'll need a newer device. Developers will be able to tap into these features with the new Map Kit API. What we don't know yet, however, is how much has changed or been added to the Map Kit API. We hope that it will remain backward compatible with older devices and previous iOS versions. Much testing will be done over the coming months to make sure both mapping solutions are supported within our apps.
Lots of new things are on the horizon with iOS 6 and these are only some of the highlights. Personally, I believe Facebook integration is going to be the most useful because we have many clients who have been asking for that feature specifically. Pass Kit certainly opens up some possibilities for exploring new types of application design and the new maps are going to be a really big deal for many. I would say the biggest challenge moving forward will be having to decide which devices and operating systems to support. At some point you have to cut ties with the past in order to keep progressing and nobody likes to alienate their users. We'll see if the high iOS adoption rate continues as it has in the past.
iOS 6 currently plans to support iPhone 3GS and higher, iPad 2, 3, and the 4th generation iPod touch. However only the iPhone 4S and iPad 3 will be able to take advantage of Siri and some of the new mapping features. The first generation iPad isn't supported at all in iOS 6, so be prepared to support multiple iOS versions for the foreseeable future.
Facebook Integration, WWDC, iOS 6, mobile application development
Geoff Bender began his programming career as a ColdFusion developer back in 2000 by writing and maintaining distance learning web applications for VCampus Corporation. He worked as a contractor to the General Services Administration (GSA) from 2001-2005 and redesigned several websites for the Chief Financial Officers Council, Chief Information Officers Council, and several other executive agencies for which he received recognition from the Executive Office of the President. From 2005-2007 he created energy analysis software for Pace Global Energy Services and Gazprom. Since 2007 he has worked as a senior ColdFusion developer for Segue Technologies on the Unites States Air Force's MPES project and has doubled as Segue's lead mobile developer for Apple's iOS platform. Read more from Geoff Bender
How Will the iPhone 5's Larger Screen Affect Developers?
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A Reaction to "The Negative Impact Of iOS On Android"
Google I/O 2013: Day 2 Recap
Download Segue's New eBook "The Impact of Mobile: Strategies and Considerations for Your Business"
KHIMA 2012
Make the Most of a Technical Job Fair | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 3,338 |
\section{Introduction}
Since the experimental confirmation of the theory of general relativity
\cite{GR} succeeded in 1919 \cite{Eddington},
a lot of calculations of the gravitational bending of light
have been done not only for black holes
\cite{Hagihara, Ch, MTW, Darwin, Bozza, Iyer, Bozza+, Frittelli, VE2000, Virbhadra, VNC, VE2002, VK2008, Zschocke}
but also for other objects such as wormholes and gravitational monopoles
\cite{ERT, Perlick, Abe, Toki, Nakajima, Gibbons, DA, Kitamura,Tsukamoto,Izumi,Kitamura2014,Nakajima2014,Tsukamoto2014}
Gibbons and Werner (2008) proposed an alternative way of deriving
the deflection angle of light \cite{GW2008}.
They assumed that the source and receiver are located
at an asymptotic Minkowskian region and they used the Gauss-Bonnet theorem
to a spatial domain described by the optical metric,
for which a light ray is described as a spatial curve.
Ishihara et al. have recently extended Gibbons and Werner's idea
in order to investigate
finite-distance corrections
in the small deflection case
(corresponding to a large impact parameter case)
\cite{Ishihara2016}
and also in the strong deflection limit
for which the photon orbits may have the winding number
larger than unity \cite{Ishihara2017}.
In particular, the asymptotic receiver and source
have not been assumed.
However, the earlier treatments \cite{Ishihara2016, Ishihara2017}
are limited within the spherical symmetry.
It is not clear whether the Gauss-Bonnet method with using the optical metric
can be extended to axisymmetric cases or not.
This is mostly because there can exist
off-diagonal (time-space) components of the spacetime metric
in an axisymmetric spacetime.
The time-space components
seem to make it unclear whether the optical metric can be constructed.
After the gravitational lensing by a spinning object
\cite{ES, Ibanez, AK}
and that by a relativistic binary \cite{Kopeikin}
were discussed extensively by perturbative approaches such as
the post-Newtonian approximation,
Werner (2012) \cite{Werner2012} proposed the use of the
Kerr-Randers optical geometry on this issue
\cite{Kerr-bending}.
To be more precise, he used the osculating Riemann approach
in Finsler geometry
in order to discuss the lensing by the Kerr black hole,
for which the metric can be written in the Randers form.
However, this approach requires that
the endpoints (namely, the source and the receiver)
of the photon orbit are in Euclidean space,
for which angles can be easily defined.
This requirement is mainly because
jump angles at the vertices in the Gauss-Bonnet theorem
are problematic in the Finsler geometry.
Namely, it is unlikely that the Finsler geometry
can be used for computing the finite-distance corrections.
Therefore, the main purpose of the present paper is
to extend the earlier formulation in Refs. \cite{Ishihara2016, Ishihara2017},
especially in order to examine finite-distance corrections to
the deflection angle of light in the axisymmetric spacetime,
for which the gravitational deflection of light
may include gravitomagnetic effects
(e.g. \cite{ES, Ibanez, AK, Kopeikin}).
The geometrical setups in the present paper are not
those in the optical geometry,
in the sense that the photon orbit has a non-vanishing
geodesic curvature,
though the light ray in the four-dimensional spacetime
obeys a null geodesic.
This paper is organized as follows.
Section II discusses a possible extension
to stationary and axisymmetric spacetimes.
In particular, it is shown that
the proposed definition of the deflection angle
is coordinate-invariant by using the Gauss-Bonnet theorem.
Section III uses the Kerr metric as a known example of
the stationary and axisymmetric spacetimes
in order to discuss how to compute
the gravitational deflection angle of light
by the proposed method.
Section IV is devoted to conclusion.
In Appendix A, the deflection angle of light is computed
at the second order of the mass and the spin parameter
in order to examine whether
the deflection angle is in agreement with the known one.
Throughout this paper, we use the unit of $G=c=1$,
and the observer may be called the receiver
in order to avoid a confusion between $r_O$ and $r_0$ by using $r_R$.
\section{Extension to axisymmetric spacetimes}
Henceforth, we assume a stationary and axisymmetric spacetime,
for which we shall define the gravitational deflection angle of light
by using the Gauss-Bonnet theorem:
Suppose that
$T$ is a two-dimensional orientable surface with boundaries $\partial T_a$
($a=1, 2, \cdots, N$) that
are differentiable curves.
See Figure \ref{fig-GB}.
Let the jump angles between the curves be $\theta_a$
($a=1, 2, \cdots, N$).
Then, the Gauss-Bonnet theorem can be expressed as
\cite{GB-theorem}
\begin{eqnarray}
\iint_{T} K dS + \sum_{a=1}^N \int_{\partial T_a} \kappa_g d\ell +
\sum_{a=1}^N \theta_a = 2\pi ,
\label{localGB}
\end{eqnarray}
where
$K$ denotes the Gaussian curvature of
the surface $T$,
$dS$ is the area element of the surface,
$\kappa_g$ means the geodesic curvature of $\partial T_a$,
and $\ell$ is the line element along the boundary.
The sign of the line element is chosen such that it is
compatible with the orientation of the surface.
\subsection{Stationary, axisymmetric spacetime}
We consider a stationary axisymmetric spacetime.
The line element for this spacetime is \cite{Lewis,LR,Papapetrou}
\begin{align}
ds^2=&g_{\mu\nu}dx^{\mu}dx^{\nu} \notag\\
=&-A(y^p,y^q)dt^2-2H(y^p,y^q)dtd\phi \notag\\
&+F(y^p,y^q)(\gamma_{pq}dy^pdy^q)+D(y^p,y^q)d\phi^2 ,
\label{ds2-general}
\end{align}
where $\mu, \nu$ run from $0$ to $3$,
$p, q$ take $1$ and $2$,
$t$ and $\phi$ coordinates are associated with the Killing vectors,
and $\gamma_{pq}$ is a two-dimensional symmetric tensor.
It is more convenient to
reexpress this metric into
a form in which $\gamma_{pq}$ is diagonalized.
The present paper prefers the polar coordinates
rather than the cylindrical ones,
because
the Kerr metric in the polar coordinates is considered in Section III.
In the polar coordinates,
Eq. (\ref{ds2-general}) becomes \cite{Metric}
\begin{align}
ds^2=&-A(r,\theta)dt^2-2H(r,\theta)dtd\phi \notag\\
&+B(r,\theta)dr^2+C(r,\theta)d\theta^2+D(r,\theta)d\phi^2 .
\label{ds2-axial}
\end{align}
The null condition $ds^2 = 0$ is solved for $dt$ as \cite{AK}
\begin{align}
dt=& \sqrt{\gamma_{ij} dx^i dx^j} +\beta_i dx^i ,
\label{opt}
\end{align}
where
$i, j$ run from $1$ to $3$,
$\gamma_{ij}$ and $\beta_i$ are defined as
\begin{align}
\gamma_{ij}dx^idx^j \equiv&
\frac{B(r,\theta)}{A(r,\theta)}dr^2
+\frac{C(r,\theta)}{A(r,\theta)}d\theta^2
+\frac{A(r,\theta)D(r,\theta)+H^2(r,\theta)}{A^2(r,\theta)}d\phi^2 ,
\label{gamma}
\\
\beta_idx^i \equiv& -\frac{H(r,\theta)}{A(r,\theta)} d\phi .
\label{beta}
\end{align}
This spatial metric $\gamma_{ij} (\neq g_{ij})$
may define the arc length ($\ell$) along the light ray as
\begin{align}
d\ell^2 \equiv \gamma_{ij} dx^i dx^j ,
\end{align}
for which
$\gamma^{ij}$ is defined by
$\gamma^{ij}\gamma_{jk} = \delta^i_{~k}$.
Note that $\ell$ defined in this way is an affine parameter
along the light ray.
See e.g. Appendix of Ref. \cite{AK} for the proof on the affine parameter
\cite{comment-gamma}.
$\gamma_{ij}$ defines a 3-dimensional Riemannian space ${}^{(3)}M$
in which
the motion of the photon is described as a motion in a spatial curve.
The unit tangential vector along the spatial curve
is defined as
\begin{align}
e^i \equiv \frac{dx^i}{d\ell} .
\end{align}
The light ray
follows the Fermat's principle \cite{Perlick}.
By using the variational principle,
this gives the equation for the light ray as \cite{AK}
\begin{align}
e^i_{~|k}e^k=a^i ,
\label{EL}
\end{align}
where
$|$ denotes the covariant derivative with $\gamma_{ij}$
and
$a^i$ is defined as
\begin{align}
a^i \equiv
\gamma^{ij}(\beta_{k|j}-\beta_{j|k})e^k .
\label{ai}
\end{align}
Here,
\begin{align}
e^i_{~|k} e^k = \frac{de^i}{d\ell}+{}^{(3)}\Gamma^i_{~jk}e^je^k ,
\end{align}
where
${}^{(3)}\Gamma^i_{~jk}$ denotes the Christoffel symbol
associated with $\gamma_{ij}$.
The vector $a^i$ is the spatial vector that means the acceleration
originated from $\beta_i$.
In particular, $a^i$ is caused in gravitomagnetism
as discussed below in more detail.
This has an analogy as the acceleration by the Lorentz force
$\propto \vec{v} \times (\vec{\nabla} \times \vec{A}_m$)
in electromagnetism,
where $\vec{A}_m$ denotes the magnetic vector potential.
We should note that $\gamma_{ij}$ is not an induced metric.
As a result, the photon orbit
can deviate from a geodesic in ${}^{(3)}M$ with $\gamma_{ij}$
if $\beta_i \neq 0$,
even though the light ray in the four-dimensional spacetime
follows the null geodesic.
For a stationary and spherically symmetric spacetime,
one can always find a set of suitable coordinates
such that $g_{0i}$ can vanish to lead to $a^i = 0$.
In this case, the photon orbit
becomes a spatial geodesic curve in ${}^{(3)}M$.
The present paper discusses an extension to axisymmetric
cases, which allow $g_{0i} \neq 0$.
Therefore, we have to take account of non-zero $\kappa_g$
along the photon orbit in the Gauss-Bonnet theorem.
This non-vanishing $\kappa_g$ of the photon orbit
makes a crucial difference from the previous papers
\cite{Ishihara2016,Ishihara2017}
\subsection{Geodesic curvature and equatorial plane}
Let us imagine a parameterized curve in a surface.
The geodesic curvature of the parameterized curve
is the surface-tangential component
of acceleration (namely curvature) of the curve,
while the normal curvature is the surface-normal component.
The normal curvature has nothing to do with the present paper.
The geodesic curvature can be defined in the vector form as
(e.g. \cite{Math})
\begin{align}
\kappa_g \equiv \vec{T}^{\prime} \cdot \left(\vec{T} \times \vec{N}\right) ,
\label{kappag-vector}
\end{align}
where we assume a parameterized curve with a parameter,
$\vec{T}$ is the unit tangent vector for the curve
by reparameterizing the curve using its arc length,
$\vec{T}^{\prime}$ is its derivative with respect to the parameter,
and $\vec{N}$ is the unit normal vector for the surface.
In this paper,
Eq. (\ref{kappag-vector}) can be rewritten in the tensor form as
\begin{align}
\kappa_g = \epsilon_{ijk} N^i a^j e^k ,
\label{kappag-tensor}
\end{align}
where $\vec{T}$ and $\vec{T}^{\prime}$ correspond to
$e^k$ and $a^j$, respectively.
Here, the Levi-Civita tensor
$\epsilon_{ijk}$ is defined by
$\epsilon_{ijk} \equiv \sqrt{\gamma}\varepsilon_{ijk}$,
where
$\gamma \equiv \det{(\gamma_{ij})}$,
and $\varepsilon_{ijk}$ is the Levi-Civita symbol
($\varepsilon_{123} = 1$).
In the present paper, the space is ${}^{(3)}M$.
Therefore, we use $\gamma_{ij}$ in the above definitions
but not $g_{ij}$.
For a case of $a^i \neq 0$ due to $g_{0i}$,
there can exist a non-vanishing integral
of the geodesic curvature along the light ray
in the Gauss-Bonnet theorem by Eq. (\ref{localGB}).
By substituting Eq. (\ref{ai}) into $a^i$ in Eq. (\ref{kappag-tensor}),
we obtain
\begin{align}
\kappa_g = - \epsilon^{ijk} N_i \beta_{j|k} ,
\label{kappag-tensor2}
\end{align}
where we use $\gamma_{ij}e^ie^j = 1$.
Up to this point, the surface in ${}^{(3)}M$ is not specified.
Henceforth, we focus on the equatorial motion of the photon.
We choose $\theta = \pi/2$ as the equatorial plane.
Then, the unit normal vector
for the equatorial plane can be expressed as
\begin{align}
N_p = \frac{1}{\sqrt{\gamma^{\theta\theta}}} \delta_p^{\theta} ,
\label{N}
\end{align}
where we choose the upward direction without loss of generality.
For the equatorial case, one can show
\begin{align}
\epsilon^{\theta p q} \beta_{q|p}
&=-\frac{1}{\sqrt{\gamma}}\beta_{\phi,r} ,
\label{rot-beta}
\end{align}
where the comma denotes the partial derivative,
we use $\epsilon^{\theta r \phi} = - 1/\sqrt{\gamma}$
and
we note $\beta_{r,\phi} = 0$ owing to the axisymmetry.
By using Eqs. (\ref{N}) and (\ref{rot-beta}),
an explicit form of $\kappa_g$ in
Eq. (\ref{kappag-tensor2}) is obtained as
\begin{align}
\kappa_g=-\frac{1}{\sqrt{\gamma\gamma^{\theta\theta}}} \beta_{\phi,r} .
\label{kappag-final}
\end{align}
\subsection{Impact parameter and the photon directions
at the receiver and source}
We study the orbit equation on the equatorial plane
with Eq. (\ref{ds2-axial}).
Associated with the two Killing vectors,
there are the two constants of motion as
\begin{align}
E&=A(r)\dot{t}+H(r)\dot{\phi} ,
\label{EEE}
\\
L&=D(r)\dot{\phi}-H(r)\dot{t} ,
\label{L}
\end{align}
where the dot denotes the derivative with respect to the affine parameter.
As usual, we define the impact parameter as
\begin{align}
b &\equiv \frac{L}{E}
\notag\\
&=\frac{-H(r)\dot{t}+D(r)\dot{\phi}}{A(r)\dot{t}+H(r)\dot{\phi}}
\notag\\
&=\cfrac{-H(r)+D(r)\cfrac{d\phi}{dt}}{A(r)+H(r)\cfrac{d\phi}{dt}} .
\label{b}
\end{align}
In terms of the impact parameter $b$,
$ds^2=0$ leads to the orbit equation on the equatorial plane as
\begin{align}
\left(\frac{dr}{d\phi}\right)^2
=\frac{A(r)D(r)+H^2(r)}{B(r)}
\frac{D(r)-2H(r)b-A(r)b^2}{\left[H(r)+A(r)b\right]^2} ,
\label{OE}
\end{align}
where we use Eq. (\ref{ds2-axial}).
Let us introduce $u \equiv 1/r$
to rewrite the orbit equation as
\begin{align}
\left(\frac{du}{d\phi}\right)^2
= F(u) ,
\label{OE-2}
\end{align}
where $F(u)$ is
\begin{align}
F(u)
=\frac{u^4 (AD+H^2) (D-2Hb-Ab^2)}{B (H+Ab)^2} .
\label{F-axial}
\end{align}
Finally, we examine the angles at the receiver and source positions.
The unit tangent vector along the photon orbit in ${}^{(3)}M$
is $e^i$.
On the equatorial plane, its components are obtained as
\begin{align}
e^i=\frac{1}{\xi} \Big(\frac{dr}{d\phi}, 0, 1 \Big) .
\label{ei}
\end{align}
Here, $\xi$ satisfies
\begin{align}
\frac{1}{\xi}=\frac{A(r)[H(r)+A(r)b]}{A(r)D(r)+H^2(r)} ,
\label{xi}
\end{align}
which can be derived from $\gamma_{ij} e^i e^j = 1$
by using Eq. (\ref{OE}).
The unit radial vector in the equatorial plane is
\begin{align}
R^i= \Big(\frac{1}{\sqrt{\gamma_{rr}}}, 0, 0 \Big) ,
\label{R}
\end{align}
where we choose the outgoing direction for a sign convention.
Therefore, we can define the angle measured from
the outgoing radial direction by
\begin{align}
\cos \Psi \equiv&
\gamma_{ij} e^i R^j
\notag\\
=& \sqrt{\gamma_{rr}}
\frac{A(r)[H(r)+A(r)b]}{A(r)D(r)+H^2(r)}
\frac{dr}{d\phi} ,
\label{cos}
\end{align}
where Eqs. (\ref{ei}), (\ref{xi}) and (\ref{R}) are used.
This can be rewritten as
\begin{align}
\sin\Psi
=&\frac{H(r)+A(r)b}
{\sqrt{A(r)D(r)+H^2(r)}} ,
\label{sin}
\end{align}
where we use Eq. (\ref{OE}).
Note that $\sin\Psi$ by Eq. (\ref{sin})
is more convenient in practical calculations,
because it needs only the local quantities,
whereas $\cos\Psi$ by Eq. (\ref{cos}) needs the derivative as $dr/d\phi$.
\subsection{Deflection angle of light}
For the equatorial case in the axisymmetric spacetime,
we define
\begin{equation}
\alpha \equiv \Psi_R - \Psi_S + \phi_{RS} .
\label{alpha-axial}
\end{equation}
This definition seems to rely on a choice
of the angular coordinate $\phi$.
Let us consider a quadrilateral
${}^{\infty}_{R}\Box^{\infty}_{S}$,
which consists of the spatial curve for the light ray,
two outgoing radial lines from R and from S
and a circular arc segment $C_r$
of coordinate radius $r_C$ ($r_C \to \infty$)
centered at the lens
which intersects the radial lines
through the receiver or the source.
See Figure \ref{fig-Box} for the configuration such as
the domain ${}^{\infty}_{R}\Box^{\infty}_{S}$.
See also Ref. \cite{Ishihara2017} for the case that
the winding number is larger than unity.
For the asymptotically flat spacetime,
$\kappa_g \to 1/r_C$ and $d\ell \to r_C d\phi$
as $r_C \to \infty$ (See e.g. \cite{GW2008}).
Hence,
$\int_{C_r} \kappa_g d\ell \to \phi_{RS}$.
By using the Gauss-Bonnet theorem Eq. (\ref{localGB}),
Eq. (\ref{alpha-axial})
is rewritten as
\begin{align}
\alpha
=-\iint_{{}^{\infty}_{R}\square^{\infty}_{S}} K dS
+ \int_{S}^{R}
\kappa_g d\ell ,
\label{GB-axial}
\end{align}
where $d\ell$ is positive
for the prograde motion of the photon
and it is negative for the retrograde motion.
Eq. (\ref{GB-axial}) shows that $\alpha$ is coordinate-invariant
also for the axisymmetric case.
Up to this point,
equations for gravitational fields are not specified.
Therefore, the above discussion and results are not
limited within the theory of general relativity (GR)
but they are applicable to a certain class of modified gravity theories
if the light ray in the four-dimensional spacetime
obeys the null geodesic.
\section{Application to the Kerr lens}
\subsection{Kerr spacetime and $\gamma_{ij}$}
This section focuses on the Kerr spacetime as
one of the most known examples with axisymmetry.
The Boyer-Lindquist form of the Kerr metric is
\begin{align}
ds^2=&-\left(1-\frac{2Mr}{\Sigma}\right)dt^2
-\frac{4aMr\sin^2\theta}{\Sigma}dtd\phi \notag \\
&+\frac{\Sigma}{\Delta}dr^2+\Sigma d\theta^2
+\left(r^2+a^2+\frac{2a^2Mr\sin^2\theta}{\Sigma}\right)\sin^2\theta d\phi^2 ,
\label{Kerr}
\end{align}
where $\Sigma$ and $\Delta$ are denoted as
\begin{align}
\Sigma&\equiv r^2+a^2\cos^2\theta ,
\label{Sigma}
\\
\Delta&\equiv r^2-2Mr+a^2 .
\end{align}
By using Eqs. (\ref{gamma}) and (\ref{beta}),
one can see that
$\gamma_{ij}$ and $\beta_i$ for the Kerr metric are given by
\begin{align}
\gamma_{ij}dx^idx^j=&
\frac{\Sigma^2}{\Delta(\Sigma-2Mr)}dr^2
+ \frac{\Sigma^2}{(\Sigma-2Mr)} d\theta^2
\notag\\
&+ \left(r^2+a^2+\frac{2a^2Mr\sin^2\theta}{(\Sigma-2Mr)}\right)
\frac{\Sigma\sin^2\theta}{(\Sigma-2Mr)} d\phi^2 ,
\label{gamma-Kerr}
\\
\beta_idx^i=&- \frac{2aMr\sin^2\theta}{(\Sigma-2Mr)}d\phi .
\label{beta-Kerr}
\end{align}
Note that $\gamma_{ij}$ has no terms linear in the Kerr parameter $a$,
because $g_{0i} \propto H$ enters $\gamma_{ij}$
in a quadratic form through $g_{0i}g_{0j} \propto H^2$
as shown by Eq. (\ref{gamma}).
In order to see what is $\kappa_g$
for the present case,
we employ the weak field and slow rotation approximations,
for which $M$ and $a$ can be used as book-keeping parameters.
\subsection{Path integral of $\kappa_g$}
By substituting $\beta_i$ by Eq. (\ref{beta-Kerr})
into Eq. (\ref{kappag-final}), we obtain
\begin{align}
\kappa_g
=&
-\frac{2aM}{r^2(r-2M)}
\left(
\cfrac{1-\cfrac{2M}{r}+\cfrac{a^2}{r^2}}
{1+\cfrac{a^2}{r^2}+\cfrac{2a^2M}{r^3}}
\right)^{1/2}
\notag\\
=&-\frac{2aM}{r^3} +
O\left(\frac{aM^2}{r^4}\right) ,
\label{kappa-Kerr}
\end{align}
where we use the weak field and slow rotation approximations
in the last line
and the terms of $a^nM$ $(n \geq 2)$ vanish.
The path integral of $\kappa_g$ is computed as
\begin{align}
\int^{R}_{S}\kappa_gd\ell
=&
-\int^{R}_{S}
\left[
\frac{2aM}{r^3}
+ O\left(\frac{aM^2}{r^4}\right)
\right]
d\ell
\notag\\
=&
- \frac{2aM}{b^2}\int^{\phi_R}_{\phi_S} \cos\vartheta d\vartheta
+
O\left(\frac{aM^2}{b^3}\right)
\notag\\
=&
- \frac{2aM}{b^2}[\sqrt{1-b^2{u_R}^2}+\sqrt{1-b^2{u_S}^2}]
+ O\left(\frac{aM^2}{b^3}\right)
,
\label{int-kappag}
\end{align}
where we assume the prograde case $d\ell > 0$
that the orbital angular momentum of the photon
is aligned with the spin of the black hole
and
we use a linear approximation of the photon orbit
as $r= b/\cos\vartheta + O(M, a)$
and $\ell = b \tan\vartheta + O(M, a)$
in the second line.
Note that, in the retrograde case, the sign of $d\ell$ is negative
and thus the magnitude of the above path integral
remains the same but the sign is opposite.
\subsection{$\phi_{RS}$ part}
The integral of the angular coordinate $\phi$
becomes
\begin{align}
\phi_{RS}
=&
\int^R_S d\phi
\notag\\
=&
2\int^{u_0}_{0}\frac{1}{\sqrt{F(u)}}du
+\int^{0}_{u_S}\frac{1}{\sqrt{F(u)}}du +\int^{0}_{u_R}\frac{1}{\sqrt{F(u)}}du ,
\label{phi-Kerr}
\end{align}
where we use the orbit equation given by Eq. (\ref{OE-2}),
By substituting Eq. (\ref{F-axial}) into $F(u)$ in Eq. (\ref{phi-Kerr}),
we obtain
\begin{align}
\phi_{RS}
=&
\int^{u_0}_{u_S}\left(\frac{1}{\sqrt{{u_0}^2-u^2}}
+M\frac{{u_0}^3-u^3}{({u_0}^2-u^2)^{3/2}}
-2aM\frac{{u_0}^3(u_0-u)}{({u_0}^2-u^2)^{3/2}}\right) du
\notag\\
&
+\int^{u_0}_{u_R}\left(\frac{1}{\sqrt{{u_0}^2-u^2}}
+M\frac{{u_0}^3-u^3}{({u_0}^2-u^2)^{3/2}}
-2aM\frac{{u_0}^3(u_0-u)}{({u_0}^2-u^2)^{3/2}}\right) du
\notag\\
&+ O(M^2, a^2)
\notag\\
=&\left(\frac{\pi}{2}-\arcsin\Big(\frac{u_S}{u_0}\Big)
+M\frac{(2u_0+u_S)\sqrt{{u_0}^2-
u_S^2}}
{u_0+u_S}
-2aM\frac{{u_0}^3\sqrt{{u_0}^2-
u_S^2}}
{{u_0}^2+u_0u_S}\right) \notag\\
&+\left(\frac{\pi}{2}-\arcsin\Big(\frac{u_R}{u_0}\Big)
+M\frac{(2u_0+u_R)\sqrt{{u_0}^2-{u_R}^2}}{u_0+u_R}
-2aM\frac{{u_0}^3\sqrt{{u_0}^2-{u_R}^2}}{{u_0}^2+u_0u_R}\right)
\notag\\
&+ O\left(M^2 u_0^2, a^2 u_0^2\right) ,
\label{phi-Kerr1}
\end{align}
where we assume the prograde case.
For the retrograde case, the sign of the term linear in $a$
becomes opposite.
Eq. (\ref{OE-2}) gives
the relation between the impact parameter $b$ and
the inverse of the closest approach $u_0$ as
$b = u_0^{-1} + M - 2 aM u_0 +O(M^2, a^2)$
in the weak field and slow rotation approximations.
By using this relation,
$aM$ part of $\phi_{RS}$ in Eq. (\ref{phi-Kerr1}) can be rewritten
in terms of $b$ as
\begin{align}
-\frac{2aM}{b^2}\Big[\frac{1}{\sqrt{1-b^2{u_S}^2}}
+\frac{1}{\sqrt{1-b^2{u_R}^2}}\Big] .
\label{phi-Kerr2}
\end{align}
See Eq. (32) of Ref. \cite{Ishihara2016}
for $M$ part of $\phi_{RS}$.
\subsection{$\Psi$ parts}
For the Kerr metric by Eq. (\ref{Kerr}),
Eq. (\ref{sin}) becomes
\begin{align}
\sin\Psi
=&\frac{b}{r}\times \cfrac{1-\cfrac{2M}{r}+\cfrac{2aM}{br}}
{\sqrt{1-\cfrac{2M}{r}+\cfrac{a^2}{r^2}}} .
\end{align}
This is approximated as
\begin{align}
\sin\Psi
=&\frac{b}{r}
\left(1-\frac{M}{r}+\frac{2aM}{br}\right)
+
O\left(\frac{M^2}{r^2}, \frac{a^2}{r^2}, \frac{aM^2}{r^3} \right) .
\end{align}
By using this, we obtain
\begin{align}
\Psi_R-\Psi_S
=& \arcsin(bu_R)+\arcsin(bu_S)-\pi
\notag\\
& -\frac{Mb{u_R}^2}{\sqrt{1-b^2{u_R}^2}}
- \frac{Mb{u_S}^2}{\sqrt{1-b^2{u_S}^2}}
\notag\\
& +\frac{2aM{u_R}^2}{\sqrt{1-b^2{u_R}^2}}
+ \frac{2aM{u_S}^2}{\sqrt{1-b^2{u_S}^2}}
\notag\\
&
+ O\left(M^2 u_R^2, M^2 u_S^2,
a^2 u_R^2, a^2 u_S^2,
aM^2 u_R^3, aM^2 u_S^3
\right) .
\label{Psi-Kerr}
\end{align}
\subsection{Deflection angle of light in Kerr spacetime}
By substituting Eqs. (\ref{phi-Kerr2}) and (\ref{Psi-Kerr})
into Eq. (\ref{alpha-axial}),
the deflection angle of light on the equatorial plane
in the Kerr spacetime is obtained as
\begin{align}
\alpha_{prog}
=&
\frac{2M}{b}
\left(\sqrt{1-b^2{u_S}^2}+\sqrt{1-b^2{u_R}^2}\right)
\notag\\
&-\frac{2aM}{b^2}
\left(\sqrt{1-b^2{u_R}^2}+\sqrt{1-b^2{u_S}^2}\right)
+ O\left(\frac{M^2}{b^2}\right) ,
\label{alpha+}
\end{align}
where we assume the prograde motion of light.
For the retrograde case, it is
\begin{align}
\alpha_{retro}
=&\frac{2M}{b}
\left(\sqrt{1-b^2{u_S}^2}+\sqrt{1-b^2{u_R}^2}\right)
\notag\\
&+\frac{2aM}{b^2}
\left(\sqrt{1-b^2{u_R}^2}+\sqrt{1-b^2{u_S}^2}\right)
+ O\left(\frac{M^2}{b^2}\right) .
\label{alpha-}
\end{align}
Note that $a^2$ terms at the second order in the deflection angle cancel out.
See Appendix A for more detail.
For both cases, we take the far limit as $u_R \to 0$ and $u_S \to 0$.
Then, we obtain
\begin{align}
\alpha_{\infty\, prog} \to
&\frac{4M}{b}-\frac{4aM}{b^2}
+ O\left(\frac{M^2}{b^2}\right) ,
\\
\alpha_{\infty\, retro}\to
&\frac{4M}{b}+\frac{4aM}{b^2}
+ O\left(\frac{M^2}{b^2}\right) ,
\end{align}
which show that Eqs. (\ref{alpha+}) and (\ref{alpha-})
recover the asymptotic deflection angles that are known in literature
\cite{Ch, ES, Ibanez}.
\subsection{Finite-distance corrections to
the gravitomagnetic deflection angle of light}
The above calculations discuss the deflection angle of light
due to the rotation of the lens (its spin parameter $a$).
In particular, we do not assume that the receiver and the source
are located at the infinity.
The finite-distance correction to the deflection angle of light,
denoted as $\delta\alpha$,
is the difference between the asymptotic deflection angle
$\alpha_{\infty}$
and the deflection angle for the finite distance case.
It is expressed as
\begin{align}
\delta\alpha \equiv \alpha-\alpha_{\infty} .
\end{align}
Eqs. (\ref{alpha+}) and (\ref{alpha-})
suggest the magnitude of the finite-distance correction to
the gravitomagnetic deflection angle by the spin as
\begin{align}
\left| \delta\alpha_{GM} \right|
\sim&
O\left(\frac{aM}{r_S^2} + \frac{aM}{r_R^2}\right)
\notag\\
\sim&O\left(\frac{J}{r_S^2} + \frac{J}{r_R^2}\right) ,
\label{delta-alpha}
\end{align}
where $J \equiv aM$ is the spin angular momentum of the lens
and the subscript $GM$ denotes the gravitomagnetic part.
As usual, we introduce the dimensionless spin parameter as
$s \equiv a/M$.
Hence, Eq. (\ref{delta-alpha}) is rewritten as
\begin{align}
\left| \delta\alpha_{GM} \right|
\sim O\left( s\left(\frac{M}{r_S}\right)^2
+ s\left(\frac{M}{r_R}\right)^2 \right) .
\label{delta-alpha2}
\end{align}
This suggests that $\delta\alpha$
is comparable to the second post-Newtonian effect
(multiplied by the dimensionless spin parameter).
It is known that the second-order Schwarzschild contribution to $\alpha$
is $15\pi M^2/4 b^2$.
This contribution can be found also by using the present method,
especially by computing $\phi_{RS}$, where
we use a relation between $b$ and $r_0$ in $M^2$.
Please see Appendix A for detailed calculations
at the second order of $M$ and $a$,
especially the integrals of $K$ and $\kappa_g$
in the present formulation.
See also the next subsection.
Note that $\delta\alpha$ at the leading order
in the approximations does not depend on the impact parameter $b$.
In fact, $\delta\alpha$ depends much weakly on $b$.
\subsection{Possible astronomical applications}
We discuss possible astronomical applications.
First, we consider the Sun,
where we ignore its higher multipole moments.
The spin angular momentum of the Sun $J_{\odot}$ is
$\sim 2\times 10^{41} \,\mbox{m}^2\,\mbox{kg}\,\mbox{s}^{-1}$
\cite{Sun}.
Thus, $G J_{\odot} c^{-2} \sim 5 \times 10^5 \,\mbox{m}^2$,
which implies the dimensionless spin parameter as
$s_{\odot} \sim 10^{-1}$.
We assume that an observer at the Earth sees
the light bending by the solar mass, while
the source is practically at the asymptotic region.
If the light ray passes near the solar surface,
Eq. (\ref{delta-alpha2}) implies that
the finite-distance correction to this case is
of the order of
\begin{align}
\left| \delta\alpha_{GM} \right|
&\sim
O \left(\frac{J}{r_R^2}\right)
\nonumber\\
&\sim
10^{-12} \mbox{arcsec.}
\times
\left(\frac{J}{J_{\odot}}\right)
\left(\frac{1 \mbox{AU}}{r_R}\right)^2 ,
\label{alpha-Sun}
\end{align}
where $4M_{\odot}/R_{\odot} \sim 1.75 \,\mbox{arcsec.}
\sim 10^{-5} \,\mbox{rad.}$,
and $R_{\odot}$ denotes the solar radius.
This correction is around a pico-arcsecond level and thus
it is unlikely to be observed with present technology
\cite{Gaia, JASMINE}.
Please see Figure \ref{fig-Sun} for numerical calculations
of the finite-distance correction due to the receiver location.
The numerical results are consistent with
the above order-of-magnitude estimation.
The figure suggests that the dependence of $\delta\alpha$
on the impact parameter $b$ is very weak.
Next, we consider Sgr A$^{\ast}$ at the center of our Galaxy,
which is expected as
one of the most plausible candidates for the strong deflection of light.
In this case, the receiver distance is much larger than
the impact parameter of light,
while a source star may be in the central region of our Galaxy.
For Sgr A$^{\ast}$, Eq. (\ref{delta-alpha}) implies
\begin{align}
\left| \delta\alpha_{GM} \right|
&\sim
s \left( \frac{M}{r_S} \right)^2
\nonumber\\
&\sim
10^{-7} \mbox{arcsec.}
\times
\left(\frac{s}{0.1}\right)
\left(\frac{M}{4 \times 10^6 M_{\odot}}\right)^2
\left(\frac{0.1 \mbox{pc}}{r_S}\right)^2 ,
\label{alpha-Sgr}
\end{align}
where we assume the mass of the central black hole
as $M \sim 4 \times 10^6 M_{\odot}$.
This correction around a sub-microarcsecond level
is unlikely to be measured with present technology.
Please see Figure \ref{fig-Sgr} for numerical calculations
of the finite-distance correction due to the source location.
The numerical results are consistent with
the above order-of-magnitude estimation.
The figure shows that
the dependence on the impact parameter $b$ is very weak.
\subsection{Consistency of the present formulation}
Before closing this section, let us check the consistency
of the above formulation.
The Gaussian curvature is related with
the 2-dimensional Riemann tensor as
\cite{Werner2012}
\begin{align}
K
=&\frac{{}^{(3)}R_{r\phi r\phi}}{\gamma}
\notag\\
=&\frac{1}{\sqrt{\gamma}}
\left[\frac{\partial}{\partial\phi}
\left(\frac{\sqrt{\gamma}}{\gamma_{rr}}{}^{(3)}\Gamma^{\phi}_{~rr}\right)
-\frac{\partial}{\partial r}
\left(\frac{\sqrt{\gamma}}{\gamma_{rr}}{}^{(3)}\Gamma^{\phi}_{~r\phi}\right)
\right] ,
\end{align}
where ${}^{(3)}\Gamma^{i}_{jk}$ and
${}^{(3)}R_{abcd}$ are associated with $\gamma_{ij}$.
For the Kerr case, it becomes
\begin{align}
K
=&
-\sqrt{\frac{A^3}{B(AD+H^2)}}\frac{\partial}{\partial r}
\left[\frac12\sqrt{\frac{A^3}{B(AD+H^2)}}
\frac{\partial}{\partial r}\Big(\frac{AD+H^2}{A^2}\Big)\right]
\notag\\
=&
-\frac{2M}{r^3}
+ O\left(\frac{M^2}{r^4}, \frac{a^2M}{r^5}
\right) ,
\end{align}
where we use the weak field and slow rotation approximations
in the last line.
Note that $K$ has no terms linear in $a$.
This is because $\gamma_{ij}$ has no terms linear $a$
as already mentioned.
Furthermore, $a^2$ terms cancel out in $K$.
See Appendix A for more detail.
In order to compute the surface integral of the Gaussian curvature
in the Gauss-Bonnet theorem,
we need know the integration domain,
especially the photon orbit $S \to R$ for the present case.
By straightforward calculations,
the iterative solution of Eq. (\ref{OE-2}) for the Kerr case
in the weak field and slow rotation approximations
is obtained as
\begin{align}
u=&\frac{1}{b}\sin\phi+\frac{M}{b^2}(1+\cos^2\phi)
\notag\\
&-\frac{2aM}{b^3} + O\left(\frac{M^2}{b^3}, \frac{a^2}{b^3}
\right) .
\end{align}
By using this,
the surface integral of the Gaussian curvature is computed as
\begin{align}
-\iint_{{}^{\infty}_{R}\Box^{\infty}_{S}} K dS
=&
\int^{\infty}_{r_{OE}}
dr
\int_{\phi_S}^{\phi_R} d\phi
\frac{2M}{r^2}
+ O\left(\frac{M^2}{b^2}, \frac{aM^2}{b^3}\right)
\notag\\
=&
2M \int_{\phi_S}^{\phi_R} d\phi
\int_{0}^{\frac{1}{b}\sin\phi+\frac{M}{b^2}(1+\cos^2\phi)
-\frac{2aM}{b^3}} du
+ O\left(\frac{M^2}{b^2}, \frac{aM^2}{b^3}\right)
\notag\\
=&
2M \int_{\phi_S}^{\phi_R} d\phi
\Big[u\Big]^{\frac{1}{b}\sin\phi+\frac{M}{b^2}(1+\cos^2\phi)
-\frac{2aM}{b^3}}_{u=0}
+ O\left(\frac{M^2}{b^2}, \frac{aM^2}{b^3}\right)
\notag\\
=&
\frac{2M}{b}
\int_{\phi_S}^{\phi_R} d\phi
\sin\phi
+ O\left(\frac{M^2}{b^2}, \frac{aM^2}{b^3}\right)
\notag\\
=&\frac{2M}{b}\Big[\sqrt{1-b^2{u_S}^2}+\sqrt{1-b^2{u_R}^2}\Big]
+ O\left(\frac{M^2}{b^2}, \frac{aM^2}{b^3}\right) .
\label{int-K}
\end{align}
It follows that $a^2$ terms do not exist in this calculation.
By combining Eqs. (\ref{int-kappag}) and (\ref{int-K}),
we obtain
\begin{align}
-\iint_{{}^{\infty}_{R}\square^{\infty}_{S}} K dS
- \int_{R}^{S} \kappa_g d\ell
=&
\frac{2M}{b}
\left(\sqrt{1-b^2{u_S}^2}+\sqrt{1-b^2{u_R}^2}\right)
\notag\\
&-\frac{2aM}{b^2}
\left(\sqrt{1-b^2{u_R}^2}+\sqrt{1-b^2{u_S}^2}\right)
\notag\\
&+ O\left(\frac{M^2}{b^2}\right) .
\label{K-kappag}
\end{align}
This equals to the right-hand side of Eq. (\ref{alpha+}).
This means that
the present approach is consistent with the Gauss-Bonnet theorem.
\section{Conclusion}
By using the Gauss-Bonnet theorem in differential geometry,
we discussed a possible extension of the method of calculating
the bending angle of light to stationary, axisymmetric
and asymptotically flat spacetimes.
We introduced a spatial metric $\gamma_{ij}$
to define the bending angle of light,
which was shown to be coordinate-invariant.
We considered the light rays on the equatorial plane
in the axisymmetric spacetime.
We showed that the geodesic curvature of the photon orbit
with $\gamma_{ij}$ can be nonzero in gravitomagnetism,
even though
the light ray in the four-dimensional spacetime follows
the null geodesic.
Finally, we considered Kerr spacetime
in order to examine how the bending angle of light is computed
by the present method.
We made an order-of-magnitude estimate of
the finite-distance corrections for two possible astronomical cases;
(1) the Sun and (2) the Sgr A$^{\ast}$.
The results suggest that
the finite-distance corrections due to gravitomagnetism
are unlikely
to be observed with present technology.
However, our analysis on possible astronomical observations
in this paper is limited within the Kerr model.
It might be interesting to examine the gravitomagnetic
bending of light by using other axisymmetric spacetimes
in GR or in a specific theory of modified gravity.
A further study along this direction is left for future.
\begin{acknowledgments}
We are grateful to Marcus Werner for the stimulating discussions,
especially for his useful comments
and his talk on the osculating Riemann approach
at the seminar in Hirosaki university.
We would like to thank
Yuuiti Sendouda, Ryuichi Takahashi, Yuya Nakamura and
Naoki Tsukamoto
for the useful conversations.
This work was supported
in part by Japan Society for the Promotion of Science
Grant-in-Aid for Scientific Research,
No. 26400262 (H.A.), No. 17K05431 (H.A.) and
in part by by Ministry of Education, Culture, Sports, Science, and Technology,
No. 15H00772 (H.A.) and No. 17H06359 (H.A.).
\end{acknowledgments}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,053 |
export enum UserAccountStatus {
NEW,
TRIAL,
ACTIVATED,
SUSPENDED,
CLOSED
};
| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,924 |
(function( $, undefined ) {
// prevent duplicate loading
// this is only a problem because we proxy existing functions
// and we don't want to double proxy them
$.ui = $.ui || {};
if ( $.ui.version ) {
return;
}
//Helper functions and ui object
$.extend( $.ui, {
version: "1.8.4",
// $.ui.plugin is deprecated. Use the proxy pattern instead.
plugin: {
add: function( module, option, set ) {
var proto = $.ui[module].prototype;
for ( var i in set ) {
proto.plugins[ i ] = proto.plugins[ i ] || [];
proto.plugins[ i ].push( [ option, set[ i ] ] );
}
},
call: function( instance, name, args ) {
var set = instance.plugins[ name ];
if ( !set || !instance.element[ 0 ].parentNode ) {
return;
}
for ( var i = 0; i < set.length; i++ ) {
if ( instance.options[ set[ i ][ 0 ] ] ) {
set[ i ][ 1 ].apply( instance.element, args );
}
}
}
},
contains: function( a, b ) {
return document.compareDocumentPosition ?
a.compareDocumentPosition( b ) & 16 :
a !== b && a.contains( b );
},
hasScroll: function( el, a ) {
//If overflow is hidden, the element might have extra content, but the user wants to hide it
if ( $( el ).css( "overflow" ) === "hidden") {
return false;
}
var scroll = ( a && a === "left" ) ? "scrollLeft" : "scrollTop",
has = false;
if ( el[ scroll ] > 0 ) {
return true;
}
// TODO: determine which cases actually cause this to happen
// if the element doesn't have the scroll set, see if it's possible to
// set the scroll
el[ scroll ] = 1;
has = ( el[ scroll ] > 0 );
el[ scroll ] = 0;
return has;
},
isOverAxis: function( x, reference, size ) {
//Determines when x coordinate is over "b" element axis
return ( x > reference ) && ( x < ( reference + size ) );
},
isOver: function( y, x, top, left, height, width ) {
//Determines when x, y coordinates is over "b" element
return $.ui.isOverAxis( y, top, height ) && $.ui.isOverAxis( x, left, width );
},
keyCode: {
ALT: 18,
BACKSPACE: 8,
CAPS_LOCK: 20,
COMMA: 188,
COMMAND: 91,
COMMAND_LEFT: 91, // COMMAND
COMMAND_RIGHT: 93,
CONTROL: 17,
DELETE: 46,
DOWN: 40,
END: 35,
ENTER: 13,
ESCAPE: 27,
HOME: 36,
INSERT: 45,
LEFT: 37,
MENU: 93, // COMMAND_RIGHT
NUMPAD_ADD: 107,
NUMPAD_DECIMAL: 110,
NUMPAD_DIVIDE: 111,
NUMPAD_ENTER: 108,
NUMPAD_MULTIPLY: 106,
NUMPAD_SUBTRACT: 109,
PAGE_DOWN: 34,
PAGE_UP: 33,
PERIOD: 190,
RIGHT: 39,
SHIFT: 16,
SPACE: 32,
TAB: 9,
UP: 38,
WINDOWS: 91 // COMMAND
}
});
//jQuery plugins
$.fn.extend({
_focus: $.fn.focus,
focus: function( delay, fn ) {
return typeof delay === "number" ?
this.each(function() {
var elem = this;
setTimeout(function() {
$( elem ).focus();
if ( fn ) {
fn.call( elem );
}
}, delay );
}) :
this._focus.apply( this, arguments );
},
enableSelection: function() {
return this
.attr( "unselectable", "off" )
.css( "MozUserSelect", "" );
},
disableSelection: function() {
return this
.attr( "unselectable", "on" )
.css( "MozUserSelect", "none" );
},
scrollParent: function() {
var scrollParent;
if (($.browser.msie && (/(static|relative)/).test(this.css('position'))) || (/absolute/).test(this.css('position'))) {
scrollParent = this.parents().filter(function() {
return (/(relative|absolute|fixed)/).test($.curCSS(this,'position',1)) && (/(auto|scroll)/).test($.curCSS(this,'overflow',1)+$.curCSS(this,'overflow-y',1)+$.curCSS(this,'overflow-x',1));
}).eq(0);
} else {
scrollParent = this.parents().filter(function() {
return (/(auto|scroll)/).test($.curCSS(this,'overflow',1)+$.curCSS(this,'overflow-y',1)+$.curCSS(this,'overflow-x',1));
}).eq(0);
}
return (/fixed/).test(this.css('position')) || !scrollParent.length ? $(document) : scrollParent;
},
zIndex: function( zIndex ) {
if ( zIndex !== undefined ) {
return this.css( "zIndex", zIndex );
}
if ( this.length ) {
var elem = $( this[ 0 ] ), position, value;
while ( elem.length && elem[ 0 ] !== document ) {
// Ignore z-index if position is set to a value where z-index is ignored by the browser
// This makes behavior of this function consistent across browsers
// WebKit always returns auto if the element is positioned
position = elem.css( "position" );
if ( position === "absolute" || position === "relative" || position === "fixed" ) {
// IE returns 0 when zIndex is not specified
// other browsers return a string
// we ignore the case of nested elements with an explicit value of 0
// <div style="z-index: -10;"><div style="z-index: 0;"></div></div>
value = parseInt( elem.css( "zIndex" ) );
if ( !isNaN( value ) && value != 0 ) {
return value;
}
}
elem = elem.parent();
}
}
return 0;
}
});
$.each( [ "Width", "Height" ], function( i, name ) {
var side = name === "Width" ? [ "Left", "Right" ] : [ "Top", "Bottom" ],
type = name.toLowerCase(),
orig = {
innerWidth: $.fn.innerWidth,
innerHeight: $.fn.innerHeight,
outerWidth: $.fn.outerWidth,
outerHeight: $.fn.outerHeight
};
function reduce( elem, size, border, margin ) {
$.each( side, function() {
size -= parseFloat( $.curCSS( elem, "padding" + this, true) ) || 0;
if ( border ) {
size -= parseFloat( $.curCSS( elem, "border" + this + "Width", true) ) || 0;
}
if ( margin ) {
size -= parseFloat( $.curCSS( elem, "margin" + this, true) ) || 0;
}
});
return size;
}
$.fn[ "inner" + name ] = function( size ) {
if ( size === undefined ) {
return orig[ "inner" + name ].call( this );
}
return this.each(function() {
$.style( this, type, reduce( this, size ) + "px" );
});
};
$.fn[ "outer" + name] = function( size, margin ) {
if ( typeof size !== "number" ) {
return orig[ "outer" + name ].call( this, size );
}
return this.each(function() {
$.style( this, type, reduce( this, size, true, margin ) + "px" );
});
};
});
//Additional selectors
function visible( element ) {
return !$( element ).parents().andSelf().filter(function() {
return $.curCSS( this, "visibility" ) === "hidden" ||
$.expr.filters.hidden( this );
}).length;
}
$.extend( $.expr[ ":" ], {
data: function( elem, i, match ) {
return !!$.data( elem, match[ 3 ] );
},
focusable: function( element ) {
var nodeName = element.nodeName.toLowerCase(),
tabIndex = $.attr( element, "tabindex" );
if ( "area" === nodeName ) {
var map = element.parentNode,
mapName = map.name,
img;
if ( !element.href || !mapName || map.nodeName.toLowerCase() !== "map" ) {
return false;
}
img = $( "img[usemap=#" + mapName + "]" )[0];
return !!img && visible( img );
}
return ( /input|select|textarea|button|object/.test( nodeName )
? !element.disabled
: "a" == nodeName
? element.href || !isNaN( tabIndex )
: !isNaN( tabIndex ))
// the element and all of its ancestors must be visible
&& visible( element );
},
tabbable: function( element ) {
var tabIndex = $.attr( element, "tabindex" );
return ( isNaN( tabIndex ) || tabIndex >= 0 ) && $( element ).is( ":focusable" );
}
});
})( jQuery );
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,822 |
Q: accordion faq in wordpress I would like to make a simple collapsible faq in wordpress. There are accordion menu plugins out there that offer way more features than I need. But I'm having trouble getting things to look right with the Simple Content Reveal plugin.
I'm ready to try writing my own jquery code for the first time. I will need step by step instructions, or a link to same.
I will need a streamlined way of creating the markup for the faq. An example of an inefficient way of creating the markup:
id="id1" etc.
id="id2" etc.
(taken from the markup for Simple Content Reveal)
In other words, I want to be able to go from a bunch of questions and answers in notepad to the markup for the collapsible faq without too much fussy copy and paste fiddling.
Thanks!
A: Have you seen the accoridian in the JQuery framework? It's easy to use and should give you want you need.
A: Check out https://oraguide.com - It's a similar concept but everything is streamlined / hosted in the cloud. It runs directly on the page as a floating div.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 510 |
{"url":"https:\/\/tex.stackexchange.com\/questions\/215479\/how-can-i-shorten-this","text":"# How Can I Shorten This?\n\nI am trying to create the marks needed for this graph and this process is very lengthy. Is there a shorter way I could do this? I am trying to create a mark at every 1\/6 mark between 1 and 6 so that I can place each interval. Here is what I'm trying to create:\n\n\\documentclass{article}\n\\usepackage{tikz}\n\\begin{document}\n\\begin{tikzpicture}[scale=2]\n\\draw [-] (0,0)--coordinate(x axis mid)(6,0);\n\\foreach\\x\/\\xtext in {0,{1\/6}\/{1\/6},{2\/6}\/{2\/6},\n{3\/6}\/{3\/6},{4\/6}\/{4\/6},{5\/6}\/{5\/6},1,{7\/6}\/{7\/6},6}\n\\draw[shift={(\\x,0)}] (0pt,0pt)--(0pt,-2pt);\n\\draw [-] (0,0)--coordinate(y axis mid)(0,4);\n\\end{tikzpicture}\n\\end{document}\n\n\nIf I need to just hardcode everything then just let me know.\n\n\u2022 Can you give a better example of what the goal is? There is a smooth curve is it a closed form formula? What is the zigzagged line? Is that coming from a data source? \u2013\u00a0percusse Dec 5 '14 at 4:45\n\u2022 I can create the graph its self, but the labels at the bottom of the graph {13-47}, I've had to type in each marks, and I assume there's a shorter way to type it all in. \u2013\u00a0BMarc20 Dec 5 '14 at 4:49\n\u2022 Ah by marks you mean tick labels? \u2013\u00a0percusse Dec 5 '14 at 5:03\n\u2022 Exactly, I thought they were referred to as tick labels. \u2013\u00a0BMarc20 Dec 5 '14 at 5:32\n\u2022 the title of your post is absolutely useless. Be more specific please \u2013\u00a0pluton Dec 5 '14 at 8:01\n\nHere is how you put the ticks down without having to type them in one at a time by hand.\n\n\\begin{tikzpicture}[scale=2]\n\\draw [-] (0,0)--coordinate(x axis mid)(5.54,0);\n\\draw [-] (0,4)--coordinate(x axis mid)(5.54,4);\n\\draw [-] (0,0)--coordinate(y axis mid)(0,4);\n\\draw [-] (0,0.8)--coordinate(y axis mid)(5.54,0.8) node[left] at (0,0.8) {11};\n\\draw [-] (0,1.6)--coordinate(y axis mid)(5.54,1.6) node[left] at (0,1.6) {12};\n\\draw [-] (0,2.4)--coordinate(y axis mid)(5.54,2.4) node[left] at (0,2.4) {13};\n\\draw [-] (0,3.2)--coordinate(y axis mid)(5.54,3.2) node[left] at (0,3.2) {14};\n\\draw [-] (5.54,-.06)--coordinate(y axis mid)(5.54,4) node[left] at (0,4) {15};\n\\foreach\\x\/\\xtext in {0,.167,.33,...,5.54} \\draw[shift={(\\x,0)}] (0pt,0pt)--(0pt,-2pt);\n\\end{tikzpicture}\n\n\nIt will look like this when finished.","date":"2019-09-19 13:00:50","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.6141764521598816, \"perplexity\": 2616.2596105690254}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-39\/segments\/1568514573519.72\/warc\/CC-MAIN-20190919122032-20190919144032-00489.warc.gz\"}"} | null | null |
To use Loop Community, please enable JavaScript in your browser.
Looptimus
Looptimus Mini
Prime App
Track Rig
Andrew Scott Foust
andrewscottfoust
Andrew Scott Foust began composing music over 27 years ago, and writes for several mediums -- film, theater, television, multimedia, and brainwave stimulation. His writing styles include orchestral, orchestral/electronic hybrid, electronic, ambient, rock, jazz, and ethnic. His work has been compared to that of many of his influences, including James Newton Howard, Hans Zimmer, James Horner, Brian Tyler, Marco Beltrami, and James Horner. Andrew's Independent Film Biography includes: Treasure (Feature, 2016); Manifest Destiny (Short, 2016); Testament (Feature, 2016); Moment of Truth (Feature, 2016); The Hunt (Short, 2016); Necessary Evil (Web Series, 2015-present); The Interview (Short, 2015); Oneness (Documentary Short, 2014); The Writing on the Wall (Short Feature, 2013); Job (Short, 2013); Farewell Chicago (Short, 2013); Christkindl Market (Short, 2013); Inspire Me (Short, 2012); The Compound (Short, 2012); Remedy (Short Feature, 2009); and Hellblock 13 (Feature, 1999). Upcoming projects include scoring Fallaway, a feature film due to be released in 2017, and continuing to score the Necessary Evil web series. Albums credited to Andrew's name are: Testament Original Score (2016), Moment of Truth Original Score (2016); The Writing on the Wall Original Score (2013); On the Shoulders of Giants (2011); Remedy Original Score (2011); Testament Original Score (2016) and Treasure Original Score (2017). In the past couple of years, Andrew has also scored several therapeutic musical libraries targeted at brainwave stimulation for Transparent Corp., including: Thought Sounds 2: Focus; Thought Sounds 3: Relax; Thought Sounds 4: Mood Elevation; and Brain.fm, each of which contains over 14 hours of music. Andrew's love of music began when he was 15 years old, when he first picked up a guitar, and thereafter, found it difficult to put down. His love of guitar led to an interest in playing piano, bass guitar, mandolin, dulcimer, and various percussion instruments. He graduated from the Atlanta Institute of Music in 1991, where he studied Jazz Performance. He went on to study Music Composition at the University of South Carolina. Aside from currently creating musical scores, he is learning to play violin and creates sample libraries, next hoping to tackle the cello. He lives in Oviedo, Florida with his wife and two young sons. ... Read more
Patches & Bundles
Patch Bundle
One Omnisphere 2.5 Patch
Andrew Foust - Signature Producer Bundle 2
Patch Bundles
Andrew Foust - Signature Producer Bundle
Loop Community
Looptimus Foot Controller
2021 © Loop Community | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,595 |
Q: Reading time reported in the Firebug Net tab See this screenshot from Firebug's Net tab:
http://www.scdi.org/~avernet/try/firefox-times.png
I know that:
*
*The time between 1 and 2 is the time taken by my app to generate the HTML and for the data to make its way to the browser.
*The time between 3 and 4 is the time taken by my JavaScript initialization code which runs on DOMContentLoaded.
But what about the time between 2 and 3? Is that what the time Firefox takes to "render" the page? In this case, it is pretty significant (about 1.5 second). How to optimize that part?
A: The time between 2-3 is the browser parsing and rendering the contents of the file downloaded between 1-2. This includes all the HTML and any inline CSS or javascript there may be. The easiest ways to shorten this are 1) send over less data for the browser to parse 2) make sure that your HTML/CSS validates and 3) watch out for really slow CSS rules/expressions.
In general most people don't focus on how long it takes for the browser to completely render the page, but instead how quickly it starts to render on the client side. Generally called progressive rendering, it allows the browser to start displaying parts of the page before the entire page has been rendered. One of the most common reasons what this does not happen is putting the content of the page in a which prevents the browser from rendering it until it is completely parsed. This post has some decent tips on how to do this. You probably want to look at the YSlow Firefox extension, it can give you some decent tips on how to make your website faster.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,068 |
Q: Eclipse still runs project by old name I had a project named "xxx" which I renamed to "yyy". The project works fine on my phone. But Eclipse still says "Launching xxx" when I run the app. How do I remedy the situation? I've tried searching for "xxx" throughout my project, no luck.
A: I also had this problem on my Android project. Now I found the solution:
*
*Click the down arrow next to the run button.
*Select the Run Configurations item in the popup menu.
*Expand Android Application and select the item with old project name.
*Set the Name: field at right to the new project name.
*Click Apply
Hope this can fix your problem.
A: Go to the launch configurations and have a look at the configuration that´s called xxx.
In the Name field you can edit the name of the launch configuration to whatever you want.
EDIT:
Maybe this documentation article makes it much more clearer:
http://help.eclipse.org/juno/index.jsp?topic=%2Forg.eclipse.jdt.doc.user%2Freference%2Fviews%2Fdebug%2Fref-editlaunchconfig.htm
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,523 |
the state of things as they exist, as opposed to an idealistic or notional idea of them.
real life, actuality, truth, corporeality, substantiality, materiality, etc.
Our best course, however, is to apply our 12 Step program to life in this world.
I wonder why we find it hard to face reality? Today I am on a journey towards reality and it is a spiritual journey. I know I will never be completely real, a part of me will always be "diseased". I must live and treat my compulsive behavior on a daily basis — but my life is getting better.
In the past, too often I indulged in the belief that somehow or other tomorrow would be brighter or happier or richer. If we close our mind to the present, we'll only continue to do so when the tomorrow we dream of now becomes the present.
I no longer try to escape life through alcoholism. Alcohol deadens the brain cells that preside over our highest faculties and we are off to the unreal world of drunkenness.
In these times of quiet meditation, try more and more to set your hopes on the grace of God.
Our trust in others may have been shaken, but our trust in ourselves may have been shattered worse. We cannot let our past interfere with our ability to trust ourselves.
We benefit from our mistakes. We benefit from our past. And if we have made mistakes, we needed to make them in order to learn along the way.
The resolve to fulfil commitments we make to ourselves and others may be lacking until we learn to rely on the wisdom and strength offered by our Higher Power. Whatever our desires, whatever our commitments, if for the good of others and ourselves, they will come to fruition. | {
"redpajama_set_name": "RedPajamaC4"
} | 2,807 |
Gay Rights Groups to Join Others in Condemning Stop-and-Frisk - NYTimes.com
http://cityroom.blogs.nytimes.com/2012/06/04/gay-rights-groups-to-join-others-in-condemning-stop-and-frisk/
Apologies for short message; sent from iPhone.
NYT: Black Leaders and Gay Advocates Find Ways to March in Step
http://mobile.nytimes.com/article;jsessionid=0EB83CBE162661C7033954672DE90A92.w6?a=960553&f=21
BBC NEWS - Afghanistan's 'graveyard of foreigners'
http://m.bbc.co.uk/news/magazine-18369101
Article: Backed By Obama, Pride Month Takes Off
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Sent via Flipboard, your social magazine for iPad and iPhone.
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Muslim female cricket coach gets award - Top Stories
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Temple and mosque collaboration seeks to become a national interfaith model | 89.3 KPCC
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AP Mobile: Vatican criticizes US nun's book on sexuality
A story from AP Mobile:
Vatican criticizes US nun's book on sexuality
VATICAN CITY (AP) - The Vatican on Monday sharply criticized a book on sexuality written by a prominent American nun, saying it contradicted church teaching on issues like masturbation, homosexuality and marriage and that its author had a "defective understanding" of Catholic theology. The Vatican's orthodoxy office said the book, "Just Love: A Framework for Christian Sexual Ethics" by Sister Marg...
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Bowling for Peace: Why an Afghan Woman Risked Her Life to Bring Bowling to Afghanistan - ABC News
http://abcnews.go.com/m/story?id=16482303&sid=76
AP Mobile: Turkish women protest plans to curb abortion
Turkish women protest plans to curb abortion
ANKARA, Turkey (AP) - Hundreds of abortion rights demonstrators on Sunday staged the largest protest yet against plans by Turkey's Islamic-rooted government to curb abortion, which critics say will amount to a virtual ban. Women carrying banners that read "my body, my choice" and shouting anti-government slogans gathered in Istanbul's Kadikoy district. Prime Minister Recep Tayyip Erdogan has call...
▼ June 3 - June 10 (16)
Gay Rights Groups to Join Others in Condemning Sto...
NYT: Black Leaders and Gay Advocates Find Ways to ...
BBC NEWS - Afghanistan's 'graveyard of foreigners'...
Article: Muslim female cricket coach gets award - ...
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Article: The Religious Right Turns 33: What Have W...
Article: New Jersey Muslims sue to protect their r...
Article: MIDDLE EAST: Trouble In Tunisia, Gays In ...
BBC NEWS - Forced marriage campaign targets mosque...
Article: Americans Are as Likely to Be Killed by T...
AP Mobile: Vatican criticizes US nun's book on sex...
Bowling for Peace: Why an Afghan Woman Risked Her ...
AP Mobile: Turkish women protest plans to curb abo... | {
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{"url":"https:\/\/socratic.org\/questions\/how-do-you-solve-5-5-3-2d","text":"# How do you solve -5 = 5 ( 3 2d )?\n\nJan 30, 2016\n\n$d = - \\frac{1}{32}$\n\n#### Explanation:\n\ndivide both sides of the equation by 5\n\n$- \\frac{\\cancel{5}}{\\cancel{5}} = \\frac{\\cancel{5} \\left(32 d\\right)}{\\cancel{5}}$\n\nreverse equation : 32d = -1\n\ndivide both sides by 32 \u2192 d = -1\/32","date":"2021-12-05 05:47:20","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 3, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.800301730632782, \"perplexity\": 2185.4910755502992}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-49\/segments\/1637964363135.71\/warc\/CC-MAIN-20211205035505-20211205065505-00202.warc.gz\"}"} | null | null |
Zapotal de Moras är en ort i Mexiko. Den ligger i kommunen Pisaflores och delstaten Hidalgo, i den sydöstra delen av landet, km norr om huvudstaden Mexico City. Zapotal de Moras ligger meter över havet och antalet invånare är .
Terrängen runt Zapotal de Moras är huvudsakligen kuperad, men västerut är den bergig. Den högsta punkten i närheten är Cerro Palo de Agua, meter över havet, km väster om Zapotal de Moras. Runt Zapotal de Moras är det ganska tätbefolkat, med invånare per kvadratkilometer. Närmaste större samhälle är Tamazunchale, km öster om Zapotal de Moras. I omgivningarna runt Zapotal de Moras växer i huvudsak städsegrön lövskog.
Årsmedeltemperaturen i trakten är °C. Den varmaste månaden är maj, då medeltemperaturen är °C, och den kallaste är december, med °C. Genomsnittlig årsnederbörd är millimeter. Den regnigaste månaden är september, med i genomsnitt mm nederbörd, och den torraste är januari, med mm nederbörd.
Kommentarer
Referenser
Orter i Hidalgo | {
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Q: Force UIView animateWithDuration completion block to be called I have two animations which are overlapping, which, because of the way I've set my method up, causes the second one not to fire. I have a check like so in the beginning of the method:
- (void)animateHidden:(BOOL)hidden duration:(CGFloat)seconds delay:(CGFloat)delay options:(UIViewAnimationOptions)options disableUserInteraction:(BOOL)disableUserInteraction {
if (self.hidden == hidden) {
return;
}
Then, further down, my animation block looks like so:
__weak UIView *weakSelf = self;
[UIView animateWithDuration:seconds delay:delay options:options animations:^{
weakSelf.alpha = hidden ? 0 : 1;
} completion:^(BOOL finished) {
// Return user interaction to previous state
if (disableUserInteraction) {
weakSelf.userInteractionEnabled = userInteractionEnabled;
}
weakSelf.hidden = hidden;
}];
Two animations are kicked off on the same view, one before a service call and one after. If the service call happens quick enough that the view is still animating, weakSelf.hidden = hidden; will never be called, and the second animation will exit out since the hidden value wasn't updated in time.
Is there anyway that I could force the completion block on the animation block to be called? I need to update my hidden property before making the check, but can't find a way to accomplish this.
Calling [self.layer removeAllAnimations] doesn't seem to work unfortunately.
A: You can use CABasicAnimation instead of UIView animation, that will solve the problem more accurately.
You can use it like:
CABasicAnimation* opacityZero= [CABasicAnimation animationWithKeyPath:@"opacity"];
[opacityZero setToValue:[NSNumber numberWithFloat:0.0]];
[opacityZero setDuration:duration];
[[self layer] addAnimation:opacityZero forKey:@"opacityZero"];
And when your service call ends, you can call [self.layer removeAllAnimations];
Similarly, you can make the opacity one and tweak the above method as you like.
You can find more info here.
A: A __block prefixed to hidden attribute declaration should help.
Something like, @property (nonatomic) __block BOOL hidden;
A: If you are targeting iOS 10+ take a look at UIViewPropertyAnimator
https://developer.apple.com/reference/uikit/uiviewpropertyanimator?language=objc
Combined with the UIViewAnimating and UIViewImplicitlyAnimating protocols, this allows modification / interruption / pause / resume / stop / etc of the animations.
Basic example (buttons and view set in IB):
- (IBAction)startTapped:(id)sender {
_myAnimator = [UIViewPropertyAnimator
runningPropertyAnimatorWithDuration:3.0
delay:0.0
options:UIViewAnimationOptionCurveLinear
animations:^{
_theRedBox.alpha = _theRedBox.alpha > 0 ? 0 : 1;
} completion:^(UIViewAnimatingPosition finalPosition) {
// do stuff
}];
}
- (IBAction)stopTapped:(id)sender {
[_myAnimator stopAnimation:NO];
[_myAnimator finishAnimationAtPosition:UIViewAnimatingPositionEnd];
}
| {
"redpajama_set_name": "RedPajamaStackExchange"
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{"url":"https:\/\/oxfordre.com\/economics\/view\/10.1093\/acrefore\/9780190625979.001.0001\/acrefore-9780190625979-e-759","text":"Show Summary Details\n\nPage of\n\nPrinted from Oxford Research Encyclopedias, Economics and Finance. Under the terms of the licence agreement, an individual user may print out a single article for personal use (for details see Privacy Policy and Legal Notice).\n\ndate: 25 June 2022\n\nTax Audits, Economics, and Racism\n\n\u2022 Francine J. LipmanFrancine J. LipmanWilliam S. Boyd School of Law, University of Nevada Las Vegas\n\nSince 2010, Congress has significantly cut the annual budget of the Internal Revenue Service (IRS) while requiring the IRS to manage more responsibilities, including last-minute comprehensive tax reform, health care, broad-based antipoverty relief, and a variety of economic stimulus provisions. As a result, the IRS has sustained across-the-board decreases in staffing, with the most significant decreases in tax enforcement personnel. The IRS has fewer auditors than at any time since World War II, despite an explosion of concentrated income and wealth. Predictably, the tax gap, the difference between what taxpayers owe and what taxpayers pay, has skyrocketed to almost $1 trillion a year. Economists have estimated that funding the IRS will pay for itself severalfold, raising more than a trillion dollars of uncollected tax revenues over a decade. Despite evidence that funding will remedy budget shortfalls severalfold, Congress continues to defund the IRS. While the bulk of the tax gap is due to unreported income by high-income individuals, the audit rate of these households has dropped precipitously. By comparison, the lowest income wage earners are being audited five times more often than all other taxpayers. Given centuries of racist policies in the United States, households of color are disproportionately impoverished and white households are disproportionately wealthy. Accordingly, lower income working families of color, especially in the South, are audited at rates higher than their white northern counterparts. Moreover, because these households and the IRS have limited resources, many of these audits result in taxpayers losing antipoverty benefits that they have properly claimed. This discriminatory treatment is counter to Congressional intent to support these families and exacerbates existing racial income and wealth gaps. With President Biden\u2019s 2021 executive order on advancing racial equity and support for underserved communities through the federal government, the U.S. Treasury, IRS, and Congress have been charged to \u201crecognize and work to redress inequities in their policies and programs that serve as barriers to equal opportunity.\u201d Properly funding the IRS is a necessary step to advancing racial equity. Subjects \u2022 Health, Education, and Welfare Economics \u2022 Law and Economics \u2022 Public Economics and Policy Introduction The Internal Revenue Service (IRS) is the federal agency charged with tax revenue collection. In fiscal year 2020, the IRS collected$3.5 trillion in taxes, which represented approximately 96% of aggregate annual federal funding (IRS, 2020a). In its mission statement, the IRS asserts that its primary role is to enforce tax laws. The IRS\u2019 website announces that it is responsible \u201cto help the large majority of compliant taxpayers with the tax law, while ensuring that the minority who are unwilling to comply pay their fair share,\u201d among similar duties (IRS, 2020b). Nevertheless, the IRS\u2019 most recent official estimate of the \u201ctax gap\u201d or the amount of net taxes owed by taxpayers who did not \u201cpay their fair share\u201d even after IRS enforcement efforts was $1.143 trillion for the 3-year period 2011\u20132013 or$381 billion average annually (Forman et al., 2021). This amount is more than all the income taxes paid by 90% of all taxpayers (Forman et al., 2021; Rossotti & Forman, 2020, Rossotti, 2020). Assuming constant compliance rates, the U.S. Treasury has estimated that the tax gap in 2019 was $584 billion,$7 trillion over the decade, or 15% of annual tax liabilities (IRS, 2019; Forman et al., 2021). Economists have estimated that the tax gap was at least $630 billion in 2020 (Sarin & Summers, 2020). Despite these titanic uncollected tax obligations and the IRS\u2019 patent failure to accomplish its charge and stated goal every year, Congress has significantly cut the IRS budget since 2010. Budget cuts have occurred even though Congress has been requiring broader and deeper IRS engagement in tax reform, health care, antipoverty programs, and economic stimulus payments. The IRS has responded to these budget cuts and additional work with meaningful decreases in its enforcement activities even with increasing annual tax gaps. Most notably, the audit rates of corporations and high-income individuals have dropped precipitously. Audits on millionaires have plummeted 71% (Center on Budget and Policy Priorities, 2021), and those on large corporations have dropped 51% (Huang, 2020). Thus, voluntary compliance rates likely have not stayed constant and more likely have declined. Past IRS commissioners and notable economists have found that the IRS\u2019 reported estimate of the tax gap significantly understates sophisticated tax evasion among wealthy taxpayers and large corporations (Alstadsaeter et al., 2019; Debacker et al., 2020; Forman et al., 2021; Guyton et al., 2021; Johns & Slemrod, 2010). In testimony before Congress, IRS Commissioner Charles Rettig estimated that the tax gap could be as high as$1 trillion a year or almost 30% of gross revenues (Davison, 2021). Unless systemic changes are made, Americans can expect to lose 3% of gross domestic product (GDP) or $7.5 trillion in tax liabilities due and payable under current tax law over the next decade (Rossotti et al., 2020; Forman et al., 2021; Sarin, 2021). The IRS, economists, scholars, and policy experts generally agree on an effective remedy. The tax gap could be reduced by increased funding for targeted IRS enforcement that would more than pay for itself severalfold (Forman et al., 2021; Holtzblatt, 2021; Huang, 2020; U.S. Department of the Treasury, 2021). Despite this obvious and lucrative remedy, Congress has done the opposite while certain representatives simultaneously complain about increasing federal deficits. Why has Congress defunded the IRS when the annual tax gap has soared? Why has the IRS decreased audits of the highest income taxpayers and largest corporations when economists have estimated they are responsible for more than 70% of the tax gap? This article attempts to provide a critical tax framework with which to analyze this enigma. Tragically, the problem is consistent with the misallocation of funding in other government enforcement agencies (e.g., militarization of state and local police in cities that are predominately Black and excessive spending on Mexican versus Canadian border control). When laid bare, the tax system through enactment of statutes passed by Congress and enforced by the IRS privileges white wealthy households and disadvantages households of color (Lipman, 2006, 2011; Lipman et al., 2020), especially Black families (Brown, 2021). This article contributes to the critical tax literature by revealing systemic and institutional racism in the economics of the IRS\u2019 administration of tax audits. Specifically, this article demonstrates that Congress\u2019 chronic underfunding of the IRS, despite a documented substantial return, is not only inconsistent with fundamental economic goals of collecting tax revenues and reducing debt and borrowing but also grounded in racist policies. The IRS disproportionately audits low-income households of color despite evidence that the tax gap is overwhelmingly due to high-income white households underreporting their income. Lower income households that are disproportionately Black and Latinx because of centuries of racism are audited at five times the rate of all other taxpayers (Transactional Records Access Clearinghouse, 2022). Moreover, given that these households lack the necessary resources to respond timely compared to their wealthy neighbors and the IRS\u2019 inability to even answer its phones and timely open its mail, most low-income households that are audited lose properly claimed antipoverty tax benefits (National Taxpayer Advocate, 2020b). This structure is not only unjust but also undermines the integrity of and faith in the U.S. tax system. Given that the tax system funds most of the federal government through a self-assessment structure, confidence is paramount to its stability and success (Fichtner et al., 2019). This article details the depth and breadth of the racial inequities in Congress\u2019 defunding of the IRS, including the crippling cost of racist tax administration for all of us. In this article, the next section on \u201cRacial Wealth\/Income Inequality\u201d describes the demographics of the populations that are at issue in this analysis. The tax system does not work in a vacuum but, rather, is imposed on populations with existing profiles that are the result of societal values and short-term and long-term economics. Because of \u201cbaked in\u201d tax profiles from hundreds of years of economic advantage or discrimination, facially neutral laws may obscure racism that is apparent when disparate consequences are revealed (Brown, 2021). Because these demographic profiles are readily available and known, especially to legislators, seemingly even-handed laws are racist when no other rational basis exists for structures that cause patently racially discriminating results. A striking example presented is the economic overpolicing of tax benefits in communities of color (Harriot, 2019; Kiel & Fresques, 2019). As a result of targeted auditing of the Earned Income Tax Credit (EITC) despite a relatively modest or even effectively no contribution to the tax gap or aggregate net cost to the federal government, certain counties of color essentially have been denied EITC benefits. From 2012 through 2015, taxpayers in the top 100 audited counties in America, 62 counties of which are in Georgia, Mississippi, and Texas, were conspicuously poor, Black, and Latinx. Yet up to 70% of the perhaps$1 trillion annual tax gap was due to wealthy, predominately white taxpayers (Sarin & Summers, 2019). By comparison, the top 15 highest income counties in America, which are disproportionately white, have an average audit rate of 7.75 (about equal to the national average audit rate of 7.69) returns per 1,000 filers. Impoverished communities of color suffer high audit rates in America (as high as 11.8 returns per 1,000 filers) even though white wealthy households are overwhelmingly responsible for the tax gap (Harriot, 2019.\n\nThe section on \u201cTax System Design\u201d includes a brief description of foundational issues in tax system design. These structural designs generally advantage white taxpayers over taxpayers who are disproportionately individuals of color. The section of the article on \u201cTax System Institutional Racism\u201d describes Congressional defunding of the IRS that has led to a significant reduction in enforcement. Together with unjust targeting of certain social benefits, the IRS increasingly audits lower income working families, who are disproportionately impoverished and Black, at the same rate as the highest income taxpayers, who are disproportionately wealthy and white due to economic advantages. This has led to an irrational economic policing of Congressionally approved social benefits at the cost of an exploding tax gap. Moreover, this unjust targeting financially harms families of color, especially children, and their similarly economically challenged communities and businesses. The section on \u201cTax Gap Analysis\u201d presents the magnitude and components of the tax gap.\n\nThe tax gap is overwhelmingly due to wealthy white households relative to impoverished households of color. However, county-by-county audit rates show that communities of color are aggressively audited with little meaningful recourse (Harriot, 2019; Kiel & Fresques, 2019). Tragically, there are many economic consequences to these communities when as much as a trillion dollars of tax revenue annually in the United States goes uncollected. Without these resources, Congress has increased financial pressure to fund fiscal needs with new taxes and fees on honest taxpaying Americans or alternatively impose spending shortfalls on known financial needs. Fortunately, the remedy is obvious: Fund and target IRS enforcement on the perpetrators of the tax gap (Marr et al., 2021; Forman et al., 2021). Treasury must no longer financially advantage wealthy white households and disadvantage communities of color through tax enforcement. This article lends compelling evidence to confirm that the misallocation of tax enforcement on impoverished communities of color is not only unjust, inequitable, and racist but also exacerbates the racial wealth and income gaps through the tax system.\n\nRacial Wealth\/Income Inequality\n\nThis section describes the financial consequences of hundreds of years of discrimination that have advantaged white Americans and disadvantaged families and communities of color. Context matters, because government systems and institutions do not operate in a vacuum but, rather, interact with existing populations that are neither homogeneous nor treated uniformly. This has proven to be true even if the laws or Constitution demand otherwise (e.g., racial and sex-based discrimination is unconstitutional, and tax laws must be uniform). As a result of these distinctions and disparities, taxpayer profiles emerge that cannot be ignored because they impact economic consequences on a micro and a macro level. Indeed, statutory requirements based on specific taxpayer profiles (e.g., phase-in and phase-out thresholds, household structure, age-based benefits, character of income, and immigration status) are used by Congress to target certain tax benefits or burdens to specific populations (Huang & Taylor, 2019). Even laws, systems, and institutions that appear to be neutral can be discriminatory and racist in application and economic consequences (Brown, 2021). This is especially true if the playing field has not been and is not equal, causing ostensibly neutral laws and procedures to have unequal or racist impact. As a result of significant differences in power, society does not afford equal opportunity to all (McIntosh et al., 2020).\n\nCenturies of explicit and implicit discrimination suffered by communities of color, particularly Black, Latinx, and Indigenous individuals, have caused significant income and wealth inequality in America (Wiehe et al., 2018). Income and wealth gaps are not an accident but, rather, the result of centuries of federal and state policies that have systematically facilitated the financial success of white households and the impoverishment of households of color (Darity & Mullen, 2020). Substantial systemic and institutional changes and redress are necessary (rather than \u201cindividual responsibility\u201d) to narrow gaps related to insurmountable barriers such as generational asset poverty, legacies of wealth-stripping tactics in housing and lending markets, and other discriminatory practices (Kent & Ricketts, 2021).\n\nWealth and income disparities between white households and households of color have persisted for centuries. Compelling federal, state, and local data have been apparent and reported consistently demonstrating these gaps for at least three decades (Kent & Ricketts, 2021; Weller & Roberts, 2021). Even before the COVID-19 pandemic, racial income and poverty gaps were crippling. The Census Bureau reported that 2019 median income for white households was $76,057 and only$56,113 and $45,438 for Hispanic and Black households, respectively (Creamer, 2020; Semega et al., 2020). More than a quarter of Black children and 20.9% of Hispanic children fell below the poverty line in 2019, compared to 8.3% of white children (Semega et al., 2020; Wilson, 2020). The Federal Reserve notes that before the global pandemic, white families had eight times the wealth of Black families and five times the wealth of Hispanic families (Bhutta et al., 2020; Dettling et al., 2017). White families have and have had the highest median ($188,200) and mean ($983,400) family wealth, whereas Black families\u2019 median ($24,100) and mean ($142,500) wealth are less than 15% of those of white families\u2019 (Bhutta et al., 2020). In addition to the magnitude of net worth, there are substantial disparities in the nature of the assets owned by race and ethnicity. Not only are white families much more likely to receive an inheritance, own a home, hold equities, and have a retirement plan but also in all cases the values of these assets are significantly more for white households compared to households of color (Bhutta et al., 2020). The wealth gap between Black households and white households was larger in 2019 than in 2004 and 2007, before the Great Recession (Weller & Roberts, 2021). Post-2019 data suggest that the 2020\u20132021 pandemic has resulted in a similar pattern of widening the already dehumanizing racial wealth gap (Weller & Figueroa, 2021). Discriminatory tax policies have meaningfully contributed to income and wealth inequality generally and have exacerbated America\u2019s persistent racial wealth gap (Huang & Taylor, 2019; Lipman et al., 2020). Together with a long history of systemic racism in government policies and institutions and in American society at large, tax policies have built and continue to build wealth for white households at the expense of the economic well-being of households of color (Lipman et al., 2020). The federal government spends more than$400 billion annually through the income tax system supporting wealth building predominately benefiting high-income white households (Urban Institute, 2017). The top 20% of income households receive approximately 67% of aggregate homeownership and retirement subsidies. The bottom 20% of income households receive less than 1% of these tax benefits. Black, Latinx, and Indigenous families have lower median and average household incomes and receive meaningfully fewer tax benefits than white households both in total amount and as a percentage of their incomes (Huang & Taylor, 2019; Urban Institute, 2017).\n\nDespite record U.S. income inequality, not only relative to its own five decades of history but also relative to all G7 developed nations according to the Organisation for Economic Co-operation and Development, and an even more severe wealth gap that has doubled from 1989 to 2016, Congress has continued to exacerbate rather than mitigate overall and racial inequality. For example, in 2017, Congress wrote and passed into law the $1.9 trillion 2017 Tax Cut and Jobs Act (2017 TCJA). Experts have estimated that 80% of the 2017 TCJA tax benefits go to white households, resulting in a 2018 average tax cut of$2,020 for white households, $970 for Latinx households, and$840 for Black households (Schaeffer, 2020; Wiehe et al., 2018). The top 20% of income households received 78% of the 2017 TCJA aggregate tax cuts. Although the largest number of low-income households are white, because white Americans continue to outnumber other races, due to centuries of discrimination Black and Latinx households are disproportionately lower income and make up 74% of the bottom 60% of income households (Creamer, 2020; Wiehe et al., 2018). Consistent with 2017 TCJA targeting, Black and Latinx households represent 10.2% and 11.9% of tax filers but received only 5.0% and 6.7% of the benefits, respectively (Wiehe et al., 2018).\n\nRacial disparities exist even more dramatically at the highest levels of household income and wealth. In 2010, Black Americans comprised 13.6% of the population but only 1.4% of the top 1% of households by income. white households represented 96.2% of the top 1% of households by income, and Latinx households represented merely 0.9% (The Grio, 2011). Even more dramatically, the median wealth of the top 1% of white households was $8.3 million, whereas median wealth of the top 1% of Black households was less than 15% of this amount at$1.2 million. This measure of lower median wealth reflects not only fewer assets and lower values but also more debt than that of their white counterparts. Median household debt for these wealthy Black households was $1,370,000 in 2010, which was 356% higher than that of white counterparts at$300,000 (The Grio, 2011). Whiteness correlates positively with wealth (Brown, 2021; Traub et al., 2017).\n\nThe federal tax system continues to exacerbate these differences. The average tax cut in the 2017 TCJA for white households in the top 1% of income levels was more than $52,000, whereas Latinx and Black counterparts only received$19,850 and $19,290, respectively (Wiehe et al., 2018). This stark difference results from the significant 2017 TCJA tax benefits that Congress delivered for income from wealth or capital versus income from work or labor. Because of historic discrimination, even the wealthiest Black and Latinx households own relatively fewer wealth-producing assets and, therefore, a higher percentage of their income is based on labor rather than capital. Because of this economic profile, even the highest income Black and Latinx households were targeted to receive aggregate 2017 TCJA tax benefits that are less than 40% of amounts enjoyed by their white counterparts. This targeting of tax spending to wealthy white households is antithetical to mitigating the racial wealth gap and to an equitable and fair tax system. Racial income and wealth gaps cannot be explained by lack of individual responsibility, family values (e.g., marriage), education, or work (Hamilton et al., 2015). For families of color, working and studying hard do not translate into the same wealth accumulation as that of their white counterparts (Kent & Ricketts, 2021). Stratification of economic data has demonstrated that the payoff for education for Black families pales by comparison to that of white counterparts and even by comparison to white families who have invested significantly fewer resources in their education (Francis & Weller, 2020). Black families whose heads of household earned a college degree have less than 67% of the average wealth of white families headed by a high school dropout (Hamilton et al., 2015). Black families headed by individuals with professional or graduate degrees have less wealth than white families headed by individuals without a college degree but some college attendance (Hamilton et al., 2015). Recent research shows that Black college graduates\u2019 wealth declines after graduation because they are more likely to support family members financially and carry higher debt loads compared to white counterparts (Meschede et al., 2017). Racial identity is a stronger predictor of wealth than occupational sector for Black households (Addo & Darity, 2021). Similarly, even full employment does not remedy the racial wealth gap. As a result of discrimination, including \u201coccupational segregation,\u201d individuals of color earn up to$1 million less than white individuals over their lifetimes (Urban Institute, 2017). This lifetime earnings gap increases by almost 50% at the intersection of race and gender (Urban Institute, 2017). White families with a head of household who is unemployed have nearly twice the median wealth of Black families with a head of household who is employed full-time ($21,892 vs.$11,649) (Hamilton et al., 2015).\n\nEven aggregate household income fails to mitigate the racial wealth gap. At every income level, the wealth of Black households is a fraction of that of their white counterparts even though Black households save slightly more (Gittleman & Wolff, 2004). Despite incessant focus, family structure is not the cause of the racial wealth gap given that median single-parent white households have more than twice the wealth of median two-parent Black or Latinx households (Traub et al., 2017). Since the time of slavery, families of color have faced structural barriers to income and wealth accumulation while white families have received meaningful government subsidies (Hamilton et al., 2015; Lipman et al., 2020).\n\nThe global pandemic, like the Great Recession, has exacerbated income and wealth inequality especially for communities of color that have been disproportionately segregated into essential work. These workers and their families have notably fewer health care benefits and safety nets and, therefore, have suffered higher rates of COVID infection, hospitalization, and death (Monte & Perez-Lopez, 2021; Snowden & Graaf, 2021). Scholars note that economic calamities such as COIVD-19 cause a feedback loop with income and wealth inequality causing poor health and poor health exacerbating economic inequality (Snowden & Graaf, 2021). Despite record COVID relief saving approximately 18 million from monthly poverty at the height of the economic crisis in April 2020, 8 million people were pushed into poverty (Parolin et al., 2020). This increase in poverty was especially acute for Black and Latinx households as well as for the 2.5 million children who were pushed into poverty during this period (Francis & Weller, 2020). By comparison, the aggregate wealth of predominately white U.S. billionaires increased 60% from $2.9 trillion on March 18, 2020, to$4.7 trillion on July 9, 2021 (Collins, 2021). These trends have exacerbated inequality and increased the poverty gap between white and Black or Latinx individuals by approximately 1% to 2% (Parolin et al., 2020).\n\nGiven generations of systemically subsidized white households versus generationally deprived households of color, predictable financial profiles emerge for these households that are a direct result of racially targeted institutional benefits and burdens. The next section includes a brief description of how foundational structures in the U.S. tax system exacerbates benefits and burdens. These structural designs further advantage white taxpayers over taxpayers of color because of these pre-existing and persistent financial and tax profiles (Brown, 2021; Lipman et al., 2020).\n\nTax System Design\n\nUnder the Constitution, Congress has plenary power to enact U.S. tax laws. The U.S. tax system has been and is a long-standing self-assessment system. Individuals, rather than the government, generally have the burden of tax liability calculations, assessment and proof including record-keeping, documentation, preparation, and tax return filing. The legislative branch of the government passes tax laws, the president signs them into law, and the U.S. Treasury, through the IRS, enforces them. Since the late 1990s, fiscal social benefits have been increasingly delivered by the Treasury through the federal income tax system. Congress has used the tax system to deliver these benefits for several reasons, including that it has increasingly required annual earned income as a condition precedent (e.g., welfare-to-work) for means-tested benefits. Moreover, participation in these tax system benefits tends to be higher than that for other delivery methods because taxpayers with earned income must use the tax system to determine their annual earnings, tax liability, and claim any tax refunds or pay any amount due every year. Because the federal income tax withholding system is designed to over- versus underwithhold, taxpayers subject to withholding must prepare and file annual tax returns to receive their overpaid taxes or tax refunds.\n\nTaxpayers whose income comes predominately from wages are disproportionately lower income and Black or Latinx. Communities of color, compared to white wealthy households, are more likely to overpay their tax liabilities throughout the year through wage withholding and file their tax returns to collect their overpayments or tax refunds. Consequently, tax compliance for wage earners is 99% or at least twice the compliance rate for most other types of income (IRS, 2020a). Using the federal income tax system, a system that working families are already having to engage with each year to collect their tax overpayments, to similarly deliver social benefits should be efficient. As a result of this structure and delivery design, lower income wage-earning families who are predominately white, but disproportionately Black and Latinx, have been increasingly reliant on the IRS to deliver critical financial resources. Generally, because of their financial profiles and the tax system design, these families are part of the \u201clarge majority of compliant taxpayers\u201d given that as a group they are more likely to be subject to wage withholding, seeking cash refunds, including Congressionally approved and appropriated social benefits, delivered by the IRS.\n\nBy comparison, higher income white households that generally have more net worth than their counterparts of color have relatively more investment income from accumulated capital than labor income (Bhutta et al., 2020; Gebeloff, 2021). As such, white households have a relationship with the IRS that is more likely self-reporting taxable transactions, not subject to withholding, and must affirmatively self-elect to pay tax liabilities quarterly through estimated tax payments or at year end. Given this tax profile, these households are less likely to have a significant percentage of their income subject to automatic income tax withholding or even information reporting. Accordingly, these wealthy households, which are disproportionately white, engage in interactions with the IRS that can be characterized as disclosing transactions rather than reconciling income with information reported amounts (e.g., W2s and Form 1099s) to calculate and pay their tax liabilities. Whereas wages are subject to significant information reporting and withholding requirements resulting in compliance rates of 99%, business and investment income is less likely to be reported to the IRS by third parties and therefore income underreporting makes up 60% of the individual income tax gap (IRS, 2019). Recent data indicate that the compliance rate for income subject to substantial information reporting but no withholding is 95% (e.g., interest and dividend income) and only 45% for income subject to little or no information reporting, such as pass-through business income (IRS, 2019).\n\nBecause of increased tax complexity and significant income and assets, these taxpayers have the resources and motivation to engage sophisticated tax professionals, including certified public accountants and attorneys, to structure, prepare, file, and manage their tax matters. Given this financial profile and tax attributes, these high-income white households are more likely to be part of the \u201cminority who are unwilling to pay their fair share\u201d and are significant contributors to the tax gap. Economists have recently estimated that 70% of the tax gap can be traced to the top 1% of income households (Forman et al., 2021; Sarin & Summers, 2019). The next section reviews how the IRS\u2019 enforcement division differently administers these distinct households.\n\nTax System Institutional Racism\n\nTo address racial economic inequality, policymakers must not only address discriminatory substantive tax laws but also review and address how the Treasury and IRS enforce tax laws (Fichtner et al., 2019; Debacker et al., 2020). For the past 25 years, Congress has been defunding the IRS (Rossotti et al., 2020). At the same time, the number of tax returns has increased by 31%, and Congress has mandated that the IRS implement and integrate new areas of tax law, including complex tax provisions and additional reporting obligations (Rossotti et al., 2020). In fiscal year 2021, the IRS\u2019 enacted budget of $11.9 billion was$200 million less than its budget in 2010 of $12.1 billion in nominal (not adjusted for inflation) dollars (Rettig, 2021). Since 2010, Congress has decreased the IRS\u2019 budget by 22% in real terms while it simultaneously mandated implementation of significant tax legislation, in some cases retroactively, including, without limitation, the Affordable Care Act in 2010 (ACA), the 2010 Foreign Account Tax Compliance Act, Protecting Americans from Tax Hikes Act in 2015, the 2017 TCJA, and significant 2020 and 2021 COVID economic relief. In the ACA alone, the IRS successfully implemented 47 tax and insurance subsidy provisions, including at least 18 provisions affecting$1 billion or more in federal funds in the first 3 years. In 2020 and 2021, the IRS processed and distributed hundreds of millions of COVID relief payments aggregating $800 billion, including payments to millions of lower income individuals who have not been part of the IRS\u2019 145 million traditional individual taxpayer base (Holtzblatt, 2021). For decades, the IRS has been asked to do more with less. Defunding Tax Enforcement For 35 years, IRS staffing increases remained relatively consistent with GDP growth. However, since 1995, real GDP has increased by 76% and IRS staffing has decreased by 32% (Rettig, 2021). Although Congress has cut the IRS\u2019 budget across all areas, the largest budget cuts have been in IRS enforcement. IRS enforcement suffered a 26% budget decrease and a significant cut in full-time equivalent staff. The IRS\u2019 entire workforce decreased from 112,000 in 1990 to 74,000 in 2019, equal to 1973 staffing levels. More than two-thirds of full-time equivalent personnel losses occurred in enforcement activities. The IRS has fewer auditors than it has ever previously employed since World War II (U.S. Department of the Treasury, 2021). Correspondingly, tax enforcement activities have dropped precipitously. In response to the decreased budget, aggregate audit rates have decreased by 45% (Huang, 2020). However, audits have not decreased uniformly across all taxpayer types and income ranges. Audit rate reductions have been most significant for the highest income households earning$1 million or more at 75% and the largest corporations with reductions of 50% (Center on Budget and Policy Priorities, 2021; Huang, 2020). In 2011, almost 13% of millionaires and nearly all the largest corporations were audited, compared with only 3.3% of millionaires and less than half of the largest corporations in 2018 (Huang, 2020; Treasury Inspector General for Tax Administration, 2021e). The IRS made these reductions even though estimates suggest that the top 1% of household income individual filers account for as much as 70% of the tax gap (Sarin & Summers, 2019) and the top 0.5% of income households account for 20% of all underreported income (Johns & Slemrod, 2010).\n\nThe IRS, aware of this misallocation of resources, developed a \u201cGlobal High Wealth Industry Group\u201d with the experienced personnel needed to audit high-income taxpayers and the complex entities they own, including pass-through businesses, corporations, foundations, and trusts. IRS Commissioner Steven Miller, during the Bush and Obama administrations, had planned to assign almost 250 examiners to the \u201cwealth squad\u201d in 2009 (Eisenger & Kiel, 2019). However, soon after this concept was implemented, wealthy individuals successfully lobbied IRS, Treasury, and Congressional leadership. In response, Congress defunded rather than funded this well-targeted IRS enforcement effort (Eisenger & Kiel, 2019). During the Obama administration, in 2010 the IRS recommended additional tax assessments on individuals with more than $1 million in income of$5.7 billion. By 2017, during the Trump administration, this amount had dropped to $1.8 billion due to reduced enforcement (Eisenger & Kiel, 2019). Data on the deterrent effects of audits demonstrate that reduced IRS audit coverage levels during the past few decades have likely emboldened taxpayers to take more aggressive tax positions and undermined voluntary compliance rates (DeBacker et al., 2018b). In turn, public perception of integrity and fairness in the tax system generally and tax enforcement specifically has suffered given increased publicity of high-profile, high-income tax evasion, including allegations about former President Donald Trump. Any reduction in voluntary compliance rates is costly, given that a 1% decline in the rate can result in the loss of more than$30 billion in annual tax revenues (Rettig, 2021).\n\nPolicing the EITC\n\nThe smallest percentage decrease in audit rates has been for lower income working households that rely on the tax system to deliver their tax refunds including critical social benefits, specifically the EITC (Rossotti et al., 2020). Because of Congress\u2019 defunding of the IRS and targeting of EITC claimants, a lower income working family with children claiming the EITC is as likely to be audited as the top 1% of income households (approximately $500,000 or more) (Kiel, 2019a). In 2021, EITC claimants with$25,000 or less in gross receipts were audited at five times the rate as all other taxpayers (Transactional Records Access Clearinghouse, 2022).\n\nIncongruously, this is the case even though the EITC represents less than 6% of the tax gap (Fichtner et al., 2019; National Taxpayer Advocate, 2018). By comparison, underreported pass-through business income accounts for almost 50% of the tax gap due to underreported income or 35% of the tax gap (Center on Budget and Policy Priorities, 2021). Even the low 6% estimate of the EITC tax gap is likely overstated because of shortfalls in tax gap measurement, demographics of claimants, and the lack of access to tax assistance for most of these taxpayers (Fichtner et al., 2019; National Taxpayer Advocate, 2018).\n\nEITC tax gap estimates are derived from audit results that do not determine whether an EITC claim is legitimate in approximately 85% of cases (National Taxpayer Advocate, 2020b). These disallowances are characterized as overpayments even though this was not determined. Including all EITC disallowances in the EITC tax gap is misleading at best for several reasons. First, these alleged overpayments do not include EITC underpayments. Nationally, EITC participation rates average approximately 80%, with a higher percentage of EITC dollars being distributed of approximately 85% of all EITC estimated benefits (Treasury Inspector General for Tax Administration, 2018). The IRS has calculated that unclaimed EITC benefits represent approximately 40% of aggregate improper payments (National Taxpayer Advocate, 2020b). An example of how this issue might present itself is as follows: Assume a noncustodial parent claims an EITC for her child; the EITC counts as an overpayment because the qualifying child fails the household residency test (National Taxpayer Advocate, 2020b). However, the amount that the proper claimant, the custodial parent, was eligible to claim is not considered. In such cases, the actual loss to the Treasury is the net amount, if any. Moreover, these EITC benefits might be spent on behalf of the qualifying child even though the child did not reside with the noncustodial parent for the required period. Recently, when comparing actual EITC payments with estimated EITC amounts based on U.S. Census data, scholars have concluded that aggregate EITC overpayments are generally equal to aggregate EITC underpayments (Jones & Ziliak, 2019). If accurate, aggregate EITC underpayments fully offset aggregate EITC overpayments. Using this analysis, the net EITC tax gap would be negligible.\n\nSimilarly, Bastian and Jones (2020) have concluded that EITC benefits, including program expansions, pay for themselves. These scholars have monetized fiscal savings of 83% of EITC budget costs through a reduction in other government benefits and increased tax revenue. They note that federal EITC benefits will in some cases inure to the benefit of state and local governments given that EITC claimants likely spend their EITC benefits and pay state and local sales and other regressive taxes. These scholars also examined the social value of EITC benefits, including the physical health and well-being of children and members of EITC claimant households; reduced crime and criminal recidivism; reductions in drug use, suicides, and poverty; increased short-term and long-term educational successes and attainments; and increased household income, including retirement benefits. Upon reviewing this long list of societal benefits, they found \u201cstrong evidence that the EITC completely \u2018pays for itself\u2019\u201d (Bastian & Jones, 2020). Other scholars have noted that there is at least a two-time multiplier benefit effect from the EITC because these tax refunds are spent locally (Avalos & Alley, 2010). Thus, EITC benefits have been shown to stimulate financially challenged communities, including increased local purchasing power, resulting in job creation (Nichols & Rothstein, 2015).\n\nUnlike most taxpayer audits, EITC audits are predominately pre-refund audits (National Taxpayer Advocate, 2020b). This means that the refund due to the EITC claimant is frozen and not dispersed to the taxpayer until they prove affirmatively that they are eligible for the benefits. Ninety percent of self-employed taxpayer EITC audits are pre-refund and are focused on auditing the self-employed income amount, whereas 75% of EITC wage earner audits are pre-refund and focused almost exclusively (96%) on the residency of the qualifying child (Leibel et al., 2020). Therefore, unlike most audits, the taxpayer is suffering an immediate cash shortfall until they prove their eligibility rather than the government seeking monies owed to them from the taxpayer. This structure is different from most tax audits.\n\nAnother notable difference is that 99% of EITC audits are correspondence audits, meaning that EITC claimants who are audited receive a letter through the U.S. Postal Service describing the EITC audit issues to be addressed (National Taxpayer Advocate, 2020b). Researchers have found that a significant percentage of EITC correspondence audits result in the IRS denying the credits due to the taxpayer\u2019s nonresponse or insufficient response. Between 69% and 80% of audited claimants never received the notice, failed to respond, or stopped responding before an affirmative determination that they did not qualify for EITC benefits (Guyton et al., 2019; National Taxpayer Advocate, 2020b). These data demonstrate that audited EITC claimants, who are lower income and disproportionately individuals of color, most of whom are working and caring for young children, are unlikely to receive EITC tax refunds even though their claims are not determined to be invalid. By far most audited EITC claims are not confirmed to be valid (or invalid), because the taxpayer does not carry their burden of proof within the time frame according to the IRS. The IRS only confirms ineligibility of 13\u201315% of EITC audited claims, full eligibility of 6% or 7%, and partial eligibility of 2% of these claims (Guyton et al., 2019; National Taxpayer Advocate, 2020b). Because the disallowance rate is so high, 85\u201390% of EITC correspondence audits result in changes to the return (National Taxpayer Advocate, 2020b). Most of these changes deny families their EITC benefits without affirmatively determining that the families do not qualify.\n\nThe existing EITC audit structure disallows most claims without determining that the taxpayer failed to qualify. This result is due to many societal hurdles such that working families claiming the EITC do not have the resources to carry their burden of proof (National Taxpayer Advocate, 2020b). Similarly, the IRS has not allocated the necessary resources to work with claimants effectively to determine based on the facts at issue whether the taxpayers qualify for the benefits claimed (National Taxpayer Advocate, 2019). Because of these barriers, most EITC claimants who are audited have their EITC claims disallowed. Those aggregate dollars, without offset for any underpayments due to the qualifying taxpayer, and which may not represent actual overpayments, represent the EITC tax gap.\n\nBecause of lack of financial resources, time, and professional networks, EITC claimants are generally unrepresented by tax professionals. Like many taxpayers, they struggle to effectively communicate and work with the IRS (National Taxpayer Advocate, 2019). The IRS sends computer-generated letters to EITC claimants stating that they are being audited and requesting that they substantiate their EITC claims within 30 days. Given the lack of IRS infrastructure, including even timely opening written correspondence and answering telephones, correspondence audits are increasingly difficult, if not impossible, for EITC claimants to navigate (National Taxpayer Advocate, 2019, 2021; Transactional Records Access Clearinghouse, 2022). The National Taxpayer Advocate (2020b) has reported to Congress on several occasions that correspondence audits confuse and intimidate taxpayers, failing to provide them with sufficient time to respond or any IRS contact with whom to communicate.\n\nThe structure of EITC audits as pre-refund correspondence with an initial 30-day deadline and an agency that only responds to a small percentage of limited contact options undermine delivery of critical financial resources to the targeted taxpayers. Increasingly, EITC claimants struggle to document their claims to the IRS\u2019 satisfaction. The Taxpayer Advocate Service has reported that in a 2002 study of 67,000 files, 43% of audits that denied the EITC were reversed after the taxpayer received competent assistance (National Taxpayer Advocate, 2020b). Many EITC recipients do not have a tax professional representing them, and they face language barriers as well as significant time constraints given inflexible work and child care schedules. IRS services (e.g., telephone call access and taxpayer assistance centers) to assist taxpayers with their required response to receive their tax benefits have been significantly reduced (National Taxpayer Advocate, 2021).\n\nNavigating IRS telephone assistance is challenging even for experienced professionals, with more than 75% of calls unanswered (National Taxpayer Advocate, 2020a). In 2021, the IRS received more than 167 million calls, a nearly 300% increase from 2018, with only 9% of calls answered by an IRS customer service representative (National Taxpayer Advocate, 2021). The IRS telephone number that is specifically designated to support taxpayers received approximately 85 million calls, with only approximately 3% reaching a customer service representative (National Taxpayer Advocate, 2021). Twenty percent of Taxpayer Assistance Centers have been closed, and 42% of IRS copiers have been found to be inoperable. (Treasury Inspector General for Tax Administration, 2021a). EITC audit claimants must prove eligibility within short deadlines without assistance to an agency that is almost inaccessible (National Taxpayer Advocate, 2019). Given this severe lack of resources, EITC claimants, who are disproportionately lower income and individuals of color, are effectively denied meaningful opportunity to access their tax benefits.\n\nIRS research suggests that EITC correspondence audits not only have behavioral consequences that impact the taxpayer and their household but also have spillover effects to other households and the economy at large (Guyton et al., 2019). Most taxpayers subject to EITC correspondence audits suffer EITC disallowances and are less likely to claim EITC benefits or even file a tax return in subsequent years (DeBacker et al., 2018a, 2018b). Because this includes so many EITC claimants who are never affirmatively determined to not qualify for the EITC, it likely includes claimants who do qualify for the EITC and will not receive it in the year of audit or in subsequent tax years. This is antithetical to Congressional goals of targeting antipoverty EITC to these families and their communities.\n\nNotably, qualifying children disallowed on EITC audited returns are likely to be claimed by other taxpayers after the audits (Guyton et al., 2019). Thus, EITC overpayments may be materially overstated because the eligible claimant on behalf of the qualifying child did not receive any EITC benefits. Researchers found that net EITC overpayments due to failure to demonstrate the residency of a qualifying child could be overstated by 33\u201350% because the qualifying child in most cases resides in a U.S. household for more than half of the year and EITC benefits with respect to the qualifying child have not been claimed or paid out by the Treasury (Guyton et al., 2019).\n\nFinally, consistent with research that demonstrates that EITC benefits incentivize and increase wage earning, taxpayers who are denied EITC benefits pursuant to correspondence audits suffer reduced wage employment in years after being audited (Guyton et al., 2019). Not surprisingly, reduced wage employment is greater for taxpayers with young children ages 0\u20135 years in their households, perhaps due to the inability to afford child care and other work-related costs without EITC subsidies. Notably, households with individuals who are self-employed during the year of audit tend to have an increase in employee wages in tax years after the EITC audit (Guyton et al., 2019). Researchers have concluded that analogous to findings of positive EITC economic benefits, excessive EITC correspondence audits have adverse micro- and macro-economic impacts.\n\nDespite these adverse consequences, the IRS Commissioner has stated that EITC correspondence audits are \u201cthe most efficient use of available IRS examination resources\u201d (Kiel, 2019b). As a result, 43% of all 2018 IRS audits were of EITC claimants, and 37% of all audits in 2018 were EITC audits (National Taxpayer Advocate, 2020a). EITC claimants for this tax year had household income levels below $54,000. One of the stated reasons it is \u201cefficient\u201d to audit EITC claimants relative to high-income households is that the latter have significantly more resources to respond to the IRS and fight back compared to EITC claimants, as well as the IRS (Kiel, 2019b). Targeting taxpayers because they lack the capacity to respond effectively violates several statutory taxpayer rights. Moreover, designing EITC audits as pre-refund, correspondence audits in which the taxpayer must prove eligibility to receive their financial benefits to an agency that is increasingly impossible to reach is unjust. Auditing EITC claimants is not the most efficient use of IRS resources. The Treasury Inspector General for Tax Administration has repeatedly criticized the IRS\u2019 inefficiencies and misallocation of audit resources even given budget constraints resulting in a reduction of high-income audits (Treasury Inspector General for Tax Administration, 2015, 2018, 2020). The IRS has focused nearly half of its high-income audits on taxpayers earning between$200,000 and $399,999 even though these taxpayers are more likely to be wage earners and, therefore, \u201clow risk\u201d due to information reporting and withholding (Treasury Inspector General for Tax Administration, 2015). Taxpayers with incomes in the top 1% of households who are responsible for up to 70% of the tax gap have incomes at or above$500,000. The hourly audit adjustment for revenue agents auditing taxpayers with more than $5 million of income is$4,545 or 7.5 times more than the return on audits of the $200,000 to$399,999 income households (Nessa et al., 2016). A recent study found that if the IRS\u2019 enforcement budget had been increased $1 billion annually from 2002 to 2014, the IRS would have collected an additional$34 billion in revenue from large corporations, reducing the corporate tax gap by almost 20%, in addition to more revenue from individuals and other businesses (Nessa et al., 2016). Although in-person audits conducted in the field are more labor-intensive and thus more costly, the tax revenue collected on average is 10 and 8 times that for correspondence audits in 2010 and 2017, respectively (Hanlon, 2020). The Treasury Department has estimated that each dollar spent in tax enforcement activities yields $20.80, including$5.20 in direct revenue and $15.60 in indirect revenue (Hanlon, 2020). Investing in targeted tax enforcement is very lucrative. Scholars have found that even these high returns on enforcement dollars invested understate the aggregate return, especially if dollars are targeted away from lower income households toward high-income households, which are by far the greatest tax system abusers. A large payoff from high-income taxpayer audits has several components. Because of progressive tax rates, those who have higher income have larger tax liabilities; thus, discrepancies between what is owed and what is paid are likely larger in magnitude. High-income households have greater opportunity, motivation, and resources to lower their tax liabilities. These households also have higher rates of underreporting because more of their income is not subject to information reporting or tax withholding. If the IRS were to audit 50% of individuals who earn$10 million or more, 33% of those who earn between $5 million and$10 million, and 20% of those who earn $1 million or more, this would have corresponded to roughly 70,000 additional audits of those earning$1 million or more annually in 2018 (Sarin & Summers, 2019). Summers and Sarin estimate that if the IRS were to engage in this level of targeted high-income audits from 2020 through 2029, the additional tax revenue collected would be nearly $535 billion. Another reason given for excessive EITC audits other than disputable efficiency is that the Office of Management and Budget (OMB) has targeted the EITC as a high-priority program susceptible to significant improper payments. In 2002, Congress enacted the Improper Payments Information Act, a federal statutory regime focusing on waste and requiring government agencies to strictly track, monitor, and report on \u201cimproper payments\u201d (Treasury Inspector General for Tax Administration, 2020b). The Act requires agencies such as the IRS to identify high-priority programs and develop plans for reducing improper payments in those programs. Federal agencies report annual improper payments on more than 160 programs. Until 2018, the EITC was the only tax provision classified as an improper payment. The focus on the EITC rather than on other tax gap provisions that cause significantly more government waste in improper payments makes little economic sense. In 2018, despite even lower estimated tax gap contributions than the EITC, three additional tax credits were added to the targeted \u201cimproper payment\u201d watch list: the Child Tax Credit (CTC) (2% of the tax gap), the Premium Tax Credit (PTC) (less than 1% of the tax gap), and the American Opportunity Tax Credit (AOTC) (1% of the tax gap) (Treasury Inspector General for Tax Administration, 2021d). These additions to the list make even less sense given the low tax gap contributions. What these credits do have in common is that to some extent each one is refundable. However, refundability in and of itself should not render a tax provision subject to improper payment scrutiny. Researchers have determined that improper payment rates for the refundable portion of a tax credit are not more significant than the portion of the credit that offsets a tax liability. Moreover, after years of audits and disclosure, the consensus seems to be that most of the errors in the EITC are due to the complexity of the statute and targeted claimants\u2019 lack of resources to carry their burden of proof in a timely manner (Fichtner et al., 2019; Nichols & Rothstein, 2015; Transactional Records Access Clearinghouse, 2022). Treasury analysts have reported that only a minority of EITC improper payments stem from fraudulent actions (Holtzblatt & McCubbin, 2003). Given the modest contribution to the tax gap relative to most other tax provisions, the targeting of these credits is inconsistent with economic data, rational decision-making, and the government\u2019s goal to reduce waste. Other areas of the tax code that have high revenue losses, such as corporate transfer pricing or income reporting of pass-through businesses (Treasury Inspector General for Tax Administration, 2020, 2021c, 2021d), have not been identified as high-priority improper payment tax provisions. An IRS study covering the 2008\u20132010 period found that 63% of sole proprietor income was unreported and that unreported pass-through business income cost$125 billion in uncollected tax revenues per year (IRS, 2016). This amount and other significant tax provisions that are known to contribute to the tax gap are not targeted as improper payments.\n\nEvery tax dollar that goes unpaid has the same effect on the U.S. Treasury as a dollar that is \u201coverpaid\u201d by a government program. The inclusion of the EITC, CTC, AOTC, and PTC as improper payments because the government has characterized these as government outlays makes no economic sense given their relatively modest contribution to the tax gap. Because these tax provisions are contingent on certain levels of earned income, they are designed to deliver targeted benefits to lower income households, which are disproportionately families of color. More notable contributions to the tax gap, such as pass-through income, which is predominately due to wealthy white households not reporting their income, receive much less attention than improper payments. For example, the audit rates for both S Corporation and partnership returns have decreased by more than 40% since 2010 to just 0.2%, and 97 out of 100 millionaires are never audited (Sarin, 2021). The government suffers significantly more economic harm due to tax noncompliance, as evidenced by the massive annual tax gap, than from targeted improper payments. In 2018, improper payment estimates totaled $151 billion, or 4.6% of total spending for the programs, compared with the 2011\u20132013 net tax gap of$381 billion per year, or 14% of actual tax liability (Treasury Inspector General for Tax Administration, 2021d). And estimates of the 2021 tax gap are $600 billion to$1 trillion (Davison, 2021; Rettig, 2021; Sarin, 2021).\n\nFortunately, there has been pushback against this excessive scrutiny of the EITC, CTC, AOTC, and PTC as improper payments. In October 2020, the Treasury and IRS notified the OMB in a report titled \u201cBusiness Case to Eliminate Redundant Reporting of Refundable Tax Credits\u201d that they do not believe that refundable tax credits are outlays that meet the definition of payments and, therefore, should not be monitored under the Payment Integrity Information Act of 2019 (Treasury Inspector General for Tax Administration, 2021b). The report argues that these refundable credits, like deductions and tax-exempt and tax-rate preferred income, are embedded in the tax system and should not be segregated from their integral nonrefundable components or other tax provisions. The IRS argued it reviews its tax administration portfolio through a comprehensive enterprise risk management program including, but not limited to, regular tax gap analysis. It also noted that errors are \u201clargely due to the credits\u2019 statutory design and the complexity taxpayers face when self-certifying eligibility for the refundable tax credits, not internal control weaknesses, financial management deficiencies, or reporting failures\u201d (Treasury Inspector General for Tax Administration, 2021b). If OMB\u2019s goal is to reduce government waste, rather than targeting lower income households that are disproportionately Black, Latinx, and Indigenous families through excess audits of refundable tax credits, OMB should facilitate the targeting of the most significant abuse of government resources\u2014the tax gap.\n\nTax Gap Analysis\n\nDisparate Racial Impact of Audits\n\nThe disproportionate focus on EITC claimants when the tax gap is due overwhelmingly to high-income households is irrational and inequitable. Even more untenable is that the highest federal audit rates in America are in counties that are predominantly poor and Black in the rural South. The top 10 counties with the highest audit rates in 2012\u20132015 include 8 in Mississippi, 1 in Louisiana, and 1 in South Dakota. Each of these counties is home to predominately impoverished communities of color that endured audit rates higher than 40% above the national average. A map of audit intensity for this period demonstrates that the IRS concentrated audits in communities of color in the Black southern poverty belt, in U.S.\u2013Mexico border towns, and on Native American reservations (Harriot, 2019; Kiel & Fresques, 2019). Nearly every county in America where there are pockets of Black poverty experiences higher than average audit rates (Harriot, 2019).\n\nIn a recent report on EITC audits, the Treasury Inspector General for Tax Administration (2021a) notes that the southern states that experience the highest rates of EITC audits do not have the highest rates of EITC claimants but do have the highest rates of returns that trigger IRS EITC audit filters. This conclusion is not telling but, rather, is self-evident. The heavily redacted report does not contain any description of what the triggering filters are or even suggest that the triggers themselves should be re-evaluated given this disparate impact on certain states in the South that are home to the highest percentages of households of color, especially Black families. Moreover, when the Inspector General suggested that these targeted states should receive enhanced EITC education and outreach, the IRS disagreed with the recommendation, stating that it has a nationwide EITC education and outreach program. The Inspector General responded that \u201cwithout targeted outreach, based on examination results or concentration of filter rule breaks, disproportionate error rates will continue in these areas\u201d (Treasury Inspector General for Tax Administration, 2021a). Moreover, the report notes that this disparate impact is not new but, rather, that since at least the mid-1990s southern states with higher populations of communities of color have experienced relatively higher targeted EITC audits (General Accounting Office, 1998). Hence, the IRS\u2019 EITC education and outreach efforts have not been effective with regard to these taxpayers.\n\nThese data are even more egregious given that approximately 50% of EITC claimants are white and less than 20% are Black (Murray & Kneebone, 2017). The highest 15 audited counties, 12 of which are in predominately Black impoverished neighborhoods in Mississippi, have an average audit rate of 11.1 per 1,000 filers, including the highest audit rate nationwide of 11.8 in Humphreys County, Mississippi. The other 3 top audited counties are predominately non-white and disproportionately poor, including East Carroll County, Louisiana (70% Black and 38% impoverished); Oglala Lakota County, South Dakota (92.4% Indigenous and 40% impoverished); and Greene County, Alabama (80% Black and 32% impoverished). A map of the non-white population in America is comparable to a map of areas where IRS audit rates are higher than average (Harriot, 2019).\n\nIn sharp contrast, a map of the white population is comparable to where IRS audits are lower than average (Kiel & Fresques, 2019). The 10 poorest counties in the 10 whitest states in America have an average audit rate of only 8.1 per 1,000 filers. For example, Crawford County, Indiana, is 97% white and one of the poorest counties in the country, but the 7.7 audit rate per 1,000 filings is equal to the national average. Although inconsistent with tax gap data and the mission of the IRS to collect tax revenue, relatively high audit rates correlate with race and poverty.\n\nConclusion: Reconciling the Irreconcilable\n\nFunding and targeting IRS enforcement would not only pay for itself but also provide enough tax revenue to finance remedies for debilitating social problems, including ending homelessness, providing universally affordable quality child care, and rebuilding America\u2019s infrastructure, without any statutory tax law changes (Hanlon, 2020). Why has Congress moved in the opposite direction, defunding the IRS, causing reductions in enforcement during the past two decades from this economically sound and prudent move? Why is the IRS cutting back on tax enforcement of corporations and higher income taxpayers when the tax gap related to these taxpayers and the demonstrated return on these audits are much more significant than those of other audits? Why is the EITC, which scholars have determined effectively pays for itself and contributes little to the tax gap, excessively audited? Why are the only tax provisions categorized as improper payments tax provisions that disproportionately benefit households of color? Why are impoverished households of color effectively denied tax benefits with no meaningful recourse when wealthy white nonfilers owing billions of taxes are not even pursued? Why are poor households of color more likely to be targeted for audit than their white counterparts when more white households receive the EITC than households of color?\n\nThese questions, when viewed objectively with the data and details described in this article, demonstrate that consistent with many government institutions, federal tax enforcement advantages white wealthy households and disadvantages households of color. When the top 1% of income households are not paying hundreds of billions of tax liabilities due and payable annually, it is just a matter of time before historically stable voluntary compliance rates erode. The IRS\u2019 stated mission is not being fulfilled but, rather, is being upended into a two-tier tax system (Hanlon & Hendricks, 2021)\u2014a system that is separate and unequal, in which the richest predominately white households do not follow the laws and suffer few consequences while the lowest income families who are predominately households of color are denied their legal benefits without the opportunity to be heard.\n\nCenturies of racial exclusion and discrimination have been hardwired into U.S. systems and institutions enduring until now normalized, endemic, and deemed neutral even though patently improvident, unjust, and racist. Evidence of disparate racial impact of audits not only harms children of color, their families, and communities and businesses but also undermines confidence in and the integrity of U.S. tax systems and the federal government. Moreover, the annual fiscal cost to the Treasury is catastrophic. Systemic and institutional racism exacerbates, rather than mitigates, racial inequities, including racialized economic injustice, which has resulted in pernicious wealth and income inequality. Irrational, uneconomical, and racially discriminatory audits must stop. Funding IRS targeted high-income enforcement measures and building institutional resources to facilitate rather than undermine EITC participation are obvious and economically sound solutions.\n\n\u2022 Baradaran, M. (2017). The color of money: Black banks and the racial wealth gap. Belknap.\n\u2022 Bearer-Friend, J. (2022). Colorblind tax enforcement. New York University Law Review, 97, 1\u201358.\n\u2022 Bittker, B. I. (2003). The case for Black reparations. Beacon.\n\u2022 Davis, C., Guzman, M., & Schieder, J. (2021). State income taxes and racial equity: Narrowing racial income and wealth gaps with state personal income taxes. Institute on Taxation and Economic Policy.\n\u2022 Kendi, I. X. (2016). Stamped from the beginning: The definitive history of racist ideas in America. Nation Books.\n\u2022 Kendi, I. X. (2019). How to be an antiracist. Crown.\n\u2022 McGhee, H. (2021). The sum of us: What racism costs everyone and how we can prosper together. One World.\n\u2022 Rothstein, R. (2017). The color of law. Liveright.\n\u2022 Saez, E., & Zucman, G. (2019). The triumph of injustice: How the rich dodge taxes and how to make them pay. Norton.\n\u2022 Smith, A. (2015). Tax law and racial economic justice. Lexington Books.\n\u2022 Walsh, C. (2018). Racial taxation: Schools, segregation, and taxpayer citizenship, 1869\u20131973. University of North Carolina Press.","date":"2022-06-25 05:02:12","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.25329896807670593, \"perplexity\": 9146.842677967163}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-27\/segments\/1656103034170.1\/warc\/CC-MAIN-20220625034751-20220625064751-00034.warc.gz\"}"} | null | null |
Eduard Folayang Bids to Reclaim Lightweight World Title in MNL this January
Filipino martial arts veteran and two-time ONE Lightweight World Champion Eduard "Landslide" Folayang is confident he has enough left in the tank to bag another shot at the title this year.
The Team Lakay stalwart succumbed the lightweight belt in Tokyo in early 2019, falling to rival Shinya Aoki via first-round submission at ONE: A NEW ERA. It was a painful setback, but did little to deter Folayang's fighting spirit.
This year, Folayang vows to return as a better competitor, and show fans he has what it takes to be champion again.
"2019 has been an absolute roller coaster ride for me," Folayang said.
"I started the year off as champion but fell short of victory against Shinya [Aoki] in Tokyo. That's a loss that I learned a lot from and it was a very tough experience to deal with. I can honestly say however that I am a much better martial artist because of it."
Apart from taking on the legendary Aoki, Folayang also got the opportunity to challenge multiple-time lightweight champion Eddie "The Underground King" Alvarez, a more than recognizable name in the mixed martial arts ecosphere.
Despite dominating Alvarez in the early going however, Alvarez turned the corner and scored a come-from-behind victory on the strength of his wrestling and submission skills. The American secured a rear-naked choke midway through the first round, earning a spot in the ONE Lightweight Grand Prix Championship Final, which he eventually relinquished due to injury.
Although it was another painful setback, Folayang realizes the value of facing an American icon.
"After facing Eddie Alvarez of course, it was another learning experience for me," Folayang said.
"Being able to face one of the best fighters in the world, who is a former UFC and Bellator World Champion, it was a huge honor. I feel like I was winning that fight, and then one mistake and I'm on the losing end. I won't make that same mistake again next time."
For Folayang to be able to return to title contention, he has to be perfect to start the year. He believes he has to turn in inspiring performances that will catapult him back up the rankings, starting with his first bout of 2020.
Folayang is scheduled to face Pakistan's Ahmed "The Wolverine" Mujtaba at ONE: FIRE & FURY, set for the Mall of Asia Arena in Manila on Friday, 31 January. In this bout, Folayang vows to showcase his overall improvements, and that he learned valuable lessons in the past year.
"As a martial artist, I'm always learning and growing," Folayang concluded.
"I still feel like I'm at the top of my division, and I want to get back in contention in 2020. The lightweight division is one of the toughest in ONE Championship, and I want to reclaim the title again for my Filipino fans. I'm hungry as ever for victory. I will be back on top. It's all about that mindset. With the help of God, I'll be champion again." | {
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Zespół Szkół Ekonomiczno-Administracyjnych im. Stanisława i Władysława Grabskich w Kole – jedna z czterech kolskich szkół ponadpodstawowych. Położona jest nad wschodnim brzegiem Warty, na terenie osiedla Przedmieście Warszawskie. Założona w 1947 roku.
Jeden z budynków szkoły został wpisany do gminnej ewidencji zabytków.
Historia
Staraniem władz samorządowych, organizacji społecznych, kupiectwa i spółdzielczości, Kuratorium Okręgu Szkolnego Poznańskiego w roku 1947 powołało Gimnazjum i Liceum Handlowe. 4 września 1947 roku nominację na dyrektora szkoły otrzymał Leon Stawicki – absolwent Akademii Handlowej w Poznaniu. Grono pedagogiczne zostało skompletowane i wstępne egzaminy zostały przeprowadzone do 16 września, a 17 września 1947 roku w sali Starostwa Powiatowego. Szkoła przyjęła następnie nazwę Państwowe Koedukacyjne Gimnazjum i Liceum Handlowe w Kole. Pracę w szkole rozpoczęło 16 nauczycieli, w tym 6 dochodzących do szkoły z Liceum i Gimnazjum "Oświata", a do szkoły uczęszczało 212 uczniów.
W 1950 roku szkoła przeniosła się do gmachu przy ulicy Mickiewicza 14, zajmowanego przez starostwo, a przed II wojną światową będącego siedzibą liceum ogólnokształcącego. Przy szkole działał Związek Młodzieży Polskiej, Związek Harcerstwa Polskiego i chór oraz biblioteka. W 1951 roku szkoła została przekształcona w Technikum Handlowe. Na przełomie 1951 i 1952 roku postanowiono zmienić profil szkoły, pozostawiając tylko jeden profil ekonomiczny, a wprowadzając zamiast tego dwie klasy o kierunku mechanicznym. W 1954 roku szkoła została przekazana Ministerstwu Rolnictwa i przekształcona w Technikum Weterynaryjne, postanowiono jednak doprowadzić pozostałe klasy handlowe do matury zgodnie z wcześniejszym programem. Technikum Handlowe oficjalnie przestało istnieć w 1957 roku.
W 1960 roku Ministerstwo Oświaty zezwoliło na otwarcie w Kole 5-letniego Technikum Ekonomicznego, od 1961 roku prowadzono również Państwową Szkołę Techniczną dla absolwentów liceów ogólnokształcących, a w 1963 roku otwarto również Technikum Ekonomiczne dla Pracujących. Siedziba szkoły mieściła się w budynku przy ulicy Mickiewicza 1, który był jednak zbyt mały na jej potrzeby. W 1967 roku szkoła została Liceum Ekonomicznym. W 1973 roku powstało Liceum Ekonomiczne dla Pracujących (zamknięte w 1991 roku), a w 1974 roku przy szkole działało Liceum Zawodowe, uczące sprzedawców i magazynierów. W latach 70. XX wieku wprowadzono również specjalności: administracja terenowa, pracownik administracyjno-biurowy, kelner bufetowy i gastronom oraz kierunek włókienniczy (na potrzeby Widzewskich Zakładów Przemysłu Bawełnianego Wi-Ma.
Pod koniec lat 80. XX wieku rozpoczęto starania na rzecz budowy nowego budynku szkolnego. Prace rozpoczęto w 1989 roku, jednak z powodu problemów finansowych przerwano je w 1990 roku, ponownie rozpoczęto je rok później, a nowy budynek oddano do użytku 18 września 1992 roku. W 1992 roku powołano nowy typ szkoły – Technikum Zawodowe oraz wprowadzono kolejny kierunek: technik hotelarstwa. W tym samym roku wybrano również patronów szkoły, którymi zostali bracia Stanisław i Władysław Grabscy, przekazano wówczas także szkole historyczny sztandar oraz odsłonięto tablicę pamiątkową poświęconą Leonowi Stawickiemu.
W 2002 roku powołano przy Technikum Liceum Profilowane oraz Szkołę Zawodową i Szkołę Policealną, szkoła została wówczas Zespołem Szkół Ekonomiczno–Administracyjnych w Kole. W 2010 roku wmurowano kamień węgielny pod budowę sali gimnastycznej, którą ukończono w 2012 roku.
Od 1 września 1997 roku do 31 sierpnia 1998, tj. przez jeden rok szkolny funkcję dyrektora pełniła Danuta Krzyżanowska, a od 1 września 1998 roku dyrektorem był Mieczysław Drożdżewski. Od 2006 roku dyrektorem placówki była mgr Elżbieta Sztanga, a w 2016 roku dyrektorem ponownie został Mieczysław Drożdżewski. W tym samym roku powstało również Stowarzyszenie Absolwentów i Przyjaciół Kolskiego Ekonomika.
Internat
Od 1 września 1961 roku w położonym niedaleko od szkoły domu przy ulicy Sienkiewicza 7 działał internat. W internacie dostępnych było 55 miejsc, liczba mieszkańców dochodziła jednak czasem aż do 60. Warunki mieszkalne w internacie były w początkowym okresie jego funkcjonowania trudne, co spowodowane było skromnym wyposażeniem oraz niedostatecznymi funduszami, które przeznaczone miały być na przystosowanie obiektu. W 1977 roku piwnica budynku została zaadoptowana na świetlicę.
Pierwszą wychowawczynią, pracującą w internacie w latach 1961–1971 była Jadwiga Karwacka (żona przyszłego dyrektora szkoły, Michała Karwackiego). Następnie wychowawczyniami były: Anna Wielogórska, Krystyna Szymankiewicz, Izabela Żurawik, Alina Bawarska, Czesława Piguła (1976–1986), Izabela Mroczkowska (1986–1987), Elżbieta Karwacka i Anna Karolak. Długoletnią kierowniczką internatu była Zofia Rydzewska, a od 1986 roku Czesława Piguła.
W 1976 roku internat uzyskał II miejsce w konkursie na najlepszy internat w regionie. Przy internacie działała Młodzieżowa Rada Internatu, która nadzorowała działalność klubów i kółek, organizację meczy oraz inne akcje. Internat zlikwidowano w 1991 roku.
Stan obecny
W roku szkolnym 2020/2021 szkoła prowadziła rekrutację do klas:
liceum ogólnokształcące o profilu prozdrowotnym z elementami ratownictwa medycznego
liceum ogólnokształcące o profilu europejsko-medialnym z elementami dziennikarstwa
Oraz do klas technikum, nadających tytuły zawodowe:
technikum o profilu menadżersko-prawnym (technik ekonomista)
technik rachunkowości
technik geodeta
technik obsługi turystycznej/technik organizacji turystyki
W szkole działa Klub Europejczyka (współpraca z Fundacją Schumana, jako jedna z nielicznych szkół w Wielkopolsce). Poza tym przy szkole funkcjonuje również Harcerska Drużyna Wędrownicza, Szkolne Koło PCK. Szkoła brała udział w organizowaniu wydarzeń takich jak festiwal "Opole w Kole", "Ekonomalia" i "Ekonomik dla Koła".
Dyrektorzy szkoły
Lista dyrektorów szkoły od 1947 roku:
Leon Stawicki (1947–1950)
Wiktor Zieleśkiewicz (1950–1951)
Leon Stawicki (ponownie, 1951–1952)
Jerzy Horodyski (1952–1953)
Edward Szymański (1953–1954)
Józef Sobień (1954–1955)
Eugeniusz Rybacki (1955–1960)
Zofia Zdrojowa (1960–1971)
Piotr Łukaszewski (1971–1975)
Michał Karwacki (1975–1990)
Barbara Szlaga (1990–1997)
Danuta Krzyżanowska (1997–1998)
Mieczysław Drożdżewski (1998–2006)
Elżbieta Sztanga (2006–2016)
Mieczysław Drożdżewski (ponownie, od 2016)
Pracownicy szkoły
Bernard Draheim – lekarz szkolny
Mieczysław Drożdżewski – nauczyciel fizyki i dyrektor szkoły
Kazimierz Kasperkiewicz – nauczyciel języka niemieckiego
Leon Leja – jeden z założycieli szkoły, fundator i kierownik internatu
Józef Stanisław Mujta – nauczyciel historii
Stanisław Sudoł – nauczyciel księgowości w latach 1949–1951
Znani absolwenci
Mikołaj Kołodziejczak
Jan Kumider
Henryk Perzyński
Przypisy
Bibliografia
J. Burszta. "Sześćset lat miasta Koła." Poznań 1963
P. Łączkowski, M. Pochwicki. "Koło. Rozwój miasta 1948-1978." Poznań-Koło 1978
E. Jaśkowski. "Historia oświaty w mieście Kole." Koło 2001
Linki zewnętrzne
Oficjalna strona szkoły
Licea ogólnokształcące w województwie wielkopolskim
Polskie technika
Polskie licea profilowane
Polskie zespoły szkół
Zespół Szkół Ekonomiczno-Administracyjnych im. Stanisława i Władysława Grabskich w Kole | {
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Q: Can't store output from Colab into Excel I wrote the code below but was unable to save it into Excel.
!pip install selenium
!apt-get update # to update ubuntu to correctly run apt install
!apt install chromium-chromedriver
!cp /usr/lib/chromium-browser/chromedriver /usr/bin
import sys
sys.path.insert(0,'/usr/lib/chromium-browser/chromedriver')
from selenium import webdriver
chrome_options = webdriver.ChromeOptions()
chrome_options.add_argument('--headless')
chrome_options.add_argument('--no-sandbox')
chrome_options.add_argument('--disable-dev-shm-usage')
wd = webdriver.Chrome('chromedriver',chrome_options=chrome_options)
lists = ["FBRX", "GNLN", "TISI"]
for list in lists:
url = "https://finance.yahoo.com/quote/{list}?p={list}"
wd.get(url.format(list=list))
EPS = wd.find_element_by_xpath('//*[@id="quote-summary"]/div[2]/table/tbody/tr[4]/td[2]/span').text
AV = wd.find_element_by_xpath('//*[@id="quote-summary"]/div[1]/table/tbody/tr[8]/td[2]/span').text
OYT = wd.find_element_by_xpath('//*[@id="quote-summary"]/div[2]/table/tbody/tr[8]/td[2]/span').text
print(list,EPS,AV,OYT)
It will output the below table. But after that, I can't make the below into Excel. I had tried many methods but still fail. How can I fix this?
FBRX -1.6060 2,031,998 3.25
GNLN -1.0530 827,585 5.40
TISI -2.4640 545,536 10.00
A: This should do the job, replace intead of the second part of the code you posted:
lists = ["FBRX", "GNLN", "TISI"]
import pandas as pd # Import Pandas
df = pd.DataFrame(columns=range(len(lists)), index=lists) # Create empty DataFrame
for i, list in enumerate(lists):
url = "https://finance.yahoo.com/quote/{list}?p={list}"
wd.get(url.format(list=list))
EPS = wd.find_element_by_xpath('//*[@id="quote-summary"]/div[2]/table/tbody/tr[4]/td[2]/span').text
AV = wd.find_element_by_xpath('//*[@id="quote-summary"]/div[1]/table/tbody/tr[8]/td[2]/span').text
OYT = wd.find_element_by_xpath('//*[@id="quote-summary"]/div[2]/table/tbody/tr[8]/td[2]/span').text
print(list,EPS,AV,OYT)
df[i][0]=EPS # Fill line i-th, column 0
df[i][1]=AV # Fill line i-th, column 1
df[i][2]=OYT # Fill line i-th, column 2
df.to_excel("output.xlsx") # Save to excel file
Basically, you create a DataFrame, which is like an empty table, by using Pandas ("a fast, powerful, flexible and easy to use open source data analysis and manipulation tool, built on top of the Python programming language"). Then, for every loop, you fill a line of the DataFrame.
Finally, you invoke the to_excel() method to store the file as output.xlsx. You will find it in the content folder of Google Colab.
A: Build a list of results in the for loop, use Pandas to make a data frame, and from this create the spreadsheet.
lists = ["FBRX", "GNLN", "TISI"]
result=[] # empty list to start
for list in lists:
url = f"https://finance.yahoo.com/quote/{list}?p={list}" # use an f string to format
wd.get(url.format(list=list))
EPS = wd.find_element_by_xpath('//*[@id="quote-summary"]/div[2]/table/tbody/tr[4]/td[2]/span').text
AV = wd.find_element_by_xpath('//*[@id="quote-summary"]/div[1]/table/tbody/tr[8]/td[2]/span').text
OYT = wd.find_element_by_xpath('//*[@id="quote-summary"]/div[2]/table/tbody/tr[8]/td[2]/span').text
print(list,EPS,AV,OYT)
result.append([list,EPS,AV,OYT]) # add the row to the results
result
#[['FBRX', '-1.6060', '2,031,998', '3.25'],
# ['GNLN', '-1.0530', '827,585', '5.40'],
# ['TISI', '-2.4640', '545,536', '10.00']]
import pandas as pd
df = pd.DataFrame(result, columns=['List','EPS','AV','OYT'])
df.to_excel('result.xlsx')
Note that I had to make the url generation use an f string to get the url correct.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 5,623 |
\section{Introduction}
The Abelian Pure Chern Simons (CS) Theory is a mixed constrained system where one of their four constraints must be redefined in order to be a first class one. Then, after this step, we have well defined algebras of two first class constraints and two second class constraints. The BFT formalism\cite{BFFT,embed}, which enlarges the phase space variables with the introduction of the Wess Zumino (WZ) fields, has been used with the objective to embed the CS theory\cite{pcs}. As a result, the authors show many important features. Another work\cite{ncs} has also employed the BFT formalism to study a Nonabelian version of the CS theory. In this article, the authors propose two methods that overcome the problem of embedding mixed constrained systems. In an opposite side of the BFT formalism, there is another method that embeds second class constrained systems, called Gauge Unfixing (GU) formalism. It was proposed by Mitra and Rajaraman\cite{MR} and continued by Vytheeswaran\cite{Vyt,JAN}. This formalism considers part of the total second class constraints as the gauge symmetry generators while the remaining ones form the gauge fixing terms. The second class Hamiltonian must be modified in order to satisfy a first class algebra with the constraints initially chosen to be the gauge symmetry generators. This approach has an elegant property that does not extend the phase space with extra variables.
The purpose of this paper is to give a alternative scheme for the GU formalism and to apply this method to the CS theory. Our aim is to redefine the original phase space variables of a constrained system, without to introduce any WZ terms, in order to be gauge invariant fields. Then, after this procedure, we will construct functions of these gauge invariant fields which will be gauge invariant quantities. As we will see, we begin with a mixed constrained system that is the CS theory and, applying our formalism, we obtain a first class system written only in terms of the original phase space variables with many novel features. As many important constrained systems have only two second class constraints, then, in principle, we present our formalism only for systems with two second class constrains without any loss of generality. In order to clarify the exposition of the subject, this paper is organized as follows: in Section 2, we give a short review of the usual GU formalism. In Section 3, we present our formalism. In Section 4, we apply our procedure to the CS theory. In Section 5, we make our concluding remarks.
\section{A brief review of the Gauge Unfixing formalism}
Let us consider a constrained system described by the second class Hamiltonian $H$ and two second class constraints $T_1$ and $T_2$. The basic idea of the GU formalism is to select one of the two second class constraints to be the gauge symmetry generator. As example, if we choose $T_1$ as the first class constraint, then, we need to scale $T_1$ as $\,\frac{T_1} {\Delta_{12}}\equiv\tilde{T}\,$
where $\Delta_{12}=\{T_1,T_2\}\,$. The second class constraint $T_2$ will be discarded. The Poisson bracket between $\tilde{T}$ and $T_2$ is $\,\{\tilde{T},T_2\}=1\,$,
so that $\tilde{T}$ and $T_2$ are canonically conjugate. The second class Hamiltonian
must be modified in order to satisfy a first class algebra. Then, the gauge invariant Hamiltonian is constructed by the series in powers of $T_2$
\begin{equation}
\label{gh}
\tilde{H}=H+T_2\,\{H,\tilde{T}\}+\frac{1} {2!}T_2^2\,
\{ \{H,\tilde{T}\},\tilde{T}\}+
\frac{1} {3!} T_2^3\,\{\{\{ H,\tilde{T}\},\tilde{T}\},\tilde{T}\}+\ldots,
\end{equation}
where we can show that $\{\tilde{H},\tilde{T}\}=0$ and $\tilde{T}$ must satisfy a first class algebra $\{\tilde{T},\tilde{T}\}=0$. The gauge invariant Hamiltonian, Eq.(\ref{gh}),
can be elegantly written in terms of a projection operator on the second class Hamiltonian $H$
\begin{equation}
\tilde{H}= e^{T_2 \tilde{T}_{op}}:H,
\end{equation}
where $\tilde{T}_{op}\, H\equiv\{H,\tilde{T}\}$ and an ordering prescription must be adopted that is $T_2$ must come before the Poisson bracket.
\section{The improved Gauge Unfixing formalism}
Let us start with the original phase space variables written as
\begin{equation}
F=(q_i,p_i),
\end{equation}
where $\, F \,$ can describe a particle or field model. As we haven seen in Section 2, the usual GU formalism embeds directly the second class Hamiltonian. Thus, our strategy is to construct a gauge invariant function $\tilde{A}\,$ from the second class function $A\,$ by gauging the original phase space variables, using for this the idea of the GU formalism.
Denoting the first class variables by
\begin{equation}
\tilde{F}=(\tilde{q_i},\tilde{p_i}),
\end{equation}
we determine the first class function $\tilde{F}$ in terms of the original phase space variables by employing the variational condition
\begin{equation}
\label{vc}
\delta\tilde{F}=\epsilon \{\tilde{F},\tilde{T}\}=0,
\end{equation}
where $\tilde{T}$ is the scaled second class constraint chosen to be the gauge symmetry generator and $\epsilon$ is an infinitesimal parameter. Any function of $\tilde{F}\,$ will be gauge invariant since
\begin{equation}
\{\tilde{A}(\tilde{F}),\tilde{T}\}=\{\tilde{F},\tilde{T}\} \frac {\partial\tilde{A}} {\partial\tilde{F}}=0,
\end{equation}
where
\begin{equation}
\{\tilde{F},\tilde{T}\} \frac {\partial\tilde{A}} {\partial\tilde{F}}\equiv\{\tilde{q}_i,\tilde{T}\}\frac {\partial\tilde{A}}{\partial\tilde{q}_i}+ \{\tilde{p}_i,\tilde{T}\}\frac {\partial\tilde{A}}{\partial\tilde{p}_i}.
\end{equation}
Consequently, we can obtain a gauge invariant function from the replacement of
\begin{equation}
\label{sub}
A(F)\Rightarrow A(\tilde{F})=\tilde{A}(\tilde{F}).
\end{equation}
The gauge invariant phase space variables $\tilde{F}$ are constructed by the series in powers of $T_2$
\begin{equation}
\label{ff}
\tilde{F}=F+ \sum_{n=1}^{\infty} c_n\,T_2^n=F+c_1\,T_2+c_2\,T_2^2+\ldots,
\end{equation}
where this series has an important boundary condition that is
\begin{equation}
\label{bon}
\tilde{F}(T_2=0)=F.
\end{equation}
The condition above and the relation (\ref{sub}) show that when we impose the discarded constraint $T_2$ equal to zero, we reobtain the original second class system. Therefore, the relations (\ref{sub}) and (\ref{bon}) guarantee the equivalence between our first class model and the initial second class system.
The coefficients $c_n$ in the relation (\ref{ff}) are then determined by the variational condition, Eq.(\ref{vc}). The general equation for $c_n$ is
\begin{equation}
\delta\tilde{F}=\delta F +\sum_{n=1}^\infty\, (\delta c_n\, T_2^n+ n\, c_n\,T_2^{(n-1)}\delta T_2)=0,
\end{equation}
where
\begin{eqnarray}
\delta F &=&\epsilon \{F,\tilde{T}\},\\
\delta c_n &=&\epsilon \{c_n,\tilde{T}\},\\
\label{res}
\delta T_2&=&\epsilon \{T_2,\tilde{T}\} = -\,\epsilon.
\end{eqnarray}
In Eq.(\ref{res}) we assume that $\{\tilde{T},T_2\}=1$. Then, for the linear correction term $(n=1)$, we have
\begin{equation}
\label{c_1}
\delta F+ c_1\,\delta T_2=0 \;\Rightarrow \;\delta F - c_1\,\epsilon=0 \;\Rightarrow\; c_1=\frac{\delta F}{\epsilon}.
\end{equation}
For the quadratic correction term (n=2), we get
\begin{equation}
\label{c_2}
\delta c_1+2c_2\,\delta T_2=0 \;\Rightarrow\; \delta c_1-2c_2\epsilon=0 \;\Rightarrow\; c_2=\frac{1} {2}\frac{\delta c_1}{\epsilon}.
\end{equation}
For $n\geq 2$, the general relation is
\begin{eqnarray}
\label{c_n}
\delta c_n+(n+1)c_{n+1}\,\delta T_2=0\;\Rightarrow\; \delta c_n-(n+1)\,c_{(n+1)}\epsilon=0\nonumber\\ \nonumber\\ \Rightarrow\; c_{(n+1)}=\frac{1}{(n+1)}\frac{\delta c_n}{\epsilon}.
\end{eqnarray}
Using the relations (\ref{c_1}), (\ref{c_2}) and (\ref{c_n}) in Eq.(\ref{ff}) we obtain the series which determines $\tilde{F}$
\begin{equation}
\label{series}
\tilde{F}=F+ T_2\,\frac{\delta F}{\epsilon}+\frac{1}{2!}T_2^2\,\frac{\delta\delta F}{\epsilon^2}+\frac{1}{3!}T_2^3\,\frac{\delta\delta\delta F}{\epsilon^3}+\ldots\,.
\end{equation}
The expression $\tilde{F}$ can also be elegantly written in terms of a projection operator on $F$
\begin{equation}
\tilde{F}=e^{T_2\,\frac{\delta}{\epsilon}}:F,
\end{equation}
where again an ordering prescription must be adopted that is $T_2$ must come before $\frac{\delta}{\epsilon}$. Now, if we calculate the Poisson bracket between the two gauge invariant variables defined by the formula (\ref{series}) and next we take the limit $T_2 \rightarrow 0$, we get
\begin{eqnarray}
\{\tilde{F},\tilde{G}\}_{T_2=0}&=&\{F,G\}+\{F,\tilde{T}\}\{T_2,G\}-\{F,T_2\}\{\tilde{T},G\}\nonumber\\
&=&\{F,G\}+\{F,T_i\}\epsilon^{ij}\{T_j,G\}.
\end{eqnarray}
If we assume that $\{T_i,T_j\}\equiv \Delta_{ij}=\epsilon_{ij}$, being $T_1\equiv\tilde{T}$, we can write
\begin{eqnarray}
\label{dirac}
\{\tilde{F},\tilde{G}\}_{T_2=0}&=&\{F,G\}+\{F,T_i\}\Delta^{ij}\{T_j,G\}\nonumber\\
&=&\{F,G\}_D,
\end{eqnarray}
where $\Delta^{ij}\equiv\epsilon^{ij}$ is the inverse of $\Delta_{ij}\equiv\epsilon_{ij}$ and $\{F,G\}_D$ is the Dirac bracket\cite{Dirac}. Thus, we can observe that when we change the gauge invariant variables by imposing the condition $T_2=0$, we return to the original second class system where the Poisson brackets transform in the Dirac brackets. This important result also confirms the consistency of our formalism. The same result was obtained by employing the BFT formalism\cite{pcs}.
\section{The Abelian Pure Chern Simons Theory}
The CS theory, being a (2+1) dimensional field theory, is governed by the Lagrangian
\begin{equation}
\label{initial}
L = \int d^2x\,\frac {k} {2} \,\epsilon_{\mu\nu\rho}\, A^\mu\partial^\nu A^\rho,
\end{equation}
where $\,k\,$ is a constant. From the standard Dirac constrained formalism\cite{Dirac} we obtain three canonical momenta which are the primary constraints
\begin{eqnarray}
\label{pi0}
T_0\equiv\pi_0\approx 0,\\
\label{pii}
T_i\equiv\pi_i-\frac{k}{2}\, \epsilon_{ij} A^j\approx 0 \;\;(i=1,2).
\end{eqnarray}
Using the Legendre transformation we derive the canonical Hamiltonian
\begin{equation}
\label{hc}
H_c= -k \int d^2 x \,A^0\,\epsilon_{ij}\,\partial^iA^j.
\end{equation}
From the temporal stability condition of the constraint, Eq.(\ref{pi0}), we get the secondary constraint
\begin{equation}
\label{pi3}
T_3\equiv k \, \epsilon_{ij}\,\partial^i A^j\approx 0.
\end{equation}
We observe that no further constraints are generated via this iterative procedure. $T_0,T_i$ and $T_3$ are the total constraints of the model .
In order to separate the second and the first class constraints, we need to redefine the constraint (\ref{pi3}). In principle, we can suggest an expression for the constraint as (an educated guess)
\begin{eqnarray}
\label{bomega3}
\tilde{T}_3\equiv T_3+\partial^i T_i
=\partial^i\pi_i+\frac{k}{2}\,\epsilon_{ij}\,\partial^iA^j.
\end{eqnarray}
Then, $T_0$ and $\tilde{T}_3$ form the first class constraints, while
$T_i$, Eq.(\ref{pii}), forms the second class constraints satisfying the algebra
\begin{equation}
\{T_i(x),T_j(y)\}=-k\,\epsilon_{ij}\,\delta^3(x-y) \;\; (i,j=1,2).
\end{equation}
\vskip .5cm
Our formalism begins by choosing the symmetry gauge generator as
\begin{equation}
\label{g1}
\tilde{T}=-\frac{T_1}{k}=-\frac{\pi_1}{k}+\frac{A^2}{2}.
\end{equation}
We would like to note that the superscript in the Eq.(\ref{g1}) indicates a vector component and not an exponent. Then, we have the algebra $\{\tilde{T}(x),T_2(y)\}=\delta^3(x-y)$. The second class constraint $T_2=\pi_2+\frac{k}{2} A^1$ will be discarded. The infinitesimal gauge transformations generated by symmetry generator $\tilde{T}$ are
\begin{eqnarray}
\label{da}
\delta A^i=\epsilon \{A^i(x),\tilde{T}(y)\}=
-\frac{\epsilon}{k}\,\delta^i_1\,\delta^3(x-y),\\
\label{dpi}
\delta \pi_i=\epsilon \{\pi_i(x),\tilde{T}(y)\}=
-\frac{\epsilon}{2}\,\delta_i^2\,\delta^3(x-y),\\
\delta T_2=\epsilon\, \{T_2(x),\tilde{T}(y)\}=-\epsilon \,\delta^3(x-y).
\end{eqnarray}
The gauge invariant field $\tilde{A}^i$ is constructed by the series
in powers of $T_2$
\begin{equation}
\tilde{A}^i=A^i+ b_1\,T_2+b_2\,T_2^2+\ldots+b_n\,T_2^n.
\end{equation}
From the invariance condition $\delta\tilde{A}^i=0$, we can compute all the correction terms $b_n$. For the linear correction term in order of $T_2$, we get
\begin{eqnarray}
\delta A^i+b_1\delta T_2=0 \;\Rightarrow\; -\frac{\epsilon}{k}\,\delta^i_1\delta^3(x-y)-b_1\epsilon\,\delta^3(x-y)=0 \;\Rightarrow\; b_1=-\frac{1}{k}\,\delta^i_1.
\end{eqnarray}
For the quadratic term, we obtain $b_2=0$, since $\delta b_1=\epsilon\{b_1,\tilde{T}\}=0.$ Due to this, all the correction terms $b_n$ with $n\geq 2$ are null. Therefore, the gauge invariant field $\tilde{A}^\mu$ is
\begin{eqnarray}
\label{a0}
\tilde{A}^0&=&A^0,\\
\label{ai}
\tilde{A}^i&=&A^i-\frac{1}{k}\,\delta^i_1\,T_2,
\end{eqnarray}
or
\begin{eqnarray}
\label{A0}
\tilde{A}^0&=&A^0,\\
\label{A1}
\tilde{A}^1&=&A^1-\frac{1}{k}\,T_2,\\
\label{A2}
\tilde{A}^2&=&A^2,
\end{eqnarray}
where by using Eq.(\ref{da}), it is easy to show that $\delta\tilde{A}^\mu=0$. The gauge invariant field $\tilde{\pi}_i$ is also constructed by the series in powers of $T_2$
\begin{equation}
\tilde{\pi}_i=\pi_i+ c_1\,T_2+c_2\,T_2^2+\ldots+c_n\,T_2^n.
\end{equation}
From the invariance condition $\delta\tilde{\pi}_i=0$, we can compute all the correction terms $c_n$. For the linear correction term in order of $T_2$, we get
\begin{eqnarray}
\delta \pi_i+c_1 \delta T_2=0 \;\Rightarrow\; -\frac{\epsilon}{2}\delta_i^2\delta^3(x-y)-c_1\epsilon\,\delta^3(x-y)=0 \,\Rightarrow\, c_1=-\frac{1}{2}\delta_i^2.
\end{eqnarray}
For the quadratic term, we obtain $c_2=0$, since $\delta c_1=\epsilon\{c_1,\tilde{T}\}=0.$ Due to this, all the correction terms $c_n$ with $n\geq 2$ are null. Therefore, the gauge invariant field $\tilde{\pi}_i$ is
\begin{equation}
\tilde{\pi}_i=\pi_i-\frac{1}{2}\,\delta_i^2\,T_2,
\end{equation}
or
\begin{eqnarray}
\tilde{\pi}_1&=&\pi_1,\\
\tilde{\pi}_2&=&\pi_2-\frac{1}{2}\,T_2,
\end{eqnarray}
where by using Eq.(\ref{dpi}), it is easy to show that $\delta\tilde{\pi}_i=0$. The Poisson brackets between the gauge invariant fields are
\begin{eqnarray}
\label{aiaj}
\{\tilde{A}^i(x),\tilde{A}^j(y)\}=\frac {1}{k}\,\epsilon^{ij}\,\delta^3(x-y),\\
\label{pipj}
\{\tilde{\pi}_i(x),\tilde{\pi}_j(y)\}=\frac {k}{4}\,\epsilon_{ij}\,\delta^3(x-y),\\
\label{aipij}
\{\tilde{A}^i(x),\tilde{\pi}_j(y)\}=\frac {1}{2}\,\delta^i_j\,\,\delta^3(x-y).
\end{eqnarray}
We can observe that the Poisson brackets, Eqs.(\ref{aiaj}),(\ref{pipj}) and (\ref{aipij}), reduce to the original Dirac brackets\cite{pcs} since $T_2=0$, as discussed in Eq.(\ref{dirac}). The gauge invariant Hamiltonian, written only in terms of the original phase space variables, is obtained by substituting $A^\mu$ by $\tilde{A}^\mu$, Eqs.(\ref{a0}) and (\ref{ai}), in the canonical Hamiltonian, Eq.(\ref{hc}), as follows
\begin{eqnarray}
\label{fh}
\tilde{H}=k \int d^2x\ \,\partial^i\tilde{A}^0\,\epsilon_{ij}\,\tilde{A}^j=
H_c+\int d^2x \;\partial^2A^0\;T_2\nonumber\\ \nonumber\\
=\int d^2x\;[k\, \partial^iA^0\, \epsilon_{ij}\, A^j + \partial^2 A^0\,\pi_2+\frac{k}{2}\,\partial^2 A^0\, A^1].
\end{eqnarray}
Imposing the temporal stability condition of $\pi_0\,(T_0\equiv\pi_0)$
\begin{eqnarray}
\label{hpi0}
\{\pi_0,\tilde{H}\}=0 \; \Rightarrow \; k \, \epsilon_{ij}\,\partial^i A^j+\partial^2\pi_2+\frac{k}{2}\partial^2A^1= k \, \epsilon_{ij}\,\partial^i A^j+\partial^2 T_2=0
\nonumber\\ \nonumber\\ \Rightarrow k \; \epsilon_{ij}\,\partial^i \tilde{A}^j=0,
\end{eqnarray}
we get the secondary constraint
\begin{equation}
\tilde{T}_3\equiv k \, \epsilon_{ij}\,\partial^i \tilde{A}^j,
\end{equation}
that is just the secondary constraint, Eq.(\ref{pi3}), with the replacement of $A^i$ by $\tilde{A}^i$. The gauge invariant Hamiltonian $\tilde{H}$ and the irreducible constraints $T_0,\tilde{T} $ and $\tilde{T}_3$ form a set of first class algebra given by
\begin{eqnarray}
\{\tilde{H},\tilde{T}\}=0,\\
\{\tilde{H},T_0\}=\tilde{T}_3,\\
\label{ht3}
\{\tilde{H},\tilde{T}_3\}=0,\\
\label{tt3}
\{\tilde{T},\tilde{T}_3\}=0,\\
\{\tilde{T},T_0\}=0,\\
\{T_0,\tilde{T}_3\}=0,
\end{eqnarray}
where we have used relation (\ref{aiaj}) to prove Eq.(\ref{ht3}) and the condition $\,\delta \tilde{A}^i=0\,$ to prove Eq.(\ref{tt3}). Here, we would like to mention important results obtained by our formalism. First, by imposing the temporal stability of $T_0$, Eq.(\ref{hpi0}), we get, by a systematic way, an irreducible first class constraint $\tilde{T}_3$. Second, we only embed the initial second class constraint $T_1$, Eq.(\ref{pii}), and, consequently, we have all the constraints forming a first class set. Moreover, in order to reduce all the constraints of the CS theory in a second class nature it is enough to assume $T_2=0$.
Finally, the gauge invariant CS Lagrangian can be deduced by performing the inverse Legendre transformation
\begin{equation}
\label{fl}
\tilde{L}=\int d^2x\; (\,\tilde{\pi}_i\dot{\tilde{A}^i}-\tilde{H}\,),
\end{equation}
where $\tilde{H}$ is given by Eq.(\ref{fh}). As the gauge invariant Hamiltonian, $\tilde{H}$, has the same functional form of the canonical Hamiltonian, Eq.(\ref{hc}),
thus, from the inverse Legendre transformation, Eq.(\ref{fl}), we can deduce that the first class Lagrangian (written in terms of the first class variables) will take the same functional form of the original Lagrangian, Eq.(\ref{initial})
\begin{equation}
\label{fl2}
\tilde{L}=\int d^2x\,\frac {k} {2} \,\epsilon_{\mu\nu\rho}\, \tilde{A}^\mu\partial^\nu \tilde{A}^\rho.
\end{equation}
Using the Eqs.(\ref{A0}), (\ref{A1}) and (\ref{A2}), the gauge invariant Lagrangian, Eq.(\ref{fl2}), becomes
\begin{eqnarray}
\label{fl22}
\tilde{L}=\int d^2x\,\frac {k} {2}\, [\, A^0\partial^1A^2-A^0\partial^2 A^1+\frac{1}{k}\,A^0\partial^2 T_2\nonumber\\+A^1\partial^2A^0-\frac {1}{k}T_2\,\partial^2A^0-A^1\partial^0A^2+\frac{1}{k}T_2\,\partial^0A^2\nonumber\\+A^2\partial^0A^1- \frac{1}{k}A^2\partial^0T_2-A^2\partial^1A^0\,]\,.
\end{eqnarray}
The Hamilton equation of motion produces a relation for $\partial^0 A^2$ given by
\begin{equation}
\label{a2}
\partial^0 A^2=\{A^2,\tilde{H}\}=\partial^2 A^0.
\end{equation}
Then, using the Eq.(\ref{a2}) and integrating by parts in the first class Lagrangian, Eq.(\ref{fl22}), we obtain
\begin{eqnarray}
\label{gl}
\tilde{L}=\int d^2x\,\frac {k} {2}\, [\, A^0\partial^1A^2-A^0\partial^2 A^1\nonumber\\+A^1\partial^2A^0-A^1\partial^0A^2\nonumber\\
+A^2\partial^0A^1-A^2\partial^1A^0\,]
\nonumber\\\nonumber\\
=\int d^2x\,\frac {k} {2} \,\epsilon_{\mu\nu\rho}\, A^\mu\partial^\nu A^\rho.
\end{eqnarray}
We can observe that the gauge invariant Lagrangian, Eq.(\ref{gl}), reduces to the original Lagrangian, Eq.(\ref{initial}).
The relation (\ref{gl}) is also an important result because without the presence of the extra terms in the gauge invariant Lagrangian, the original gauge symmetry transformation $\;A^\mu\rightarrow A^\mu+\partial^\mu \Lambda \;$ is certainly maintained.
\section{Conclusions}
In this paper, we have improved the GU formalism by gauging the original phase space variables of a constrained system. In the
case of a system with two second class constraints, one of the constraints will be chosen to form the scaled gauge symmetry generator while the other will be discarded. The discarded constraint is used to construct a series for the gauge invariant fields. Consequently, any functions of the gauge invariant fields are gauge invariant quantities. We apply our formalism to the CS model where new results are obtained.
Our improved GU formalism can also be used to study the Nonabelian version of the Chern Simons theory\cite{ncs,kp}.
\section{Acknowledgments}
This work is supported in part by FAPEMIG, Brazilian Research Agency.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,732 |
2U.S. Senate campaign, 1972
3Later years
Winton M. Blount
American industrialist and postmaster general
Red Blount
59th United States Postmaster General
January 22, 1969 – January 1, 1972
W. Marvin Watson
E. T. Klassen
Winton Malcolm Blount
(1921-02-01)February 1, 1921
Union Springs, Alabama, U.S.
October 24, 2002(2002-10-24) (aged 81)
Highlands, North Carolina, U.S.
Branch/service
Winton Malcolm Blount Jr., known as Red Blount (February 1, 1921 – October 24, 2002), was an American philanthropist and politician who served as the United States Postmaster General from January 22, 1969, to January 1, 1972. He founded and served as the chief executive officer of the large construction company, Blount International, based in Montgomery, Alabama.
Blount was the last Postmaster General when the position was within the presidential Cabinet.
Born in Union Springs, Alabama, Blount served in the United States Army Air Forces during World War II, having trained as a B-29 pilot. However, the war ended before his training was completed. Blount's first name was spelled with a "y" on his birth certificate, but he used Winton as an adult in his business dealings to avoid having to explain the unusual spelling.[1]
In 1946, Blount and his brother William Houston Blount started a building contractor company, Blount Brothers. The company worked on such construction projects as the First Avenue Viaduct in Birmingham, the Louisiana Superdome in New Orleans, and Cape Canaveral's Complex 39A which launched Apollo 11 in Florida.
In 1952, Blount was appointed the Alabama Chairman of Citizens for Eisenhower, then in 1960 Southeastern Campaign Chairman for Richard M. Nixon's unsuccessful presidential campaign against John F. Kennedy. In 1961, Blount was elected President of the Alabama Chamber of Commerce; in 1968, President of the United States Chamber of Commerce.
In 1964, Blount was appointed by U.S. President Lyndon B. Johnson to the National Citizens Committee for Community Relations to advise the White House on the enforcement of the new Civil Rights Act of 1964 even though Blount had expressed doubts about the new law.
In 1969, Blount was appointed as the Postmaster General by U.S. President Richard Nixon, and he supervised the transition in 1971 of the U.S. Post Office Department from a Cabinet-level department of the U.S. government to a special independent executive agency. He was thus the last Cabinet-level Postmaster General, and he served as the first director of the new U.S. Postal Service. Blount's assistant Postmaster General was James M. Henderson, an advertising executive from Greenville, South Carolina, who was the unsuccessful Republican candidate for Lieutenant Governor of South Carolina in 1970. Henderson persuaded the National Aeronautics and Space Administration and the Apollo 11 astronauts to photograph the Moon for an image on a postage stamp. More than 140 million moon stamps were sold.[2]
In 1971, Blount's profile was depicted alongside that of Benjamin Franklin's on the face of a silver proof coin commemorating the inauguration of the new Postal Service. The commemorative coin was offered in a carrier with one stamp bearing a Philadelphia postmark from the old Post Office, and another from Washington D.C., placed by the new Postal Service.
U.S. Senate campaign, 1972[edit]
Blount faced in the general election the long-term incumbent Democrat, John Sparkman, who had been the 1952 Democratic candidate for vice president against Richard M. Nixon. From May 1972 to November 1972, future U.S. President George W. Bush transferred from the Texas Air National Guard to serve as the political director in Blount's campaign.
The final results were Sparkman 654,491 (65.3 percent) to Blount's 347,523 (34.7 percent).[3] Blount carried only traditionally Republican Winston and Houston counties and lost his home county of Montgomery.
Later years[edit]
Winton Blount statue in Montgomery, Alabama
In 1973, Blount returned to Blount International, Inc., becoming its president once again in 1974. From 1981 to 1984 Blount, Inc., built the King Saud University in Riyadh, Saudi Arabia.
In 1980, Blount served as national chairman of the Texan John Connally's unsuccessful primary campaign, with the nomination being won by Ronald W. Reagan of California.
In 1996, the Greenwich Publishing Group published his autobiography called Doing It My Way, which he had co-written with Richard Blodgett.
In 1999, Blount International, Inc., was sold to Lehman Brothers company for $1.35 billion.
Blount died in Highlands, North Carolina, at the age of eighty-one.
Carolyn Blount Theatre
Blount and his wife Carolyn, were philanthropists and notable patrons of the arts. Together they founded the Blount Cultural Park[4] in Montgomery, which is home to the Montgomery Museum of Fine Arts and the Alabama Shakespeare Festival. The Blounts donated the land and a 100,000 square foot theater as the new home of the Alabama Shakespeare Festival in 1985. The cost was $21.5 million and at the time was the largest private donation to an American theater.
In 1980, Blount received the Golden Plate Award of the American Academy of Achievement.[5]
The Winton M. Blount Elementary School in Montgomery County, completed in 2003, is named in his honor. Located on the city's rapidly growing east side, it is one of the largest elementary schools in the region.
The Blount Undergraduate Initiative, a liberal arts honors program for Blount Scholars, was started at the University of Alabama. Blount Scholars reside in the Blount Living Learning Center on the campus.
The Winton M. Blount Center for Postal Studies and the Winton M. Blount Research Chair, both at the Smithsonian National Postal Museum, were founded with an endowment from the Blount estate.
Lera, Thomas, ed. The Winton M. Blount Postal History Symposia: Select Papers, 2006—2009. Smithsonian Contributions to History and Technology, no. 55. Washington, D.C.: Smithsonian Institution Scholarly Press, 2010.
^ Blodgett, Richard. "Winton M. Blount Jr". The Encyclopedia of Alabama. Retrieved April 6, 2018.
^ "James M. Henderson (1921-1995)". knowitall.org. Retrieved May 4, 2014.
^ Cook, Rhodes (2013). America Votes 30: 2011-2012, Election Returns by State. CQ Press. p. 57. ISBN 978-1-4522-9017-1.
^ blountculturalpark.org
^ "Golden Plate Awardees of the American Academy of Achievement". www.achievement.org. American Academy of Achievement.
Blount, Winton M. (1996). Doing It My Way. Greenwich Publishing Group. ISBN 0-944641-19-9
Winton M. Blount at Find a Grave
United States Postmaster General
Party political offices
John Grenier
Republican nominee for U.S. Senator from Alabama
(Class 2)
1972 Vacant
Title next held by
Albert L. Smith Jr.
United States Postmasters General
Confederal
G. Granger
Cabinet level
Post Office Department
F. Granger
Collamer
A. Brown
Creswell
Tyner
Wanamaker
Wynne
Cortelyou
W. Brown
Hannegan
Gronouski
Bolger
Donahoe
DeJoy
Cabinet of President Richard Nixon (1969–1974)
Spiro Agnew (1969–1973)
Gerald Ford (1973–1974)
William P. Rogers (1969–1973)
Henry Kissinger (1973–1974)
Secretary of the Treasury
David M. Kennedy (1969–1971)
John Connally (1971–1972)
George Shultz (1972–1974)
William E. Simon (1974)
Melvin Laird (1969–1973)
Elliot Richardson (1973)
James R. Schlesinger (1973–1974)
John N. Mitchell (1969–1972)
Richard Kleindienst (1972–1973)
William B. Saxbe (1974)
Postmaster General
Winton M. Blount (1969–1971)
Secretary of the Interior
Wally Hickel (1969–1970)
Rogers Morton (1971–1974)
Secretary of Agriculture
Clifford M. Hardin (1969–1971)
Earl Butz (1971–1974)
Secretary of Commerce
Maurice Stans (1969–1972)
Peter G. Peterson (1972–1973)
Frederick B. Dent (1973–1974)
Secretary of Labor
James Day Hodgson (1970–1973)
Peter J. Brennan (1973–1974)
Secretary of Health, Education, and Welfare
Robert Finch (1969–1970)
Elliot Richardson (1970–1973)
Caspar Weinberger (1973–1974)
Secretary of Housing and Urban Development
George W. Romney (1969–1973)
James Thomas Lynn (1973–1974)
John A. Volpe (1969–1973)
Claude Brinegar (1973–1974)
Director of the Bureau of the Budget
Robert Mayo (1969–1970)
Director of the Office of Management and Budget
Roy Ash (1973–1974)
Ambassador to the United Nations
Charles Yost (1969–1971)
George H. W. Bush (1971–1973)
John A. Scali (1973–1974)
Counselor to the President
Arthur F. Burns (1969)
Daniel Patrick Moynihan (1969–1970)
Bryce Harlow (1969–1970)
Donald Rumsfeld (1970–1971)
Anne Armstrong (1973–1974)
Dean Burch (1974)
Kenneth Rush (1974)
Retrieved from "https://en.wikipedia.org/w/index.php?title=Winton_M._Blount&oldid=1119782524"
Alabama Republicans
United States Army Air Forces bomber pilots of World War II
Candidates in the 1972 United States elections
People from Union Springs, Alabama
Philanthropists from Alabama
Politicians from Montgomery, Alabama
Military personnel from Alabama
National Humanities Medal recipients
Nixon administration cabinet members
Staunton Military Academy alumni
Writers from Montgomery, Alabama
Military personnel from Montgomery, Alabama
Use mdy dates from June 2019 | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8 |
Q: Using svg-android library
i'm trying to use svg-android to display a road map i exported from openstreetmap.
I follow the steps from the tutorial and it worked great with a test.svg graphic (3KB). But the exported map is arround 500KB. When i try to load the map i get an SVGParseException:
System.err: com.larvalabs.svgandroid.SVGParseException: java.lang.NumberFormatException
System.err: at com.larvalabs.svgandroid.SVGParser.parse(Unknown Source)
System.err: at com.larvalabs.svgandroid.SVGParser.getSVGFromResource(Unknown Source)
System.err: at my.package.view.SVGMapView.loadSVGImage(SVGMapView.java:141)
line 141 says:
svg = SVGParser.getSVGFromResource(getResources(), R.raw.test);
is there a possibility to preload the svg image in an extra thread, or is there a better solution for my problem?
thanks
A: What is happening in this case is that the svg library for Android is quite limited, in that it doesn't support the full SVG spec. The map you saved includes some features that svg-android simply can't manage. Unfortunately, there isn't a whole lot you can do about it, except to try a different format.
Threading would not make the problem any better, incidentally. This would make the loading of the image happen in the background, but it would not fix the fundamental problem, that the SVG file simply contains things that can't be parsed.
What you can try is to load the file via an offline SVG tool, and re-save it with the required format, SVG Basic 1.1.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 131 |
The RADstat Radial Artery Compression System is just one of Merit Medical's many innovative products for radial approach. The RADstat provides the clinical advantages of controlled hemostasis, patient comfort, and safety at the conclusion of your radial artery procedures.
Categories : "Catheters, Vascular, Guiding, Coronary Artery" | {
"redpajama_set_name": "RedPajamaC4"
} | 8,260 |
Contact the Hounds
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Why Grigor Dimitrov, "The Guy with a Black Heart", can win the US Open
Published 2 years ago - Mark Harding - 2y ago 50
Citi Open Tennis 2017. By Keith Allison from Hanover, MD, USA - Grigor Dimitrov, CC BY-SA 2.0, https://commons.wikimedia.org/w/index.php?curid=61468161
As the one-time boyfriend of Serena Williams and Maria Sharapova (not at the same time), Grigor Dimitrov is now attracting headlines for his on-court expertise. With the US Open starting Monday and with many of the world's best players either out injured or under a fitness cloud, the Bulgarian's time could be now. MARK HARDING reports:
GRIGOR DIMITROV, the Bulgarian who was too good for Nick Kyrgios in the final of the Cincinnati Masters 1000 last Sunday, is back to a single digit world ranking for the first time in three years. And there couldn't be a better time to launch the Grand Slam assault for which many believe he's been destined.
Dimitrov's straight sets win in the Cincinnati final, coupled with the last-man-standing nature of next week's US Open, has put him into the frame as one of the favourites at Flushing Meadows.
The last Grand Slam of the season starts on Monday but has been hit with an unprecedented list of withdrawals and injury concerns.
Grigor Dimitrov at the Citi Open Tennis 2017. Pic: Keith Allison – CC BY-SA 2.0
Three of the four men's semi-finalists from last year are out for the rest of the season – winner Stan Wawrinka with knee surgery, Novak Djokovic with his chronic elbow injury and Kei Nishikori who became the latest withdrawal last week with a torn tendon in his wrist.
Throw in the serious fitness concerns for Andy Murray with a dodgy hip and Roger Federer with old man's back, and the prospects of some new blood on the victory dais are strong.
Federer played injured in the final of the Canadian Open two weeks ago and withdrew from the Cincinnati Masters to recover for New York. Murray has not played since his Wimbledon quarter final loss and officially surrendered his world number one ranking on Monday morning when Rafael Nadal regained it for the first time in three years.
Nadal was beaten in the quarter-finals in Cincinnati by Kyrgios but looms as the only player among the "Big Four" or "Big Five" with even a half decent preparation going into the Open.
The other form players look to be seventh seed Dimitrov, whose win over Kyrgios secured his third title of the season, and 20-year-old fourth seed Alexander Zverev, who beat the injured Federer in the Canadian Open the week before, to claim his fifth title of the season.
At 26, Dimitrov is in the prime of his career, and was in command over Kyrgios claiming his first Masters 1000 title without dropping a set and losing only one of his 53 service games for the week.
Back in 2014 he rose to number eight in the world but was considered a less than dedicated player, better known for his romantic exploits than any triumphs on the court.
Former girlfriends include those less than chummy rivals Serena Williams and Maria Sharapova and in the last few years he's been dating Lewis Hamilton's ex, the former Pussycat Doll, Nicole Scherzinger. When he was in a two-year relationship with Sharapova, there was plenty of talk that the feud between the two leading female players in the world was linked to their rivalry over Dimitrov's affection.
But Williams denied it. "If she wants to be with the guy with a black heart, go for it," she said in a 2013 Rolling Stone interview.
Six-time US Open winner Williams, of course, is currently off the tour awaiting the impending birth of her first child with entrepreneur Alexis Ohanian.
And the player she beat in two of those finals, Victoria Azarenka will also miss the 2017 tournament because a custody battle has prevented her from taking her eight-month-old son out of California to New York.
Last year's winner Angelique Kerber seems totally out of form, 2011 winner Sam Stosur is out injured and the only other past winners at Flushing Meadows are Sharapova (2006) and Svetlana Kuznetsova (2004).
That leaves Wimbledon winner Garbine Muguruza as the clear cut favourite to take her first US Open.
In the women's singles final in Cincinnati last week, Muguruza gave a command performance, denying Simona Halep the chance to take the number one world ranking in the process.
The Spaniard completely demolished Halep – instead of allowing her the number one ranking, she allowed her just one game, 6-1, 6-0.
That means Czech Karolina Pliskova will be number one seed at Flushing Meadows, but it's the number three seed Muguruza who everyone will fear.
Although she is a two-time Grand Slam winner, Muguruza had never won two tournaments in a season until Cincinnati. But at 23, she is in magnificent touch and can be expected to add to that tally before the year is out.
Author: Mark Harding
MARK HARDING is one of the most experienced and versatile sportswriters in Australia. He is a former news columnist for The Herald, sports editor for the Herald Sun, Chief Sportswriter for the Sunday Herald Sun and Chief Sportswriter for Australia's first weekly national sports magazine, Sports Weekly. He currently produces television shows on international sport for overseas markets.
MARK HARDING is one of the most experienced and versatile sportswriters in Australia. He is a former news columnist for The Herald, sports editor for ... More »
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Why tennis is on the nose
Published 10m ago - 25 bookmarks
Kiwis the unluckiest losers ever July 15th, 2019
A Test of faith for cricket fans July 12th, 2019
Big wheels hot to trot July 9th, 2019
No forgetting the missing medals July 8th, 2019
So Grand to get real racing again July 2nd, 2019
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By using this site you agree to the use of cookies, more info. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 4,898 |
import socket
import urllib
import logging
# Location for the program to output logs
logfile = "/var/log/dnscheck.log"
# Where the "current" IP address is stored.
ipfile = "/var/spool/ipaddr"
# File containing the URL used to update DNS
apifile = "/etc/api_url"
# Service to check external IP. There are several if you google.
service = "http://icanhazip.com/"
def fileExists(filename):
try:
with open(filename): pass
except IOError:
print '%s does not exist. Touch it.' % (filename)
exit(1)
# Ensure required files exist
fileExists(logfile)
fileExists(ipfile)
fileExists(apifile)
# Cleans up apiurl and sets it to a variable
a = open(apifile, 'r')
apiurl = a.read().strip()
a.close()
# Sets logging format
logging.basicConfig(format='%(asctime)s %(message)s',filename=logfile,level=logging.DEBUG)
ip = urllib.urlopen(service).read().strip()
# Sets the current IP to be the IP one delivered by the IP service
f = open(ipfile, 'r+')
current_ip = f.read().strip()
if ip == current_ip:
# If all's good, carry on
logging.info('All Gravy: %s = %s' % (ip, current_ip))
else:
try:
socket.inet_aton(ip)
except socket.error:
# Making sure we aren't getting a "service unavailable" or similar
logging.error("Response '%s' recieved from service '%s' does not seem to be valid. Exiting." \
% (ip, service))
exit(1)
logging.info("NO MATCH: %s != %s. File /var/spool/ipaddr changed to %s" % (ip, current_ip, current_ip))
output = urllib.urlopen(apiurl).read()
logging.info(output)
f.seek(0)
f.write("%s" % (ip))
f.truncate()
f.close
| {
"redpajama_set_name": "RedPajamaGithub"
} | 1,199 |
Baitarani est une rivière située dans l'état de l'Orissa en Inde. Elle forme un delta commun avec le Mahanadi et le Brahmani.
Géographie
D'une longueur de .
Notes et références
Cours d'eau en Inde
Géographie de l'Odisha | {
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{"url":"http:\/\/blog.alexbeutel.com\/13\/php-and-acrobatcom\/","text":"# Alex Beutel's Blog\n\n## PHP and Acrobat.com\n\n#### June 5th, 2008 \u00b7 No Comments\n\nAnyway, regardless of the poor GUI congruity, I would like to discuss the API.\u00a0 The site has a few public libraries at first appearance, and I must hand it to Adobe that their Java library looks extremely clean and easy to use.\u00a0 But the Python library \u2013 not even a library, although probably the easiest reading of all of their online documentation.\u00a0 The writer of the blog even states that he has given up and decided to use the Java library \u2013\u00a0 encouraging.\u00a0 Anyway, disappointed in not even an attempt at a PHP implementation, I decided to give it a shot.\u00a0 I essentially went as far as the writer of the Python blog post: authenticate, get sessionid, and get a list of files you have on your account.\u00a0 (Note this requires PEAR\u2019s HTTP_Request package.) Also, I know this is very ugly code and I\u2019m possitive could and should be done much cleaner.\u00a0 However, it works if your just trying to take the first steps and get some output.\u00a0 If anyone wants to clean it up or continue on with a PHP implementation, feel free and let me know how it goes.\u00a0 However, until they open up the platform to worthwhile features, it is sadly not worth my time.\u00a0 Hopefully Adobe soon realizes the mistake of being so possessive and thinks a little more creatively about how to monetize their technology.\u00a0 Anyway, here is the code; enjoy:\n\n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 < ?php $acrobat_api_key = \"xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx\";$acrobat_shared_secret = \"xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx\"; $acrobat_base_url = \"https:\/\/api.share.acrobat.com\/webservices\/api\/v1\/\";$acrobat_username = \"your_username@somecompany.com\"; $acrobat_password = \"your_acrobat.com_password\"; function getAuthToken() { global$acrobat_api_key, $acrobat_shared_secret,$acrobat_base_url, $acrobat_password,$acrobat_username; $a = new HTTP_Request();$a->setURL($acrobat_base_url.\"auth\/\");$a->setMethod(\"POST\"); $time = time();$data = \"POST https:\/\/api.share.acrobat.com\/webservices\/api\/v1\/auth\/ \".$time;$md5 = md5($data.$acrobat_shared_secret); $auth = \"AdobeAuth apikey=\\\"\".$acrobat_api_key.\"\\\",data=\\\"\".$data.\"\\\",sig=\\\"\".$md5.\"\\\"\"; $request_body = \"\\n\".$acrobat_username.\"\\n\".$acrobat_password.\"\\n\";$a->addHeader(\"Authorization\", $auth);$a->setBody($request_body);$a->sendRequest(); $xml =$a->getResponseBody(); $regex = \"[a-zA-Z0-9]+\";$i = ereg($regex,$xml, $matches);$p = xml_parser_create(); $i = xml_parse_into_struct($p, $matches[0],$vals, $index);$j = xml_parser_free($p); return$vals[0]['value']; } function getSession($auth_token) { global$acrobat_api_key, $acrobat_shared_secret,$acrobat_base_url; $a = new HTTP_Request();$a->setURL($acrobat_base_url.\"sessions\/\");$a->setMethod(\"POST\"); $time = time();$data = \"POST https:\/\/api.share.acrobat.com\/webservices\/api\/v1\/sessions\/ \".$time;$md5 = md5($data.$acrobat_shared_secret); $auth = \"AdobeAuth apikey=\\\"\".$acrobat_api_key.\"\\\",data=\\\"\".$data.\"\\\",sig=\\\"\".$md5.\"\\\"\"; $request_body = \"\\n\".$auth_token.\"\\n\"; $a->addHeader(\"Authorization\",$auth); $a->setBody($request_body); $a->sendRequest();$xml = $a->getResponseBody();$regex = \"[a-zA-Z0-9]+\"; $i = ereg($regex, $xml,$matches); $p = xml_parser_create();$i = xml_parse_into_struct($p,$matches[0], $vals,$index); $j = xml_parser_free($p); \u00a0 $regex = \"[a-zA-Z0-9]+\";$i = ereg($regex,$xml, $matches2);$p = xml_parser_create(); $i = xml_parse_into_struct($p, $matches2[0],$vals2, $index);$j = xml_parser_free($p);$response[0] = $vals[0]['value'];$response[1] = $vals2[0]['value']; return$response; } function getList($session,$secret) { global $acrobat_api_key,$acrobat_shared_secret, $acrobat_base_url;$a = new HTTP_Request(); $a->setMethod(\"GET\");$time = time(); $data = \"GET \/webservices\/api\/v1\/dc\/ apikey=\".$acrobat_api_key.\" calltime=\".$time.\" sessionid=\".$session; $md5 = md5($data.$secret);$url = $acrobat_base_url.\"dc\/?apikey=\".$acrobat_api_key.\"&calltime=\".$time.\"&sessionid=\".$session.\"&sig=\".$md5;$a->setURL($url);$a->sendRequest(); $xml =$a->getResponseBody(); return $xml; }$auth = getAuthToken(); $response = getSession($auth); $session =$response[0]; $secret =$response[1]; echo getList($session,$secret); ?>\n\n### 0 responses so far \u2193\n\n\u2022 There are no comments yet...Kick things off by filling out the form below.","date":"2016-09-27 23:59:45","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.27536308765411377, \"perplexity\": 2081.0266231106107}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 5, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2016-40\/segments\/1474738661289.41\/warc\/CC-MAIN-20160924173741-00226-ip-10-143-35-109.ec2.internal.warc.gz\"}"} | null | null |
As a successful business owner, you're always on the lookout for results-driven solutions that can help make your company more efficient. That's why the professionals at Henry Enterprises specialize in VoIP and office phone installation in Atlanta. Since 2006, we've been providing small and mid-sized businesses in the greater Marietta and Atlanta areas with the VoIP and office phone installation services necessary for running a highly efficient and successful company.
VoIP phone systems can be critical to a business, as it allows company leaders to avoid the charges typically associated with traditional landlines. Henry Enterprises makes it easier to take advantage of the benefits of VoIP and office phones, as our experts can help you set up your office phones and ensure that they're operating correctly. We also provide your office phone systems with continuous support to ensure that any issues are immediately handled.
If you're ready to experience better VoIP and office phone installation services in Atlanta, contact the experts at Henry Enterprises for all your phone installation and IT service needs. Browse our website for more information on our IT services, or for questions or comments please contact us. | {
"redpajama_set_name": "RedPajamaC4"
} | 2,913 |
{"url":"https:\/\/proofwiki.org\/wiki\/Set_Union\/Examples\/2_Arbitrarily_Chosen_Sets_of_Complex_Numbers","text":"# Set Union\/Examples\/2 Arbitrarily Chosen Sets of Complex Numbers\n\n $\\displaystyle A$ $=$ $\\displaystyle \\set {3, -i, 4, 2 + i, 5}$ $\\quad$ $\\quad$ $\\displaystyle B$ $=$ $\\displaystyle \\set {-i, 0, -1, 2 + i}$ $\\quad$ $\\quad$\n$A \\cup B = \\set {3, -i, 0, -1, 4, 2 + i, 5}$","date":"2019-03-23 05:26:32","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 2, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.999731719493866, \"perplexity\": 104.1389176495631}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-13\/segments\/1552912202723.74\/warc\/CC-MAIN-20190323040640-20190323062640-00464.warc.gz\"}"} | null | null |
Time's Rx: More Politics, More Politicians, More Lincoln Worship
By Thomas DiLorenzo
by Thomas J. DiLorenzo
Recently by Thomas DiLorenzo: Propagandist for State-Run Media Wants Even More of YourMoney
"Lincoln as political strategist is front and center in Steven Spielberg's new film. He trades votes, dangles patronage, hedges principles and tiptoes on the brink of deceit. He pleads, cajoles and threatens."
~ David Von Drehle, "Lincoln to the Rescue: What the Master Politician of 1862 Can Teach the Presidential Hopefuls of 2012" (Time magazine, Nov. 5, 2012)
"Lincoln was a master politician, which means that he was a consummate conniver, manipulator, and liar."
~ Murray N. Rothbard, "Two Just Wars: 1776 and 1861"
Steven Spielberg must have grown a Pinocchio-sized nose when he announced recently that his forthcoming movie about Lincoln, based on the book Team of Rivals by the confessed plagiarist Doris Kearns-Goodwin, was not a political movie since it will be released after the election (See my LewRockwell.com review of Goodwin's book entitled "A Plagiarist's Contribution to Lincoln Idolatry"). Time magazine let the cat out of Spielberg's bag in its November 5 issue, which is a glowing tribute to politics, politicians, big government, and most of all, to the legend of Abraham Lincoln.
A picture of actor Daniel Day-Lewis portraying Lincoln is on the cover with the headline, "What Would Lincoln Do?" The issue includes a long-winded essay by Lincoln historian/cultist David Von Dehle; a "viewers guide" by the dishonest Doris Kearns Goodwin; and a story of "How Daniel Day-Lewis Became Lincoln."
The purpose of the Lincoln legend has always been to assert that our "salvation" lies in politics, not in God. Lincoln is our secular "god," and our rulers will never let us forget it. That is why the U.S. government has spent millions over the past several years on the publication of dozens of books, conferences, movies, documentaries, plays, etc. to commemorate Abe's 200th birthday (That was 2009 and the "celebration" is still going strong). That is the purpose of the upcoming Spielberg movie and its celebration in Time and elsewhere.
Truth and Lies About Politics and Politicians
In his Time essay David Von Drehele continues the century-and-a-half long deification of Lincoln (the worst kind of blasphemy) by celebrating what a lying, conniving, politician he was. He approvingly quotes Lincoln's law partner, William Herndon, as having said that Lincoln was the "mostly secretive man that ever existed." One wonders why he had to be so "secretive" if what he was doing was in "the public interest," as we are constantly told.
Lincoln was first and foremost a sleazy, small-minded, patronage politician from Illinois. As Drehle writes, he always paid "small-minded attention to politics" and "spent dozens of hours each week painstakingly distributing the rapidly growing number of federal jobs at his disposal." Even when the Confederates were racking up battlefield victory after victory, and threatening to capture Washington, D.C., Lincoln "nevertheless devoted huge blocks of time to selecting tax collectors authorized by the first internal-revenue act."
He did all of this, says Drehle, to gain support for "holding the union together." Wrong, Mr. Drehle. He did this to destroy the voluntary union of the founding fathers and replace it with an imperialistic empire. The idea of a voluntary union is apparently one of those "principles" that Drehle is so happy that Lincoln "hedged" on. He threatened war over tariff tax collection in his first inaugural address, and then followed through with his threat after duping the Confederates into firing the first shot at Fort Sumter (where no one was harmed, let alone killed, save one horse).
Lincoln is also worshipped in Time for having "hedged principles" and "tiptoed on the brink of deceit" by committing treason by invading the Southern states (Article 3, Section 3 of the U.S. Constitution defines treason as "only levying war upon the states . . . " which of course is exactly what Lincoln did. Other hedging of principles about which we are supposed to be thrilled is his illegal suspension of Habeas Corpus, mass imprisonment of tens of thousands of Northern political critics without due process; the shutting down of hundreds of opposition newspapers; censorship of the mails; confiscation of firearms; rigging of elections; deportation of an opposition party congressman (Clement L. Vallandigham); illegally orchestrating the secession of West Virginia, the last slave state to enter the union; and worse.
Lincoln's Greatest Failure
Lincoln was indeed a master politician, as described in the quote at the top of this article by Murray Rothbard. As such, his greatest failure was that he did not use his famous political skills to do what all the rest of the world did about slavery and end it peacefully. This includes all of the Northern states as well as Great Britain, Spain, France, Denmark, Sweden, The Netherlands, and all other countries where slavery existed in the nineteenth century (See Greatest Emancipations by Jim Powell, along with Slavery in New York published by the New York Historical Society; Disowning Slavery by Joanne Pope-Melish; and the Web site, "Slavery in the North").
Instead of working diligently to end slavery peacefully in the British tradition, Lincoln's unprincipled, deceitful, threatening, and dictatorial behavior that is so heavily praised by Spielberg, Goodwin, Drehle, and Time, led to the death of more than 800,000 Americans according to brand new estimates of "Civil War" deaths, along with the maiming for life of more than twice that number. Standardizing for today's population, that would be the equivalent of more than 8 million American deaths in a four-year war.
But not to worry. As Drehle soothingly informs us, Lincoln's conniving, manipulating, and deceitful behavior is what enabled him to sign "the visionary bills that created the transcontinental railroad, the modern fiscal system, the homesteading movement, and the nation's land-grant universities." "Never has there been a moment in history when so much was all compressed into a little time, Drehle quotes one political contemporary of Lincoln's as having said. The domestic policies of the Lincoln administration were labeled The New Deal, a phrase that would be plagiarized by FDR seventy years later.
The government-subsidized transcontinental railroads were colossally inefficient and led to the biggest corruption scandal in history up to that point; and the "modern fiscal system" in the form of the National Currency Acts and Legal Tender Acts nationalized the money supply, leading to endless monetary manipulation and boom-and-bust cycles caused by subsequent generations of wily politicians like Lincoln. Most of the land given away under the Homestead Act went to large corporate supporters of the Republican Party in the mining, railroad, forestry, and other industries as historian Ludwell Johnson showed; and the land-grant acts opened the door to the effective nationalization and politicization of higher education along with the plague of political correctness. Hurrah for Lincoln!
The fact that the Republican Party was able to railroad the country into the old Whig Party mercantilist political agenda of corporate welfare, protectionist tariffs, and a nationalized monetary system gives the lie to the story told by Doris Kearns-Goodwin and Steven Spielberg that Lincoln was such an unmatched genius when it came to politics. Once the Southern Democrats left the union, thereby forfeiting any right to say anything about the extension of slavery into the Territories – THE big slavery issue of the 1860 election — the Republican Party had the ability to do whatever it wanted, regardless of Lincoln's input.
Most of the major problems with American society today, from poverty and unemployment to crime, declining standards of living, and more, are caused by the politicization of society that has been relentlessly ongoing for generations and which is celebrated and deified by leftists like Steven Spielberg and Doris Kearns-Goodwin. They keep dragging out the rotted stench of Lincoln's corpse disguised by professional actors, makeup artists, and cinematography to keep the booboisie dumb and happy and uneducated about their own history.
If America's founders were alive today, many of them would throw tomatoes at the screen upon viewing Spielberg's upcoming movie about Lincoln. Thomas Jefferson would likely throw the first "pitch" since he believed that government needed to be "bound by the chains of the Constitution," so untrustworthy were politicians and politics. In his Farewell Address George Washington reminded Americans that politicians are, as a rule, "cunning, ambitious, and unprincipled men"; and Thomas Paine wrote that government was "a necessary evil," at best. This is exactly the opposite view of the infantile rantings of Time magazine and Spielberg's Lincoln movie.
Thomas DiLorenzo Archives at Mises.org
The Best of Thomas DiLorenzo
Thomas J. DiLorenzo [send him mail] is professor of economics at Loyola University Maryland and the author of The Real Lincoln; How Capitalism Saved America; Lincoln Unmasked; Hamilton's Curse; Organized Crime: The Unvarnished Truth About Government; and most recently, The Problem With Socialism.
Previous article by Thomas DiLorenzo: Propagandist for State-Run Media Wants Even More of Your Money
Looking Beyond Election Day: The Issues That Threaten To Derail the Nation
Americans Proudly Voting for Evil | {
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} | 3,154 |
Q: Errors build gradle After adding the apply plugin: 'com.google.gms.google-services'. I am getting following errors
An error occurs after sync.ERROR: No such property:
applicationVariants for class: java.lang.String
Open File.
apply plugin: 'com.android.application'
android {
compileSdkVersion 29
buildToolsVersion "29.0.2"
defaultConfig {
minSdkVersion 16
targetSdkVersion 29
versionCode 1
versionName "1.0"
testInstrumentationRunner "androidx.test.runner.AndroidJUnitRunner"
}
repositories {
maven { url 'https://jitpack.io' }
}
buildTypes {
release {
minifyEnabled false
proguardFiles getDefaultProguardFile('proguard-android-optimize.txt'), 'proguard-rules.pro'
}
}
}
dependencies {
implementation fileTree(dir: 'libs', include: ['*.jar'])
implementation 'androidx.appcompat:appcompat:1.1.0'
implementation 'com.google.firebase:firebase-analytics:17.2.1'
implementation 'androidx.constraintlayout:constraintlayout:1.1.3'
implementation 'com.google.android.material:material:1.0.0'
implementation 'androidx.cardview:cardview:1.0.0'
implementation 'com.github.bumptech.glide:glide:4.7.1'
implementation 'com.github.PhilJay:MPAndroidChart:v2.2.4'
testImplementation 'junit:junit:4.12'
androidTestImplementation 'androidx.test:runner:1.2.0'
androidTestImplementation 'androidx.test.espresso:espresso-core:3.2.0'
implementation("com.mikepenz:materialdrawer:6.0.8@aar") {
transitive = true
}
}
apply plugin: 'com.google.gms.google-services'
A: Try to add
classpath 'com.google.gms:google-services:4.3.3'
and delete the line with "apply plugin".
It should work.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 290 |
{"url":"https:\/\/blog.krugazor.eu\/2022\/12\/04\/dev-diaries-advent-of-code\/","text":"# [Dev Diaries] Advent of Code\n\nI've been really interested in Julia for a while now, tinkering here and there with its quirks and capabilities.\n\nThis year, I've decided to try and do the whole of Advent of Code using that language.\n\nFirst impressions are pretty good:\n- map, reduce, and list\/array management in general are really nice, being first-class citizens. I might even get over the fact that indices start at 1\n- automatic multithreading when iterating over collections means that some of these operations are pretty speedy\n- it's included in standard jupyterhub images, meaning that my server install gives me access to a Julia environment if I am not at my computer for some reason\n\nNow it's kind of hard to teach old dogs new tricks, so I'm sure I misuse some of the features by thinking in \"other languages\". We'll see, but 4 days in, I'm still fairly confident.","date":"2023-02-05 01:06:08","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.5669437050819397, \"perplexity\": 2615.66459947062}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2023-06\/segments\/1674764500158.5\/warc\/CC-MAIN-20230205000727-20230205030727-00257.warc.gz\"}"} | null | null |
\section{Introduction}
Interest in the dynamics of icebergs has been driven by the desire to describe various natural phenomena (e.g.~rolling of icebergs) as well as
practical considerations associated with shipping and protection of offshore structures in arctic environments.
Allaire's \cite{Allaire1972} study of iceberg stability was motivated by the need to assess mitigation strategies, such as towing of icebergs, to reduce threats posed by icebergs to offshore structures.
Allaire identified readily-identifiable above-water characteristics, such as the ratio of waterline width to above-water height, to estimate stability for a menagerie of iceberg shapes -- Blocky, Drydock, Dome, Pinnacled, Tabular, Growler.
Bailey \cite{Bailey1994}, motivated by similar concerns, examined stability of icebergs in terms of rolling frequency.
The potential for iceberg stability considerations to be dynamic even in calm water due to underwater melting/dissolution was considered by Deriabyn \& Hjorth \cite{DH2009}.
They were also interested to identify what practical, above-water, observations could be made to predict stability changes driven by underwater changes in iceberg morphology.
Ship design and the design of other man-made floating objects has no doubt driven much scientific
and technical work in this field.
We make no attempt to review this literature but interested readers may find resources in the work
of M\'{e}gel \& Kliava \cite{MK2010} and Wilczynski \& Diehl \cite{WD1995}.
Historically speaking, scientific thought on this dates back to Archimedes (c.~287--212/211 B.C.).
See for example Rorres \cite{Rorres2004}, a
fascinating article on the original work of Archimedes and extensions thereof.
Whereas icebergs and ships are complex three dimensional floating
objects, the floating objects that are the focus of the present work are
those whose configurations can effectively be characterized in
two-dimensions. Specifically, we shall consider `long' objects whose
cross sections are constant for the full length of the object.
Such shapes have been the
focus of popular online Apps, such as Iceberger~\cite{Iceberger} and the remixed
version\cite{IcebergerRemix}.
These
effective two-dimensional floating objects have proven to be
mathematically tractable yet rich in observable phenomena. Prediction of
the stable orientations for a long beam with square-cross section and
uniform density, for example, was considered by Reid \cite{Reid1963}.
Depending on the ratio of the density of the object to the density of
the fluid any rotation of the square can be a stable floating
orientation (i.e.~any orientation from flat side up to corner up). This
configuration has been recently revisited both experimentally and
analytically by Feigel and Fuzailov \cite{FF2021}. These authors
validated experimentally that for a small range of density ratios near
$0.25$ (and also similarly near $0.75$) the full range of stable
orientations can be realized. Another view of this which we discuss in
more detail in our work is that owing to the four-fold symmetry of the
square, there can be either four or eight stable orientations of the
floating square depending on the density ratio. We explore how these
results change for what we denote as `off-center' squares.
The case of a long `floating plank' of rectangular cross section was the
focus of work by Delbourgo \cite{Delbourgo1987}. Here, in addition to
the density ratio, another parameter -- the aspect ratio of the
rectangle -- appears. Delbourgo identified in this density ratio vs.
aspect ratio space the existence of six characteristic floating
configurations in terms of (1) long side up or short side up, (2) top
side parallel or not parallel to the waterline, and (2) the number of
submerged vertices. Further studies have explored other cross sectional
shapes and investigated details of the breaking of left-right symmetries
of the floating shapes as the density ratio is varied (e.g.~see
Erd\"{o}s, Schibler, \& Herndon \cite{Erdos_etal1992_part1} for square
and equilateral triangle cross sections and Erd\"{o}s, Schibler, \&
Herndon \cite{Erdos_etal1992_part2} for the three-dimensional shapes of
the cube, octahedron, and decahedron). Work in this area has focused on
homogeneous objects with uniform density. We shall relax this
assumption in our present work to include some special classes of
non-uniform density in which the center of gravity of the square no
longer resides at its centroid (cf. Definition~\ref{defcog}).
An excellent review of many important mathematical ideas -- Archimedes'
Principle, Center of Gravity, Center of Buoyancy, and the notion of
Metacenter -- related to floating objects is the work of Gilbert
\cite{Gilbert1991}. One particularly useful concept is that of the
potential energy of floating objects. There it is shown that if one
can compute the potential energy landscape as a function of all possible
orientations of the object one can identify stable floating
configurations by the locations of local minima of the potential energy
function. This is one of the main objectives of our computations as we
then use this to identify stable orientations.
The present work shares some of the spirit of the paper by Feigel and
Fuzailov \cite{FF2021} to revisit these questions both theoretically and
experimentally. Our experiments, however, are conducted with 3D
printed shapes. While much of our theoretical effort has been on objects with square cross
section, our methodology is motivated by the
recognition that 3D printing offers the opportunity to float objects
whose cross sections are effectively limited only by ones own creativity
in defining new shapes. An example shape we analyze is the `Mason M' shown in Figure~\ref{fig-intro_fig_MasonM}.
\begin{figure}[tb]
\includegraphics[width=0.8\textwidth]{IMG_8488.JPG}
\caption{The floating Mason M. }
\label{fig-intro_fig_MasonM}
\end{figure}
This paper is organized as follows. In Section~\ref{sec:math}, we introduce definitions and
terminology, outline prior results for long floating objects of uniform density with
square cross section, and state our analytical results for the case of long floating
objects with square cross section with non-uniform density.
In Section~\ref{sec:3DPrinting} we give a detailed description of how to 3D print floating objects.
This section contains sufficient details and accompanying code so that interested readers would be
able to print their own objects and perform their own experiments.
Note that we have additionally provided codes and files in a GitHub repository~\cite{GITHUB}.
In Section~\ref{sec:Experiments} we describe how we obtain experimental results on
our 3D printed floating objects.
In Section~\ref{sec:compexp} we describe our code for computing
stable floating configurations for objects with general polygonal cross sections.
In Section~\ref{sec:Results} we describe the results of our floating experiments and
relate them to our theoretical results for several cases involving square cross sections
and a selected case of a nontrivial cross section.
In Section~\ref{sec:conclusion} we give our conclusions and discuss some open problems.
\section{Mathematical Models for Floating Objects}
\label{sec:math}
\subsection{Definitions}
In this section, we give some basic definitions and concepts that will be needed for
the remainder of our analysis.
\begin{definition}[Center of Gravity]\label{defcog}
If the mass distribution is given by a continuous
density function of $\rho(x,y,z)$ within a domain $\Omega$,
then the center of gravity can be obtained by
$$(G_x,G_y,G_z)=\frac{1}{M_{\rm{obj} }}\iiint_{\Omega}(x,y,z) \, \rho(x,y,z) \; dV \;,$$
where $M_{\rm{obj}}$ is the object's mass.
In the case of uniform density, i.e. $\rho$ is a constant independent of $x,y$ and $z$,
the center of gravity is called the centroid.
\end{definition}
For a long object of length $L$ with uniform cross section,
with uniform density in the long direction, i.e. $\rho(x,y,z) = \rho(x,y)$ is independent of $z$,
the center of gravity is given by
\[
\vec{G} = (G_x,G_y)= \frac{L}{M_{\rm{obj} }} \iint_\Omega (x,y) \rho(x,y) \; dA
\]
with $G_z = L/2$ (relative to one end of the object).
\begin{lemma}
For an object of length $L$ with a polygonal cross-section with uniform
constant density $\rho$, we can compute the area and center of gravity as
sums involving only the vertices of the polygon. In particular, let
\[\{ (x_1,y_1),\dots,(x_N,y_N),(x_1,y_1) \}
\]
be the vertices of the cross section polygon,
oriented counterclockwise. Then the mass of the object is
\[
M_{\rm{obj}} = \rho L A \;,
\]
where the area $A$ of the polygon of cross section is given by
\begin{eqnarray}\label{greenarea}
A = \frac{1}{2} \sum_{k = 1}^N (x_k + x_{k+1}) (y_{k+1}- y_k) \;,
\end{eqnarray}
a result also known as the shoelace formula, and the center of gravity $\vec{G} = (G_x,G_y)$ is given by
\begin{eqnarray}\label{greencenter}
G_x &=& \frac{1}{6 A} \sum_{k = 1}^N (x^2_k + x_k x_{k+1} + x^2_{k+1}) (y_{k+1}- y_k) \\
G_y &=& \frac{1}{6 A} \sum_{k = 1}^N - (y^2_k + y_k y_{k+1} + y^2_{k+1}) (x_{k+1}- x_k) \, . \nonumber
\end{eqnarray}
\end{lemma}
\begin{proof}
According to Green's theorem
\[
\iint_\Omega \left( \frac{dg}{dx}-\frac{df}{dy} \right) \; dA=\oint_{d\Omega}\, f \; dx+g \; dy,
\]
Choose $(f,g) = (0,x)$ so that $\frac{dg}{dx}-\frac{df}{dy}=1$. We can parametrize
the line segment between $(x_k,y_k)$ and $(x_{k+1},y_{k+1})$ by
$(x,y) = (1-t)(x_k,y_k)+t(x_{k+1},y_{k+1})$ where $t\in(0,1)$.
For this line segment, we get $dx=(x_{k+1}-x_{k}) dt$ and
$dy=(y_{k+1}-y_k) dt$. Now we evaluate the integral from Green's theorem:
\begin{eqnarray*}
\int_0^1 x \; dy &=& \int_0^1(x_k+t(x_{k+1}-x_k))(y_{k+1}-y_k) \; dt \\
&=& x_k(y_{k+1}-y_k)+\frac{1}{2}(x_{k+1}-x_k)(y_{k+1}-y_k) \\
&=& \frac{1}{2}(x_{k+1}+x_k)(y_{k+1} -y_k) \; .
\end{eqnarray*}
Now we use this to calculate the full area:
\[
A=\iint_\Omega \;
dA=\oint_{d\Omega} x \; dy=\frac{1}{2}\sum_{k=1}^N(x_{k+1}+x_k)(y_{k+1}-y_k) \;.
\]
Now we turn our
attention to the calculation of $G_x$. We use Green's theorem
but this time with $(f,g) = (0,x^2/2)$
in order to satisfy $\frac{dg}{dx}-\frac{df}{dy}=x$. Again for the line segment
from $(x_k,y_k)$ to $(x_{k+1},y_{k+1})$
we get
\begin{eqnarray*}
\iint_{\Omega}xdA &=& \oint_{d\Omega}\frac{x^2}{2} \; dy \\
&=&\frac{1}{2}\int_0^1(x_k+t(x_{k+1}-x_k))^2(y_{k+1}-y_k) \; dt \\
&=&\frac{1}{6}(x_k^2+x_k x_{k+1}+x_{k+1}^2)(y_{k+1}-y_k) \; .
\end{eqnarray*}
Since $\rho$ is constant, we get that $G_x$ is equal to $\rho L/M_{\rm obj}$ times this
integral, but $M_{\rm obj} = \rho L A$, and this gives the factor of $1/A$ written
in the formula above.
In a similar way, using Green's theorem with
$(f,g) = (-y^2/2,0)$, we get
\[ \iint_{\Omega}ydA = -\frac{1}{6}(y_k^2+y_k y_{k+1}+y_{k+1}^2)(x_{k+1}-x_k) \; . \]
This gives the equation for $G_y$ stated above.
\end{proof}
\begin{definition}[Buoyancy]
Buoyancy is a force exerted on an object that is wholly or partially submerged
in a fluid. The magnitude of this force is equal to the weight of the displaced fluid.
Buoyancy relates to the density of the fluid, the volume of the displaced
fluid, and the gravitational field; it is independent of the mass and density
of the immersed object. The buoyancy force acts vertically upward at the
centroid of the displaced volume. The {\em center of buoyancy} is given by
%
\begin{equation}
(B_x,B_y,B_z) = \frac{1}{V_{\rm{sub}}} \iiint_{\Omega_{\rm{sub}}} (x,y,z) dV,
\end{equation}
where $V_{\rm{sub}}$ is the submerged volume of the object, and $\Omega_{\rm{sub}}$ is the
submerged domain. Like in the case of center of gravity, in the uniform
cross section case $B_z = L/2$. We use the notation $\vec{B} = (B_x,B_y)$.
Note that $\vec{B}$ is the centroid of the submerged domain.
\end{definition}
We now state one of the major results necessary for understanding floating objects.
\begin{theorem}[Archimedes' Principle]
The upward buoyant force exerted on an object wholly or partially
submerged is equal to the weight of the displaced fluid.
In the absence of other forces, such as surface tension, this can be expressed in
the force balance as
\begin{eqnarray} \label{eq:buoy}
M_{\rm{obj}} g & = & \rho_{\rm{f}} V_{\rm{sub}} g,
\end{eqnarray}
where $g$ is acceleration due to gravity, $\rho_{\rm{f}}$ is the density of the fluid,
and $V_{\rm{sub}}$ is the submerged volume of the object.
\end{theorem}
Observe that~\eqref{eq:buoy} represents a balanced (net zero) equation of
competing forces with the left terms representing gravitational force and right
term representing the opposing force of buoyancy. Note that if the object has uniform
density, then the mass of the
object can be written as $M_{\rm{obj}} = \rho_{\rm{obj}} V_{\rm{obj}}$.
In this case, it follows that
\begin{eqnarray}
\frac{V_{\rm{sub}}}{V_{\rm{obj}}} & = & \frac{\rho_{\rm{obj}}}{\rho_{\rm{f}}}.
\end{eqnarray}
For our purposes, Archimedes' Principle determines the appropriate waterline
intersections defining a submerged volume whose value relative to the total volume
matches the appropriate density ratio. However, it
is important to note that satisfying Archimedes' Principle is not a sufficient
condition for determining a stable equilibrium. An equilibrium orientation of a
floating body occurs when the center of gravity and the center of buoyancy are
vertically aligned. If $\vec{G}$ lies directly below $\vec{B}$ the equilibrium is stable,
whereas if $\vec{G}$ lies
above $\vec{B}$ the equilibrium may or may not be stable. We present an alternative
approach using energy principles similar to that of Erd{\"o}s~\cite{Erdos_etal1992_part1}
and Gilbert~\cite{Gilbert1991}. After
identifying a waterline that is consistent with Archimedes' Principle, we define a unit
vector normal to the waterline, by keeping the object fixed and rotating the frame of
reference (waterline) by angle $\theta$ to generate all orientations
satisfying Archimedes' Principle. The stable positions of a floating body
occur at the minima of the potential energy. The
potential energy function for a floating body is given by
\begin{eqnarray} \label{eq:PEfunction}
U(\theta) = \hat{n}(\theta)\cdot (\vec{G}-\vec{B}(\theta)) \; ,
\end{eqnarray}
where $\hat{n}$ is the unit normal vector to the waterline pointing out of
the water, and $\theta$ is the rotation angle of the waterline. Note that $\vec{B}(\theta)$ and
$\hat{n}(\theta)$ depend on $\theta$, but $\vec{G}$ is independent of $\theta$.
Below, we derive formulas for the stable floating configurations by
finding minima for $U(\theta)$.
\subsection{Square Cross Section Revisited}\label{subsec:squarerevisit}
The conditions for stability of a long floating object with square cross
section have been investigated theoretically by Reid \cite{Reid1963} and
experimentally and theoretically more recently by Feigel \& Fuzailov
\cite{FF2021}. We revisit this configuration here with the goal of
identifying the stable equilibrium configurations via the entire
potential energy landscape. The square has four-fold symmetry, and we
exploit this here in the specific identification of a center of buoyancy
formula. We are also interested in situations in which the center of
gravity is not at the center of the square and so explore the breaking
of this four-fold symmetry in the potential energy for floating objects
with square cross sections.
Rather than fix a waterline and consider different orientations of the
square we fix a reference frame on the square with corners at $(1,-1)$,
$(1,1)$, $(-1,1)$, $(-1,-1)$ and consider different orientations of the
waterline. Three configurations are relevant as shown in
Figure~\ref{fig-square_diagram} -- the first has the waterline
intersecting opposite sides of the square and the second and third have the
waterline intersecting adjacent sides of the square. We work out these
three cases below and then give the generalization for all orientations.
For our $[-1,1]^2$ square, the cross sectional area is $A_{\rm{obj}} = 4$. If
we denote by $A_{\rm{sub}}$ the submerged area, Archimedes' Principle requires
that
\begin{eqnarray}
\label{archimedes}
\frac{A_{\rm{sub}}}{A_{\rm{obj}}} = R,
\end{eqnarray}
where $R \in (0,1)$ is the density ratio $\rho_{\rm{obj}}/\rho_{\rm{f}}$
of the floating object to the fluid. We shall assume that the object's
density is uniform throughout but if it were not the appropriate
interpretation
of $\rho_{\rm{obj}}$ for the application of Archimedes' Principle would
be the effective density -- i.e. the object's mass divided by the volume
of the object. Note that in the present context we work in terms of
cross sectional area; corresponding volumes would be obtained by
multiplying the cross sectional area by the length of the object in the
third dimension.
Below we outline the computation of the center of buoyancy, $\vec{B}(\theta)$, as a function of orientation $\theta$ for the two cases in which (1) the waterline intersects opposite sides of the square and (2) the waterline intersects adjacent sides of the square.
\begin{figure}[h!]
\begin{center}
\includegraphics[height=0.35\textwidth]{square_caseA.pdf}
\includegraphics[height=0.35\textwidth]{square_caseB.pdf}\\ \vspace{0.05in}
\includegraphics[height=0.37\textwidth]{square_caseC.pdf}
\end{center}
\caption{The sketch on the upper left shows the configuration in which the waterline
(blue) intersects opposite sides of the square. The sketch on the upper right
shows the configuration in which the waterline intersects adjacent sides
of the square for $R> 1/2$. The sketch on the bottom
shows the configuration in which the waterline intersects adjacent sides
of the square for $R< 1/2$.}
\label{fig-square_diagram}
\end{figure}
\subsubsection{Waterline Intersects Opposite Sides of Square}
Here we define the waterline by the equation
\begin{eqnarray}
\label{eq:waterline_case1}
y & = & x \tan \theta + H,
\end{eqnarray}
where $\theta$ is the slope of the waterline and $H$ is the y-intercept
(see Figure~\ref{fig-square_diagram}). With the water assumed to occupy
the region below the waterline, the submerged area can be written in
terms of $H$ as
$A_{\rm{sub}} = 2 (1 + H)$.
Therefore, Archimedes' Principle requires $R = (1+H)/2$, or equivalently $H = 2R - 1$.
Note that for $R \in(0,1)$ it follows that $H \in (-1,1)$.
We define waterline intersection points $(-1,y_L)$ and $(1,y_R)$ and note that
\begin{eqnarray}
y_L = - \tan \theta + H, \quad
y_R = \tan \theta +H.
\end{eqnarray}
By definition, the configuration under consideration requires that
$y_L \in [-1,1]$ and $y_R \in [-1,1]$. Furthermore, the largest and smallest
$\theta$ occur for $y_R = \pm 1, y_L = \mp 1$, meaning that
$-\pi/4 \le \theta \le \pi/4$ and $-1 \le \tan \theta \le 1.$
Combining these facts with the definitions of $y_L$ and $y_R$, we get
\begin{eqnarray}
\tan \theta + H \le 1 \hspace{0.25in} \mbox{and} \hspace{0.25in} -\tan \theta + H \le 1 \hspace{0.25in} \mbox{if $H \ge 0$}, \\
-\tan \theta + H \ge -1 \hspace{0.25in} \mbox{and} \hspace{0.25in} \tan \theta + H \ge -1 \hspace{0.25in} \mbox{if $H \le 0$},
\end{eqnarray}
These can be rewritten as
\begin{eqnarray}
\label{eq:tan_theta_A}
-1 + | H | \le \tan \theta \le 1 - | H |.
\end{eqnarray}
This range of $\tan \theta$ corresponds to a range of $\theta$ values
$[\theta_1^{\min},\theta_1^{\max}]$ contained in $[-\pi/4,\pi/4]$. By symmetry,
there is a corresponding configuration when rotated by $\pm \pi/2$ and $\pm \pi$.
The submerged area in this configuration is defined by the four points $(1,-1)$, $(1,y_R)$, $(-1,y_L)$, and $(-1,-1)$.
We use \eqref{greencenter} to find the center of buoyancy as the centroid of the
submerged boundary region.
In particular, let $(x_k,y_k)$ be given by $\{ (1,-1), (1,y_R), (-1,y_L),(-1,-1),(1,-1) \}$.
Then $\vec{B}(\theta) = (B_x(\theta),B_y(\theta))$ where
\begin{eqnarray*}
B_x(\theta) & = & \frac{1}{6 A_{\rm{sub}}} \sum_{k=1}^{4} (x_k^2 + x_k x_{k+1} + x_{k+1}^2)(y_{k+1}-y_k)\\
B_y (\theta) & = & \frac{1}{6 A_{\rm{sub}}} \sum_{k=1}^{4} -(y_k^2 + y_k y_{k+1} + y_{k+1}^2)(x_{k+1}-x_k) \;.
\end{eqnarray*}
Computing these sums, combined with the values of $y_L$ and $y_R$ and the fact that $A_{\rm{sub}} = 2(1+H)$,
we find that the center of buoyancy takes the form
\begin{eqnarray}
\vec{B}(\theta) = \vec{B}_1(\theta) & \equiv & \frac{1}{2 (1+H)} \Big( \frac{2}{3} \tan \theta , -1 + H^2 + \frac{1}{3} \tan^2 \theta \Big),
\end{eqnarray}
where $\theta$ can take on any value defined by the inequalities~(\ref{eq:tan_theta_A}). For use below we define this specific form for the center of buoyancy as $\vec{B}_1(\theta)$.
\subsubsection{Waterline Intersects Adjacent Sides of Square}
A similar approach can be applied to the second configuration shown in the upper right sketch of Figure~\ref{fig-square_diagram}.
Here we give expressions for the results when $R \ge 1/2$ and when $R < 1/2$.
{\bf Case 1: $R \ge 1/2$.}
Here we assume that the waterline intersects the left and top sides of the square at points $(-1,y_L)$ and $(x_R,1)$ so that three corners of the square are submerged.
We consider the case $R< 1/2$ in the next section although note that this case can be carefully extracted from the
present case (according to Gilbert \cite{Gilbert1991}, Feigel \& Fuzailov \cite{FF2021}, among others).
Here we identify the waterline by
\begin{eqnarray}
y & = & (x - x_R) \tan \theta + 1,
\end{eqnarray}
where $y_L = - (1 + x_R) \tan \theta + 1$.
This waterline cuts a triangular region of area $\frac{1}{2} (1+ x_R) (1- y_L)$ from the original square. This means that
$A_{\rm{sub}} = 4 - \frac{1}{2} (1+x_R) (1- y_L)$ and
\begin{eqnarray}
R = \frac{A_{\rm{sub}}}{A_{\rm{obj}}} & = & \frac{ 4 - \frac{1}{2} (1+x_R) (1- y_L)}{4} = \frac{ 4 - \frac{1}{2} (1+x_R)^2 \tan\theta}{4}.
\end{eqnarray}
Rearranging this gives $x_R$ in terms of $R$ and the waterline slope $\tan \theta$
\begin{eqnarray}
(1+ x_R)^2 & = & \frac{8 - 8 R}{\tan \theta}.
\end{eqnarray}
Conditions on $\theta$ come from the requirement that $0 \le (1+x_R) \le 2$ and $-1 \le y_L \le 1$. The first of these reveals that
\begin{eqnarray}
0 \le \frac{2 - 2 R}{\tan \theta} \le 1.
\end{eqnarray}
For the case under consideration $0 < \theta < \frac{\pi}{2}$. It follows that $\tan \theta \ge 2 - 2R$.
Equality corresponds to the waterline passing through the point $(1,1)$ and $(-1,y_L)$.
The other extreme corresponds to the waterline passing through the point $(-1,-1)$ and $(x_R,1)$. This has
$\tan \theta = 2/(1+x_R)$.
Here
the triangular area is $\frac{1}{2} 2 (1+x_R)$ which means $R = (4 - (1+x_R))/4$ or $(1+x_R) = 4 - 4R$. Since $\theta$
cannot exceed this angle we have $\tan \theta < 2/(4-4R)$. Thus, for this configuration the value of $\tan \theta$ is
constrained by
\begin{eqnarray} \label{theta2minmax}
2 - 2R \le \tan \theta \le \frac{1}{2-2R}.
\end{eqnarray}
As in the previous case,
the center of buoyancy is obtained by calculating the centroid
of the submerged area using \eqref{greencenter}. In particular, using
the counterclockwise oriented
vertices of the submerged polygon:
\[
\{(x_R,1),(-1,y_L),(-1,-1),(1,-1),(1,1)\} \; ,
\]
we can calculate the following integral
\begin{eqnarray}
\vec{B}(\theta) & = & \frac{1}{A_{\rm{sub}} } \iint_{\Omega_{\rm sub}} (x,y) \; dA
\end{eqnarray}
as a sum.
Evaluating this integral gives
\begin{eqnarray}
\vec{B}(\theta) = \vec{B}_2^{+}(\theta) & \equiv & \frac{1}{A_{\rm{sub}}} \Big( 1 - \frac{1}{2} (y_L + 1) - \frac{1}{6} (x_R^3 + 1) \tan\theta , \nonumber \\
& & \mbox{} -1 + \frac{1}{2} (1-x_R) + \frac{(1-y_L^3)}{6\tan\theta} \Big).
\end{eqnarray}
Recall that $A_{\rm{sub}} = 4R$ and
\begin{eqnarray}
y_L = - \tan \theta (1 + x_R) + 1,\quad
(1+ x_R)^2 = \frac{8 - 8 R}{\tan \theta},
\end{eqnarray}
where $\tan \theta$ satisfies \eqref{theta2minmax}.
This condition gives a range of
$\theta$ values given by $[\theta_2^{+ \min},\theta_2^{+ \max}]$ contained in $[0,\pi/2]$.
Again by symmetry, we get a corresponding set of angles by adding $\pm \pi/2, \pm \pi$.
{\bf Case 2: $R < 1/2$.} Here assume that the waterline intersects the square at points $(x_L,-1)$ and $(1,y_R)$ so that only the lower right corner of the square is submerged.
Here we identify the waterline by
\begin{eqnarray}
y & = & \tan \theta (x - x_L) - 1,
\end{eqnarray}
where $y_R = \tan \theta (1 - x_L) - 1$.
This waterline cuts a triangular region of area $A_{sub} = \frac{1}{2} (1+ y_R) (1- x_L)$ from the original square. This means that
\begin{eqnarray}
R = \frac{A_{\rm{sub}}}{A_{\rm{obj}}} & = &\frac{1}{8} (1+ y_R) (1- x_L) = \frac{(1-x_L)^2 \tan\theta}{8}.
\end{eqnarray}
Rearranging this gives $x_L$ in terms of $R$ and the waterline slope $\tan \theta$
\begin{eqnarray}
(1- x_L)^2 & = & \frac{8 R}{\tan \theta}.
\end{eqnarray}
Conditions on $\theta$ come from the requirement that $0 \le (1- x_L) \le 2$. This translates to
\begin{eqnarray}
\tan \theta \ge 2 R.
\end{eqnarray}
Also the condition $-1 \le y_R \le 1$ leads to
\begin{eqnarray}
0 \le \tan \theta \le \frac{2}{1 - x_L}.
\end{eqnarray}
Using $8R = (1-x_L) (1+ y_R)$ leads to $0 < \tan \theta < 1/(2R)$.
So, together these require
\begin{eqnarray} \label{theta2minus}
2R \le \tan \theta \le \frac{1}{2R}.
\end{eqnarray}
As before, the center of buoyancy satisfies
\begin{eqnarray}
\vec{B}(\theta) & = & \frac{1}{A_{\rm{sub}} }\int_{\Omega_{\rm sub}} (x, y) \; dA \;,
%
%
%
%
%
\end{eqnarray}
which can be calculated as a sum involving the vertices of the submerged polygonal
cross section via ~\eqref{greencenter}.
It follows that
\begin{eqnarray}
\vec{B}(\theta) &=& \vec{B}_2^{-}(\theta) \\
& \equiv & \frac{1}{A_{\rm{sub}}} \Big( \frac{y_R+1}{2} - \frac{(1-x_L^3)}{6} \tan \theta ,
- \frac{(1-x_L)}{2} + \frac{1+y_R^3}{6\tan \theta} \Big) \; .\nonumber
\end{eqnarray}
Recall that $A_{\rm{sub}} = 4R$ and
\begin{eqnarray}
y_R = \tan \theta (1 - x_L) - 1,\quad
(1- x_L)^2 & = & \frac{8 R}{\tan \theta},
\end{eqnarray}
where $\tan \theta$ satisfies \eqref{theta2minus}.
\subsubsection{Potential Energy Expressions: Square Cross Section}
As defined in ~\eqref{eq:PEfunction} the potential energy function is given by
\[
U(\theta) = \hat{n}(\theta) \cdot (\vec{G} - \vec{B}(\theta)) \; ,
\]
where the unit normal to the waterline can be expressed as a function of
$\theta$ as $\hat{n}(\theta) = ( - \sin \theta, \cos \theta )$. For the square
defined above with uniform density the center of gravity
$\vec{G}=(0,0)$. However, we are interested in a generalization of
the square where the center of gravity, by some means, is not
necessarily located at the center but rather has coordinates $\vec{G} =
(G_x, G_y)$. Note that as long as Archimedes' Principle is applied with
the appropriate mass of the object, the calculations presented above for
the center of buoyancy are independent of the location of the center of
gravity. So, in what follows we treat $\vec{G}$ as nonzero in general.
For $R \ge 1/2$ define
\begin{eqnarray}
U_{B_1}(\theta) & = & \hat{n}(\theta) \cdot \vec{B}_1(\theta) \, , \mbox{ for } -1 + | H | \le \tan \theta \le 1 - | H | \, ,
\end{eqnarray}
which corresponds to a range of $\theta \in [\theta_1^{\min}, \theta_1^{\max}]$
defined by~\eqref{eq:tan_theta_A}.
Also define
\begin{eqnarray}
U_{B_2^+}(\theta) & = & \hat{n}(\theta) \cdot \vec{B}_2^+(\theta) \, , \mbox{ for } 2 - 2R \le \tan \theta \le \frac{1}{2-2R} \, ,
\end{eqnarray}
which corresponds to a range of $\theta \in [\theta_2^{+ \min}, \theta_2^{+ \max}]$
defined by~\eqref{theta2minmax}.
We can write the potential energy function $U(\theta)$ as follows
\begin{eqnarray}
\label{eq:PE_formula_SQUARE}
U(\theta) & = & \left\{
\begin{array}{ll}
\hat{n}(\theta) \cdot \vec{G} - U_{B_1}(\theta) & \theta \in [\theta_1^{\min}, \theta_1^{\max}] \\
\hat{n}(\theta) \cdot \vec{G} - U_{B_1}(\theta \pm \frac{\pi}{2}) & \theta \pm \frac{\pi}{2} \in [\theta_1^{\min}, \theta_1^{\max}] \\
\hat{n}(\theta) \cdot \vec{G} - U_{B_1}(\theta \pm \pi) & \theta \pm \pi \in [\theta_1^{\min}, \theta_1^{\max}] \\
& \\
\hat{n}(\theta) \cdot \vec{G} - U_{B_2^+}(\theta) & \theta \in [\theta_2^{+ \min}, \theta_2^{+ \max}] \\
\hat{n}(\theta) \cdot \vec{G} - U_{B_2^+}(\theta \pm \frac{\pi}{2}) & \theta \pm \frac{\pi}{2} \in [\theta_2^{+ \min}, \theta_2^{+ \max}] \\
\hat{n}(\theta) \cdot \vec{G} - U_{B_2^+}(\theta \pm \pi) & \theta \pm \pi \in [\theta_2^{+ \min}, \theta_2^{+ \max}] \\
\end{array}
\right.
\end{eqnarray}
A similar formula applies when $R < 1/2$ (replace $B_2^+$ with $B_2^-$ and the
corresponding range for $\tan \theta$ given in~\eqref{theta2minus}).
\subsection{Squares With Off-Center Weights}
We also explore the case of a square cross section with an off-center weight parallel to the long axis of the object. Specifically we consider
3D printed objects with a hole in the square that can be filled with a material of different density. In our experiments we had the option to leave
the hole as void space or to insert a nail cut to fit the object. In either case, before floating the object tape was placed over the holes to prevent
water from filling the space.
For such a configuration we can predict the modified center of gravity $\vec{G} \neq 0$. In particular, consider the same square with corners
at $(1,-1)$, $(1,1)$, $(-1,1)$, $(-1,-1)$ with a hole with circular cross section at point $(a,b)$ with $a \in (0,1)$, $b \in (0,1)$, and radius $r_H$. When such an object
is printed there is a border around the hole whose thickness we denote by $t$ and whose density is $\rho_{\rm PLA}$ (i.e.~the density of the solid print material).
With the hole filled with a nail whose density
is $\rho_{\rm nail}$ we can compute the center of gravity of the object as a whole (printed object plus nail) as
\begin{eqnarray}
\label{eq:COG_hole1}
M_{\rm{obj}} \vec{G} & = & L \left\{ \int_{\Omega_0} \rho(\vec{x}) \vec{x} \; dA + \int_{\Omega^{{\rm hole}+{\rm border}}} \rho(\vec{x}) \vec{x} \; dA \right\},
\end{eqnarray}
where $M_{\rm{obj}}$ is the mass of the whole object (including the nail if one is inserted), $L$ is the length of the object, $\Omega_0$ denotes the cross-sectional domain of the square
excluding the hole and border and $\Omega^{{\rm hole}+{\rm border}}$ denotes the circular cross section that includes the (printed) border of the hole and
the hole, and $\rho(\vec{x})$ denotes the material density at position $\vec{x}$ in the plane.
The square printed without a hole will have some void space in its interior and this can be controlled by changing the infill of the print. In our
squares printed with a hole this infill region gets replaced by the hole plus the border material of the hole. Therefore, it is convenient to rewrite
the formula~(\ref{eq:COG_hole1}) for center of gravity $\vec{G}$ as
\begin{eqnarray}
\label{eq:COG_hole2}
\frac{M_{\rm{obj}}}{L} \vec{G} & = & \int_{\Omega_0} \rho(\vec{x}) \; \vec{x} \; dA + \int_{\Omega^{{\rm hole}+{\rm border}}} \rho(\vec{x}) \; \vec{x} \; dA \nonumber \\
& & \mbox{} + \int_{\Omega^{{\rm hole}+{\rm border}}} \rho_{\rm infill} \; \vec{x} \; dA - \int_{\Omega^{{\rm hole}+{\rm border}}} \rho_{\rm infill} \; \vec{x} \; dA, \nonumber \\
& = & \int_{\Omega} \rho(\vec{x}) \; \vec{x} \; dA + \int_{\Omega^{{\rm hole}+{\rm border}}} (\rho(\vec{x}) - \rho_{\rm infill}) \; \vec{x} \; dA,
\end{eqnarray}
where $\Omega$ denotes the cross section of the square undisturbed by a hole. Under our assumption of a square with uniform density the
first integral in this expression equates to the zero vector. That is, for a square without the off-center hole the center of gravity is located at $(0,0)$.
This requires that the infill is sufficiently symmetric about the center of the square so that it negligibly moves the center of
gravity away from $(0,0)$.\footnote{This appears to be a good approximation for the {\em grid} infill pattern but not, for example, the {\em cat} infill pattern or for {\em grid} at very low infills.}
It follows that for the off-center square the center of gravity can then be estimated as
\begin{eqnarray}
\label{eq:COG_hole3}
\frac{M_{\rm{obj}}}{L} \vec{G} & = & \int_{\Omega^{{\rm hole}+{\rm border}}} (\rho(\vec{x}) - \rho_{\rm infill}) \; \vec{x} \; dA, \nonumber \\
& = &(\rho_{\rm nail} - \rho_{\rm infill}) \int_{0}^{2\pi} \int_0^{r_H} \vec{x} r\; dr \; d\theta \nonumber \\
& & \mbox{} + (\rho_{\rm PLA} - \rho_{\rm infill}) \int_{0}^{2\pi} \int_{r_H}^{r_H+t} \vec{x} r \; dr \; d\theta,
\end{eqnarray}
where each of the density terms in these expressions are assumed to be independent of position. These integrals can be evaluated writing
$\vec{x} = (a + r \cos \theta, b + r \sin \theta)$. It follows that
\begin{eqnarray}
\label{eq:COG_hole4}
\frac{M_{\rm{obj}}}{L} \vec{G} & = & \pi (\rho_{\rm nail} - \rho_{\rm infill}) r_H^2 (a,b)
+ \pi (\rho_{\rm PLA} - \rho_{\rm infill}) [ (r_H+t)^2 - r_H^2] (a,b),\nonumber \\
& = & \left\{ \pi(\rho_{\rm nail} - \rho_{\rm infill}) r_H^2
+ \pi (\rho_{\rm PLA} - \rho_{\rm infill}) [ 2 r_H t + t^2 ] \right\} (a,b).
\end{eqnarray}
So, for the off-center square with hole at $(a,b)$ the center of gravity is shifted towards $(a,b)$ from the origin by terms proportional to density differences and
cross-sectional areas. Note that all of the quantities in this expression can be determined by straightforward measurements and are listed in Table \ref{Table-OffCenter}.
Practically speaking, our prints are not completely uniform in the direction orthogonal to the square face since the top and bottom square faces are solid PLA.
An improved estimate for the center of gravity that accounts for the two end faces of the square of thickness $t$ with density $\rho_{\rm PLA}$ is
\begin{eqnarray}
\label{eq:COG_hole4b}
M_{\rm{obj}} \vec{G} & = & \Big\{ \left[ (\rho_{\rm nail} - \rho_{\rm infill}) (\pi r_H^2)
+ (\rho_{\rm PLA} - \rho_{\rm infill}) \pi (2 r_H t + t^2) \right] (L-2t) \nonumber \\
& & \mbox{} + 2 t (\rho_{\rm nail} - \rho_{\rm PLA} ) (\pi r_H^2) \Big\} (a,b), \nonumber \\
& = & M_{\rm nail} (a,b) + \Big\{ \left[ - \rho_{\rm infill} (\pi r_H^2)
+ (\rho_{\rm PLA} - \rho_{\rm infill}) \pi (2 r_H t + t^2) \right] (L-2t) \nonumber \\
& & \mbox{} - 2 t \rho_{\rm PLA} (\pi r_H^2) \Big\} (a,b).
\end{eqnarray}
That is, the new center of gravity, $\vec{G}$, is shifted towards the
hole location $(a,b)$ by an amount related to the mass of the nail (we
use $M_{\rm nail}=0$ for an open hole) and terms related to the
thickness of the hole and the material it replaces (either infill or
boundary).
\begin{table}[ht]
\caption{Various parameter values for 3D prints with square cross section and a hole.
The values of $M_{\rm nail}$ and $\rho_{\rm nail}$ were obtained by noting that each nail was 60 mm in length and 2 mm in radius and that 25 nails
weighed $137.51$ g.}\label{Table-OffCenter}
\renewcommand\arraystretch{1.5}
\noindent\[
\begin{array}{|c|c|c|}
\hline
\mbox{Parameter} & \mbox{Description} & \mbox{Value} \\ \hline
I
& \makecell[c]{\mbox{Infill Fraction} \\ (\mbox{Infill \% /100})}
& 0.05 ... 0.95 \\ \hline
s
& \mbox{Length of Side of Square}
& 30 \; \mbox{mm}\\ \hline
L
& \mbox{Length of Object}
& 60 \; \mbox{mm}\\ \hline
\rho_{\rm PLA}
& \mbox{Density of PLA}
& 1.15 \mbox{ g cm}^{-3}\\ \hline
M_{\rm nail}
& \mbox{Mass of Nail}
& 5.5004 \mbox{ g}\\ \hline
\rho_{\rm nail}
&\makecell[c]{\mbox{Density of Nail} \\ M_{\rm nail}/{V_{\rm nail}} }
& 7.295 \mbox{ g cm}^{-3} \\ \hline
\rho_{\rm infill}
& \makecell[c]{\mbox{Effective Density of Infill} \\ \rho_{\rm PLA} \times I}
& \mbox{varies with Infill} \\ \hline
r_H
& \mbox{Radius of Hole}
& 2.5 \; \mbox{mm} \\ \hline
t
& \mbox{Thickness of Solid Border}
& 0.8 \; \mbox{mm} \\ \hline
\end{array}
\]
\end{table}
The predicted effective density for the block of square cross section is
\begin{eqnarray}
\rho^{\rm eff}_{\rm square} & = & \frac{M_{\rm square} }{V_{\rm ext}},
\end{eqnarray}
where the total mass of the object is
\begin{eqnarray}
M_{\rm square} & = & (V_{\rm ext} - V_{\rm int})\rho_{\rm PLA} + V_{\rm int} I \rho_{\rm PLA},
\end{eqnarray}
and $V_{\rm ext} = s^2 L$ and $V_{\rm int} = (s - 2t)^2 (L - 2t)$.
When the block is printed with a hole of radius $r_H$ parallel to the long axis the predicted effective density is
\begin{eqnarray} \label{eq:effective_density_hole}
\rho^{\rm eff}_{\rm square + hole} & = & \frac{1}{V_{\rm ext}} \Big\{
M_{\rm square} + M_{\rm nail} - \pi r_H^2 [ 2 t + (L - 2t) I ] \rho_{\rm PLA} \nonumber \\
& & \mbox{} + \pi [ (r_H +t)^2 - r_H^2] (L - 2t) (\rho_{\rm PLA} - I \rho_{\rm PLA})
\Big\}
\end{eqnarray}
The effective density of the object without the nail filling the hole is calculated by the same formula with $M_{\rm nail}$ set to zero.
Various comparisons between this theory and our experimental observations and measurements are given below. First, however,
we need to create our floating objects.
\section{Methods for 3D Printing}
\label{sec:3DPrinting}
\begin{figure}[tb]
\includegraphics[width=0.7\textwidth]{densityest.pdf}
\caption{Density of prints as a function of infill. Prints
have 30mm by 30mm cross section and
60mm length. The predicted values
without hole (dashed red) and with hole (solid green), graphed
along with the measured values without hole (red x) and with hole (green o). }
\label{densityest}
\end{figure}
\begin{figure}[tb]
\includegraphics[width=0.5\textwidth]{OpenSCAD.png}
\caption{This shows three cubes in OpenSCAD. The leftmost cube is at the ``true" center. The
other two cubes have a hole on the diagonal line of the cross section. All cubes are
shown with the longest direction vertical. This is the orientation in which we printed all cubes.}
\label{firstfig}
\end{figure}
In order to experiment with floating objects,
we have opted to experiment by designing and 3D printing them. This has
the advantage that we can easily create any object we can describe mathematically.
In addition, we can vary the density of our print by changing the infill density, a parameter
which is set at the time of printing. In this section, we describe the full workflow
needed -- and we have kept our presentation accessible to those with no 3D printing experience,
in the hopes of making it possible for anyone with an interest to create their own experiments.
The process consists of three steps: first, we need to design the objects in
design software. We then need to give the print specific parameters,
within a {\it slicer} software, where the choice of slicer software depends on the printer. Finally, we
print the objects on a 3D printer. We detail the workflow of these steps here.
\subsection{Design}
We have opted to design the objects in
Open SCAD, which is a free command
line computer aided design (CAD) system. Since we are interested in creating objects with a fixed cross section,
we are able to do so in just a few lines of code.
For convenience, we include syntax here so a reader could create their own. Copies of both
sample code and stl files are available from~\cite{GITHUB}.
To create a box with height 60 mm
and a 30 mm by 30 mm square cross section, we use the command
\begin{verbatim}
cube([30,30,60]);
\end{verbatim}
For our off-center weight experiments, we have placed a hole of radius 2.5 mm lengthwise
in the interior of the box. This is done by taking the set difference between
the box above and a cylinder. In order to create a cylinder of height 60 mm and
radius 2.5 mm, we use the command
\begin{verbatim}
cylinder (h = 60, r=2.5, center = true, $fn=100);
\end{verbatim}
The command {\tt center = true} centers the object so it is easier to position it with respect to the cube.
The command {\$fn=100} indicates that the circle should be estimated by a 100-sided polygon.
In order to have the cylindrical hole to be displaced from the center of the cube, we use the
{\tt translate} command.
Putting this all together to create a vertical hole that is displaced by 10 mm diagonally
from the center of the cube, we use the command sequence:
\begin{verbatim}
difference() {
cube([30,30,60], center =true);
translate([10,10,0])
cylinder (h = 80, r=2.5, center = true, $fn=100);
}
\end{verbatim}
While most of our floating objects were simple cubes with and without holes,
in Section~\ref{sec:polygoncode} we also considered more
complicated objects, where the cross section was given as a polygon in the form
$\{(x_1,y_1),(x_2,y_2),\dots,(x_n,y_n)\}$.
This includes for example the Mason M in Figs.~\ref{fig-intro_fig_MasonM} \&~\ref{masonfloat}.
In order to create objects with general polygonal cross sections in OpenSCAD,
we first create a polygon with the {\tt polygon} command, and then we
can turn this into a solid with fixed cross section using the
{\tt linear\_extrude} command. For example,
the following creates a cylinder of height 60mm with a cross section which is a
polygon determined by the ordered points $(0,0),(50,0),(60,40),(50,20)$.
\begin{verbatim}
points=[[0,0],[50,0],[60,40],[50,20]];
linear_extrude(height=60) polygon(points);
\end{verbatim}
\subsection{Slicing and Printing} We now describe the printing parameters set
within the slicing software.
In order to speed up printing and keep objects light, a 3D printed
object is usually partially hollow inside, printed with a lattice
pattern filling a fixed {\em infill fraction} of the object interior.
We denote this quantity by $I$. The fact that we can vary the infill fraction is quite
useful for us, since our goal is to see how the stable floating
orientations change with density. To be consistent, we did not vary
the {\em infill pattern}; we printed all of our prints with the {\em grid} infill pattern.
For further consistency, all of our floating objects were printed on a Makerbot Replicator
5th Generation printer and sliced in Makerbot Print proprietary software.
The mass of a print is most significantly affected by the infill fraction, but this
is not the only factor. In addition, an outer border layer of the print is printed at 100\% infill
for a fixed thickness on the sides, and a fixed thickness on the top and bottom.
For the most part, the default values for all thickness is
0.8 mm, the thickness of two {\em shells},
where a shell is $0.4$ mm, i.e. the diameter
of a standard extruder nozzle.
In order to calculate the predicted mass of a print, we need to know $\rho_{\rm PLA}$,
the density of PLA. Most sources state that this value is around 1.24 -- 1.25 g cm$^{-3}$, though~\cite{DAetal} used the value 1.17 g cm$^{-3}$. This number can vary quite significantly
depending on the brand of PLA, and therefore we decided to measure the value for our lab conditions.
In particular, we printed a number of squares that
were 30 mm by 30 mm by 1.6 mm. Since the
the top and bottom of a print are $0.8$ mm solid filament,
the print is guaranteed to be 100\% infill.
We printed fifteen test tiles, roughly half with Makerbot brand filament
and half with an off brand filament. Most of our test tiles were printed in part on
the same Makerbot printer and slicer as the floating objects, but we also printed
some on a Monoprice Mini, but we
found that the printer used was not an important factor for the mass of the test tiles, but the
brand was. For Makerbot brand filament and off-brand filament
respectively, our measured densities were $1.082 \pm 0.017$ and
$1.152\pm 0.010$ in g cm$^{-3}$. We have chosen the value $\rho_{PLA} = 1.15$ g cm$^{-3}$ for our
calculations.
Taking into account the infill percentage, shells, and measured value
for $\rho_{PLA}$, we expect the mass of our object to be given by
$\rho_{\rm PLA}$ times $V_{\rm ext}$, the volume of the outer layer plus
$\rho_{\rm PLA}$ times $I$, the infill fraction, times $V_{\rm int}$,
the volume of the interior of the print. If there is a nail embedded in
the hole, then we additionally have to include this value in our
calculation. We have described this calculation above in
\eqref{eq:effective_density_hole}. Figure~\ref{densityest} shows the predicted values
for prints without a nail hole (dashed red) with a nail hole (solid green).
We also show the measured values for the prints we have made without a nail hole
(red x) and with a nail hole (green o).
It is critical for the print to be uniform in the longest direction, as
our calculations consider this direction as completely invariant.
Therefore we printed with the long direction going from top to bottom so
that the infill is identical at each cross section.
Since our prints were printed on a Makerbot printer, we have used the
Makerbot proprietary slicing software Makerbot Print. However, there is
nothing about the process that could not be modified to other slicer
software.
The objects are ready to float!
\section{Experiments and Data Acquisition}
\label{sec:Experiments}
Once the objects were printed our objectives turned to floating these objects and obtaining measurements associated with the
stable floating orientations that we could compare with the theory.
After floating the objects in a test tank to observe qualitative behavior (e.g.~confirming the objects floated, identifying the number of stable orientations, etc.)
we turned to gathering quantitative information in the form of stable floating orientations.
We used a tank with clear flat sides and filled with tap water (see Figure~\ref{experimentalsetup}).
In order to measure angles associated with a stable floating orientation the object was carefully placed by itself in the tank and allowed to
come to rest. In order to ease the task of keeping the object in a position with its square cross section facing the side of the tank where the
camera was positioned we placed vertical guides a small distance away from the object. One of these guides was a ruler that we could later
use in the image analysis for calibration. A typical view of a floating object is shown in Figure~\ref{fig-typical_experiment}.
\begin{figure}[tb]
\includegraphics[width=0.8\textwidth]{IMG_8718.JPG}
\caption{Our experimental setup involves floating 3D printed objects mostly with
square cross sections. An occasional print had density ratio $R >1$ and did not float. }
\label{experimentalsetup}
\end{figure}
\begin{figure}[tb]
\includegraphics[width=0.8\textwidth]{IMG_8704.JPG}
\caption{A typical view of the experimental set up to measure angles associated with stable floating orientations. Vertical guides were
used as an aid to keep the object floating in the part of the tank on which the camera was focused. Care was taken to assure that
contact with underwater objects was avoided and any incidental contact of the object with the guides did not alter its floating orientation.
We also took care to prevent contact of object with the sides of the tank.}
\label{fig-typical_experiment}
\end{figure}
Digital images were obtained with a Canon EOS Rebel XSi used in manual focus mode. A remote shutter release was used to avoid bumping the camera,
which was mounted on a tripod sitting on the same table as the tank. Care was also taken to line up the camera at the water level and to have the object floating
in a direct line to the camera. A certain amount refraction could be observed especially in directions off the main viewing axis.
We used {\tt Matlab's} {\tt grabit.m} software to extract information from each image such as the one in Figure~\ref{fig-typical_experiment}.
We first calibrated the view by selecting points on the ruler in view on the right, taking care to use points above the waterline to avoid
distortion of the ruler by the water.
For a floating square we then identified 6 points in the image. Two of these points were chosen on the waterline relatively far from the
object on both sides so that the orientation of the waterline could be obtained. Four other points were chosen at the four corners of the square (clockwise starting from the top of the square).
With this information we obtained four vectors by taking differences of adjacent vertices and used $\cos \theta = a^T b / \| a \|_2 \|b \|_2$ where $b$ is a waterline vector and
$a$ is one of square-side vectors. In the example of Figure~\ref{fig-typical_experiment} one pair of sides (northwest and southeast) were used to identify an estimate for $\theta$ while
the other pair of sides (northeast and southwest) were used to estimate the complementary angle with respect to $\pi/2$.
In the case of the Mason M, we used a similar approach but chose four points along the bottom two `legs' of the M to make angle measurements.
For prints with holes, we covered the holes (void or filled with a nail) with waterproof tape to keep water out. In cases with no hole or when the hole was in the center of the object,
we used a very small amount of nail polish to mark one corner of the square. This allowed us to assess asymmetry of the object that was present either unplanned or by design.
For each object we first measured its mass (with hole either left as a void or filled with a nail) using a digital scale and from that obtained an effective density
according to $\rho_{\rm{obj}} = M_{\rm{obj}} / V_{\rm{obj}}$.
This corresponds to the material density for a uniform object or the effective uniform density for a non-uniform object.
The volume of the object $V_{\rm{obj}}$ was computed either from measurements of the dimension and known formulas (e.g. width times length times height for a rectangular box)
or using {\tt polyarea} in {\tt Matlab} (for more general cross sections) multiplied by the 3D print scaling.
\section{Computational Approaches}
\label{sec:compexp}
Various {\tt Matlab} codes were developed to compute results and analyze our floating shapes.
\subsection{Square Cross Sections}
Various {\tt Matlab} codes developed for the square cross sections have been posted in
a GitHub repository~\cite{GITHUB}.
These include
\begin{itemize}
\item {\tt SQUARE\_PE\_GxGy.m}: This code is based on the potential energy formulas outlined in the section on the square.
It generates for given values for the density ratio $R$ and the center of gravity $(G_x,G_y)$ the computed potential
energy landscape and includes options to plot the potential energy landscape and the square floating in a stable orientation. This code
was used to generate the theoretical predictions in Figures~\ref{fig-square_PE_and_SHAPE_10}, \ref{fig-square_PE_and_SHAPE_31n},
and~\ref{fig-square_PE_and_SHAPE_56}, for example.
\item {\tt SQUARE\_ANGLES\_GxGy\_R\_Looper.m}: This code is based on the formulas given in the section on the square and plots for a given
center of gravity $(G_x,G_y)$ and specified range $R \in [R_{min},R_{max}]$ the stable orientation angles. This code, for example,
was used to generate Figures~\ref{fig-THETA_VS_R_zeroG} and~\ref{fig-THETA_vs_R_32nail}.
\end{itemize}
\subsection{General Polygonal Cross Sections}\label{sec:polygoncode}
In the case of a long floating object of uniform density
with a general polygonal cross section,
though it is no longer possible to give as
detailed an analysis as in the case of a square, we are still able to apply Archimedes' Principle
and calculate the center of gravity, center of buoyancy, and the potential energy of a floating
configuration, as we describe below.
\subsubsection{Computation of Stable Floating Configurations}
When doing the calculations for a general polygon, we wrote a program that
takes two vectors with the $x$ and $y$ values of our polygon and a density
ratio and goes through the following algorithm. Firstly, it takes the shape
of the given polygon and calculates the center of gravity of the object,
assuming a uniform density throughout. Secondly, we identify the correct
placement of the waterline determined by Archimedes' Principle that establishes
the correct submerged area to total area ratio. This is done
by use of a bisection method where at an orientation we take the lowest
point of our object and create a waterline through it and make that our lower
bound. We then take the highest point of our object and make that our upper
bound. We then calculate the area ratio of each of our bounds and find
the midpoint of our upper and lower bounds and calculate the area ratio
for the waterline going through the midpoint. If the waterline through the
midpoint is above the correct placement, it becomes our new upper bound and
if it is below the correct placement, then it becomes the new lower bound.
We apply the bisection method until the correct waterline is found
for our original orientation. The correct placement of our waterline in the
case of uniform density is where the waterline splits the object into two
areas where the submerged area relative to the total area
is equal to the desired density ratio
(e.g. for an iceberg with uniform density, the line will be such that the
new submerged area created by the line relative to the area of the original polygon
will match the density ratio $0.8912$). Thirdly, we compute the center of
buoyancy of the object by applying the same method used for the center of
gravity except using the submerged area determined by the polygon and the
waterline. Finally, we calculate the potential energy function for our polygon at the
orientation and repeat the process for all angles.
The input to this code is a planar polygonal region, oriented counterclockwise and a density
ratio of the object relative to the water.
The output is a plot of the potential energy landscape with respect to the
angle. By default, the computation is performed for uniform density. However,
it is possible to compute this information for objects with non-uniform density
if one inputs the center of gravity.
\section{Results}
\label{sec:Results}
\subsection{Floating Squares: Symmetric Case}
Figure~\ref{fig-THETA_VS_R_zeroG} shows stable equilibrium angles as a function
of density ratio $R$ for objects with square cross sections and center of
gravity at the center of the square, $\vec{G}=(0,0)$. Various experimental
results are shown for 3D printed shapes with different effective densities.
These effective densities have been modified as described earlier by adjusting the infill as well as
printing objects with a hole at the center which we can leave as void space or
fill with a denser object, such as a nail.
As a visualization, we show several potential energy landscapes and selected
shape orientations predicted from the theory and observed experimentally.
Figure~\ref{fig-square_PE_and_SHAPE_10} shows the potential energy landscape for
$\vec{G}=(0,0)$ for a case with $R=0.23296$ which corresponds to a region in
parameter space where eight stable orientations exist. The eight orientations
in this case come in pairs, as indicated in the lower portions of the Figure~\ref{fig-square_PE_and_SHAPE_10}.
The eight experimentally-observed orientations are shown by the points at $R=0.23296$ in
Figure~\ref{fig-THETA_VS_R_zeroG}.\footnote{A keen eye will note both blue dots and red
dots in this sequence in Figure~\ref{fig-THETA_VS_R_zeroG}. These two different sets of angle estimates correspond to the two different
angle measurements described in the earlier section on Experiments and Data Aquisition.}
Figure~\ref{fig-square_PE_and_SHAPE_31n} shows the potential energy landscape
for $\vec{G}=(0,0)$ for a case with $R=0.4856$ which corresponds to a region in
parameter space where four stable orientations exist. These orientations
correspond to the object floating with the corner straight up.
Experimental measurements for these angles correspond the angle measurements shown at $R=0.4856$ in Figure~\ref{fig-THETA_VS_R_zeroG}.
Figure~\ref{fig-square_PE_and_SHAPE_56} shows the potential energy landscape for
$\vec{G}=(0,0)$ for a case with $R=0.9322$ which corresponds to a region in
parameter space where four stable orientations exist. These orientations
correspond to the object floating with the flat side of the square straight up.
Experimental measurements for these angles correspond the angle measurements shown at $R=0.9322$ in Figure~\ref{fig-THETA_VS_R_zeroG}.
A more thorough exploration of the parameter space particularly in the regions around $R=0.25$ and $R=0.75$ where eight stable orientations can be identified
has recently been done by Feigel \& Fuzailov
\cite{FF2021}.
\begin{figure}[h!]
\begin{center}
\includegraphics[width=4.0in, angle = 0]{exp_theory_Gzero_10_56_23n_31n_35_35n.pdf}
\end{center}
\caption{This plot shows stable floating orientations versus density ratio $R$ for $\vec{G}=(0,0)$. The marks show various measured equilibrium orientations for several
of our 3D printed objects.
}
\label{fig-THETA_VS_R_zeroG}
\end{figure}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=2.75in, angle = 0]{square_PE_10.pdf} \\
\includegraphics[width=2.0in, angle = 0]{square_10extra.pdf}
\includegraphics[width=2.0in, angle = 0]{square_10.pdf} \\
\includegraphics[width=1.8in, angle = 0]{IMG_8614_cropped.JPG} \hspace{0.2in}
\includegraphics[width=1.8in, angle = 0]{IMG_8613_cropped.JPG}
\vspace{0.15in}
\end{center}
\caption{The upper plot shows the potential energy landscape for the square with $\vec{G}=(0,0)$ and $R=0.23296$. There are eight stable equilibria.
Two stable floating configuration corresponding to the orientations closest to $\theta=0$ are shown in the plots in the second row. By symmetry these also match with the
other stable orientations on $\theta \in [-\pi,\pi]$. Corresponding experimental images are also shown in the bottom row. Measured angles for this case are
shown in Figure~\ref{fig-THETA_VS_R_zeroG}.}
\label{fig-square_PE_and_SHAPE_10}
\end{figure}
\begin{figure}[h!]
\begin{center}
\includegraphics[height=2.1in, angle = 0]{square_PE_31n.pdf}
\includegraphics[height=2.0in, angle = 0]{square_31n.pdf} \\
\includegraphics[width=1.5in, angle = 0]{IMG_8692_cropped.JPG}
\vspace{0.15in}
\end{center}
\caption{The upper left plot shows the potential energy landscape for the square with $\vec{G}=(0,0)$ and $R=0.4856$. There are four stable equilibria
corresponding to $\theta = \frac{\pi}{4} \pm \frac{\pi}{2} n$ for integer $n$. The upper right plot shows that the square floats with vertex pointing upwards.
These four stable orientations are also observed experimentally (one such orientation is shown in the image). Measured angles for this case are
shown in Figure~\ref{fig-THETA_VS_R_zeroG}.}
\label{fig-square_PE_and_SHAPE_31n}
\end{figure}
\begin{figure}[h!]
\begin{center}
\includegraphics[height=2.1in, angle = 0]{square_PE_56.pdf}
\includegraphics[height=2.0in, angle = 0]{square_56.pdf} \\
\includegraphics[width=1.5in, angle = 0]{IMG_8631_cropped.JPG}
\vspace{0.15in}
\end{center}
\caption{The upper left plot shows the potential energy landscape for the square with $\vec{G}=(0,0)$ and $R=0.9322$. There are four stable equilibria
corresponding to $\theta = 0 \pm \frac{\pi}{2} n$ for integer $n$. The upper right plot shows that the square floats deep in the water with flat side up.
These four stable orientations are also observed experimentally (one such orientation is shown in the image). Measured angles for this case are
shown in Figure~\ref{fig-THETA_VS_R_zeroG}.}
\label{fig-square_PE_and_SHAPE_56}
\end{figure}
\subsection{Floating Squares: Breaking Symmetry}
Figure~\ref{fig-PEplots31-32-33} show the potential energy landscape for three
different prints corresponding to square cross sections with nail-filled holes at {\bf A}: $(0,0)$ (upper left plot),
{\bf B:} $(0.3,0.3)$ (upper right plot), and {\bf C}: $(0.45,0.45)$ (lower plot).
Note that the coordinates for the holes are given in units of $s/2$ where $s$ is the length of
the side of the square. These three have density ratios
of $R=0.4856$ for Case {\bf A},
$R=0.4874$ for Case {\bf B},
and $R=0.4911$ for Case {\bf C}.
For Case {\bf A} with nail-filled hole at $(0,0)$ already discussed in
Figures~\ref{fig-THETA_VS_R_zeroG} and~\ref{fig-square_PE_and_SHAPE_31n},
four stable orientations, with a corner of the square pointing straight up, are predicted
theoretically and observed experimentally.
Experiments for Case {\bf B}, with a nail-filled hole at $(0.3,0.3)$,
are shown in Figure~\ref{fig-EXP_plots_32nail_cropped}.
In this case the center of gravity $\vec{G}$ is no longer at the center of the square and the
symmetry is broken. Despite this broken symmetry, four stable orientations are still observed experimentally
as shown in Figure~\ref{fig-EXP_plots_32nail_cropped}. Our
theory predicts that $(G_x,G_y) = (0.06789,0.06789)$ and the corresponding
potential energy plot is shown by the solid curve in the upper right plot of
Figure~\ref{fig-PEplots31-32-33}. There are only two stable
orientations predicted at this value of $\vec{G}$ and so our theory
does not match the experimental observations. However, two other curves are shown in the
upper right plot in Figure~\ref{fig-PEplots31-32-33} -- the dashed
curve has $(G_x,G_y) = (0.05,0.05)$ and the dash-dotted curve has $(G_x,G_y) =
(0.04,0.04)$. These curves with nearby values of $\vec{G}$ indicate that there are two other stable orientations nearby.
One explanation for the discrepancy between experiment and theory is that the center of gravity of our print is not exactly where
we predict it to be, perhaps due to uncertainties in the infill structure of the print.
Also, there is evidence of menisci at the solid--liquid--air contact line in Figure~\ref{fig-EXP_plots_32nail_cropped} suggesting that surface tension could provide
a large enough force to hold the print in an otherwise slightly unstable configuration.
For Case {\bf C}, with a nail-filled hole at $(0.45,0.45)$ and $(G_x,G_y)=(0.1017,0.1017)$ the potential energy landscape shown in the lower plot of Figure~\ref{fig-PEplots31-32-33}
indicates that only two stable equilibria exist. For this case both theory and experiment are
in agreement on the number of stable equilibria.
The experimental images for this case are not shown but are very similar to the upper left and lower left images of
Figure~\ref{fig-EXP_plots_32nail_cropped}. Corresponding stable orientations with the nail to the left or right as in the upper right and lower right
images of Figure~\ref{fig-EXP_plots_32nail_cropped} no longer exist for Case {\bf C}.
\begin{figure}[h!]
\begin{center}
\includegraphics[width=2.25in, angle = 0]{PEplot_31nail.pdf}
\includegraphics[width=2.25in, angle = 0]{PEplot_32nail_3curves.pdf} \\
\includegraphics[width=2.25in, angle = 0]{PEplot_33nail.pdf} \\
\end{center}
\caption{Potential energy plots for squares with nail-filled holes at {\bf A}: $(0,0)$ (upper left plot),
{\bf B:} $(0.3,0.3)$ (upper right plot), and {\bf C}: $(0.45,0.45)$ (lower plot).
The black curves (solid, dashed, or dash-dotted) show the potential energy function defined in equation~(\ref{eq:PE_formula_SQUARE}).
The open red circles indicate the theoretical local minima of the potential energy. The vertical red dashed lines show the angles at which experimentally-floating squares appear to be stable.
Case {\bf A} has four-fold symmetry and four stable orientations are predicted theoretically and observed experimentally (see
also Figure~\ref{fig-square_PE_and_SHAPE_31n}).
For Case {\bf B}, in which the symmetry is broken, our theory predicts only two stable orientations but we observe four experimentally (these four orientations are
shown in Figure~\ref{fig-EXP_plots_32nail_cropped}). The dashed and dash-dotted black curves in the upper right plot show two other potential energy landscapes
for nearby values of $\vec{G}$ (see text for details) indicating the presence of nearby stable states.
For Case {\bf C}, the square is farther from symmetric and both theory and experiment predict only two stable
orientations. We do not show experimental images for Case {\bf C}, but they are similar to the upper left and lower left images in Figure~\ref{fig-EXP_plots_32nail_cropped}.}
\label{fig-PEplots31-32-33}
\end{figure}
\begin{figure}[tb]
\includegraphics[width=0.4\textwidth]{IMG_8697_cropped.JPG}
\includegraphics[width=0.4\textwidth]{IMG_8698_cropped.JPG} \\
\includegraphics[width=0.4\textwidth]{IMG_8700_cropped.JPG}
\includegraphics[width=0.4\textwidth]{IMG_8701_cropped.JPG}
\caption{Four floating orientations for Case {\bf B} in Figure~\ref{fig-PEplots31-32-33} with a nail-filled hole at $(0.3,0.3)$ giving a nonzero center of gravity $\vec{G}$.
When the hole is {\em up} or {\em down} the stable
orientations correspond to corner straight up. When the hole is {\em left}
or {\em right} the top corner of the square is deflected counterclockwise or
clockwise, respectively.}
\label{fig-EXP_plots_32nail_cropped}
\end{figure}
As we have just observed, when $\vec{G} \neq 0$ the symmetry of the square is
broken and the predicted number of stable equilibria change. We display this in
Figure~\ref{fig-THETA_vs_R_32nail} for four cases $\vec{G} = (0.01,0.01)$,
$(0.02,0.02)$, $(0.04,0.04)$, and $(0.06789,0.06789)$. On the last two of these
we have plotted the four experimentally-observed stable orientation angles for the print denoted
Case {\bf B} with a nail-filled hole at $(0.3,0.3)$. As just discussed for Case {\bf B},
our theory predicts $\vec{G}=(0.06789,0.06789)$ and only two equilibrium values
of $\theta$ exist for this case as shown in the lower right plot of Figure~\ref{fig-THETA_vs_R_32nail}.
Reduction in the value of $\vec{G}$ to $(0.04,0.04)$, for example as indicated in the lower
left plot of Figure~\ref{fig-THETA_vs_R_32nail} shows four stable orientations at
the density ratio, $R=0.4874$, of Case {\bf B}. The upper two plots corresponding
to $\vec{G} = (0.01,0.01)$ and $(0.02,0.02)$. Especially in comparison to
the predicted stable angles shown in Figure~\ref{fig-THETA_VS_R_zeroG} these plots reveal
interesting bifurcation structure as the square symmetry is broken. Note that
in addition to floating squares with four or eight stable orientations, when the symmetry
is broken in this way (moving the center of gravity towards a corner) there are also
situations where either three or six stable orientations are predicted.
\begin{figure}[tb]
\includegraphics[width=0.45\textwidth]{THETA_vs_R_G0p01.pdf}
\includegraphics[width=0.45\textwidth]{THETA_vs_R_G0p02.pdf} \\
\includegraphics[width=0.45\textwidth]{THETA_vs_R_32nail_G0p04.pdf}
\includegraphics[width=0.45\textwidth]{THETA_vs_R_32nail_G0p06789.pdf} \\
\caption{Stable equilibrium angles versus density ratio $R$ for off-center squares. These plots have $\vec{G} = (0.01,0.01)$ (upper left), $(0.02,0.02)$ (upper right),
$(0.04,0.04)$ (lower left), and $(0.06789,0.06789)$ (lower right).
Experimentally-measured equilibrium angles for Case {\bf B} corresponding to $R=0.4874$,
described in the text and in Figures~\ref{fig-PEplots31-32-33} and~\ref{fig-EXP_plots_32nail_cropped},
are shown in both the lower left and lower right plots.
The full sequence of plots in this figure should be compared to the one for the symmetric square in Figure~\ref{fig-THETA_VS_R_zeroG} which has $\vec{G}=(0,0)$.}
\label{fig-THETA_vs_R_32nail}
\end{figure}
\subsection{Results for General Polygonal Cross Sections: The Mason M}
As an example of a floating shape with nontrivial cross sectional area we chose the Mason M.
This print was made based on a counter-clockwise-oriented set of points describing the shape of the M.
The cross-sectional area of the Mason M, $A_M$, was obtained using Matlab's {\tt
polyarea.m} applied to the point set described above. This value adjusted by a pixel
to millimeter (mm) conversion factor used to scale for 3D printing gave the
area. In particular, we found that $A_M = 126,550 \cdot (0.06)^2 \mbox{ mm}^2 = 455.58$
mm$^2$. The length of our Mason M was $70$ mm, giving a volume of $31,891$
mm$^{3}$. Since its mass was $27.92$g its corresponding effective density is
$\rho_{\rm eff} = 0.8755$ g cm$^{-3}$, which, in comparison to the density of water, is fairly close to the typical density ratio of an iceberg in a
polar sea.
Figure~\ref{mason} shows the potential energy landscape along with predicted stable configurations
for the Mason M.
The four stable orientations of the floating Mason M are shown in Figure~\ref{masonfloat}.
\begin{figure}[tb]
\includegraphics[width=0.8\textwidth]{MasonMPEPlot.pdf}
\caption{The Mason M potential energy plot where potential energy depends on the orientation angle of the waterline with respect to the 3D Mason M Print (zero angle corresponds
to an M in its usual upright orientation). Each vertical red dotted line corresponds to an experimentally found stable orientation. The local minima of the graph define stable orientations theoretically calculated using our code.
See also Figure~\ref{masonfloat}.}
\label{mason}
\end{figure}
\begin{figure}[tb]
\includegraphics[width=0.4\textwidth]{IMG_8668.JPG}
\includegraphics[width=0.4\textwidth]{IMG_8670.JPG} \\
\includegraphics[width=0.4\textwidth]{IMG_8671.JPG}
\includegraphics[width=0.4\textwidth]{IMG_8674.JPG}
\caption{The four stable orientations of the floating Mason M. The top left orientation matches up with the left most red dotted line in Figure~\ref{mason}. The top right orientation matches up with the second left-most red-dotted line in Figure~\ref{mason}. The bottom left orientation matches up with the second-right most red dotted line in Figure~\ref{mason}. The bottom right orientation matches up with the right-most red dotted line in Figure~\ref{mason}. }
\label{masonfloat}
\end{figure}
Figure~\ref{calving_MasonM} shows another variation of the full Mason M (with feathers) inspired by calving events that can happen with real icebergs.
These two plots show stable floating orientations, computed using the general polygonal code, where a {\em calving } event of shedding a feather results in a
new stable floating orientation (right plot). The red line in the plot on the right shows the pre-calving waterline position.
\begin{figure}[tb]
\includegraphics[width=0.4\textwidth]{335MasonThreePieceIceberg2.png}
\includegraphics[width=0.398\textwidth]{FeatherBreaksOffMasonM4.png}
\caption{The full Mason M (with feathers) and its floating orientation after a {\em calving} event where the upper feather is removed. The red line shows pre-calving waterline.}
\label{calving_MasonM}
\end{figure}
\section{Conclusion and Open Problems}\label{sec:conclusion}
\subsection{Motivation}
The equilibria of floating bodies have been studied since antiquity. Results on
their stability associated with metacentric concepts that date back to
eighteenth-century continue to play a major role in areas of naval architecture
and the study of icebergs.
The field has recently gained mathematical interest, especially on Ulam's
floating body problem. In problem 19 from the Scottish Book Ulam asks:
``Is a solid of uniform density which will float in water in every position a sphere?"
\cite{ScottishBook}.
Counterexamples to Ulam's problem in the plane for $\rho = 1/2$ go
back to Auerbach \cite{Auerbach1938}, and for $\rho \neq 1/2$ to Wegner who also
obtained results for non-convex bodies (holes in the body are allowed) in
\cite{Wegner2020}. Most recently Florentin {\it et al.} \cite{Florentin2022}
gave an affirmative answer for a class of origin symmetric n-dimensional convex
bodies with $\rho = 1/2$ relative to water. While counterexamples in the
plane exist, Ulam's floating body problem in higher dimensions is open to the best of our
knowledge.
\subsection{Limitations}
Using 3D printed models we were able to produce and collect experimental results
in agreement with the theory. Our results and experimentation process can be
reproduced readily, increasing access to 3D printers within educational
facilities gives way for students to experiment with stability and generate
different scenarios including Ulam's floating body problem.
The biggest challenge faced when producing our 3D samples is related to
density. To design infill patterns and infill densities using computer-aided
design(CAD), we produced samples to measure precision and increase the accuracy
of our experiment and identify possible sources of experimental errors. A
limitation in the 3D printing process is the difficulty in producing
low-density objects to desired accuracy. To maintain an even distribution of
mass, considerations must be taken with respect to the infill pattern. Zigzag,
grid, triangle, and concentric patterns are recommended when an even
distribution is desired. While Makerbot's cat infill model is not recommended
for experimenting with homogenous objects as it is asymmetric, it made for
interesting observations and ultimately motivated further investigation into
non-homogeneous objects, and it's also really cute.
Our work here has focused on effectively two-dimensional shapes.
Mathematical challenges for 3D floating shapes have been examined
(e.g.~Erd\"{o}s {\it et al.} \cite{Erdos_etal1992_part2} and Wegner \cite{Wegner2009}) and of course most realistic floating objects such as
icebergs are three dimensional. Approaches using 3D Print design are likely to
prove highly useful for future studies in these directions.
\section{Acknowledgements}
The authors would like to thank the Mason Experimental Geometry Lab (MEGL) and
Mason's Math Maker Lab, particularly Maker Lab staff Patrick Bishop and MEGL member Will Howard,
for supporting this project.
We would also like to thank
the Department of Physics at George Mason University of the use of a digital scale.
The research of E.S. was partially supported by the
Simons Foundation under Awards~636383.
\bibliographystyle{amsalpha}
\section*{This is an unnumbered first-level section head}
This is an example of an unnumbered first-level heading.
\specialsection*{This is a Special Section Head}
This is an example of a special section head%
\footnote{Here is an example of a footnote. Notice that this footnote
text is running on so that it can stand as an example of how a footnote
with separate paragraphs should be written.
\par
And here is the beginning of the second paragraph.}%
.
\section{This is a numbered first-level section head}
This is an example of a numbered first-level heading.
\subsection{This is a numbered second-level section head}
This is an example of a numbered second-level heading.
\subsection*{This is an unnumbered second-level section head}
This is an example of an unnumbered second-level heading.
\subsubsection{This is a numbered third-level section head}
This is an example of a numbered third-level heading.
\subsubsection*{This is an unnumbered third-level section head}
This is an example of an unnumbered third-level heading.
\begin{lemma}
Let $f, g\in A(X)$ and let $E$, $F$ be cozero
sets in $X$.
\begin{enumerate}
\item If $f$ is $E$-regular and $F\subseteq E$, then $f$ is $F$-regular.
\item If $f$ is $E$-regular and $F$-regular, then $f$ is $E\cup
F$-regular.
\item If $f(x)\ge c>0$ for all $x\in E$, then $f$ is $E$-regular.
\end{enumerate}
\end{lemma}
The following is an example of a proof.
\begin{proof} Set $j(\nu)=\max(I\backslash a(\nu))-1$. Then we have
\[
\sum_{i\notin a(\nu)}t_i\sim t_{j(\nu)+1}
=\prod^{j(\nu)}_{j=0}(t_{j+1}/t_j).
\]
Hence we have
\begin{equation}
\begin{split}
\prod_\nu\biggl(\sum_{i\notin
a(\nu)}t_i\biggr)^{\abs{a(\nu-1)}-\abs{a(\nu)}}
&\sim\prod_\nu\prod^{j(\nu)}_{j=0}
(t_{j+1}/t_j)^{\abs{a(\nu-1)}-\abs{a(\nu)}}\\
&=\prod_{j\ge 0}(t_{j+1}/t_j)^{
\sum_{j(\nu)\ge j}(\abs{a(\nu-1)}-\abs{a(\nu)})}.
\end{split}
\end{equation}
By definition, we have $a(\nu(j))\supset c(j)$. Hence, $\abs{c(j)}=n-j$
implies (5.4). If $c(j)\notin a$, $a(\nu(j))c(j)$ and hence
we have (5.5).
\end{proof}
\begin{quotation}
This is an example of an `extract'. The magnetization $M_0$ of the Ising
model is related to the local state probability $P(a):M_0=P(1)-P(-1)$.
The equivalences are shown in Table~\ref{eqtable}.
\end{quotation}
\begin{table}[ht]
\caption{}\label{eqtable}
\renewcommand\arraystretch{1.5}
\noindent\[
\begin{array}{|c|c|c|}
\hline
&{-\infty}&{+\infty}\\
\hline
{f_+(x,k)}&e^{\sqrt{-1}kx}+s_{12}(k)e^{-\sqrt{-1}kx}&s_{11}(k)e^
{\sqrt{-1}kx}\\
\hline
{f_-(x,k)}&s_{22}(k)e^{-\sqrt{-1}kx}&e^{-\sqrt{-1}kx}+s_{21}(k)e^{\sqrt
{-1}kx}\\
\hline
\end{array}
\]
\end{table}
\begin{definition}
This is an example of a `definition' element.
For $f\in A(X)$, we define
\begin{equation}
\mathcal{Z} (f)=\{E\in Z[X]: \text{$f$ is $E^c$-regular}\}.
\end{equation}
\end{definition}
\begin{remark}
This is an example of a `remark' element.
For $f\in A(X)$, we define
\begin{equation}
\mathcal{Z} (f)=\{E\in Z[X]: \text{$f$ is $E^c$-regular}\}.
\end{equation}
\end{remark}
\begin{example}
This is an example of an `example' element.
For $f\in A(X)$, we define
\begin{equation}
\mathcal{Z} (f)=\{E\in Z[X]: \text{$f$ is $E^c$-regular}\}.
\end{equation}
\end{example}
\begin{xca}
This is an example of the \texttt{xca} environment. This environment is
used for exercises which occur within a section.
\end{xca}
The following is an example of a numbered list.
\begin{enumerate}
\item First item.
In the case where in $G$ there is a sequence of subgroups
\[
G = G_0, G_1, G_2, \dots, G_k = e
\]
such that each is an invariant subgroup of $G_i$.
\item Second item.
Its action on an arbitrary element $X = \lambda^\alpha X_\alpha$ has the
form
\begin{equation}\label{eq:action}
[e^\alpha X_\alpha, X] = e^\alpha \lambda^\beta
[X_\alpha X_\beta] = e^\alpha c^\gamma_{\alpha \beta}
\lambda^\beta X_\gamma,
\end{equation}
\begin{enumerate}
\item First subitem.
\[
- 2\psi_2(e) = c_{\alpha \gamma}^\delta c_{\beta \delta}^\gamma
e^\alpha e^\beta.
\]
\item Second subitem.
\begin{enumerate}
\item First subsubitem.
In the case where in $G$ there is a sequence of subgroups
\[
G = G_0, G_1, G_2, \ldots, G_k = e
\]
such that each subgroup $G_{i+1}$ is an invariant subgroup of $G_i$ and
each quotient group $G_{i+1}/G_{i}$ is abelian, the group $G$ is called
\textit{solvable}.
\item Second subsubitem.
\end{enumerate}
\item Third subitem.
\end{enumerate}
\item Third item.
\end{enumerate}
Here is an example of a cite. See \cite{A}.
\begin{theorem}
This is an example of a theorem.
\end{theorem}
\begin{theorem}[Marcus Theorem]
This is an example of a theorem with a parenthetical note in the
heading.
\end{theorem}
\begin{figure}[tb]
\blankbox{.6\columnwidth}{5pc}
\caption{This is an example of a figure caption with text.}
\label{firstfig}
\end{figure}
\begin{figure}[tb]
\blankbox{.75\columnwidth}{3pc}
\caption{}\label{otherfig}
\end{figure}
\section{Some more list types}
This is an example of a bulleted list.
\begin{itemize}
\item $\mathcal{J}_g$ of dimension $3g-3$;
\item $\mathcal{E}^2_g=\{$Pryms of double covers of $C=\openbox$ with
normalization of $C$ hyperelliptic of genus $g-1\}$ of dimension $2g$;
\item $\mathcal{E}^2_{1,g-1}=\{$Pryms of double covers of
$C=\openbox^H_{P^1}$ with $H$ hyperelliptic of genus $g-2\}$ of
dimension $2g-1$;
\item $\mathcal{P}^2_{t,g-t}$ for $2\le t\le g/2=\{$Pryms of double
covers of $C=\openbox^{C'}_{C''}$ with $g(C')=t-1$ and $g(C'')=g-t-1\}$
of dimension $3g-4$.
\end{itemize}
This is an example of a `description' list.
\begin{description}
\item[Zero case] $\rho(\Phi) = \{0\}$.
\item[Rational case] $\rho(\Phi) \ne \{0\}$ and $\rho(\Phi)$ is
contained in a line through $0$ with rational slope.
\item[Irrational case] $\rho(\Phi) \ne \{0\}$ and $\rho(\Phi)$ is
contained in a line through $0$ with irrational slope.
\end{description}
\bibliographystyle{amsalpha}
\section{}
\subsection{}
\begin{theorem}[Optional addition to theorem head]
\end{theorem}
\begin{proof}[Optional replacement proof heading]
\end{proof}
\begin{figure}
\includegraphics{filename}
\caption{text of caption}
\label{}
\end{figure}
\begin{equation}
\end{equation}
\begin{equation*}
\end{equation*}
\begin{align}
& \\
&
\end{align}
| {
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} | 4,337 |
package TrinityCore.Exceptions;
public class DBUpdateInvalidFilenameException extends Exception {
/**
*
*/
private static final long serialVersionUID = 1L;
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 103 |
Lyft Reports 61% Decline in Q2 Revenues, Lyft Stock Slightly Down in Pre-Market
Aug 13 2020 · 11:57 UTC by Darya Rudz · 3 min read
Following the Q2 2020 earnings report, Lyft stock fell. On August 12, it closed 0.42% down, at $30.52 per share. In the pre-market trade today, it slightly declined.
San Francisco-based ridesharing company Lyft Inc (NASDAQ: LYFT) has announced its Q2 revenues. The company has underperformed some expectations because of challenging conditions in which Lyft had to perform but managed to beat on earnings thanks to cost-cutting efforts.
In the quarter that ended on June 30, Lyft generated $339.3 million in revenue compared to $867.3 million in Q2 2019. In other words, revenue fell 61% in the quarter. Meanwhile, Refinitiv Consensus analysts were predicting $337 million. Further, Lyft reported a $265.8 million adjusted net loss for Q2 2020. In contrast, a net loss in the second quarter of 2019 was $197.3 million. Lyft's earnings per share were negative $1.41, adjusted loss per share accounted for 86 cents versus an expected 99 cents.
Lyft Q2 Performance
Despite not the best Q2 performance, Lyft has pointed out that by the end of July, the company had managed to recover. According to Lyft, its monthly rides increased by 78% in July, as compared to April.
Lyft co-founder and CEO Logan Green said:
"While rideshare rides in the quarter were down significantly year-over-year, we are encouraged by the recovery trends we are beginning to see, with monthly rideshare rides in July up 78% compared to April. Lyft's second-quarter results reflect an operating environment that was not only challenging for our core ridesharing business, but also for our valued riders and drivers and the communities we serve. Our performance reinforces our belief that Lyft is taking on the critical work necessary to emerge from the crisis as a stronger company."
Besides, Lyft has boasted a significant growth in the number of active riders. In the second quarter of this year, active riders accounted for $8.7 million people. Revenue per active rider totaled $39.06.
Following the Q2 2020 earnings report, Lyft stock fell. On August 12, it closed 0.42% down, at $30.52 per share. In the pre-market trade today, it slightly declined. Lyft market cap is $9.4 billion, Lyft stock is 29.06% down year-to-date.
Lyft May Suspend Ride-Hailing Operations in California
Founded in 2012, Lyft is one of the largest transportation networks in the US and Canada. It offers ride-hailing, scooter- and bike-sharing, and vehicle renting.
At present, Lyft is facing multiple lawsuits in the US over alleged misclassification of drivers and wage theft. Previously, the company considered drivers strictly as independent contractors. Like others in the "gig economy," including Doordash and Instacart, Lyft has argued that workers want freedom and flexibility that they cannot get if they are classified as employees. However, California authorities are insisting on providing Lyft drivers with employment benefits. In response, Lyft is considering suspending its ride-hailing operations in California starting on August 21.
next Business News, Editor's Choice, Market News, News, Stocks
Author Darya Rudz
Darya is a crypto enthusiast who strongly believes in the future of blockchain. Being a hospitality professional, she is interested in finding the ways blockchain can change different industries and bring our life to a different level.
By Benjamin Godfrey December 7th, 2022
Business News, News, Technology News, Transportation News Uber and Motional Floats Autonomous Driving Taxis in Las Vegas
The partnership between Uber and Motional will not be the first time the latter startup has inked a similar partnership with other ride-hailing giants such as Lyft and Via Networks.
By Benjamin Godfrey August 5th, 2022
Business News, Market News, News, Stocks, Wall Street LYFT Shares Up 7.5% after Posting Better-than-Expected Q2 2022 Earnings
With the current outlook of the global industry, Lyft is giving a conservative projection for its future earnings as it is anticipating the full year of 2022 revenue growth that will be slower than the 36% achieved in 2021.
By Bhushan Akolkar December 7th, 2021
Blockchain News, Business News, Cryptocurrency news, IPO News, News OpenSea Faces Criticism Over Its Public Listing Plans, Former Lyft Executive Joins as CFO
The newly appointed OpenSea CFO Brian Roberts puts some light on the company's IPO plan. However, the OpenSea community feels dejected and abandoned as an IPO plan will most likely mean that there shall be no token airdrop. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 2,119 |
Experimenteel proza is de aanduiding voor een van traditioneel proza afwijkende vorm van literaire tekst door experimenten met vorm en inhoud. Het afwijken van conventies creëert vaak een vervreemdingseffect bij de lezer.
Een bekend Nederlands werk dat geldt als een vorm van experimenteel proza is Het boek Ik van Bert Schierbeek (1951). Ook staan er voorbeelden in de bundel Het mes in het beeld (1976), samengesteld door Jacq Vogelaar.
Een vorm van experimenteel proza in de Engelstalige literatuur is de cut-up-methode, een collage-vorm zoals bedacht door Brion Gysin en ontwikkeld door William S. Burroughs en Alexander Trocchi.
Zie ook
Vijftigers
Atonale poëzie
Experimentele muziek
Referentie
Literatuurwetenschap | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,520 |
Bicycle Accident with a Pot Hole? or Road Debris? Who Picks up the Medical Bills?
Road debris and poor road conditions can be the cause of accidents to both vehicles and cyclists. However, for a cyclist road debris poses a very dangerous threat. Often a motor vehicle can simply run over the road debris. Cyclists don't always get that choice. Riding in bike lanes, paths, or roadway shoulders can present an extra ordinary danger of bicycle accidents caused by road debris. It only takes a bit of glass, a stray piece of lumber or branches, an old piece of car tire lying in the way and the cyclist will need to react quickly. Jetting out into the lane of traffic to avoid road debris is certainly legal in Arizona and most states, however it isn't always a good idea or safe depending on the flow of traffic. 40% of all fatal bike accidents in 2012 were caused by rear end collisions. Its easy to see why cyclists are not always comfortable jetting out into traffic for fear of being hit by a car from behind.
Simply running over the road debris may be the only option cyclists practically posses. This can cause flat tires, bent wheels, or direct impact wrecks. Some debris can't be run over or even the classic "bunny hop" isn't always an option such as when you come across a shopping cart, or garbage can, etc. Either way there are some basic elements to prove in order to find compensation.
A bicycle accident caused by road debris can happen with anything in the road that is unsafe for a cyclist to come into direct impact with, not just a shopping cart. The tricky issue is finding someone who is responsible for leaving the debris in the road. Finding negligence is the key to finding any sort of financial recovery.
2) The breach of care caused the injured cyclist' damages.
In a bicycle accident case involving road hazards, the negligent party could be a government agency (i.e. responsible for maintaining the road), or a private party (such as a trucking company that is obligated to secure and transport cargo in a reasonably safe manner).
In such cases the government entity in question would likely be the state or municipal government with direct responsibility for vehicle or the road maintenance. However, claims of negligence against government entities can be made particularly difficult because the government may have sovereign immunity to lawsuits. Sovereign tort immunity can limit the government's liability considerably, and in many instances the government will still be entirely immune from suit.
Even if sovereign immunity is not applicable, there may still be special requirements for bringing a personal injury claim against a government entity. The rules in this regard also differ from state to state, but typically a "notice of claim" must be filed within a certain period of time after the accident. The applicable period of time is defined by statute, but is typically sixty days. If a notice of claim is not filed with the government agency within the prescribed period of time, the cyclist may have waived any right to bring a lawsuit.
Looking now at the private party example, when a bike accident is caused by a road hazard or road debris created by a private party's negligence (truck cargo falling onto a roadway or into the bike path), all of the facts must be closely examined in order to determine who is liable.
For example, if a vehicle is hauling cargo that would present a serious road hazard if it were to become unsecured and fall onto the highway/bike lane (i.e. pipes, landscaping limbs, construction materials, etc.), the driver of the transporting vehicle owes a duty to cyclists who also use the road to take reasonable precautions to keep the cargo secure. This would include driving in a manner that will keep the cargo from falling onto the roadway or bike lane.
It gets interesting if the same driver is an employee who is transporting cargo for an employer, (like a transportation company or retail distributor), then there is the issue of employer liability for the bicycle accident, under a legal doctrine known as respondeat superior. This rule of liability holds an employer liable for the harmful acts (torts) committed by employees who are acting within the normal course of employment. The reason this gets interesting is that while drivers may only carrier minimum insurance limits their employers may carry higher insurance limits making the cyclist's chances of recovery far greater. In order to be successful here the cyclist must show that the negligent tort was actually committed during the scope of employment, rather than during a purely personal activity on the part of the employee. | {
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<project xmlns="http://maven.apache.org/POM/4.0.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
xsi:schemaLocation="http://maven.apache.org/POM/4.0.0 http://maven.apache.org/xsd/maven-4.0.0.xsd">
<modelVersion>4.0.0</modelVersion>
<parent>
<groupId>net.bluemind</groupId>
<version>3.1.4-SNAPSHOT</version>
<artifactId>net.bluemind.bm-agent.handlers.server</artifactId>
</parent>
<artifactId>net.bluemind.bm-agent.server.ping</artifactId>
<packaging>eclipse-plugin</packaging>
</project>
| {
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{"url":"https:\/\/chat.stackexchange.com\/transcript\/71\/2021\/9\/20","text":"5:35 AM\nCan someone explain what does \"decay\" mean in nuclear physics ? I know about some nuclei decays into lighter nuclei to get stability but that lighter nuclei can be assumed to be a part of that decaying nuclei (together with some more nucleons) . So can we similarly say that an electron is a constituent of a W- boson because W- bosons decay into electrons and anti neutrino ?\n\n5:46 AM\nAlso do the quarks inside a proton experience coulomb force because of charges on them ?\n\n6:22 AM\n@Ankit Yes, the quarks do experience the Coulomb force, but this is relatively small compared to the strong force so it doesn't play a large role in reactions of hadrons.\n\n1 hour later\u2026\n7:30 AM\n@Ankit A nucleus is a composite object made up from protons and neutrons, and in a nuclear reaction like uranium fission all that happens is the neutrons and protons separate and rearrange into different nuclei (and free neutrons).\nBut a fundamental particle like a W boson is not composite i.e. it is not made up from other particles. Instead it can transform into other particles. This happens because quantum field theory allows fundamental particles to be created and destroyed.\nIn effect what happens in the W\u207b \u27f6 e\u03bd reaction is that the W particle is destroyed, and the energy released is used to create the electron and the antineutrino.\n\n8:08 AM\nevening @JohnRennie :)\n\n@antimony Hi :-)\n\n3 hours later\u2026\n10:58 AM\n0\n\nI just answered a question and edited it within a short period. But this is what I saw: What happened to the grace period of 5 minutes for editing a post?\n\n11:22 AM\n@DanielUnderwood FWIW, John Baez was doing a blog-like thing called This Week's Finds in Mathematical Physics on Usenet, before the WWW existed and before the term \"blog\" was invented. In a sense, he was one of the inventors of blogging.\n\n@PM2Ring blogging is not much new\nPeople have been doing regular articles for a long time\nSometimes in websites, sometimes in newspapers!\nalso in newsletters, for old nerds\n\n@Slereah Fair point. In that case Benjamin Franklin was a very early blogger. :)\n\nAlso Luther\nEarly blogging\n\nThe thing about blogs (and This Week's Finds) is combining personal \"what's happening in my life\" stuff with a technical column. That didn't really happen much before blogs.\nBen Franklin also extensively practiced sock-puppetry. He used a huge number of pseudonyms, to make it less obvious that a large number of the articles in his newspaper & almanac were written by him.\n\n11:43 AM\nGonzo journalism\n\n12:01 PM\n@PM2Ring yeah I actually saw some usenet stuff a while back (I think on his site) and went on a little dive\nit seems that unmoderated lists these days are \"interesting\" and I didn't see much activity on moderated lists unfortunately\nkind of makes me sad to miss the early eras of the internet before my time\n\nI didn't have an internet connection back then, but I was active on FidoNet. I think things were a little more civilised back then. We still needed moderators, but they rarely needed to do much. On FidoNet, the technology itself had a moderating effect: arguments are less likely to spiral into a frenzy of anger when there's a day between replies. ;)\nBut I wish I'd been on Usenet when Terry Pratchett was active there.\n\n2 hours later\u2026\n2:19 PM\nHey!\nSo there is this cactus diagram in Feynman diagrams\nWhat process does the loop show?\n\nit's a 3-loop correction to the free propagator\n\nNo I mean\nIs this correct??\n\n2:42 PM\nit's just a diagram\nhow could it be \"incorrect\"?\n\nCan someone help me out.. I have been taught that electric field and magnetic fields are like two different faces of same coin . They are just the same thing viewed from different perspective. But if that's true : Why does one form a closed loop while the other can't ?\n\n@ACuriousMind no I meant the momenta I have labelled\nBecause I don't understand whether it is a particle decaying into 3 particles or a particle decaying into two and annihiting which gives a 3rd\n@Ankit I don't know about faces but it's like one can't live without other\n\n@Korra it's a diagram that contributes to the propagator, there is no \"decay\" here\nyou have a particle entering from the left, doing stuff, then a particle just like it leaving at the right - why do you think this is a \"process\" at all?\n@Ankit the \"different faces of same coin\" means that if you accept special relativity + Coulomb's law, then you get the rest of electromagnetism automatically, i.e. you can't have electric fields without magnetic fields because what is a pure electric field in one frame is an electromagnetic field in another frame\n\n@ACuriousMind I don't understand. What do you mean by contributes to the propagator?\n\nit's not supposed to mean that electric and magnetic fields have no differences\n@Korra let's take a step back - why did you draw this diagram to begin with?\ni.e. what are you trying to compute?\n\n2:52 PM\n@ACuriousMind No I just found it in Schroeder and I was just wondering what it implied\n\nA diagram alone doesn't mean anything\nyou need to know at least what theory it has been drawn for (Standard Model? Scalar $\\phi^4$? Something else?) and what particles the lines represent to say anything\nbut generally, this is a diagram with one input and one output and both are the same - that's not a decay, it's just one way for a particle to \"do nothing\" and just propagate.\n\n@ACuriousMind phi 4\n@ACuriousMind so it's not an annihilation process?\n\n@ACuriousMind shape of the line tells you the theory, obviously\nis it wavy or curly???\n\n@Korra why would it be?\nAn \"annihilation\" for me involves particles going into the process that don't come out again, and in particular usually a particle and its antiparticle\n\n2 hours later\u2026\n4:52 PM\nwhat are the ways to interpret integrating the solution to a D.E.?\nsolution of D.E. being an integral curve\nfinding the area under the integral curve\n\n5:04 PM\nIt depends on what ur integrating with respect to @geocalc33\n\nHi everyone! Does anyone study physics as if it is their hobby? Not some student in a university to score marks or is working professionally\n\n@cOnnectOrTR12 there aren't actually many h bar regulars who are currently physics students\/researchers\n\n5:24 PM\nI meant in a general sense. Does somebody study because they love it.\n\n@ACuriousMind so complete electric fields in one frame becomes magnetic field in the other . But shouldn't both have the same properties then ?\n\n@Ankit no, it's not that the same vector field that's electric in one frame just becomes the magnetic field in another frame\nyou have to actually do the Lorentz transformation on the field\n\nHello. If we have a system, and we consturct the lagrange function of this system and then insert our Additional condiitons into the lagrange Function.. For example then we will recieve a lagrange function that is only dependend on two variables. Do we say then that the system have only two degrees of freedom of motion?\nWhat if the lagrangian we constructed without inserting the additional conditions contain three variables (the conditions for example eliminate one) do we say the system has three degrees of freedom?\n\n@ACuriousMind okay.. so does that transformation account for those differences in their properties ?\n\nAn example: $L = \\frac{1}{2}m(\\dot{x}^2 + \\dot{y}^2)$ is a free particle Lagrangian with two degrees of freedom. If we want to constrain it to the surface of a circle we can add a constraint using a Lagrange multiplier, by adding $\\frac{1}{2}\\lambda(x^2 + y^2 - R^2)$ to the Lagrangian, if we now choose polar coordinates the constraint vanishes and there is only one degree of freedom, $\\theta$\n\n5:35 PM\n@ACuriousMind can you tell me how crucial are the numericals in understanding some concept in physics?\n\n@geocalc33 finding the curve whose which satisfies the differential equation which says it and it's derivatives are related in some way\n\nIn addition to the question ia sked, i am also intrigued to know, if the time is explicit in the lagrange function thus L(x1....xi,t) do we say that the freedom degrees are in this case i + 1 ? or do we not consider it ?\n\nTime is treated as a parameter that the functions $x_1,x_2,...$ depend on as explicit functions via $x_1 = x_1(t)$, if $L$ depends explicitly on $t$ we don't interpret it as an additional variable we treat it as a parameter\nIn special relativity that changes but we then constrain it to be related to the other coordinates, but we can also treat it as a parameter that the others depend on if we want to\n\nis the Big Rip model compatible with multiverse theory?\n\n@bolbteppa Can you check my previous question on the degrees of freedom.\n\n5:44 PM\nI just commented on the degrees of freedom in my post before with an example of a free particle vs. one constrained to a circle and losing a degree of freedom in doing this\n\nIf one universe exponentially gets larger how could it still be separate from other universes?\n\nthere is no \"multiverse theory\"\nyou're gonna have to ask about a specific theory\n\n@bolbteppa My apologies i did not notice.\nSo What i took from that , is yes, the number of variables in the lagrangian are my degrees of freedom. And no, time is not considered as a degree of a freedom, even if it explicitly appears as t in the lagrangian\n@bolbteppa what if i have a lagrangian dependent on for example $L( \\phi, \\theta)$ then i would say my lagrangian depends on phi and theta.. which are two degrees of freedom, however if insert a condition for example $\\phi = \\omega * t$ where as $\\omega = const$ then i will now have one degree of freedom. Did i understand this correctly.\n\nThe time point is right, but the degrees of freedom point is not, in the example above I had two variables $(x,y)$ but we seen when we went to polar coordinates that only one variable really exists, $\\theta$ (because $R$ is constant, in general it would be a variable, e.g. if you change the free particle Lagrangian I started with to polar coordinates, but when I add the constraint one disappears)\nYes\n\nBut why does changing the coordinate system change the degrees of freedom if we do not add constraints? or is that not what you meant?\n\n5:50 PM\n@Slereah can you tell?\n\nBecause if you did not add the conidition you would still get two... nvm i got it i understand now.. Thanks @bolbteppa\n\n@cOnnectOrTR12 i think you can understand most of physics through description, but if you want to test theory you need to understand how to do math :P\n\nIt doesn't, when I add the constraint $\\frac{\\lambda}{2}(x^2+y^2-R^2)$, $\\lambda$ is a new 'variable', the 'equation of motion' for $\\lambda$ just enforces $x^2+y^2-R^2 = 0$ so I can then solve this for $y = \\sqrt{R^2-x^2}$ and re-insert this into the original Cartesian coordinate Lagrangian and see it's all in terms of $x$. But you need to examine it and realize this, naively at the beginning it looks like $x$ and $y$ are two variables\n\nYup i got what you mean.\n\nThis obviously gets very tricky quick and you need to be careful with 'holonomic constraints' vs other types etc\n\n5:54 PM\n@RonaldVilliers what theory?\n\nDo people ever use non-holonomic constraints\nThey seem very reasonable but I've never seen them in use\nProbably too practical a tool for me to read\n\nI'm just not sure, I keep meaning to get into this but I'm just hoping to come across some super easy explanation that makes it all trivial :(\n\nscientists in movies don't do enough bibliography\nThat's like half the job\n\n6:43 PM\n@RonaldVilliers I'm integrating under a real analytic integral curve w.r.t. the independent var.\nIf i integrate each integral curve like this, im mapping each integral curve to a real scalar\n\n6:59 PM\n@gls got any suggestions for quantum simulators? there's the list on Quantiki here but it's a bit overwhelming\n(also Quirk seems neat)\n\n7:20 PM\n@Semiclassical it is, isn't it? The main developer is active on qc.SE btw, if you have any questions in that direction\n@Semiclassical you've gotta be a bit more specific here. To do what exactly?\npersonally, I've never really found the need to use any \"dedicated quantum simulator\". Most of the time \"quantum simulation\" amounts to matrix multiplication anyway (at least, what I believe you mean with \"quantum simulation\" here), or solving some first-order differential equation if you work with dynamical systems. Not that there aren't cases in which this isn't trivial but... working in python, I found qutip to have pretty much all I needed\n\n7:41 PM\n@geocalc33 In the example of it being a force field that your D.E describes, your integral curve is the force at every point on the curve, and your integral w.r.t time of that integral curve gives the \"impulse\". If you integrate w.r.t its position along some axis, you get what is called \"work\" done by the curve along that axis.\nI might be wrong but I believe that's what the usage is in physics.\n\n@glS yeah, that was a bit too broad. i'm looking at student resources\/tools for a QC course\nfor creating reasonably simple circuits Quirk seems top-notch\nesp. for the kinds of problems one sees in, say, Nielsen and Chuang\n\n7:57 PM\nDo you guys know when you have a linear differential equation with constant coefficitions and you solve it with teh exponential function $f(x) = e^(lambda*x)$\nDoes this also work if the coeeficients are not constant?\n\nit doesn't, no\nyou can generalize the method, but it won't be as simple as that\n\nhow can i solve an equation of following form then\n$\\ddot x + c(t) x = 0$\n\noh, second order\nyeah, that's gonna be unpleasant\nfor instance, mathematica refuses to solve it\n\nNice\n\n(for arbitrary c)\n\n8:01 PM\nwhat if i knew exactly what c is\nthe actual function that i have is something of this sort:\n$\\ddot {\\theta} + K* sin( \\omega *t) \\theta =0$\n\nthen maaaaybe. for instance, when $c=t$ you get Airy functions: wolframalpha.com\/input\/?i=dsolve+x%27%27%2Bt+x%3D0\nhmmmm\n\n@Semiclassical to play around for that, yes, definitely. You can also have fun building the tools you need yourself, which might be also even more fun\/better for learning (assuming you have the time). I always found Mathematica to be best tool for learning and playing around like that\n\ni'm so spoiled by Mathematica access\nanalytically, anyways\nMathematica's symbolic solution doesn't seem any better\n\nCan i write you in private chat in german\n\ni'd rather not. there's really not much more for me to say\n\n8:05 PM\nWell alrighty then.lol\n\n@Semiclassical with MMA it's not too hard to do \"circuit builders\" that you can dynamically interact with, e.g. i.stack.imgur.com\/osjEV.gif\n\noh, that's cute\nmy main use of MMA for quantum has simply been to rely on KroneckerProduct and PauliMatrix :P\nand do linear algebra\n\n@Semiclassical what do you mean?\n\nas in, to compute unitary matrices\nand do matrix multiplication\nnothing sophisticated\nbut matrix multiplication doesn't need to be sophisticated\n\n@Semiclassical I mean... almost all calculations in (this brand of) QM boil down to some form of that anyway. Being able to do more is cool in MMA mostly because it allows to visualise things in dynamical and flexible ways\n\n8:12 PM\nyeah\notherwise MMA is the proverbial crane crushing a fly\n\nyou can find the code for the above on GitHub here by the way. I haven't touched it in a fairly long time though, so I can't promise it even works anymore. I just did that to play around when I wanted to visualise a few things about gates etc\n\nneat\nyeah, that's pretty short\n\n2 hours later\u2026\n9:59 PM\nIf a given transformation produces a lagrangiagian of the form $L_{new}= L_{old} + \\dot r * r$ then it is not symmetrical transformation? ( Because as far as i know, the lagrangian needs to differ by a total time derivation, and i dont think there is a function F which produces the given right term by a derivation, .. right?\nWell.. maybe if we set $F = r^2\/2$.. does that work and then its okay to do this transformation? ... what about one where we get instead of $\\dot r * r$ we get $\\dot r *t$ ?\n\n$\\dot{r}r$ doesn't look like a total derivative\nso probably not\n\nwhat about $d\/dt F$ $F= r^2 \/ 2$ this produces $\\dot r *r$!\n\nTrue\nThen that does sound like it would be a symmetry!\n\nWhat about the second example i gave, where we have instead $\\dot r * t$ i can not seem to integrate this function.. even with parts","date":"2021-10-16 13:36:19","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7107136845588684, \"perplexity\": 859.9906372136106}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-43\/segments\/1634323584567.81\/warc\/CC-MAIN-20211016105157-20211016135157-00531.warc.gz\"}"} | null | null |
The Putative RNA-Dependent RNA Polymerase RDR6 Acts Synergistically with ASYMMETRIC LEAVES1 and 2 to Repress BREVIPEDICELLUS and MicroRNA165/166 in Arabidopsis Leaf Development
Hong Li, Lin Xu, Hua Wang, Zheng Yuan, Xiaofeng Cao, Zhongnan Yang, Dabing Zhang, Yuquan Xu, Hai Huang
Hong Li
National Laboratory of Plant Molecular Genetics, Shanghai Institute of Plant Physiology and Ecology, Shanghai Institute for Biological Sciences, Graduate School of Chinese Academy of Sciences, Shanghai 200032, China
Lin Xu
National Laboratory of Plant Molecular Genetics, Shanghai Institute of Plant Physiology and Ecology, Shanghai Institute for Biological Sciences, Graduate School of Chinese Academy of Sciences, Shanghai 200032, ChinaCollege of Life Science and Biotechnology, Shanghai Jiao Tong University, Shanghai 200030, China
Zheng Yuan
Xiaofeng Cao
Institute of Genetics and Developmental Biology, Chinese Academy of Sciences, Beijing 100101, China
Zhongnan Yang
College of Life and Environment Sciences, Shanghai Normal University, Shanghai 200234, China
Dabing Zhang
College of Life Science and Biotechnology, Shanghai Jiao Tong University, Shanghai 200030, China
Yuquan Xu
Hai Huang
Published August 2005. DOI: https://doi.org/10.1105/tpc.105.033449
The Arabidopsis thaliana ASYMMETRIC LEAVES1 (AS1) and AS2 genes are important for repressing class I KNOTTED1-like homeobox (KNOX) genes and specifying leaf adaxial identity in leaf development. RNA-dependent RNA polymerases (RdRPs) are critical for posttranscriptional and transcriptional gene silencing in eukaryotes; however, very little is known about their functions in plant development. Here, we show that the Arabidopsis RDR6 gene (also called SDE1 and SGS2) that encodes a putative RdRP, together with AS1 and AS2, regulates leaf development. rdr6 single mutant plants displayed only minor phenotypes, whereas rdr6 as1 and rdr6 as2 double mutants showed dramatically enhanced as1 and as2 phenotypes, with severe defects in the leaf adaxial-abaxial polarity and vascular development. In addition, the double mutant plants produced more lobed leaves than the as1 and as2 single mutants and showed leaf-like structures associated on a proportion of leaf blades. The abnormal leaf morphology of the double mutants was accompanied by an extended ectopic expression of a class I KNOX gene BREVIPEDICELLUS (BP) and high levels of microRNA165/166 that may lead to mRNA degradation of genes in the class III HD-ZIP family. Taken together, our data suggest that the Arabidopsis RDR6-associated epigenetic pathway and the AS1-AS2 pathway synergistically repress BP and MIR165/166 for proper plant development.
In higher plants, leaf primordia initiate from flanks of the shoot apical meristem (SAM) (Bowman et al., 2002). The initiation of leaf primordia coincides with the downregulation of the expression of several class I KNOTTED1-like homeobox (KNOX) genes (Byrne et al., 2000; Ori et al., 2000; Semiarti et al., 2001), which are required for the maintenance and growth of the SAM (Long et al., 1996; Bowman and Eshed, 2000; Volbrecht et al., 2000). Leaf development also requires the establishment of proximodistal, mediolateral, and adaxial-abaxial polarities (Hudson, 2000). The adaxial-abaxial polarity refers to the two opposing faces of a leaf blade, which have distinct cell types that have different biological functions (McConnell et al., 2001). It was reported that leaf primordia isolated from the SAM at the anlage stage could only form a small radial leaf without adaxial differentiation (Sussex, 1954, 1955). This result indicates that the establishment of the adaxial-abaxial axis is critical for subsequent asymmetric leaf development (Bowman et al., 2002).
In Arabidopsis thaliana, several genes have been identified for the formation of the adaxial-abaxial polarity, including class III HD-ZIP genes for promoting adaxial fate (McConnell and Barton, 1998; McConnell et al., 2001; Emery et al., 2003) and members of the YABBY and KANADI families for specifying leaf abaxial identity (Chen et al., 1999; Sawa et al., 1999; Siegfried et al., 1999; Eshed et al., 2001; Kerstetter et al., 2001). In addition, the ASYMMETRIC LEAVES1 (AS1) and AS2 genes are also responsible for establishing leaf polarity by specifying leaf adaxial identity (Xu et al., 2002, 2003). AS1 encodes a protein that contains an R2-R3 MYB domain (Byrne et al., 2000; Sun et al., 2002), suggesting that it may bind to DNA. AS2 encodes a plant-specific protein that can associate with AS1 (Iwakawa et al., 2002; Xu et al., 2002, 2003). These two genes have demonstrated roles in repressing class I KNOX genes (Byrne et al., 2000; Ori et al., 2000; Semiarti et al., 2001) and promoting leaf vein development (Semiarti et al., 2001; Sun et al., 2002). Recent studies have also revealed that in early leaf development, AS1 and AS2 are required for a proper auxin distribution and response (Zgurski et al., 2005). Additionally, AS1 and AS2 positively regulate the PHABULOSA (PHB) gene, a class III HD-ZIP family member (Lin et al., 2003; Xu et al., 2003). Although AS1 and AS2 functions have been studied extensively, it is unclear whether other genes function together with AS1 and AS2 for leaf patterning. If these genes exist, it would therefore be important to determine what roles they play in leaf development.
In both plants and animals, double-stranded RNA (dsRNA) that is processed to short RNAs (∼21 to 24 nucleotides) can trigger two coupled types of RNA-mediated gene silencing events: posttranscriptional gene silencing (PTGS) and transcriptional gene silencing (TGS) (Cogoni and Macino, 1999; Lipardi et al., 2001; Matzke et al., 2001; Nishikura, 2001; Sijen et al., 2001; Ahlquist, 2002; Aufsatz et al., 2002). Members of the RNA-dependent RNA polymerase (RdRP) family use small RNA molecules to prime dsRNA synthesis (Lipardi et al., 2001; Sijen et al., 2001) and have been defined as one of the important factors in PTGS and TGS. In recent years, genes encoding putative RdRPs have been isolated and characterized from several species, including tomato (Lycopersicon esculentum), Neurospora crassa, Caenorhabditis elegans, and Arabidopsis (Schiebel et al., 1993, 1998; Cogoni and Macino, 1999; Dalmay et al., 2000; Mourrain et al., 2000; Smardon et al., 2000). In Arabidopsis, mutations in the RDR6 gene, which encodes a putative RdRP protein, causes defects in PTGS (Dalmay et al., 2000; Mourrain et al., 2000). In addition, a more recent study revealed that the RDR6 gene is required for vegetative phase change (Peragine et al., 2004). However, because rdr6 mutant plants do not show severe morphology defects, the role of RdRPs in leaf pattern specification is largely unknown.
MicroRNAs (miRNAs) are endogenous ∼20- to 22-nucleotide RNAs that contribute important functions in animal and plant development by causing mRNA cleavage or protein translational repression (Bartel, 2004). The Arabidopsis miRNAs miR165 and miR166 differ by only one nucleotide and were found to share perfect complementarity with the regions of class III HD-ZIP genes encoding the START domain (Rhoades et al., 2002). A single nucleotide change within the START-encoding regions of some of these genes resulted in dominant mutations that caused aberrant adaxial-abaxial polarity and abnormal venation in leaves (McConnell et al., 2001; Emery et al., 2003; Zhong and Ye, 2004). Recent in vitro and in vivo experiments have shown that miR165/166 can indeed cause degradation of mRNAs of several HD-ZIP genes (Emery et al., 2003; Tang et al., 2003; Mallory et al., 2004; Zhong and Ye, 2004). Studies investigating the mechanisms of miRNA actions raise an important question: what gene(s) or pathway(s) regulates the level of miRNA gene expression in developmental processes? It was reported that the Arabidopsis gene ARGONAUTE1 (AGO1) both acts in and is regulated by the miRNA pathway (Kidner and Martienssen, 2004; Vaucheret et al., 2004). However, it is not clear whether other factors are also involved in the regulation of miRNA expression.
In this study, we describe the characterization of rdr6 single mutants and rdr6 as2 double mutants, which suggest a novel function of the previously reported RDR6 gene in leaf development. We report that the ectopic expression of a class I KNOX gene BREVIPEDICELLUS (BP) was extended and that miR165/166 levels were dramatically increased in the rdr6 as2 mutant leaves. We propose that the AS1-AS2 pathway and the RDR6-associated epigenetic pathway are both required for repression of BP and MIR165/166 in normal leaf development.
RDR6 Is Involved in Leaf Development
To identify additional genes functioning in the AS1-AS2 regulatory network, we conducted a genetic screen for enhancers and suppressors of the as2-101 mutant and identified two mutants showing similar enhanced as2 phenotypes. Genetic experiments revealed that these two mutants were allelic, and the single as2 enhancer mutant had nearly normal phenotypes (see Methods). We mapped this enhancer mutation to a 21-kb region on chromosome 3 (BAC T9C5), which contains seven predicted genes (Figure 1A). Sequencing of these candidate genes revealed that both of the as2 enhancer alleles carried mutations that introduce stop codons into the coding sequence of the RDR6, SDE1, or SGS2 genes (in this study, we refer to this gene as RDR6 for convenience), which encodes a previously reported RdRP protein (Figure 1B). Complementary experiments confirmed that mutations in the RDR6 gene caused an enhancement of as2 phenotypes (see Methods); we therefore renamed the as2 enhancer alleles as rdr6-3 as2-101 and rdr6-4 as2-101, respectively.
Molecular Identification of the AS2 ENHANCER1 Gene.
(A) Fine-structure mapping. Seven putative genes (denoted by arrows) were identified between markers T9C5-5 and T9C5-6. The ScaI-XbaI genomic fragment containing the RDR6 gene was used in the complementation experiment.
(B) The RDR6 gene structure and positions of the nucleotide changes in rdr6-3, rdr6-4, and sde1-1 mutants. The yellow box indicates a region encoding the RNA recognition motif, and the red box represents a region encoding the RdRP domain (http://www.ncbi.nlm.nih.gov/BLAST).
(C) RT-PCR shows that RDR6 was expressed in all plant tissues examined.
(D) RDR6 expression was not affected by as1 and as2 mutations, and rdr6 mutation did not alter expression of the AS1 or AS2 genes. The numbers in (C) and (D) indicate the relative abundance of gene transcripts, which were calculated using the band intensity of the first lane as 1.0. as1-101, as2-101, and rdr6-3 are in the Ler genetic background.
RDR6 expression was found in all plant tissues examined (Figure 1C). The molecular genetics relationship between RDR6 and AS1/AS2 suggests that these genes may influence each other's expression. Therefore, we analyzed RDR6 expression in the as1-101 and as2-101 backgrounds and AS1 and AS2 expression in the rdr6-3 background (Figure 1D). The RT-PCR data revealed no obvious changes between the wild type and mutants, suggesting that direct transcriptional regulations do not occur between the RDR6 and AS1 and AS2 genes. These results indicate that the RDR6 gene may act separately from the AS1/AS2 pathway in the regulation of plant development.
Phenotypes of rdr6 Single Mutants and rdr6 as2 Double Mutants
To further understand the role of RDR6 in leaf development, we analyzed leaf phenotypes of rdr6-3 as2-101 plants. Compared with wild-type (Figure 2A) and as2-101 (Figure 2B) plants, rdr6-3 as2-101 (Figure 2C) and rdr6-4 as2-101 (Figure 2D) displayed severe phenotypes, with anthocyanin in some early-appearing rosette leaves. In addition, rdr6-3 as1-101 and rdr6-3 as2-101 double mutants showed similar phenotypes (Figure 2E). Because AS1 and AS2 can form protein complexes and may regulate the same downstream targets, the similar phenotypes in rdr6-3 as1-101 and rdr6-3 as2-101 suggest that the RDR6 gene or its product interacts with the AS1-AS2 pathway in leaf development. Because rdr6-3 as2-101 and rdr6-4 as2-101 exhibited similar overall phenotypes, we focused our additional phenotypic characterizations mainly on the rdr6-3 and rdr6-3 as2-101 mutants.
Phenotypes of Single and Double Mutants.
(A) to (D) Morphological observations of wild-type and mutant seedlings. Wild-type Ler (A), as2-101 (B), rdr6-3 as2-101 (C), and rdr6-4 as2-101 (D).
(E) Statures of wild-type, as1-101, as2-101, rdr6-3, rdr6-3 as1-101, and rdr6-3 as2-101 plants at the early flowering stage. Note that rdr6-3 as1-101 and rdr6-3 as2-101 plants display similar phenotypes.
(F) rdr6-3 plants display distorted young rosette leaves (arrowhead).
(G) and (H) rdr6-3 (Ler ecotype) plants show some minor phenotypic changes.
(G) An additional inflorescence appears at the proximal end of some secondary inflorescences (arrowhead).
(H) Some cauline leaves are replaced by a filamentous structure (arrowhead).
(I) and (J) Phenotypic alterations of the previously reported sde1-1 mutant (Columbia-24 [Col-24] ecotype).
(I) An additional small inflorescence (arrowhead) that is similar to that of rdr6-3 in (G).
(J) A filamentous structure (arrowhead) appeared at the position where a cauline leaf should grow in the wild-type plants.
(K) A diagram summarizing the phenotypic changes observed in the rdr6-3 mutant. The rdr6-3 mutant shows a slightly reduced plant stature. Arrowheads indicate the following abnormalities: (1) additional inflorescence, (2) without cauline leaves or with a small filamentous structure, and (3) with some class IV inflorescences that were not seen in wild-type plants. Red circles indicate inflorescences.
All mutant plants except sde1 (Dalmay et al., 2000) in (I) and (J) are in the Ler genetic background. Bars = 5 mm in (A) to (J).
The rdr6-3 plants displayed only minor phenotypes, including a slightly reduced plant stature with slightly distorted young rosette leaves (Figure 2F) and an increased number of secondary inflorescences (8.9 ± 1.0 in the rdr6-3 mutant versus 5.9 ± 1.0 in the wild type, n = 20, P < 0.01). In addition, some rdr6-3 plants produced an extra small inflorescence at the base of some secondary inflorescences (Figure 2G; 34 small inflorescences/120 rdr6-3 plants; none were found in 100 wild-type plants). Furthermore, many rdr6-3 plants produced secondary inflorescences without a cauline leaf or with a variously sized filamentous structure at their proximal ends (Figure 2H; 118/242 rdr6-3 plants; 3/100 wild-type plants).
Analysis of the previously isolated sde1-1 single mutant (allelic to rdr6) revealed that although sde1-1 and rdr6-3 are from different ecotypes, they produce similar morphological abnormalities (Figures 2I and 2J; for comparison, see Figures 2G and 2H). In addition, plants with phenotypes similar to those of rdr6-3 as2-101 and rdr6-4 as2-101 mutant plants (Figures 2C and 2D) were observed in the F2 progeny of a cross between sde1-1 and as2-101 mutants (data not shown). Phenotypic analyses of the rdr6 mutant plants indicate that although rdr6 mutant phenotypes were relatively mild, the RDR6 gene has multiple functions in development (Figure 2K).
rdr6 as2 Exhibits Extended Ectopic Expression of BP
AS1 and AS2 repress the KNOX genes during leaf development, and leaves of some as1 and as2 alleles are serrated or even lobed because of the ectopic expressions of KNOX genes (Ori et al., 2000; Semiarti et al., 2001). Because the rdr6-3 as2-101 plants showed more lobed leaves (0 in 44 as2-101 plants and 32 in 44 rdr6-3 as2-101 plants), we examined by analyzing leaf morphology and expression of a class I KNOX gene BP in as2 and rdr6 as2 leaves whether RDR6 is also involved in repressing KNOX genes. We found that ectopic leaf primordia appeared frequently on the adaxial side of rdr6-3 as2-101 leaves (Figure 3A), and some of the ectopic leaf primordia eventually formed leaf-like structures (Figure 3B; 4 in 44 rdr6-3 as2-101 plants). To examine whether the expression of BP was altered in the rdr6-3 as2-101 leaves, we introduced a BP:β-glucuronidase (GUS) fusion into rdr6-3, as2-101, or rdr6-3 as2-101 plants by crosses and examined GUS staining in these mutant plants. BP was repressed in wild-type (Figure 3C) and rdr6-3 leaves (data not shown), whereas it was expressed in both as2-101 (Figure 3D) and rdr6-3 as2-101 leaves (Figure 3E), especially in sinuses of leaf lobes and leaf veins (Figures 3D, 3E, 3G, and 3H). In rdr6-3 as2-101 leaves, GUS staining was also observed in the ectopic leaf primordium (Figure 3F). Interestingly, BP was expressed strongly at the distal ends of each major leaf vein (Figures 3E and 3H) of the double mutants, but this pattern was not observed in the as2-101 single mutant (see Supplemental Figure 1 online). These BP expression observations suggest that RDR6 may negatively regulate BP in as2-101 mutant leaf blades.
Phenotypes of Early Leaves and BP Expression in rdr6-3 as2-101 Mutant Plants.
(A) A young rdr6-3 as2-101 leaf showing primordium-like structures on the adaxial side (arrowhead).
(B) Some of the ectopic primordia on the leaf blade can eventually form a leaflet structure.
(C) Wild-type leaves carrying BP:GUS did not show any GUS activity.
(D) and (E) GUS staining was visible in sinuses of leaf lobes and major leaf veins in as2-101 (D) and rdr6-3 as2-101 mutants (E). Note that some rosette leaves of as2-101 in a mixed Col-Ler background contained lobes.
(F) to (H) Close-ups of GUS staining in rdr6-3 as2-101 mutant leaves.
(F) GUS activity was shown at the tip of a major vein (arrowhead) in an ectopic leaf primordium.
(G) GUS staining in sinuses of leaf lobes.
(H) GUS staining at the tip of a major leaf vein.
Leaves in (A) and (B) were from mutant plants in the Ler background, and leaves or leaf tissue in all other images were from the F2 plants of a cross between as2-101 rdr6-3 (Ler) and a transgenic line carrying the BP:GUS fusion (Col). Bars = 80 μm in (B), 100 μm in (F) and (H), 200 μm in (A) and (G), 2 mm in (C) and (D), and 1 mm in (E).
rdr6 as2 Has Severe Defects in Leaf Vein Formation and Adaxial-Abaxial Polarity
Leaf vein development is severely affected in the as1 and as2 mutants (Semiarti et al., 2001; Sun et al., 2002). To determine whether RDR6 is involved in regulating vein formation, we examined the leaves, sepals, and petals of the as2-101 and rdr6-3 as2-101 plants. Venations in all rdr6-3 leaves, sepals, and petals were similar to those in wild-type plants but showed a simple pattern in the as2-101 mutant (Figures 4A to 4D). The venation pattern in the rdr6-3 as2-101 mutant was even simpler than that of the as2-101 single mutant (Figures 4A to 4D). To gain more detailed information of leaf vein development, we analyzed the secondary and tertiary veins by scoring the number of branching points (NBPs) (Hamada et al., 2000). NBPs were found to be dramatically reduced in rdr6-3 as2-101 leaves, especially in the fine veins (Figures 4E and 4F). These results indicate that RDR6 is also involved in the vascular development of lateral organs.
Abnormalities of Leaf Vascular Patterns of rdr6-3 as2-101 Mutant Plants.
(A) Venations of cotyledons in wild-type, as2-101, rdr6-3, and rdr6-3 as2-101 plants.
(B) Venations of the first rosette leaves in wild-type, as2-101, rdr6-3, and rdr6-3 as2-101 plants.
(C) Venations of petals in wild-type, as2-101, rdr6-3, and rdr6-3 as2-101 flowers.
(D) Venations of sepals in wild-type, as2-101, rdr6-3, and rdr6-3 as2-101 flowers. Note that venations of all leaves, sepals, and petals became very simple in the rdr6-3 as2-101 mutant plants.
(E) and (F) Quantitative analyses of NBPs in wild-type and rdr6-3 as2-101 leaves. Bars show standard deviation. Secondary leaf veins (E); tertiary leaf veins (F).
All mutants are in the Ler genetic background. Bars = 1 mm in (A) and (B) and 5 mm in (C) and (D).
We reported previously that the as2-101 mutant is defective in leaf adaxial-abaxial polarity, showing abaxialized lotus- and needle-like leaves (Xu et al., 2002, 2003). To determine whether RDR6 plays a role in the adaxial-abaxial polarity formation of lateral organs, we analyzed leaf phenotypes of rdr6-3 as2-101 by scanning electron microscopy. Similar to the as2-101 mutant, we observed lotus-like (Figure 5A) and needle-like (Figure 5B) structures among rdr6-3 as2-101 rosette leaves but with a much higher frequency in rdr6-3 as2-101 than in as2-101 (90% versus 15% of the first-pair rosette leaves). The needle-like leaves in rdr6-3 as2-101 showed long and narrow epidermal cells (Figure 5B) similar to those of as2 (Xu et al., 2003) and phantastica (phan) (Waites and Hudson, 1995) but different from those of phb-1d (McConnell and Barton, 1998) and 35S:AS2 transgenic plants (Xu et al., 2003), suggesting that these leaves are abaxialized. In the as2-101 single mutants, lotus- and needle-like leaves only appeared in the first pair of rosette leaves. Strikingly, the rdr6-3 as2-101 plants showed lotus- and needle-like structures at all positions of rosette leaves, and even some cauline leaves were needle like (data not shown).
Aberrant Adaxial-Abaxial Polarity in Leaves and Petals of the rdr6-3 as2-101 Mutant.
(A) A lotus leaf structure in rdr6-3 as2-101 plants. White line indicates the approximate position where sections were prepared for images in (C) and (D).
(B) A needle-like leaf in rdr6-3 as2-101 plants. Note that lotus- and needle-like leaves reflect a severe loss of adaxial-abaxial leaf polarity.
(C) and (D) Transverse sections through petioles near the blade.
(C) Wild-type Ler.
(D) rdr6-3 as2-101 double mutant. x, xylem; ph, phloem.
(E) to (J) Epidermal patterns of leaves.
(E) Adaxial epidermis of wild-type Ler.
(F) Abaxial epidermis of Ler.
(G) rdr6-3 as2-101 adaxial epidermis.
(H) rdr6-3 as2-101 abaxial epidermis.
(I) Patches appeared on the adaxial side of an rdr6-3 as2-101 leaf (arrows).
(J) A close-up of epidermal cells in a patch on the adaxial side of an rdr6-3 as2-101 leaf.
(K) to (N) Epidermal patterns of petals.
(K) Adaxial epidermis of Ler.
(L) Abaxial epidermis of Ler.
(M) Adaxial epidermis of rdr6-3 as2-101.
(N) Abaxial epidermis of rdr6-3 as2-101.
Arrowheads in (F), (H), and (J) point a long and irregularly shaped cell that reflects the abaxial characters of a leaf. All mutant plants are in the Ler genetic background. Bars = 25 μm in (A) and (B), 50 μm in (E), (F), (H), and (J), 100 μm in (I), 20 μm in (G), (K), and (M), and 10 μm in (L) and (N).
The vascular patterns in a series of sections of petioles at the position close to the blade were examined (Figure 5A, white line). In wild-type petioles, xylem develops on the adaxial pole of the vascular bundle, whereas phloem develops on the abaxial bundle pole (Figure 5C). By contrast, rdr6-3 as2-101 showed ectopic development of abaxial phloem tissue surrounding the xylem in petiole (Figure 5D), which is consistent with the view that rdr6-3 as2-101 leaves are abaxialized.
To further test the hypothesis that RDR6 function is required for adaxial-abaxial polarity formation of lateral organs, we analyzed leaf epidermal cells from the rdr6-3 as2-101 mutant. The adaxial epidermis of wild-type Landsberg erecta (Ler) leaves was characterized by an undulating surface composed of uniformly sized cells (Figure 5E), and the abaxial epidermis was characterized by smaller and less uniformly sized cells (Figure 5F; McConnell and Barton, 1998; Xu et al., 2003). The expanded leaves of as1 and as2 and all rdr6-3 leaves showed a similar epidermal pattern to that of wild-type plants (data not shown). By contrast, the adaxial side of rdr6-3 as2-101 mutant leaves contained both adaxial epidermal cells (Figure 5G) and patches of abaxialized cells (Figures 5I and 5J). Cells in these patches were similar to those on the abaxial side of both the wild-type (Figure 5F) and rdr6-3 as2-101 leaves (Figure 5H). The mosaic adaxial-abaxial cells on the adaxial side of a lamina were also observed in the phan mutant leaves in Antirrhinum majus (Waites and Hudson, 1995) but not seen in as1 or as2 alleles. Interestingly, petals of rdr6-3 as2-101 also demonstrated a severe defect of adaxial-abaxial polarity, which was not observed in the as2-101 and rdr6-3 single mutants (data not shown). Wild-type adaxial petal epidermis shows cone-shaped cells with straight lines (Figure 5K), whereas the abaxial petal epidermis shows cobblestone-shaped cells with wavy lines (Figure 5M). Adaxial epidermal cells in the rdr6-3 as2-101 petals (Figure 5L) were different from those in the wild type (Figure 5K) but rather similar to the abaxial epidermal cells of petals in both wild-type (Figure 5M) and rdr6-3 as2-101 double mutant plants (Figure 5N). Phenotypes of leaves and petals in the rdr6-3 as2-101 mutant plants further support the hypothesis that RDR6 function is required, along with the AS1-AS2 pathway, for adaxial-abaxial polarity formation.
In addition to the enhancement of as2 abnormalities observed in leaves and petals, the rdr6-3 as2-101 mutant also showed other abnormal phenotypes. These included a markedly slowed growth of leaf primordia (Figures 6A to 6D) and defective floral organs. The carpel surfaces were wrinkled, and sepals, petals, and stamens were small in size (Figures 6E and 6F). The aberrant floral organs formed at very early flower developmental stages, when narrowed sepals failed to enwrap the inner-whorl organs (Figure 6G). Mature rdr6-3 as2-101 flowers also showed some needle-like sepals and petals (data not shown). The pleiotropic rdr6-3 as2-101 phenotypes indicate that the RDR6 gene is required for both vegetative and reproductive developmental processes.
rdr6-3 as2-101 Mutation Affects Other Developmental Processes.
(A) to (D) Six-day-old seedlings showed retarded rosette leaf growth in the rdr6-3 as2-101 mutant. Wild-type Ler (A); as2-101 (B); rdr6-3 (C); rdr6-3 as2-101 (D).
(E) Inflorescence phenotypes of wild-type, as2-101, rdr6-3, and rdr6-3 as2-101.
(F) An rdr6-3 as2-101 flower showing the short outer three whorls of organs.
(G) Abnormal flower phenotypes in the rdr6-3 as2-101 mutant appeared during very early developmental stages, when sepals failed to enwrap the inner floral organs.
All mutant plants are in the Ler genetic background. Bars = 80 μm in (A) to (D), (F), and (G) and 1 mm in (E).
miR165/166 Are Repressed by RDR6, AS1, and AS2
Both the differentiation of vascular tissue and the establishment of adaxial-abaxial polarity in Arabidopsis leaves are known to require the five class III HD-ZIP family genes: PHB, PHAVOLUTA (PHV), REVOLUTA (REV), ATHB8, and ATHB15 (Baima et al., 1995, 2001; McConnell and Barton, 1998; McConnell et al., 2001; Emery et al., 2003; Ohashi-Ito and Fukuda, 2003; Dinneny and Yanofsky, 2004). Four of these genes share a region that is complementary to the sequence of miR165, whereas the same region of ATHB15 matches the sequence of another miRNA, miR166 (Figure 7A). Because PHB is regulated by AS1 and AS2 (Lin et al., 2003; Xu et al., 2003) and RDR6 and AS1/AS2 synergistically regulate leaf adaxial-abaxial polarity and vascular development, we examined levels of miRNA165/166 and the five HD-ZIP transcripts in wild-type and rdr6-3 as2-101 mutant leaves.
Analyses of Gene Expression.
(A) Sequences of miR165, miR166, and the region encoding the START domain of class III HD-ZIP proteins. Note that the circled C and U residues denote the nucleotide at which miR165 and miR166 differ.
(B) miRNA filter hybridizations. Lengths of RNA fragments in nucleotides (nt) and probes used in hybridizations are indicated on the left and right of each hybridization image, respectively. RNA gel blots were first probed by miRNAs, and the same filters were then analyzed by 5S RNA probe. Results were consistent from two separate experiments, using different preparations of RNA samples. Hybridization intensity was measured by phosphor image analysis, and the numbers indicate the relative abundance of miR165 levels, calculated using the band intensity of the first lane (Ler) as 1.0.
(C) Steady state levels of mRNA of class III HD-ZIP genes in rdr6-3 as1-101 (right) and rdr6-3 as2-101 (left). RNA was quantified for the indicated mRNA by real-time RT-PCR using primers surrounding the cleavage site. Quantification was normalized to that of ACTIN and then to the value of the wild-type plants, whose value was arbitrarily fixed at 1. Bars show standard error.
(D) and (E) In situ hybridization using an antisense PHB probe on transverse sections of leaf primordia in wild-type Ler (D) and rdr6-3 as2-101 (E).
(F) and (G) In situ hybridization using an antisense REV probe on transverse sections of leaf primordia in wild-type Ler (F) and rdr6-3 as2-101 (G). Arrowheads indicate the earlier-stage leaf primordia. All mutants analyzed are in the Ler genetic background.
Because miR165 and miR166 differ by only one nucleotide (Figure 7A) and molecular hybridization may not be able to distinguish one from the other, the hybridization signals with the miR165 probe probably reflect the levels of both transcripts. miR165/166 transcripts were detected at low levels in the wild-type Ler leaves, and their levels were increased slightly in as1-101, as2-101, and rdr6-3 single mutant leaves (Figure 7B). Strikingly, the miR165/166 level in rdr6-3 as1-101 and rdr6-3 as2-101 double mutants was dramatically elevated (Figure 7B), indicating that RDR6, AS1, and AS2 likely downregulate miR165/166. To test whether the RDR6, AS1, and AS2 regulation was specific for miR165/166, we examined levels of miR157 and miR159, which are also expressed in leaves (Reinhart et al., 2002). We found that the accumulation of these two miRNAs did not differ between the wild-type and mutant plants (Figure 7B), indicating that not all miRNAs are affected by RDR6, AS1, and AS2.
To determine whether increased miR165/166 levels can cause cleavage of transcripts of class III HD-ZIP genes in leaves, we performed RT-PCR using gene-specific primers spanning the predicted cleavage site. Compared with the real-time RT-PCR products from Ler leaves, those from rdr6-3 as2-101 (Figure 7C, left) and rdr6-3 as1-101 (Figure 7C, right) had decrease levels of PHB, REV, ATHB8, and ATHB15 transcripts, whereas the ATHB15 transcript, which does not completely match the miR165 sequence, was affected to a lesser extent. The PHV transcripts were not detected under our experimental conditions. To investigate whether the altered expression levels of these genes were also accompanied by changes in expression patterns, we performed PHB and REV in situ hybridization analyses. In wild-type plants, PHB and REV transcripts accumulated in the adaxial domain of a leaf primordium (Figures 7D and 7F). However, although PHB (Figure 7E) and REV (Figure 7G) transcripts were detected in the earlier-stage leaf primordium (arrowheads), they were reduced markedly in leaf primordia at the stage when leaf polarity began to establish. These results suggest that the increased miR165/166 levels may result in transcript degradations of the HD-ZIP genes.
Localization of miR165/166
It was previously reported that miR165 was accumulated in the abaxial domain of leaves, so that only transcripts of class III HD-ZIP genes in the abaxial domain were eliminated, whereas those in the adaxial domain can normally function to promote the adaxial cell fates (Kidner and Martienssen, 2004). However, this model could not explain why the increased miR165/166 levels (supposedly in the abaxial domain) resulted in degradation of class III HD-ZIP transcripts that are located in the adaxial domain in rdr6-3 as2-101 leaves. To more clearly examine the localization of miR165/166 in leaf primordium, we performed in situ hybridizations using 4-concatenate copies of miR165 as a probe and following a protocol by Drews et al. (1991). At the torpedo stage, miR165/166 signals were detected throughout the entire embryo, with strongest hybridization in the distal parts of cotyledons and roots (Figure 8A). To our surprise, miR165/166 in the leaf primordium and young leaf did not show an abaxially accumulated pattern but was instead detected throughout the entire organ (Figure 8C). To ensure that this miR165/166 distribution pattern was correct, we repeated the in situ hybridization experiment using a different experimental protocol (Long and Barton, 1998). Again, miR165/166 signals were detected throughout the leaf primordia (Figure 8E). To avoid a potential artificial effect of the probe consisting of the 4-concatenate miR165 copies, we also used a sequence containing the predicted pre-miR165a sequence (Reinhart et al., 2002) as a probe to perform in situ hybridization experiments. Although the hybridization signals were very weak, they did not show a polar miR165/166 distribution (Figure 8G). miR165 sense probes did not produce hybridization signals under corresponding conditions (Figures 8B, 8D, 8F, and 8H). Taken together, our results reveal a nonpolar miR165/166 distribution pattern in leaf primordia, unlike that reported previously (Kidner and Martienssen, 2004).
In Situ Localization of miR165/166 Expression in Wild-Type Ler Plants.
Hybridizations were performed with the antisense miR165 probe ([A], [C], [E], and [G]) or the sense miR165 probe ([B], [D], [F], and [H]). In (A) to (F), 4-concatenate miR165 was used as a probe. In (G) and (H), pre-miR165 sequence was used as a probe.
(A) and (B) Torpedo-stage embryos. miR165/166 were detected throughout the entire embryo in (A), but no signal was found in (B).
(C) and (D) Longitudinal sections of plant vegetative apices. miR165/166 were expressed in the SAM, leaf primordial, and young leaves in (C) but were undetectable in (D).
(E) and (F) Transverse sections of plant vegetative apices. miR165/166 hybridization signals were detected throughout the leaf primodia in (E), but no signal was detected in (F).
(G) Transverse sections of plant vegetative apices. miR165/166 signals were detected everywhere in the leaf primordium, though the signals were relatively weak.
(H) An antisense pre-165 could not detect miR165/166 signals.
FILAMENTOUS FLOWER Expression in rdr6-3 as2-101 Leaves
Our previous work has shown that rdr6-3 as2-101 mutant plants display abaxialized leaves (Figure 5) and the adaxial-promoting factors do not function properly (Figure 7). However, it is not known how abaxial-promoting factors, such as YABBY, might be affected in the double mutant leaves. To test for possible changes in YABBY gene functions in the abaxial fate of leaves, we analyzed the expression of a YABBY family member, FILAMENTOUS FLOWER (FIL), in the rdr6-3 as2-101 mutant by RT-PCR. In comparison with wild-type, as2-101, and rdr6-3 leaves, FIL transcripts were dramatically increased in the rdr6-3 as2-101 leaves (Figure 9A). FIL is usually expressed in the abaxial side of leaves (Figure 9B) but was extended throughout the entire primordium (Figure 9C, arrow) or to the adaxial side of young leaves (Figure 9C, arrowheads) in the rdr6-3 as2-101 double mutant. These results indicate that similar to BP and miR165/166, FIL is repressed by the AS1-AS2 and RDR6 pathways in leaf development.
Expression of the FIL Gene.
(A) RT-PCR detection of FIL transcript levels in wild-type, as2-101, rdr6-3, and rdr6-3 as2-101 leaves. Numbers indicate the relative abundance of gene transcripts and were calculated using band intensity of the first lane (Ler) as 1.0.
(B) and (C) In situ hybridization using an antisense FIL probe to transverse sections of leaf primordia in wild-type Ler (B) and rdr6-3 as2-101 (C) that is in the Ler genetic background. Note that the FIL expression was extended to the entire leaf primordium (arrow) and the adaxial side of young leaves (arrowheads).
Overexpression of MIR165a
The Arabidopsis genome contains two genes for miR165: MIR165a and MIR165b (Reinhart et al., 2002). To test whether an elevated level of miR165 affects leaf polarity and vein formation in rdr6-3 as2-101, we introduced a 35S:MIR165a fusion into wild-type Ler, as2-101, and rdr6-3 plants. The increased miR165 levels in the transgenic plants were verified by RNA filter hybridization (see Supplemental Figure 2 online). The Ler background yielded 27 transgenic lines showing similar phenotypes of varying severity. Generally, the rosette leaves of these plants were smaller and round, with leaf margins slightly curled downward, resembling the margins of as1/as2 leaves (Figure 10A). The as2-101 background yielded 27 lines with similar phenotypes to each other (Figure 10B). The leaf shape was similar to that of as2-101 plants, but the leaf surfaces became ruffled, similar to those of rdr6-3 as2-101 double mutant leaves. In addition, these plants showed an increased frequency of lotus leaves compared with that in the as2-101 plants (62% versus 1% of the first-pair rosette leaves, in plants grown on plates at 22°C). In comparison, the first pair of rosette leaves in 22 35S:MIR165a/rdr6-3 transgenic lines resembled the expanded as2-101 leaves, with down-curled leaf margins (Figure 10C; for comparison, see Figure 2B). Two other 35S:MIR165a/rdr6-3 lines displayed even stronger leaf phenotypes, showing lotus leaf structures (Figure 10D) or needle-like leaves with anthocyanin accumulation (Figure 10E). In addition to the abnormal leaf polarity, transgenic lines also showed reduced leaf venation (Figures 10F and 10G).
Phenotypes of 35S:MIR165a Transgenic Plants.
(A) A 35S:MIR165a/Ler seedling, showing small and round leaves with margins slightly curled downward. C, cotyledon.
(B) A 35S:MIR165a/as2-101 seedling with ruffled leaf surfaces. Arrowheads indicate the lotus leaves.
(C) A 35S:MIR165a/rdr6-3 seedling. First-pair rosette leaves resemble those of the as2-101 mutant plants.
(D) A 35S:MIR165a/rdr6-3 transgenic plant showing a lotus leaf structure (arrowhead).
(E) A 35S:MIR165a/rdr6-3 transgenic plant displaying severe phenotypes with abaxialized needle-like leaves (arrowheads).
(F) Comparison of venation between wild-type (left) and 35S:MIR165a/Ler (right) leaves, showing that venation of the 35S:MIR165a/Ler transgenic line was simplified. Bars = 1 mm in (A) to (F).
(G) Quantitative analyses of NBPs in wild-type and 35S:MIR165a/Ler transgenic plants.
(H) Real-time RT-PCR to examine steady state levels of mRNA of class III HD-ZIP genes in wild-type and 35S:MIR165a/Ler plants. Bars show standard error.
To investigate whether the altered leaf phenotypes in the transgenic plants are due to cleavage of class III HD-ZIP transcripts in a manner similar to that in the rdr6-3 as2-101 mutant, we performed real-time RT-PCR using rosette leaves of the T2 generation of 35S:MIR165a/Ler transgenic plants. In comparison with wild-type plants, the levels of PHB, REV, ATHB8, and ATHB15 transcripts in the 35S:MIR165a/Ler were reduced to varying degrees (Figure 10H), similar to those in rdr6-3 as2-101 and rdr6-3 as1-101 mutant plants (Figure 7C). The results from the 35S:MIR165a transgenic plants strongly support the idea that an increased level of miR165 can affect leaf polarity and venation.
RdRP is an enzyme that uses single-stranded RNAs as templates to synthesize dsRNAs (Lipardi et al., 2001; Matzke et al., 2001; Nishikura, 2001; Sijen et al., 2001). Cleavage of dsRNAs by RNase III helicase (Dicer) generates small interfering RNAs (siRNAs), which are recruited by the RNA-induced silencing complex for PTGS/TGS of their cognate genes (Vaucheret et al., 2001; Aufsatz et al., 2002; Hutvagner and Zamore, 2002; Vaistij et al., 2002; Volpe et al., 2002). The biological functions of RDR6 were previously thought to be associated with transgene silencing in transgenic plants (Dalmay et al., 2000; Mourrain et al., 2000; Vaistij et al., 2002) and virus resistance (Mourrain et al., 2000; Ahlquist, 2002). In this study, we demonstrate that the RDR6 function is also required for the specification of pattern in the leaf. The fact that RDR6 is involved in the mechanism for enhancing the as1/2 mutant phenotype suggests that PTGS/TGS may be required for normal plant development.
as1 and as2 mutant plants produce abaxialized leaves (Sun et al., 2002; Xu et al., 2002, 2003). We reported previously that expression of the PHB gene was enhanced in 35S:AS1/Ler and 35S:AS2/Ler transgenic plants and that expression of the FIL gene was elevated in as1-101 and as2-101 mutant plants (Xu et al., 2003). These results, together with other data (Lin et al., 2003; Engstrom et al., 2004), suggest that AS1 and AS2 are genetically upstream of the PHB and FIL genes in the regulation of leaf polarity. However, it was not clear how AS1 and AS2 might influence these downstream genes for leaf polarity formation. In this work, we propose that (1) AS1 and AS2 upregulate the PHB and REV genes for specifying leaf adaxial identity via the repression of miR165/166, and (2) the as1 and as2 phenotypes might be caused at least partially by the altered transcript levels of HD-ZIP III genes.
This hypothesis is supported by two lines of evidence. First, miR165/166 levels were elevated in the as1 and as2 single mutants and were dramatically increased in the rdr6 as1 and rdr6 as2 double mutants. These miR165/166 accumulations may be accompanied by cleavage of transcripts from class III HD-ZIP family members. Second, overexpression of MIR165a in the as2-101 and rdr6-3 single mutants resulted in a more severe defect in adaxial-abaxial leaf polarity than that seen in the as2-101 single mutant, indicating that the phenotype is a direct consequence of the change in miR165/166 content. Together, these data indicate that miRNA is an important link between AS1-AS2 and class III HD-ZIP genes in the regulatory network of leaf development.
The proposed model that miR165 is accumulated in the abaxial domain of leaf primordium (Kidner and Martienssen, 2004) cannot explain some observations about class III HD-ZIP expression levels. For example, the PHB transcript level in the phb-1d mutant was elevated throughout the leaf, indicating that miR165/166 activities exist in the adaxial domain of leaf primordia (McConnell et al., 2001; Bao et al., 2004). Furthermore, the expression patterns of each class III HD-ZIP gene are distinguishable, with the REV transcripts in the more expanded range in the adaxial side of lateral organs than those of PHB and PHV (Emery et al., 2003) and the ATHB-8 transcripts only in the vasculature (Baima et al., 1995). These results suggest that miR165/166 are not the sole factor affecting HD-ZIP distribution.
In this study, we report that miR165/166 are distributed throughout the leaf primordium. It is possible that miR165/166 expression may change over developmental stages of leaves. For example, according to the previous report, the miR165/166 distribution in P1-stage primordia seemed different from that in P2- and P3-stage primordia (Kidner and Martienssen, 2004). In fact, the miR165/166 distribution pattern in P1-stage primordia is similar to that of our in situ hybridization results, with signals in both adaxial and abaxial sides. In the older P2 and P3 primordia, signals became concentrated in the abaxial cells (Kidner and Martienssen, 2004). Additionally, we investigated whether the signal that is strongly accumulated in the cell walls of the abaxial domain of P2- and P3-stage primordia (Kidner and Martienssen, 2004) reflects a real cellular signal. Many previous in situ hybridization experiments using different probes indicated that signals at these stages of leaf primordia appear in the cytoplasm instead of in the cell walls (Bowman and Eshed, 2000; Byrne et al., 2000; Kerstetter et al., 2001; McConnell et al., 2001; Emery et al., 2003).
Our 35S:MIR165a transgenic results showed that in addition to its function in the leaf polarity formation, miR165 may have other regulatory functions during leaf development, including vascular development and leaf shape control. These data also imply that miR165 may be required for the development of the entire leaf, not only the abaxial leaf domain. The Arabidopsis genome contains two miR165 and seven miR166 copies (Rhoades et al., 2002). It will be important in the future to determine the expression pattern for each of these miRNAs by miRNA promoter:reporter fusions, which may improve our understanding of their roles in leaf development.
We observed dramatically enhanced FIL gene expression in rdr6-3 as2-101 mutant plants, with an expanded expression domain. Although it was previously proposed that the PHB pathway negatively regulates YABBY genes (Siegfried et al., 1999; Eshed et al., 2001; Bowman et al., 2002), our data suggest that the enhanced FIL expression may result from reduced HD-ZIP activity in the rdr6-3 as2-101 mutant plants. Alternatively, the increased FIL transcripts in the rdr6-3 as2-101 leaves may also result from defective PTGS/TGS, similar to those of BP and miR165/166.
Although it has been well documented that miRNAs play important roles in gene regulation in plants and animals, very little is known about how miRNA genes are regulated. Our data provide important information indicating that the AS1-AS2 pathway and the RDR6 pathway are both required for miR165/166 regulation. The RDR6 and AS1-AS2 pathways both negatively regulate BP and MIR165/166, but these regulations appeared to be processed separately. This idea was supported by the observation that RDR6 expression in the as1 and as2 mutants and AS1 and AS2 expression in the rdr6 mutant were not obviously different from that in wild-type plants. However, the rdr6 as2 double mutant showed much more severe phenotypes than either of the single mutants, indicating that the AS1-AS2 and RDR6 pathways may synergistically repress BP and MIR165/166 in leaves. It is not clear how these two pathways act to regulate their downstream targets. One possibility is that in addition to the downregulation of BP and MIR165/166 through the DNA binding function, AS1-AS2 may also be involved directly or indirectly in the generation of siRNAs used in the RDR6 pathway to repress BP and MIR165/166. Alternatively, these two proteins might interact with or affect the regulation of AGO1, which is known to play a role in both the miRNA and siRNA pathways. AS1-AS2 functions may be so critical that plants with a loss of function in the RDR6 gene do not show severe plant phenotypes. Although the AS1-AS2 pathway is disrupted in the as1 and as2 mutants, the RDR6 pathway can partially repress BP and MIR165/166. This regulation then attenuates the severity of plant phenotypes caused by as1 and as2 mutations. Plants with loss of function in both AS1-AS2 and RDR6 result in the abnormal BP and MIR165/166 actions, leading to leaves with more severe lobes, ectopic leaf primordia, and abnormal adaxial-abaxial polarity and venation.
Plant Materials and Growth Conditions
Arabidopsis thaliana as1-101 and as2-101 mutants in the Ler background were generated as described previously (Sun et al., 2000, 2002; Xu et al., 2002). Seeds of sde1 (Col-24) and a BP:GUS transgenic line (Col) were kindly provided by D. Baulcombe (John Innes Centre, Norwich, UK) and S. Hake (University of California, Berkeley, CA), respectively. For generation of as2 enhancers, as2-101 seeds (Ler) were ethyl methanesulfonate mutagenized (0.1%), and ∼40,000 M2 plants from 1395 M1 lines were screened. To test whether the enhanced as2 phenotypes were due to a second site mutation, we pollinated the new mutant flowers with wild-type Ler pollen. The F1 progeny showed wild-type phenotypes, and F2 plants segregated with a distribution of 295 wild type, 78 as2-101, and 27 enhanced mutants, close to a 12:3:1 ratio. This suggested that the phenotypic enhancement was due to a mutation in an unlinked gene and that the new mutation alone did not cause obvious phenotypic changes. We then analyzed F3 plants of F2 wild-type-like plants and identified 16 F3 families that did not segregate for as2 mutants. We crossed one plant from each of these 16 families to as2-101. From these 16 crosses, one parent plant, whose 13 independent F2 families all yielded approximately one-sixteenth enhanced mutants, was considered to be the homozygous single as2-enhancing mutant. This plant was named as2 enhancer1 (ae1-1), and only this plant or its progeny was used for further work. The ae1-1 as2-101 mutant was backcrossed to wild-type Ler five times before phenotypic analysis.
Allelism tests between the two enhancer mutants were performed by pollinating the ae1-1 flowers with pollen from F1 plants of a cross between the second mutant and Ler. A total of 91 F1 plants consisted of 47 wild-type-like plants, 24 as2-101 mutants, and 20 enhanced plants, indicating that the two enhancer mutations were allelic. Therefore, the second as2 enhancer mutant was designated ae1-2 as2-101.
Map-Based Cloning
Mapping of the AE1 locus was performed by analysis of an F2 population from a cross between ae1-1 as2-101 and the polymorphic Col ecotype. The AE1 locus was mapped to the proximal arm of chromosome 3, near the simple sequence length polymorphic marker nga6. A set of simple sequence length polymorphic markers was used to detect polymorphisms between the Col and Ler ecotypes, and the AE1 locus was mapped to a 21-kb region (BAC T9C5), which contains seven predicted genes. Sequencing of these candidate genes from ae1-1 as2-101 and ae1-2 as2-101 revealed that a gene called RDR6 (also called SDE1 or SGS2) contained nucleotide substitutions that resulted in premature stop codons in both alleles.
For the complementation experiment, a 6.85-kb ScaI-XbaI genomic fragment containing the 4.0-kb RDR6 gene plus 0.85 and 2.0 kb of upstream and downstream sequences, respectively, was isolated from TAC clone K1J14 and inserted into the pCAMBIA1301 transformation vector. We then transformed ae1-1 mutant plants with this 6.85-kb RDR6 fragment and examined the transgenic T1 plants for complementation of the ae1 phenotype (the distorted young rosette leaves that appear in almost all ae1 plants). Eleven independent transgenic lines were obtained, and seven of those showed complete rescue of ae1 phenotypes. The transgenic plants were verified by PCR with one vector-specific primer (5′-TGATGGCATTTGTAGGAGC-3′) and one RDR6-specific primer (5′-TGCCCGAGAATCCAAATC-3′). Therefore, the ae1-1 as2-101 and ae1-2 as2-101 mutants were renamed rdr6-3 as2-101 and rdr6-4 as2-101, respectively.
RNA extraction was performed as described previously (Xu et al., 2003) with leaves from 20-d-old seedlings, and reverse transcription was performed with 1 μg total RNA using a kit (Fermentas, Vilnius, Lithuania). PCR was performed in the presence of the double-stranded DNA-specific dye SYBR green (Shenyou, Shanghai, China) following the manufacturer's instructions. Amplification was monitored in real time with the fluorometric thermal cycler Rotor-Gene 2000 (Corbett Research, Sydney, Australia). PCR was performed with the following gene-specific primers: 5′-TGTGGAGAATGGAACCAC-3′ and 5′-CTAGCAGAGTTCCTTTCC-3′ for PHB (exon4/exon7), 5′-ATCTGTGGTCACAACTCC-3′ and 5′-TAGCGACCTCTCACAAAC-3′ for REV (exon3/exon8), 5′-GCTACCACAGATACTAGC-3′ and 5′-TCGCAAGGTCTAATGAGG-3′ for ATHB-8 (exon3/exon8), 5′-TCAAAGGCAACTGGAACC-3′ and 5′-GTGCAAGTACTTTGGGTG-3′ for ATHB-15 (exon4/exon9), and 5′-TGGCATCA(T/C)ACTTTCTACAA-3′ and 5′-CCACCACT(G/A/T)AGCACAATGTT-3′ for ACTIN. For real-time PCR, quantifications of each cDNA sample were made in triplicate, and the consistent results from at least two separately prepared RNA samples were used. For each quantification, conditions were, as recommended, 1 ≥ E ≥ 0.80 and r2 ≥ 0.980, where E is the PCR efficiency and r2 corresponds to the correlation coefficient obtained with the standard curve. For each quantification, a melt curve was realized at the end of the amplification experiment by steps of 0.5°C from 55 to 99°C. Results were normalized to that of ACTIN. PCR experiments for AS1, AS2, and RDR6 were performed with the following primers: 5′-CTGCGCCTCAACCGCCAATC-3′ and 5′-CCTTACATTACATTACAAGTTAC-3′ for AS1, 5′-TCCTCCGGCGAAAATGTC-3′ and 5′-CCGGCGAGTAAGTTGATGC-3′ for AS2, 5′-GGGACCTGTACTTTGTGGCTTGG-3′ and 5′-GGGCATGGACCAGATGTGACCC-3′ for RDR6 (exon1/exon2), and 5′-CTTACTTCAATCCCCAGG-3′ and 5′-CTTTTGGACATGATAAACCC-3′ for FIL (exon2/exon7). The PCR products were then analyzed by gel electrophoresis, and the relative abundance of gene transcripts was calculated by the GIS-2016 image system (Tanon, Shanghai, China) using the first-lane product as 1.0.
Construction of MIR165a Transgenic Plants
For overexpression of MIR165, a 141-bp MIR165a precursor was PCR amplified using genomic DNA from Ler plants with gene-specific primers 5′-GGGTTAAGCTATTTCAGTTG-3′ and 5′-AGAGGCAATAACATGTTGG-3′, confirmed by sequencing, and inserted into the pMON530 vector, downstream of the 35S promoter. This construct was introduced into Ler, as2-101, and rdr6-3 plants by Agrobacterium tumefaciens–mediated transformation. The transgenic lines were verified by PCR using a 35S-specific primer (5′-GCTCCTACAAATGCCATCA-3′) and a primer matching the MIR165a precursor sequence (5′-AGAGGCAATAACATGTTGG-3′). miR165 overexpression was confirmed by miRNA filter hybridization (see Supplemental Figure 2 online).
miRNA Filter Hybridization
Total RNA was extracted as described previously (Huang et al., 1995), and ∼5 to 10 μg RNA per lane was separated on a denaturing 19% polyacryamide gel (18 × 16 cm) containing 8 M urea, with each of the sense strands used as a positive control. Antisense probes (5′-GGGGGATGAAGCCTGGTCCGA-3′ for miR165, 5′-GTGCTCTCTATCTTCTGTCAA-3′ for miR157, and 5′-TAGAGCTCCCTTCAATCCAAA-3′ for miR159) were 32P-end labeled, and hybridization was performed according to the method described by Chen (2004).
Detection of GUS Activity and in Situ Hybridization
Histochemical detection of GUS activity was performed with 5-bromo-4-chloro-3-indolyl β-d-glucuronic acid (X-Gluc) as a substrate. Leaf tissue was placed in X-Gluc solution [750 μg/mL X-Gluc, 100 mM NaPO4, pH 7, 3 mM K3F3(CN)6, 10 mM EDTA, and 0.1% Nonidet P-40] under a vacuum for 10 min at room temperature, then incubated overnight at 37°C. In situ hybridizations were performed as previously described (Drews et al., 1991; Long and Barton, 1998) using 10-d-old seedlings. The probes were made from cDNA clones containing sequences from exons 4 to 7 for PHB, exons 2 to 7 for FIL, and exons 3 to 8 for REV or from a pGEM7Z(+) plasmid harboring a fragment of the 4-concatenate miR165 or a fragment of the predicted pre-miR165a (Reinhart et al., 2002).
Fresh tissue from wild-type and mutant plants was examined using a SZH10 dissecting microscope (Olympus, Tokyo, Japan) and photographed using a Nikon E995 digital camera (Nikon, Tokyo, Japan). Wild-type and mutant plant tissue was observed by scanning electron microscopy as previously described (Chen et al., 2000). Vascular patterns and vein numbers were analyzed with a Zeiss dissecting microscope (Jena, Germany) using the dark-field setting, according to our previously described methods (Sun et al., 2002).
The authors thank D. Baulcombe and Plant Bioscience Ltd. for the sde1-1 seeds, S. Hake for the BP:GUS transgenic seeds, Q. Lin and L. Pi for the rdr6-4 as2-101 seeds, The Ohio State University Arabidopsis Stock Center for TAC clone K1J14, X. Gao, J. Mao, H. Dai, and Y. Dou for their assistance with the scanning electron microscopy, and H. Ma, S. Luan, X. Chen, G. Tang, and W. Shen for helpful discussions and critical reading of the manuscript. This research was supported by grants from the Chinese Administration of Science and Technology (863), the Chinese National Scientific Foundation (30421001, 30370751, and 90208009), and the Shanghai Scientific Committee to H.H.
The author responsible for distribution of materials integral to the findings presented in this article in accordance with the policy described in the Instructions for Authors (www.plantcell.org) is: Hai Huang (hhuang{at}sippe.ac.cn).
↵1 These authors contributed equally to this work.
Revised May 25, 2005.
Published July 8, 2005.
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You are going to email the following The Putative RNA-Dependent RNA Polymerase RDR6 Acts Synergistically with ASYMMETRIC LEAVES1 and 2 to Repress BREVIPEDICELLUS and MicroRNA165/166 in Arabidopsis Leaf Development
The Plant Cell Aug 2005, 17 (8) 2157-2171; DOI: 10.1105/tpc.105.033449 | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 6,749 |
The in-spire-ing builds of Azacore!
You don't know true pain until you've tried to build a round object in Minecraft. Our cube-based game just isn't cut out for spherical creations. I once tried to build a giant egg, and just ended up with a big, cream oblong of failure. The local chickens were so disgusted, they pecked me to death. I deserved it, too.
That's why I'm always impressed when someone manages to pull off sloped, curved and round builds in Minecraft. How did they do it? Witchcraft? Probably witchcraft. It was witchcraft, wasn't it?
Actually, YES! Well, actually, no. These curved towers and spherical domes are the hard work of Azacore, a Turkish builder who specialises in spires to inspire! (which was almost the much better name of this article, until I realised Marsh had already used it. Curse you, Marsh)
Azacore was actually reluctant to get into Minecraft, worrying that playing a computer game "wouldn't improve me much". Luckily, a friend of Azacore's was having none of it.
"He wanted me to join him and everything started with that," explains Azacore. "We used to play Minecraft to explore new lands, hunting mobs or trying to survive. But building wasn't on my mind until I discovered the creative mode."
But in a game about cubes, how did he make round structures with such ease? What's Azacore's secret? "Thank you!" he says, when we compliment his spherical skills. "I can say that I am not one of the best builders but I believe that I can put my ideas into my creations correctly."
"Patience is a very important thing that every builder should have," advises Azacore, of the perseverance required to improve your building skills. "As I said, finishing projects and planning them requires patience. You can't create some qualified things in one night.
"Confidence is another important thing you should have. You can't think that you are not good enough to do a project or share it to the community if you want to have success and be happy. There is always gonna be better builders and good projects in this industry. Focusing on being unique and being happy is what you should aim [for], not to get angry to each other and argue."
"Also, sometimes seeing other perfect creations or builders makes me really ambitious. When I feel like that, I just focus on my project and ask myself, am I doing my best? Being ambitious, that's the only motivation I have."
Still, in a game that lets you create almost anything, why commit yourself to realism? What is it Azacore prefers about realistic builds?
"Realistic buildings requires more effort.
"If you decide to make a realistic build, you must be able to do some texturing and choose correct concepts," Azacore continues. "I have a project named 'Island of Daqhat'. It was one of the projects that I have tried a realistic build."
"Castorotto helped me to discover this style and I really liked it. Also I tried it on my last project, named 'Gecturova Palace'. They take a lot of time, but when you finish it, you will see it totally deserves all of the time you gave."
"Being ambitious, that's the only motivation I have."
Azacore's style isn't completely dominated by realism, though. He's also shown a flair for sci-fi, with his vision for a futuristic, sustainable city, The Aviona.
"I am always into something futuristic and modern," explains Azacore, of how he developed The Aviona. "When I hear 'futurism' and 'modern' words, there is a city that appears in my mind and I feel excited. I planned it like I am living on this city, so I felt like that I need to do other stuff (highways, bridges, cars and other things) to complete it as a sustainable city.
"So, planning the project before was the reason that this project looks different (I don't usually plan my projects). I wasn't sure that I will have great result when I am done with this, but now, I am pretty sure."
Well, I'm so inspired, I might just have another go at building something spherical in Minecraft! Or maybe I'll just take a nap. For more of Azacore's work, follow him on Twitter or take a look at his Planet Minecraft portfolio!
Renders by Krylin, Castorotto, Killerack, JoeBricksy and Hylarion | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 6,713 |
package org.bpmscript.test;
/**
*
*/
public interface ITestCallback<T> {
void execute(T services) throws Exception;
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,059 |
Dobričevo (izvirno ) je naselje v Srbiji, ki upravno spada pod Občino Bela Crkva; slednja pa je del Južnobanatskega upravnega okraja.
Demografija
V naselju živi 189 polnoletnih prebivalcev, pri čemer je njihova povprečna starost 42,9 let (40,7 pri moških in 45,1 pri ženskah). Naselje ima 78 gospodinjstev, pri čemer je povprečno število članov na gospodinjstvo 2,90.
To naselje je v glavnem madžarsko (glede na rezultate popisa iz leta 2002), a v času zadnjih treh popisov je opazno zmanjšanje števila prebivalcev.
Viri in opombe
Glej tudi
seznam naselij v Srbiji
Naselja Južno-banatskega upravnega okraja | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 2,754 |
package com.querydsl.spatial;
import org.jetbrains.annotations.Nullable;
import org.geolatte.geom.GeometryCollection;
import org.geolatte.geom.Point;
import com.querydsl.core.types.Expression;
import com.querydsl.core.types.dsl.Expressions;
import com.querydsl.core.types.dsl.NumberExpression;
/**
* A MultiSurface is a 2-dimensional GeometryCollection whose elements are Surfaces, all using coordinates from
* the same coordinate reference system. The geometric interiors of any two Surfaces in a MultiSurface may not
* intersect in the full coordinate system. The boundaries of any two coplanar elements in a MultiSurface may
* intersect, at most, at a finite number of Points. If they were to meet along a curve, they could be merged into a
* single surface.
*
* @author tiwe
*
* @param <T>
*/
public abstract class MultiSurfaceExpression<T extends GeometryCollection> extends GeometryCollectionExpression<T> {
private static final long serialVersionUID = 4133386816772862010L;
@Nullable
private transient volatile PointExpression<Point> centroid, pointOnSurface;
@Nullable
private transient volatile NumberExpression<Double> area;
public MultiSurfaceExpression(Expression<T> mixin) {
super(mixin);
}
/**
* The area of this MultiSurface, as measured in the spatial reference system of this MultiSurface.
*
* @return area
*/
public NumberExpression<Double> area() {
if (area == null) {
area = Expressions.numberOperation(Double.class, SpatialOps.AREA, mixin);
}
return area;
}
/**
* The mathematical centroid for this MultiSurface. The result is not guaranteed to be on
* this MultiSurface.
*
* @return centroid
*/
public PointExpression<Point> centroid() {
if (centroid == null) {
centroid = GeometryExpressions.pointOperation(SpatialOps.CENTROID, mixin);
}
return centroid;
}
/**
* A Point guaranteed to be on this MultiSurface.
*
* @return point on surface
*/
public PointExpression<Point> pointOnSurface() {
if (pointOnSurface == null) {
pointOnSurface = GeometryExpressions.pointOperation(SpatialOps.POINT_ON_SURFACE, mixin);
}
return pointOnSurface;
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,008 |
Guyruita is a genus of South American tarantulas that was first described by J. P. L. Guadanucci in 2007.
Species
it contains six species, found in Venezuela and Brazil:
Guyruita atlantica Guadanucci, Lucas, Indicatti & Yamamoto, 2007 – Brazil
Guyruita cerrado Guadanucci, Lucas, Indicatti & Yamamoto, 2007 (type) – Brazil
Guyruita giupponii Fukushima & Bertani, 2018 – Brazil
Guyruita isae Fukushima & Bertani, 2018 – Brazil
Guyruita metallophila Fonseca-Ferreira, Zampaulo & Guadanucci, 2017 – Brazil
Guyruita waikoshiemi (Bertani & Araújo, 2006) – Venezuela, Brazil
See also
List of Theraphosidae species
References
Theraphosidae genera
Spiders of South America
Theraphosidae | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 1,662 |
Top NFL Photos: Week 8
See all the game results and top pictures from Week 8 of the NFL.
Andre Johnson of the Indianapolis Colts catches a 4th quarter touchdown pass against Bene' Benwikere of the Carolina Panthers during their game on November 2, 2015 in Charlotte, North Carolina. The Panthers defeated the Colts 29-26.
Ronnie Hillman of the Denver Broncos runs in a touchdown against Micah Hyde of the Green Bay Packers in the second quarter at Mile High on November 1, 2015 in Denver, Colorado. The Broncos defeated the Packers 29-10.
PITTSBURGH, PA - NOVEMBER 01: Antonio Brown #84 of the Pittsburgh Steelers celebrates a 1st quarter touchdown during the game against the Cincinnati Bengals at Heinz Field on November 1, 2015 in Pittsburgh, Pennsylvania. (Photo by Jared Wickerham/Getty Images)
CLEVELAND, OH - NOVEMBER 1: Free safety Rashad Johnson #26 of the Arizona Cardinals intercept a pass intended for wide receiver Taylor Gabriel #18 of the Cleveland Browns during the second half at FirstEnergy Stadium on November 1, 2015 in Cleveland, Ohio. The Cardinals defeated the Browns 34-20. (Photo by Jason Miller/Getty Images)
CHICAGO, IL - NOVEMBER 01: Quarterback Teddy Bridgewater #5 of the Minnesota Vikings passes the football in the second quarter against the Chicago Bears at Soldier Field on November 1, 2015 in Chicago, Illinois. (Photo by Jonathan Daniel/Getty Images)
LONDON, ENGLAND - NOVEMBER 01: Charcandrick West #35 of the Kansas City Chiefs looks to hold off Glover Quin #27 of the Detroit Lions during the NFL match between Kansas City Chiefs and Detroit Lions at Wembley Stadium on November 01, 2015 in London, England. (Photo by Charlie Crowhurst/Getty Images)
ATLANTA, GA - NOVEMBER 01: Jameis Winston #3 of the Tampa Bay Buccaneers fakes a pass while rushing the ball during the second half against the Atlanta Falcons at the Georgia Dome on November 1, 2015 in Atlanta, Georgia. (Photo by Kevin C. Cox/Getty Images)
BALTIMORE, MD - NOVEMBER 01: Wide receiver Steve Smith #89 of the Baltimore Ravens eludes Jason Verrett #22 and strong safety Jahleel Addae #37 of the San Diego Chargers during the first half at M&T Bank Stadium on November 1, 2015 in Baltimore, Maryland. (Photo by Patrick Smith/Getty Images)
BALTIMORE, MD - NOVEMBER 01: Quarterback Joe Flacco #5 of the Baltimore Ravens is sacked by nose tackle Sean Lissemore #98 of the San Diego Chargers during the second half at M&T Bank Stadium on November 1, 2015 in Baltimore, Maryland. (Photo by Patrick Smith/Getty Images)
PITTSBURGH, PA - NOVEMBER 01: A.J. Green #18 scores a 4th quarter touchdown during the game against the Pittsburgh Steelers at Heinz Field on November 1, 2015 in Pittsburgh, Pennsylvania. (Photo by Jared Wickerham/Getty Images)
HOUSTON, TX - NOVEMBER 01: Ryan Succop #4 of the Tennessee Titans kicks a 35 yard field goal in the first quarter against the Houston Texans at Reliant Park on November 1, 2015 in Houston, Texas. (Photo by Bob Levey/Getty Images)
HOUSTON, TX - NOVEMBER 01: DeAndre Hopkins #10 of the Houston Texans makes a touchdown catch against Jason McCourty #30 of the Tennessee Titans in the second quarter on November 1, 2015 at NRG Stadium in Houston, Texas. (Photo by Thomas B. Shea/Getty Images)
NEW ORLEANS, LA - NOVEMBER 01: Marcus Murphy #23 of the New Orleans Saints has the ball stripped by New York Giants defensive back Craig Dahl #43 at Mercedes-Benz Superdome on November 1, 2015 in New Orleans, Louisiana. (Photo by Chris Graythen/Getty Images)
ST. LOUIS, MO - NOVEMBER 1: Janoris Jenkins #21 of the St. Louis Rams trips up Mike Davis #22 of the San Francisco 49ers in the second quarter at the Edward Jones Dome on November 1, 2015 in St. Louis, Missouri. (Photo by Michael B. Thomas/Getty Images)
ST. LOUIS, MO - NOVEMBER 1: Todd Gurley #30 of the St. Louis Rams runs the ball up the sideline against the San Francisco 49ers in the second quarter at the Edward Jones Dome on November 1, 2015 in St. Louis, Missouri. (Photo by Dilip Vishwanat/Getty Images)
NEW ORLEANS, LA - NOVEMBER 01: New Orleans Saints quarterback Drew Brees #9 throws a pass against the New York Giants at Mercedes-Benz Superdome on November 1, 2015 in New Orleans, Louisiana. (Photo by Chris Graythen/Getty Images)
NEW ORLEANS, LA - NOVEMBER 01: Odell Beckham #13 of the New York Giants celebrates a first quarter touchdown against the New Orleans Saints at the Mercedes-Benz Superdome on November 1, 2015 in New Orleans, Louisiana. (Photo by Sean Gardner/Getty Images)
Reshad Jones of the Miami Dolphins breaks up a pass intended for Rob Gronkowski of the New England Patriots on October 29, 2015 in Foxboro, Massachusetts. The Patriots defeated the Dolphins 36-7. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 3,689 |
\section{Introduction}
The widely accepted paradigm for galaxy formation is the hierarchical merger model which dictates that galaxies form via continuous mergers with smaller objects (e.g. \nocite{cole1994}{Cole} {et~al.} 1994). This scenario is a natural consequence of the $\Lambda$ cold dark matter ($\Lambda$CDM) model of structure formation, which has been highly successful in explaining both the observed structure from the large redshift surveys (2dF Galaxy Redshift Survey (2dFGRS); \nocite{Colless01}{Colless} {et~al.} 2001, Sloan Digital Sky Survey (SDSS); \nocite{stoughton2002}{Stoughton} {et~al.} 2002), and the anisotropy in the cosmic microwave background \nocite{Sper03}({Spergel} {et~al.} 2003). In the context of this model one would naively expect the most massive galaxies to also be the youngest as they have been `built up' slowly via mergers.
However traditionally early-types are thought to have formed early and rapidly, with a vast amount of observational evidence points supporting this conclusion. The homogeneous nature of massive early-type galaxy properties, such as small scatter in the colour-magnitude relation (CMR) \nocite{Vis77,Bower92,Terl2001,aragon93,stanford95,ellis97,stanford98}({Visvanathan} \& {Sandage} 1977; {Bower}, {Lucey} \& {Ellis} 1992; {Terlevich}, {Caldwell}, \& {Bower} 2001; {Aragon-Salamanca} {et~al.} 1993; {Stanford}, {Eisenhardt}, \& {Dickinson} 1995; {Ellis} {et~al.} 1997; {Stanford}, {Eisenhardt}, \& {Dickinson} 1998, among others) and fundamental plane (FP) \nocite{Dress1987,Burstein1997}({Dressler} {et~al.} 1987; {Burstein} {et~al.} 1997), and the lack of evolution in these relations with redshift \nocite{Kodama1998,Vandokkum2003}({Kodama} {et~al.} 1998; {van Dokkum} \& {Stanford} 2003), is consistent with a scenario in which most, if not all massive early-types, formed at high redshift (at least $z>2$) and have experienced only passive evolution of their stellar populations since.
While this could simply be a result of selection bias \nocite{dokkum2001}({van Dokkum} \& {Franx} 2001), the lack of direct evidence of strong evolution in the population of early-type galaxies since $z\sim$1 remains a serious problem for the hierarchical model of galaxy formation. In recent years much work has gone into reconciling these differences. While theoretical models have moved towards consistency with the CMR and FP \nocite{Kauffmann98, delucia2005}({Kauffmann} \& {Charlot} 1998; {De Lucia} {et~al.} 2005, among others), observational studies based on the spectroscopic and morphological properties of early-types have found significant populations which show evidence for recent star formation and/or interactions. A morphologically based study by \nocite{michard2004}{Michard} \& {Prugniel} (2004) found a significant number ($\sim30$ per cent) of nearby ($z\sim0.01$) early-type galaxies showed evidence of recent interactions/mergers, although 40 per cent of these showed no evidence for a young stellar population. A similar study of 86 nearby bulge-dominated red galaxies by \nocite{vandokkum2005} {van Dokkum} {et~al.} (2005) found 71 per cent had evidence of tidal interactions. However given that both of these studies were undertaken at low redshift the volume sampled was too small for significant numbers of LRG analogues to be present. Moving to higher redshifts, \nocite{Willis2002}{Willis} {et~al.} (2002) found evidence for current star formation, in the form of detection of the {[O~\sc{ii}]}\/ emission line, in over 20 per cent of a sample of 415 luminous field early-types at $z\sim0.3$. While these studies show that evolution is occurring in at least some of the early-type population, it remains unclear if all early-types have experienced evolution of this type. Another contentious point is whether early-type galaxy acquire mass predominately in the form of star forming gas or already formed stars via so called `dry mergers' (\nocite{bell2005} Bell et al. 2005).
In this study we look for evidence of recent star formation in a sample of Luminous Red Galaxies (LRGs). LRGs are luminous ($L>3L^*$) early-type galaxies, analogous to bright cluster galaxies (BCG), selected via their red colours which are broadly consistent with a passively evolving stellar population. These galaxies are ideal candidates for the purposes of this study as they have been shown to have relatively homogeneous spectral properties \nocite{eis01} ({Eisenstein} {et~al.} 2001), enabling any deviation due to recent star formation episodes to be readily identified. They are also the most massive galaxies, which, if the hierarchical merger model is to be correct, must also have the most vigorous merger histories. Thus a sufficiently large sample of LRGs provides the perfect test bed for current theories of galaxy formation/evolution.
Here we probe the star formation histories of our LRG sample via their spectral properties, in particular the {[O~\sc{ii}]}\/(3727\AA) emission and {H${\delta}$}\/(4101\AA) absorption lines and the D4000 index. LRGs are selected from both the SDSS and 2dF-SDSS LRG and QSO (2SLAQ) surveys, resulting in a sample of {5,697}\/ LRGs covering a redshift range of $0.2<z<0.7$. Details of the sample selection are presented in Section \ref{sec:sam}. Section \ref{sec:meth} describes the analysis and modeling performed, with the subsequent results presented in Section \ref{sec:results}. The implications and conclusions to be drawn from these results are then presented in Sections \ref{sec:disc}, and \ref{sec:conc}, respectively.
Where necessary, we have assumed a flat cosmology with $\Omega_m=0.3$, $\Omega_{\Lambda}=0.7$ and H$_0=70$ kms$^{-1}$Mpc$^{-1}$.
\section{The 2SLAQ LRG survey} \label{sec:sam}
Completed in August 2005, the 2SLAQ survey has collected spectra and measured redshifts for over 10,000 high redshift QSOs and $\sim$ 14,000 LRGs in the redshift range $0.45<z<0.8$. The survey is essentially a high redshift extension to the SDSS LRG survey, utilising the 2dF facility on the Anglo-Australian Telescope to go deeper than was possible with the SDSS survey telescope. The 2SLAQ dataset has already been utilised to produce photometric redshifts (\nocite{pad04}{Padmanabhan} {et~al.} 2005), and a large photo-z LRG catalogue (Lahav {et~al. }\/ 2006), as well as probe the evolution of the LRG luminosity function from $z=0.2$ to $z=0.55$ (Wake {et~al. }\/ 2006).
While a detailed description of the survey is presented in Cannon {et~al. } (2006), we briefly review the pertinent points here. The 2SLAQ survey was designed to be an extension of the SDSS LRG survey which sampled LRGs in the redshift range $0.15<z<0.5$, to higher redshifts (\nocite{eis01}{Eisenstein} {et~al.} 2001). The SDSS LRG survey utilised two colour selections in $g-r$ and $r-i$ colour space. One colour selection was used to sample LRGS at redshifts less than 0.4 (cut I), where the 4000\AA\/ break features prominently in the $g$ band, while another (cut II) was used for higher redshifts, where the 4000\AA\/ break is located in the $r$ band. The two cuts were necessary as the 4000\AA\/ break dominates the colour evolution of massive early-type galaxies, such as LRGs, and as such the transition from one band to another causes the track taken by the galaxy in colour-colour space to change considerably. In addition to the colour cut, a sliding magnitude limit was utilised for the low redshift cut I LRGs as the colours of LRGs at $z<0.4$ are quite similar to less luminous star forming galaxies at lower redshifts. The 2SLAQ survey utilised a colour selection similar to the higher redshift, cut II, SDSS colour cut with some key differences. As the number of fibres available to 2SLAQ survey per sq deg. was significantly different ($\sim 67$ per sq deg. for 2SLAQ as compared to only $\sim 2$ per sq deg. for SDSS cut II targets) the colour selection has to be `loosened' to provide enough targets to fill a 2dF field. This can be seen in Figure \ref{fig:ccpaper} which shows the position of the 2SLAQ LRGs used in this study with respect to both the 2SLAQ and SDSS cut II colour cuts. A passive evolution track, provided by Bruzual and Charlot (2003) models, is shown as the solid dashed line. The SDSS LRG survey, with its smaller number of targets per field cuts very close to the passive evolution track and thus goes close to only selecting `red and dead', passively evolving, galaxies. By contrast the increased availability of fibres from 2dF allows the 2SLAQ selection to be quite broad in $g-r$ colour. This has a distinct advantage over SDSS in that LRGs with a range of star formation histories are allowed by the 2SLAQ selection, not just strictly passive evolution. In addition to the colour cuts a magnitude limit of $i_{Dev}<19.8$ is imposed so as to ensure that reasonable signal to noise ($\sim3$) could be achieved in 4 hrs.
Another key difference between the 2SLAQ and SDSS cut II selections is the grouping and prioritization of targets based on a number of colour cuts. LRGs which lie above the line marked 'Sample 8' were the main goal of the 2SLAQ survey and given the highest priority in targeting. The jump in $r-i$ from the SDSS cut II selection and the 2SLAQ sample 8 cut is a result of the desire to acquire distinctly higher redshift LRGs than those in SDSS. Sample 9 LRGs were given lower priority and are essentially lower redshift targets closer to the redshift range of the SDSS cut II LRGs. As sufficient sample 8 and 9 targets were not necessarily available in each 2SLAQ field a small number of `fibre-fillers' were selected below the Sample 9 cut. These are even lower redshift LRGs in the region sampled by SDSS cut I.
\begin{figure}
\includegraphics[angle=270,scale=0.6]{ccpaper.ps}
\caption{Colour-colour diagram for LRGs selected in this study. The solid lines show the region selected by the SDSS cut II, the dashed lines represent the 2SLAQ selections. The dot-dashed line shows the track taken by a passively evolving early-type galaxy model. The circles are located at $\Delta z=0.1$ intervals, starting at $z=0.2$ (lower left) and ending at $z=0.6$ (top right). The sharp bend in the track near $z=0.4$ occurs where the 4000\AA\/ break goes from the $g$ to the $r$ band. }
\label{fig:ccpaper}
\end{figure}
The 2SLAQ observations were performed using exclusively the 2dF spectrograph 2 with a 600 lines per mm $V$ grating. This gives a dispersion of 2.2\AA\/ per pixel and a resolution of about 5\AA\/. The detector used was a Tek1024 CCD with 1024 $\times$ 1024 pixels. Thus using 6150\AA\/ central wavelength the resulting spectra have a wavelength coverage from 5050\AA\/ to 7250 \AA\/. This coverage was chosen to ensure that the Ca H\&K lines were always present in the spectra across the target redshift range of the survey.
In this study we select 2SLAQ LRGs which fall into the Sample 8 and Sample 9 selections. In addition only LRGs which have confident redshifts are selected by requiring the redshift quality flag be greater than or equal to 3. Quality flags on 2SLAQ LRGs are set by the redshift code Zcode, a derivative of the code used to determine redshifts for the 2dFGRS survey. A quality flag of 3 or greater indicates a high level of confidence in the stated redshift (see Cannon et al. 2006 for details).
We also require that both the {[O~\sc{ii}]}\/ and {H${\delta}$}\/ lines are within the wavelength coverage of the spectra and that neither line is in close proximity to the strong sky emission lines at 5577\AA\/, 5900\AA\/, 6300\AA\/ and 7244\AA\/. The signal-to-noise ratio per pixel, averaged across the spectrum, is also required to exceed 3.5 as it was found that lower signal to noise data produces too many false line detections, as will be discussed in Section \ref{sec:def}
These requirements bring the number of 2SLAQ LRGs utilised in this study to 5,697. It should be noted that all magnitudes and colours throughout are on the ABmag scale, in line with the 5-band SDSS photometric system (see \nocite{fukugita1996}{Fukugita} {et~al.} 1996).
\section{Methodology} \label{sec:meth}
\subsection{Measuring Equivalent Widths}\label{sec:methew}
Equivalent widths (EW) of known spectral features are measured using a pseudo-Lick passband flux adding approach. The flux in a set band around the known line wavelength is computed and compared to a continuum level. The continuum is derived by calculating the average flux level in two sidebands and interpolating across the region of interest using these values. For the {H${\delta}$}\/ and H$\gamma$ lines we use the Lick standard {H${\delta}$}$_A$ and H$\gamma_A$ definition for the passband and sidebands \nocite{worthey1997} (Worthey \& Ottaviani 1997), while for the {[O~\sc{ii}]}\/ line we use the definition from Balogh {et~al. } (1999). These definitions are presented in Table \ref{tab:mocklines}. It should be noted that the passband definitions for the absorption lines are the same as those used in the output from Bruzual and Charlot (2003) models. Note that throughout this paper we define a negative equivalent width as emission and a positive value as absorption in a stated line.
D4000 break strengths are also measured for each spectrum in the sample. We define the D4000 index as per \nocite{balogh99}{Balogh} {et~al.} (1999), namely the ratio of the flux in two 100\AA\/ windows centred on 4050 and 3900\AA. While the 2SLAQ spectra are not flux calibrated, we find that the change in spectrograph response is insignificant compared to the intrinsic error in the spectrum and thus the D4000 indices are unaffected.
Errors on the equivalent widths are calculated utilising equation A8 from \nocite{boh83}{Bohlin} {et~al.} (1983). Errors in the continuum are based on the standard error in the mean of the sideband flux; errors in the line are based on variance spectrum calculated by the 2dFDR pipeline. It should be noted that while the equivalent width, and D4000, errors take into account `random' errors such as photon counting statistics, they do not include contributions from systematic errors in the spectra, such as poor sky-subtraction or flat-fielding. Contributions from these sources to the equivalent width measure could be as high as a few percent, and as such the quoted errors are likely underestimates of the true error. While this may be of concern for future users of the data presented in Table 1, this is not considered a problem here as the error on the indices does not play a major role in any of the results presented.
A listing of the equivalent width measures on the {[O~\sc{ii}]}\/ and {H${\delta}$}\/ line, as well as the D4000 indices for all {5,697}\/ 2SLAQ LRGs used in this study can be at \url{http://lrg.physics.uq.edu.au/publi.html}.
\section{Results} \label{sec:results}
\subsection{Definitions based on {[O~\sc{ii}]} and {H${\delta}$}}\label{sec:def}
In this section we present a number of spectral classifications based on the {[O~\sc{ii}]}\/ and {H${\delta}$}\/ equivalent widths which will be used in the subsequent analysis. We split the LRGs into 4 categories based on their position in the {EW\{\hdel\}}-{EW\{\OII\}}\/ space.
\begin{enumerate}
\item Passive - LRGs with no significant {[O~\sc{ii}]}\/ emission ({EW\{\OII\}}$>-8$\AA) or {H${\delta}$}\/ absorption ({EW\{\hdel\}}$<2$\AA), indicating an old passively evolving stellar population.
\item k+a - LRGs with significant {H${\delta}$}\/ absorption ({EW\{\hdel\}}$>2$\AA) but no {[O~\sc{ii}]}\/ emission ({EW\{\OII\}}$>-8$\AA).
\item em - LRGs with significant {[O~\sc{ii}]}\/ emission ({EW\{\OII\}}$<-8$\AA) but no {H${\delta}$}\/ absorption ({EW\{\hdel\}}$<2$\AA).
\item em+a - LRGs with significant {H${\delta}$}\/ absorption ({EW\{\hdel\}}$>2$\AA) and significant {[O~\sc{ii}]}\/ emission ({EW\{\OII\}}$>2$\AA).
\end{enumerate}
The implementation of this classification scheme quantitatively involves a careful determinination of what a `significant' amount of {[O~\sc{ii}]}\/ emission or {H${\delta}$}\/ absorption is in light of the quality of the dataset. Physically the divisions in {EW\{\hdel\}}--{EW\{\OII\}}\/ space should be designed in such a way to isolate LRGs which have star formation histories that are distinctly different from simply passive evolution. In the high signal-to-noise, and resolution limit this is relatively easy as passive evolution models have no {[O~\sc{ii}]}\/ emission and low levels of {H${\delta}$}\/. However in the low signal-to-noise, low resolution regime, in which the 2SLAQ LRG spectra predominately lie, variations in the {EW\{\hdel\}}\/ and {EW\{\OII\}}\/ will be dominated by noise rather than intrinsic physical properties. Thus rather than use a physical justification for our {EW\{\hdel\}}\/ and {EW\{\OII\}}\/ divisions, we calculate threshold values at which it is unlikely that an LRG has a spectrum of a passively evolving stellar population in the presence of noise.
To achieve this we introduce `mock' {H${\delta}$}\/ and {[O~\sc{ii}]}\/ passbands into our equivalent width analysis. The wavelengths of these `mock' passbands are positioned in quiet regions of the LRG spectrum away from known spectral lines such that any significant equivalent width measures will be purely a result of noise. The passbands and sidebands used in the mock analysis are found in Table \ref{tab:mocklines}. For each spectrum in the 2SLAQ LRG sample the equivalent width of the `mock' line index is measured using the method described in Section \ref{sec:methew}. As well as giving us a benchmark with which to determine the optimum {EW\{\hdel\}}\/ and {EW\{\OII\}}\/ threshold values, this analysis has the advantage that for any arbitrary set of {EW\{\hdel\}}\/ and {EW\{\OII\}}\/ thresholds we have a good estimate for the false detection rate, i.e. the number of LRGs we expect to fall into our k+a, em+a or em sample due simply to noise.
\begin{table*}
\caption{Passbands and side continuum bands used to measure the mock {H${\delta}$}\/ and mock {[O~\sc{ii}]}\/ equivalent widths.}
\label{tab:mocklines}
\centerline{
\begin{tabular}{|l|l|l|l|}
\hline
Index &Line passband (\AA)&Blue continuum sideband (\AA)&Red continuum sideband(\AA)\\
\hline
{H${\delta}$} & 4083.5 -- 4122.25 & 4041.6 -- 4079.75 & 4128.5 -- 4161.0 \\
{[O~\sc{ii}]} & 3713 -- 3741 & 3653 -- 3713 & 3741 -- 3801 \\
H$\gamma$ & 4319.75 -- 4363.5 & 4283.5 -- 4319.75 & 4367.25 -- 4419.75 \\
mock {H${\delta}$} &4230.5 -- 4242.25& 4165.6 -- 4199.75& 4245.5 -- 4271.0\\
mock {[O~\sc{ii}]} &3590.0 -- 3617&3480.0 -- 3550.0&3617.0 -- 3641.0\\
\hline
\end{tabular}
}
\end{table*}
Figure \ref{fig:EWdist} shows the distribution of {[O~\sc{ii}]}\/ and {H${\delta}$}\/ equivalent widths for both the real and mock index definitions. Note again that negative equivalent widths indicate emission while positive indicate absorption. The low signal to noise of the 2SLAQ data is apparent in the spread of the mock equivalent widths for both lines. The distribution of mock equivalent widths covers the same range as the real equivalent widths for both {H${\delta}$}\/ and {[O~\sc{ii}]}\/, meaning it is impossible to define any divisions which will eliminate all false positives. Thus we try and define divisions that will minimise the number of false positives while still selecting a statistically significant number of LRGs in each of our classifications. It can be seen that the {H${\delta}$}\/ mock equivalent width distribution drops significantly at $\sim 2$\AA, creating a large difference between the real and mock distributions. If we use this value to define `significant' {H${\delta}$}\/ absorption the number of combined false positives in the k+a and em+a categories is 102, while the number of LRGs with real {EW\{\hdel\}}$>2$\AA\/ is 330. Thus using a division at {EW\{\hdel\}}=2\AA\/ results in 30.1 per cent of k+a and em+a's being false positives. If we decrease the division to 1\AA\/ the ratio of false positives to real detections increases to 33.5 per cent, while increasing the threshold to 5\AA\/ only decreases the ratio to 29.9 per cent, hardly worth a decrease in number of real detections of 275 (600 per cent).
By a similar justification we define the {EW\{\OII\}}\/ division. The distribution of mock OII equivalent widths is seen to drop significantly at $\sim-8$\AA. Using this value as our {EW\{\OII\}}\/ division gives a false positive to real detection ratio of 43.4 per cent. Decreasing to -5\AA\/ gives a ratio of 52.7 per cent, while increasing to -20\AA\/ gives a ratio of 54.9 per cent.
\begin{figure}
\includegraphics[angle=270,scale=0.6]{EWdist.ps}
\caption{Distribution of real {H${\delta}$}\/ (top) and {[O~\sc{ii}]}\/ (bottom) equivalent widths (solid line) and mock {H${\delta}$}\/ (top) and {[O~\sc{ii}]}\/ (bottom) equivalent widths (dashed line). The low signal to noise of the 2SLAQ spectra is apparent from this figure as the mock equivalent width distributions cover a similar range to the real equivalent width distributions despite the fact that the there should be no strong features in the passband regions in the mock analysis. The dotted lines shows the equivalent width thresholds which define the classification scheme used throughout the paper.}
\label{fig:EWdist}
\end{figure}
\subsection{Spectral Properties of 2SLAQ LRGs}\label{sec:rsf}
Using the selection criteria outlined in the preceding section, we can determine the fraction of LRGs in each of the four categories. Table \ref{tab:fract} shows the number of galaxies in each category, and what fraction of the total population they constitute.
\begin{table*}
\caption{Fraction of each spectral type and properties of their combined spectrum.}
\label{tab:fract}
\centerline{
\begin{tabular}{l|l|l|l|l|l|l|l}
\hline
Spectral Type & Number & Fraction (per cent) & Corrected fraction (per cent)& D4000 & {EW\{\OII\}} (\AA) & {EW\{\hdel\}} (\AA) & EW$\{$H$\gamma\}$ (\AA)\\
\hline
Passive & 4612 & $81 \pm 1$ & $88\pm1$ &$1.75 \pm 0.01$& $-1.0 \pm 0.1$ & $-1.67 \pm 0.08$ & $-5.83 \pm 0.08$ \\
k+a & 225 & $3.9 \pm 0.3$ & $2.7\pm0.2$ & $1.53 \pm 0.01$ & $-2.3 \pm 0.1$ &$3.7 \pm 0.1$ & $-1.7 \pm 0.01$ \\
em+a & 101 & $1.8 \pm 0.2$ & $1.2\pm0.1$ &$1.50 \pm 0.01$ &$-12.1 \pm 0.1$ & $3.9 \pm 0.1$ & $-1.6 \pm 0.1$\\
em & 759 & $13.3 \pm 0.5$ & $ 8.6\pm0.4$& $1.71 \pm 0.01$ & $-11.7 \pm 0.1$ &$-1.37 \pm 0.09$ & $-5.53 \pm 0.08$\\
\hline
\end{tabular}
}
\end{table*}
Errors on the stated fractions are calculated assuming Poisson statistics.
The corrected fractions are calculated by subtracting the estimated false detection rate calculated in Section \ref{sec:def} from the measured fraction. The false detection rates for the {H${\delta}$}\/ and {[O~\sc{ii}]}\/ line are transformed into rates for the k+a, em+a and em classifications by assuming that the false detection rate for a line is spread evenly over the classifications requiring it. For example, 30.1 per cent of {H${\delta}$}\/ detections in k+a and em+a LRGs are false detections, thus if they are spread evenly across both classifications the false detection rate in k+a and em+a LRGs (due to only {H${\delta}$}\/) is 20.8 and 9.3 per cent respectively. In the case of the em+a classification we define the false detection rate to be sum of the false detection rate from both {H${\delta}$}\/ and {[O~\sc{ii}]}.
The efficiency of the selection method in isolating passively evolving ellipticals is again apparent from Table \ref{tab:fract} with over 80 per cent of LRGs having the spectral features indicative of an old passively evolving stellar population.
A number of example spectra for each of the spectral classes are shown in Figure \ref{fig:exspec}. Spectral features discussed are marked. It can be seen that in the spectra with strong {H${\delta}$}\/, the other, higher order, Balmer lines are also observed.
\begin{figure}
\includegraphics[angle=270,scale=0.7]{exspec.ps}
\caption{Example spectra for the k+a (top three), em+a (middle three) and em (bottom three) spectral classifications. Spectra have been converted to rest frame wavelengths, and smoothed by a Gaussian with FWHM=0.8\AA\/. Spectral features discussed in the text are marked. }
\label{fig:exspec}
\end{figure}
The combined spectra for each spectral type are presented in Figure \ref{fig:combspec}. The combined spectra are produced by first de-redshifting each spectrum, and rebinning to a common dispersion. The spectra are first normalised using the mean flux in a 100\AA\/ window (4000-4100\AA\/). The top and bottom 10 per cent of values at each pixel are then excluded. The mean of the remaining values at each pixel is then used to produce the combined spectrum. For each combined spectrum the D4000 index and equivalent widths of the {H${\delta}$}\/, H$\gamma$, H$\beta$ and {[O~\sc{ii}]}\/ lines have been measured using the methods presented in Section \ref{sec:methew}, with the results presented in Table \ref{tab:fract}.
\begin{figure}
\includegraphics[angle=270,scale=0.6]{combospec.ps}
\caption{Combined spectrum for the four spectral classifications. Quantities measured on the spectra are presented in Table \ref{tab:fract}. Note the increase in the absorption strength of the higher order Balmer lines (H$\gamma$,H$\epsilon$, etc) in the the k/em+a combined spectra.}
\label{fig:combspec}
\end{figure}
While it is generally accepted that {H${\delta}$}\/ is an efficient indicator of a young stellar population, the presence of strong {H${\delta}$}\/ absorption should be accompanied by increased absorption in the other Balmer lines. To test this we measure the equivalent width of the H$\gamma$ line in the combined spectra, with the results presented in Table \ref{tab:fract}. H$\gamma$ alone is utilised as the lower order Balmer lines (H$\beta$, H$\alpha$) are not inside the wavelength coverage of many of the higher redshift spectra. It can be seen that for classifications which pass the {EW\{\hdel\}}$>2$\AA\/ cut, k+a and em+a, the equivalent width of H$\gamma$, is significantly greater in absorption than that found in the passive combined spectrum. It should be noted that the H$\gamma$ equivalent widths quoted in Table \ref{tab:fract} appear to be in emission (i.e. negative) as emission in the nearby passbands used to estimate the continuum dominates moderately low levels of absorption in the line itself. The ratio of the Calcium H to K lines is also noticably greater in the k+a and em+a combined spectrum than in the Passive spectrum (Figure 4), This can be attributed to increased absorption in the H$\epsilon$ line, which is coincident with the Calcium H line. Thus we can be satisfied that our selection based on {H${\delta}$}\/ alone has been effective in isolating LRGs with overall increased Balmer line absorption, and hence potentially younger stellar populations.
Figure \ref{fig:d4000hist} shows the D4000 distributions for the k+a (bottom), em+a (middle) and em (top) spectral classifications. The whole 2SLAQ sample is designated by the solid line, while the D4000 distribution of only the passive LRGs is shown by the dashed line. The D4000 index is well known to be sensitive to recent star formation, with lower values indicating the increasing presence of a young A star population. As expected the D4000 indices for LRGs in the 2SLAQ sample suspected to have recent star formation,(k+a \& em+a) are noticably less than that for the passively evolving LRGs. The em+a LRGs also show significantly lower D4000 indices than the k+a LRGs suggesting that the em+a galaxies have experienced more recent, or ongoing given the presence of the {[O~\sc{ii}]}\/ line, star formation. Interestingly the em LRGs have D4000 indices which are broadly consistent with the passive LRGs. While a KS test shows that all three distributions are statistically inconsistent with the passive population, with p-values of 2.4$\times10^{-6}$, 2.6$\times10^{-17}$ and 6.6$\times10^{-22}$ for the em, em+a and k+a LRGs respectively, a significant fraction of the em LRG population are found to have D4000 indices as large as those found in the passive population. This is in stark contrast to the k+a and em+a LRG populations which are very rarely found at high D4000 index (i.e. D4000$>2$). This would suggest that while recent star formation is unambigously responsible for k+a and em+a LRGs, the origins of em LRG population are not so clear.
\begin{figure}
\includegraphics[angle=270,scale=0.6]{d4000hist.ps}
\caption{Distribution of D4000 indices for k+a (bottom), em+a (middle) and em (top) LRGs. In each case the distribution is marked with a solid line, while the distribution of passive LRGs is marked with a dashed line. The k+a and em+a LRGs show systemically lower D4000 indices than the passive LRGs. This, along with their increased {H${\delta}$}\/, confirms the presence of a younger stellar population in these LRGs. Significant numbered of em LRGs show D4000 strengths that are as large as those found in the passive population, suggesting that a large fraction of em LRGs do not possess significant populations of young stars.}
\label{fig:d4000hist}
\end{figure}
\subsection{Redshift Dependence} \label{sec:zdep}
To test the redshift dependence of the classification fractions, the 2SLAQ LRGs are divided into 2 subsamples between $0.45<z<0.55$ and $0.55<z<0.65$. In order to increase the redshift range of the analysis a low redshift sample for comparison is provided by SDSS MAIN survey galaxies with $0.1<z<0.2$. While the SDSS also conducted an LRG survey the selection criteria for SDSS LRGs is much stricter than for 2SLAQ, so strict that only $\sim$700 2SLAQ LRGs would be selected by in the SDSS survey at $z=0.2$. It is for this reason that we utilise galaxies from the SDSS MAIN survey for comparison.
As the 2SLAQ LRGs were selected by an observed-frame colour selection some effort must be made to ensure our comparative sample from SDSS is consistent with the colour selections of 2SLAQ. Indeed effort must also be made to ensure that the colour selections are consistent within the redshift range covered by 2SLAQ itself. The simplest way to accomplish this is to use an independent rest frame selection in colour-magnitude space on both the 2SLAQ and SDSS MAIN galaxies. To determine the appropriate boundaries of this selection we present the M$_i$ and rest frame $g-i$ evolution of the 2SLAQ galaxies with redshift in Figure \ref{fig:photevol}. Absolute magnitudes for the 2SLAQ galaxies are produced via the use of model k+e corrections based on \nocite{Bruz03} Bruzual and Charlot (2003;henceforth BC03) models. The models assume simple passive evolution of the stellar population from a single epoch of high redshift star formation. This sort of model has been found to approximate the colour evolution of LRGs to $\sim0.1$ mag \nocite{wake2006} (Wake {et~al. } 2006), which is satisfactory for our purposes here. While ideally k-corrections could be derived directly from the spectra, the 2SLAQ spectra are not flux-calibrated, nor do they have the significant wavelength coverage required for such calculations. Significant redshift evolution is shown in both the $g-i$ colour and M$_i$ of the LRGs in Figure \ref{fig:photevol}. The M$_i$ evolution is a result of the $i_{Dev}<19.8$ magnitude limit of the 2SLAQ survey, while the increase in the distribution of $g-i$ colours to bluer values is a result of the colour selection becoming `looser' at higher redshifts (as can be seen to some extent in Figure \ref{fig:ccpaper}. It can be seen that a cut at $g-i>0.8$ (as shown by the dashed line) will produce a sample which is reasonably consistent in colour with redshift. Similarly a cut at $M_i<-22$ will produce a sample which is close to volume-limited. It is on this cut-down `homogeneous' sample of 2SLAQ LRGs that the following analysis is performed.
\begin{figure}
\includegraphics[angle=270,scale=0.6]{colevol.ps}
\caption{Rest-frame $g-i$ and $M_i$ redshift evolution for the 2SLAQ LRGs. Rest-frame quantities are produced via k+e corrections based on a Bruzual and Charlot (2003) model track. The model assume a single epoch of star formation for the LRG stellar population at high redshift, followed by passive evolution. The dashed line shows the cuts utilised in the text to produce a sample of LRGs which are unbiased in colour and luminosity with redshift.}
\label{fig:photevol}
\end{figure}
In a similar fashion we select galaxies from the SDSS MAIN survey which have rest-frame $g-i>0.9$ and M$_i<-22.0$. As the SDSS spectra have a wide wavelength coverage, and good spectrophotometric calibration k corrections can be derived directly from the spectra. This has been done for the DR4 MAIN galaxies by \nocite{Blanton2005} Blanton {et~al. }\/ (2005) and can be found in the NYU SDSS value-added catalogue (VAC) available at \url{http://wassup.physics.nyu.edu/vagc/}. K corrections in the NYU VAC are produced via the use of the kcorrect software (v3.4) described in \nocite{Blanton2003} Blanton {et~al. }\/ (2003). As the VAC only provides k-corrected photometry the M$_i$ cut is adjusted slighty to -22.2 to take into account of the M$_i$ evolution from $z=0$ to $z=0.15$ predicted by the BC03 models used to k+e correct the 2SLAQ LRGs.
The results of this analysis are presented in Figure \ref{fig:corrfrac} and Table \ref{tab:fracevol}. In each subsample from 2SLAQ, and for the low-$z$ SDSS galaxies, we calculate the number of each spectral classification present, and the fraction of the bin that this number constitutes. Errors are again calculated assuming Poisson statistics. Since the LRGs are not uniformly distributed inside each bin the bin centres are taken to be the median redshift of the all the LRGs in a given bin.
\begin{table*}
\caption{Redshift dependence of classification fractions. Quoted errors are calculated assuming Poisson statistics. The fractions are calculated by first producing a truncated sample which is uniform in colour and luminosity with redshift, and then correcting the fractions using the same analysis as described in Section \ref{sec:def}. The low redshift $z\sim0.17$ point is measured using SDSS MAIN galaxies with the same rest-frame colours and luminosities as the 2SLAQ LRGs.}
\label{tab:fracevol}
\begin{tabular}{l|l|l|l|l|l|l|l|l|l|l}
\hline
$z$ & N[LRGs] & N[k+a] & Per cent & Corrected & N[em] & Per cent & Corrected & N[em+a] & Per cent & Corrected \\
\hline
0.17 & 20781 & 143& $0.68\pm 0.05$& $0.67 \pm 0.05$ &2115 & $10.2\pm 0.2$ &$7.2\pm0.2$ &107 & $0.51 \pm 0.04$ & $0.50\pm0.04$\\
0.49 & 2610 & 46 & $1.8\pm 0.4$&$0.9\pm0.3$ &303 &$13\pm1$&$10\pm1$ &16&$0.6\pm0.2$& $0.3\pm0.1$\\
0.57 & 1141 & 33 & $2.9\pm0.6$&$1.8\pm0.4$ &78&$6.8\pm0.9$&$4\pm1$ &7&$0.6\pm0.3$& $0.3\pm0.2$\\
\hline
\end{tabular}
\end{table*}
In order to correct for the occurrence of false detections we again apply corrections to the fractions estimated using the results of the `mock' line analysis from Section \ref{sec:def}. By dividing the `mock' equivalent width measures on {H${\delta}$}\/ and {[O~\sc{ii}]}\/ into the same redshift bins as the real analysis we produce corrections which are indicative of the underlying signal to noise distribution in each bin. This has the advantage of also eliminating any possible bias that may arise from varying signal to noise across the redshift range.
The raw and corrected fractions are presented in Figure \ref{fig:corrfrac} with the values shown in Table \ref{tab:fracevol}.
The effect of the $g-i>0.9$ and M$_i<-22$ cuts on the number of k+a and em+a LRGs is quite dramatic. Only 79 out of the original 225 k+a's and even more dramatically only 23 out of the original 101 em+a LRGs pass the cuts. However this is not all that surprising given the strong correspondence between k+a and em+a features and low D4000, which can be taken as an effective proxy for $g-i$ colour.
It can be seen from Figure \ref{fig:corrfrac} that only the k+a LRG fraction shows a clear trend of increasing with redshift. The em LRG fraction shows a strong increase between the SDSS $z=0.17$ sample and 2SLAQ LRGs at $z=0.49$, but then shows a significant drop in the highest redshift bin. Little can be said about the em+a LRG fraction as the numbers in the 2SLAQ bins are too low.
In order to quantify the redshift dependence of the k+a fraction in Figure \ref{fig:corrfrac} a $(1+z)^n$ fit has been performed on the corrected fractions. Fitting is performed via weighted linear regression in log$(z)$ vs log(fraction) space. The fit is shown by the dashed line in Figure \ref{fig:corrfrac}. The k+a fraction is found to obey a $(1+z)^{2.8\pm0.7}$ relation.
\begin{figure}
\includegraphics[angle=270,scale=0.35]{fracevol.ps}
\caption{Redshift dependence for the raw (crosses) and corrected (squares) fraction of each classification with redshift. For comparison the fraction of each classification in a sample of low redshift ($z\sim 0.15$) SDSS MAIN galaxies is shown. The SDSS MAIN galaxies are required to have the same luminosity and colour range as the 2SLAQ LRGs by placing simple cuts in rest-frame $g-i$ and $M_i$. While the em and em+a fractions do not show any overall trend with redshift, the k+a fraction shows a strong increase. Fitting a $(1+z)^n$ relation to the k+a fraction increases gives $n=2.8\pm0.7$. The fit is shown by the dashed line.}
\label{fig:corrfrac}
\end{figure}
\section{Discussion}\label{sec:disc}
\subsection{Comparison with previous work}
In recent years many authors have looked for recent and/or ongoing star formation amongst samples of early-type galaxies. \nocite{Fukugita2004} Fukugita {et~al. }\/ (2004) performed a spectroscopic study of 420 E/S0 $z\sim 0.12$ galaxies selected from SDSS. They found evidence of ongoing star formation, in the form of H$\alpha$ emission, in 19 (4.5 per cent) and k+a like spectral properties in 15 (3.6 per cent). \nocite{Yi2005} Yi {et~al. }\/ (2005) also identified early-types with recent star formation in SDSS, this time using GALEX Near-UV and SDSS $r$-band photometry. $\sim15$ per cent of their sample of 39 bright (M$_r<-22$), early-type, $z<0.13$ galaxies was found to have evidence of recent star formation via the use of NUV-$r$ colour. Moving to higher redshifts Doherty {et~al. }\/ (2005) and Le Borgne {et~al. }\/ (2005) both find significant fractions ($\sim 30$, and 50 per cent, respectively) of k+a's amongst massive galaxies at $z\sim1$.
A significant fraction of 2SLAQ LRGs fall into the em category ($6.8\pm 0.3$ per cent), although this result is not completely unexpected as a study by \nocite{Willis2002}{Willis} {et~al.} (2002) found over 20 per cent of their sample of luminous field early type galaxies had significant {[O~\sc{ii}]}\/ emission. Similarly \nocite{eis03} Eisenstein {et~al. }\/ (2003) found that $\sim$ 10 per cent of their sample of massive bulge dominated galaxies had emission line components.
However it is difficult to make concrete comparisons between these results and those presented here. This is because the fraction of early-types with young stellar populations is very sensitive to the sample selection. This can even be seen here, with significant differences in the fraction of k+a and em+a LRGs between the whole sample in Section \ref{sec:rsf} and cut-down sample used in Section \ref{sec:zdep}. Most previous studies, including those discussed above, use a selection based on morphological information. This is distinctly different from the colour based selection used in 2SLAQ survey. It should be expected that morphology based studies of early-types will find greater fractions of galaxies with young stellar populations than we find here as the colour selection is strongly biased against the selection of galaxies with large populations of young stars. Thus while the absolute fractions of k+a and em+a LRGs quoted here are not directly comparable to other work on massive early-types, the observed increase with redshift should be consistent between the studies.
This notion is not only supported qualitatively by the jump in the number of `young' early-types between $z\sim0.1$ and $z\sim1$ but also quantitatively by a comparison of the measured redshift dependence of the k+a fraction here and in the study of \nocite{leborgne2005} Le Borgne {et~al. } (2005). Le Borgne {et~al. }\/ (2005) performed a study of the spectral properties of massive (M$>10^{10.02}$M$_{\sun}$) galaxies selected from the Gemini Deep Deep Survey (GDDS; see \nocite{abraham2004} Abraham {et~al. } 2004) and SDSS MAIN galaxy sample. While they did not base their selection on morphology or colour, and hence found a significantly greater number of k+a than we find, they found an evolution of (1+z)$^{2.5\pm0.7}$ across a redshift range of the $0.1<z<1.2$. Le Borgne {et~al. } (2005) note that this value is very close to the predicted evolution of the galaxy merger rate in $\Lambda$CDM semi-analytic models of $(1+z)^{3.2}$ \nocite{lefevre2000}(Le F{\` e}vre {et~al. } 2000). Interestingly the fraction of k+a and em+a LRGs found here is very close to $4\pm1$ per cent fraction of massive galaxies in close pairs found by Bell {et~al. }\/ (2006). Thus if k+a and/or em+a activity is triggered by mergers, the fractions and evolutionary trends we find here are reasonably consistent with other merger indicators in the literature.
\subsection{{H${\delta}$}\/ strong LRGs} \label{sec:hdelstrong}
If we accept the interpretation that the observed {H${\delta}$}\/ absorption in the k+a and em+a LRGs is a result of recent star formation, which seems likely given the weaker D4000 indices and observed absorption in the higher order Balmer lines (see Section \ref{sec:rsf}), then a small, but significant, number of the LRG population ($\sim1$ per cent) has been forming stars within the last 2 Gyr. This is an important result as it shows that evolution is occurring in the massive early-type population at redshifts less than 0.7.
To try and quantify the level of star formation required to produce the observed {EW\{\hdel\}}\/ we turn to the spectral synthesis models of \nocite{Bruz03}{Bruzual} \& {Charlot} (2003). A distinct advantage of using these models is that they produce output measurements of the indices discussed here (D4000 and {H${\delta}$}\/) measured in same fashion as outlined in Section \ref{sec:meth}. All of the models presented in this Section assume a Salpeter (1955) IMF, solar metallicity, and no dust reddening.
While constant star formation in a galaxy will produce the required level of {H${\delta}$}\/, this scenario has two major problems. Firstly k+a LRGs show no {[O~\sc{ii}]}\/ emission, suggesting that there is no ongoing star formation occurring, however it is possible that the {[O~\sc{ii}]}\/ could be missing due to preferential dust obscuration or even aperture effects. Secondly, models show that galaxies with continuous star formation will mostly be outside of the LRG colour selection. Figure \ref{fig:consfmod} shows model tracks for two constant star formation models and a purely passive evolution model. In each of the constant star formation models a large fraction of the stellar population is formed at high redshift ($z\sim3$), with low levels of constant star formation responsible for 10 and 5 per cent of the stars at age 10 Gyr. The 10 per cent model track falls well outside of the 2SLAQ colour selection, while the 5 per cent model track just enters the 2SLAQ selection at $z>0.55$. The typical {EW\{\hdel\}}\/ of the model spectra in the redshift range probed by 2SLAQ is $\sim2.9$\AA\/ and $\sim1.6$\AA\/ for the 10 per cent and 5 per cent model respectively. Thus the 10 per cent model spectra would be selected in our k+a sample, but not in 2SLAQ and the 5 per cent model would be selected in 2SLAQ, but not as a k+a. As the 5 per cent model only just falls into the 2SLAQ selection we consider it unlikely that continuous star forming models can explain the k+a LRGs in 2SLAQ.
\begin{figure}
\centering
\includegraphics[angle=270,scale=0.35]{consfmod.ps}
\caption{Model $g-r$, $r-i$ tracks for two constant star formation models (crosses and asterisks), and a passive evolution model (triangles). The constant star formation models assume most of their stars are formed at high redshift, with a low level of constant star formation occurring since. The crosses represent a model in which 90 percent of the stellar population at age 10 Gyr was formed at high redshift, the asterisks represent a model where 95 per cent were formed at high redshift. The dashed line shows the Sample 9 2SLAQ selection described in Section \ref{sec:sam}. The passive evolution model assumes that all of the stars are formed at high redshift, and have experienced only passive evolution since. The circles indicate redshift of $z=0.4$ and the tracks mark the evolution from z=0.8 (near the upper left border) to $z=0.4$ at $\Delta z=0.025$ intervals. Assuming a formation age of $z=3$ for the model, the typical {EW\{\hdel\}}\/ in the redshift range probed by 2SLAQ is $\sim2.9$\AA\/ and $\sim1.6$\AA\/ for the 10 per cent and 5 per cent model respectively. Thus it can be seen that any galaxy experiencing a level of constant star formation high enough to pass our {EW\{\hdel\}}$>2$\AA\/ cut would not be selected by the 2SLAQ colour selection.}
\label{fig:consfmod}
\end{figure}
Thus we confine ourselves to models in which a significant episode of star formation has occurred and subsequently ceased. In order to simplify the models we only consider scenarios in which an instantaneous burst of star formation is superimposed on an old stellar population. While it is likely that star formation histories with longer periods of star formation are responsible for the k/em+a population, the tracks taken by such models after star formation has ceased are nearly indistinguishable from the instantaneous burst models. The only quantitative difference is that longer star burst models require that a larger fraction of the LRGs mass be consumed in star formation to achieve the same level of {H${\delta}$}\/ absorption. This can be seen from Figure \ref{fig:bursthd} which shows the relationship between burst length, and peak {EW\{\hdel\}}\/ for models which consume 2, 5, and 10 per cent of galactic stellar mass in new star formation. In all cases the models superimpose a burst of constant star formation on an old (7.4 Gyr) stellar population. The peak {EW\{\hdel\}}\/ is found to not only be dependent on the size of the burst (i.e. the total number of new stars created) but is also strongly dependent on the period over which the burst occurs. Indeed for bursts in the range 500-2000 Myr the peak {EW\{\hdel\}}\/ is dominated by the star formation rate, not the total size of the burst. This can be seen if we take an arbitrary peak {EW\{\hdel\}}\/ and look at the star formation rate (in per cent of galactic stellar mass per year) required for the three burst sizes presented in Figure \ref{fig:bursthd}. Using {EW\{\hdel\}}\/=4\AA\/ as an example, we estimate star formation rates for the 2 per cent, 5 per cent, and 10 per cent models of $6.6\times10^{-9}$, $4.2\times10^{-9}$ and $5.0\times10^{-9}$ per cent per year, respectively. It can be seen that these values are in relatively good agreement.
\begin{figure}
\centering
\includegraphics[angle=270,scale=0.35]{bursthd.ps}
\caption{Effect of changing the length of the star burst on the peak {EW\{\hdel\}}\/. Bursts consuming 2 (crosses), 5 (circles), and 10 (asterisks) per cent of galactic stellar mass are shown. The peak {EW\{\hdel\}}\/ is seen to decrease with increasing the burst length. It is likely that the star formation rate, not the total size of the burst, is the dominating factor in determining the peak {EW\{\hdel\}}\/. }
\label{fig:bursthd}
\end{figure}
Figure \ref{fig:mod4000} plots the track taken in {EW\{\hdel\}}\/- D4000 space by models in which star bursts consuming 1, 2, and 5 per cent of stellar mass have occurred. In each case the model assumes an instantaneous burst occurs in a passively evolving stellar population which formed 7.4 Gyr before burst. Also shown in Figure \ref{fig:mod4000} is the number density of LRGs plotted in grey scale. As expected a slight trend of increasing {EW\{\hdel\}}\/ with decreasing D4000 is observed. Reasonable agreement is found between the {H${\delta}$}\/ strong LRGs and the model tracks. Given that we have only presented tracks for a limited range of models it should be possible to produce models in a similar vein to those presented which can match any observed {EW\{\hdel\}}\/. However this is not the case for all values of D4000. The dotted vertical line at D4000=1.65 is used to crudely divide between those {H${\delta}$}\/ strong LRGs which roughly agree with the models and those which don't. Of the 326 {H${\delta}$}\/ strong LRGs in 2SLAQ 98 (30.1 per cent) have D4000$>1.65$. Many of the previous E+A/{H${\delta}$}\/-strong studies have also identified a population of red {H${\delta}$}\/ strong galaxies with photometric properties that are too red to be consistent with models \nocite{cou87,Blake2004,Pogg99, Balogh2005}({Couch} \& {Sharples} 1987; {Blake} {et~al.} 2004; {Poggianti} {et~al.} 1999; {Balogh} {et~al.} 2005). While dust and super solar metallicities can be called upon to redden the model tracks, and hence explain the discrepancies observed, it has been repeatedly shown that these effects, when used in plausible amounts, can only move the tracks shown in Figure \ref{fig:mod4000} by at most 0.1 in D4000 \nocite{balogh99,Pracy2005} (Balogh et~al. 1999, Pracy et~al. 2005), not nearly enough to explain the reddest {H${\delta}$}\/ strong LRGs. Curiously the fraction of red {H${\delta}$}\/ strong LRGs in 2SLAQ is exactly equal to the predicted number of false positives in the sample. Given this it would seem probable that most, if not all, of the red {H${\delta}$}\/ strong LRGs in this study are simply false detections. If this is true than the origin of the k+a and em+a LRG population can be most readily explained by recent bursts of star formation, on the scale of 1 per cent of galactic stellar mass, in otherwise passive LRGs.
\begin{figure}
\includegraphics[angle=270,scale=0.45]{mod4000.ps}
\caption{Number density of LRGs in the D4000-{EW\{\hdel\}}\/ plane. The plane is broken down into 0.1x1 cells, the grey scale representing the logarithm of the number of LRGs in the cell. The scale goes from light to dark, with the darkest spot equal to 316 (10$^{2.5}$) LRGs. Also plotted are model tracks for a series of models assuming bursts of star formations consuming 5 (top), 2, and 1 (bottom) per cent of stellar mass in new star formation. Typical errors on both indices are shown in the top right corner. A significant number of LRGs have {EW\{\hdel\}}\/ and large D4000 indices which cannot be explained by these simple models. These are analogous to red {H${\delta}$}-strong galaxies found in the literature (e.g. {Couch} \& {Sharples} 1987). }
\label{fig:mod4000}
\end{figure}
\subsection{em LRGs}\label{sec:discem}
The origin of the em LRGs is more ambiguous as the observed {[O~\sc{ii}]}\/ emission could originate from either ongoing star formation or AGN. Typically the nature of emission lines in optical spectra can be determined via the use of line ratios ( e.g.\nocite{Baldwin1981} Baldwin et al. 1981), or even more unambigously by their radio properties. Unfortunately neither of these diagnositics are readily applicable here. The traditional optical line ratios used for classifying AGN/SF are H$\beta$, [OIII] 5007\AA, and H$\alpha$, all of which are have wavelengths too red to appear inside the wavelength coverage of 2SLAQ spectra. Sadler {et~al. }\/ (2006) have performed a crossmatching of the 2SLAQ LRGs to radio sources in both the FIRST and NVSS catalogues. Of the 13784 2SLAQ LRGs with confident redshifts only 378 have corresponding radio sources in FIRST, this is despite FIRST covering 96.5 per cent of the 2SLAQ survey area. Of the 759 em LRGs found in the sample presented here, only 21 (2.8 per cent) have a FIRST radio detection within 5'', very close to the overall radio detection rate of 2.7 per cent. Similarly Sadler {et~al. }\/ (2006) find that the fraction of radio detections with {[O~\sc{ii}]}\/ emission is the same as the fraction in the whole 2SLAQ sample. However while strong radio continuum emission can unambigously identify an AGN, the converse, i.e. lack of radio emission constitutes a lack of AGN activity, is not true. Thus while we can be confident that at least 2.8 per cent of em LRGs have AGN, little can be said about the remaining 97.2 per cent from available radio data.
However despite the lack of data with which to accurately classify each em LRGs, we can muse about the origins of em LRGs. A strong piece of evidence against a star forming origin for all em LRGs is the lack of correlation between {[O~\sc{ii}]}\/ emission and lower D4000 indices. The D4000 index is very sensitive to any population of young stars, as seen in the case of the k+a and em+a LRGs in Figure \ref{fig:d4000hist}. Thus unless we are observing an LRG during the very short period of time at the very beginning of a star formation episode before substantial numbers of young stars have been formed, their should be a clear relation between the D4000 index and current star formation. However if the {[O~\sc{ii}]}\/ emission originates from AGN activity this should have no discernable effect on the D4000 index. Given this it is unlikely that the large number of em LRGs with relatively large D4000 indices have star-forming origins. However given the large spread in the D4000 index seen in the passive LRG population (Figure \ref{fig:d4000hist}) it is impossible to say whether the em LRGs with low D4000 index are actively star forming.
\subsection{Recent Star Formation in LRGs and the $\Lambda$CDM Paradigm} \label{sec:lcdm}
Assuming that recent and or ongoing star formation is the cause of the observed spectral characteristics of the k/em+a LRGs, which is likely given the arguments of the previous sections, a number of well-known phenomena can be called upon as potential candidates for origin of star formation in LRGs.
Given that LRGs are akin to massive early-type galaxies a sizable fraction will reside in groups or clusters, making a small, but significant, number of them bright cluster or even cD galaxies. Thus it is plausible that these central cluster LRGs may be at the focus of a cooling flow. The presence of optical emission lines in 20--30\% of all brightest cluster galaxies in X-ray selected samples has been confirmed in a number of studies (Donahue et al. 1992; Crawford et al. 1999) and an extreme population of galaxies with massive starbursts (50--200 M$_\odot$yr$^{-1}$) has been identified \nocite{allen99} (Allen 1995; Crawford et al. 1999). These galaxies could be the progenitors of the k/em+a LRGs if the starburst is truncated although they would be preferentially found in the brightest LRGs.
Another possibility is that the bursts of star formation are being created as a result of LRG-galaxy mergers or interactions. This ties in well with the idea that LRG evolution is dominated by hierarchical merging. Indeed in this model one would naively expect (and indeed it has been shown from N body simulations) that the frequency of mergers would decrease significantly with increasing time (decreasing redshift), which is qualitatively in line with the results demonstrated here.
However it is difficult to make quantitative assertions about the origin of k/em+a LRGs as it is impossible to determine which of these hypotheses is responsible, if at all. Another complication is the potential for differences between the k+a and em+a classes. Previous studies of traditional k+a's and em+a analogues at low redshift have found systematic differences between the two classes, suggesting different formation mechanisms (Balogh {et~al. }\/ 2005).
Regardless of the physical nature of the star formation in LRGs, it is reasonably safe to assume that the star forming gas is coming from an external origin. This is in agreement with the core principles of $\Lambda$CDM cosmology. Results from the current generation of hydrodynamic N-body cosmological simulations suggest that the most massive galaxies increase in mass significantly from $z<1$ \nocite{delucia2005} (De Lucia {et~al. }\/ 2005), with the bulk of this increase coming from accretion of intra-cluster gas, or via mergers with smaller galaxies \nocite{murali2002} ({Murali} et~al. 2002). By consideration of the expected timescale of the k+a signature we can crudely estimate the number of LRGs affected by k+a activity since $z=0.8$. Converting the redshifts of the bins used in Section \ref{sec:zdep} into look-back time results in a $0.36\times t^{0.85\pm0.2}$ dependence, where $t$ is the look-back time in Gyr. By simply integrating we can use this dependence to estimate the fraction of LRGs which undergo a k+a phase between $0<z<0.8$ (or $0<t<7$) as $8$ per cent. For comparative purposes we consider both the models of De Lucia {et~al. }\/ (2005) and the observational evidence presented by Bell {et~al. }\/ (2006). De Lucia {et~al. }\/ (2005) predict that $\sim50$ per cent of massive early-types gain 50 per cent of their stellar mass between $0<z<0.8$. Similarly Bell {et~al. }\/ (2006) predict from there measure of the close pair fraction that $\sim20$ per cent of massive galaxies will undergo a major merger between $0<z<0.8$. Thus even if k+a, or em+a, activity was associated with a major merger event that doubled the mass of the progenitor LRG, which is unlikely given the models presented in Section 5.2, this would only account for $\sim 16$ per cent of the required mass growth in massive early-types in the models, and only $40$ per cent of the predicted number of mergers in massive galaxies from observations. It is clear from this crude comparison that the level of k+a and em+a activity is not sufficient to explain the bulk of the mass growth in massive early types. This is in line with recent results which suggest that red or `dry' mergers are responsible for the growth of massive early-type galaxies (van Dokkum et~al. 2005; Bell et~al. 2005).
\section{Conclusion}\label{sec:conc}
We have determined the recent star formation histories of a sample of {5,697}\/ LRGs based on the equivalent widths of the {H${\delta}$}\/ and {[O~\sc{ii}]}\/ lines. While the majority ($>$80 per cent) show the spectral properties of an old, passively evolving, stellar population, a significant number of LRGs show evidence for recent and/or ongoing star formation in the form of k+a (2.7 per cent), em+a (1.2 per cent) or em LRGs (8.6 per cent). By dividing the sample into 2 redshift subsamples from $0.45<z<0.55$ and $0.55<z<0.65$, and comparing to a $z\sim0.15$ sample selected from SDSS, it is observed that the fraction of k+a LRGs increases with redshift as $(1+z)^{2.8\pm0.7}$.
Spectral synthesis models, utilising the code of \nocite{Bruz03}{Bruzual} \& {Charlot} (2003), suggest that the k/em+a LRGs could originate from passive LRGs which undergo a starburst in which material equivalent to $\sim 1$ per cent of the stellar mass is consumed in new star formation.
Several origins for k+a and em+a LRGs are considered, including cooling flows and mergers, however identification of the exact formation mechanism, or even if k+a and em+a LRGs share a common origin, is not possible with the current data. It is clear that k+a and em+a activity represents a signpost of recent evolution in LRGs, however by considering the life time of the k+a/em+a phase we estimate that only 8 per cent of LRGs will experience a k+a or em+a phase between $z=0.8$ and the present. By comparing this with the semi-analytic galaxy formation models of De Lucia et~al. (2005) we conclude that k+a/em+a activity cannot be responsible for the predicted mass growth of massive ellipticals since $z=0.8$.
\section*{Acknowledgments}
IGR is supported by a UQCS scholarship. KAP is supported by an EPSA University of Queensland Research Fellowship and a UQRSF grant. ACE and IRS acknowledge support from the Royal Society.\\
The 2SLAQ survey was made possible through the dedicated efforts of the staff at the Anglo-Australian Observatory, both in creating the 2dF instrument and supporting it on the telescope. \\
Funding for the creation and distribution of the SDSS Archive has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society. The SDSS Web site is http://www.sdss.org/.\\
The SDSS is managed by the Astrophysical Research Consortium (ARC) for the Participating Institutions. The Participating Institutions are The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, the Korean Scientist Group, Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington.\\
We also thank the anonymous referees for the many useful comments which greatly improved the paper.
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{"url":"http:\/\/mathoverflow.net\/questions\/47545\/what-does-it-mean-to-extend-a-2d-topological-conformal-field-theory-to-deligne","text":"# What does it mean to extend a 2d (topological) conformal field theory to Deligne-Mumford space?\n\nFor 2D (topological) conformal field theory the corresponding moduli space is the space of Riemann surface with boundary, right? What does it mean by extending the theory to Deligne-Mumford space? How can we do that in terms of the methods we have by now? Thanks for any expository answers!\n\n-\n\nHere is my rough understanding. In a TCFT we have chains on moduli spaces $\\widetilde{M}$ of Riemann surfaces with parameterized boundary acting (in the sense of operads, PROPs, whatever) on a chain complex $V$. The action should be compatible with the various gluing maps.*\n\n(For simplicity, let's just deal with closed TCFTs, and not open or open-closed TCFTs.)\n\nI think that to extend to DM space means something like the following:\n\nFirst, we would like to have an action of moduli spaces $M$ of Riemann surfaces with unparameterized boundary -- which is the same up to homotopy as moduli spaces of Riemann surfaces with marked points and no boundary** -- which is compatible with the action of $\\widetilde{M}$. Compatible here means, I think, compatible with the map $\\widetilde{M} \\to M$ which forgets the parameterization. Moreover we want the action of chains on $M$ to be compatible with the various gluing maps, which are well-defined up to homotopy.***\n\nFinally, we would like to extend this action from chains on $M$ to chains on $\\overline{M}$, the Deligne-Mumford spaces of stable Riemann surfaces with marked points and no boundary. The actions should be compatible with $M \\hookrightarrow \\overline{M}$. Moreover the action of $\\overline{M}$ should be compatible with the various gluing maps.****\n\nSee pages 62 and 63 of Kontsevich-Soibelman for some details. The statement is that, if the Calabi-Yau category corresponding to your (open) TCFT satisfies the \"degeneration conjecture\" (an analogue of Hodge-de Rham degeneration), then there exists an extension to DM space. Recall that Costello proved that TCFTs correspond to Calabi-Yau categories.\n\nAlso take a look at the first two sections of this paper of Teleman.\n\nFor an alternative approach to these sorts of questions, see this paper of Costello.\n\n* The gluing maps here are the obvious gluing maps.\n\n** The homotopy equivalence induces a quasi-isomorphism of the chain complexes. We're working with chain complexes everywhere, and it's OK to replace things with quasi-isomorphic things.\n\n*** I think that we can define maps, for instance, $M_{g,n} \\times M_{g',n'} \\to M_{g+g',n+n'-2}$ by taking two Riemann surfaces with marked points and gluing them together at some specified marked points to obtain a nodal Riemann surface, and then smoothing out that node. This doesn't really make sense on the level of topological spaces because there's no canonical way to smooth out the node. However, again since we're working not with spaces but chains on spaces, I think this is OK because the different ways of smoothing out the node are the same, up to homotopy; in other words, there are many different possible maps of topological spaces $M_{g,n} \\times M_{g',n'} \\to M_{g+g',n+n'-2}$, but they're all homotopic, so on the level of chains the different maps are also (chain) homotopic.\n\n**** The gluing maps here are the standard maps $\\overline{M}\\_{g,n} \\times \\overline{M}\\_{g',n'} \\to \\overline{M}\\_{g+g',n+n'-2}$. This is essentially the standard notion of \"cohomological field theory\" as defined by Kontsevich-Manin.\n\n-\n@Kevin, is $\\overline{M}$ the moduli space of stable Riemann surface with boundary (because for $M$ it is so)? Thanks! \u2013\u00a0 Hao Nov 27 '10 at 23:03\n@Hao: I have edited my answer, maybe this will clarify things. \u2013\u00a0 Kevin H. Lin Nov 27 '10 at 23:49\n@Kevin, I don't understand why everything is defined \"up to homotopy\",is TCFT only \"up to homotopy\"?(it is not obvious according to the definition) \u2013\u00a0 Hao Nov 28 '10 at 11:07\n@Hao: I have added some footnotes. \u2013\u00a0 Kevin H. Lin Nov 29 '10 at 4:23","date":"2014-09-20 12:24:42","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9413208365440369, \"perplexity\": 325.7884020437253}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2014-41\/segments\/1410657133132.72\/warc\/CC-MAIN-20140914011213-00038-ip-10-196-40-205.us-west-1.compute.internal.warc.gz\"}"} | null | null |
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