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https://zh.wikipedia.org/wiki/%E6%8B%89%E6%A2%85%E5%8F%82%E6%95%B0 | # 拉梅参数
• 拉梅参数λ，又称拉梅第一参数
• 剪切模量μ，又称拉梅第二参数，也可记为$G$
$\sigma=2\mu \varepsilon +\lambda \; \mathrm{tr}(\varepsilon)I$
## 参考文献
• F. Kang, S. Zhong-Ci, Mathematical Theory of Elastic Structures, Springer New York, ISBN 0-387-51326-4, (1981)
• G. Mavko, T. Mukerji, J. Dvorkin, The Rock Physics Handbook, Cambridge University Press (paperback), ISBN 0-521-54344-4, (2003)
$(\lambda,\,G)$ $(E,\,G)$ $(K,\,\lambda)$ $(K,\,G)$ $(\lambda,\,\nu)$ $(G,\,\nu)$ $(E,\,\nu)$ $(K,\, \nu)$ $(K,\,E)$ $(M,\,G)$
$K=\,$ $\lambda+ \tfrac{2G}{3}$ $\tfrac{EG}{3(3G-E)}$ $\tfrac{\lambda(1+\nu)}{3\nu}$ $\tfrac{2G(1+\nu)}{3(1-2\nu)}$ $\tfrac{E}{3(1-2\nu)}$ $M - \tfrac{4G}{3}$
$E=\,$ $\tfrac{G(3\lambda + 2G)}{\lambda + G}$ $\tfrac{9K(K-\lambda)}{3K-\lambda}$ $\tfrac{9KG}{3K+G}$ $\tfrac{\lambda(1+\nu)(1-2\nu)}{\nu}$ $2G(1+\nu)\,$ $3K(1-2\nu)\,$ $\tfrac{G(3M-4G)}{M-G}$
$\lambda=\,$ $\tfrac{G(E-2G)}{3G-E}$ $K-\tfrac{2G}{3}$ $\tfrac{2 G \nu}{1-2\nu}$ $\tfrac{E\nu}{(1+\nu)(1-2\nu)}$ $\tfrac{3K\nu}{1+\nu}$ $\tfrac{3K(3K-E)}{9K-E}$ $M - 2G\,$
$G=\,$ $\tfrac{3(K-\lambda)}{2}$ $\tfrac{\lambda(1-2\nu)}{2\nu}$ $\tfrac{E}{2(1+\nu)}$ $\tfrac{3K(1-2\nu)}{2(1+\nu)}$ $\tfrac{3KE}{9K-E}$
$\nu=\,$ $\tfrac{\lambda}{2(\lambda + G)}$ $\tfrac{E}{2G}-1$ $\tfrac{\lambda}{3K-\lambda}$ $\tfrac{3K-2G}{2(3K+G)}$ $\tfrac{3K-E}{6K}$ $\tfrac{M - 2G}{2M - 2G}$
$M=\,$ $\lambda+2G\,$ $\tfrac{G(4G-E)}{3G-E}$ $3K-2\lambda\,$ $K+\tfrac{4G}{3}$ $\tfrac{\lambda(1-\nu)}{\nu}$ $\tfrac{2G(1-\nu)}{1-2\nu}$ $\tfrac{E(1-\nu)}{(1+\nu)(1-2\nu)}$ $\tfrac{3K(1-\nu)}{1+\nu}$ $\tfrac{3K(3K+E)}{9K-E}$ | {"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": 0, "img_math": 66, "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": 0.9909759759902954, "perplexity": 235.84425771115136}, "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-2014-15/segments/1398223204388.12/warc/CC-MAIN-20140423032004-00241-ip-10-147-4-33.ec2.internal.warc.gz"} |
http://slideplayer.com/slide/2305406/ | Phase Changes Courtesy www.lab-initio.com. CA Standards Students know energy is released when a material condenses or freezes and is absorbed when a material.
Presentation on theme: "Phase Changes Courtesy www.lab-initio.com. CA Standards Students know energy is released when a material condenses or freezes and is absorbed when a material."— Presentation transcript:
Phase Changes Courtesy www.lab-initio.com
CA Standards Students know energy is released when a material condenses or freezes and is absorbed when a material evaporates or melts.Students know energy is released when a material condenses or freezes and is absorbed when a material evaporates or melts.
Water phase changes Temperature remains __________ during a phase change. constant
Effect of Pressure on Boiling Point
Phase Diagram Represents phases as a function of temperature and pressure. Critical temperature: temperature above which the vapor can not be liquefied. Critical pressure: pressure required to liquefy AT the critical temperature. Critical point: critical temperature and pressure (for water, T c = 374°C and 218 atm).
Phase changes by Name
Water
Carbon dioxide Phase Diagram for Carbon dioxide
Carbon
Phase Diagram for Sulfur
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https://www.transtutors.com/questions/assess-and-predict-the-performance-of-an-active-low-pass-filter--19368.htm | # Assess and predict the performance of an active low pass filter...
In this exercise, the goal is to analyse, assess and predict the performance of an active low pass filter whose circuit diagram is given in Figure 1. The circuit comprises two passive and one active kind of component: the components labelled ’R1’ and ’R2’ are resistors. Their value is measured in Ohms (named after Georg Simon Ohm, unit symbol: ?). As one Ohm is quite small, it is usual to specify resistances in Kiloohms, K? where of course 1K? = 1000?. The components labelled ’C1’ and ’C2’ are capacitors and their value is measured in Farads (named after Michael Faraday, unit symbol: F). As one Farad is a very large capacitance it is more usual to specify capacitances in µF (Microfarads) or even nF (Nanofarads) where 1F = 106µF = 109nF. The third type of component in the circuit is the operational amplifier with whose function and specification we will not concern
ourselves. These components together function as a low pass filter, i.e. signals presented at the input (vin) will get transformed to the output (vout) and the transformation is (to a good approximation) linear. The signal’s amplitude (i.e. voltage) at the output is different from the signal’s amplitude at the input and the relation is given by vout vin (?) = ? 2 c -?2 + i ?c Q ? + ?2 c . (1) In this equation, ? is the frequency of the input signal and i is the complex root of unity, i.e. we have i 2 = -1. Note that the ratio of input and output signal is a complex number where the number’s modulus, i.e. vout vin (?) gives the signal amplitude ratio. The parameters Q and ?c in equation (1) depend on the component values according to the following formulae: ?c = r 1 R1R2C1C2 Q = 1 R1 + R2 · r R1R2C1 C2 . Task 1 Two data files have been made available on Moodle containing measurements (in the unit ?) of two types of resistors all specified to have resistance R = 4700?. The first type (data in film.dat) are film-type resistors where the resistor is initially produced with too low a resistance and then some of the material is abraded (removed) until the resistance is high enough. The second type (data in comp.dat) is the carbon-composition type where the material is simply pressed into shape without further processing. For each of these two data files, find the minimal, maximal value as well as mean, median, upper and lower quartile and standard deviation of the resistance. Perform a t-test to see whether the average resistance of film type resistors is different from that of carbon-composition type resistors. [5] 4 Task 2 Plot a histogram of the distribution for each of the two resistor data sets from above and produce a QQ-plot (using qqnorm) to compare the quantiles to the normal distribution. Do the samples look as though they come from a normal distribution? How would you describe the deviation for film type resistors? In order to fit another distribution for the film type resistors, take the maximum of the film type resistors and for each resistor subtract its value from the maximum value: R˜ i = (max{R1, R2, . . . , Rn}) - Ri Now fit a Gamma distribution to the transformed values, R˜ i . To do this, compute the mean and variance of the transformed values and use the method of moments (see STAT2001) to infer the scale and location parameter of the Gamma distribution. To check your fit, generate a large sample (at least N = 10000 samples) from the gamma distribution with the parameter values you estimated (use e.g. rgamma to do this) and use a qqplot (use qqplot) to check whether your newly fitted distribution fits the data. [5] Task 3 We now wish the investigate the behaviour of the circuit given in figure 1, more precisely its amplitude response given by formula (1). For the values R1 = R2 = 4600? and C1 = 33nF and C2 = 4.7nF, plot the amplitude ratio of the filter for a frequency ranging from ?min = 100 to ?max = 60000. Also plot the attenuation (measured in decibel, dB) as a function of frequency which is given as D(?) = -20 log10 vout vin (?) (2) over the same frequency range. Can you see why the filter is called a low-pass filter? [3] Task 4 The filter to be constructed is required to have an attenuation of no more than 0.5dB for frequencies below ?1 = 18500, i.e. the amplitude ratio has to be at least vout vin (?) > 10-0.025 when ? < ?1 (this is called the passband). Also, the filter must attenuate frequencies above ?2 = 42000 by at least 12dB, i.e. the amplitude ratio must be no more than vout vin (?) < 10-0.6 when ? > ?2 (this is called the stopband). Using the mean and variances found above for the carbon composition resistors for R1 and R2, and using a statistical model of C1[nF] ~ N (33, 2.5) and C2[nF] ~ N (4.7, 0.05) for the capacitors, simulate the circuit’s amplitude response at the frequencies ?1 and ?2. What percentage of circuits produced will fail to meet the requirements? Provide a confidence interval for your estimate!
Attachments: | {"extraction_info": {"found_math": false, "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": 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": 0.8721615076065063, "perplexity": 1134.4964987503645}, "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-2021-21/segments/1620243989526.42/warc/CC-MAIN-20210514121902-20210514151902-00374.warc.gz"} |
http://chronicle.com/blognetwork/castingoutnines/tag/integral/ | Tag Archives: integral
December 16, 2010, 2:30 pm
A problem with "problems"
I have a bone to pick with problems like the following, which is taken from a major university-level calculus textbook. Read it, and see if you can figure out what I mean.
This is located in the latter one-fourth of a review set for the chapter on integration. Its position in the set suggests it is less routine, less rote than one of the early problems. But what’s wrong with this problem is that it’s not a problem at all. It’s an exercise. The difference between the two is enormous. To risk oversimplifying, in an exercise, the person doing the exercise knows exactly what to do at the very beginning to obtain the information being requested. In a problem, the person doesn’t. What makes an exercise an exercise is its familiarity and congruity with prior exercises. What makes a problem a problem is the lack of these things.
The above is not a problem, it is an exercise. Use the
March 21, 2010, 7:32 pm
Calculus reform's next wave
There’s a discussion going on right now in the Project NExT email list about calculus textbooks, the merits/demerits of the Stewart Calculus textbook, and where — if anywhere — the “next wave” of calculus reform is going to come from. I wrote the following post to the group, and I thought it would serve double-duty fairly well as a blog post. So… here it is:
——-
I’d like to add my \$0.02 worth to this discussion just because (1) I’m a longtime Stewart Calculus user, having used the first edition (!) when I was an undergrad and having taught out of it for my entire career, and (2) I’m also a fairly consistent critic of Stewart’s calculus and of textbooks in general.
I try to see textbooks from the viewpoints of my students. From that vantage point, I unfortunately find very little to say in favor of Stewart’s franchise of books, including the current edition, all of the…
January 19, 2010, 9:22 pm
Piecewise-linear calculus, part 3: Integration
This is probably the last of three articles on how piecewise-linear functions could be used as a helpful on-ramp to the big ideas in calculus. In the first article, we saw how it’s possible to develop some of the main conceptual ideas of the derivative, without much of the technical notation or jargon, by using piecewise-linear functions. In the second article, we saw how to use the piecewise-linear approach to develop an alternative limit-based definition of the derivative of a function at a point. To wrap things up, in this article I’ll discuss how this same sort of approach can help in students’ first contact with integration, again by way of a hypothetical classroom exercise.
When we took this approach with derivatives, we used the travels of three college students from their dorm rooms to the cafeteria. Each student had a different graph showing his position as a (piecewise-linear)…
May 12, 2009, 1:02 pm
Four things I used to think about calculus, and what I've replaced them with
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I’ve been teaching calculus since 1993, when I first stepped into a Calculus for Engineers classroom at Vanderbilt as a second-year graduate student. It hardly seems possible that this was 16 years ago. I can’t say whether calculus itself has changed that much in that span of time, but it’s definitely the case that my own understanding of how calculus is used by professionals in the real world has developed, from having absolutely no idea how it’s used to learning from contacts and former students doing quantitative work in business amd government; and as a result, the way I conceive of teaching calculus, and the ways I implement my conceptions, have changed.
When I was first teaching calculus, at a rate of roughly three sections a year as a graduate student and then 3-4 sections a year as a newbie professor:
• I thought that competency in calculus consisted in…
May 5, 2008, 1:48 pm
Deconstructing dx
Asking the following question may make me less of a mathematician in some people’s eyes, and I’m fine with that, but: How do you explain the meaning of the differential dx inside an integral? And more importantly, how do you treat the dx in an integral so that, when you get to u-substitutions, all the substituting with du and dx and so on means more than just a mindless crunching of symbols?
Here’s how Stewart’s Calculus does it:
• In the section introducing the definite integral and its notation, it says: “The symbol dx has no official meaning by itself; $$\int_a^b f(x) \, dx$$ is all one symbol.” (What kind of statement is that? If dx has “no official meaning”, then why is it there at all?)
• In the section on Indefinite Integrals and the Net Change Theorem, there is a note — almost an afterthought — on units at the very end, where there is an implied connection between…
• The Chronicle of Higher Education
• 1255 Twenty-Third St., N.W.
• Washington, D.C. 20037 | {"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": 1, "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": 0.707021176815033, "perplexity": 860.4749164371251}, "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-2014-42/segments/1414637904760.56/warc/CC-MAIN-20141030025824-00010-ip-10-16-133-185.ec2.internal.warc.gz"} |
http://www.r-bloggers.com/author/neil-gunther/ | Blog Archives
Restaurant Performance Sunk by Selfies
July 17, 2014
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An interesting story appeared over the weekend about a popular NYC restaurant realizing that, although the number of customers they served on a daily basis is about the same today as it was ten years ago, the overall service has significantly slowed. Naturally, this situation has led to poor online reviews so, the restaurant hired a firm to...
How to Remember the Poisson Distribution
July 3, 2014
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The Poisson cumulative distribution function (CDF) $$F(α,n) = \sum_{k=0}^n \dfrac{α^k}{k!} \; e^{-α} \label{eqn:pcdf}$$ is the probability of at most $n$ events occurring when the average number of events is α, i.e., $\Pr(X \le n)$. Since \eqref{eqn:pcdf} is a probability function, it cannot have a value greater than 1. In R, the CDF is given by the...
Importing an Excel Workbook into R
June 5, 2014
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The usual route for importing data from spreadsheet applications like Excel or OpenOffice into R involves first exporting the data in CSV format. A newer (c. 2011) and more efficient CRAN package, called XLConnect, facilitates reading an entire Excel workbook and manipulating worksheets and cells programmatically from within R. XLConnect doesn't require a running installation...
Importing an Excel Workbook into R
June 4, 2014
By
usually import Excel data in CVS format A new package in CRAN facilitates reading in entire Excel workbook and selecting worksheets and cells from there. example.... require(XLConnect)# Load Excel workbook into memorywb # Convert a sheet to a data frame df sheet = "SGI-NUMA", startRow = 3, endRow =...
Melbourne’s Weather and Cross Correlations
April 1, 2014
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During a lunchtime discussion among recent GCaP class attendees, the topic of weather came up and I casually mentioned that the weather in Melbourne, Australia, can be very changeable because the continent is so old that there is very little geographical relief to moderate the prevailing winds coming from the west. In general, Melbourne...
Facebook Meets Florence Nightingale and Enrico Fermi
February 18, 2014
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Highlighting Facebook's mistakes and weaknesses is a popular sport. When you're the 800 lb gorilla of social networking, it's inevitable. The most recent rendition of FB bashing appeared in a serious study authored by a couple of academics in the Depar...
Response Time Percentiles for Multi-server Applications
December 25, 2013
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In a previous post, I applied my rules-of-thumb for response time (RT) percentiles (or more accurately, residence time in queueing theory parlance), viz., 80th percentile: $R_{80}$, 90th percentile: $R_{90}$ and 95th percentile: $R_{95}$ to a cellphone application and found that the performance measurements were not completely consistent. Since the data appeared in a journal blog, I...
Laplace the Bayesianista and the Mass of Saturn
September 15, 2013
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I'm reviewing Bayes' theorem and related topics for the upcoming GDAT class. In its simplest form, Bayes' theorem is statement about conditional probabilities. The probability of A, given that B has occurred, is expressed as: $$\Pr(A|B) = \dfrac{\Pr(B|A)\times\Pr(A)}{\Pr(B)} \label{eqn:bayes}$$ In Bayesian language, $\Pr(A|B)$ is called the posterior probability, $\Pr(A)$ the prior probability, and $\Pr(B|A)$ the...
GDAT Class October 14-18, 2013
August 25, 2013
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This is your fast track to enterprise performance analysis and capacity planning with an emphasis on applying R statistical tools to your performance data. Early-bird discounts are available for the Level III Guerrilla Data Analysis Techniques class O... | {"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": 2, "x-ck12": 0, "texerror": 0, "math_score": 0.2577154338359833, "perplexity": 3971.1381406180267}, "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-2015-18/segments/1429246639191.8/warc/CC-MAIN-20150417045719-00149-ip-10-235-10-82.ec2.internal.warc.gz"} |
http://www.gradesaver.com/textbooks/math/algebra/intermediate-algebra-6th-edition/chapter-3-section-3-3-graphing-linear-functions-exercise-set-page-150/60 | ## Intermediate Algebra (6th Edition)
$x=-2$ and $x=2$
We are given that $|5x|=10$, so $5x=10$ and $5x=-10$. We can solve both equations to find solutions for x. For $5x=10$, divide both sides by 5. $x=2$ For $5x=-10$, divide both sides by 5. $x=-2$ | {"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": 0.9487051367759705, "perplexity": 133.2924478019144}, "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-2017-09/segments/1487501170839.31/warc/CC-MAIN-20170219104610-00385-ip-10-171-10-108.ec2.internal.warc.gz"} |
http://tex.stackexchange.com/tags/loops/hot | # Tag Info
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One way of doing this is using leaders: \documentclass{article} \newcommand\kitty{\leavevmode\xleaders\hbox{kitty!}\hfill\kern0pt} \begin{document} This is a test. \kitty \par This is a test. \noindent \kitty \end{document} The general format for constructing leaders is \leaders<box or rule><glue> (which repeats <box or rule>). ...
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2015 CHRISTMAS EDITION Here I introduce my first triple-burst firework, with "For unto us" as the inner burst, "a child is born" as the second burst, and "Lord!" as the outer burst. The code can be found in the MWE later in this post. I wish a blessed Christmas season to all. 2015 NEW YEAR'S EDITION 2014 EDITION: Merry Christmas! The syntax is \...
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Requires xelatex: \documentclass{article} \usepackage{color} \XeTeXinterchartokenstate = 1 \newXeTeXintercharclass \vowelsclass \XeTeXcharclass \a \vowelsclass \XeTeXcharclass \e \vowelsclass \XeTeXcharclass \i \vowelsclass \XeTeXcharclass \o \vowelsclass \XeTeXcharclass \u \vowelsclass \XeTeXcharclass \A \vowelsclass \XeTeXcharclass \E \...
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Edit: To give some indications for this question (What's the maximum number of pages a PDF produced by pdfTeX can have?), I tried my second version with a limit of 2.500.000 pages. The PDF produced (in approximatively 30 minutes) contains 1112672090 bytes. Here is a variation of your first solution (this document can't be terminated!): \documentclass{...
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This answer has four five six four routines: the last update: leaner code 6, as I understand better my hacky use of \pdfescapestring and could remove some superfluous extras (if they had been really needed, these extras would not have been enough anyhow). the very last update: improved sub-routine for merging in code 6 bringing at least a 2x speed ...
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This is just for practicing with LaTeX3 code. \documentclass{article} \usepackage{xparse,xcolor} \ExplSyntaxOn \NewDocumentCommand{\colorize}{mm} { \cs_set:cpn { maryjane_color_#1: } { \textcolor{#2}{#1} } } \tl_new:N \l_maryjane_text_tl \NewDocumentCommand{\changecolors}{ O{aeiou} m } { \tl_set:Nn \l_maryjane_text_tl { #2 } \tl_map_inline:nn { #1 }...
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The pgffor package allows for-loop style repetition using the following format: \foreach \<cmd> in {1,...,<total>} {% % stuff } Using this as base, the following is probably what you're after: \documentclass{beamer}% http://ctan.org/pkg/beamer \usepackage{graphicx}% http://ctan.org/pkg/graphicx \usepackage{pgffor}% http://ctan.org/pkg/...
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Look, ma! No loops! :) Borrowed from the TeXbook, exercise 21.8 (p. 225). \documentclass{minimal} \usepackage[a4paper,margin=2mm]{geometry} \usepackage{graphicx} \sbox0{% \includegraphics{image}% \kern2mm \vrule width 0pt depth 2mm} \setlength{\parindent}{0pt} \begin{document} \null \cleaders\hbox to\textwidth{\leaders\copy0\hfill}\vfill \end{...
27
To answer the specific question you are asking, here is a complete minimal example. \documentclass{standalone} \usepackage{pgfmath} \begin{document} \def\names{{"Katie","Frank","Laura","Joe"}}% \pgfmathparse{\names[2]}\pgfmathresult \end{document} So, you need to use the pgfmath parser to do the job through \pgfmathparse and then use the result of the ...
26
\documentclass{article} \usepackage{graphicx} \usepackage{pgffor} \def\pdfappendix#1#2{% \foreach \index in {1, ..., #2} {% \includegraphics[scale=0.6]{#1\index.pdf}\par% }} \begin{document} \pdfappendix{pdf/test}{4} \end{document} The above code will the thing you want. However I haven't tested it extensively. I just tested this minimal ...
26
The main loop for comma separated lists in LaTeX3 is \clist_map_inline:nn The first argument is an explicit list, the second argument tells LaTeX what to do with each item. For instance, we want to print an enumerate environment from the items: \documentclass{article} \usepackage{xparse} \ExplSyntaxOn \NewDocumentCommand{\makeenumerate}{ m } { \begin{...
23
How about using a chunk with <<results=tex, echo=FALSE>>=? It will allow you to: (a) paste together the LaTeX code you'd like to run (i.e. 200 \begin{frame} ... \includegraphics ... \end{frame} constructs); and (b) place that constructed text verbatim in the *.tex file produced by Sweave(). For more details, see here. It's a FAQ! <<...
20
You can define recursive macros that call themselves until some termination is found; a solution to your problem can be as follows: \makeatletter % we need to use kernel commands \newcommand{\twoimages}{% \begin{figure}[!htb] \@twoimagesi } \newcommand\@twoimagesi{\@ifnextchar\stopimages{\@twoimagesend}{\@twoimagesii}} \newcommand\@twoimagesii[6]{% \@...
20
My first LaTeX3 answer! Yay! :) The l3clist package has a lot of built-in commands to deal with comma-separated lists. Here's an attempt: \documentclass{article} \usepackage{expl3} \usepackage{xparse} \ExplSyntaxOn \NewDocumentCommand \countItems { m } { \clist_count:N #1 } \NewDocumentCommand \countInlineItems { m } { \clist_count:n {#1} } \...
19
For the sake of completeness, in Luatex: \newcommand{\pdfappendix}[2]{ \directlua{ for index=1,#2 do tex.print("\includegraphics[scale=0.6]{pdf/#1"..index..".pdf}") end}
19
Use a primitive \loop with \repeat and \unless testing. \documentclass[pagenumber=footright, DIV=20, fontsize=16]{scrartcl} \usepackage[automark]{scrlayer-scrpage} \pagestyle{scrheadings} \ihead{} \ofoot[\pagemark]{\pagemark} \chead{} \cfoot[]{} \ohead{} \newcounter{loopcntr} \begin{document} \loop\unless\ifnum\value{loopcntr}=500 \mbox{} \newpage \...
19
18
A loop and a counter: Code \documentclass{article} \makeatletter \newcommand*{\length}[1]{% \@tempcnta\z@ \@for\@tempa:=#1\do{\advance\@tempcnta\@ne}% The length of the list #1 is \the\@tempcnta.% } \makeatother \begin{document} \length{0,1,54,1,3} \def\mylist{0,1,54,1,3} \length\mylist \end{document} Output The length of the list 0,1,54,...
17
I don't think that this is possible. However, in your case the / notations isn't really necessary: \begin{tikzpicture} \foreach \y [count=\i] in {0,0.25,...,1} { \only<\i>{ \draw (0,0) rectangle (1,1); \draw (0,0) -- (1,\y); } } \end{tikzpicture} For more complicated cases, when one variable is dependent on the other via some ...
17
No packages: \documentclass{article} \makeatletter \newcount\my@repeat@count \newcommand{\myrepeat}[2]{% \begingroup \my@repeat@count=\z@ \@whilenum\my@repeat@count<#1\do{#2\advance\my@repeat@count\@ne}% \endgroup } \makeatother \begin{document} \myrepeat{4}{x} \myrepeat{4}{\myrepeat{2}{x}} \end{document} Why the group? It allows nested ...
16
This answer may be more generic than specifically relating to TikZ/PGF. (La)TeX is a macro-based language, so it does not work as expected compared to other languages when dealing with "arrays". For example, while \names[2] should yield Laura where \def\names{Katie, Frank, Laura, Joe} (indexing from 0), (La)TeX considers [2] to have no connection to \...
16
Using the wonderful python.sty package (see github) and some embedded python code, this is very easy: \documentclass{article} \usepackage{python} \usepackage{graphicx} \begin{document} \begin{python} import os directory = "." extension = ".png" files = [file for file in os.listdir(directory) if file.lower().endswith(extension)] for file in files: ...
16
You can use the additional facilities of foreach macro given in the manual by adding pgfmath package too. For some reason, (initially 4) option is not working if TikZ is not fully loaded so you can define it externally. \documentclass{article} \usepackage{pgffor,pgfmath} \begin{document} \def\lastx{4} \foreach \x[count=\xi from 2,remember=\x as \lastx] ...
16
The following code will do what is asked, using the plain TeX construction \loop ... \if ... \repeat: \documentclass{article} \title{The Song That Never Ends} \author{by Norman Martin} \begin{document} \maketitle % \noindent This is the song that never ends. \newline \loop \iftrue Yes, it goes on and on my friends. \newline Some people started ...
15
\documentclass{article} \usepackage{longtable} \newcounter{xyz}\newcounter{uvw} \makeatletter \newtoks\@tabtoks \newcommand\addtabtoks[1]{\@tabtoks\expandafter{\the\@tabtoks#1}} \newcommand*\resettabtoks{\@tabtoks{}} \newcommand*\printtabtoks{\the\@tabtoks} \makeatother \pagestyle{empty} \begin{document} \resettabtoks \loop\ifnum\theuvw<10\relax \...
14
To abort the loop after the current iteration simply \let the internal \iterate macro to \relax. If you want to skip the rest of the loop code you can use a macro defined to \fi\iffalse for this (as Bruno already said). Abort at end of current iteration: \documentclass{article} \begin{document} \newcount\mycount \mycount=1 \loop\ifnum\mycount<13 ...
14
\usepackage{multido} \newcommand\pdfappendix[2]{% \multido{\I=1+1}{#2}{% \includegraphics[scale=0.6]{pdf/#1\I.pdf}}}
14
\documentclass{article} \usepackage{tikz} \begin{document} \begin{tikzpicture} \foreach[count=\i] \txt in {20,18,...,2} \node at (\i,0) {\txt}; \end{tikzpicture} \end{document} Note: It is always possible to cauculate one variable using the other one. Or you can't use ... in pgffor. So you can also use: \begin{tikzpicture} \foreach[evaluate=\y using int(...
14
The syntax for \@for is \@for\cs:=<list>\do{<code>} Here <list> is either a comma separated list of tokens or a macro expanding to such a list. Thus, the calls \@for\next:=abc, def, gh ,ij\do{<code>} and \def\mylist{abc, def, gh ,ij} \@for\next:=\mylist\do{<code>} are equivalent. Notice that LaTeX doesn't really ...
14
There is a package lambda-lists by Alan Jeffrey for "Lists in TeX's mouth". Here's an example in plain TeX: \catcode@=11 \input lambda.sty \catcode`@=12 \tracingmacros=1 % check out the log file afterwards! \def\mylist{\Listize[1, 2 ,3,,4=foo,5,]} \def\myfun#1{do something with #1\def\foo{}} \def\fooDefined?{\ifdefined\foo foo's defined\else foo's ...
Only top voted, non community-wiki answers of a minimum length are eligible | {"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": 0.9706088304519653, "perplexity": 17076.239246955127}, "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-2016-30/segments/1469257828010.15/warc/CC-MAIN-20160723071028-00052-ip-10-185-27-174.ec2.internal.warc.gz"} |
http://en.wikibooks.org/wiki/Real_Analysis/Arc_Length | # Real Analysis/Arc Length
Real Analysis Arc Length
Suppose we have a parametric curve in three dimensions, $f(t)=(x_1(t),x_2(t),x_3(t))$. Of course, it would be required that all three functions be continuous. This essentially defines a curve, since it is a continuous image of the real numbers onto the real 3-space.
Now, we can define the arc length of this curve over an interval. Say the interval is [a,b]. Now divide [a,b] into partitions, $a=a_0, and call this partition P. Take the sum of the distances $|f(a_n)-f(a_{n-1})|$, to get $\sum_{i=1}^n \sqrt{\sum_{j=1}^3 (x_j(a_i)-x_j(a_{i-1}))^2}$, and call this sum L(P). Now, take the supremum of the lengths, $\sup\{L(P)\in R|P$ is a partition$\}$. If this number is finite, we call it a rectifiable curve.
Now we establish a sufficient and necessary condition for a curve in 3-space to be rectifiable (note: this can easily be extended to an n-space through an analogous argument).
Theorem:
A continuous curve in three dimensions is rectifiable if and only if all of its component functions are functions of bounded variation.
Proof:
Theorem:
If a curve f(x) in 3-space is continuously differentiable in all 3 components, then it is rectifiable and the length from f(a) to f(b) is $\int_a^b |f'(x)| dx$.
Proof: | {"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": 0, "img_math": 7, "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": 0.9727864265441895, "perplexity": 822.9661716009605}, "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-2014-23/segments/1406510258086.28/warc/CC-MAIN-20140728011738-00417-ip-10-146-231-18.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/109950/number-of-one-to-one-functions-such-that-fi-neq-i/110183 | # Number of One to One functions such that $f(i)\neq i$
Given the sets $A=\{1,\dots,4\}$ and $B=\{1,\dots,7\}$ how many one to one functions are there from $A$ to $B$ such that $f(i)\neq i$ ?
I used inclusion exclusion to first find the number of one to one functions:
$S_1 = f(a)=f(b) , S_2 = f(a)=f(b)=f(c) , S_3 = f(a)=f(b)=f(c)=f(d)$
$$7^4 - \binom{4}{2}\cdot 7^3 + \binom{4}{3}\cdot 7^2 - \binom{4}{4}\cdot 7^1=532$$
I then repeated using a similar approach for eliminating cases of $f(a)=a$, etc...
$$532 - \binom{4}{1}\cdot6^3 + \binom{4}{2}\cdot5^2 - \binom{4}{3}\cdot4^1 + \binom{4}{4}\cdot 3^0$$
Are my solutions correct?
EDIT
I see that the number of one to one functions is $7\cdot6\cdot5\cdot4=840$ and that makes sense. But I still can't seem to get it to work using inclusion exclusion.
$U$ would be the group of all possible functions, $7^4=2401$.
$S_1 =$ where $f(a)=f(b)$
$S_2 =$ where $f(a)=f(b)$ and $f(c)=f(d)$
$S_3 =$ where $f(a)=f(b)=f(c)$
$S_4 =$ where $f(a)=f(b)=f(c)=f(d)$
-
I think you chose the hard way to do the first part - the number of one to one functions is just $7\times6\times5\times4$ (which isn't $532$). – Gerry Myerson Feb 16 '12 at 10:38
I see what you're saying, but I don't understand why I can't seem to get the inclusion exclusion approach to work. – Robert S. Barnes Feb 16 '12 at 11:00
Check this out en.wikipedia.org/wiki/Derangement – Jernej Feb 16 '12 at 11:40
Notice that you have 6 conditions: $f(a)=f(b)$, $f(a)=f(c)$, $f(a)=f(d)$, $f(b)=f(c)$, $f(b)=f(d)$, and $f(c)=f(d)$.
So the first three terms in the inclusion-exclusion are $$7^4-6\times7^3+{6\choose2}7^2$$ Now the next term is trickier. If the three conditions that hold are $f(a)=f(b)$, $f(a)=f(c)$, and $f(b)=f(c)$, that contributes $7^2$, but if the three conditions are $f(a)=f(b)$, $f(b)=f(c)$, and $f(c)=f(d)$, then the contribution is only $7$. So so far we have $$7^4-6\times7^3+{6\choose2}7^2-4\times7^2-16\times7$$ Now if 4, 5, or 6 conditions hold, the contribution is 7, so you get $$7^4-6\times7^3+{6\choose2}7^2-4\times7^2-16\times7+{6\choose4}7-6\times7+7$$ With any luck, I haven't missed anything, and that comes out to $840$ (and you can see that I wasn't kidding when I said this was the hard way). | {"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": 1, "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": 0.9698771834373474, "perplexity": 172.43346815381867}, "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/1410657132883.65/warc/CC-MAIN-20140914011212-00016-ip-10-196-40-205.us-west-1.compute.internal.warc.gz"} |
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# An atom has a stationary stateE_1=0.00 eV,E_2=2.0 eV and E_3=5.0 eV. What wavelengths are observed in the absorption spectrum and in the emission spectrum of this atom?
Arun Kumar IIT Delhi
7 years ago
$E_{initial}-E_{final}=E_{photon}$
$E_{photon}=hc/\lambda$
Absorption
$1 \to 2,2 \to 3,1 \to 3$
Emission
$3 \to 2,2 \to 1,3 \to 1$
Arun Kumar
IIT Delhi | {"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": 0, "img_math": 0, "codecogs_latex": 4, "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": 0.443560391664505, "perplexity": 28881.16568022556}, "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/1637964362230.18/warc/CC-MAIN-20211202145130-20211202175130-00518.warc.gz"} |
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### Standalone LaTeX editor/renderer for Windows?
Is there any small and simple program (or even library) that can render LaTeX locally as you type? I'm looking for something pretty much like this page, which auto-renders immediately as you type, ... | {"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": 1, "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": 0.9963169097900391, "perplexity": 4252.857209046403}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "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-2020-24/segments/1590348526471.98/warc/CC-MAIN-20200607075929-20200607105929-00458.warc.gz"} |
https://pytorch.org/docs/master/generated/torch.nn.ReLU6.html | # ReLU6¶
class torch.nn.ReLU6(inplace: bool = False)[source]
Applies the element-wise function:
$\text{ReLU6}(x) = \min(\max(0,x), 6)$
Parameters
inplace – can optionally do the operation in-place. Default: False
Shape:
• Input: $(N, *)$ where * means, any number of additional dimensions
• Output: $(N, *)$ , same shape as the input
Examples:
>>> m = nn.ReLU6()
>>> input = torch.randn(2)
>>> output = m(input) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 3, "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": 0.5308864116668701, "perplexity": 21056.752115127805}, "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-2020-45/segments/1603107876307.21/warc/CC-MAIN-20201021093214-20201021123214-00092.warc.gz"} |
https://www.jobilize.com/online/course/2-5-geometric-mean-descriptive-statistics-by-openstax?qcr=www.quizover.com | # 2.5 Geometric mean
Page 1 / 1
The mean (Arithmetic), median and mode are all measures of the “center” of the data, the “average”. They are all in their own way trying to measure the “common” point within the data, that which is “normal”. In the case of the arithmetic mean this is solved by finding the value from which all points are equal linear distances. We can imagine that all the data values are combined through addition and then distributed back to each data point in equal amounts. The sum of all the values is what is redistributed in equal amounts such that the total sum remains the same.
The geometric mean redistributes not the sum of the values but the product of multiplying all the individual values and then redistributing them in equal portions such that the total product remains the same. This can be seen from the formula for the geometric mean, $\stackrel{~}{x}$ : (Pronounced x-tilde)
$\stackrel{~}{x}={\left(\prod _{i=1}^{n}{\pi }_{i}\right)}^{\frac{1}{n}}=\sqrt[n]{{x}_{1}*{x}_{2}\bullet \bullet \bullet {x}_{n}}={\left({x}_{1}*{x}_{2}\bullet \bullet \bullet {x}_{n}\right)}^{\frac{1}{n}}$
where $\pi$ is the mathematical symbol that tells us to multiply all the ${x}_{i}$ numbers in the same way capital Greek sigma tells us to add all the ${x}_{i}$ numbers. Remember that a fractional exponent is calling for the nth root of the number thus an exponent of 1/3 is the cube root of the number.
The geometric mean answers the question, "if all the quantities had the same value, what would that value have to be in order to achieve the same product?” The geometric mean gets its name from the fact that when redistributed in this way the sides form a geometric shape for which all sides have the same length. To see this, take the example of the numbers 10, 51.2 and 8. The geometric mean is the product of multiplying these three numbers together (4,096) and taking the cube root because there are three numbers among which this product is to be distributed. Thus the geometric mean of these three numbers is 16. This describes a cube 16x16x16 and has a volume of 4,096 units.
The geometric mean is relevant in Economics and Finance for dealing with growth: growth of markets, in investment, population and other variables the growth of which there is an interest. Imagine that our box of 4,096 units (perhaps dollars) is the value of an investment after three years and that the investment returns in percents were the three numbers in our example. The geometric mean will provide us with the answer to the question, what is the average rate of return: 16 percent. The arithmetic mean of these three numbers is 23.6 percent. The reason for this difference, 16 versus 23.6, is that the arithmetic mean is additive and thus does not account for the interest on the interest, compound interest, embedded in the investment growth process. The same issue arises when asking for the average rate of growth of a population or sales or market penetration, etc., knowing the annual rates of growth. The formula for the geometric mean rate of return, or any other growth rate, is:
${r}_{s}={\left({x}_{1}*{x}_{2}\bullet \bullet \bullet {x}_{n}\right)}^{\frac{1}{n}}-1$
Manipulating the formula for the geometric mean can also provide a calculation of the average rate of growth between two periods knowing only the initial value ${a}_{0}$ and the ending value ${a}_{n}$ and the number of periods, $n$ . The following formula provides this information:
${\left(\frac{{a}_{n}}{{a}_{0}}\right)}^{\frac{1}{n}}=\stackrel{~}{x}$
Finally, we note that the formula for the geometric mean requires that all numbers be positive, greater than zero. The reason of course is that the root of a negative number is undefined for use outside of mathematical theory. There are ways to avoid this problem however. In the case of rates of return and other simple growth problems we can convert the negative values to meaningful positive equivalent values. Imagine that the annual returns for the past three years are +12%, -8%, and +2%. Using the decimal multiplier equivalents of 1.12, 0.92, and 1.02, allows us to compute a geometric mean of 1.0167. Subtracting 1 from this value gives the geometric mean of +1.67% as a net rate of population growth (or financial return). From this example we can see that the geometric mean provides us with this formula for calculating the geometric (mean) rate of return for a series of annual rates of return:
${r}_{s}=\stackrel{~}{x}-1$
where ${r}_{s}$ is average rate of return and $\stackrel{~}{x}$ is the geometric mean of the returns during some number of time periods. Note that the length of each time period must be the same.
As a general rule one should convert the percent values to its decimal equivalent multiplier. It is important to recognize that when dealing with percents, the geometric mean of percent values does not equal the geometric mean of the decimal multiplier equivalents and it is the decimal multiplier equivalent geometric mean that is relevant.
## Formula review
The Geometric Mean: $\stackrel{~}{x}={\left(\prod _{i=1}^{n}{\pi }_{i}\right)}^{\frac{1}{n}}=\sqrt[n]{{x}_{1}*{x}_{2}\bullet \bullet \bullet {x}_{n}}={\left({x}_{1}*{x}_{2}\bullet \bullet \bullet {x}_{n}\right)}^{\frac{1}{n}}$
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
how did you get the value of 2000N.What calculations are needed to arrive at it
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Got questions? Join the online conversation and get instant answers! | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 14, "mathjax_tag": 0, "mathjax_inline_tex": 0, "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": 0.7848943471908569, "perplexity": 787.9050211713154}, "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-2020-10/segments/1581875143455.25/warc/CC-MAIN-20200217235417-20200218025417-00208.warc.gz"} |
https://de.maplesoft.com/support/help/Maple/view.aspx?path=Groebner/InitialForm | InitialForm - Maple Help
Groebner
InitialForm
compute the initial form of a polynomial
WeightedDegree
compute the weighted degree of a polynomial
Calling Sequence InitialForm(f, T) InitialForm(f, W, V) WeightedDegree(f, W, V)
Parameters
f - polynomial or list or set of polynomials T - ShortMonomialOrder W - list or vector of rational weights V - list of variable names
Description
• The WeightedDegree command computes the weighted degree of a polynomial f with respect to a vector of rational weights W. The output is a rational number, the weighted degree of f, which is similar to the ordinary degree except that each power of a variable ${V}_{i}$ contributes ${W}_{i}$ to the degree of each term, instead of 1.
• The InitialForm command extracts the terms of f with maximal weighted degree. The output is a polynomial. One can also specify a monomial order T instead of a vector of weights, and the first row in a matrix representation for T will be used automatically. See the MatrixOrder help page for more details.
Examples
> $\mathrm{with}\left(\mathrm{Groebner}\right):$
> $f≔{x}^{3}+{x}^{2}y+{y}^{2}$
${f}{≔}{{x}}^{{3}}{+}{{x}}^{{2}}{}{y}{+}{{y}}^{{2}}$ (1)
> $\mathrm{WeightedDegree}\left(f,\left[1,2\right],\left[x,y\right]\right)$
${4}$ (2)
> $\mathrm{InitialForm}\left(f,\left[1,2\right],\left[x,y\right]\right)$
${{x}}^{{2}}{}{y}{+}{{y}}^{{2}}$ (3)
> $M≔\mathrm{MatrixOrder}\left(\mathrm{tdeg}\left(x,y\right),\left[x,y\right]\right)$
${M}{≔}\left[\left[{1}{,}{1}\right]{,}\left[{0}{,}{-1}\right]\right]$ (4)
> $\mathrm{InitialForm}\left(f,\mathrm{tdeg}\left(x,y\right)\right)$
${{x}}^{{3}}{+}{{x}}^{{2}}{}{y}$ (5) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 13, "mathjax_tag": 0, "mathjax_inline_tex": 0, "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": 0.97044837474823, "perplexity": 1259.575555987168}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "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-2022-05/segments/1642320304528.78/warc/CC-MAIN-20220124094120-20220124124120-00369.warc.gz"} |
https://www.bradford-delong.com/2019/02/gunpowder-empire-should-we-generalize-mark-elvins-high-level-equilibrium-trap-hoisted-from-the-archives.html | ## "Gunpowder Empire": Should We Generalize Mark Elvin's High-Level Equilibrium Trap?: Hoisted from the Archives
Hoisted from the Archives: "Gunpowder Empire": Should We Generalize Mark Elvin's High-Level Equilibrium Trap?: OK. Popping the distraction stack again. A chance remark by the extremely sharp Cosma Shalizi when he came through Berkeley has caused me to spend a lot of time meditating upon a passage written by Bob Allen:
Robert Allen (2006): The British Industrial Revolution in Global Perspective: "The different trajectories of the wage-rental ratio created different incentives to mechanize production.... It was not Newtonian science that inclined British inventors and entrepreneurs to seek machines that raised labour productivity but the rising cost of labour... due to... Britain’s success in the global economy... in part the result of state policy... Britain['s] vast and readily worked coal deposits...
...Cost reductions were greatest at British factor prices, so the new technologies were adopted in Britain and not on the continent.... British technology was not cost-effective at continental input prices.... The necessary R&D was profitable in Britain (under British conditions) but unprofitable elsewhere.... Why did the industrial revolution lead to modern economic growth? I have argued that the famous inventions of the British industrial revolution were responses to Britain’s unique economic environment and would not have been developed anywhere else. This is one reason that the Industrial Revolution was British. But why did those inventions matter?... Wouldn’t the French, or the Germans, or the Italians, have produced an industrial revolution by another route? Weren’t there alternative paths to the twentieth century?... In previous occasions when important inventions were made... a one-shot rise in productivity.... The nineteenth century was different–the First Industrial Revolution turned into Modern Economic Growth. Why? Mokyr’s answer is that scientific knowledge increased enough to allow continuous invention. Technological improvement was certainly at the heart of the matter, but... the nineteenth century engineering industry was a spin-off of the coal industry. All three of the developments that raised productivity in the nineteenth century depended on... the steam engine and cheap iron... closely related to coal.... There is no reason to believe that French technology would have led to the engineering industry, the general mechanization of industrial processes, the railway, the steam ship, or the global economy. In other words, there was only one route to the twentieth century–and it went through northern Britain...
But what if not?
Let as start between 1500 and 1750, in the age of the Gunpowder Empires...
That world is, by and large, Malthusian. There are exceptional region-eras in which there is a considerable margin above bare biological subsistence. And the ruling classes are rich, both much richer than the peasants upon whom they rest, and much richer, comparing half-millennium to half-millennium, than their predecessor ruling classes. For their slaves and peasants, not so much, but Cicero lived much better in terms of accessible technology and material comfort than Patroklos, Aaron the Just than Cicero, John of Gaunt than Aaron the Just, Thomas Jefferson than John of Gaunt.
Thus for the bulk of the population, or so it appears to me, for two millennia--at least since the founding of the Han and the Roman Empires--increasing numbers and resource depletion ate up all of the benefits from slowly-advancing technologies. When I try to assess economic growth in the very longest run, I come up with global rates of growth of total factor productivity on the order of 0.02%/year. That is 1%/century. That is enough to support a population growth rate of 7%/century--the doubling of human populations every millennium that we appear to see since 4000 BC.
Looking forward from even as late as 1750, therefore, it is not insane to project that the Gunpowder Empire is in the natural course of events the climax socioecological state of the Sociable Language-Using East African Plains Ape. The notional quartering of farm sizes worldwide from 500 BC to 1500 had been offset by the development of maize, of double-crop wet rice, of the combination of the iron axe and the moldboard plow that could turn northern temperate forests into farms, the domestication of cotton, and the breeding of the merino sheep. People in 1500 were as well fed and clothed as they had been in 500 BC.
But what would have been the next agricultural miracle technologies--besides the potato? You would have needed a number of them to attain continued total factor productivity growth at 0.02%/year to compensate for the further quartering of farm sizes that would have been inevitable had population growth continued and human numbers topped 2 billion in 3500.
And where would the breakthrough to steampower--or even to enough fodder to feed enough draft animals for oxen and horses to replace or even supplement human backs and thighs--to interrupt this Gunpowder-Empire climax socioecology of the Sociable Language-Using East African Plains Ape come from? Heron of Alexandria's aeolipile was 1500 years old. If the Hellenistic, Roman, Byzantine, Abbasid, Tang, Sung, and Ming Eras could not show any signs of a breakthrough to steam, what were the odds some other civilization would have done it had eighteenth-century Britain not been there?
Important questions. Unanswerable questions--at least by me. Not, mind you, that I want to positively and definitively assert that the Gunpowder-Empire is the climax socioecology of the Sociable Language-Using East African Plains Ape in the natural course of events. But I do wonder.
#noted #hoistedfromthearchives #economicgrowth #economichistory #industrialrevolution #robertallen #joelmokyr #highighted | {"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": 0.49496176838874817, "perplexity": 6463.282263794598}, "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-2021-39/segments/1631780053918.46/warc/CC-MAIN-20210916234514-20210917024514-00103.warc.gz"} |
https://www.gamedev.net/forums/topic/324765-problems-with-usb-joystick-on-freebsd/ | # Problems with USB joystick on FreeBSD
This topic is 4728 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
Hi all, I have a fairly plain install of FreeBSD 5.3-RELEASE installed [EDIT: upgraded to 5.4 on advice from xor], and am having problems getting my USB joystick to work. It's a Microsoft Sidewinder Force Feedback 2 Joystick' (from the label on the bottom). It works fine on other systems. I am attempting to use it with two PLib-based games, FlightGear and TORCS. Both games and PLib are freshly installed from a recently CVSup-ed ports tree, and are the latest version according the the web-based ports browser. (plib-1.8.4, FlightGear-0.9.8, torcs-1.2.3.) The joystick is on /dev/uhid0, from dmesg | grep Joystick': uhid0: Microsoft SideWinder Force Feedback 2 Joystick, rev 1.10/a.00, addr 3, iclass 3/0 I've verified that it seems to be connected right; the output from `cat /dev/uhid0 | uuencode -' seems to correspond to the movements and button presses I make on the joystick. js_demo from FlightGear (seems to be a plib example program also) doesn't find any joysticks. However, I've verifed that the USB HID code in plib's jsBSD.cxx seems to be getting compiled. Any ideas? I've searched everywhere I can think of and can't seem to find anything. Thanks, - Pete [Edited by - Pete_ on June 10, 2005 11:26:56 AM]
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Tried updating to 5.4?
##### Share on other sites
Nope, I hadn't, but that's a good idea, although a bit scary. [wink] I'll back up and attempt it now. Wish me luck! (This will be my first upgrade, I just started using FreeBSD a few months ago.)
Thanks,
- Pete
##### Share on other sites
Well, I successfully upgraded to 5.4 (from source, not reinstall), and recompiled plib, flightgear, and torcs. Unfortunatly, they still don't seem to understand my joystick. dmesg output is still the same as with 5.3. Any ideas on what else I could try? [smile]
Thanks,
- Pete
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• 15 | {"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": 0.1737895905971527, "perplexity": 7860.085723032281}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "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-2018-22/segments/1526794864063.9/warc/CC-MAIN-20180521102758-20180521122758-00495.warc.gz"} |
https://tbc-python.fossee.in/convert-notebook/Applied_Physics_by_P_K_Mittal/Chapter_05_Principles_of_Quantum_Mechanics_1.ipynb | Chapter 5:Principles of Quantum Mechanics¶
Example 5.1 , Page no:102¶
In [1]:
import math
from __future__ import division
#given
lambda1=1; #in Angstrom (wavelength)
m=1.67E-27; #in Kg (mass of neutron)
h=6.625E-34; #in J-s (Planck's constant)
e=1.6E-19; #in C (charge of electron)
#calculate
lambda2=lambda1*1E-10; #since lambda is in Angstrom
#Since lambda=h/(m*v)
#Therefore we have
v=h/(m*lambda2); #calculation of velocity
K=m*v**2/2; #calculation of kinetic energy
K1=K/e; #changing unit fro J to eV
#result
print"The velocity is v=",round(v,3),"m/s";
print"The kinetic energy is K=",'%.3E'%K,"J";
print"\t\t =",'%.3E'%K1,"eV";
The velocity is v= 3967.066 m/s
The kinetic energy is K= 1.314E-20 J
= 8.213E-02 eV
Example 5.2 , Page no:103¶
In [2]:
import math
from __future__ import division
#given
K=50; #in eV (Kinetic energy)
m0=9.1E-31; #in Kg (mass of electron)
h=6.625E-34; #in J-s (Planck's constant)
e=1.6E-19; #in C (charge of electron)
#calculate
K=K*e; #changing unit from eV to J
#Since K=m*v^2/2
#Therefore v=sqrt(2*K/m)
#Since lambda=h/(m*v)
#Therefore we have
lambda1=h/math.sqrt(2*m0*K); #calculation of wavelength
lambda2=lambda1*1E10; #changing unit from m to Angstrom
#result
print"The wavelength is =",'%.3E'%lambda1,"m";
print"\t\t =",round(lambda2,3),"Angstrom";
The wavelength is = 1.736E-10 m
= 1.736 Angstrom
Example 5.3 , Page no:104¶
In [3]:
import math
from __future__ import division
#given
E=2000; #in eV (Kinetic energy)
m=9.1E-31; #in Kg (mass of electron)
h=6.625E-34; #in J-s (Planck's constant)
e=1.6E-19; #in C (charge of electron)
#calculate
E=E*e; #changing unit from eV to J
#Since E=m*v^2/2
#Therefore v=sqrt(2*E/m)
#Since lambda=h/(m*v)
#Therefore we have
lambda1=h/math.sqrt(2*m*E); #calculation of wavelength
lambda2=lambda1*1E9; #changing unit from m to nanometer
#result
print"The wavelength is =",'%.3E'%lambda1,"m";
print"\t\t =",round(lambda2,4),"nm";
The wavelength is = 2.745E-11 m
= 0.0275 nm
Example 5.4 , Page no:104¶
In [4]:
import math
from __future__ import division
#given
m_e=9.1E-31; #in Kg (mass of electron)
m_n=1.676E-27; #in Kg (mass of neutron)
h=6.625E-34; #in J-s (Planck's constant)
c=3E8; #in m/s (velocity of light)
#calculate
E_e=m_e*c**2; #rest mass energy of electron
E_n=2*E_e; #given (kinetic energy of neutron)
#Since K=m*v^2/2
#Therefore v=sqrt(2*K/m)
#Since lambda=h/(m*v)
#Therefore we have
lambda1=h/math.sqrt(2*m_n*E_n); #calculation of wavelength
lambda2=lambda1*1E10; #changing unit from m to Angstrom
#result
print"The wavelength is =",'%.3E'%lambda1,"m";
print"\t\t =",'%.3E'%lambda2,"Angstrom";
The wavelength is = 2.827E-14 m
= 2.827E-04 Angstrom
Example 5.5 , Page no:104¶
In [5]:
import math
from __future__ import division
#given
V=1600; #in V (Potential)
#calculate
lambda1=12.27/math.sqrt(V); #calculation of wavelength in Angstrom
#result
print"The wavelength is =",round(lambda1,3),"Angstrom";
print "Note : The answer in the book is wrong "
The wavelength is = 0.307 Angstrom
Note : The answer in the book is wrong
Example 5.6 , Page no:105¶
In [6]:
import math
from __future__ import division
#given
E=1000; #in eV (Kinetic energy of photon)
K=1000; #in eV (Kinetic energy of electron)
m0=9.1E-31; #in Kg (mass of electron)
h=6.6E-34; #in J-s (Planck's constant)
c=3E8; #in m/s (velocity of light)
e=1.6E-19; #in C (charge on electron)
#calculate
E=E*e; #changing unit from eV to J
lambda_p=h*c/E; #For photon E=hc/lambda
lambda_p1=lambda_p*1E10; #changing unit from m to Angstrom
#Since K=m*v^2/2
#Therefore v=sqrt(2*K/m)
#Since lambda=h/(m*v)
#Therefore we have
K=K*e; #changing unit from eV to J
lambda_e=h/math.sqrt(2*m0*K); #calculation of wavelength
lambda_e1=lambda_e*1E10; #changing unit from m to Angstrom
#result
print"For photon,the wavelength is =",'%.3E'%lambda_p,"m";
print"\t\t\t =",round(lambda_p1,1),"Angstrom";
print"For electron,the wavelength is =",'%.3E'%lambda_e,"m";
print"\t\t\t =",round(lambda_e1,2),"Angstrom";
For photon,the wavelength is = 1.238E-09 m
= 12.4 Angstrom
For electron,the wavelength is = 3.868E-11 m
= 0.39 Angstrom
Example 5.7 , Page no:105¶
In [7]:
import math
from __future__ import division
#given
lambda1=1.66*10**-10; #in m (wavelength)
m=9.1*10**-31; #in Kg (mass of electron)
h=6.626*10**-34; #in J-s (Planck's constant)
e=1.6E-19; #in C (charge on electron)
#calculate
#Since lambda=h/(m*v)
#Therefore we have
v=h/(m*lambda1); #calculation of velocity
K=m*v**2/2; #calculation of kinetic energy
K1=K/e; #changing unit from J to eV
#result
print"The velocity of electron is v=",'%.2E'%v,"m/s";
print"The kinetic energy is K=",'%.2E'%K,"J";
print"\t\t =",round(K1,3),"eV";
print "Note: The answer in the book for kinetic energy is wrong "
The velocity of electron is v= 4.39E+06 m/s
The kinetic energy is K= 8.75E-18 J
= 54.714 eV
Note: The answer in the book for kinetic energy is wrong
Example 5.8 , Page no:106¶
In [8]:
import math
from __future__ import division
#given
T=400; #in K (temperature)
m=6.7E-27; #in Kg (mass of He-atom)
h=6.6E-34; #in J-s (Planck's constant)
k=1.376E-23; #in J/degree (Boltzmann constant)
#calculate
#Since lambda=h/(m*v)
#E=mv^2/2;
#Therefore lambda=h/sqrt(2*m*E)
#E=kT
#Therefore lambda=h/sqrt(2*m*k*T)
lambda1=h/math.sqrt(2*m*k*T)
lambda2=lambda1*1E10; #changing unit from m to Angstrom
#result
print"The de-Broglie wavelength of He-atom is =",'%.2E'%lambda1,"m";
print"\t\t\t\t =",round(lambda2,4),"Angstrom";
The de-Broglie wavelength of He-atom is = 7.69E-11 m
= 0.7685 Angstrom
Example 5.9 , Page no:106¶
In [9]:
import math
from __future__ import division
#given
m_e=9.1E-31; #in Kg (mass of electron)
m_p=1.6E-27; #in Kg (mass of proton)
h=6.626E-34; #in J-s (Planck's constant)
c=3E8; #in m/s (velocity of light)
#calculate
E=m_e*c**2; #in J (rest energy of electron)
#Since lambda=h/(m*v)
#E=mv^2/2;
#herefore lambda=h/sqrt(2*m*E)
#Also E=m_e*c^2;
#therefore lambda=h/sqrt(2*m_p*m_e*c^2)
lambda1=h/math.sqrt(2*m_p*m_e*c**2); #calculation of wavelength
lambda2=lambda1*1*10**10; #changing unit from m to Angstrom
#result
print"The de-Broglie wavelength of proton is =",'%.2E'%lambda1,"m";
print"\t\t\t\t =",'%.2E'%lambda2,"Angstrom";
The de-Broglie wavelength of proton is = 4.09E-14 m
= 4.09E-04 Angstrom
Example 5.10 , Page no:106¶
In [10]:
import math
from __future__ import division
#given
V=10000; #in V (Potential)
#calculate
lambda1=12.27/math.sqrt(V); #calculation of wavelength in Angstrom
#result
print"The wavelength is =",round(lambda1,3),"Angstrom";
The wavelength is = 0.123 Angstrom
Example 5.11 , Page no:107¶
In [11]:
import math
from __future__ import division
#given
V=100; #in V (Potential)
n=1; #order of diffraction
d=2.15; #in Angstrom (lattice spacing)
#calculate
lambda1=12.27/math.sqrt(V); #calculation of wavelength in Angstrom
#Since 2*d*sind(theta)=n*lambda
#therefore we have
theta=math.asin(n*lambda1/(2*d)); #calculation of glancing angle
theta1=theta*180/3.14;
#result
print"The wavelength is =",round(lambda1,3),"Angstrom";
print"The glancing angle is =",round(theta1,1),"degree";
print "Note: In question V=100 eV but the solution is using V=100V "
The wavelength is = 1.227 Angstrom
The glancing angle is = 16.6 degree
Note: In question V=100 eV but the solution is using V=100V
Example 5.12 , Page no:107¶
In [12]:
import math
from __future__ import division
#given
V=344; #in V (Potential)
n=1; #order of diffraction
theta=60; #in degree (glancing angle)
#calculate
lambda1=12.27/math.sqrt(V); #calculation of wavelength in Angstrom
#Since 2*d*sind(theta)=n*lambda
#therefore we have
#result
print"The wavelength is =",round(lambda1,3),"Angstrom";
print"The spacing of the crystal is =",round(d,4),"Angstrom";
The wavelength is = 0.662 Angstrom
The spacing of the crystal is = 0.3819 Angstrom
Example 5.13 , Page no:107¶
In [13]:
import math
from __future__ import division
#given
r=0.53*10**-10; #in m (radius of first Bohr orbit)
h=6.6*10**-34; #in J-s (Planck's constant)
m=9.1*10**-31; #in Kg (mass of electron)
n=1; #First Bohr orbit
pi=3.14; #value of pi used in the solution
#calculate
#Since 2*pi*r=n*lambda and lambda=h/(m*v)
#Threfore we have v=h*n/(2*pi*r*m)
v=h*n/(2*pi*r*m); #calculation of velocity
#result
print"The velocity of electron is =",'%.3E'%v,"m/s";
The velocity of electron is = 2.179E+06 m/s
Example 5.14 , Page no:108¶
In [14]:
import math
from __future__ import division
#given
dx=0.2; #in Angstrom (uncertainty in the position)
h=6.6E-34; #in J-s (Planck's constant)
m0=9.1E-31; #in Kg (mass of electron)
pi=3.14; #value of pi used in the solution
#calculate
dx=dx*1E-10; #since dx is in Angstrom
#Since dx*dp=h/4*pi (uncertainty relation)
dp=h/(4*pi*dx); #calculation of uncertainty in the momentum
#since dp=m*dv
dv=dp/m0; #calculation of uncertainty in the velocity
#result
print"The uncertainty in the momentum is dp=",'%.3E'%dp,"Kg-m/";
print"The uncertainty in the velocity is dv=",'%.3E'%dv,"m/s";
The uncertainty in the momentum is dp= 2.627E-24 Kg-m/
The uncertainty in the velocity is dv= 2.887E+06 m/s
Example 5.15 , Page no:108¶
In [15]:
import math
from __future__ import division
#given
m_e=9.1E-31; #in Kg (mass of electron)
m_p=1.67E-27; #in Kg (mass of proton)
dx_p=1; #in nanometer (uncertainty in position of electron)
dx_n=1; #in nanometer (uncertainty in position of proton)
#calculate
#since dp=h/(4*pi*dx)
#since h/(4*pi) is constant and dx is same for electron and proton
#therefor both electron and proton have same uncertainty in the momentum
#since dv=dp/m and dp is same for both
#therefore dv_e/dv_p=m_p/m_e
#therefore
K=m_p/m_e; #ratio of uncertainty in the velocity of electron and proton
#result
print"The ratio of uncertainty in the velocity of electron to that of proton is =",round(K);
The ratio of uncertainty in the velocity of electron to that of proton is = 1835.0
Example 5.16 , Page no:108¶
In [16]:
import math
from __future__ import division
#given
dx=5*10**-15; #in m (radius of nucleus or uncertainty in the position)
h=6.6*10**-34; #in J-s (Planck's constant)
m=1.67E-27; #in Kg (mass of proton)
pi=3.14; #value of pi used in the solution
e=1.6E-19; #in C (charge of electron)
#calculate
#Since dx*dp=h/4*pi (uncertainty relation)
dp=h/(4*pi*dx); #calculation of uncertainty in the momentum
p=dp; #minimum value of momentum to calculate mimimum kinetic energy
K=(p**2)/(2*m); #calculation of minimum kinetic energy of proton
K1=K/e; #changing unit from J to eV
K2=K1/1E6; #changing unit from eV to MeV
#result
print"The minimum uncertainty in the momentum of proton is dp =",'%.3E'%dp,"Kg-m/s";
print"The minimum kinetic energy of proton is K=",'%.3E'%K,"J";
print"\t\t\t\t \t =",'%.3E'%K1,"eV";
print"\t\t\t\t\t =",round(K2,1),"MeV";
The minimum uncertainty in the momentum of proton is dp = 1.051E-20 Kg-m/s
The minimum kinetic energy of proton is K= 3.307E-14 J
= 2.067E+05 eV
= 0.2 MeV
Example 5.17 , Page no:109¶
In [17]:
import math
from __future__ import division
#given
K=1; #in KeV (kinetic energy of electron)
dx=1; #in Angstrom (uncertainty in the position)
h=6.63E-34; #in J-s (Planck's constant)
m=9.1E-31; #in Kg (mass of electron)
pi=3.14; #value of pi used in the solution
e=1.6E-19; #in C (charge of electron)
#calculate
dx=dx*1E-10; #since dx is in Angstrom
#Since dx*dp=h/4*pi (uncertainty relation)
dp=h/(4*pi*dx); #calculation of uncertainty in the momentum
K=K*1E3*1.6E-19; #changing unit from KeV to J
p=math.sqrt(2*m*K); #calculation of momentum
poc=(dp/p)*100; #calculation of percentage of uncertainty
#result
print"The uncertainty in the momentum of electron is dp=",'%.3E'%dp,"Kg-m/s";
print"The momentum of electron is p=",'%.3E'%p,"Kg-m/s";
print"The percentage of uncertainty in the momentum is =",round(poc,1);
The uncertainty in the momentum of electron is dp= 5.279E-25 Kg-m/s
The momentum of electron is p= 1.706E-23 Kg-m/s
The percentage of uncertainty in the momentum is = 3.1
Example 5.18 , Page no:109¶
In [18]:
import math
from __future__ import division
#given
v=6.6E4; #m/s (speed of electron)
poc=0.01; #percentage of uncertainty
h=6.63E-34; #in J-s (Planck's constant)
m=9E-31; #in Kg (mass of electron)
pi=3.14; #value of pi used in the solution
#calculate
p=m*v; #calculation of momentum
dp=(poc/100)*p; #calculation of uncertainty in the momentum
#Since dx*dp=h/4*pi (uncertainty relation)
dx=h/(4*pi*dp); #calculation of uncertainty in the position
#result
print"The momentum of electron is p=",'%.3E'%p,"Kg-m/s";
print"The uncertainty in the momentum of electron is dp=",'%.3E'%dp,"Kg-m/s";
print"The uncertainty in the position of electron is dx=",'%.3E'%dx,"Kg-m/s";
The momentum of electron is p= 5.940E-26 Kg-m/s
The uncertainty in the momentum of electron is dp= 5.940E-30 Kg-m/s
The uncertainty in the position of electron is dx= 8.887E-06 Kg-m/s
Example 5.19 , Page no:111¶
In [19]:
import math
from __future__ import division
#given
lambda1=1; #in Angstrom (wavelength)
pi=3.14; #value of pi used in the solution
dlambda=1E-6; #uncertainty in wavelength
#calculate
lambda2=lambda1*1E-10; #sinc lambda is in Angstrom
#By uncertainty principle, dx*dp>=h/(4*pi) --(1)
#since p=h/lambda -----(2)
#Or p*lambda=h
#diffrentiting this equation
#p*dlambda+lambda*dp=0
#dp=-p*dlambda/lambda ----(3)
#from (2) and (3) dp=-h*dlambda/lambda^2 ---(4)
#from (1) and(4) dx*dlambda>=lambda^2/4*pi
#Or dx=lambda^2/(4*pi*dlambda)
dx=lambda2**2/(4*pi*dlambda); #calculation of uncertainty in the position
#result
print"The uncertainty in the position of X-ray photon is dx=",'%.3E'%dx,"m";
print "Note: wavelength accuracy is given as 1 in 1E8 but in book solution has used 1 in 1E6 "
print " ANSWEER IS WRONG IN THE TEXTBOOK"
The uncertainty in the position of X-ray photon is dx= 7.962E-16 m
Note: wavelength accuracy is given as 1 in 1E8 but in book solution has used 1 in 1E6
ANSWEER IS WRONG IN THE TEXTBOOK
Example 5.20 , Page no:111¶
In [20]:
import math
from __future__ import division
#given
dt=1*10**-8; #in sec (average life time)
pi=3.14; #value of pi used in the solution
#calculate
#Since dE*dt>=h/(4*pi) (uncertainty relation for energy)
#and E=h*v v is the frequency
#therefore we have dv>=1/(4*pi*dt)
dv=1/(4*pi*dt); #calculation of minimum uncertainty in the frequency
#result
print"The minimum uncertainty in the frequency of the photon is dv=",'%.3E'%dv,"sec^-1";
The minimum uncertainty in the frequency of the photon is dv= 7.962E+06 sec^-1
Example 5.21 , Page no:111¶
In [21]:
import math
from __future__ import division
#given
dt=1E-12; #in sec (average life time)
h=6.63E-34; #in J-s (Planck'c constant)
pi=3.14; #value of pi used in the solution
e=1.6*1E-19; #in C (charge of electron)
#calculate
#Since dE*dt>=h/(4*pi) (uncertainty relation for energy)
dE=h/(4*pi*dt); #calculation of minimum uncertainty in the energy
dE1=dE/e; #changing unit from J to eV
#result
print"The uncertainty in the energy of the photon is dE=",'%.3E'%dE,"J";
print"\t\t\t\t\t =",'%.3E'%dE1,"eV";
The uncertainty in the energy of the photon is dE= 5.279E-23 J
= 3.299E-04 eV
Example 5.22 , Page no:111¶
In [22]:
import math
from __future__ import division
#given
dT=2.5E-14; #in sec (average life time)
h=6.63E-34; #in J-s (Planck'c constant)
pi=3.14; #value of pi used in the solution
e=1.6*1E-19; #in C (charge of electron)
#calculate
#Since dE*dt>=h/(4*pi) (uncertainty relation for energy)
dE=h/(4*pi*dT); #calculation of minimum uncertainty in the energy
dE1=dE/e; #changing unit from J to eV
#result
print"The uncertainty in the energy of the photon is dE=",'%.3E'%dE,"J";
print"\t\t\t\t\t =",'%.3E'%dE1,"eV";
The uncertainty in the energy of the photon is dE= 2.111E-21 J
= 1.320E-02 eV
Example 5.23 , Page no:112¶
In [23]:
import math
from __future__ import division
#given
a=2; #in Angstrom (length of the box)
m=9.1E-31; #in Kg (mass of electron)
h=6.626E-34; #in J-s (Planck'c constant)
n2=2; n4=4; #two quantum states
e=1.6*1E-19; #in C (charge of electron)
#calculate
a=a*1E-10; #since a is in Angstrom
#Since E_n=n^2*h^2/(8*m*a^2) (Energy corresponding to nth quantum state)
E2=n2**2*h**2/(8*m*a**2); #calculation of energy corresponding to the 2nd quantum state
E21=E2/e; #changing unit from J to eV
E4=n4**2*h**2/(8*m*a**2); #calculation of energy corresponding to the 4nd quantum state
E41=E4/e; #changing unit from J to eV
#result
print"The energy corresponding to the 2nd quantum state is E2=",'%.3E'%E2,"J";
print"\t\t\t\t\t\t =",'%.3E'%E21,"eV";
print"The energy corresponding to the 4nd quantum state is E4=",'%.3E'%E4,"J";
print"\t\t\t\t\t\t =",'%.3E'%E41,"eV";
The energy corresponding to the 2nd quantum state is E2= 6.031E-18 J
= 3.769E+01 eV
The energy corresponding to the 4nd quantum state is E4= 2.412E-17 J
= 1.508E+02 eV
Example 5.24 , Page no:113¶
In [24]:
import math
from __future__ import division
#given
a=1E-10; #in m (width of the well)
m=9.1E-31; #in Kg (mass of electron)
h=6.626E-34; #in J-s (Planck'c constant)
n1=1; n2=2; n3=3; #ground and first two excited states
e=1.6*1E-19; #in C (charge of electron)
#calculate
#Since E_n=n^2*h^2/(8*m*a^2) (Energy corresponding to nth quantum state)
E1=n1**2*h**2/(8*m*a**2); #calculation of energy corresponding to the Ground state
E11=E1/e; #changing unit from J to eV
E2=n2**2*h**2/(8*m*a**2); #calculation of energy corresponding to the 1st excited state
E21=E2/e; #changing unit from J to eV
E3=n3**2*h**2/(8*m*a**2); #calculation of energy corresponding to the 2nd excited state
E31=E3/e; #changing unit from J to eV
#result
print"The energy corresponding to the ground state is E1=",'%.3E'%E1,"J";
print"\t\t\t\t\t =",'%.3E'%E11,"eV";
print"The energy corresponding to the 1st excited state is E2=",'%.3E'%E2,"";
print"\t\t\t\t\t =",'%.3E'%E21,"eV";
print"The energy corresponding to the 2nd excited state is E3=",'%.3E'%E3,"J";
print"\t\t\t\t\t =",'%.3E'%E31,"eV";
print " There is slight variation in the answer due to round off error"
The energy corresponding to the ground state is E1= 6.031E-18 J
= 3.769E+01 eV
The energy corresponding to the 1st excited state is E2= 2.412E-17
= 1.508E+02 eV
The energy corresponding to the 2nd excited state is E3= 5.428E-17 J
= 3.392E+02 eV
There is slight variation in the answer due to round off error
Example 5.25 , Page no:113¶
In [25]:
import math
from __future__ import division
#given
dx=1E-8; #in m (length of box or uncertainty in the position)
h=6.626E-34; #in J-s (Planck'c constant)
m=9.1E-31; #in Kg (mass of electron)
#calculate
#From uncertainty principle dx*dp=h and dp=m*dv
#therefore we have
dv=h/(m*dx); #calculation of minimum uncertainty in the velocity
dv1=dv*1E-3; #changing unit from m/s to Km/s
#result
print"The minimum uncertainty in the velocity of electron i dv=",'%.3E'%dv,"m/s";
print"\t\t\t\t\t\t =",round(dv1,2),"Km/s";
print "Note: There is slight variation in the answer due to round off error"
The minimum uncertainty in the velocity of electron i dv= 7.281E+04 m/s
= 72.81 Km/s
Note: There is slight variation in the answer due to round off error
Example 5.26 , Page no:113¶
In [26]:
import math
from __future__ import division
#given
a=4E-10; #in m (length of the box)
m=9.1E-31; #in Kg (mass of electron)
h=6.626E-34; #in J-s (Planck'c constant)
n1=1; #ground state
e=1.6*1E-19; #in C (charge of electron)
#calculate
#Since E_n=n^2*h^2/(8*m*a^2) (Energy corresponding to nth quantum state)
E1=n1**2*h**2/(8*m*a**2); #calculation of energy corresponding to the ground state
E11=E1/e; #changing unit from J to eV
#result
print"The minimum energy of electron is E1=",'%.3E'%E1,"J (Note: The answer in the book is wrong due to printing error)";
print"\t\t\t\t =",round(E11,3),"eV";
The minimum energy of electron is E1= 3.769E-19 J (Note: The answer in the book is wrong due to printing error)
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https://arxiv.org/search/?searchtype=author&query=Fournier%2C+D | # Showing 1–26 of 26 results for author: Fournier, D
.
1. arXiv:1805.06141 [pdf, other
Sensitivity kernels for time-distance helioseismology: efficient computation for spherically-symmetric solar models
Abstract: The interpretation of helioseismic measurements, such as wave travel-time, is based on the computation of kernels that give the sensitivity of the measurements to localized changes in the solar interior. These are computed using the ray or the Born approximation. The Born approximation is preferable as it takes finite-wavelength effects into account, but can be computationally expensive. We propos… ▽ More
Submitted 16 May, 2018; originally announced May 2018.
2. arXiv:1804.02311 [pdf, ps, other
Comparison of Travel-Time and Amplitude Measurements for Deep-Focusing Time--Distance Helioseismology
Abstract: The purpose of deep-focusing time--distance helioseismology is to construct seismic measurements that have a high sensitivity to the physical conditions at a desired target point in the solar interior. With this technique, pairs of points on the solar surface are chosen such that acoustic ray paths intersect at this target (focus) point. Considering acoustic waves in a homogeneous medium, we compa… ▽ More
Submitted 22 March, 2018; originally announced April 2018.
Comments: 18 pages, 10 figures
3. arXiv:1710.09456 [pdf
Straightforward measurement of thermal properties of anisotropic materials: the case of Bi2Se3 single crystal
Abstract: We show that by a simple two-steps measurement protocol one can extract the thermal properties of anisotropic insulator materials. We focus on Bi2Se3 single crystal, a layered crystal with individual sheets held together by Van der Waals force, presenting strong heat diffusion anisotropy. Since the shape of the sample does not allow experiments in the perpendicular direction the challenge is to me… ▽ More
Submitted 25 October, 2017; originally announced October 2017.
4. arXiv:1709.02156 [pdf, other
Atmospheric radiation boundary conditions for high frequency waves in time-distance helioseismology
Abstract: The temporal covariance between seismic waves measured at two locations on the solar surface is the fundamental observable in time-distance helioseismology. Above the acoustic cut-off frequency ($\sim$5.3~mHz), waves are not trapped in the solar interior and the covariance function can be used to probe the upper atmosphere. We wish to implement appropriate radiative boundary conditions for computi… ▽ More
Submitted 7 September, 2017; originally announced September 2017.
Journal ref: A&A 608, A109 (2017)
5. arXiv:1707.08566 [pdf, ps, other
Problems in computational helioseismology
Abstract: We discuss current advances in forward and inverse modeling for local helioseismology. We report theoretical uniqueness results, in particular the Novikov-Agaltsov reconstruction algorithm, which is relevant to solving the non-linear inverse problem of time-distance helioseismology (finite amplitude pertubations to the medium). Numerical experiments were conducted to determine the number of freque… ▽ More
Submitted 25 July, 2017; originally announced July 2017.
Comments: Oberwolfach Report, Computational Inverse Problems for Partial Differential Equations, 14 May - 20 May 2017. https://www.mfo.de/occasion/1720/www_view
6. arXiv:1612.08991 [pdf, other
The amplitude of the cross-covariance function of solar oscillations as a diagnostic tool for wave attenuation and geometrical spreading
Abstract: Context. In time-distance helioseismology, wave travel times are measured from the two-point cross-covariance function of solar oscillations and are used to image the solar convection zone in three dimensions. There is, however, also information in the amplitude of the cross-covariance function, for example about seismic wave attenuation. Aims. Here we develop a convenient procedure to measure the… ▽ More
Submitted 28 December, 2016; originally announced December 2016.
Comments: accepted for publication in A&A
Journal ref: A&A 599, A111 (2017)
7. arXiv:1611.01666 [pdf, other
Computational helioseismology in the frequency domain: acoustic waves in axisymmetric solar models with flows
Abstract: Local helioseismology has so far relied on semi-analytical methods to compute the spatial sensitivity of wave travel times to perturbations in the solar interior. These methods are cumbersome and lack flexibility. Here we propose a convenient framework for numerically solving the forward problem of time-distance helioseismology in the frequency domain. The fundamental quantity to be computed is th… ▽ More
Submitted 5 November, 2016; originally announced November 2016.
Comments: Accepted on 3 Nov 2016 for publication in Astronomy and Astrophysics
Journal ref: A&A 600, A35 (2017)
8. arXiv:1503.09084 [pdf, other
Pinsker estimators for local helioseismology
Authors: D. Fournier, L. Gizon, M. Holzke, T. Hohage
Abstract: A major goal of helioseismology is the three-dimensional reconstruction of the three velocity components of convective flows in the solar interior from sets of wave travel-time measurements. For small amplitude flows, the forward problem is described in good approximation by a large system of convolution equations. The input observations are highly noisy random vectors with a known dense covarianc… ▽ More
Submitted 3 February, 2016; v1 submitted 29 March, 2015; originally announced March 2015.
MSC Class: 74G75
Journal ref: Inverse Problems, 2016, 32, 105002
9. arXiv:1406.5335 [pdf, ps, other
Generalization of the noise model for time-distance helioseismology
Abstract: In time-distance helioseismology, information about the solar interior is encoded in measurements of travel times between pairs of points on the solar surface. Travel times are deduced from the cross-covariance of the random wave field. Here we consider travel times and also products of travel times as observables. They contain information about e.g. the statistical properties of convection in the… ▽ More
Submitted 20 June, 2014; originally announced June 2014.
MSC Class: 62M10 (Primary) 60H40 (Secondary)
Journal ref: A&A 567, A137 (2014)
10. arXiv:1403.7152 [pdf
Management of dangerous goods in container terminal with MAS model
Abstract: In a container terminal, many operations occur within the storage area: containers import, containers export and containers shifting. All these operations require the respect of many rules and even laws in order to guarantee the port safety and to prevent risks, especially when hazardous material is concerned. In this paper, we propose a hybrid architecture, using a Cellular Automaton and a Multi-… ▽ More
Submitted 27 March, 2014; originally announced March 2014.
Comments: 8 pages. The 15th International Conference on Harbor, Maritime \& Multimodal Logistics, Athènes : Greece (2013)
11. arXiv:1311.2409 [pdf, other
Application of a Hough search for continuous gravitational waves on data from the 5th LIGO science run
Abstract: We report on an all-sky search for periodic gravitational waves in the frequency range $\mathrm{50-1000 Hz}$ with the first derivative of frequency in the range $-8.9 \times 10^{-10}$ Hz/s to zero in two years of data collected during LIGO's fifth science run. Our results employ a Hough transform technique, introducing a $χ^2$ test and analysis of coincidences between the signal levels in years 1… ▽ More
Submitted 17 March, 2014; v1 submitted 11 November, 2013; originally announced November 2013.
Comments: Accepted in Classical and Quantum Gravity. Science summary of results available at http://www.ligo.org/science/Publication-S5CWHough/index.php
Report number: LIGO Document P1300071
12. arXiv:1201.4681 [pdf, ps, other
Performance of the LHC, ATLAS and CMS in 2011
Authors: Daniel Fournier
Abstract: The path taken by the LHC team to reach 3.6 10$^{33}$ cm$^{-2}$ s$^{-1}$ instantaneous luminosity, and to deliver 5.6 fb$^{-1}$ per experiment is summarized. The main performances of the two experiments are highlighted, in particular the way they managed to cope with the already high level of "pile-up". Selected Standard Model and top physics results are given, and the status of the limits on the… ▽ More
Submitted 23 January, 2012; originally announced January 2012.
Comments: Presented at the 2011 Hadron Collider Physics symposium (HCP-2011), Paris, France, November 14-18 2011, 12 pages, 26 figures
13. arXiv:1111.2673 [pdf, other
Surface-enhanced charge-density-wave instability in underdoped Bi2201
Abstract: Neutron and x-ray scattering experiments have provided mounting evidence for spin and charge ordering phenomena in underdoped cuprates. These range from early work on stripe correlations in Nd-LSCO to the latest discovery of charge-density-waves in YBCO. Both phenomena are characterized by a pronounced dependence on doping, temperature, and an externally applied magnetic field. Here we show that t… ▽ More
Submitted 9 May, 2013; v1 submitted 11 November, 2011; originally announced November 2011.
Comments: A high-resolution version with supplementary material can be found at http://www.physics.ubc.ca/~quantmat/ARPES/PUBLICATIONS/Articles/Bi2201_PG_Q2.pdf
Journal ref: Nature Communications 4, 1977 (2013)
14. arXiv:1105.1862 [pdf, ps, other
Reply to "Comment on arXiv:1012.1484v1 Structural origin of apparent Fermi surface pockets in angle-resolved photoemission of Bi_2Sr_{2-x}La_xCuO_{6+δ} by King et al."
Abstract: Reply to comment by Zhou et al. (arXiv:1012.3602) on arXiv:1012.1484 / Phys. Rev. Lett. 106, 127005 (2011). ▽ More
Submitted 10 May, 2011; originally announced May 2011.
Comments: 2 pages
15. arXiv:1012.4305 [pdf, ps, other
A Layer Correlation technique for pion energy calibration at the 2004 ATLAS Combined Beam Test
Authors: E. Abat, J. M. Abdallah, T. N. Addy, P. Adragna, M. Aharrouche, A. Ahmad, T. P. A. Akesson, M. Aleksa, C. Alexa, K. Anderson, A. Andreazza, F. Anghinolfi, A. Antonaki, G. Arabidze, E. Arik, T. Atkinson, J. Baines, O. K. Baker, D. Banfi, S. Baron, A. J. Barr, R. Beccherle, H. P. Beck, B. Belhorma, P. J. Bell , et al. (460 additional authors not shown)
Abstract: A new method for calibrating the hadron response of a segmented calorimeter is developed and successfully applied to beam test data. It is based on a principal component analysis of energy deposits in the calorimeter layers, exploiting longitudinal shower development information to improve the measured energy resolution. Corrections for invisible hadronic energy and energy lost in dead material in… ▽ More
Submitted 12 May, 2011; v1 submitted 20 December, 2010; originally announced December 2010.
Comments: 36 pages, 12 figures, accepted by JINST
Report number: ATL-COM-CAL-2010-006
Journal ref: JINST 6 (2011) P06001
16. arXiv:1012.1484 [pdf, other
Structural origin of apparent Fermi surface pockets in angle-resolved photoemission of Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+δ}$
Abstract: We observe apparent hole pockets in the Fermi surfaces of single-layer Bi-based cuprate superconductors from angle-resolved photoemission (ARPES). From detailed low-energy electron diffraction measurements and an analysis of the ARPES polarization-dependence, we show that these pockets are not intrinsic, but arise from multiple overlapping superstructure replicas of the main and shadow bands. We f… ▽ More
Submitted 7 December, 2010; originally announced December 2010.
Comments: 5 pages, 4 figures
Journal ref: Phys. Rev. Lett. 106, 127005 (2011)
17. arXiv:1007.4027 [pdf, other
Loss of nodal quasiparticle integrity in underdoped YBa2Cu3O6+x
Abstract: Arguably the most intriguing aspect of the physics of cuprates is the close proximity between the record high-Tc superconductivity (HTSC) and the antiferromagnetic charge-transfer insulating state driven by Mott-like electron correlations. These are responsible for the intimate connection between high and low-energy scale physics, and their key role in the mechanism of HTSC was conjectured very ea… ▽ More
Submitted 22 July, 2010; originally announced July 2010.
Comments: Nature Physics, in press. A high-resolution version can be found at http://www.physics.ubc.ca/~quantmat/ARPES/PUBLICATIONS/Articles/YBCO_Z.pdf
Journal ref: Nature Physics 6, 905 (2010)
18. arXiv:0905.2609 [pdf, ps, other
Mixed pairing symmetry in κ-(BEDT-TTF)_2 X organic superconductors from ultrasonic velocity measurements
Abstract: Discontinuities in elastic constants are detected at the superconducting transition of layered organic conductors κ-(BEDT-TTF)_{2}X by longitudinal and transverse ultrasonic velocity measurements. Symmetry arguments show that discontinuities in shear elastic constants can be explained in the orthorhombic compound only if the superconducting order parameter has a mixed character that can be of tw… ▽ More
Submitted 15 May, 2009; originally announced May 2009.
Comments: 5 pages, LaTeX,3 figures
Journal ref: Phys. Rev. B 80, 220511 (2009)
19. arXiv:0901.0512 [pdf
Expected Performance of the ATLAS Experiment - Detector, Trigger and Physics
Authors: The ATLAS Collaboration, G. Aad, E. Abat, B. Abbott, J. Abdallah, A. A. Abdelalim, A. Abdesselam, O. Abdinov, B. Abi, M. Abolins, H. Abramowicz, B. S. Acharya, D. L. Adams, T. N. Addy, C. Adorisio, P. Adragna, T. Adye, J. A. Aguilar-Saavedra, M. Aharrouche, S. P. Ahlen, F. Ahles, A. Ahmad, H. Ahmed, G. Aielli, T. Akdogan , et al. (2587 additional authors not shown)
Abstract: A detailed study is presented of the expected performance of the ATLAS detector. The reconstruction of tracks, leptons, photons, missing energy and jets is investigated, together with the performance of b-tagging and the trigger. The physics potential for a variety of interesting physics processes, within the Standard Model and beyond, is examined. The study comprises a series of notes based on… ▽ More
Submitted 14 August, 2009; v1 submitted 28 December, 2008; originally announced January 2009.
20. arXiv:0806.2578 [pdf
Probing thermal waves on the free surface of various media: Surface Fluctuation Specular Reflection Spectroscopy
Abstract: Thermal motion gives rise to fluctuations in free surfaces; the propagation of the thermally excited waves on such surfaces depends on the mechanical properties of the medium. Their measurement can therefore provide information on those properties. We have developed an optical tool to probe the thermally excited waves on free surfaces: Surface Fluctuation Specular Reflection (SFSR) spectroscopy.… ▽ More
Submitted 16 June, 2008; originally announced June 2008.
21. arXiv:0709.1094 [pdf, ps, other
Response Uniformity of the ATLAS Liquid Argon Electromagnetic Calorimeter
Authors: M. Aharrouche, J. Colas, L. Di Ciaccio, M. El Kacimi, O. Gaumer, M. Gouanere, D. Goujdami, R. Lafaye, S. Laplace, C. Le Maner, L. Neukermans, P. Perrodo, L. Poggioli, D. Prieur, H. Przysiezniak, G. Sauvage, I. Wingerter-Seez, R. Zitoun, F. Lanni, L. Lu, H. Ma, S. Rajago palan, H. Takai, A. Belymam, D. Benchekroun , et al. (77 additional authors not shown)
Abstract: The construction of the ATLAS electromagnetic liquid argon calorimeter modules is completed and all the modules are assembled and inserted in the cryostats. During the production period four barrel and three endcap modules were exposed to test beams in order to assess their performance, ascertain the production quality and reproducibility, and to scrutinize the complete energy reconstruction cha… ▽ More
Submitted 7 September, 2007; originally announced September 2007.
Comments: Accepted by NIM A
Journal ref: Nucl.Instrum.Meth.A582:429-455,2007
22. arXiv:cond-mat/0612431 [pdf, ps, other
Competition between magnetism and superconductivity in the organic metal $κ$-[BEDT-TTF]$_2$Cu[N(CN)$_2$]Br
Abstract: Ultrasonic velocity and attenuation measurements on the quasi-two-dimensional organic conductor $κ$-[BEDT-TTF]$_2$Cu[N(CN)$_2$]Br give the first determination of the coexistence zone of the antiferromagnetic and superconducting phases which extends deep in the metallic part of the pressure-temperature phase diagram of these salts. This zone is identified from a precise control of the ordering in… ▽ More
Submitted 16 December, 2006; originally announced December 2006.
23. arXiv:physics/0605127 [pdf
Luminosity measurement at ATLAS - development, construction and test of scintillating fibre prototype detectors
Abstract: We are reporting about a scintillating fibre tracker which is proposed for the precise determination of the absolute luminosity of the CERN LHC at interaction point 1 where the ATLAS experiment is located. The detector needs to track protons elastically scattered under micro-rad angles in direct vicinity to the LHC beam. It is based on square shaped scintillating plastic fibres read out by multi… ▽ More
Submitted 16 May, 2006; originally announced May 2006.
Journal ref: Nucl.Instrum.Meth.A568:588-600,2006
24. arXiv:cond-mat/0209536 [pdf, ps, other
Mott Transition, Compressibility Divergence and P-T Phase Diagram of Layered Organic Superconductors: An Ultrasonic Investigation
Authors: D. Fournier, M. Poirier, M. Castonguay, K. Truong
Abstract: The phase diagram of the organic superconductor $κ$-(BEDT-TTF)$_2$Cu[N(CN)$_2$Cl has been investigated by ultrasonic velocity measurements under helium gas pressure. Different phase transitions were identified trough several elastic anomalies characterized from isobaric and isothermal sweeps. Our data reveal two crossover lines that end on the critical point terminating the first-order Mott tran… ▽ More
Submitted 23 September, 2002; originally announced September 2002.
Comments: 4 pages, 5 figures
25. arXiv:hep-lat/9903020 [pdf, ps, other
Periodic vacuum and particles in two dimensions
Abstract: Different dynamical symmetry breaking patterns are explored for the two dimensional phi4 model with higher order derivative terms. The one-loop saddle point expansion predicts a rather involved phase structure and a new Gaussian critical line. This vacuum structure is corroborated by the Monte Carlo method, as well. Analogies with the structure of solids, the density wave phases and the effects… ▽ More
Submitted 5 December, 1999; v1 submitted 11 March, 1999; originally announced March 1999.
Comments: Final version, additional references and the proof of reflection positivity added, 41 pages, 16 figures
Journal ref: Phys.Rev. D61 (2000) 065008
26. arXiv:hep-ex/9409003 [pdf, ps, other
Determination of the branching ratios $Γ(K_L \to 3 π^0) / Γ(K_L \to π^+ π^- π^0)$ and $Γ(K_L \to 3 π^0) / Γ(K_L \to πe ν)$
Authors: A. Kreutz, M. Holder, M. Rost, R. Werthenbach, K. J. Peach, H. Blümer, R. Heinz, K. Kleinknecht, P. Mayer, B. Panzer, B. Renk, H. Rohrer, A. Wagner, E. Augé, D. Fournier, L. Iconomidou-Fayard, O. Perdereau, A. C. Schaffer, L. Serin, L. Bertanza, A. Bigi, P. Calafiura, M. Calvetti, R. Carosi, R. Casali , et al. (5 additional authors not shown)
Abstract: Improved branching ratios were measured for the $K_L \to 3 π^0$ decay in a neutral beam at the CERN SPS with the NA31 detector: $Γ(K_L \to 3 π^0) / Γ(K_L \to π^+ π^- π^0) = 1.611 \pm 0.037$ and $Γ(K_L \to 3 π^0) / Γ(K_L \to πe ν) = 0.545 \pm 0.010$. From the first number an upper limit for $ΔI =5/2$ and $ΔI = 7/2$ transitions in neutral kaon decay is derived. Using older results for the Ke3/… ▽ More
Submitted 21 September, 1994; originally announced September 1994.
Journal ref: Z.Phys.C65:67-74,1995 | {"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": 0.7719660997390747, "perplexity": 8357.314853928361}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "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-2018-22/segments/1526794868248.78/warc/CC-MAIN-20180527111631-20180527131631-00063.warc.gz"} |
http://thecollegepanda.com/12-classic-sat-math-questions/ | # 12 Classic SAT Math Questions You Must Know How to Solve
Most tests you take in your average math class are straightforward and obvious. As long as you’ve studied the concepts, you know what to do when you encounter a problem. You know what to expect.
On the SAT, however, even great math students may not know where to begin. Even if you know all the concepts, you won’t always know which ones to apply and how. To answer the tough questions, you need a combination of experience and a willingness to try things out.
I always warn new students that the SAT Math is unlike most tests they’ve done in school. But when they ask how it’s different, I usually have to resort to vague terms like “problem-solving, creative thinking, and word questions.”
So here are 12 SAT questions that illustrate frequently tested ideas and ways of thinking that go beyond standard school material. I’ve included questions across all test topics—from algebra to geometry to logic.
All of them are tough! Try them on your own. Hints are available at the bottom and answers will be available in another post.
#### The Questions
1. If $$2^x + 2^x + 2^x + 2^x = 2^{16}$$, what is the value of $$x$$?
2. The lengths of two sides of a triangle are $$4$$ and $$9$$. What is the greatest possible integer length of the third side?
3. A car traveled $$10$$ miles at an average speed of $$30$$ miles per hour and then traveled the next $$10$$ miles at an average speed of $$50$$ miles per hour. What was the average speed, in miles per hour, of the car for the $$20$$ miles?
4. The average (arithmetic mean) age of a group of $$15$$ teachers is $$40$$ years. If $$6$$ additional teachers are added to the group, then the average age of the $$21$$ managers is $$44$$ years. What is the average age of the $$6$$ additional managers?
5. Let the function $$f$$ be defined by $$f(x) = x^2 + 18$$. If $$a$$ is a positive number such that $$f(2a) = 3f(a)$$, what is the value of $$a$$?
6. A tech company bought a number of computers for its employees: $$6$$ costing $$1600$$ each, $$4$$ costing $$1200$$ each, and $$y$$ costing $$900$$ each, where $$y$$ is a positive odd integer. If the median price for all the exercise machines purchased by the fitness center was $$1200,$$ what is the greatest possible value of $$y$$?
7. The coordinates $$(x, y)$$ of each point on the circle above satisfy the equation $$x^2 + y^2 = 25$$. Line $$l$$ is tangent to the circle at point $$C$$. If the $$x$$-coordinate of point $$C$$ is $$3$$, what is the slope of $$l?$$
8. What is the length of $$CD$$ in the figure above?
A) $$4$$
B) $$4\sqrt{2}$$
C) $$6$$
D) $$6\sqrt{2}$$
9. If $$0\leq a \leq b$$ and $$(a + b)^2 – (a-b)^2 \geq 9$$, what is the least possible value of $$b$$?
10. In acute triangle $$ABC$$, the measure of angle $$A$$ is equal to $$2x^\circ + 20^\circ$$ and the measure of angle $$B$$ is equal to $$x^\circ + 46^\circ$$. If $$\sin\angle A = \cos\angle B$$, what is the value of $$x$$?
11. $f(t) = 800(1,000)^{\frac{t}{27}}$ The function $$f$$ above represents the current total population of sand sharks off the coast of Greenland $$t$$ years after 1980. To the nearest year, how many years did (or will) it take for the population to be 10 times larger than it was in 1980?
12. In order to fulfill a prescription for 200 milliliters (mL) of a medication at a 55% solution, a pharmacist must mix $$x$$ mL of a 40% solution with $$y$$ mL of a 60% solution. What is the value of $$x$$?
#### Hints
1. The answer is NOT 4. You can only add exponents when the terms are being multiplied. Think about how many $$2^{x}$$s there are.
2. The answer is NOT “as big as you want.” Look up the Triangle Inequality Theorem.
3. The answer is NOT 40. This is much harder than that. Remember that
distance $$=$$ rate $$\times$$ time
4. Think about the sums of all the ages.
5. No hint for this one. If you truly understand functions, you’ll get this.
6. No hint for this one either.
7. What is the slope of $$\overline{OC}$$?
8. Know your special triangles (30-60-90 and 45-45-90).
9. First, expand (FOIL) and simply. Now how do the values of $$a$$ and $$b$$ affect each other when they are increased or decreased?
10. You’ll have to use a certain trigonometric identity.
11. Use the fact that $$1,000 = 10^3$$
12. 200 milliliters of a 55% solution contains how many milliliters of the actual medication?
I’m not going to post answer explanations (at least for now), because I want you to figure these out on your own. What I will do is post the answers, so you can check/review your work.
1. $$14$$
2. $$12$$
3. $$\frac{75}{2}$$ or $$37.5$$
4. $$54$$
5. $$6$$
6. $$9$$
7. $$-\frac{3}{4}$$
8. $$D$$
9. $$\frac{3}{2}$$ or $$1.5$$
10. $$8$$
11. $$9$$
12. $$50$$
### 22 thoughts on “12 Classic SAT Math Questions You Must Know How to Solve”
1. Maroosh Qazi says:
Please can you explain 1,5, 9 to me in brief. For q1 I keep getting 16/3. For q 9 I only got so far in the working out as ab> or =9/4 But did not know what to do after that.
But it is q 5 where i am really stuck and don’t even know where to start. I am sure I am forgetting some really simple rule but please can you guide me. Your help as always will be much appreciated!!
2. Maroosh Qazi says:
I don’t know where my earlier post has gone about the problems I had with q1), q5), q9).
Q 5 i didn’t even know where to start and i am sure I am making some really obvious mistake but please help me.
For Q1 I keep getting 16/3 and for Q9) I got up to the point when ab> or = to 2.25. But then after that I can’t figure out what to do. Please help me with these. I will remain very grateful.
3. perfectscorer says:
Hi Maroosh.
For #1, think of it as replacing the $$2^x$$ with any variable. To illustrate I’ll use $$y$$. That way it’s just $$y+y+y+y$$. You can simply rewrite that as $$4(y)$$. If you now replace the $$y$$ with the original $$2^x$$, you’ll have $$4(2^x) = 16$$. Divide both sides by $$4$$. So $$(2^x)=4$$. Therefore $$x=2$$.
For #5, the key is to take each “a” function one at a time. $$f(2a) = (2a)^2 + 18 = 4a^2 + 18$$. Next, $$3f(a)=3 (a^2 + 18) = 3a^2 + 54$$. Next step is to set the two “a” functions equal to each other. $$4a^2+54 = 3a^2 + 54$$. You should get $$a^2 = 36$$. And voila! $$a = 6$$.
For #9, I didn’t do this as Phu suggested. The easiest method is to notice that the least possible value of $$b$$ occurs when $$b$$ is equal to $$a$$. With this in mind just write $$b$$ in place of $$a$$. That is, $$(b+b)^2-(b-b)^2$$. When simplified, you should get $$(2b)^2$$ which is $$4b^2$$. So $$4b^2$$ is greater than or equal to $$9$$. Again the least possible value of $$b$$ occurs when that inequality is equal to $$9$$. So just write the equation: $$4b^2=9$$. Jingle bells! You get $$b = \dfrac{3}{2}$$.
I hope my explanations were of help Maroosh. Cheers and goodluck!
• Jingle Bells! I love it!
Fantastic explanations. I’ve edited your responses with math type.
• Maroosh Qazi says:
Thank you for posting such amazing help in the form of these questions. Please make more pages on your website with problems like these. i have finished all your worksheets now i think. Please also respond to my email when i sent to you regarding answers for the 12 tricky sat questions problems for which you said we should email you for answers. Thank you very much
• delfi says:
can’t the least possible value for b be 1? Or if a is negative, -1?
• Maroosh Qazi says:
Thank you very much. I am very grateful. Yes your explanation of each question’s solution was very clear and I finally understood why I was getting these questions repeatedly wrong. Sorry for not replying sooner but I have just checked my email. The quicker method you suggested for q 9 also works really well. Thank you once again
4. perfectscorer says:
Ooopsies I made a typo in my explanation for #1. The correct solution is $$4(2^x) = 2^{16}$$. $$4$$ is just $$2^2$$. So really you have $$(2^2)(2^x) = 2^{16}$$. Divide both sides by $$(2^2)$$. You get $$(2^x) = 2^{14}$$. Recall that dividing exponents with the same bases just means keeping the same base and subtracting the bottom exponent from the top. That’s how I got $$2^{(16-2)} = 2^{14}$$. So $$x= 14$$.
Cheers!
• Jones says:
No perfect score for you that time! That was more than a typo since you didn’t check against your own answer key 😉
5. ami says:
Hi, I got most of them but I just need help with 1 problem. I can’t understand problem 7.
6. Waania says:
7) slope = change in x / change in y
change in x – given = 3
change in y ( plug in) = 3^2 + y^2 = 25 —-> y=4
— So slope = -3/4. (Since line is sloping downwards, the gradient is negative so there will a minus sign attached to the slope. )
• Kristian says:
Actually, the slope is rise/ run or (change of y)/ (change of x). using the equation given, we find that x=3 (given) and y= 4. So the slope of the line is 4/3; but that is not the slope we are looking for. 4/3 is the slope of the line that runs from the origin to point C. We are looking for the line that is tangent to the circle and perpendicular to the line from the origin to point C. So the slope of the tangent line will be the negative reciprocal of the slope 4/3. There for the answer is -3/4. Perpendicular slopes are always negative reciprocals of each other.
7. g says:
For number 2, I’m getting 10. Why is the answer 12?
• Jing says:
because the sum of the lengths of any two sides of a triangle must be greater than the third side.
check out this website: regentsprep.org/regents/math/geometry/GP7/LTriIneq.htm
hope it helped! Good luck on your SAT!
8. Emily says:
How do you do #6?
Shouldn’t the answer for Q.6 be 8?
• Nope. First of all, the question stipulates that y is a positive odd integer. If it helps, list all the numbers out.
10. sat mom says:
I am having problems with #1 in one area you have the answer as 14 in an email reply you have answer as 2
Please show me how to do the problem
11. pf says:
cant do number 3,5 and 9
12. pf says:
can anyone show me how to do 3? i know its probably ez but im just not getting it
• It takes 1/3 of an hour to travel the first 10 miles. Then it takes 1/5 of an hour to travel the last 10 miles. That’s 1/3 + 1/5 = 8/15 of an hour. To get the average speed, divide the total distance by the total time: 20/(8/15) = 37.5
13. nairah says:
can someone please explain number 12? | {"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": 1, "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": 0.7585541605949402, "perplexity": 405.06744171505557}, "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-2017-51/segments/1512948513512.31/warc/CC-MAIN-20171211125234-20171211145234-00370.warc.gz"} |
http://eprint.iacr.org/2015/1073 | ## Cryptology ePrint Archive: Report 2015/1073
Practical Witness Encryption for Algebraic Languages Or How to Encrypt Under Groth-Sahai Proofs
David Derler and Daniel Slamanig
Abstract: Witness encryption (WE) is a recent powerful encryption paradigm, which allows to encrypt a message using the description of a hard problem (a word in an NP-language) and someone who knows a solution to this problem (a witness) is able to efficiently decrypt the ciphertext. Recent work thereby focuses on constructing WE for NP complete languages (and thus NP). While this rich expressiveness allows flexibility w.r.t. applications, it makes existing instantiations impractical. Thus, it is interesting to study practical variants of WE schemes for subsets of NP that are still expressive enough for many cryptographic applications.
We show that such WE schemes can be generically constructed from smooth projective hash functions (SPHFs). In terms of concrete instantiations of SPHFs (and thus WE), we target languages of statements proven in the popular Groth-Sahai (GS) non-interactive witness-indistinguishable and zero-knowledge proof framework. This allows us to provide a novel way to encrypt. In particular, encryption is with respect to a GS proof and efficient decryption can only be done by the respective prover. The so obtained constructions are entirely practical. To illustrate our techniques, we apply them in context of privacy-preserving exchange of information.
Category / Keywords: public-key cryptography / witness encryption, smooth projective hash functions, Groth-Sahai proofs, encryption, privacy
Date: received 4 Nov 2015, last revised 3 Feb 2017
Contact author: david derler at iaik tugraz at
Available format(s): PDF | BibTeX Citation
Short URL: ia.cr/2015/1073
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https://rd.springer.com/chapter/10.1007/978-0-85729-198-1_5 | # Document Image Analysis
Part of the Advances in Pattern Recognition book series (ACVPR)
## Abstract
One of the main distinguishing features of a document is its layout, as determined by the organization of, and reciprocal relationships among, the single components that make it up. For many tasks, one can afford to work at the level of single pages, since the various pages in multi-page documents are usually sufficiently unrelated to be processed separately. This chapter discusses the processing steps that lead from the original document to the identification of its class and of the role played by its single components according to their geometrical aspect: digitization (if any), low-level pre-processing for documents in the form of images or expressed in term of very elementary layout components, optical character recognition, layout analysis and document image understanding. This results in two distinct but related structures for a document (the layout and the logical one), for which suitable representation techniques are introduced as well.
## Keywords
Basic Block Document Image Text Line Optical Character Recognition Intellectual Property Right
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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http://theojf.blogspot.com/2006/12/poisson-brackets-and-scalar-fields.html | ## 05 December 2006
### Poisson brackets and scalar fields
Today's* ODEs class was rather amazing. In standard Yasha style, the topics darted around (he once explained that "It is impossible to be lost in my class. Because topic changes every two minutes, so if you are lost, you won't be lost."): a taste of KM theory, a dash of geodesics on ellipsoids, and a little infinite-dimensional Hamiltonian systems.
It is this last discussion that I found rather mind-blowing. We did not say anything new; rather, we started defining what will eventually give us the quantum behavior of fields, from an entirely classical viewpoint.
Consider one PDE \d u(x,t)/\d t = F(u), where u is a function and F is some map from functions to functions. Let's say, for example, that we're interested in complex functions on the circle: u:S\to\C is what the physicists would call a (complex) scalar field. Let V be the set of all scalar fields; I will not be precise what conditions I want (presumably some smoothness conditions, say complex-analytic, and perhaps some convergence conditions, for instance that the square integral converges. I will call maps from V \to \R "functionals" and those from V \to V "operators"; V is a (complex) vector space, so it makes sense to talk about (real-, complex-, anti-) linear functionals and operators. For instance, \d/\dx is a linear operator; (1/2\pi) \int_0^{2\pi} -- g(x) dx is a linear functional. (I will from now on write \int for \int_0^{2\pi}; consistent with half of mathematics, the volume of the circle is 2\pi.) Rather than thinking of my problem as a PDE, I should think of it as an ODE in this infinite-dimensional space.
Imposing analyticity, etc., conditions on V curtails the freedom of functions: the value of a function at a point largely determines the value at nearby points. We ought to perform a change-of-basis so that we can better tell functions apart: let's assume, for instance, that each function has a Fourier expansion
u(x) = u_0 + \sum p_k e^{-ikx} + q_k e^{ikx}
(Given, of course, by
u_0 = (1/2\pi) \int u(x) dx; p_k = (1/2\pi) \int u(x) e^{ikx} dx; q_k = (1/2\pi) \int u(x) e^{-ikx} dx.)
((Sometime soon I will figure out what I believe to be the proper class of functions with which to do physics. One might hope for (complex) holomorphic, or for complex analytic, or for real C^\infty, or real analytic, or maybe just real integrable. But the Fourier transformation is vital to modern physics, and none of these is particularly the class of things with natural Fourier transforms, because I often end up with \delta functions. I ought to study the Fourier transform a bit more, because I don't understand something basic: it seems that the \delta functions supply a continuum of basis states, whereas the fourier modes are countable. But every delta function can fourier-transform, and modulo convergence this should be a change-of-basis. Perhaps it has something to do with the fact that the Fourier transform doesn't care about individual values of functions, just their integrals. We really ought to pick a class of "functions" so that Fourier really is a legitimate "change-of-basis" in the appropriate infinite-dimensional sense.))
Then our manifold V is, more or less, an odd-dimensional manifold. We cannot hope to put a symplectic structure on it. On the other hand, the ps and qs so naturally line up that we really want to write down \omega = \sum a_k dp_k \wedge dq_k, and we can do so on the even-dimensional subspace \{u_0 = 0\}. (The coefficients a_k have yet to be determined; \omega is a symplectic form for any choice of a_k, and we should choose judiciously to match other physics. Throughout this entry, I eschew the Einstein summation conventions.)
Well, almost. This \omega is almost certainly not going to converge if you feed it most pairs of functions, and I think that to restrict our functions to those that have Fourier expansions that converge rapidly enough is premature, especially since we have yet to determine the a_k. Rather, Yasha suggests, we should discuss the Poisson bracket, which is what really controls physics.
How so? you ask. And what, fundamentally, is a Poisson bracket? Consider our original Poisson bracket \{F,G\} = \omega(X_G,X_F), where X_F is defined by \omega(X_F,-) = dF(-). Then unwrapping definitions gives that \{F,G\} = dF(X_G) = X_G[F], where on the RHS I'm treating X_G as a differential operator. Our Poisson bracket knows exactly the information needed: given a Hamiltonian H, the flow is generated by the vector field X_H = \{-,H\}.
In general, a Poisson bracket is any bracket \{,\} satisfying
(a) Bilinearity (for now \R-linear; perhaps we will ask for \C-linear soon?)
(b) Anti-symmetry and Jacobi (i.e. \{,\} is a Lie bracket)
(c) It behaves as a (first-order) differential operator in each variable: \{FG,H\} = F\{G,H\} + \{F,H\}G.
Condition (c) guarantees that a Poisson bracket never cares about overall constants in F, etc.: \{F,G\} depends only on dF and dG. Symplectic forms, being non-degenerate, are dual to antisymmetric _0^2-tensors (two raised indices), and Poisson brackets are exactly of this form. But Poisson brackets need not be nondegenerate to give us physics. Indeed, the Poisson bracket as described is plenty to define a vector field to be the "derivative" of each function. (Not quite the gradient, but an antisymmetric version of one.) And this is what's needed.
So, to describe the physics of our system, it suffices to pick an appropriate Poisson bracket. Returning now to the system we were originally interested in, of scalar fields on the circle, our Hamiltonians should be functionals of u(x). Let's assume that every functional (at least all the physical ones) can be written in Taylor expansion as polynomials in p_k and q_k. Then to define the Poisson bracket, and continuing to ignore issues of convergence, it suffices to define the brackets between our various coefficients p_k, q_l, and u_0. Given \omega = \sum a_k p_k \wedge q_k (on our subspace of u_0=0), we get \{p_k,q_k\} = a_k^{-1}, and all other brackets are 0.
What would be nice now is to find some physical reason to pick particular a_k, or to even motivate a Poisson bracket of this form at all. Perhaps you vaguely recall a physicists telling you that the Hamiltonian density functional for free scalar fields should look something like h(u(x)) = 1/2 (u^2 + m^2 u'^2), where u'(x) = du/dx. Then the Hamiltonian would be the integral of this: H(u) = \int_0^{2\pi} h(u(x)) dx = u_0^2/2 + \sum_{k=1}^\infty (1-m^2k^2) p_k q_k. With the Poisson bracket given, we can solve this explicitly: p_k(t) = p_k(t=0) e^{(m^2k^2-1) a_k t} and q_k(t) = q_k(t=0) e^{(1-m^2k^2) a_k t}. But this doesn't particularly match physical expectations --- why, for m^2 small and positive and a_k positive, should we expect fields to tend to develop lots of p_k oscillation for large k and lots of q_k oscillation for small k, and for the rest of the oscillation to die?
I'll come back to this kind of physical justification, and perhaps argue my way to a Hamiltonian and a Poisson bracket from the other direction, later. First, I want to explain why Yasha likes this set-up, via mathematical, rather than physical, elegance.
Many interesting Hamiltonians, Yasha observes, are of forms similar to the one I considered in the previous example: the functional H(u) is defined as the integral of some density functional h(x,u(x),u'(x),...). Let's consider this case. Yasha, in fact, uses a particularly restricted case: isotropy is easy (no x dependence), but Yasha also says no derivatives: h = h(u). Then H(u) = (1/2\pi) \int h(u(x)) dx
Then what happens? Well, \dot{q_k} = \{H,q_k\} = a_k \dH/\dp_k = (1/2\pi) \int a_k \dh/\dp_k, and \dot{p_k} = (-1/2\pi) \int a_k \dh/\dq_k/. Plugging these into \dot{u}(x) = \sum \dot{p_k} e^{ikx} + \dot{q_k} e^{-ikx} gives
\dot{u}(x) = (1/2\pi) \int \sum [-a_k \dh/\dq_k e^{ikx} + a_k \dh/\dp_k e^{-ikx}].
Can we recognize this as anything simpler? Recall the chain rule: \dh/\du = \sum (\dh/\dq_k \dq_k/\du + \dh/\dp_k \dp_k/\du). Then, since q_k = (1/2\pi) \int e^{ikx} u(x) dx, we see that \dq_k/\du(x) = (1/2\pi) e^{ikx}. So we see that
h'(u)(x) = \dh/\du(x) = (1/2\pi) \sum [ \dh/\dq_k e^{ikx} + \dh/\dp_k e^{-ikx} ]
This isn't quite what we want, because we have opposite signs on the two a_k. But if we differentiate h'(u) with respect to x, we get
\d/\dx [h'(u)(x)] = (1/2\pi) \sum [ ik \dh/\dq_k e^{ikx} + -ik \dh/\dp_k e^{-ikx} ]
And so, if we pick a_k = k, we see that
\dot{u}(x) = i \d/\dx [h'(u)]
I've been a bit sloppy with this calculation, and you may have trouble following the factors of 2\pi. In particular, I write \int, when I probably should have written \int_{y=0}^{2\pi} dy. But then I would have had to keep track of what's a function of what. Anyway, somewhere in here there's a delta-function, and the formula is correct.
Yasha doesn't do this calculation, preferring one a bit more general and rigorous, which I will sketch:
He observes that since we're a vector space, we can identify points and tangent vectors. Then what are the cotangent vectors? Our vector space of functions has a natural dot product: <u,v> = (1/2\pi) \int_0^{2\pi} u(x) v(x) dx; where now I'm thinking of u and v not as points but as tangent vectors at 0. So to each vector u(x) I can identify the linear functional (1/2\pi) \int u(x) -- dx, which Yasha calls \delta u. Then, knowing that he's chosen {p_k,q_k} = k, Yasha guesses a Poisson bracket:
P(\delta u,\delta v) = (1/2\pi i) \int u v' dx
Recalling the expressions for p_k and q_k as functions of u, we can recognize dp_k = \delta[e^{-ikx}] and dq_k = \delta[e^{ikx}]. Then we can check whether P is the proper Poisson bracket (really the tensor form, eating the derivatives of the functions we would feed into \{,\}) by evaluating it on our ps and qs:
\{p_k,q_k\} = P(e^{-ikx},e^{ikx}) = (1/2\pi i) int e^{-ikx} ik e^{ikx} dx = k; all other brackets are 0, and P is antisymmetric by integration by parts, so must be correct.
Then if F and G are two (real- or complex-valued) functionals on our space of scalar fields, what is their bracket \{F,G\}(u)? Let's say that F and G have the nice form F(u) = (1/2\pi) int f(u(x)) dx (and G is similar). Then \{F,G\} = P(dF,dG) ... what is dF? Well, it's the linear part of F. If \epsilon v is a small change in u, then
(1/\epsilon) (F(u + \elpsilon v) - F(u)) = (1/2\pi) \int f'(u(x)) v(x) dx
where f'(u) is the functional derivative of f with respect to u. So we can recognize dF(u) as \delta[f'(u)], and conclude that
\{F,G\}(u) = (1/2\pi i) \int (f'(u)) (g'(u))' dx
where on the second multiplicand, the inside prime is w.r.t. u, and the outside is w.r.t. x.
Then \dot(u)? Well, for any function(al) F(u), we have \dot{F} = \{H,F\}. u is not a functional, of course, but it is a vector of functionals: u(y) = (1/2\pi) \int u(x) 2\pi \delta(x-y) dx. So du(y) is the covector field (in x) given by \delta[2\pi \delta(x-y)]. (And I'm unfortunately using \delta for too many things, because I want it is an operator and as a Dirac delta function.) So, all in all,
\dot{u}(y) = -\{u(y),H\} = (-1/2\pi i) \int 2\pi \delta(x-y) (h'(u))' dx = i d/dx [h'(u)].
I would like to complete my discussion of scalar fields from entirely a different direction. Given a unit circle, I'd like to describe the propagation of "free scalar fields" around the circle, where now I'm thinking of these as some sort of wave. Remembering very little physics, I can imagine two different interesting dynamics. Either all waves move the same speed, regardless of their shape, or waves propagate at different speeds, with the "high-energy" ones moving faster.
Let's write down some differential equations and see what happens. I'm interested in \dot{u} = some functional of u. Of course, we should demand some isotropy, so x should not appear explicitly. What are the effects of different terms? Keeping everything linear — I want free field propagation, so everything should superimpose — we could ask about \dot{u} = cu, for constant c, but this is boring: the value of the field at a point never cares what the value is ant neighboring points. (Indeed, the whole field evolves by multiplication by e^{ct}. If, for instance, c=i, then sure, different "modes" move at different "speeds", but this is the wrong analysis, since really the whole field is just rotating by some time-varying phase.)
More interesting is if \dot{u} = -u', say. Then expanding u(x) = \sum_{-\infty}^\infty u_k e^{ikx}, we can solve and conclude that \dot{u_k} = -ik u_k, and \dot{u(x)} = u(x-t). So this is what happens if waves travel all at constant velocity.
But let's say that the kinds of waves we care about are surface waves. For instance, we might have a taught string, and waves are small oscillations. Then really physics should act to even out curvatures: we should expect an upwards pull on any point where the field has positive curvature. If we don't remember freshman mechanics, we might write down \dot{u} = u'', which gives us u_k(t) = e^{-k^2 t} u_k(0). This isn't bad: different modes move with velocity proportional to t. It's not quite perfect, though, because really it's the force in that direction, not the derivative, so really we should have acceleration \ddot{u} = u''. Then we get back our original waves, except we have left-movers and right-movers. (More generally, we can add a mass term, and get H(u) = (1/2\pi) \int (1/2) [\dot{u}^2 - (u')^2 + m^2 u^2] = 1/2 \sum_{-\infty}^\infty [\dot{u_k}\dot{u_{-k}} + (k^2 + m^2) u_k u_{-k}], and the modes really do move at different velocities.)
Anyway, the point is that I really do expect, in this world, to have 2\infty total dimensions: \Z worth of "position" coordinates u_k and \Z momentum coordinates, not the \Z/2 of each that Yasha was considering. By just inventing conjugate momentum coordinates v_k to position coordinates u_k, we can get, for the free field, such simple equations of motion as \dot{u_k} = v_{-k} and \dot{v_k} = (k^2+m^2) u_{-k}.
So why does every quantum field theory course start quantizing the (real) scalar field by expanding in Fourier modes and imposing a nontrivial bracket between the coefficients? Because the (free) equations of motion, not the original setup, demand relationships between the fourier modes of u and \dot{u}, and the nontrivial bracket is between u and \dot{u}.
Perhaps next time I will venture into the realm of quantum mechanics. I'd really like to understand how the classical Poisson bracket becomes the quantum Lie bracket, and where the hell that i\hbar comes from. First, of course, I will have to talk more about sets, Hilbert spaces, and the like, and I'll probably stay finite-dimensional for a while. Eventually, of course, I want to describe Feynman diagrams, and tie them back to the Penrose birdtracks and the tensors that started this series of entries.
That is, of course, if I ever get that far. I tend to be distracted by other time-consuming tasks: I am only a few hours of work away from being done applying to graduate schools.
*Of course, I started this entry a few weeks ago. | {"extraction_info": {"found_math": false, "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": 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": 0.9585840702056885, "perplexity": 1408.0000437726726}, "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-2014-49/segments/1416400380464.40/warc/CC-MAIN-20141119123300-00259-ip-10-235-23-156.ec2.internal.warc.gz"} |
https://www.lpsm.paris/smile/publication.php?titre=Foutel-Rodier2019Kingman'scoalescent | # SMILE
## Kingman's coalescent with erosion
### 2019
Consider the Markov process taking values in the partitions of $\mathbb{N}$ such that each pair of blocks merges at rate one, and each integer is eroded, i.e., becomes a singleton block, at rate $d$. This is a special case of exchangeable fragmentation-coalescence process, called Kingman's coalescent with erosion. We provide a new construction of the stationary distribution of this process as a sample from a standard flow of bridges. This allows us to give a representation of the asymptotic frequencies of this stationary distribution in terms of a sequence of hierarchically independent diffusions. Moreover, we introduce a new process called Kingman's coalescent with immigration, where pairs of blocks coalesce at rate one, and new blocks of size one immigrate at rate $d$. By coupling Kingman's coalescents with erosion and with immigration, we are able to show that the size of a block chosen uniformly at random from the stationary distribution of the restriction of Kingman's coalescent with erosion to $\{1, \dots, n\}$ converges to the total progeny of a critical binary branching process.
# Bibtex
@article{FRLS2019KingmanErosion,
author = {Foutel-Rodier, F{\'e}lix and Lambert, Amaury and Schertzer, Emmanuel},
title = {Kingman's coalescent with erosion},
journal = {arXiv:1907.05845},
eprint = {arXiv:1907.05845},
year = {2019},
url = {https://arxiv.org/abs/1907.05845}
}
View the PDF. | {"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": 0.9585531949996948, "perplexity": 766.3244970576416}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "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-2019-35/segments/1566027314696.33/warc/CC-MAIN-20190819073232-20190819095232-00529.warc.gz"} |
https://brilliant.org/problems/basics-7/ | # Basics
Calculus Level 2
$$\displaystyle \int (3x-4)^{3}dx = ?$$
If your answer comes as $$\frac{1}{a}(3x-4)^{b}+C$$. Submit it as $$a+b$$.
Note: Here $$C$$ is Constant of integration.
× | {"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": 1, "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": 0.7851498126983643, "perplexity": 6269.950311517354}, "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-2017-43/segments/1508187824931.84/warc/CC-MAIN-20171022003552-20171022023552-00183.warc.gz"} |
https://blogs.scientificamerican.com/history-of-geology/the-expanding-earth/ | The prevailing geological model of the early 19th century was characterized by an almost static earth, maybe slowly cooling and shrinking, until the molten interior would eventually be completely frozen and solidified. However at the beginning of the 20th century collected evidence suggested that earth´s crust was quite more mobile - both in horizontal and vertical directions - than previously thought.
In 1956 Laszlo Egyed, professor at the Geophysical Institute of the Eötvös-University in Budapest, based on variations of the sea level in the geological past, proposed that earth was slowly and constantly growing! According to his reconstruction todays continents are the remains of the ancient crust of a smaller planet, surrounded by younger rocks generated along fractures at the Mid-Ocean-Ridges. He explained the supposed increasing volume of our planet by modifications of mineral phases in the earth´s interior, as minerals are known to change the crystal-structure in relation to changing heat and pressure. An even stranger explanation was suggested by German physicist Pascual Jordan in 1966 - the expanding earth was imputable to the general dilatation of the space-time continuum.
Most work on the Expanding Earth/Growing Earth hypothesis was done by the German engineer Klaus Vogel, famous for his elaborate globes with the continents fitting on a 20% smaller earth.
Influenced by Vogel´s globes, the Australian geologist Samuel Warren Carey (1912-2002) will become one of the most eminent supporters of the Expanding Earth Hypothesis.
Fig.1. S. Warren Carey and Klaus Vogel discussing an Expanding Earth globe (image from CAREY 1988, it is believed that the use of low-resolution images qualifies as fair use under United States copyright law).
The complex geology of New Guinea convinced Carey that complex movements of earth's crust were necessary to explain the structural geology of mountains. He developed a model with horizontal movements along the Mid Ocean Ridges and transform faults, but stated that "Subduction is a mythos!" He then explained vertical movements as superficial features of very complicated moving cone structures, reaching down to the earth´s core.
However the Expanding Earth hypothesis failed and fails to provide a convincing mechanism to explain the supposed increase of earth´s mass or volume over time. Also simple measurements of the circumference of earth with satellites, as even Carey admitted, could disprove or prove an increase in the radius of earth. Modern satellite measurements are accurate enough to show the movements of earth´s plates as proposed by Alfred Wegener in 1912, however failed to find any real evidence for an expanding earth, except in the internet...
Bibliography:
CAREY, S.W: (1988): Theories of the Earth and Universe: a History of Dogma in the Earth Sciences. Stanford: 419
OLDROYD, D.R. (2007): Die Biography der Erde. zur Wissenschaftsgeschichte der Geologie. Zweitausendeins-Verlag: 518 | {"extraction_info": {"found_math": false, "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": 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": 0.8060013651847839, "perplexity": 3663.8931465032683}, "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-2017-09/segments/1487501171043.28/warc/CC-MAIN-20170219104611-00410-ip-10-171-10-108.ec2.internal.warc.gz"} |
https://openmdao.org/newdocs/versions/latest/_srcdocs/packages/solvers.linear/linear_block_jac.html | # linear_block_jac.py¶
Define the LinearBlockJac class.
class openmdao.solvers.linear.linear_block_jac.LinearBlockJac(**kwargs)[source]
Bases: openmdao.solvers.solver.BlockLinearSolver
Linear block Jacobi solver.
Parameters
**kwargsdict
Options dictionary.
SOLVER = 'LN: LNBJ'
__init__(**kwargs)
Initialize attributes.
Add a recorder to the solver’s RecordingManager.
Parameters
recorder<CaseRecorder>
A recorder instance to be added to RecManager.
cleanup()
Clean up resources prior to exit.
does_recursive_applies()
Return True.
Block linear solvers make recursive apply_linear calls.
Returns
bool
True if solver makes recursive apply_linear calls on its subsystems.
get_reports_dir()
Get the path to the directory where the report files should go.
If it doesn’t exist, it will be created.
Returns
str
The path to the directory where reports should be written.
property msginfo
Return info to prepend to messages.
Returns
str
Info to prepend to messages.
record_iteration(**kwargs)
Record an iteration of the current Solver.
Parameters
**kwargsdict
Keyword arguments (used for abs and rel error).
solve(mode, rel_systems=None)
Run the solver.
Parameters
modestr
‘fwd’ or ‘rev’.
rel_systemsset of str
Set of names of relevant systems based on the current linear solve. | {"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": 0.2638898491859436, "perplexity": 20499.748701632925}, "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-2022-49/segments/1669446711637.64/warc/CC-MAIN-20221210005738-20221210035738-00034.warc.gz"} |
https://www.gamedev.net/forums/topic/569143-opengl-rotation-help/ | # OpenGL openGL rotation help
This topic is 3012 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
greeting, I'm currently a bit stuck on rotation's and its doing my head in as it should be relatively simply, but essentially i need an object i have to face a known point in space...its up orientation is not important just that it turns to face this point in space. I'm also using vectors, so i dont have any matrices holding and information on the objects current transformation. any help would be awesome cheers
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So you're looking for a rotation that transforms the look vector from its initial direction (i.e. where it points to when the object is not rotated) to its target direction (i.e. pointing towards the aimed location). If these 2 vectors are distinct, then you can use the cross-product to compute the normal of the plane of rotation and the dot-product to compute the angle between them. Then you have an axis/angle rotation representation which can be converted into any other rotation representation.
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okay i just attempted something in code and it didnt work out....okay...so. Your advice makes perfect sense
rotationAxis = CurrentLookVec X DesiredLookVec;
float angle =
CurrentLookVec X DesiredLookVec/ CurrentLookVec.mag * DesiredLookVec.mag;
this give me me the angle and the axis to rotate about...but i'm using glRotatef();
how do i get openGL to rotate about an axis i define?
EDIT: at the moment this is how im trying to calculate the rotation
glPushMatrix( ); Fvector look = Wanderer->get_pEntityVelocity( ) - Wanderer->get_pEntityPosition( ); float angleX = look.y/sqrtf(((look.y * look.y) + (look.z * look.z))); angleX = acosf(angleX); float angleY = look.x/sqrtf(((look.x * look.x) + (look.z * look.z))); angleY = acosf(angleY); glTranslatef( 0, 0, 0 ); glRotatef( RAD_TO_DEG( angleX ),1,0,0 ); glRotatef( RAD_TO_DEG( angleY ),0,1,0 ); glTranslatef( Wanderer->get_pEntityPosition( ).x, Wanderer->get_pEntityPosition( ).y, Wanderer->get_pEntityPosition( ).z ); glColor3f( 0,1,0 ); glutSolidCone( 1,2,20,20 ); glPopMatrix( );
[Edited by - homojedi on April 23, 2010 6:50:06 AM]
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glRotate(angle,axisX,axisY,axisZ);
That is how you get to rotate on an arbitrary axis.
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so....would i do this?
rotationAxis = CurrentLookVec X DesiredLookVec;
float angle =
CurrentLookVec . DesiredLookVec/ CurrentLookVec.mag * DesiredLookVec.mag;
glrotate(angle,rotationAxis.x,rotationAxis .y,rotationAxis.z);
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Quote:
Original post by homojediso....would i do this?rotationAxis = CurrentLookVec X DesiredLookVec;float angle = CurrentLookVec . DesiredLookVec/ CurrentLookVec.mag * DesiredLookVec.mag;glrotate(angle,rotationAxis.x,rotationAxis .y,rotationAxis.z);
In principal: Yes. But there are 2 caveats. You may have overseen them or neglected beliberately, I don't know, so I tell you:
Let i be the initial look vector and d the desired one.
Then
a := i x d
gives the unnormalized axis of rotation. You can normalize it yourself
a / |a|
but when used as glRotate's x, y, z values, OpenGL will normalize the axis anyway.
Further, the angle between the both vectors is
β := acos( ( i . d ) / ( |i| * |d| )
which has to be converted to degrees, of course, before handed over to glRotate.
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https://community.plm.automation.siemens.com/t5/NX-Design-Forum/Radial-dimension-in-drafting/td-p/425151 | Cancel
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Pioneer
Hi,
I am trying to figure out how to drag the radial dimension arrow and change th orientation from the elbow but in NX it seems difficult to do that. Every time I drag the arrow it changes the length not the angle/orientation. I know in solid edge you can manually drag the dimension arrow in whatever orientation you want but I am having trouble doing the same in NX.
Thanks.
Dag
16 REPLIES
# Re: Radial dimension in drafting
Siemens Honored Contributor
Are you in dimension edit/create mode, or are you just dragging the dimension on the drawing sheet?
Regards, Ben
# Re: Radial dimension in drafting
Pioneer
Just trying to drag them . I am not in edit mode. Here is a pic.
# Re: Radial dimension in drafting
Pioneer
The pic didn't attach in the previous post.
# Re: Radial dimension in drafting
Siemens Honored Contributor
Are these dimensions from imported data (e.g., imported DXF/DWG)?
# Re: Radial dimension in drafting
Pioneer
The drawing is made from imported solid model if that is what you meant.
# Re: Radial dimension in drafting
Siemens Honored Contributor
So the line I've highlighted red below can only be made longer? You cannot change it's angle, to say the green lines?
# Re: Radial dimension in drafting
Pioneer
No. The moment I try to change the angle or shorten the length it lengthens the same line and also lengthen the horizontal line. I cannot seem to manipulate the two lines individually from the elbow.
# Re: Radial dimension in drafting
Siemens Honored Contributor
Can you upload an example part file?
# Re: Radial dimension in drafting
Pioneer
I am having trouble uploading a part file. I get this error. "The contents of the attachment doesn't match its file type". If possible can you upload a simple part with radial dimensioning in draft and I can try to compare the setting. I am not sure whether my setting is wrong or NX doesn't have the capability to easily move around radial dimensions unlike solid edge. | {"extraction_info": {"found_math": false, "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": 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": 0.8913375735282898, "perplexity": 2652.421262184737}, "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-2018-47/segments/1542039742970.12/warc/CC-MAIN-20181116025123-20181116050231-00010.warc.gz"} |
https://doc.cgal.org/5.0.2/Manual/preliminaries.html | CGAL 5.0.2 - Manual
General Information
The chapter explains some basic features of CGAL such as thread safety, code deprecation, checking of pre- and postconditions and altering the failure behavior, and how to control inlining.
These concepts are further developed in the Developer Manual.
Namespace CGAL
All names introduced by CGAL, especially those documented in these manuals, are in a namespace called CGAL, which is in global scope. A user can either qualify names from CGAL by adding CGAL::, e.g., CGAL::Point_2< CGAL::Exact_predicates_inexact_constructions_kernel >, make a single name from CGAL visible in a scope via a using statement, e.g., using CGAL::Point_2;, and then use this name unqualified in this scope, or even make all names from namespace CGAL visible in a scope with using namespace CGAL;. The latter, however, is likely to give raise to name conflicts and is therefore not recommended.
CGAL is progressively being made thread-safe. The guidelines which are followed are:
• it should be possible to use different objects in different threads at the same time (of the same type or not),
• it is not safe to access the same object from different threads at the same time, unless otherwise specified in the class documentation.
If the macro CGAL_HAS_THREADS is not defined, then CGAL assumes it can use any thread-unsafe code (such as static variables). By default, this macro is not defined, unless BOOST_HAS_THREADS or _OPENMP is defined. It is possible to force its definition on the command line, and it is possible to prevent its default definition by setting CGAL_HAS_NO_THREADS from the command line.
C++14 Support
After being based on the C++ standard released in 1998 (and later refined in 2003) for a long time, CGAL is now based on a newer major version of the standard, C++14.
Functor Return Types
CGAL functors support the result_of protocol. If a functor F has the same return type across all overloads of operator(), the nested type F::result_type is defined to be that type. Otherwise the return type of calling the functor with an argument of type Arg can be accessed through CGAL::cpp11::result_of<F(Arg)>::type .
Checks
Much of the CGAL code contains assert statements for preconditions, and postconditions of functions as well as in the code. These assertions can be switched on and off per package and the user can change the error behaviour. For details see Section Checks of Chapter Chapter_STL_Extensions_for_CGAL.
Compile-time Flags to Control Inlining
Making functions inlined can, at times, improve the efficiency of your code. However this is not always the case and it can differ for a single function depending on the application in which it is used. Thus CGAL defines a set of compile-time macros that can be used to control whether certain functions are designated as inlined functions or not. The following table lists the macros and their default values, which are set in one of the CGAL include files.
Macro Name Default
CGAL_KERNEL_INLINE inline
CGAL_KERNEL_MEDIUM_INLINE
CGAL_KERNEL_LARGE_INLINE
CGAL_MEDIUM_INLINE inline
CGAL_LARGE_INLINE
CGAL_HUGE_INLINE
If you wish to change the value of one or more of these macros, you can simply give it a new value when compiling. For example, to make functions that use the macro CGAL_KERNEL_MEDIUM_INLINE inline functions, you should set the value of this macro to inline instead of the default blank.
Note that setting inline manually is very fragile, especially in a template context. It is usually better to let the compiler select by himself which functions should be inlined or not. | {"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": 0.485080748796463, "perplexity": 1409.0421650223182}, "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-2021-49/segments/1637964358786.67/warc/CC-MAIN-20211129164711-20211129194711-00566.warc.gz"} |
http://stats.stackexchange.com/questions/5414/pitfalls-of-linear-mixed-models/5417 | # Pitfalls of linear mixed models
What are some of the main pitfalls of using linear mixed-effects models? What are the most important things to test/watch out for in assessing the appropriateness of your model? When comparing models of the same dataset, what are the most important things to look for?
-
This is a good question.
Here are some common pitfalls:
1. Using standard likelihood theory, we may derive a test to compare two nested hypotheses, $H_0$ and $H_1$, by computing the likelihood ratio test statistic. The null distribution of this test statistic is approximately chi-squared with degrees of freedom equal to difference in the dimensions of the two parameters spaces. Unfortunately, this test is only approximate and requires several assumptions. One crucial assumption is that the parameters under the null are not on the boundary of the parameter space. Since we are often interested in testing hypotheses about the random effects that take the form: $$H_0: \sigma^2=0$$ This a real concern. The way to get around this problem is using REML. But still, the p-values will tend to be larger than they should be. This means that if you observe a significant effect using the χ2 approximation, you can be fairly confident that it is actually significant. Small, but not significant, p-values might spur one to use more accurate, but time-consuming, bootstrap methods.
2. Comparing fixed effects: If you plan to use the likelihood ratio test to compare two nested models that differ only in their fixed effects, you cannot use the REML estimation method. The reason is that REML estimates the random effects by considering linear combinations of the data that remove the fixed effects. If these fixed effects are changed, the likelihoods of the two models will not be directly comparable.
3. P-values: The p-values generated by the likelihood ratio test for fixed effects are approximate and unfortunately tend to be too small, thereby sometimes overstating the importance of some effects. We may use nonparametric bootstrap methods to find more accurate p-values for the likelihood ratio test.
4. There are other concerns about p-values for the fixed effects test which are highlighted by Dr. Doug Bates [here].
I am sure other members of the forum will have better answers.
Source: Extending linear models with R -- Dr. Julain Faraway.
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The common pitfall which I see is the ignoring the variance of random effects. If it is large compared to residual variance or variance of dependent variable, the fit usually looks nice, but only because random effects account for all the variance. But since the graph of actual vs predicted looks nice you are inclined to think that your model is good.
Everything falls apart when such model is used for predicting new data. Usually then you can use only fixed effects and the fit can be very poor.
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http://math.stackexchange.com/users/58802/pgmath | # PGMath
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# 8 Questions
4 $\mathbb{Z}$ as a free product of two groups 4 Diffeomorphisms between factors in diffeomorphic product manifolds 2 Decomposition of a quotient group into products 2 Existence of a Lie subgroup 1 Sectional curvature of orbits generated by an isometric action
# 79 Reputation
+5 Sectional curvature of orbits generated by an isometric action +20 $\mathbb{Z}$ as a free product of two groups +20 Diffeomorphisms between factors in diffeomorphic product manifolds +5 Decomposition of a quotient group into products
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# 11 Tags
0 differential-geometry × 3 0 combinatorics 0 lie-algebras × 2 0 reference-request 0 lie-groups × 2 0 semi-riemannian-geometry 0 group-theory × 2 0 abstract-algebra 0 graph-theory × 2 0 geometry
# 2 Accounts
Mathematics 79 rep 5 MathOverflow 21 rep 3 | {"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": 0.3332536220550537, "perplexity": 3565.614058604349}, "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-2014-23/segments/1405997858581.26/warc/CC-MAIN-20140722025738-00200-ip-10-33-131-23.ec2.internal.warc.gz"} |
https://www.computer.org/csdl/mags/so/1995/03/s3029-abs.html | The Community for Technology Leaders
Issue No. 03 - May (1995 vol. 12)
ISSN: 0740-7459
pp: 29-41
ABSTRACT
In many distributed computing environments, failures are reported in a way that violates even the simplest notions of consistency. The authors argue that such practices are at the root of reliability problems, examine several distributed computing technologies in terms of their consistency, and present strategies for implementing consistent failure reporting.
INDEX TERMS
CITATION
Kenneth P. Birman, Bradford B. Glade, "Reliability Through Consistency", IEEE Software, vol. 12, no. , pp. 29-41, May 1995, doi:10.1109/52.382182
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https://brilliant.org/problems/side-length-of-triangle/ | # Side Length of Triangle
Geometry Level 3
Let $$D$$ be a point on side $$BC$$ of triangle $$ABC$$ such that $\overline{AB}=7, \overline{BD}=6, \overline{AD}=5, \overline{CD}=3.$ Then what is the square of the length of side $$AC?$$
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https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1155 | ## Absorption Cross Section of Scalar Field in Supergravity Background
• Abstract: It has recently been shown that the equation of motion of a massless scalar field in the background of some specific p branes can be reduced to a modified Mathieu equation. In the following the absorption rate of the scalar by a D3 brane in ten dimensions is calculated in terms of modified Mathieu functions of the first kind, using standard Mathieu coefficients. The relation of the latter to Dougall coefficients (used by others) is investigated. The S-matrix obtained in terms of modified Mathieu functions of the first kind is easily evaluated if known rapidly convergent low energy expansions of these in terms of products of Bessel functions are used. Leading order terms, including the interesting logarithmic contributions, can be obtained analytically.
$Rev: 13581$ | {"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": 0.7379970550537109, "perplexity": 355.7302881137295}, "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-2015-22/segments/1432207932596.84/warc/CC-MAIN-20150521113212-00302-ip-10-180-206-219.ec2.internal.warc.gz"} |
https://www.hsu-hh.de/ees/en/ | Electrical Power Systems
Prof. Dr.-Ing.habil. Detlef Schulz
The department is headed since the end of 2005 by Prof. Dr.-Ing. habil. Detlef Schulz and covers the spectrum of conventional and regenerative power plants, transmission and distribution grids, grid coupling of decentralized power generators, electrical systems and electromobility up to energy-efficient consumers.
interested in research ?
Teaching includes lectures, exercises and labs in the following areas:
• Electrical energy supply
• Calculation of grid errors and grid Operation
• Basics of high voltage Engineering
• Transient processes in high-voltage grids
• Regenerative energy systems in grid Operation
• Energy economics
The following topics are forcus of research:
• Electrical energy systems under new Parameters
• Grid integration of decentralized generation plants
• Grid identification via measurement of the frequency-dependent grid impedance
• Future structure of energy supply
• Electromobility in the distribution Network
• Electrical aircraft systems
DLab – Distributed Energy Laboratory | {"extraction_info": {"found_math": false, "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": 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": 0.8183753490447998, "perplexity": 18523.018266251685}, "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-2020-45/segments/1603107916776.80/warc/CC-MAIN-20201031062721-20201031092721-00208.warc.gz"} |
https://stats.stackexchange.com/questions/131485/collinearity-in-multivariate-regression-with-huge-amounts-of-data | # Collinearity in multivariate regression with huge amounts of data
Take the following example:
I wish to predict physical performance as a function of height and weight. I already know weight negatively affects performance. Height also negatively affects performance, but I don't know if this is only because of the weight, or if there is a positive correlation between height and performance when disregarding the correlated weight. So, I measure the heights and weights of thousands of individuals, and measure their performance. I then model performance with multivariate regression: $p = (a * \text{height}) + (b * \text{weight}$). The estimated coefficients $\hat{a}$ and $\hat{b}$ turn out to be 0.2 and -1 respectively when using "lm" in R. The individual significances of these estimated coefficients are very high according to the t-tests (as is shown in a table when using the R command "summary" of a linear model made with the command "lm"), and their std. errors are very low. I therefore conclude that height is positively correlated with performance when disregarding the negative effects of weight. When is this conclusion a mistake?
To rephrase, if I have plenty of data and the std. error is very low for the estimated coefficients of both correlated variables (say $x_1$ and $x_2$) in the regression summary produced by the R command "summary", is there any reason (in general) why I should distrust the estimated coefficients for $x_1$ and $x_2$? I.e. can the collinearity mean that these estimated coefficients do not necessarily reflect the real coefficients even though the standard errors shown by the regression summary are very low?
• Why not check for collinearity and see? Jan 6, 2015 at 22:28
• I already know these variables are highly correlated, but that is not the question here. The question concerns how correlated variables affect inference when there is a large amount of data Jan 6, 2015 at 22:36
• Correlation is not the same as colinear. Look at the condition indexes to see if there is a severe effect. Jan 6, 2015 at 22:38
• @PeterFlom (+1) for the useful CI remark.. Jan 7, 2015 at 8:51
• @PeterFlom Thanks for pointing that out. I don't really think it answers the question though. Perhaps I was a bit unclear in my formulation Jan 12, 2015 at 21:33
To add to the other excellent answers; "It depends" If multicollinearity is the only problem with the model, its effect would asymptotically vanish, when $n$ gets large enough. But, in practice, it might well be other problems with the model, which might interfere with multicolinearity!
Very specifically, if (some of) the regressor variables (the $x$'s) are measured with error, the problems caused by that will be amplified by multicollinearity, and I'm afraid that might happen in such a way that larger sample sizes will not help to much. I will try to add some simulations to this answer to illustrate/investigate that aspect. | {"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": 0.8409615755081177, "perplexity": 459.1743858889206}, "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/1674764499911.86/warc/CC-MAIN-20230201045500-20230201075500-00398.warc.gz"} |
http://math.stackexchange.com/questions/50132/differentiate-a-matrix-trace | # differentiate a matrix trace
Let $A,B,X$ be square matrices of the same size. I know $\ \displaystyle \frac{\mathrm{d}~ \mathrm{trace} (AX)}{\mathrm{d}X}=A.\quad$
Is it true that $\displaystyle \frac{\mathrm{d}~ B~ \mathrm{trace} (AX)}{dX}=B\otimes A$, where $\otimes$ means the Kronecker product?
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Hmm... sort of, but for clarity you really should write how the derivative is applied to a tangent vector. In other words, you should specify what is the directional derivative, say, in the direction of some square matrix $Y$. – Willie Wong Jul 7 '11 at 17:06
Let me give an argument why you shouldn't write it as a Kronecker product, at least not as how you've written it.
The Kronecker product is a nice way to represent tensor products of linear operators. That is to say, if $L_1:V_1 \to W_1$ is a linear operator between vector spaces $V_1$ and $W_1$, and if $L_2:V_2\to W_2$ is a linear operator, we can pick bases of $V_1, V_2, W_1, W_2$ and express the linear operators as matrices $[L_1]$ and $[L_2]$, while expressing vectors $v_1\in V_1$ and $v_2\in V_2$ relative to the bases as column vectors $[v_1]$ and $[v_2]$. Now, the nice property of the Kronecker product, is that the tensor product $L_1\otimes L_2$, which is a linear transformation from the tensor product space $V_1\otimes V_2$ to the tensor product space $W_1\otimes W_2$, can be written relative to the natural bases of those tensor product spaces, as
$$[L_1\otimes L_2] = [L_1] \otimes_K [L_2]$$
(here using $\otimes_K$ to denote the Kronecker product operation on matrices). The advantage to this is that we can do the same for the vectors $v_1,v_2$: the vector $v_1\otimes v_2\in V_1\otimes V_2$ can be represented in the same basis as above, simply by
$$[v_1\otimes v_2] = [v_1] \otimes_K [v_2]$$
AND the results
$$(L_1\otimes L_2)(v_1\otimes v_2) = (L_1v_1 \otimes L_2 v_2) \in W_1\otimes W_2$$
also represents nicely
$$[L_1v_1\otimes L_2v_2] = [L_1][v_1]\otimes_K[L_2][v_2] = \left([L_1]\otimes_K [L_2]\right)\left([v_1]\otimes_K [v_2]\right)$$
(Just to clarify: the first term is taking the basis representation of the vector $L_1v_1\otimes L_2v_2]$; the second term is the Kronecker product of the two vectors formed by the multiplication of the matrix representations $[L_i]$ of the linear operators with the column representation $[v_i]$ of the vectors; the third term is the matrix multiplication of a larger matrix, obtained by the Kronecker product of the matrices of the linear operators, against a larger vector, obtained by the Kronecker product of the column vectors.)
All this is to say that, when one writes "Kronecker product", one needs to do so relative to the correct matrix representation of a linear operator, because the power of the Kronecker product lies in this compatibility. (There actually is a nice commutative diagram here, for those who know what commutative diagrams are.)
Now, if you just take $A$ and $B$ to be square matrices and taking the Kronecker product $A\otimes_K B$ of that, you are not respecting the true nature of the objects $A$ and $B$. What is $A$? Writing it as a square matrix "suggests" that you are thinking of it as a linear operator between two vector spaces of the same dimension. But, this is in fact not the case.
Consider the expression
$$\frac{d}{dX} tr(AX) = A$$
Recall from multivariable calculus, or from real analysis, that the derivative of a function, evaluated at a point, is a linear functional. It takes input a tangent direction and outputs a real number (let's assume everything is real valued). Well, in this case your underlying space is the space of square matrices. And so the derivative takes as input a square matrix, and outputs a real number. That is: the derivative of $tr(AX)$ in the $Y$ direction, where $Y$ is a square matrix, is
$$\lim_{t\to 0} \frac{1}{t}\left( tr(A(X+tY)) - tr(AX)\right) = tr(AY)$$
So $A$ here on the right hand side of the derivative expression is actually a linear operator sending square matrices to real numbers via the operation $Y\mapsto tr(AY)$.
So let us say we are looking at $N\times N$ matrices. $A$ on the right hand side of the derivative expression should be now taking to be a linear transformation from $V\to \mathbb{R}$, where $V$ is now the space of $N\times N$ matrices. So the "correct representation" of $A$, using that you can identify the space of $N\times N$ matrices as a vector space $V$ of $N^2$ dimensions, is $[A]$ a matrix that is $1\times N^2$ (which you can get by "unfolding" the rows of $A$).
So the correct representation of the tensor product $B\otimes A$ using a Kronecker product, properly capturing the nature of $A$ in your equation for the derivative of $B~tr(AX)$, is the Kronecker product of $[B]$ against $[A]$, where $[A]$, as above, should be a corresponding $1\times N^2$ matrix, representing the fact that it is a linear transformation from an $N^2$ dimensional vector space to the real numbers, while $[B]$ should be analogously described by thinking about what it really stands for.
(As you mentioned in the comment to leonbloy's answer, $B$ is obtained from applying the Leibniz rule to $tr(BX)tr(AX)$. So $B$ actually should also be written as $[B]$, some $1\times N^2$ matrix. By thinking like this, you clearly see how the positive semi-definiteness of matrices $A$ and $B$ are completely irrelevant when it comes to considering the convexity of the function $tr(BX)tr(AX)$.)
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I am trying to digest your argument. Thank you for your time. – Sunni Jul 8 '11 at 15:26
This somewhat depends on how you define a derivative of a matrix with respect to a matrix.
First, the natural way of defining the derivative of a scalar function $g(X)$ with respect to a matrix $X$ is another matrix $Y$ os same size as $X$:
where $$\frac{d g(X)}{d X} = Y \;\; \Leftrightarrow \;\; Y_{i,j}=\frac{\partial g(X)}{\partial x_{i,j}}$$
Applying this definition you get your first identity. Now, if we derive a matrix function with respect to a matrix, you get either a 3D matrix (a tensor). Or, alternatively, you can express it as a block matrix ($n^2 \times n^2$). And in the particular case in which we must derive a matricial function of the form $B g(X)$, (with $B$ not dependent on $X$) we get (with this definition) a Kronecker product, as the natural generalization of the scalar case.
Added 2: To illustrate the discussion in the comments. What the OP wanted to write was
$$\frac{\partial tr(A X)}{\partial X} = A$$
$$\frac{\partial \; tr(A X) \; tr(B X)}{\partial X} = A \; tr(B X) + B \; tr(A X)$$
$$\frac{\partial \; B \; tr(A X)}{\partial X} = B \otimes A$$
with $A$ and $B$ positive definite. Hence
$$\frac{\partial^2 \; tr(A X) \; tr(B X)}{\partial X^2} = B \otimes A + A \otimes B$$
and conclude from this that, as this last matrix is positive definite, the Hessian of the function $tr(A X) \; tr(B X)$ is PSD and hence the function is convex.
This (as Willie Wong points out in the comments, and contrarily to what I first tended to believe) is false, and this shows that one must be careful when working with different definitions of matrix derivatives, when the order of the indexes matters.
To compute (safely) the Hessian, recall $X$, our 'variable', can be regarded as a $N \times N$ or as a $N^2 \times 1$ matrix (we can write ${\mathbf x} = vect(X)$ where $vect()$ is the operator that 'stacks' the matrix into a column vector). In this formulation, it's easy to see that the first derivative must be expressed as
$$\frac{\partial tr(A X)}{\partial {\bf x}} = {\bf a} = vect(A)$$
and $$\frac{\partial^2 \; tr(A X) \; tr(B X)}{{\bf x}^2} = {\bf a}^T {\bf b} + {\bf b}^T {\bf a}$$
The analogy is evident, but it is less evident is they are equivalent, or if this matrix on the LHS (of size $N^2 \times N^2$) is also guaranteed to be PSD. Well, it's not. An example:
Let $A=\pmatrix{ 7 &1\cr1& 3\cr}$, $B = \pmatrix{ 5 &2\cr2& 1\cr}$ , both PSD.
Lets compute both Hessians (the correct and the false one) :
>>> D=vec(A)*vec(B)' + (vec(A)*vec(B)')'
D =
70 19 19 22
19 4 4 7
19 4 4 7
22 7 7 6
>>> min(eig(D))
ans = -3.1664
>>> E = kron(A,B)+kron(B,A)
E =
70 19 19 4
19 22 4 7
19 4 22 7
4 7 7 6
>>> min(eig(E))
ans = 0.98603
We see that, while $E$ is PSD, as it should, the $D$, "true second derivative" matrix is not positive definite. And that both matrices are equivalent only up to some row/colum rearrangement ... and of course, PSD is sensitive to such rearrangements.
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So in the natrual sense, my derivation is correct? – Sunni Jul 7 '11 at 17:37
I'd say yes. But bear in mind that there can be more than one "natural" definition, eg trasposing the row-column indexes, or the "order" of the blocks (i.e., the order of the Kronecker product) – leonbloy Jul 7 '11 at 17:39
My consideration starts here.... Let $A,B$ be positive semidefinite and consider $f(X)=trace (AX) trace (BX)$ defined on positive semidefinite cone. The Hessian of $f(X)$ is $A\otimes B+B\otimes A$, which implies $f(X)$ is convex, but it seems not true if I use the definition to verify convexity of $f(X)$. – Sunni Jul 7 '11 at 17:48
Interesting! Perhaps you should expand your question with this. I'm not 100% sure of the implication (though I'm inclined to believe it). I'm curious about your (contra)verification. – leonbloy Jul 7 '11 at 18:08
@Sunni: I don't see how you expect the Hessian condition gives rise to convexity. The tangent space at a point in the pos. semidef. cone is ALL the square matrices. So you can't guarantee that the Hessian is itself pos. semidef. (as a bilinear form on the space of square matrices). For example, take $tr(AB) = 0$ and evaluate the Hessian on $Y = A-B$. – Willie Wong Jul 7 '11 at 18:20 | {"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": 1, "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": 0.9678997993469238, "perplexity": 148.83999827157956}, "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-2014-35/segments/1408500830074.72/warc/CC-MAIN-20140820021350-00448-ip-10-180-136-8.ec2.internal.warc.gz"} |
https://mb.math.cas.cz/mb131-1/7.html | MATHEMATICA BOHEMICA, Vol. 131, No. 1, pp. 63-84, 2006
# Measures of traceability in graphs
## Varaporn Saenpholphat, Futaba Okamoto, Ping Zhang
Varaporn Saenpholphat, Department of Mathematics, Srinakharinwirot University, Sukhumvit Soi 23, Bangkok, 10110, Thailand; Futaba Okamoto, Ping Zhang, Department of Mathematics, Western Michigan University, Kalamazoo, MI 49008, USA, e-mail: ping.zhang@wmich.edu
Abstract: For a connected graph $G$ of order $n \geq3$ and an ordering $s v_1$, $v_2, \cdots, v_n$ of the vertices of $G$, $d(s) = \sum_{i=1}^{n-1} d(v_i, v_{i+1})$, where $d(v_i, v_{i+1})$ is the distance between $v_i$ and $v_{i+1}$. The traceable number $t(G)$ of $G$ is defined by $t(G) = \min\left\{d(s)\right\},$ where the minimum is taken over all sequences $s$ of the elements of $V(G)$. It is shown that if $G$ is a nontrivial connected graph of order $n$ such that $l$ is the length of a longest path in $G$ and $p$ is the maximum size of a spanning linear forest in $G$, then $2n-2 - p \le t(G) \le2n-2 - l$ and both these bounds are sharp. We establish a formula for the traceable number of every tree in terms of its order and diameter. It is shown that if $G$ is a connected graph of order $n \ge3$, then $t(G)\le2n-4$. We present characterizations of connected graphs of order $n$ having traceable number $2n-4$ or $2n-5$. The relationship between the traceable number and the Hamiltonian number (the minimum length of a closed spanning walk) of a connected graph is studied. The traceable number $t(v)$ of a vertex $v$ in a connected graph $G$ is defined by $t(v) = \min\{d(s)\}$, where the minimum is taken over all linear orderings $s$ of the vertices of $G$ whose first term is $v$. We establish a formula for the traceable number $t(v)$ of a vertex $v$ in a tree. The Hamiltonian-connected number $\hcon(G)$ of a connected graph $G$ is defined by $\hcon(G) = \sum_{v \in V(G)} t(v).$ We establish sharp bounds for $\hcon(G)$ of a connected graph $G$ in terms of its order.
Keywords: traceable graph, Hamiltonian graph, Hamiltonian-connected graph
Classification (MSC 2000): 05C12, 05C45
Full text available as PDF (smallest), as compressed PostScript (.ps.gz) or as raw PostScript (.ps). | {"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": 0.8139305114746094, "perplexity": 237.74305277900652}, "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-2022-27/segments/1656104277498.71/warc/CC-MAIN-20220703225409-20220704015409-00149.warc.gz"} |
http://amj.math.stonybrook.edu/html-articles/Files/16-53/ | Research ContributionArnold Mathematical Journal
Received: 7 December 2015 / Revised: 28 July 2016 / Accepted: 2 August 2016
# q-Polynomial Invariant of Rooted Trees
Józef H. PrzytyckiDepartment of Mathematics The George Washington University Washington, DC 20052 USA, University of Maryland College Park, College Park USA,
University of Gdańsk, Gdańsk Poland
przytyck@gwu.edu
### Abstract
We describe in this note a new invariant of rooted trees. We argue that the invariant is interesting on it own, and that it has connections to knot theory and homological algebra. However, the real reason that we propose this invariant to readers of Arnold Journal of Mathematics is that we deal here with an elementary, interesting, new mathematics, and after reading this essay readers can take part in developing the topic, inventing new results and connections to other disciplines of mathematics, and likely, statistical mechanics, and combinatorial biology.
###### Keywords
Tree, Invariant, Quantum plane, UnimodalityKauffman bracket, Gaussian polynomial
$\newcommand\Z{{\mathbb Z}}$
## 1 Introduction
### 1.1 Quantum Plane
We know well the Newton binomial formula:
$\displaystyle \begin{eqnarray*} (x+y)^n= \sum_{i=0}^n {n \choose i} x^iy^{n-i}. \end{eqnarray*}$
Of course we assume here that the variables commute, that is $yx=xy$.
We can also visualize formulas for coefficients of $(x+y)^n$ by considering the tree $T_{b,a}$ of two long branches of length $b$ and $a$ respectively, coming from the root (Fig. 1). We can ask now how many different ways there are to “pluck” the tree $T_{b,a}$ one leaf at a time. Of course we can tear (like in the child’s play “likes not like”) the left or right branch. In total: the left should be torn $b$ times and the right $a$ times so the answer about the number of different pluckings is clearly ${a+b \choose a}$. Our notes present a dramatic generalization of this example.
We can ask now what happens with the binomial formula if we weaken commutativity by replacing it with $yx=qxy$ ($q$ commutes with $x$ and $y$). In applications in physics, $q$ is often taken to be a complex number but it is better to work generally with the ring $Z[q]$ and q-commutative11By $q$-commutative we understand exactly $yx=qxy$. polynomials of variables $x$ and $y$ over this ring (we call this ring of polynomials the quantum plane or noncommutative plane). The formula for $(x+y)^n$ in the quantum plane was known already in the XIX century, but if we do not know the result it is good to first work out small examples: $$(x+y)^2= y^2+ xy +yx + x^2= y^2 + (1+q)xy +x^2,$$ \begin{multline*} (x+y)^3= y^3+ xy^2+ yxy +y^2x + x^2y+ xyx + yx^2 +x^3\\ = y^3 + (1+q+q^2)xy^2 + (1+q+q^2)x^2y+ y^3, \end{multline*} \begin{multline*} (x+y)^4= y^4 + xy^3+ yxy^2 +y^2xy + y^3x + x^2y^2 + xyxy\\ + xy^2x + yx^2y + yxyx + y^2x^2 + x^3y+ x^2yx + xyx^2 + yx^3 + x^4 \\= y^4 + (1+q+q^2+q^3)xy^3 + (1+ q + 2q^2+ q^3 + q^4)x^2y^2 + (1+q+q^2+q^3)x^3y +x^4 \\= y^4+(1+q+q^2+q^3)xy^3 + (1+q^2)(1+q+q^2)x^2y^2+ (1+q+q^2+q^3)x^3y +x^4 .\end{multline*} Observe that we can think of $1+q+\cdots+q^{n-1}$ as a $q$-analogue of the number $n$. We define formally $[n]_q=1+q+\cdots+q^{n-1}$. In particular, for $q=1$, $[n]_q=n$. In the same vein we define $q$ factorial of the $q$-number $[n]_q$ as: $[n]_q!=[n]_q[n-1]_q\cdots [2]_q[1]_q$, and $q$-analogue of the binomial coefficient22Called also the Gaussian polynomial, $q$-polynomial of Gauss, Gaussian binomial coefficient, Gaussian coefficient, or $q$-binomial coefficient. by $\binom{n}{i}_q = \frac{[n]_q!}{[i]_q! [n-i]_q!}$. Sometimes to stress symmetry, $i \leftrightarrow n-i$, of the Gaussian polynomial we write $\binom{n}{i,n-i}_q$. We also observe that the coefficient of $x^2y^2$ in $(x+y)^4$ is $(1+q^2)(1+q+q^2)= \frac{1+q+q^2+q^3}{1+q}(1+q+q^2)=\frac{[4]_q[3]_q}{[2]_q}= \binom{4}{2}_q$.
In the notation we introduced, our calculations can be concisely written as:
$\displaystyle \begin{eqnarray*} &\displaystyle (x+y)^2= y^2 +[2]_qxy +x^2,\\ &\displaystyle (x+y)^3= y^3 + [3]_qxy^2 + [3]_qx^2y+x^3,\\ &\displaystyle (x+y)^4= y^4+ [4]_qxy^3 + \binom{4}{2}_qx^2y^2 + [4]_qx^3y+ x^4. \end{eqnarray*}$
Now it is not difficult to guess the general formula for $(x+y)^n$ in the quantum plane:
###### Proposition 1.1.
([MacMahon1916]; see e.g. [Kac and Cheung2002]; [Mansour and Schork2011]; [Mansour and Schork2016]) If $yx=qxy$ then
$\displaystyle \begin{eqnarray*} (x+y)^n= \sum_{i=0}^n {n \choose i}_qx^iy^{n-i}. \end{eqnarray*}$
###### Proof.
The simplest proof is by induction on $n$ however one can also find proofs without words, interpreting combinatorially left and right sides of the equation.
Inductive proof We already checked the formula for $n\leq 4$, and we should add that we need the convention (as in the classical case). that $[0]_q!=1$ and consequently ${n \choose 0}_q=1 ={n \choose n}_q$. Now we perform the inductive step (from $n-1$ to $n$):
$\displaystyle \begin{eqnarray*} (x+y)^n=& (x+y)(x+y)^{n-1}=(x+y)\sum_{i=0}^{n-1} {n-1 \choose i,n-i-1}_qx^iy^{n-i-1}\\ =&\sum_{i=0}^{n-1} {n-1 \choose i,n-i-1}_qx^{i+1}y^{n-i-1} +\sum_{i=0}^{n-1}q^i{n-1 \choose i,n-i-1}_qx^iy^{n-i}\\ =&\sum_{i=0}^n\left({n-1 \choose i-1,n-i}_q +q^i{n-1 \choose i,n-i-1}_q\right)x^iy^{n-i}. \end{eqnarray*}$
We use here the convention that ${n-1 \choose -1,n}_q=0$.
We are left now to check that
$\displaystyle \begin{eqnarray*} {n-1 \choose i-1,n-i}_q +q^i{n-1\choose i,n-i-1}_q)={n \choose i}_q. \end{eqnarray*}$
We encourage the reader to check it by themselves before looking at the following calculation.
1. (i)
\begin{multline*}[a+b]_q= 1+q+\cdots+q^{a+b-1}= (1+q+\cdots+q^{a-1}) + q^a(1+q+\cdots+q^{b-1})\\ = [a]_q+q^a[b]_q= [b]_q+q^b[a]_q\end{multline*}
2. (ii)
$\displaystyle \begin{eqnarray*} \binom{a+b}{a,b}_q=&\frac{[a+b]_q!}{[a]_q! [b]_q!}=[a+b]_q\frac{[a+b-1]_q!}{[a]_q! [b]_q!}\\ =&([a]_q+q^a[b]_q)\frac{[a+b-1]_q!}{[a]_q! [b]_q!}= \frac{[a+b-1]_q!}{[a-1]_q! [b]_q!} + q^a \frac{[a+b-1]_q!}{[a]_q! [b-1]_q!}\\ =&\binom{a+b-1}{a-1,b}_q + q^a\binom{a+b-1}{a,b-1}_q= \binom{a+b-1}{a,b-1}_q\\& +\, q^b\binom{a+b-1}{a-1,b}_q. \end{eqnarray*}$
$\square$
We can now go back to the tree $T_{b,a}$ and play the game in the $q$-fashion that is the leaf taken from the right ($a$) branch is counted as $1$ but the leaf taken from the left is counted with the weight $q^a$. Thus we eventually get not the plucking number but the plucking polynomial $Q(T_{b,a})$ which by definition satisfies the recursive relation $Q(T_{b,a})= Q(T_{b,a-1}) + q^aQ(T_{b-1,a})$. We also notice that $Q(T_{0,a})=Q(T_{b,0})=1$, thus we immediately recognize that the plucking polynomial is $Q(T_{b,a})= \binom{a+b}{a,b}_q$. This is the starting point to our definition of the polynomial of plane rooted trees mentioned in the title of the note.
We can repeat our considerations with many variables, $x_1,x_2,\ldots,x_k$. If variables commute we get the familiar multinomial formula (e.g. familiar to every student taking multivariable calculus):
$\displaystyle \begin{eqnarray*} (x_1+x_2+\cdots+x_k)^n= \sum_{a_1,\ldots,a_k; \sum a_i=n}^n {n \choose a_1,\ldots,a_k}x_1^{a_1} x_2^{a_2}\cdots x_k^{a_k}, \end{eqnarray*}$
where ${n \choose a_1,\ldots,a_k} = \frac{[n]!}{[a_1]!\ldots[a_k]!}$. As before the pleasant interpretation of ${n \choose a_1,\ldots,a_k}$ is the number of pluckings of a tree $T_{a_k,\ldots,a_2,a_1}$ of $k$ long branches of length $a_k,\ldots,a_2,a_1$, respectively, as illustrated in Fig. 2.
We can now consider a noncommutative space with $x_jx_i=qx_ix_j$, for $i $\displaystyle \begin{eqnarray*} (x_1+x_2+\cdots+x_k)^n= \sum_{a_1,\ldots,a_k; \sum a_i=n}^n {n \choose a_1,\ldots,a_k}_qx_1^{a_1} x_2^{a_2}\cdots x_k^{a_k}, \end{eqnarray*}$where$ {n \choose a_1,\ldots,a_k}_q = \frac{[n]_q!}{[a_1]_q!\ldots[a_k]_q!}$. To prove the formula we can again use an induction on$ n$and again the following two properties are of value: 1. (i)$ [a_1+a_2+\cdots+a_k]_q= [a_1]_q + q^{a_1}[a_2]_q + q^{a_1+a_2}[a_2]_q+\cdots+q^{a_1+a_2+\cdots+a_{k-1}}[a_k]_q.$2. (ii) $\displaystyle \begin{eqnarray*} {a_1+a_2+\cdots+a_k \choose a_1,a_2,\ldots,a_k}_q =& {a_1+a_2+\cdots+a_k-1 \choose a_1-1,a_2,\ldots,a_k}_q\\ &+\, q^{a_1}{a_1+a_2+\cdots+a_k-1 \choose a_1,a_2-1,\ldots,a_k}_q\\ &+\cdots + q^{a_1+a_2+\cdots+a_{k-1}} {a_1+a_2+\cdots+a_k-1 \choose a_1,a_2,\ldots,a_k-1}_q. \end{eqnarray*}$As in the$ q$-binomial case, we can interpret the$ q$-multinomial coefficients by$ q$-plucking the tree$ T_{a_k,\ldots,a_2,a_1}$, that is assuming the following plucking formula $\displaystyle \begin{eqnarray*} Q(T_{a_k,\ldots,a_2,a_1}) =& Q(T_{a_k,\ldots,a_2,a_1-1}) + q^{a_1}Q(T_{a_k,\ldots,a_2-1,a_1})\\ &+\,q^{a_1+a_2}Q(T_{a_k,\ldots,a_3-1,a_2,a_1}) + \cdots + q^{a_1+a_2+\cdots+a_{k-1}}Q(T_{a_k-1,\ldots,a_2,a_1}). \end{eqnarray*}$The recursion is the same as for the$ q$-multinomial coefficient so we conclude that $\displaystyle \begin{eqnarray*} Q(T_{a_k,\ldots,a_2,a_1}) = {a_1+a_2+\cdots+a_k \choose a_1,a_2,\ldots,a_k}_q. \end{eqnarray*}$One can find more properties of$ q$-binomial coefficients in [Kac and Cheung2002] and [Mansour and Schork2016]. The quantum plane relation$ yx=qxy$can be generalized to the$ q$-deformed or quantized Weyl algebra where$ yx-qxy=h$; see Chapter 7 of [Mansour and Schork2016]. The generalization to rooted trees is not clear, or at least it is not unique. Our$ q$-polynomial is motivated by the Kauffman bracket relation in knot theory ([Dabkowski et al.2015]; [Dabkowski and Przytycki2016]). Possibly a connection of$ q$-deformed Weyl algebra to other quantum invariants of knots, developed by [Fenn and Turaev2007], can lead to other$ q$-polynomial invariants of trees. I would encourage readers to look in this direction. In [Asakly et al.2013] the relation of the Weyl algebra to labeled rooted trees is given but I do not see a clear relation with our work. ## 2 Recursive Definition of$ q$-Polynomial of Plane Rooted Tree Our description of the quantum plane and noncommutative space is already over one hundred years old (e.g. MacMahon 1854–1929, [MacMahon1916]). It may, therefore, look surprising that a simple generalization to rooted trees, which we present here, is totally new. Maybe the explanation lies in the observation that, because there are so many$ q$-analogues, a new one is studied only if there is an outside reason to do so (like the Jones revolution in knot theory, in my case). Perhaps our$ q$-polynomial is buried somewhere in a work of MacMahon contemporaries? We start our definition from the polynomial of a plane (that is embedded in the plane) rooted tree. In Corollary 2.3(iii) we show that the polynomial does not depend on the plane embedding and is therefore an invariant of rooted trees. In our work we use the convention that trees are growing up (like in) (Fig. 3). ###### Definition 2.1. Consider the plane rooted tree$ T$(compare ) (Fig. 3). We associate to$ T$the polynomial$ Q(T,q)$(or succinctly$ Q(T)$) in the variable$ q$as follows. 1. (i) If$ T$is the one vertex tree, then$ Q(T,q)=1$. 2. (ii) If$ T$has some edges (i.e.$ |E(T)|>0$) then $\displaystyle \begin{eqnarray*} Q(T,q)=\sum_{v \in \mbox{ leaves }}q^{r(T,v)}Q(T-v,q), \end{eqnarray*}$where the sum is taken over all leaves, that is vertices of degree$ 1$(not a root), of$ T$and$ r(T,v)$is the number of edges of$ T$to the right of the unique path connecting$ v$with the root (an example is given in) (Fig. 3). In Fig. 4 we give an example of the expansion by our formula and if we complete the calculation we get the polynomial$ Q(T)$: $\displaystyle \begin{eqnarray*} &1+4q+9q^2+17q^3+28q^4+41q^5+56q^6+ 71q^7+83q^8+91q^9+94q^{10}\\ &\quad+\,91q^{11}+ 83q^{12}+ 71q^{13}+ 56q^{14}+ 41q^{15}+ 28q^{16}+ 17q^{17}+9q^{18}\\&\quad+\,4q^{19}+q^{20}. \end{eqnarray*}$33We show later that it is in fact equal to$ [2]_q^2[4]_q{8\choose 3,5}_q;$Corollary 2.3 (ii). As an example we can check that for$ T_{1,1,\ldots,1}$a star with$ n$rays we get$ Q(T_{1,1,\ldots,1}) = [n]_q!$. In particular,$ Q(\bigvee)= (1+q)=[2]_q$. One can look at a proof of the formula by direct induction on$ n$, but of course it is a very special case of the last formula of Sect. 1. The first important result in our theory of$ Q(T)$polynomials is the product formula for trees glued along their roots (wedge or pointed product). ###### Theorem 2.2. Let$ T_1 \vee T_2$be a wedge product of trees$ T_1$and$ T_2$. Then: $\displaystyle \begin{eqnarray*} Q(T_1 \vee T_2)= \binom{|E(T_1)|+|E(T_2)|}{|E(T_1)|}_qQ(T_1)Q(T_2). \end{eqnarray*}$###### Proof. We proceed by induction on the number of edges of$ T$,$ |E(T)|$, with the obvious initial case of no edges in one of the trees, that is$ |E(T_1)|=0$or$ |E(T_2)|=0$. For simplicity we write$ E_i$for$ |E(T_i)|$. Let$ T$be a rooted plane tree with$ E_1E_2\neq 0$, then we have: $\displaystyle \begin{eqnarray*} &Q(T)= \sum_{v\in L(T)} q^{r(T,v)}Q(T-v)\\ &\quad=\sum_{v\in L(T_1)} q^{r(T_1,v)+E_2 }Q(T_1-v)\vee T_2)+ \sum_{v\in L(T_2)} q^{r(T_2,v)}Q(T_1\vee (T_2-v))\\ &\quad\stackrel{inductive\ assumption}{=} \sum_{v\in L(T_1)} q^{r(T_1,v)+E_2 }{E_1+E_2-1 \choose E_1-1,E_2}_q Q(T_1-v)Q(T_2)\\ &\qquad+ \sum_{v\in L(T_2)} q^{r(T_2,v)}{E_1+E_2-1 \choose E_1,E_2-1}_qQ(T_1)Q(T_2-v)\\ &\quad= Q(T_2)q^{E_2}{E_1+E_2-1\choose E_1-1,E_2}_q\sum_{v\in L(T_1)} q^{r(T_1,v)}Q(T_1-v)\\ &\qquad+ Q(T_1){E_1+E_2-1 \choose E_1,E_2-1}_q\sum_{v\in L(T_2)} q^{r(T_2,v)}Q(T_2-v)\\ &\quad\stackrel{definition}{=} Q(T_1) Q(T_2)\left(q^{E_2}{E_1+E_2-1 \choose E_1-1,E_2}_q +{E_1+E_2-1\choose E_1,E_2-1}_q\right)\\ &\quad= Q(T_1) Q(T_2){E_1+E_2\choose E_1,E_2}_q \mbox{ as needed}. \end{eqnarray*}$46One can modify the polynomial$ Q(T)$so that the formula of Theorem 2.2 can be interpreted as a homomorphism. For this we take$ Q'(T)=\frac{Q(T)}{[|E(T)|]_q!}$. With this definition we have$ Q'(T_1\vee T_2)= Q'(T_1)Q'(T_2)$. A disadvantage of such an approach is that$ Q'(T)$is not ncessarily a polynomial but only a rational function.$ \square$Directly from Theorem 2.2 we conclude several properties of the$ q$-polynomial,$ Q(T)$, which by the nature of its definition, as pointed up before, we propose to be called the plucking polynomial. We should stress, in particular, part (iii) which establishes the independence of the polynomial of its plane embedding. ###### Corollary 2.3. 1. (i) Let a plane tree be a wedge product of$ k$trees that is $\displaystyle \begin{eqnarray*} T=T_{k} \vee \cdots \vee T_2 \vee T_1, \; \mbox{ then } \end{eqnarray*}$$\displaystyle \begin{eqnarray*} Q(T)= \binom{E_k+E_{k-1}+\cdots+E_1}{E_k,E_{k-1},\ldots,E_1}_qQ(T_k)Q(T_{k-1})\cdots Q(T_1). \end{eqnarray*}$where$ E_i=|E(T_i)|$is the number of edges in$ T_i$. 2. (ii) (State product formula) $\displaystyle \begin{eqnarray*} Q(T) = \prod_{v\in V(T)}W(v), \end{eqnarray*}$where$ W(v)$is a weight of a vertex (we can call it a Boltzmann weight) defined by: $\displaystyle \begin{eqnarray*} W(v)= \binom{|E(T^v)|}{|E(T^v_{k_v})|,\ldots,|E(T^v_{1})|}_q, \end{eqnarray*}$where$ T^v$is a subtree of$ T$with root$ v$(part of$ T$above$ v$, in other words$ T^v$grows from$ v$) and$ T^v$may be decomposed into wedge of trees as follows:$ T^v= T^v_{k_v} \vee \cdots \vee T^v_2 \vee T^v_{1}.$3. (iii) (Independence from a plane embedding) Plucking polynomial,$ Q(T)$does not depend on a plane embedding, it is therefore an invariant of rooted trees. 4. (iv) (Change of root). Let$ e$be be an edge of a tree$ T$with the endpoin ts$ v_1$and$ v_2$. Denote by$ E_1$the number of edges of the tree$ T_1$with the root$ v_1$and$ E_2$the number of edges of the tree$ T_2$with the root$ v_2$, where ###### Proof. (i) The formula (i) follows by using$ (k-1)$-times the product formula of Theorem 2.2 and the fact that the$ q$-multinomial coefficient is a product of binomial coefficients: $\displaystyle \begin{eqnarray*} &\binom{a_k+a_{k-1}+\cdots+a_2+a_1}{a_k,a_{k-1},\ldots,a_2,a_1}_q\\ &\quad\stackrel{def.}{=} \frac{[a_k+a_{k-1}+\cdots+a_2+a_1]_q!}{[a_k]_q![a_{k-1}]_q!\ldots[a_2]_q![a_1]_q!}\\ &\quad=\frac{[a_2+a_1]_q!}{[a_2]_q! [a_1]_q!}\cdot\frac{[a_3+a_2+a_1]_q!}{[a_3]_q! [a_2+a_1]_q!}\cdot\, \cdots \,\cdot \frac{[a_k+a_{k-1}+\cdots+a_2+a_1]_q!}{[a_k]_q! [a_{k-1}+\cdots+a_2+a_1]_q!}\\ &\quad= \binom{a_2+a_1}{a_2,a_1}_q\binom{a_3+a_2 + a_1}{a_3,a_2+a_1}_q\binom{a_4+a_3+a_2 + a_1}{a_4,a_3+a_2+a_1}_q\\ &\qquad\cdots \binom{a_k+a_{k-1}+\cdots+a_2+a_1}{a_k,a_{k-1}+\cdots+a_2+a_1}_q \end{eqnarray*}$(ii) The formula (ii) follows by using (i) several times. (iii) Independence of embedding follows from the fact that the state product formula (ii) does not depend on the embedding. (iv) We compare product formulas of Theorem 2.2 for$ v_1$and$ v_2$and we get: $\displaystyle \begin{eqnarray*} Q(T,v_1)=&{E_1+E_2+1 \choose E_1, E_2+1}_q Q(T_1)Q(T_2)\quad \mbox{ and }\\ Q(T,v_2)=& {E_1+E_2+1 \choose E_1+1, E_2}_q Q(T_1)Q(T_2), \end{eqnarray*}$from which the formula of (iv) follows directly.$ \square$There are other nice properties of$ Q(T)$(e.g. the observation that it has polynomial time complexity) and I am sure readers will discover more. Here we give a few properties which have some importance in knot theory. ###### Corollary 2.4. 1. 1.$ Q(T)$is of the form$ c_0+c_1q+\cdots+c_Nq^N$where: (i)$ c_0=1=c_N$,$ c_i>0$for every$ i\leq N$, (ii)$ c_i=c_{N-i}$, that is$ Q(T)$is a palindromic polynomial (often, less precisely we say symmetric polynomial), (iii) the sequence$ c_0,c_1,\ldots,c_N$is unimodal, that is for some$ j$: $\displaystyle \begin{eqnarray*} c_0\leq c_1 \leq \cdots \leq c_j \geq c_{j+1} \geq \cdots \geq c_N \end{eqnarray*}$(in our case$ j= \lfloor\frac{N}{2}\rfloor$or$ \lceil\frac{N}{2}\rceil$). (iv) For a nontrivial tree$ T$, that is a tree with at least one edge, we have: $\displaystyle \begin{eqnarray*} c_1 = \sum_{v\in V(T)} (k_v-1), \end{eqnarray*}$where$ k_v= deg_{T^v}(v)$is the number of edges growing up from$ v$, that is the degree of$ v$in the tree$ T^v$growing from$ v$(as in Corollary 2.3 (ii)). In particular, if$ T$is a binary tree,$ c_1(T)$is the number of vertices of$ T$which are not leaves. 2. 2. 1. (i)$ Q(T)$is a product of$ q$-binomial coefficients (of type$ {a+b\choose a}_q$). 2. (ii)$ Q(T)$is a product of cyclotomic polynomials. 77 Recall that$ n$th cyclotomic polynomial is a minimal polynomial which has as a root$ e^{2\pi i/n}$. We can write this polynomial as:$ \Psi_n(q)=\prod_{\omega^n=1,\omega^k\neq 1, k. For example $\Psi_4(q)=1+q^2$ , $\Psi_6(q)=1-q+q^2$ .
3. 3.
The degree of the polynomial $N=deg Q(T)$ can be described by the formula:
$\displaystyle \begin{eqnarray*} N=deg Q(T)=\sum_{v\in V(T)}\left(\sum_{1\leq i < j \leq k_v}E_i^vE_j^v\right), \end{eqnarray*}$
where, as in Corollary 2.3(ii) $T^v$ is a subtree of $T$ with the root $v$ (part of $T$ above $v$, in other words $T^v$ is growing from $v$) and $T^v$ can be presented as a bouquet of trees: $T^v= T^v_{k_v} \vee \cdots \vee T^v_2 \vee T^v_{1}.$
###### Proof.
1(i) follows easily from the definition of the plucking polynomial. Namely we see that the constant term is obtained in a unique way by always plucking the most rightmost leaf from the tree (repeating this each time in the calculation). Thus $c_0=1$. Similarly, the highest power of $q$ is obtained uniquely by always plucking the leftmost leaf of the tree. The condition that $c_i>0$ for any $i\leq N$ requires a more careful look at the recursive computation of $Q(T)$ and the proof is absolutely elementary; we leave it to the reader because in (iii) we provide much a stronger condition (but using a nontrivial fact proven by [Sylvester1878]). (1)(ii) We start from observing the symmetry of $q$-binomial coefficients; namely we have:
$\displaystyle \begin{eqnarray*} {a+b \choose a,b}_{q^{-1}} = q^{-ab} {a+b \choose a,b}_q. \end{eqnarray*}$
Then we use an easy observation that a product of symmetric polynomials is symmetric, and the fact we proved already and formulated in (2) that the polynomial $Q(T)$ is always a product of binomial coefficients. (1) (iii) Follows from the nontrivial fact, originally proved by Sylvester that $q$-binomial coefficients are unimodal and from a simple observation that a product of symmetric (i.e. palindromic) positive unimodal polynomials is symmetric unimodal (see [Stanley1989]; [Wintner1938]). (1) (iv) The formula for $c_1$ follows from the observation that ${a+b \choose a, b}_q= 1+q+\cdots$ for $a,b >0$ and more generally, ${a_1+a_2+\cdots+a_k \choose a_1,a_2,\ldots,a_k}_q = 1+ (k-1)q + \cdots$ for $a_1,a_2,\ldots,a_k >0$. Then the conclusion follows from the product formula of Corollary 2.3. (2) and (3): These conditions follow directly from the product formula of Corollary 2.3(ii). $\square$
With regard to Corollary 2.4(iii) we can ask: for which trees, is $Q(T)$ strictly unimodal, that is
$\displaystyle \begin{eqnarray*} c_0 < c_1 < \cdots < c_j > c_{j+1} > \cdots > c_N \end{eqnarray*}$
for some $j$; compare the computation for the tree of Fig. 3 (see also [Pak and Panova2013]).
As I was stressing from the beginning, and by now many readers may agree, the $q$-polynomial (plucking polynomial) is interesting on its own. However, I would have never constructed or discovered it if I had not observed its shadow in my knot theory research. Concretely it was my work with M.Dabkowski and his student C.Li concerning skein modules of generalized (lattice) crossings (Fig. 5), which gave some initial motivation ([Dabkowski et al.2015]). In that paper we do not use $Q(T)$, as it was observed after the paper was completed. We will use it, however, in future research ([Dabkowski and Przytycki2016]). Knot theory also motivates specific generalizations of the plucking polynomial by enhancing it with a delay function, $f: L(V) \to {\mathcal N}=\{n\in \Z\ | \ n \geq 1\}$. This function regulates which leaves are used in the recursive formula (Definition 2.1) and which are “delayed”. In fact we have much flexibility in the definition so we challenge a reader to play with possibilities.
The relation of the plucking polynomial to the Kauffman bracket skein modules is precise but difficult to describe succinctly. To have a concrete idea we can say that it concerns the study of the generalized (lattice) crossing (Fig. 5), under the assumption that we resolve every crossing using the Kauffman bracket skein relation , and replace every trivial component by the Laurent polynomial $-A^2 - A^{-2}$.
One can generalize the plucking polynomial to any graph. If a graph $G$ has a base-point $b$ then the invariant $Q(G,b)$ is a collection (multiset) of plucking polynomials of spanning trees $G$ with the root $b$ ([Przytycki2016]). I challenge the reader to study connections of this invariant with known invariants of graphs.
Our polynomial also has relations to homological algebra: let $\mathcal C$ be a chain complex, that is a sequence of abelian groups, $C_n$, and homomorphisms $\partial_n:C_n \to C_{n-1}$, so that $\partial_{n-1} \partial_n = 0$. On the basis of a chain complex we build homology groups by defining $H_n(\mathcal C)= \ker \partial_n/im(\partial_{n+1})$. Very often in topology and homological algebra the boundary operation $\partial_n$ is an alternating sum of homomorphisms, called face maps: $\partial_n= \sum_{i=0}^n (-1)^id_i$. M. Kapranov asked about what happens if $(-1)^i$ is replaced by $q^n$, that is we define
$\displaystyle \begin{eqnarray*} \partial^q_n= \sum_{i=0}^n q^id_i. \end{eqnarray*}$
He noticed that if $q$ is a $k$th root of unity different from $1$ (i.e. $q^k=1, q\neq 1$) then the $k$th iteration of $\partial^q$ is the zero map ($\partial^q_{n-k+1}\ldots\partial^q_{n-1} \partial^q_n = 0$) ([Kapranov2016]). The fact that Kapranov’s idea is related to our $q$-polynomial is clear, however deep connections require careful study: possibly you—the reader—could make a breakthrough.
###### Acknowledgements
J. H. Przytycki was partially supported by the GWU REF Grant, and Simons Collaboration Grant-316446. The author would like to thank a referee for directing his attention to [Asakly et al.2013] and [Mansour and Schork2011]; [Mansour and Schork2016].
## References
• [Asakly et al.2013] Asakly, W., Mansour, T., Schork, M.: Representing elements of the Weyl algebra by labeled trees. J. Math. Phys. 54(2), 023514 (2013)
• [Dabkowski et al.2015] Dabkowski, M.K., Li, C., Przytycki, J.H.: Catalan states of lattice crossing. Topol. Appl. 182, 1–15 (2015). [math.GT]
• [Dabkowski and Przytycki2016] Dabkowski, M.K., Przytycki, J.H.: Catalan states of lattice crossing II (2016) (in preparation)
• [Fenn and Turaev2007] Fenn, R., Turaev, V.: Weyl algebras and knots. J. Geom. Phys. 57, 1313–1324 (2007)
• [Kac and Cheung2002] Kac, V., Cheung, P.: Quantum calculus. Universitext, Springer (2002)
• [Kapranov2016] Kapranov, M.M.: On the q-analog of homological algebra. J. Knot Theory Ramif. (2016). (to appear)
• [Loday1998] Loday, J.L.: Cyclic homology. Grund. Math. Wissen. Band, vol. 301. Springer, Berlin (1992) (2nd edn, 1998)
• [MacMahon1916] MacMahon, P.A.: Combinatory analysis, vol. 2. Cambridge University Press, Cambridge (1916) (vol. 1, 1915)
• [Mansour and Schork2011] Mansour, T., Schork, M.: The commutation relation $xy=qyx +hf(y)$ and Newton’s binomial formula. Ramanujan J. 25, 405–445 (2011)
• [Mansour and Schork2016] Mansour, T., Schork, M.: Commutation relations, normal ordering, and Stirling numbers. CRC Press, Taylor & Francis Group, USA (2016)
• [Pak and Panova2013] Pak, I., Panova, G.: Strict Unimodality of $q$-Binomial Coefficients. C. R. Acad. Sci. Paris, Ser. I 351(11–12), 415–418 (2013). [math.CO]
• [Przytycki2016] Przytycki, J.H.: Knots and graphs: two centuries of interaction. In: Proceedings of Knots-2013, Mohali, India. To appear in Contemporary Mathematics, vol. 670 (2016)
• [Stanley1989] Stanley, R.P.: Log-concave and unimodal sequences in algebra, combinatorics, and geometry, vol. 576, pp. 500–535. Annals of the New York Academy of Sciences, New York (1989)
• [Sylvester1878] Sylvester, J.J.: Proof of the hithero undemonstrated Fundamental Theorem of Invariants. Philos. Mag. 5, 178–188 (1878) [reprinted in Coll. Math. Papers, vol 3. Chelsea, New York 1973, 117–126 (1973)]
• [Wintner1938] Wintner, A.: Asymptotic distributions and infinite convolutions. Edwards Brothers, Ann Arbor (1938) | {"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": 1, "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": 0.9502146244049072, "perplexity": 4347.686941424129}, "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-2017-39/segments/1505818689775.56/warc/CC-MAIN-20170923175524-20170923195524-00561.warc.gz"} |
https://stacks.math.columbia.edu/tag/0BZ3 | Lemma 22.34.1. Let $R$ be a ring. Let $(A, \text{d})$, $(B, \text{d})$, and $(C, \text{d})$ be differential graded $R$-algebras. Let $N$ be a differential graded $(A, B)$-bimodule. Let $N'$ be a differential graded $(B, C)$-module. Assume (22.34.0.1) is an isomorphism. Then the composition
$\xymatrix{ D(A, \text{d}) \ar[rr]^{- \otimes _ A^\mathbf {L} N} & & D(B, \text{d}) \ar[rr]^{- \otimes _ B^\mathbf {L} N'} & & D(C, \text{d}) }$
is isomorphic to $- \otimes _ A^\mathbf {L} N''$ with $N'' = N \otimes _ B N'$ viewed as $(A, C)$-bimodule.
Proof. Let us define a transformation of functors
$(- \otimes _ A^\mathbf {L} N) \otimes _ B^\mathbf {L} N' \longrightarrow - \otimes _ A^\mathbf {L} N''$
To do this, let $M$ be a differential graded $A$-module with property (P). According to the construction of the functor $- \otimes _ A^\mathbf {L} N''$ of the proof of Lemma 22.33.2 the plain tensor product $M \otimes _ A N''$ represents $M \otimes _ A^\mathbf {L} N''$ in $D(C, \text{d})$. Then we write
$M \otimes _ A N'' = M \otimes _ A (N \otimes _ B N') = (M \otimes _ A N) \otimes _ B N'$
The module $M \otimes _ A N$ represents $M \otimes _ A^\mathbf {L} N$ in $D(B, \text{d})$. Choose a quasi-isomorphism $Q \to M \otimes _ A N$ where $Q$ is a differential graded $B$-module with property (P). Then $Q \otimes _ B N'$ represents $(M \otimes _ A^\mathbf {L} N) \otimes _ B^\mathbf {L} N'$ in $D(C, \text{d})$. Thus we can define our map via
$(M \otimes _ A^\mathbf {L} N) \otimes _ B^\mathbf {L} N' = Q \otimes _ B N' \to M \otimes _ A N \otimes _ B N' = M \otimes _ A^\mathbf {L} N''$
The construction of this map is functorial in $M$ and compatible with distinguished triangles and direct sums; we omit the details. Consider the property $T$ of objects $M$ of $D(A, \text{d})$ expressing that this map is an isomorphism. Then
1. if $T$ holds for $M_ i$ then $T$ holds for $\bigoplus M_ i$,
2. if $T$ holds for $2$-out-of-$3$ in a distinguished triangle, then it holds for the third, and
3. $T$ holds for $A[k]$ because here we obtain a shift of the map (22.34.0.1) which we have assumed is an isomorphism.
Thus by Remark 22.22.5 property $T$ always holds and the proof is complete. $\square$
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https://www.physicsforums.com/threads/develop-a-formula-for-the-sa-of-a-cone.636375/ | # Develop a formula for the SA of a cone
1. Sep 16, 2012
1. The problem statement, all variables and given/known data
Develop a formula for radius as a function of surface area for a cone with height three times its diameter.
2. Relevant equations
∏rs + ∏r^2 = SA
s = √(h^2+r^2)
H = 3d or 6r
3. The attempt at a solution
Dont know what values to use for s = √(h^2+r^2).
Last edited: Sep 16, 2012
2. Sep 16, 2012
### LCKurtz
You are given that the height is 3 times the diameter, so you can get s in terms of r. Put that in your formula for SA and solve for r in terms of SA.
3. Sep 16, 2012
Would my h value be 3 and my r value be 0.5 ?
4. Sep 16, 2012
I also realized I made the error 3D=1H instead of vice versa.
5. Sep 16, 2012
### LCKurtz
No, $r$ isn't given. It is one of the variables you are to use. It and SA are the variables in your requested equation. $H = 3D = 6r$.
6. Sep 16, 2012
blah
7. Sep 16, 2012
### LCKurtz
Why bother with that? You need s in terms of r to plug into your SA equation.
8. Sep 16, 2012
s=√(h^2+6r^2), the answer is r=√SA/∏(1+√37). How do they get rid of the H ?
9. Sep 16, 2012
Would that be the proper thing for S?
10. Sep 16, 2012
### LCKurtz
You have $s=\sqrt{h^2+r^2}$ and you have $h = 6r$. Put that in for the $h$ in the $s$ equation. Then put that result in for the $s$ in your SA equation. Then solve that for $r$.
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https://www.nature.com/articles/nphys3422?error=cookies_not_supported&code=8b05ae2d-25c1-4df6-bbc9-eaf7b78a6e0c | # Spectrum of controlling and observing complex networks
## Abstract
Recent studies have made important advances in identifying sensor or driver nodes, through which we can observe or control a complex system. But the observational uncertainty induced by measurement noise and the energy required for control continue to be significant challenges in practical applications. Here we show that the variability of control energy and observational uncertainty for different directions of the state space depend strongly on the number of driver nodes. In particular, we find that if all nodes are directly driven, control is energetically feasible, as the maximum energy increases sublinearly with the system size. If, however, we aim to control a system through a single node, control in some directions is energetically prohibitive, increasing exponentially with the system size. For the cases in between, the maximum energy decays exponentially when the number of driver nodes increases. We validate our findings in several model and real networks, arriving at a series of fundamental laws to describe the control energy that together deepen our understanding of complex systems.
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## Acknowledgements
We thank E. Guney, C. Song, J. Gao, M. T. Angulo, S. P. Cornelius, B. Coutinho and A. Li for discussions. This work was supported by Army Research Laboratories (ARL) Network Science (NS) Collaborative Technology Alliance (CTA) grant ARL NS-CTA W911NF-09-2-0053; DARPA Social Media in Strategic Communications project under agreement number W911NF-12-C-002; the John Templeton Foundation: Mathematical and Physical Sciences grant number PFI-777; European Commission grant numbers FP7 317532 (MULTIPLEX) and 641191 (CIMPLEX).
## Author information
Authors
### Contributions
All authors designed and performed the research. G.Y. and G.T. carried out the numerical calculations. G.Y. did the analytical calculations and analysed the empirical data. G.T., B.B., J.-J.S., Y.-Y.L. and A.-L.B. analysed the results. G.Y. and A.-L.B. were the main writers of the manuscript. G.T., B.B. and Y.-Y.L. edited the manuscript. G.Y. and G.T. contributed equally to this work.
### Corresponding author
Correspondence to Albert-László Barabási.
## Ethics declarations
### Competing interests
The authors declare no competing financial interests.
## Supplementary information
### Supplementary information
Supplementary information (PDF 1507 kb)
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Yan, G., Tsekenis, G., Barzel, B. et al. Spectrum of controlling and observing complex networks. Nature Phys 11, 779–786 (2015). https://doi.org/10.1038/nphys3422
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Scientific Reports (2020) | {"extraction_info": {"found_math": false, "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": 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": 0.8579433560371399, "perplexity": 19529.370946757233}, "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-2020-29/segments/1593655886095.7/warc/CC-MAIN-20200704073244-20200704103244-00320.warc.gz"} |
https://arxiv.org/abs/hep-th/9712112 | hep-th
# Title:Dynamic D8-branes in IIA string theory
Authors:A. Chamblin (Cambridge U., DAMTP), M.J. Perry (Cambridge U., DAMTP)
Abstract: In this paper we perform a detailed investigation of the Dirichlet eight-brane of the Type IIA string theory, when the effects of gravity are included. In particular, consider what happens when one allows the ten-form field strength $F_{10}$ to vary discontinuously across the worldvolume of the brane. Since the ten-form is constant on each side of the brane ($d*F_{10} = 0$), a variation in the bulk term $\int F_{10}*F_{10}$ gives rise to a net pressure acting on the surface of the brane. This means that the infinite planar' eight-brane is no longer a static configuration with these boundary conditions. Instead, a static configuration is found only when the brane compactifies' to the topology of an eight-sphere, $S^8$. These spherical eight-branes are thus bubbles which form boundaries between different phases of the massive Type IIA supergravity theory. While these bubbles are generically unstable and will want to expand (or contract), we show that in certain cases there is a critical radius, $r_c$, at which the (inward) tension of the brane is exactly counterbalanced by the (outward) force exerted by the pressure terms. Intuitively, these `compactified' branes are just spherical bubbles where the effective cosmological constant jumps by a discrete amount as you cross a brane worldsheet. We argue that these branes will be unstable to various semi-classical decay processes. We discuss the implications of such processes for the open strings which have endpoints on the eight-brane.
Comments: 24 pages REVTeX plus 2 figures Subjects: High Energy Physics - Theory (hep-th) Report number: DAMTP R-97/61 Cite as: arXiv:hep-th/9712112 (or for this version)
## Submission history
From: Andrew Chamblin [view email]
[v1] Thu, 11 Dec 1997 09:59:50 UTC (26 KB) | {"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": 0.8529711961746216, "perplexity": 1123.3541483905542}, "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-2019-43/segments/1570986655554.2/warc/CC-MAIN-20191014223147-20191015010647-00212.warc.gz"} |
http://idlesummers.com/ | ## A few big innings and many small; Ratings 12th August Russell Degnan
4th TestEnglandvIndia
Pre-rating1039.11161.7
Form-40.2+20.3
Expected MarginEngland by 6 runs
Actual MarginEngland by 266 runs
Post-rating1053.21140.5
Six ducks.
That more or less sums up India's opening day effort, losing four wickets for eight runs, all caught behind with poor footwork and hard hands. Anderson had the ball on a string, though it was Broad who took the bulk of the wickets, ending with 6/25. Dhoni's counter-attacking 71 was ugly, but somewhat effective, and only a partnership with Ashwin - almost certainly in India's best six batsmen, if not their best six bowlers - kept the scoreboard from being embarrassing.
India bowled quite well, for the most part. But they lost either side of the new ball, when Root and Buttler turned a handy lead into an impregnable one. They are also, somewhat inexplicably, unable to play Moeen Ali, whose bowling is handy, accurate, but not something to repeatedly collapse to, though the damage at the top was done by Anderson again. As hinted after the last test, India under Dhoni, when the game is drifting, don't fight very hard.
There is little else to add. History suggests India will again fail to turn up at the Oval, although they are not incapable of winning, nor England of losing, as was shown at Lord's. England's confidence is up now though, including, most importantly, that of Cook in his young bowlers, which both lessens the load on Anderson and Broad (if he plays), and prevents the sort of crises of confidence that afflicted Kerrigan and Borthwick. If India do lose at the Oval, it will be a sad end to a series that promised much, but ended as a mauling.
1st TestSri LankavPakistan
Pre-rating1038.41093.9
Form+15.3-19.1
Expected MarginSri Lanka by 22 runs
Actual MarginSri Lanka by 7 wickets
Post-rating1043.81086.8
Revenge for Sri Lanka, after Pakistan's heist earlier in the year, and in nearly identical circumstances. Younis Khan's magnificent 177 provided the guts of a competitive 451, but he was matched by the insatiable Sangakarra's 221 and Mathews 91. The 82 run lead gave Sri Lanka just enough to press for victory after a productive first session on the final day. Herath, naturally, provided the pressure, bowling taking 6/48 from 30.2 overs. They were held up late by Sarfraz Ahmed, whose 52 not out almost gave Pakistan enough time and runs to survive until the rain came. It did, almost literally as Sri Lanka walked off, having chased 99 in 17 overs.
The win doesn't change the rankings, but tightens the group of sub-continental rivals and England, with another two test matches to potentially shake things up. A series win for Sri Lanka would round out an impressive sequence of results in the past three months. And the impressive career of Jayawardene. His home record has always vastly exceeded that away from Sri Lanka, making it harder for his batting to be appreciated by anything beyond the raw numbers filtered through the scorecard. It is a record that speaks to a vulnerability to bounce, and to bowlers who could provide it; but that is a minor quibble against almost 12 thousand runs. Few players have ever dominated attacks when conditions were in his favour more than Jayawardene, and few have ever made it look as easy either.
Only TestZimbabwevSouth Africa
Pre-rating560.21295.4
Form+25.2-19.6
Expected MarginSouth Africa by 318 runs
Actual MarginSouth Africa by 9 wickets
Post-rating570.71289.1
Series rating723.31132.4
Even the dodgy internet streams couldn't get me coverage of this match, but the general consensus is of a game where Zimbabwe fought hard, without actually ever looking like doing anything but losing by a significant margin. Taylor remains their only batsman of class, although Mutumbami made useful contributions, and they'll be pleased with the wickets of Nyumbu and the discipline of Chatara. Zimbabwe have so many structural problems it is hard to know where to start: an inability to keep players; a lack of funds to run domestic cricket, pay players and train consistently; on-going governance issues and debt so deep they are almost insolvent.
This could have been much worse, but South Africa came to do the job, and did it, nothing more. What they didn't do is achieve the margin, which slips them closer to Australia in second place, with relative form likely to drag them closer still when each next plays.
Only Women's TestEnglandvIndia
There are no ratings for women's test matches, but it is worth discussing such a rare event. The format has been almost exclusively played by Australia and England for the past eight years, and the BCCI ought to be commended for getting their players to play the format. What will happen is less clear, as with little test cricket form to digest from either side, the only known factor is that India has struggled in recent tournaments, while England have defeated Australia in two Ashes contests, even if they've failed to win major trophies.
Not that finding out what is happening will be easy. The ECB has put money into professional contracts, but failed to invest in even basic streaming to help supporters follow the game. The BCCI haven't even done the former, and the game stagnates there, as does so much Indian women's sport. South-east Asian women's sides on a shoe-string are more likely to challenge the anglo-hegemony in a decade or two, as they have the willingness to push the sport to their female population. But with the other test nations investing and growing women's cricket, it may take several more decades to restore a sense of parity. This contest might be rarer still in another eight years.
Rankings at 13th August 2014
1.South Africa1289.1
2.Australia1273.7
3.India1112.0
4.Pakistan1086.8
5.England1068.1
6.Sri Lanka1043.8
7.New Zealand937.8
8.West Indies870.2
12.Zimbabwe570.7
10.Ireland594.8
11.Afghanistan587.6
13.Scotland430.3
14.Namibia383.4
15.Kenya276.4
16.U.A.E.257.3
17.Netherlands182.4
Shaded teams have played fewer than 2 games per season. Non-test team ratings are not comparable to test ratings as they don't play each other.
Cricket - Ratings - Test 14th August, 2014 00:34:44 [#] [0 comments]
## Turning luck, turning pitch; Ratings 4th August Russell Degnan
2nd TestSri LankavSouth Africa
Pre-rating1032.71302.6
Form+15.9-21.0
Expected MarginSouth Africa by 85 runs
Actual MarginMatch Drawn
Post-rating1038.41295.4
Series rating1091.11244.1
One of a string of outstanding games that Sri Lanka has played of late, this time coming down on the wrong side of a draw, having had South Africa against it for the final three days. Hashim Amla was the hero, batting for an incredible 541 deliveries, merely 164 runs, and one dismissal. It would nevertheless have been for nought had the tail not fought through 17 overs with as many as all 9 players around the bat, and the spinners working away. Herath and Perera performed their own herculean feats, the former bowling 90 overs in the match, taking 9/111, the latter 85.5 overs, taking 8/129.
The scoring rates show clearly both how difficult were South Africa finding it to make runs, and how comparatively easily the Sri Lankans scored of Imran Tahir (3/197 off 51). Sri Lanka batted a mere 175 overs, making 650 runs, while South Africa survived, and not much else, scoring 441 off 246 overs. Mathews declaration leaving 369 runs was, in retrospect, excessive, but with 107 scheduled overs to play, he could not depend on either rain or South Africa shutting shop.
Ultimately, he tourists took the series, and the mace, for which they must be commended. They retained number one spot on these rankings too, which seemed in doubt had they lost; their next fixture against Zimbabwe requires a monumental victory, but it would surprise if they failed to provide one. After flirting with passing England, Sri Lanka will need to beat Pakistan and hope India regain some form to climb into fifth.
3rd TestEnglandvIndia
Pre-rating1039.11161.7
Form-40.2+20.3
Expected MarginIndia by 11 runs
Actual MarginEngland by 266 runs
Post-rating1053.21140.5
After flirting with playing well enough to win, then ultimately failing all summer, England finally got the luck it needed in one fell swoop. This was a thorough smashing in the end, having declared twice for the loss of only 11 wickets, and wrapping up the match early on day 5, when even the optimists were predicting a day of hard slog. Anderson got his lines and more importantly, his lengths right, taking 7 wickets, and Moeen Ali took 8 in a performance that can only lead to future disappointment.
But the important thing was runs, loads of them, from Cook (dropped early), Bell (lucky to survive an lbw on nought), Ballance (who looks genuinely classy) and as they accelerated, Buttler (lucky, but with a license). That gave the bowlers some added rest before they got to work, and the time later to have a breather before setting into India again. By contrast, India were listless after a grinding first day that only saw two wickets, and positively generous while batting. The way England climbed all over them when they were behind was reminiscent of 2011.
Youth is not an excuse for a lack of backbone, not poor catching (particularly in the slips). It would seem inexplicable that Ashwin remain out of the side, as they need a spinner who can be relied on to rest their seam attack. His batting isn't a bad bonus either, for spectators and India. Both sides have gifted away wins to the other, which will make fools of those predicting the tests to come. This test, like the two that proceeded it, might have been quite different. England though, appear slightly superior with the ball, which should be enough.
2 TestsSri LankavPakistan
Pre-rating1038.41093.9
Form+15.3-19.1
Expected MarginSri Lanka by 22 runs
Another series predicted to be very close. Sri Lanka have a lesser home advantage against Pakistan, who can draw on the talents of Saeed Ajmal, and are accustomed to pitches of a similar nature. In their last match, Sri Lanka's negativity threw away a safe position, but Mathews seems to have learnt (a little) from this, and it will be a tighter tactical battle. If a turner, such as the one found for South Africa, is procured, both sides are capable of winning from a favourable toss. One a slightly quicker deck, Pakistan probably have a slight edge, if they can keep Sangakarra quiet.
Only TestZimbabwevSouth Africa
Pre-rating560.21295.4
Form+25.2-19.6
Expected MarginSouth Africa by 318 runs
A victory by more than an innings is predicted for this match, and given Zimbabwe's struggles against Afghanistan, it would be a surprise if it wasn't provided. Zimbabwe could surprise, and did so a year ago against Pakistan (who beat South Africa in their subsequent test), but turmoil seems to have enveloped their setup again, as finances are strained, and the players are unlikely to be anywhere near prepared enough to face the South African attack. Getting their southern neighbours to bat twice will be an achievement.
Rankings at 4th August 2014
1.South Africa12955.4
2.Australia1273.7
3.India1140.5
4.Pakistan1093.9
5.England1053.2
6.Sri Lanka1038.4
7.New Zealand937.8
8.West Indies870.2
12.Zimbabwe560.2
10.Ireland594.8
11.Afghanistan587.6
13.Scotland430.3
14.Namibia383.4
15.Kenya276.4
16.U.A.E.257.3
17.Netherlands182.4
Shaded teams have played fewer than 2 games per season. Non-test team ratings are not comparable to test ratings as they don't play each other.
Cricket - Ratings - Test 4th August, 2014 22:54:28 [#] [0 comments]
## A sports draft without tanking Russell Degnan
The odd thing about sports drafts is that, as currently constructed, they are really about who is bad. Because the best picks go to the worst teams, they reward and even encourage poor play; particularly at the back-end of the season, but increasingly across multi-year rebuilding strategies, across a whole season.
Needless to say, owners who aren't bad don't like it. Partly for financial reasons: in an NBA environment where 5 or 6 teams are tanking, a fifth of regular season games are pointless, which hurts teams both good and bad. Partly for fairness, as the draft is increasingly perceived as a lottery: a way to beat the sensible construction of a team by throwing the dice.
Tanking itself, does and doesn't work, depending on the specific situation.
Deliberately losing games (either by resting players or odd rotations) at the tail-end of the season will work a bit: it improves draft position which is worth more wins (though not necessarily a lot more), and if young players are tested, it improves knowledge of a roster's capability.
Drafting players who can't play - as the Sixers have - with the aim of staying early in the draft for multiple years probably can work, if the right players turn up. But it is unlikely trading good contracts for cap space (through short-term bad contracts) improves wins in the future. Free agents rarely provide more wins than their contracts, and a bad team is much more likely to have to over-pay than one in contention.
Unless you are Cleveland. Cleveland's third lottery victory in four years is the other driving force behind proposed changes to the NBA Draft. LeBron may of returned without Wiggins, but it made it an sensible choice for a player looking to escape from an old team to one he could build on. The combination of repeatedly making poor draft choices, and poor trade choices, and an unusual streak of luck sits poorly with NBA owners. And not because hey believe in competitive balance, but because they don't - and nether do fans.
When the league talks about competitive balance, they want every team to be a possible contender every year. Baseball almost gets to that, but basketball isn't close, and is unlikely to ever be close, because there just aren't enough star players. But like the concept of equality - on which it is based - it isn't true that owners want balance. They want dynasties and the chance to prove they are the smartest and canniest owners. In other words, not equality of outcomes, but equality of opportunities.
Any solution that encourages a team to play badly has a downside. It isn't clear that the current weighted odds are optimum. But as Zach Lowe points out, playing with the percentages of lottery odds on the margins incentives a different set of teams to play badly. But the alternative proposal, of a wheel that gave each team a set rotating pick, isn't necessarily better either, because it defeats the reason he draft exists in the first place: teams are not born equal.
Teams are unequal for many reasons: big markets have more cash, even with a salary cap limiting their options; teams with better players and coaches can attract better free agents; some teams are in better cities to live in. The point of the draft is to mitigate those effects by helping teams that are struggling (ie. losing). But helping down the track is a second order effort, equivalent to providing welfare, but no education. The alternative to a draft that incentivizes losing, is one that mitigates the effect of the most important starting assets: cash and draft picks.
Read Wages of Wins and it will tell you that wins are poorly correlated with spending. This is not because in a free market the biggest team couldn't buy titles - football proves they certainly can - but because in the NBA the market for players is distorted by rookie and maximum contracts and the salary cap, so a lot of the money goes to players providing fewer wins than they ought. Nevertheless, you can measure those distortions, and by extension, calculate which teams have benefited from circumstance, and adjust the lottery accordingly.
Big market spending is the easiest to calculate, because it basically comes to how much a team has spent over and above the salary cap. Every $1.6 million corresponds to one extra win, and therefore can be offset against expected value in the draft lottery. The Draft is an uneven distributor of talent, because some years are better than others, but on the average, the value of each pick over and above their salary can be modelled, and adjusted over the previous four years. Both Arturo Galletti and Nate Silver both calculated similar numbers for the value of each pick: around$30 million over 4 years for number 1 picks, and \$2-4 million for number 30 picks. Traded picks would still apply to the original team, as the trade was valued at the pick (presumably). That's the tedious but easy part.
Star players limited by max contracts, on the other hand is more complex, because although the number of wins earnt above their salary can be calculated, not all players in this category are on the max (LeBron for example) and a team shouldn't necessarily be penalised for finding the right guy. One option is to just ignore it, as it affects relatively few players (albeit the most important ones); another would be to apply it to designated players (either designated or acquired through trade) at the difference between the maximum 25% and the players salary. This is, broadly speaking, close to the expected difference in value, and subtly penalises teams with star players.
Playoff revenue advantage is the final piece. Teams earn more for making the playoffs, as well as gaining a free market advantage. At the same time, excessive offsets here would provide incentives to miss the playoffs. Keeping every team in the lottery means every team would look to make the playoffs, but adjusting for series played, reduces the advantages gained by being consistently good. Technically this money isn't used unless it goes into salary spending, but it covers teams who have attracted stars at below maximum salaries, closing a potential loophole.
Put it together and it produces something like this[1]:
The draft rank comes out roughly where it should, given the recent history of those teams: Utah, Philadelphia, Atlanta and Milwaukee have neither picked early, nor spent heavily, nor had deep playoff runs, and therefore find themselves high in the draft. Future years would see them drop, effectively replicating the wheel system for teams spending near the cap.
Conversely, it would be a difficult system to game, as there is a lower limit to improving draft lottery position: not making the playoffs, not exceeding the cap, not having a designated player. Many teams are in that position, so there is no value in completely blowing up a side to chase the number one pick. For borderline playoff teams like Atlanta, the value in reducing salary slightly, or skipping the playoffs would be a half a percent improvement in lottery odds. Not nearly enough to play for.
Equalization involves adjusting the lottery odds to offset the expected deficit from spending and recent drafts. Nine teams last season exceeded the average value of a draft selection, and therefore fall out of the lottery. The remaining teams have between a one and nine percent chance of winnings, as follows:
In the long term, such a selection would encourage teams to stay close to the cap, unless they can win - which is broadly what the NBA wants - and even out draft picks, rewarding teams who picked well, and giving no solace to those who don't. Teams would have a pretty good idea of their draft position several years in advance, because they would know their salary, their likely playoff position, and their previous picks. Trading for picks becomes slightly dangerous, because it allows the trader to up their salary without consequence. Or traded picks would likely be protected at both ends.
There is no perfect draft method, but this one would at least end tanking, and reward sound management. Which for owners, who are in the game to prove their savviness, and for fans, who want their team to win, not to lose, would be a big improvement.
[1] Draft value is taken from Nate Silver's piece, divided by four, for a yearly value. Designated players are listed in Larry Coon's cap FAQ. Team salaries from Story Teller.
## Tails wagging the dog; Ratings 23rd July Russell Degnan
2nd TestEnglandvIndia
Pre-rating1054.21152.3
Form-40.1+6.2
Expected MarginEngland by 9 runs
Actual MarginIndia by 95 runs
Post-rating1039.11161.7
Until one ball before lunch on the final day this was a fluctuating match that England ought to have won. What is apparent is that they fundamentally cannot do so, regardless of what is offered. Having wasted a green pitch on the opening morning with short bowling, England still managed to have India 7/145 after tea, before Rahane's counter-attack found support from Binny and the rest of the tail. They turned 4/211 - with only Kumar finding swing to trouble the top-order - into 319 - still a lead. And in the second innings, had removed the specialist batsmen with India only 211 in front. Jadeja and Kumar's 99 run stand was, in the context, as vital as Ishant Sharma's bouncers inducing a collapse of 6/50 either side of lunch on the final day; a point when, again, England had got themselves into a position to challenge for victory.
Sharma's 7/74 and Dhoni's willingness to try a spell of short pitched bowling looks like genous only in hindsight. The spell was not near as menacing as England made it look; runs flowed at first, and the balls that took wickets were well wide of off-stump and easily left by clear-headed batsmen. England though are far from that. Prior's departure leaves only Cook, Bell, Broad and Anderson of the core that formed England's best side. The batsmen in that group are woefully out of form, and even the performances of the youth cannot hide it. The bowlers must be nearing exhaustion, having clocked nearly 200 overs each in the past 6 weeks, and Broad carrying a long-term injury.
India look a settled and confident side only by comparison. The batting has been failing, the sins hidden by the tail, whiich can't be relied on. Dhoni is struggling which they cannot afford when playing five bowlers, even if 7-9 are competent, and occasionally match-winning. If England can click, they can challenge and win this series. It would be a shock if that happens with Cook at the helm however.
1st TestSri LankavSouth Africa
Pre-rating1035.61299.4
Form+28.7-36.6
Expected MarginSouth Africa by 82 runs
Actual MarginSouth Africa by 153 runs
Post-rating1032.71302.6
Contrary to my preview, a relative lack of impact from Imran Tahir and Duminy - the undeserved wicket of Sangakarra nowithstanding - didn't impact South Africa at all. The reason is that Dale Steyn is a genius, and Morne Morkel is very tall and awkward to face. The latter primarily contributed in taking out the tail. Steyn did as Steyn has done for going on 371 test wickets, taking 9/99 for the match. South Africa were challenged only once after Elgar (103) and du Plessis (80) got them away to a start. For a brief moment, after de Villiers was dismissed a 5/266, Sri Lanka were placed to put pressure on South Africa with the bat. Duminy's even 100 not out got them to 9/455 declared. Sri Lanka could only respond with sporadic scores from Tharanga, Mathews and Sangakarra, none going over 100, when they needed more.
South Africa having declared in both innings, the second after a race to set a target that showed admirable aggression; this was a more emphatic victory than the score suggests. Whether it will be repeated depends on Steyn. Morkel remains a useful support; the spinners added litle, and Philander went wicketless on his least friendly surface. It would surprise if the next match wasn't closer, but this was an impressive victory by the tourists in their new era.
Rankings at 23rd July 2014
1.South Africa1302.6
2.Australia1273.7
3.India1161.7
4.Pakistan1093.9
5.England1039.1
6.Sri Lanka1032.7
7.New Zealand937.8
8.West Indies870.2
12.Zimbabwe560.2
10.Ireland594.8
11.Afghanistan587.6
13.Scotland430.3
14.Namibia383.4
15.Kenya276.4
16.U.A.E.257.3
17.Netherlands182.4
Shaded teams have played fewer than 2 games per season. Non-test team ratings are not comparable to test ratings as they don't play each other.
Cricket - Ratings - Test 24th July, 2014 01:54:11 [#] [0 comments]
## ICC Conference and ACC AGM with Shahriar Khan; Associate and Affiliate Cricket Podcast Russell Degnan
In the wake of the ICC Conference in Melbourne, Andrew Nixon (@andrewnixon79) and Russell Degnan (@idlesummers) look at the news - or lack of - from changes in the ICC. Russell speaks to media manager of the Asian Cricket Council, Shahriar Khan about the recent success of Asian sides, the leadup to the Asian Games, and some of the ICC conference outcomes, as they affect Asian cricket. There are reviews of World Cricket League Division 4, ICC Europe Division 2, and cricket in Romania and Scotland. The episode ends with some governance news from Kenya, Canada and Nepal.
Direct Download Running Time 88min. Music from Martin Solveig, "Big in Japan"
The associate and affiliate cricket podcast is an attempt to expand coverage of associate tournaments by obtaining local knowledge of the relevant nations. If you have or intend to go to a tournament at associate level - men's women's, ICC, unaffiliated - then please get in touch in the comments or by email.
Cricket - Associate - Podcast 21st July, 2014 00:24:48 [#] [0 comments]
## Grind until a fine paste; Ratings 16th July Russell Degnan
1st TestEnglandvIndia
Pre-rating1067.61150.1
Form-52.9+7.3
Expected MarginEngland by 9 runs
Actual MarginMatch Drawn
Post-rating1054.21152.3
England's rating slips a little further, on a pitch offering little to the bowlers, but which nevertheless offered both sides ample opportunities to press for victory. That they didn't came down to the last wicket partnerships between Kumar and Shami, that lifted India from 9/346 to 457; and between Root and Anderson, that took England from 9/298 to 496. Anderson's heroics with the bat came on the back of 38 overs in he first innings, and 59 in the match, which probably explains why England failed to Jadeja, Binny and Kumar when at 6/184 the game promised one final twist.
Bowling short and in the channel instead of full at the stumps didn't help either. On a pitch with no bounce, little pace, and sapped by the workload - there remain another four tests, lest we forget - bowling in the low-80s left the batsmen (and the bowlers masquerading as such) with far too much time. With Lord's promising to be flat, and neither captain likely to be take undue risks, we are in line for an attritional series marked by the odd inexplicable match-losing collapse. In this, England's squad bowling and batting depth probably tilt things in their favour. India's decision to play five batsmen could haunt them at some point, but if they win the toss and bat, they could have England in the field six days in nine. For a team already looking jaded, that's a worrying prospect.
The ratings now predict an English victory by a single run. Attritional cricket might lack a certain sexiness, but it still brings interesting narratives. And the longer the stays in the balance, the more interesting they become.
2 TestsSri LankavSouth Africa
Pre-rating1035.61299.4
Form+28.7-36.6
Expected MarginSouth Africa by 82 runs
South Africa enter this test as favourites, but their form, and the loss of both their captain and most solid batsman in the last year means they are probably not at quite that level. Sri Lanka's win in England showed a resilience they have often lacked while travelling. If they can couple that with the natural advantages playing on turning tracks at home gives them, then this could be a close contest.
The key for South Africa will be Imran Tahir. Leg spinners - or at least Warne - enjoyed Sri Lankan conditions, when the pitch wasn't completely dead. If he can contribute in ways he hasn't always on seaming, bouncing southern hemisphere pitches, then the South African seamers will be sufficiently strong to cover for any batting frailties. If not, South Africa's attack looks thin, and the tourists could be a middle order failure from Amla, du Plessis and AB de Villiers from an undefendable total.
Rankings at 16th July 2014
1.South Africa1299.4
2.Australia1273.7
3.India1152.3
4.Pakistan1093.9
5.England1054.2
6.Sri Lanka1035.6
7.New Zealand937.8
8.West Indies870.2
12.Zimbabwe560.2
10.Ireland594.8
11.Afghanistan587.6
13.Scotland430.3
14.Namibia383.4
15.Kenya276.4
16.U.A.E.257.3
17.Netherlands182.4
Shaded teams have played fewer than 2 games per season. Non-test team ratings are not comparable to test ratings as they don't play each other.
Cricket - Ratings - Test 16th July, 2014 22:15:14 [#] [0 comments]
## A tale of two hundreds; Ratings 10th July Russell Degnan
3rd TestWest IndiesvNew Zealand
Pre-rating880.7931.1
Form-24.9+11.8
Expected MarginWest Indies by 25 runs
Actual MarginNew Zealand by 53 runs
Pre-rating870.2937.8
Series rating902.8910.6
A competitive series ended with a match that looked tighter on the scoreboard than it felt at the finish. The West Indies were set 308 runs on the final day, and were on track time-wise to make it. But despite getting to 254, an earlier collapse to 7/144, primarily to Southee (3/28), meant that they were always unlikely, and the new ball did for Taylor to end the contest.
Although 20 players got past 20 in the match, only one went on to make a score: Williamson's 161 being the major difference between the sides, With the ball Roach's 8/116 was the best of any bowler, but like the runs, the wickets were largely shared, and New Zealand's strength in depth allowed them to maintain pressure throughout the match. New Zealand's recent record is very good, but the series rating indicates both how close this series was, and that the gap to the top remains to be bridged. They have a capable side though, and enough youth - particularly in Williamson whose potential exceeds any - to maintain an upward trajectory.
2nd TestEnglandvSri Lanka
Pre-rating1087.31022.9
Form-53.9+13.7
Expected MarginEngland by 82 runs
Actual MarginSri Lanka by 100 runs
Post-rating1067.61035.6
Series rating1008.41108.4
A test that in many ways resembled Sydney 2008, whether from the grandstand finish, the persistent sledging from the winning side, or the failure to capitalise on a dominant position from the eventual losers. The umpiring was (fortunately) generally better, and the acrimony (fortunately) not long lasting. The turning point came from Mathews, beginning with his 4/44 in England's innings, and hitting a high-point in his 160 that took the match away from England. Mathews is a captain who, six months ago, basically gave away a test from negativity, so he'd have appreciated similarly generous field placings from Cook, that allowed him to aggressively hit through the ball without fear of being caught, while keeping the score ticking over.
For England, the positives were the performance of their young batsmen, with both Robson and Moeen Ali scoring tons; the latter a masterclass of concentration and resistance that deserved to secure the draw. Plunkett, and to a lesser extent Jordan both bowled well, but Cook's failure trust his young players, and tendency to look to Broad and Anderson cost them. Anderson had a very good series, but he is better as a stike-bowler than a work-horse, and will be lucky to last the summer, with seven tests in such quick succession.
Sri Lanka achieved a famous victory, and their pace bowlers belied their reputation and averages (albeit averages mostly achieved in unfavourable conditions) to out-bowl the home side. But their batting looked terribly dependent on Sangakarra, and they need bigger scores from the rest of their top-6 to challenge sides who remember how to win matches.
5 TestsEnglandvIndia
Pre-rating1067.61150.1
Form-52.9+7.3
Expected MarginEngland by 9 runs
A series for the present regime, with five tests in seven weeks between cricket's biggest money-earners, if not their most in-form sides. India had a better tour of South Africa than is recognised, and might have won with better captaincy, or some more consistent performances from their pace attack. England, are a mess. Their youth looks promising, but is being let down by their senior players, and either a lack of belief, or captaincy that leads one to believe they can't win.
At home, against a still inexperienced Indian batting lineup, and a still weak Indian pace attack, England ought to win. The ratings don't indicate one side or another, but India have not won away of late, and that will matter. Much may depend on whether their secondary bowling can cover for the inevitable slumps that so much cricket in such a short period will bring. If it comes to that, England probably can find adequate replacements, whereas India almost certainly cannot. But runs matter too, and if India can adjust to conditions (or as is apparent at Trent Bridge, find them to their liking), they have the talent to score heavily. With both sides rebuilding, and neither with any great confidence it should be an interesting, if occasionally poorly played series.
Rankings at 10th July 2014
1.South Africa1299.4
2.Australia1273.7
3.India1150.1
4.Pakistan1093.9
5.England1067.6
6.Sri Lanka1035.6
7.New Zealand937.8
8.West Indies870.2
12.Zimbabwe560.2
10.Ireland594.8
11.Afghanistan587.6
13.Scotland430.3
14.Namibia383.4
15.Kenya276.4
16.U.A.E.257.3
17.Netherlands182.4
Shaded teams have played fewer than 2 games per season. Non-test team ratings are not comparable to test ratings as they don't play each other.
Cricket - Ratings - Test 10th July, 2014 01:07:13 [#] [0 comments]
## World Cup Group Qualification Russell Degnan
As per the last world cup, but this time more interactive, and theoretically better. The axes show the goal difference in the final group games. The flag shows the team that ought to be in the place. This cannot show where two teams are equal, and therefore puts the team with the current highest goals scored - taking into account the minimum ascertained from goal difference - in the highest place.
+5+4+3+2+1Draw+1+2+3+4+5
+5
+4
+3
+2
+1
Draw
+1
+2
+3
+4
+5
Football 24th June, 2014 02:01:25 [#] [0 comments] | {"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": 0.16951270401477814, "perplexity": 5330.973223422239}, "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-2014-35/segments/1408500815050.22/warc/CC-MAIN-20140820021335-00205-ip-10-180-136-8.ec2.internal.warc.gz"} |
http://www.newton.ac.uk/seminar/20100729173017451 | skip to content
# Limits of self-similar graphs and criticality of the Abelian Sandpile Model
Date:
Thursday 29th July 2010 - 17:30 to 17:45
Venue:
INI Seminar Room 1
Abstract:
We consider covering sequences of (Schreier) graphs arising from self-similar actions by automorphisms of rooted trees. The projective limit of such an inverse system corresponds to the action on the boundary of the tree and its connected components are the (infinite) orbital Schreier graphs of the action. They can be approximated by finite rooted graphs using Hausdorff-Gromov convergence. An interesting example is given by the Basilica group acting by automorphisms on the binary rooted tree in a self-similar fashion. We give a topological as well as a measure-theoretical description of the orbital limit Schreier graphs. In particular, it is shown that they are almost all one-ended with respect to the uniform distribution on the boundary of the tree. We study the statistical-physics Abelian Sandpile Model on such sequences of graphs. The main mathematical question about this model is to prove its criticality -- the correlation between sites situated far away each from the other is high -- what is typically done by exhibiting, asymptotically, a power-law decay of various statistics. In spite of many numerical experiments, the criticality of the model was rigorously proven only in the case of the regular tree. We show that the Abelian Sandpile Model on the limit Schreier graphs of the Basilica group is critical almost everywhere with respect to the uniform distribution on the boundary of the tree.
The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
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https://codereview.stackexchange.com/questions/114966/generate-symmetric-ascii | # Generate Symmetric Ascii
Have you got any suggestions to improve this code? The idea is to generate a one-line string that is visually symmetric.
Revisions at Github
<p id="display"></p>
<script>
var display = document.getElementById('display');
var chars = [33,34,39,42,43,45,46,48,58,61,72,73,77,79,84,92,94,95,111,124];
var double_chars = [40,41,47,92,60,62,91,93,123,125];
var double_chars_assoc = {40:41,47:92,60:62,91:93,123:125,
41:40,92:47,62:60,93:91,125:123};
function generateSymmetricAscii() {
var ascii_string = "";
var left_side = [];
for(var i=0; i< randomInt(2,50); i++) {
if(randomBool() == true) {
left_side.push(randomChoice(chars));
}
else {
left_side.push(randomChoice(double_chars));
}
}
var right_side = left_side.slice(0);
right_side.reverse();
for(var i=0; i < right_side.length; i++) {
if(inArray(right_side[i], double_chars) == true) {
previous_char = right_side[i];
right_side[i] = double_chars_assoc[previous_char];
}
}
var total_array = left_side.concat(right_side);
for(var i=0; i < total_array.length; i++) {
ascii_string += String.fromCharCode(total_array[i]);
}
return ascii_string;
}
function randomInt(min, max) { return Math.floor(min + (Math.random() * (max - min))); }
function randomChoice(choices) { return choices[randomInt(0, choices.length-1)]; }
function randomBool() { return Math.random() >= 0.5; };
function inArray(needle, haystack) {
var length = haystack.length;
for(var i = 0; i < length; i++) {
if(haystack[i] == needle) return true;
}
return false;
}
display.innerHTML = generateSymmetricAscii();
</script>
• if(haystack[i] == needle) - wouldn't you want strict equivalence, if(haystack[i] === needle), instead? – eis Dec 24 '15 at 11:45
• Can you explain what this code does in your question? – Nic Hartley Dec 24 '15 at 15:32
Wheel re-use
I Iike your usage of helper functions, inArray can be simplified by the use of indexOf:
function inArray(x, xs) {return xs.indexOf(x) != -1}
Repetition
You repeat left_side.push(randomChoice twice. You should avoid repetition in code and state each concept or action once and just once.
FP
This part of your code would benefit from Functional Programming:
var total_array = left_side.concat(right_side);
for(var i=0; i < total_array.length; i++) {
ascii_string += String.fromCharCode(total_array[i]);
}
return ascii_string;
Becomes:
return left_side.concat(right_side).map( String.fromCharCode).join("");
That looks much more declarative.
• How about return String.fromCharCode.call(left_side.concat(right_side));? That does exactly the same as your FP section. – Ismael Miguel Dec 24 '15 at 18:10
• @IsmaelMiguel If you feel like it is simpler, use it. Where is the equivalent of map though? – Caridorc Dec 24 '15 at 18:13
• The map equivalent is what you have on your answer. But that is way clucky: String.fromCharCode() actually accepts n parameters. Using String.fromCharCode.call(array) will actually be somewhat faster than array.map(String.fromCharCode).join(''). With your implementation, you have to: 1) mutate an array (horrible idea for performance), 2) run String.fromCharCode n times and 3) .join(''). With String.fromCharCode.call(array), you cut down your operations a lot. But whichever one is cleaner to you. I'm just saying an alternative that I've used before. – Ismael Miguel Dec 24 '15 at 18:19
• @IsmaelMiguel Cool I did not know that fromCharCode could have multiple arguments. Is this common in Javascript? – Caridorc Dec 24 '15 at 18:24
• As common as using Array.prototype.slice.call(arguments) and Object.prototype.toString.call(object). I'm sure you have seen both. – Ismael Miguel Dec 24 '15 at 18:25
Your coding style is inconsistent. Sometimes you use whitespace around your operators, sometimes you do not. Sometimes you put functions on one line, sometimes you put them on multiple lines. Which one you use seem to be up to random chance, which makes it harder to read your code.
variable == boolean is a bad practice. If variable evaluates to a boolean value true, then you can just use variable. Likewise, if you need the inverse, use !variable. If you want to test if the variable is true and of type boolean, use the === operator.
Javascript processes variable declarations in a context before executing the code. This process is called variable hoisting. This means that when you declare variables in the middle of a function, they are moved to the top. To avoid confusion why variables are defined before you declare them, or why local variables are used when you expected global variables to be used, I would recommend declaring all variables at the beginning of the context.
You are using more or less global variables with common names. This means that if you add another script, you might overwrite the contents of your current variables. I would recommend making it a closure:
(function() {
})();
Your code would benefit from some comments. For example, a comment above the loop that substitutes characters with their symmetric counter part would become more intuitive that way.
You are using magic numbers in randomInt(2,50). Consider replacing 2 and 50 with a variable, and define these variables at the top. This allows you to change such arbitrary values without having to touch the logic part of your program.
### Logic errors
Your function randomInt(min, max) will return an integer between min (included) and max (excluded). Your function randomChoice(choices) will select an element between 0 (included) and length-1 (excluded). This means that it is impossible to get the last element from choices back as a result.
Your function inArray(..) can produce false-positives if the types of the elements in your Array and the needle are not the same.
### Other improvements
You use your own function inArray(..), but you can accomplish the same by just using indexOf(..) and testing if the result is > -1.
You are using an Array and an Object for keys of an Object, and the Object itself. To get the keys of an Object, use Object.keys( variable ). With this you avoid bugs related to out-of-sync variables.
Omit the extra == true in conditions:
if(randomBool())
Use the ternary if operator to compact your code:
left_side.push(randomChoice(randomBool() ? chars : double_chars))
If this seems to dense for you, you can also extract the inner expression like this:
var options = randomBool() ? chars : double_chars;
left_side.push(randomChoice(options))
• The use of ternary if is one of personal preference. I personally dislike using it outside simple assignments, because it makes grouping the right things together harder for me, thus making it less readable for me. – Sumurai8 Dec 24 '15 at 14:45
• Yes, I think this is a corner case. I also thought about extracting the parameter to randomChoice into a local variable. I'll change that so we have two simple lines instead of one slightly more complex one. But I still prefer the ternary operator. – lex82 Dec 24 '15 at 15:51
• @Sumurai8 His suggestion avoids the repetition of left_side.push(randomChoice according to DRY principle, so it is objectively better. – Caridorc Dec 24 '15 at 15:51
• @carldorc I extracted the charArray parameter on purpose. I'll just provide both versions in the answer. – lex82 Dec 24 '15 at 15:55 | {"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": 0.30049604177474976, "perplexity": 2759.259580353548}, "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-2019-47/segments/1573496665573.50/warc/CC-MAIN-20191112124615-20191112152615-00193.warc.gz"} |
http://cs.stackexchange.com/questions/21613/why-cant-we-flip-the-answer-of-a-ndtm-efficiently | # Why can't we flip the answer of a NDTM efficiently?
I read several times that it is not possible to flip the answer of a NDTM efficiently. However, I don’t understand why. For instance, given a NDTM $M$ that runs in $O(n)$, this text (section 3.3) states that it is unclear how another NDTM $T$ can determine in $O(n^{100})$ time how to flip $M$’s answer.
My Problem is as follows: A NDTM outputs $1$ iff there exists a sequence of non-deterministic choices that leads to the accepting state. Furthermore, there exists a universal NDTM $NU$ that can simulate every NDTM with only a small (logarithmic) overhead. So why can’t we construct T as follows: First, simulate M with the universal NDTM which should be possible in time $O(n\log n)$. Then output 1 – M’s answer. This would mean that we can flip the answer of any linear NDTM in time $O(n\log n)$.
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A nondeterministic Turing machine accepts if at least one path accepts; it only rejects if all paths reject. This asymmetry makes it hard to "flip answers".
For example, suppose you have a nondeterministic Turing machine $M$ that has two paths for input $w$: one accepts, the other rejects. $M$ has at least one accepting path for $w$, so it accepts. Suppose we want to produce a machine that accepts exactly the inputs that $M$ rejects. The obvious first attempt is to take $M$ and make its accepting states reject, and its rejecting states accept. $M$ has one accepting path for $w$ and one rejecting path; this new machine $M'$ has one rejecting path and one accepting path. So it still accepts $w$, which it was supposed to reject!
A nondeterministic machine can't look at all its paths simultaneously and take action based on what all of those paths do. If you like, you can think of it as a form of parallelism where the threads are forbidden to communicate with each other. When all of the threads have finished the program must ask itself the following question: "Did at least one of my threads accept?" If the answer is yes, it is legally obliged to accept; if the answer is no, it is legally obliged to reject. It cannot do anything else.
When you simulate a nondeterministic machine $M$ using another one, $M'$, each path of $M'$ simulates one path of $M$ and sees only that path. It can't say, "If all those other paths rejected, I'll accept" because it can't see the other paths; it can only see itself. So all it could possibly say is things like, "If the path I simulated accepted, I'll reject" or "If the path I simulated accepted, I'll accept too". Then, at the end of the computation, the machine has to say, "If any of my paths accepted, I'll accept too", leading to the problem I described above. To invert the behaviour of $M$, each path of $M'$ needs to say, "If the path I simulated accepted, I reject; else, I accept" and, at the end of the computation, the machine needs to say, "If all of my paths accepted, I accept; else, I reject." This is because, if all of the simulator's paths accepted, that means all of $M$'s paths rejected, so $M$ rejected, so the simulator needs to accept. But the simulator isn't a valid nondeterministic Turing machine because it isn't using the legally mandated acceptance criterion. It can't do that.
The only way we know to figure out if a nondeterministic machine rejects its input is to try every possible path and verify that they all reject. After all, if even one of them accepted, the machine would accept the input. But trying every possible path is exponentially slower than trying just one.
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The problem is that NDTM are inherently non-symmetric: the time $O(n)$ means that they have $O(n)$ steps to guess an accepting path if exists, and will reject otherwise (if no accepting path exists).
The problem is that if your machine $NU$ is really in $O(n log( n))$, it means that it guesses in $n log (n)$ steps a witness that $M$ rejects the input. This might not be possible to do, because there are no witnesses of rejection of $M$, just witnesses of acceptance. Rejection is the absence of witness, so it is not easy to prove rejection in a short time.
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actually technically you are asking the P$\stackrel{?}{=}$coNP($\stackrel{?}{=}$NP) question which is open. it is widely conjectured but not proven that they are not equal. the other answers are intuitive sketches/circumstantial evidence why they are not equal.
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Actually, he's asking something similar to co-NP=NP: it's perfectly possible that P and NP are different but NDTMs can be efficiently negated. – David Richerby Feb 19 '14 at 0:45 | {"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": 0.9112251400947571, "perplexity": 710.8490404287234}, "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-2015-18/segments/1429246660743.58/warc/CC-MAIN-20150417045740-00312-ip-10-235-10-82.ec2.internal.warc.gz"} |
http://www.tianranchen.org/teaching/calc3/det/ | Matrix determinant
The determinant is an important numerical value that can be computed from a square matrix. The determinant of a matrix $A$ is usually denoted by $\det(A)$ or $|A|$. One geometric interpretation of determinant is the signed scaling factor of the transformation represented by the matrix.
2x2 cases
For a 2x2 matrix, we have simple formula for its determinant:
$\det \begin{bmatrix} a & b \\ c & d \end{bmatrix} = ad - bc.$
It is easy to verify that the absolute value of the determinant is exactly the area of the parallelogram spanned by the two column vectors. The sign of the determinant tells us about the “orientation” of this parallelogram (homework).
3x3 cases
For a 3x3 matrix, the formula is much more complicated:
$\det \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix} = aei + bfg + cdh - ceg - bdi - afh.$
This looks rather complicated. I would not recommend anyone to spend much energy memorizing this formula. Instead, we should use the cofactor expansion:
$\det \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix} = a \det \begin{bmatrix} e & f \\ h & i \end{bmatrix} - b \det \begin{bmatrix} d & f \\ g & i \end{bmatrix} + c \det \begin{bmatrix} d & e \\ g & h \end{bmatrix}$
In this formula, each 2x2 determinant is called a minor. Similar to the 2x2 cases, we have a nice geometric interpretation for the 3x3 matrix determinant: It is the “signed volume” of the parallelepiped spanned by the three column vectors. | {"extraction_info": {"found_math": true, "script_math_tex": 3, "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": 0.9743648767471313, "perplexity": 202.9455258636046}, "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-2017-47/segments/1510934805417.47/warc/CC-MAIN-20171119061756-20171119081756-00089.warc.gz"} |
https://dsp.stackexchange.com/questions/8937/why-are-there-only-a-few-high-frequency-components-in-the-discrete-cosine-transf | # Why are there only a few high frequency components in the Discrete Cosine Transform?
I am learning about the Discrete Cosine Transform (DCT) and I read somewhere that, in general, images have very few high frequency components. Can someone give me an intuitive explanation for why this is so? Is this assumption violated in any scenario?
## 4 Answers
There are two parts to the answer. One has to do with the nature of sharp edges, the second has to do with the how imaging systems (lenses and the human eye) work.
As @PeterK's example demonstrates artificial (human created) images tend to have large regions of one color with sharp transitions between the regions. This is similar to a square wave. But if you look at the fourier transform of a square wave it will be a decreasing sum of the odd frequencies: $$\sum_{n=1, 3, 5, ...}\frac{1}{n} \sin{ n \omega t}$$
Images of the natural world also often have regions of slowly changing color with sharp transitions where one object overlaps another. There can actually be a lot of high frequency "texture" in an image (grass, leaves, a pebbly beach, waves on water that is relatively far away, whispy clouds) but the sharp edges of the occlusions (overlaps) obey the same square-wave fall-off in frequencies beyond the fundamental frequency (the average distance between tree trunks, blades of grass, etc.)
The second part of the answer is that imaging systems (camera lenses/eyes) can not make out features smaller than a certain minimum angular resolution. Images outside of the imaging systems depth of field will be blurred because lenses have focal points. But even objects inside the depth of field will be blurred. This is because the aperture through which the light must pass must be reasonably large (several mm) in order to let in enough light. But this means that point-sources of light actually create a circle of confusion that essentially acts as a low-pass filter.
Because of this the human eye, for example, is more sensitive at some frequencies than others. In the below image the contrast differences across horizontal scans in the image are the same, but your eye is more sensitive to mid-frequency contrast differences than high-frequency contrast differences. (You may have to adjust the distance from the image to your eye to see the effect line up with the black line drawn on the image.)
High frequencies correspond to rapid changes in pixel intensity over a small displacement (a few pixels) - most "natural" images have large features which change relatively slowly so most of the information is in the lower spatial frequency range. High frequencies tend to be mainly noise, sharp edges or very fine textured features.
Note also that a similar general principle also applies to audio - most of the information is in the lower part of the audible range, while the higher frequencies are mainly noise and less important details.
Regarding exceptions: Scanned monochrome documents, especially drawings/engravings/comics/technical blueprints, can have high frequency components, due to the sharp edges, fill patterns and use of cross-hatching.
First, most images have pixel values that are always positive. For example, 8-bit grey-scale images usually have pixel values in the range from 0 to 255. So a fundamental reason for images having "smaller" high-frequency components is that there is always a large "DC" (zero-frequency) component.
Take, for example, this test image.
Most of the background has a value of about 140 or so, as can be seen from this cross-section at row 543.
This image is obviously a test image, and so contains several elements of higher-than-normal frequency. However, even this image does not contain much energy in the high frequency range, as can be seen from taking the FFT of the same row 543 (with the mean-value removed). | {"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": 1, "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": 0.711992084980011, "perplexity": 603.9009350353514}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "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-2019-47/segments/1573496668699.77/warc/CC-MAIN-20191115171915-20191115195915-00150.warc.gz"} |
https://bkms.kms.or.kr/journal/view.html?doi=10.4134/BKMS.b150623 | - Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
On commutativity of skew polynomials at zero Bull. Korean Math. Soc. 2017 Vol. 54, No. 1, 51-69 https://doi.org/10.4134/BKMS.b150623Published online August 25, 2016Printed January 31, 2017 Hai-Lan Jin, Fatma Kaynarca, Tai Keun Kwak, and Yang Lee Yanbian University, Afyon Kocatepe University, Daejin University, Pusan National University Abstract : We, in this paper, study the commutativity of skew polynomials at zero as a generalization of an $\alpha$-rigid ring, introducing the concept of strongly skew reversibility. A ring $R$ is be said to be \emph{strongly $\alpha$-skew reversible} if the skew polynomial ring $R[x;\alpha]$ is reversible. We examine some characterizations and extensions of strongly $\alpha$-skew reversible rings in relation with several ring theoretic properties which have roles in ring theory. Keywords : strongly $\alpha$-skew reversible ring, reversible ring, $\alpha$-rigid ring, skew polynomial ring, Dorroh extension MSC numbers : Primary 16W20, 16U80; Secondary 16S36 Downloads: Full-text PDF | {"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": 0.25342831015586853, "perplexity": 6852.260537261599}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "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-2021-17/segments/1618038078021.18/warc/CC-MAIN-20210414185709-20210414215709-00315.warc.gz"} |
http://christophermeiklejohn.com/life/2017/04/29/one-year.html | # Christopher Meiklejohn
home lasp research courses publications videos code curriculum vitae
## Reflections on One Year of Grad School
29 Apr 2017
As of March 28th, 2017, I’ve been a graduate student for one year at the Université catholique de Louvain, funded by a fellowship from the Erasmus Mundus Joint Doctorate program in the European Union. This post chronicles my journey of obtaining a visa, moving to Belgium, and the experiences from the first year of my Ph.D.
The expectation was that I would quit my job at Basho in August 2015, which I did, take some short-term contracting assignments while preparing to move, obtaining the required paperwork, and generally wrapping up my life in the United States before setting off. This didn’t go exactly according to plan, because of complicated circumstances around obtaining a visa.
## Moving to San Francisco
I took a job at a company in San Francisco as a temporary assignment – they knew I would only be there for few months before I obtained my visa for Belgium – and subsequently moved immediately to San Francisco from Paris, where I had been living for a few months at the end of my time at Basho, given they were a remote company. With a quick stop over in Providence, I sold and donated all of my belongings (to various charitable organizations, friends, etc.) which included a very large vinyl record collection, four turntables and recording equipment, over 1,500 novels and literature, a bunch of vintage computers including a several SparcStations, a SGI Indy, and my original Commodore 64, and my car. It was sad to see it all go, but it was time to start a new life; a new life abroad!
I was both excited, and naive.
Given that I thought I was leaving San Francisco in a few short months, I arranged to stay in an Airbnb in the Tenderloin when I arrived, and then later find a longer-term apartment that would be somewhat cheaper if I needed to stay longer. This ended up turning into a situation where I was switching Airbnb’s every week, because I couldn’t find something that was both available and cheap enough to stay in for an extended period of time.
Once I arrived, I began working on obtaining a visa for Belgium. It’s actually unclear if this visa was actually needed as it’s mainly required for entry only if your country doesn’t participate in the visa waiver program, but when I went to obtain my resident card, I was not required to show it to any one in my commune, nor did I need to have the visa renewed when it expired this March. Alas, I followed the university’s instructions.
## Getting the Visa
Getting the visa ended up being a complicated process. I arranged to see a doctor in SF on Russian Hill who does immigration exams and went through a rudimentary physical examination. The form he was instructed to fill out, that I printed from the Belgian consulate’s website, looked so fake that he didn’t believe the form was real at first. He then went to the website himself and found out that the form was, in fact, a real form and proceeded to fill it out and gave it to me. I took this form to a notary in SF to get it notarized, and they didn’t accept it; they needed the doctor to sign it. I told the doctor this and then arranged to have the form notarized; they scheduled an appointment and then were visited the notary who obtained the signed forms.
This also wasn’t enough. I later found out that I needed the form designated from an international notary (keep in mind, this form states that I didn’t have tuberculosis or the plague) and I’d have to repeat the process. I took the form to an international notary, who was mobile and wasn’t there when I arrived in the office, and later had to schedule an appointment. I was then informed that this form needed to go to Sacramento, that’s the only place where the officiant was, and I’d have to supply an overnight postage prepaid, or have the courier drive there themselves to pick it up, as I didn’t have a car, if I needed to get it in the following days.
[So far, we’ve spend $500, given FBI fingerprints, overnight background checks, and a medical report that wasn’t covered under insurance.] I received the notarized report a few days later and schedule a single day flight to Los Angeles to visit the Belgian consulate to apply for the visa. I arrived in Los Angeles about 4 hours before my appointment, which had to be scheduled 72 hours in advance [I had schedule the appointment before receiving the notarized forms, in the hope they would arrive in time – the first time I did this they didn’t and I had to cancel my appointment with the consulate.] The Belgian consulate was extremely nice – there was no one there when I arrived early and said I would wait, so they saw me immediately, didn’t care that I had not provided enough copies of one of the forms and had incorrectly filled out a section of another and I was out of there within 25 minutes. They said I would receive the visa back the following day, and that they would send it overnight postage, which I provided to them when I arrived. In the mean time, I’ve been moving from apartment to apartment, saying week by week in private rooms in different neighborhoods: the Tenderloin, Mission, etc. I eventually ended up leaving my suitcase at work instead of moving it from location to location and bringing clothes home in a smaller bag. Eventually, I landed a place to stay where I no longer needed to move. I tried looking for something more longer-term or a sublet, but I either received no response, they didn’t want someone with such a short-time frame, or someone who was traveling quite a bit for conferences and to obtain the visa. One of the places I stayed with Airbnb, the renter was extremely irritated [for some reason, in that I just wasn’t there or coming and going too often] that I was traveling a bunch: I was gone for a trip to Sweden for a conference, and then a conference in Las Vegas, both to present work-in-progress or peer-reviewed published work. [Total expenditure on the visa: roughly$1,500, with flights, exams, and paperwork.]
The day after I receive my visa, I receive an email from my advisor stating that if I’m not in Belgium to sign the forms by March 28th, I forfeit my fellowship. I’m about to book a trip to Belgium, waiting for a response from my advisor that states I can only be reimbursed for the travel to Belgium and not prepaid even though I’m provided with a “moving” allowance, when the Brussels airport is attacked by terrorists.
I have three days to book a ticket to Charles de Gaulle, travel to Belgium by train, and make it there with one day to spare. I arrive and find out I don’t have to physically sign anything after all, and check into my university flat.
[Last minute one-way flight to Charles de Gaulle: $1,800] Meanwhile, I had quit my short-term job and was told that given I didn’t stay a year, I would forfeit all of my stock options and have to repay my relocation benefits, even though they knew before I started I wouldn’t be there for more than a year because I was going to grad school. We ended up coming to an agreement around this, but this is what I get for not being more diligent with reading employment contracts. ## The First Year: Accomplishments and Criticisms My first year at the university was decent. Let’s look at what happened during this year. • I spent over 200 days at affiliated universities and conferences, and wasn’t at my home university; • I attended EuroSys, ICFP, ECOOP, and various other academic events; • I assisted in organizing Curry On; • I started the PMLDC workshop at ECOOP on distributed programming; • I co-chaired the Code Mesh conference; • I visited Cambridge, Kent, Minho, Oxford, IMDEA, and other universities on research visits; • I spoke at Percona, Erlang User Conference, Erlang Factory, CRAFT Conference, numerous Papers We Love meetups, GOTO London, GOTO Chicago; • I was a subreviewer for CloudCom, and shadow PC for EuroSys; • I TA’d two courses; one on Cloud Computing and one on Distributed Algorithms; • I mentored two students in the Google Summer of Code, one of which presented a paper based on his work at AGERE! 2016; • I performed a large scale evaluation of Lasp for the SyncFree project and ran a live demo of our research prototype at the final review at the European Commission [scary!]; • I scaled Lasp to 1024+ nodes, challenged the design of distributed Erlang and showed higher scalability in Erlang than ever demonstrated before; • I was the recipient of a Microsoft Research internship in Redmond this summer; • Our Lasp prototype is used by one company and the supporting infrastructure is used by another. It’s been a whirlwind year, but I’m still feeling stressed out, overwhelmed, and upset. Why is that? • I haven’t published enough papers; we tried to publish a few things related to our work but spend the better part of the year doing an evaluation for the EU that totaled at over 9,900+ euros; • Erasmus does not provide enough money nor time for student. The salary is good, but the costs involved in obtaining visa’s, moving and relocating every year is a pain. In fact, I basically have spent two months out of the year dealing with logistics around moving to Belgium and moving to Portugal and will have to repeat this process in another year; • Relocating every year is counterproductive, as much as it’s supposed to facilitate and support integration in the European Union; • I’m the only person in my lab, I sit alone and work alone. In fact, there were multiple times this year where I was supposed to have a lab mate, but they were put into other offices instead. This is why I prefer to travel to do anything collaborative with my coworkers. • Moving takes a toll; it distracts from research, and cuts into your time; • Is three years enough for a Ph.D.? The funding that is provided only covers three years, but it seems that most of the students in my lab have needed at least a fourth, and have had to find additional funding for it. Now, those are all academic complaints, but let’s talk about more practical complaints as an international student in Europe: • I haven’t been able to defer my loans from my undergraduate studies yet. This is a problem because the payment is over 1/2 of my rent as a Ph.D. student; • Required travel and expenses have left me, at times, with over 3,000 euros of outstanding expenses. It has taken the university, at times, over 12 months to reimburse me for these expenses; • Having to move every year means that you need to find an apartment every year. I’ve had problems where Portugal landlords haven’t responded, even yet, to my requests, and I haven’t been able to secure my apartment, which is required to get a visa and resident card; • Expedited passport renewals in the US are expensive – I’ve paid over$400 for this – and required for me to maintain my student status at return to the university from abroad;
• Belgian income, even if tax-free, is taxed in the United States, if you are a citizen: the double taxation agreement only works on taxes paid – if you’re tax free, you don’t pay taxes and therefore don’t get any benefits;
• Working alone and moving from lab to lab sucks. It’s impossible to have a community and feel like you have a support system when you move every year. While the European Commission might think you are promoting integration by moving people from country to country, what it is not doing is making it so people can have good working relationships and be healthy.
My time has been wonderful, but I sometimes wonder what it would be like if the environment was more conducive to ensuring, first-class, that Ph.D. students had the time and resources to perform good research without feeling like they were running against the clock. | {"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": 0.1513475775718689, "perplexity": 1750.3932246677316}, "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-2018-47/segments/1542039741294.2/warc/CC-MAIN-20181113062240-20181113084240-00456.warc.gz"} |
https://www.acmicpc.net/problem/11210 | 시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
2 초 256 MB 24 11 3 20.000%
## 문제
After your boat ran out of fuel in the middle of the ocean, you have been following the currents for 80 days. Today, you finally got your radar equipment working. And it’s receiving signals!
Alas, the signals come from the “radar” station owned by the eccentric lighthouse keeper Hasse. Hasse’s radar station (which does not work quite like other radar stations) emits continuous signals of three different wave-lengths. Therefore, the only interesting thing you can measure is the phase of a signal as it reaches you. For example, if the signal you tuned on to has a wave-length of 100 meters and you are 1456 meters from the station, your equipment can only tell you that you are either 56, or 156, or 256, or . . . meters away from the lighthouse.
So you reach for your last piece of paper to start calculating – but wait, there’s a catch! On the display you read: “ACCURACY: 3 METERS”. So, in fact, the information you get from this signal is that your distance from Hasse’s radar station is in the union of intervals [53, 59] ∪ [153, 159] ∪ [253, 259] ∪ . . . .
What to do? Since the key to surviving at sea is to be optimistic, you are interested in what the smallest possible distance to the lighthouse could be, given the wavelengths, measurements and accuracies corresponding to the three signals.
Given three positive prime numbers m1, m2, m3 (the wavelengths), three nonnegative integers x1, x2, x3 (the measurements), and three nonnegative integers y1, y2, y3 (the accuracies), find the smallest nonnegative integer z (the smallest possible distance) such that z is within distance yi from xi modulo mi for each i = 1, 2, 3. An integer x' is within distance y from x modulo m if there is some integer t such that x ≡ x' + t (mod m) and |t| ≤ y.
## 입력
There are three lines of input. The first line is m1 m2 m3, the second is x1 x2 x3 and the third is y1 y2 y3. You may assume that 0 < mi ≤ 106, 0 ≤ xi < mi, and 0 ≤ yi ≤ 300 for each i. The numbers m1, m2, m3 are all primes and distinct.
## 출력
Print one line with the answer z. Note that the answer might not fit in a 32-bit integer.
## 예제 입력 1
11 13 17
5 2 4
0 0 0
## 예제 출력 1
2095
## 예제 입력 2
941 947 977
142 510 700
100 100 100
## 예제 출력 2
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https://borea.mnhn.fr/fr/characterization-defensin-oyster-crassostrea-gigas-recombinant-production-folding-solution-structure | # Characterization of a defensin from the oyster Crassostrea gigas. Recombinant production, folding, solution structure, antimicrobial activities, and gene expression
Titre Characterization of a defensin from the oyster Crassostrea gigas. Recombinant production, folding, solution structure, antimicrobial activities, and gene expression Type de publication Journal Article Year of Publication 2006 Auteurs Gueguen, Y, Herpin, A, Aumelas, A, Garnier, J, Fievet, J, Escoubas, J-M, Bulet, P, Gonzalez, M, Lelong, C, Favrel, P, Bachère, E Journal The Journal of Biological Chemistry Volume 281 Pagination 313–323 ISSN 0021-9258 Résumé In invertebrates, defensins were found in arthropods and in the mussels. Here, we report for the first time the identification and characterization of a defensin (Cg-Def) from an oyster. Cg-def mRNA was isolated from Crassostrea gigas mantle using an expressed sequence tag approach. To gain insight into potential roles of Cg-Def in oyster immunity, we produced the recombinant peptide in Escherichia coli, characterized its antimicrobial activities, determined its solution structure by NMR spectroscopy, and quantified its gene expression in vivo following bacterial challenge of oysters. Recombinant Cg-Def was active in vitro against Gram-positive bacteria but showed no or limited activities against Gram-negative bacteria and fungi. The activity of Cg-Def was retained in vitro at a salt concentration similar to that of seawater. The Cg-Def structure shares the so-called cystine-stabilized alpha-beta motif (CS-alphabeta) with arthropod defensins but is characterized by the presence of an additional disulfide bond, as previously observed in the mussel defensin (MGD-1). Nevertheless, despite a similar global fold, the Cg-Def and MGD-1 structures mainly differ by the size of their loops and by the presence of two aspartic residues in Cg-Def. Distribution of Cg-def mRNA in various oyster tissues revealed that Cg-def is mainly expressed in mantle edge where it was detected by mass spectrometry analyses. Furthermore, we observed that the Cg-def messenger concentration was unchanged after bacterial challenge. Our results suggest that Cg-def gene is continuously expressed in the mantle and would play a key role in oyster by providing a first line of defense against pathogen colonization. | {"extraction_info": {"found_math": false, "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": 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": 0.8374226689338684, "perplexity": 16116.834648897055}, "config": {"markdown_headings": true, "markdown_code": false, "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-2020-24/segments/1590347426801.75/warc/CC-MAIN-20200602193431-20200602223431-00427.warc.gz"} |
http://www.halfbakedmaker.org/ | # Monroe Calculating Machine Company at the Internet Archive
I've recently come into a large cache of original documents from the Monroe Calculating Machine Company, spanning from 1919 to the 1970s. Most of these are Machine Service Bulletins, which were sent out approximately weekly to Monroe field offices around the country. These MSBs ran the gamut from one-pagers describing how to fix something, to 100-page manuals showing in detail how to disassemble, reassemble, and adjust an entire model of calculator.
There are also some course books, instruction manuals, ads, a newsletter or two, reference cards.
I've scanned all of these, and placed them on the Internet Archive for anyone to read!
Of particular interest are:
• The 1919 instruction book for the Monroe Calculating Machine [link]. The machine depicted is a model D, but 1919 would put it in the model G era.
• Machine Service Bulletin 34 [link], a full disassembly, assembly, and adjustment guide to the K-0 and KA-0 calculators.
• Machine Service Bulletin 40 [link], a full disassembly, assembly, and adjustment guide to the K-1AA and K-2AA calculators.
• Machine Service Bulletin 45 [link], showing what a bad day they were having.
• Machine Service Bulletin 95C [link], illustrated parts guide for various L and LA calculators with prices for each part.
• Machine Service Bulletin 116 [link] (with its supplement 116A [link]), a full disassembly, assembly, and adjustment guide to the MA-213 calculator.
• Book 1 in the Service Training Course [link].
Enjoy! And if you have any Monroe publications that aren't in the Archive, please let me know, I'd like to add them.
# Elektronika MS-1103 (Электроника МС-1103) Manual
Probably because of my RPN Nixie calculator project, I got interested in Soviet-era calculators. There are some MC-1103 calculators on eBay, so I bought two. The first one came without a manual, so I decided to open it and reverse-engineer it.
As you can see, it works. Interestingly, it truncated pi. If it rounded, it should end in a 3. I plugged it in to a 110-to-220 converter. However, US AC voltage is 120 which means that I actually get 240 VAC out. This would result in increased AC voltages inside, but the DC voltages should not be affected if they were regulated.
The above image shows the power supply removed from the case. There's a big transformer on right, and what appears to be four series pass transistors. Each such section also had a multi-turn potentiometer, presumably for fine adjust of voltage, and a chip. There were actually two types of chips: кпен2г (KPEN2G) and кп142ен1г (KP142EN1G).
From cpu-ukraine's article on Soviet chip identification, I learned that Soviet chips were all marked in a nation-wide standardized way. KP meant commercial use, plastic package. 142 was the chip family, EN was the type, and 1G was the model.
I also learned, by piecing together statements on various forums and Russian chip resellers that KPEN2G was shorthand for KP142EN2G (so they are the same chip, different models), that they were linear adjustable voltage regulators, that 1 meant Vin max 20v, Vout 3-12v and 2 meant Vin max 40v, Vout 12-30v, and G meant 0.2% regulation. I also found that they were equivalent to the LM723 regulator, but with a different pinout.
The pass transistors were КТ817А and КТ817Б (KT817B). These are NPN power transistors, A meaning 25v max and B meaning 45v max, and they were equivalent to the BD175 transistor.
Putting all this together, I was able to draw a schematic. The power supply provides regulated 5v, 15v, -15v, and -27v.
Anyway, as I was poking around with my multimeter with the power on, I heard a hissing sound and quickly cut the power. One of the capacitors had sprung a leak! Further investigation showed that it had taken its voltage regulator and series pass transistor with it. Maybe I shorted something? In any case, I had to replace these, and I used an LM317, a three-terminal adjustable voltage regulator which combined the chip and the pass transistor.
After a really messy install, the power supply worked again.
Then I got the second calculator, and it came with a manual. And the manual included schematics. Aside from the missing connection between the transformer's terminal 12 and the other end of the VD21, I got most of it right.
Anyway, here's the scan of the user manual I put up on the Internet Archive. Enjoy!
# Raise3D N2: Vibrations (and solution)
Suddenly, a new feature appears :( The y-axis is nice and smooth but the x-axis is vibrating when it moves. It vibrates so hard that it seems to lose steps. Here's a print where the next layer is shifted over to the left a bit.
Sent these to Raise3D. Let's see if there are some adjustments I can make to get rid of the vibration.
Update: After a day of working with Raise3D, no progress with anything we tried. Everything seems good, nothing loose, broken, wobbly, shaky, or out of alignment except one of the screws on one of the bushings is stripped and wouldn't tighten. Replaced, still no good.
Thinking back, when my friend helped me set this printer up, and we tried the first print, he did notice a vibration in the x-axis, but I didn't pay attention because the print seemed to be going okay. I thought maybe it was normal. Clearly not.
The next day, I got some grease. Not SuperLube (PTFE grease), which is THE grease to have, but unfortunately because it's so good, nobody stocks it.
Instead I got some silicone grease. It seems thick, but in any case I liberally coated the rods and packed the bearings where they meet the rods, and... no vibrations! The printer is really quiet now.
Trying a small print now, and will follow up with a larger 15-hour job to see how this stuff holds up. Will also replace this grease with SuperLube once I get it in.
About 14 hours in.... This is the Vanderbilt mansion [Thingiverse 10485], model scaled to 50%, 0.15 mm layer height, 10% infill.
# Raise3D N2: second impression
The next print failed.
I started this up before I went to bed, and in the morning I found the head merrily moving around a few inches above the prints. What probably happened is what Raise3D suggested previously when I said that the purge cycle didn't purge anything: the "third-party" filament clearly was not being fed.
I looked closer at the feed point.
Now, this image was from after I unloaded the filament, cut off the faulty bit, and was about to load it back in. Here's the faulty bit:
There are a few features to note here. First, on the right, we have the toothmarks from the feeder gear. This is normal. Then, we have a circular depression where the feeder gear ground into the filament. This is not normal, and is what happens when the filament gets stuck. Finally, on the left side you can see a bend in the filament. Also, the filament has changed from semitransparent white to opaque white. This is the result of the filament being bent.
For example:
Bending the filament like this produced the exact same result. Now, here's a look at the whole feed path.
Note that there is nothing preventing the filament from being bent around that sharp radius. The printer is relying on the roll of filament being easy to move as the head moves around, and I am not convinced that is true for a 1kg roll of 1.75mm ABS. I used LD Product's brand of natural ABS.
My Ultimaker2 has a tube that runs all the way from the feeder gear in the back up to the extruder. No sharp radius possible. I don't know if the method Raise3D is using is new or not, but I'm a little suspicious.
At this point I am not ready to blame the printer. It could be the filament. I have some Toy Builder Labs 1.75mm ABS filament coming. Raise3D only sells PLA filament, not ABS. So can the printer handle ABS? It's supposed to. Raise3D has also acquired Toy Builder Labs, so I can only hope that the filament Toybuilder sells will (eventually) be compatible with the printer.
While I'm waiting for the Toy Builder Labs filament to come in, I'm going to redo the print using the PLA filament that came with the printer.
Now, when I removed the ABS roll, I found that the filament had come off the roll and was wound around the filament holder. That would absolutely cause an increase in drag.
This is fairly typical. Sometimes filament comes off the roll, and then you're in trouble. The solution is to add a plate which holds the filament on the roll.
I'm going to see if the same problem happens with the PLA. It might not because PLA is not as stiff as ABS and may not come off the roll. After that print, I'm going to print up a plate out of PLA which will fit behind the roll and hopefully help this situation.
I haven't lost hope!
# Raise3D N2: first impressions
Got my Raise3D N2 today. The good news is, it worked right out of the box. A few standouts were that I didn't have to level the bed, the touch screen is awesome, and the whole thing looks great. It's also very very quiet.
51 kg of fun
All the things in the box
All the things inside the thing in the box, except for the drill which is shown for size.
Set up and almost ready to go
However, there are a few things that need fixing. Some are pretty minor. Some are major. I emailed Raise3D all of these, and they got back to me within half an hour! In no particular order (Raise3D's response in italics):
1. The quick-start guide (section C step 3) says to unscrew the 2 nuts holding the Z-axis in place. I'd use the word clamps instead of nuts. Also I'd say to unscrew the 2 screws on each of the two clamps holding the Z-axis in place. It's just clearer that way.
2. The quick-start guide (section G step 4) says that the USB storage included with the printer comes loaded with already sliced models. It did not.
3. Sorry, there's Chinglish in the software, which is sad because the printer looks so good. If you make these changes, it will look much better:
[Note: Chinglish really bothers me. It's not hard to find a native speaker of English that knows Chinese. Or heck, even a native speaker of English that doesn't know Chinese, who can do a second pass on the wording like I just did. I don't think there's any excuse for manuals not to be in good, grammatical English.]
a. "Task Finished! Please take the models off from the bed." -> "Task finished! Please take the models off the bed." (don't capitalize the "f" in "finished", and use "off" instead of "off from").
b. Under the extruder loading screen: "When the extruder gear started rotating, feed the filament into right extruder;" -> "When the extruder gear starts rotating, feed the filament into right extruder." (started -> starting, don't use a semicolon at the end of the sentence; use a period. There's a reason for the semicolon and separating list items isn't it :) ).
c. Also under the extruder loading screen: "When hot end reached target temperature, press "Load" button to next operation." -> "When hot end reaches target temperature, press "Load" button to continue." (reached -> reaches, and you need a verb after "to")
yes, we will change that for the next update.
4. The BuildTak has bubbles in it. This is very very bad, since the part will not be flat.
We have complained about that to BuildTak a lot also. For now, please use a needle to poke each bubble to release the air and flat it.
5. Under Utilities, the strange symbol in the upper left (which I now recognize as a stepper motor) disables the motors. But there doesn't seem to be a way to re-enable the motors. Pressing that button again just goes right back to saying it disabled the motors.
It is just a one motion button--to disable the motors so that you can push the extruder around. As soon as you use the touchscreen to move the extruder, it will go back on(enable).
6. When I pressed the disable motor button, cancelled the dialog, pressed it again, cancelled the dialog, and did it a few more times, eventually the response became slow and then the touch screen did not respond to touches any more. It did eventually go back to the home screen, and I saw the temperature monitors were still working, but the touch screen remained unresponsive. The only solution was to turn off the printer and turn it on again.
That is an issue we are working on right now. Also do not hold the button for too long otherwise it may freeze and you have to turn it off and on again.
7. Speaking of turning the printer off, the power switch is located in a very inconvenient place. The thing is nearly 60 cm deep, and it's hard to reach around to get to the switch. I suggest that the next iteration have the switch on the front or on the side near the front.
8. No ground. The power cable that comes with the printer is two-prong with some kind of small green wire hanging off it. This is very very bad. Power cables should use all three prongs, and the case should be grounded using the ground wire. This is a shock hazard and you could be barred from importing this printer into the US unless you ground the machine properly.
[Note to all: I admit I'm probably wrong about this thing being barred from the US for not being grounded. Still, it's a good idea, no?]
We will switch to a standard 3-prong plug.
9. The purge cycle at the start of a print worked fine, but then the purged stuff didn't get wiped off onto the BuildTak. It actually was being dragged around during the print. I had to reach in there and pull it out.
Sometimes it wipes and sometimes it does not. We will think about a way to solve this.
10. After the print is done, the bed does not move down to the bottom. I have to manually move it. But moving it seems to be difficult: I went to Utilities and hit the Z-down button. It moves at most 10mm at a time, and it doesn't move continuously. I have no idea how I'm supposed to move the bed down. On the other printers I've used, the bed moves all the way down after the print is done so you can remove the print easily.
Ya, we are thinking about the Z movement. We might add a button to tell Z axis to move the bottom instead of 10mm a step.
11. When stopping a print, the print should stop immediately and the heaters should turn off. I found that if I wanted to cancel a print just after I started a print, the "Stopping print" message came up, and then did nothing. The nozzle and bed seemed to continue to heat up. I would expect that stopping the print would completely stop the process.
That is a Marlin thing. It has to heat up to desired Temperature before it can stop. We will think about a way to get around this.
12. When heating up, the nozzle temp gauge goes up but the bed temp gauge stays at "25/0" until the nozzle temp turns green, then the bed temp suddenly changes to "75/100". It's like the bed is heating up, but the gauge does not show its temp until the nozzle has completed heating up.
Again, this is also a Marlin thing. We have already fixed this. Please update the firmware and it should be fine. You can find it on our website under download.
13. When I started my second print, the nozzle and bed heated up, then the bed calibrated itself, then the purge cycle began, but nothing came out. Then the print started, and still nothing came out. I verified that the feeder gears were turning. It looks like the purge cycle isn't purging enough to fully load the extruder.
It seems that the filament is stripped due to gear teeth grinding. You can take off the cover and check whether the filament is actually going in or not. If the filament is not going in, then you need to unload the filament and re-load it again. Also using 3rd party filament may cause clogging issue.
A little tip is to always load a little bit filament before printing. If there is something wrong, you can spot it sooner.
Right now I have the printer printing a 17 hour job as a kind of torture test. We'll see how it goes, but from Raise3D's responsiveness so far, and the quality of the one print I finished, after all the usual initial bugs are worked out, this looks like it will be an excellent printer!
# Cleaning a TRS-80 model III keyboard
I have a TRS-80 model III.
It has a keyboard. It doesn't work so well. Some keys don't work, others are flaky.
So I opened it up and popped the keycaps off.
I removed the keyboard assembly. It's an Alps 12KE010C.
Well, that explains some of the keys not working at all. The only thing protecting the keyboard PCB from the plastic post in the base of the computer is... nothing. Oh Radio Shack. Were you already beginning the long slow slide into oblivion?
Still doesn't explain flaky keys. So I desoldered a key, since that's the only way to get them out.
I measured the resistance when pressing the key.
160kohms?! That's just wrong! Let's open this thing up. It's easy: you just pry on these tabs with your fingernails and they just pop apart.
The inside of the bottom contains the contacts.
Those little dimples are supposed to press into the rubber conductive material inside the dome. And press they did. I suspect these keys weren't meant to stand up to much use. 640k keypresses ought to be enough for anyone.
Lacking true contact cleaner, I just scratched up the contacts and dimples with a screwdriver to maybe get rid of oxidation. I also rotated the dome 90 degrees so the dimples can press into fresh rubber. I put the key together and...
87 ohms! That's more like it.
63 more keys to go :(
# Driving Nixie tubes with a MAX6922 VFD driver
The MAX6922 is a driver for VFDs. It takes standard 3.3v or 5v logic inputs via something close to SPI, and controls 32 separate outputs. Each output can be pulled low, sinking 15mA, or pulled high to a separate high voltage supply (up to 76 VDC), sourcing 45mA.
You can also daisy chain the drivers to add as many outputs as you want.
It's alive! Pro Trinket on left, transistors "stored" on the breadboard, MAX6922 on SchmartBoard PLCC adapter.
It seems like a powerful enough chip to replace the standard 74141/K155ID1 chips, with a more convenient input as well. Here's a circuit I put together showing the MAX6922 driving three IN-12B tubes. I left out the decimal points, since they would require 33 outputs, not 32. Since the drivers can be daisy chained, this wouldn't be a limitation.
Is it worth it? You can get them at Digikey, quantity 1, for USD 7.45 each, with price breaks at 10, 25, and so on, with a bit of shipping. For the same circuitry, you'd need three K155ID1s (about USD 1.50 each, plus shipping from Ukraine, Russia, or some other former Soviet Bloc country). So that would ordinarily deal the K155ID1 a win, but then, do you want to drive that decimal point? You need more parts. Do you not want to use up pins on your microcontroller? Then you need a GPIO expander running on I2C or SPI. Do you want the driver within the next few days? Then you probably shouldn't get a K155ID1.
I'm not going to argue about availability. There are probably a bazillion K155ID1s still out there, and likely MAX6922s will never be produced in such quantities. Nevertheless, the MAX6922 is worth a hard look if you need to drive a few Nixies.
# Project: Nixie tube calculator, Part 3
CORDIC, or Coordinate Rotation Digital Computer, is a venerable algorithm used by calculators to calculate trigonometric and logarithmic functions and their inverses: sin, cos, tan, sinh, cosh, tanh, ln, exp.
Rather than give an explanation here, I know of no better explanation than that given by Richard Parris.
The CORDIC algorithm uses some number of constants, and then successive additions or subtractions and shifts, followed by one multiplication at the end to give the answer. Since it consists of two of the simplest possible mathematical operations, it is fast enough and simple enough to be implemented by quite limited processors.
Now, since my calculator is meant to be able to represent the magnitude of any number up to 10100 to an accuracy of 10-100, I decided to use 200 digits (or so) to represent any number using the 100.100 format, or 100 digits for the integer part, and 100 digits for the fractional part.
This meant that I needed all the CORDIC constants, to at least 200 digits, in this format. I wrote a Mathematica notebook which does this for me, which you can see in PDF format.
# Project: Nixie tube RPN calculator, part 2
If I go to my HP48 calculator (or the Android or iOS versions thereof) and enter 1 3 ÷, the answer you'll get is .333333333333, 12 digits. Now, if I enter 3 x I get .999999999999. And this is correct, since the calculator makes the assumption that all digits past the displayed answer are 0.
If, however, I do this with 32-bit floating point calculations, we see that the closest floating point representation of 1/3 is 0.3333333432674407958984375 (exactly). How should that be displayed? If I display it as 0.3333333 then I'm lying, because the closest representation of that is actually 0.333333313465118408203125. But if I display it as 0.33333334 then I'm inaccurate because there is no way that is 1/3.
Two things come to mind.
So really, we should be using multiple-precision decimal arithmetic, but even that has problems. To solve the 1 3 ÷ 3 x problem, we could add one guard digit and round, which means .999999999999(9) will be displayed as 1. Even so, there will always be errors, sometimes fatal ones. There is a whole field around this issue.
But this is a calculator. We can provide an answer and assume that the human knows what context their calculation has, so even if they use the HP48 and see .999999999999, they'll know when this is 1 and when it is not 1.
If, however, we want to use scientific notation, then no matter how many digits of precision we use, we run into all the floating point problems again because N digits of precision plus an exponent is the definition of floating point.
Maybe we shouldn't let the point float? What if we want to be able to represent all numbers between 1x102 (100) and 1x10-2 (0.01) to an accuracy of 1x10-2? Then we need 4 digits. If our 4-digit representation is ABCD, then the actual number represented is ABCDx10-2, always. If ABCD = 0001 the number is 1x10-2 (0.01). and if ABCD = 9999 then the number is 99.99, or 1x102 - 1x10-2 (close enough, there's always going to be that upper bound missing). The exponent never changes, which means the point does not float. Add a sign bit and you've got arithmetic.
So where do we find a multiple-precision library? The Gnu Multiple Precision library (GMP) holds out some hope. Let's play with it for a bit.
Let's try 1+2:
#include <gmp.h>
int main() {
mpz_t x, y, z;
mpz_init(x);
mpz_init(y);
mpz_init(z);
mpz_set_ui(x, 1);
mpz_set_ui(y, 2);
gmp_printf("%Zd\n", z);
}
This will simply print 3. So far, so good. But when we use mpz_tdiv_q instead of mpz_add, the answer is zero because 1/2 with the result rounded to an integer towards zero is zero.
This is where our assumed exponent comes in. When we divide Xx10-2 by Yx10-2 we get [X/Y]x100 because mantissas divide while exponents subtract. I use [X/Y] to indicate the integer result of X/Y rounded towards zero. But we want an answer that is a multiple of 10-2. The only way to do this is add more precision to the numerator: Xx102 x10-2. Now we get the correct answer, [X x102/Y] x10-2.
#include <gmp.h>
int main() {
mpz_t x, y, z;
mpz_init(x);
mpz_init(y);
mpz_init(z);
mpz_set_ui(x, 10000);
mpz_set_ui(y, 200);
mpz_tdiv_q(z, x, y);
mpz_t intPart, fracPart;
mpz_t hundred;
mpz_init(intPart);
mpz_init(fracPart);
mpz_init_set_ui(hundred, 100);
mpz_tdiv_qr(intPart, fracPart, z, hundred);
gmp_printf("%Zd x 10^-2\n", z);
gmp_printf("%Zd.%02Zd\n", intPart, fracPart);
}
The output of this program is:
50 x 10^-2
0.50
And that is correct. For multiplication, we will end up with twice as many digits as we need, so we just round off.
So much for the four functions. What about exponentiation and roots? Trigonometric functions? For that we'll need the incredible magical CORDIC algorithm, which I'll talk about in part 3.
# Project: Nixie tube RPN calculator
Nixie tubes are neat. They're nostalgic, and not too hard to get working. Russia still has bazillions of them.
Here's an actual calculator that was sold, for money, made with Nixie tubes:
The 1972 Casio model AS-C. Image copyright Nigel Tout of vintagecalculators.com.
Everyone's making clocks with them.
Nixie clock built by (and image copyright) Tomasz Watorowski, 2014.
Some are rethinking calculators with them.
Nixie calculator project (and image copyright) Spike Tsasmali, 2010.
So I thought it would be fun to go bigger, and interactive, but not too crazy. So that's where the Reverse Polish Notation Nixie calculator comes in. Like the venerable HP-48, it should have four visible stack levels. I would use IN-12B tubes, since they are top-read and have a decimal separator: a comma, which makes it compatible with most of South America, Europe and Asia.
## Reverse Polish Notation
Polish Notation was invented by the Polish logician Jan Łukasiewicz in 1924. He was stuck in Poland under German occupation during World War II, and after the war he emigrated to Ireland. It wasn't until 1954 that Reverse Polish Notation came into being, but it wasn't used in calculators and computers until the early 1960s. RPN was certainly inspired by Łukasiewicz's work.
## Alternate History
In my alternate history, Łukasiewicz did not leave Poland after the war. He was deported from Poland to the USSR as part of Operation Osoaviakhim to work on mathematics and help other captured scientists. However, the Soviets quickly realized the utility of Polish Notation, except reversed, in calculations, and by the 1950s were building large RPN desk-calculators with Nixie tube displays.
## Features
Here are the features I want to support:
• 4-level stack display
• scientific notation
• IEEE 754 double-precision floating point (binary64, which is 15-17 decimals of precision)
• Functions 10x , e x , log 10 , ln
• Functions x 2 , x y , √x, y √x
• Trigonometric functions (arc) sin, cos, tan (h)
• π, e
• Stack operations drop, dup, swap, rot3
• Auxilliary memory store and recall
## Display
I want to have enough digits on each stack level to display a double-precision number to 17 digits with 3 digits of exponent. To represent scientific notation, instead of the usual practice of using "E" or a space to separate the mantissa from the exponent, I'd use a light shining through a panel overlay between the 3rd and 4th digits, showing either " + "or " - ". So O.778+O43 would be 0.778x1043 . Negative numbers would also be represented by having a " - " panel light on the far left side.
The interesting thing about this representation is that numbers not needing an exponent, which are those having an exponent of 0, could either be displayed with that exponent ( +OOO ) or, probably better, by leaving off the exponent and leaving the last three digits blank. That would make exponentiated and non-exponentiated numbers line up.
Infinity could be represented by OO and NaN by lighting all the commas.
## Insides
As for electronics, as I said above, I'd use IN-12B tubes. These require a supply of 170VDC. Russia also has bazillions of K155ID1 chips, which drive these tubes, except for the decimal separator, for which I'd just use a simple transistor driver. This driver chip is pin-for-pin compatible with (and sadly much more available than) the 74141. One could use any 4-to-16 decoder and couple it with some high-voltage tolerant circuitry, but then you'd have essentially built a K155ID1.
I'd run the whole thing off of (of course) an Arduino. Now, each stack level has 20 digits times 5 bits each (4 for the BCD digit, and 1 for the separator), plus at least three indicators (sign, exponent signs). That's 103 bits per level, times 4 levels is 412 bits.
Conveniently, there are chips which take I2C and can latch many outputs (or read many inputs). There are two nice ones:
Each can be programmed with a 7-bit address, so there is no cramped address space to deal with.
If I want to be modular, each stack level can be powered using three of the NXP chips, or two of the Cypress chips. The NXP chips seem more approachable to me.
## Keyboard
I figure the keyboard will be a 4x8 matrix, which should be able to handle all the functions plus digits as long as I have a shift key.
Keys without shift functions (18):
• 0-9
• .
• SH (shift)
• +, -, x, ÷
• CHS (change sign)
• EE (enter exponent)
• HYP (hyperbolic, for trigonometric functions)
Keys with shift functions (12):
• sin / asin
• cos / acos
• tan / atan
• log / 10x
• ln / ex
• x2 / √x
• xy / y√x
• 1/x / x!
• π / e
• DROP / DUP
• ROT2 / ROT3
• STO / RCL
These 30 keys would be placed in a 4x8 matrix, not necessarily physically but electrically. Each row of eight keys would be read via I2C, with a full keyboard scan happening many times per second.
# Setting up a Huanyang VFD for a CNC router spindle
I recently bought a CNCRouterParts Benchtop Pro. It is a 24"x24" router. The thing is, it's a kit. It comes in six boxes if you get the plug-and-play electronics package with it, and you have to put it together. But it doesn't come with everything you need.
• You need a Windows computer to drive it (with Mach3), and of course a monitor, keyboard, and mouse to run it.
• Then you need a raised surface to put the whole thing on -- you're not going to leave this on your garage floor. I got a shelving unit from McMaster (48x36 2-shelf), then I bought some wheels off of eBay -- because everything in a workshop must be on wheels. The "feet" on the shelving unit were 1/4-20 bolts, so locking wheels with 1/4-20 threads worked perfectly. Then I hacked up some cross-bracing for stability.
• Also, you need to buy a spindle and a VFD to control it. And a spindle cable to connect the VFD to the spindle. And then you need a 220V circuit for the VFD, and a power cable to connect that circuit to the VFD. The Huanyang VFD seems to be the one you find all over eBay. Everyone's got one.
• Preferably the spindle has an ER20 collect chuck. You will need a set of ER20 collets.
• Dust collection is absolutely necessary. You do not want to breathe in the fine particulates that the router generates. So, you can either get a complete dust collector, or you can do what most people do: make one out of a ShopVac with a HEPA filter (otherwise you're not getting the harmful fines), an Oneida Dust Deputy DIY cyclonic dust separator, a bucket and a Gamma Seal lid with some hoses to connect them all.
• Don't forget end mills to actually cut with.
• How about toolpathing? A G-Code file tells your router what path it should take, but you have to get from your design to G-Code. This is where V-Carve comes in. I decided to get V-Carve Pro. You get a discount from CNCRouterParts if you buy a router from them. However, you can probably get away with Fusion 360. It is free, runs on Windows and OSX, does parametric design (parametric or go home) and can output G-Code.
The kit is obviously not meant to be turn-key. It is not for the impatient or the easily frustrated. But it is cheaper than most solutions, and many of those solutions still need most of the above extra things.
All the things
## The 220V circuit (in the US)
What amperage circuit is needed? Well, the most common spindle is 2.2kW, which means 10 amps (2200 divided by 220). You'll need a little extra to compensate for power loss in the cable, so figure 15 amps.
But wait! The age of gasoline is nearing an end, and wouldn't you like your house to be ready for an electric car? A car charger typically runs off 220V, and the higher amperage the better. So I opted to get a 50A circuit -- 40A for a Tesla charger, plus a bit for cable loss.
The plug gives you four wires: ground, a neutral, and two hots. While each slot in a breaker box is 110V, consecutive slots are 180 degrees out of phase with each other, which is why 220V breakers take up two slots. That's how you get 220V. The voltage between the neutral and any hot is 110V, because the neutral is the conductor between the two slots and the hots are on either side.
I'll be putting a 15A breaker in the circuit between the breaker box and the VFD, because I don't trust the VFD to have its own fuse.
## The spindle cable
For some reason, this was the hardest thing to obtain. It needs to be four-conductor shielded cable. It must be shielded because without a shield, such a cable will spew RF all over the place, which is bad for nearby electronics. Like, the stuff that is controlling your motors. The shield must be connected to ground on both ends.
I went to surplus stores, and by extreme chance found some, but the wires were too thick to fit in the connector that came with the spindle. You can get some from Soigeneris, but only if they have it in stock.
For some reason, there seem to be only two makers of this kind of cable: Alpha and Lapp.
I got some from Element14: Lapp Kabel Ölflex servo cable, 4 conductor, 1.5mm wires (24M9570). They sell it by the meter. I ordered 10 units, but because I'm a stupid American, I thought it was by the foot. I ended up getting more than I needed, but better too much than too little.
I wish someone sold this cable with the connector already on it.
## The VFD
It turns out that setting up the VFD was the hardest part of the whole project. For one thing, the VFD is very programmable. There are lots and lots of parameters you can set for all sorts of custom circumstances.
But mainly it was difficult because the instruction manual, nominally in English, is horribly written. You can search the webs and find lots of pages on how to set up the parameters in the VFD for your particular motor, but I've found some of the information to be wrong. So here is yet another page on how to set up a VFD, for a particular spindle. I'll try to explain what the parameters really mean.
Scary temporary testing. The shield has not yet been hooked up to ground.
## But first, some myths
Here are a few myths I've found which just make no sense, and I really need to put these first. If you ever see these on a VFD page, don't pay attention to that section.
Myth #1: You need to set up the parameters in a particular order.
No. You don't. If you set PD013 to 8, that's factory reset. So of course, you would do that first. But you can set the other parameters in any order you like.
Myth #2: The max RPM of your motor should be divided by the value of parameter PD010, and that should be entered into PD144.
No. For some settings it is just coincidence that PD010 x PD144 = Max RPM. In reality, they have absolutely nothing to do with each other.
## The spindle parameters
First, gather your spindle's operating parameters. If you bought one off eBay from China, you only get this data: power (kW), voltage (V), air or water cooled, max RPM. The spindle I bought is 2.2kW, 220V, air cooled, 24000 rpm max.
You're also supposed to know the spindle's maximum operating frequency. This is often 400Hz for the ones you get off eBay.
## The VFD parameters
First, reset the VFD to factory settings. You don't know where that thing's been. On the front panel, hit PROG (or PRGM), and then the up and down buttons until you reach PD013. Hit SET. Change the value to 8 using the up and down buttons. Hit SET again. Now your VFD is reset.
For the next parameters, I've renamed them to make some kind of sense. For setting multi-digit values, use up and down to increase and decrease the value, and the >> key to move one digit to the right.
PD001: Command source. Set to 0. 0 means you're controlling the spindle via the front panel controls. 1 means you're using controls that you've wired up to the screw terminals. 2 means you're going to control it using RS-485.
PD002: Speed control source. Set to 1. 0 means you're controlling the speed through the up and down front panel buttons. 1 means you're going to control the speed with either the knob on the front or an external potentiometer. 2 means RS-485.
When PD002 is set to 1, there is also a jumper next to the screw terminals that you have to set. If the jumper is on the right pair, the control is the front panel knob. If the jumper is on the left pair, the control is via an external potentiometer connected to the screw terminals. Make sure the jumper is on the right-side pair.
By the way, I found setting 0 pretty weird. You only get to see the speed as a frequency, not as RPM.
PD003: Default frequency. If PD002 was set to 0, this is the frequency the motor will start running at. The frequency is directly related to the speed. Since we set PD002 to 1, we can leave this alone. But you can set it to something like 200 Hz to start at mid-range.
PD004: Rated frequency: Apparently this is for motors with a fixed frequency. Since the spindle is variable frequency, this setting can be ignored.
PD005 through PD010 set three points on a voltage/frequency curve. As the motor ramps up to your desired speed, it follows this curve. The manual usefully shows three types of curve: constant torque, low torque, and high torque. I've set mine to the values for the constant torque graph (why not).
I think that if you get a VFD with a spindle, the particular model of VFD comes with different factory settings for these depending on the spindle. Which is nice.
PD005: High-end frequency: 400 Hz
PD006: Middle frequency: 2.5 Hz
PD007: Low-end frequency: 0.5 Hz
PD008: High-end voltage: 220 V
PD009: Middle voltage: 15 V
PD010: Low-end voltage: 8 V
PD011: Minimum allowed frequency. Set to 120 Hz. Air-cooled spindles are not meant to stay at low speeds, otherwise they overheat. I understand that water-cooled spindles can go as slow as you want.
PD070: Speed control input: Set to 1. This means that the speed will be controlled by an input voltage between 0 and 5V. This is what the front panel knob delivers. 0 means 0-10V. 2 means the control is by an input current between 0 and 20mA. 3 means 4-20mA. 4 is a combination of voltage and current.
PD071: Speed control responsiveness: Leave at the factory setting of 20.
PD072: High-end frequency: Set to 400. This sets the frequency represented by the top end of the speed control.
PD073: Low-end frequency: Set to 120. This sets the frequency represented by the bottom end of the speed control.
Now skip straight to...
PD141: Rated motor voltage: Set to 220V.
PD142: Rated motor current: Set to 11A. Why not 10? Because there will always be some loss in the spindle cable. This compensates for that. But feel free to set it to 10A. The worst that can happen is that your motor loses power at the top end.
PD143: Number of motor poles: Set to 4. This is the number of magnetic poles in the motor. It should be either 2 or 4, and is 4 for the 2.2kW spindle.
PD144: RPM at 50Hz: Set to 3000. Since the max RPM is 24000 at 400Hz, this means that the RPM at 50Hz will be 3000.
That's it!
## Testing
Now twist the knob all the way counterclockwise so that you'll start at the lowest speed setting. You can now hit the RUN button and your spindle should start rotating clockwise if you're looking at it from above. If it rotates counterclockwise, press STOP, shut off the power, unplug the VFD, and swap any two of the motor wires. Then try again.
The display may now be showing a frequency rather than a rotational speed -- that is, the HZ light above the display may be lit. Hit >> until the ROTT light above the display is lit. That's RPM.
Now slowly turn the knob clockwise. You should get all the way to 24000 RPM.
Hitting >> until A is lit shows you the current being used by the motor. With no load, mine ran at 1.1A.
# How I didn't crack the Voynich Manuscript
I’ve been interested on and off in the Voynich Manuscript, mostly because it appeals to my appreciation of old occult books. Looking at the book, it’s clear there is a lot of structure in its writing. It’s clearly not, say, solely a work of art such as the Codex Seraphinianus. The history of the Voynich and the cracking attempts against it can be found all over the place. I particularly enjoyed Nick Pelling’s book, Curse of the Voynich. It might be fun, I thought, to take a look at it myself.
First step was assigning letters to each glyph. There is a standard format called EVA that has been used to transcribe the Voynich, but I found it too cumbersome. Although EVA can be transformed to any other format due to its expressiveness, that transformation would also rely on an already-completed transcription. I really wanted to start with a fresh eye.
Warning! Yes, I am aware of other researchers’ theories. The idea is that I’ll use my own theory and see where it takes me. Maybe I’ll make a bad decision. In any case, I reserve the right to modify my theories!
Using the images of the Voynich as my starting point, I looked through the first few pages and settled on a basic alphabet of glyphs, closely modeled on EVA:
Again, this is just my initial take: 25 glyphs. I’m not taking into account other, more rare glyphs at this point. Major differences between my notation and EVA are that my ‘g’ is EVA ‘m’, my ‘v’ is EVA ’n’, my ‘q’ is EVA ‘qo’, and my ‘x’ is EVA ‘ch'. I also specifically include an ‘m' and an ’n' symbol for EVA ‘iin’ and ‘in’, respectively.
The one ‘q’ I found with an accent above it, I just decided to render as ‘Q’. Likewise, the ‘x’ with an accent above I render as ‘X’. The tabled gallows characters ‘f’, ‘k’, ‘p’, and ’t’ are represented as capital letters. This doesn’t mean that they are the same character. This is just a mapping of glyphs to ASCII.
Next, I transcribed some pages using this mapping. I decided to use ‘^’ for a character indicating the beginning of a “paragraph”, including the beginning of any obviously disconnected text areas. Similarly, ‘\$’ marks the end of a “paragraph”. A period is a space between “words”. Occasionally I had to make a judgement call as to whether there was a space or not. Furthermore, lines always end in either a period or, if the line is the last in a paragraph, an end-paragraph symbol.
Finally, any character that I could not figure out or that doesn’t fit in the mapping is replaced by an asterisk.
Thus, the first paragraph on the first page is transcribed as follows:
Again, there are many caveats: I had to make judgement calls on some glyphs and spacing. I’m also aware that Nick Pelling has a theory that how far the swoop on the v goes is significant, and clearly I’m ignoring that.
In any case, after transcribing a few pages, I became aware of certain patterns, such as -am nearly always appearing at the end of a word, and three-letter words being common. I did a character frequency analysis, and found that ‘o’ was the most common character, with ‘y’, ‘a’, and ‘x’ being about 50% of the frequency of ‘o’. Way at the bottom were 'F', 'f', and 'Q'.
Then I did another frequency analysis, this time of trigrams. Most common were ‘xol’, ‘dam’, and ‘xor’. Then I asked, how often do the various trigrams appear at the beginning of a word and at the end of a word? The top five beginning trigrams were ‘xol’, ‘dam’, ‘xor’, ‘Xol’, and ‘xod’, while the top five ending trigrams were ‘xol’, ‘xor’, ‘dam’, ‘Xol’, and ‘ody'.
Are these basic lexemes? I began to suspect that lexemes could encode letters or syllables.
I turned to page f70v2, which is the Pisces page. There were 30 labels, each next to a lady. The labels were things like ‘otolal’, ‘otalar’, ‘otalag’, ‘dolarag’… Most looked like the words were composed of three two-letter lexemes: ‘ot’, ‘ol’, ‘al’, ‘ar’, ‘dol’, ‘ag’, and so on.
So I decided to look for more lexemes by picking the most common trigram, ‘xol’, and looking for words containing it. These were: ‘xol’, ‘otxol’, ‘o*xol’, ‘ypxol’, ‘dxol’, ‘xolam’, ‘xolo’, ‘xololy’, ‘xolTog’, ‘opxol’, ‘btxol’, ‘xoldy’, ‘xolols’. That would make as the lexemes ‘ot-’, ‘yp-‘, ‘d-‘, ‘-am’, ‘-o’, ‘-oly’, ‘-Tog’, ‘op-‘, ‘bt-‘, ‘-dy’, and ‘-ols’.
Similarly, for ‘xor’, we get lexemes ‘d-‘, ‘xeop-‘, ‘k-‘, ‘ot-‘, ‘bp-‘, ‘ok-‘, ’t-‘, ‘-am’, and ‘Xk-‘. At least in the first few pages.
So certain lexemes seemed to come up often, namely ‘ot-‘, ‘ok-‘, ‘op-‘, ‘d-‘, ‘-am’, ‘-dy’.
One possibility that no doubt has already been discounted decades ago is that each lexeme corresponds to a letter. So something common like ‘xol’ could be ‘e’. Because there are so many lexemes, clearly a letter could be encoded by more than one lexeme. Or maybe each lexeme encodes a syllable, so ‘xol’ could be ‘us’. I tend to doubt the polyalphabetic hypothesis, since then I would expect to see perhaps more uniform statistics.
Maybe the labels in Pisces encode numbers. If that’s the case, then by Benford’s Law, ‘ot-‘ would probably encode the numeral 1, since that appears in the first position 16 out of 30 times, and ‘ok-‘ could be 2, appearing 8 times.
Anyway, that’s as far as I’ve gotten.
# Machine Learning: Sparse RBMs
In the previous article on Restricted Boltzmann Machines, I did a variety of experiments on a simple data set. The results for a single layer were not very meaningful, and a second layer did not seem to add anything interesting.
In this article, I'll work with adding sparsity to the RBM algorithm. The idea is that without somehow restricting the number of output neurons that fire, any random representation will work to recover the inputs, even if that representation has no organizational power. That is, the representation learned will likely not be conducive to learning higher-level representations. Sparsity adds the constraint that we want only a fraction of the output neurons to fire.
The way to do this is by driving the bias of an output neuron more negative if it fires too often over the training set. Or, if doesn't fire enough, increase the bias. Octave code here. The specific function I added is lateral_inhibition.
I used the same data set based on horizontal and vertical lines, 5000 patterns. I settled on 67 output neurons, 500 epochs, with momentum, changing halfway through. I decided that a fraction of 0.05 would be interesting, meaning that on average I would want 67 x 0.05 = 3.35 output neurons activated over all 5000 patterns. In order to compensate for the tendency for biases to be very negative due to the sparsity constraint, I set the penalty for weight magnitudes to zero so that weights can become stronger to overcome the effect of the bias.
The change in bias is controlled by a sparsity parameter. I ran the experiment with various sparsity parameters from 0 (no sparsity) to 100, and here are the costs and activations:
The magnitude of the sparsity parameter doesn't seem to have much effect. Although you can't tell from the graph, there is in fact a small downward trend in the average active outputs. Right around 10, the average active outputs reaches the desired 3.35, where it stays up to about 80, and then it starts dropping again. So 10 seems like a good setting for this parameter.
Here are the patterns that each neuron responds to, with differing sparsity parameters:
Sparsity 0:
Sparsity 1:
Sparsity 5:
Sparsity 10:
Sparsity 50:
Sparsity 100:
Sparsity 200:
With no sparsity, we get the expected near-random plaid patterns, and nearly all neurons have something to say about any given pattern. With even a little sparsity, however, the patterns do clean themselves up, although not by much, and by sparsity 200, the network learns nothing at all.
One possibility that the patterns really don't look that sparse is that we wanted the average neurons activated over the entire data set to be 5%. But how much of the data set actually contains a non-empty image? In fact, about 49% of the data set is empty.
What if we require that no data instance be empty? This time a sparsity of 0.05 ends up with a relatively terrible log J of -1.8, compared to the previous result of about -2.4. However, increasing the sparsity to 0.07 gives us a log J of -2.6, which is better than before. This is also expected, since more neurons will be able to represent patterns more closely. And yet, we get better representation anyway:
Sparsity 10:
Sparsity 20:
Sparsity 50:
Sparsity 100 has very poor results.
The visualization is a bit misleading, because although there are pixels that are other than full white, those pixels don't imply that the neuron will be activated with high probability for those other pixels. The maximum weight turns out to be 11.3, with the minimum being -4.7. The visualization routine clips the values of the weights to [-1,+1] meaning that anything -1 or lower is black, while anything +1 or higher is white. However, by using visualize(max(W+c', -0.5)), we can take into account some of the threshold represented by the (reverse) bias from output to input. We also clip at -0.5 so that we can at least see the outlines of each neuron.
So here is another run with sparsity 50:
We can see that, in fact, each neuron does respond to a different line, and that just about 18 lines are represented, as expected.
# Reverse engineered part
After fiddling around with the part from the previous article, I think I might have a reverse engineered technical diagram. I still don't know enough about early 20th century mechanical design techniques to know if this is what they would have done, but it should be enough to at least remanufacture this part.
I also realized that I haven't actually described the part! There are two registers on the typical Monroe calculator, an upper register which indicates operation count (useful for multiplication and division) and a lower register which indicates total. There's a crank which, when turned one way, zeroes out the upper register, and when turned the other way, zeroes out the lower register. The part that I reverse engineered is shown in the original 1920 US patent 1,396,612 by Nelson White, "Zero setting mechanism" in Figure 5. In the patent, the part, 32, is described as follows:
The shaft 60 is normally locked or held against rotation by a rigid arm 32, pivoted upon the shaft 84, and at its free end engaging a peripheral notch 33, of a plate or disk 34, secured to the gear 12...
So the next step might be to make an OpenSCAD file for the part, and put it on Thingiverse so that anyone can recreate the part. It probably can't be 3D-printed at this point, since it really needs to be a metal part. Even Shapeways, which can 3D print metal parts from stainless steel combined with bronze, can only achieve a 1mm detail, and this thing is much more detailed than that.
Full-sized files in various formats: AI | PDF | SVG | PNG
UPDATE: See the thing on Thingiverse.
# Reverse engineering mechanical parts
Or,
Numerology that sorta kinda works!
One of my half-baked projects is to take apart an early 20th century Monroe mechanical calculator and reverse engineer it so that I have a full set of engineering diagrams of every part. This would enable anyone to recreate broken parts and fix their calculator.
Reverse engineering the design of an early 20th century mechanical part has a lot in common with numerology. If the numbers coincidentally fit, then they're probably right. If they almost, but not quite fit, then they're probably right anyway.
Here's a part that I scanned on an Epson Perfection V700 scanner. This scanner is based on a CCD, not LiDe, which means that it has non-zero depth of field. That means that you can scan a part that has height and it won't end up too blurry. I scanned the part at 1400 dpi so that I could optically measure it. The thing sticking out at the top is just a screwdriver that I used to hold the part horizontal.
I could pop this into Illustrator and use the pen tool to trace around the part, but all this would get me is an outline of this particular part with no insight into why it had that particular outline. This part was designed, not evolved. It was designed to work with other parts. So clearly its measurements and the relationships between one bit of the part and another are not arbitrary.
For example, take the hole at the top. It fits over a shaft. Now, "the ancients" probably didn't use shafts of arbitrary diameter. They were standard, and since this was an American design, that meant fractions of an inch, specifically inverse powers of two: 1/2, 1/4, 1/8, and so on. The hole at the top measures between 0.187" and 0.188" on my calipers. But 3/16" is 0.1875", so it makes sense that the engineers designed this hole to be exactly 3/16". This fits around the shaft that is 0.001" under 3/16", which I suppose is a standard undersized shaft.
The 1910 Cyclopedia of Mechanical Engineering, edited by Howard Raymond, has this to say on page 129 in the section on mechanical drawing: "Keep dimensions in even figures, if possible. This means that small fractions should be avoided… Even figures constitute one of the trade-marks of an expert draftsman. Of course a few small fractions, and sometimes decimals, will be necessary. Remember, however, that fractions must in every case be according to the common scale; that is, in sixteenths, thirty-seconds, sixty-fourths, etc.; never in thirds, fifths, sevenths, or such as do not occur on the common machinist's scale."
In Illustrator, I pulled up the image and drew a circle of diameter 3/16", placing it so that it fit exactly into the hole in the image. Now I had the center of that hole, and I could draw more concentric circles. Because I could measure these diameters directly on the part, I used those diameters: 3/8" and 7/16".
The measurements in the image were done using VectorScribe.
Note that while the inner circle and middle circle (diameter 3/8") fit exactly, the outer circle (7/16") does not. The outer circle does not seem to be quite concentric, but numerology: if it's nearly right, it probably is. By moving the outer circle a few thous, I was able to get a good registration. Under high magnification, I was able to tell that the inner subpart was welded onto the sheet metal subpart, so all this indicates that there were several steps involved in manufacturing this part: first, turn the small subpart on a lathe. Then create the larger subpart from sheet metal. Then weld the two together. Welding the two together was apparently not an extremely exact procedure.
After moving the large circle to its new center, the centers no longer coincide.
Now for the rest of the part. Using SubScribe, I drew a circular arc on a circular-looking feature. Then I measured its radius.
0.283" x 2 = 0.566" is close enough to a diameter of 9/16" to say that this was the intent of the original engineer. I drew the circle, and then measured the distance between the centers.
0.568" is again close enough to 9/16". And not coincidentally, this second center coincides precisely with the location of another shaft on the machine. That certainly nails down the intent of the engineer.
I can now draw the inner tangent line between the two circles (done again using SubScribe):
The length and angle of this line in fact do not matter, since there is one and only one inner tangent line connecting these two circles in the right direction. Certainly 0.269 is close to 7/64, but that was not the design constraint. The line had to be tangent to the two circles, and drawing inner and outer tangent lines were geometric constructions that were familiar to the ancients.
We can now draw another concentric circle corresponding to the outer outline of the part, and draw an outside tangent line. Again, knowledge of design intent lets us set the outer circle's diameter at 7/8", which seems to fit precisely onto the part.
The more excitable among you may have noticed by now that the inner surface of the inner tab appears to be a circular arc, and you would be right. Drawing the circle freehand gives us a diameter of 0.439", which is close enough to 7/16" as to fix that measurement. But right now I won't analyze the tab, since I want to get the larger part done.
Near the bottom of the part, we can draw some tangent lines.
I did this in SubScribe by picking a point on the straight section of the part, then drawing a line tangent to the circle. Then I extended the line outwards. Now those lines could have started anywhere on the circle. Why these particular points? Let's draw some lines intersecting the centers. I'll also rotate the diagram so that the inter-center segment is horizontal.
The angle that the rightmost tangent line forms with the horizontal, 67.35 degrees, is irrelevant, since the constraint for that intersection point was based on an outer tangent line. But consider the angle formed between that angle and the next intersection: 125.71 - 67.35 = 58.36 degrees. This is close to 60 degrees, a nice round angle. For the intersection in the inner circle, the angle is 171.76 - 67.35 = 104.41, which is very close to 105 degrees, which is 60 + 45, more round angles. So the design intent seems clear: the outer intersection is 60 degrees from the outer tangent line, while the inner intersection is 45 degrees away from that. Let's move the intersections and construct the tangent lines so these relations become exact.
As mentioned above, this pawl fits into a hole on a gear located on a shaft. There are three shafts so far, let's call them A, B, and C. The pawl fits on shaft A, goes around shaft B, and the gear it locks is on shaft C. We know that the distance between shaft A and shaft B is 9/16". I also know from direct measurement that the distance between shaft C and shaft B is also 9/16". However, the distance between shaft A and shaft C is irregular: 0.977", not close to any fraction at all. This may be due to some constraint that we do not yet know about.
However, let's pretend that 0.977" is eventually determined through some constraint, and place the location of shaft C on the diagram.
(Update, 17 Dec 2012: It turns out that a line drawn from B perpendicular to A-C has a length of very close to 9/32", which makes A-C tangent to the 9/16" diameter circle around B. Maybe that's why the shafts are where they are: A-B is 9/16", B-C is 9/16", and A-C is tangent to the 9/16" diameter circle around B.)
I also put a circle of diameter 3/16" (shaft C's diameter), and another of diameter 3/8" around shaft C's center, which corresponds to the size of shaft C's bushing where the hole is. You can imagine the pawl fitting into a hole on the bushing by looking at the diagram.
It seems fairly clear that the pawl's end is designed to fit into the hole. The end also isn't square; it is tapered. Remember that inner tab? There is a cam which that inner tab rides on. The large diameter for the cam measures 17/32", and the small diameter measures 29/64". When the cam is rotated so that the large diameter pushes the inner tab, the pawl lifts out of the hole. When the cam small diameter is against the tab, the pawl is inside the hole. I can add the two cam diameters and then rotate the image of the pawl to simulate the two states.
In the hole (locked state):
Out of the hole (unlocked state)
Clearly one design criteria we can deduce is that the width of the pawl's end at the outside of the hole when the pawl is in the locked state must be equal to the width of the hole, and the pawl must thereafter taper. Measuring the width of the pawl in the locked state at the hole gives 0.081". Perhaps not surprisingly, this is the diameter of the hole as measured with calipers. In fractions, this is near enough to 13/16", a drill size that any mechanical engineer would have had.
Here I've drawn the outline of the hole along with its centerline. I've made the depth just deep enough for the pawl's end. We can see that the tapered pawl end does indeed fit in the hole.
Resetting the part to its design position, I found that I could draw a line along the outer outline of the pawl tangent to shaft C's outline:
The angle formed between the C-B line and the beginning of the construction line is 129 degrees. It is not a very round angle, and if the angle were not too important, it would make more sense to have it be round, perhaps divisible by 5.
Another possibility is to look at the angle formed by a radial line with the intersection:
Relative to our reference angle at the right, this is 91.57 degrees. Too far away from 90 degrees; a line placed at 90 degrees intersects the upper outline nowhere near the right place. The radial line is also 31.57 degrees from the 60-degree line. This could be significant, since 31.5 is exactly 7/10 of 45 degrees, and placing a radial line at 31.5 degrees produces an intersection very nearly at the drawn intersection.
I don't know enough about early 20th century mechanical design techniques to know if this would be reasonable: angles measured in tenths of 45 degrees.
If you'd like to have a try at figuring this out, here's the Illustrator file.
# Machine Learning: Restricted Boltzmann Machine
The Restricted Boltzmann Machine is an autoencoder which uses a biologically plausible algorithm. It uses a kind of Hebbian learning, which is the biologically plausible idea that "neurons that fire together, wire together".
Suppose we have an input layer of dimension Nin and an output layer of dimension Nout, with no hidden layer in between. All input units are connected to all output units, but input units are not connected to each other, and output units are not connected to each other, which is where the Restricted comes in the name.
Let the input units be binary, so either 0 or 1. Further, each output unit uses the logistic function, so that the output of unit j is:
\begin{align*} z_j &= b_j + \sum_{i=1}^{N_{in}} w_{ij}x_i \\ p_j &= \frac{1}{1+e^{-z_j}} \\ y_j &= \begin{cases} 1 & \text{ if } uniformrandom(0,1) < p_j \\ 0 & \text{ otherwise } \end{cases} \end{align*}
bj is the bias term for output unit j, and wij is the weight from input unit i to output unit j. Note that we're treating the logistic function as a probability, but this time the outputs are binary rather than the probability, so that an output unit j is on with probability pj. That is, the output unit is stochastic.
Now, to make this an autoencoder, we want to feed the outputs backwards to the inputs, which works as follows:
\begin{align*} z_i &= c_i + \sum_{j=1}^{N_{out}} w_{ij}y_j \\ p_i &= \frac{1}{1+e^{-z_i}} \\ x'_i &= \begin{cases} 1 & \text{ if } uniformrandom(0,1) < p_i \\ 0 & \text{ otherwise } \end{cases} \end{align*}
We're just doing the same thing in reverse, except that there is a bias ci now associated with each input unit. There is some evidence that this kind of feedback happens biologically.
After this downward pass, we perform one more upward pass, but this time using the probability input rather than the reconstructed input:
\begin{align*} z'_j &= b_j + \sum_{i=1}^{N_{in}} w_{ij}p_i \\ p'_j &= \frac{1}{1+e^{-z'_j}} \\ y'_j &= \begin{cases} 1 & \text{ if } uniformrandom(0,1) < p'_j \\ 0 & \text{ otherwise } \end{cases} \end{align*}
We do this for every input sample, saving all the values for each sample. When all the m samples have been presented (or, in batch learning, when a certain proportion m of the samples have been presented) we update the biases and weights as follows:
\begin{align*} \Delta w_{ij} &= \eta\frac{1}{m}\sum_{k=1}^{m} x_i p_j - \eta\frac{1}{m}\sum_{k=1}^{m} p_i p'_j \\ &= \eta \left ( \langle x_i p_j \rangle - \langle p_i p'_j \rangle \right ) \\ \Delta b_j &= \eta \left ( \langle p_j \rangle - \langle p'_j \rangle \right )\\ \Delta c_i &= \eta \left ( \langle x_i \rangle - \langle p_i \rangle \right )\\ \end{align*}
And that's the Restricted Boltzmann Machine. There are other refinements such as momentum and regularization which I won't cover, but which are implemented in the example Octave file. There are also many extremely helpful hints as to parameter settings in Hinton's paper A practical guide to training restricted Boltzmann machines.
As an example (Octave code here), I set up a 9x9 array of inputs which correspond to pixels (0=off, 1=on), so my input dimension is 81. I generate a bunch of samples by placing some random vertical and horizontal lines in, but with more lines being less likely. According to the paper, a good initial guess as to the number of output units is based on the number of bits a "good" model of the input data would need, multiplied by 10% of the number of training cases, divided by the number of weights per output unit.
Each sample has zero horizontal lines with probability 0.7, one horizontal line with probability 0.21, and two horizontal lines with probability 0.09, with a vanishingly small probability of three lines, and likewise with vertical lines, and each line can be at any of nine positions, which means that a "good enough" model of the input would need something like 9 bits for the horizontal lines and 9 bits for the vertical lines, or 18 bits. With 3000 or so samples, 300 x 18 / 81 = 67 output units.
I also used 2000 epochs, averaging weights through time, a momentum term which starts at 0.5, then switches to 0.9 halfway through, a learning rate which starts at 1, then switches to 3 halfway through, and a regularization parameter of 0.001.
I set aside 10% of the samples as cross-validation, and measure the training and cross-validation costs. The cost (per sample per pixel) is defined as:
$J = -\frac{1}{mN_{in}}\sum_{i=1}^{N_{in}} \sum_{k=1}^m \left ( x_i^{(k)} \ln{p'_i^{(k)}} + \left ( 1- x_i^{(k)} \right ) \ln{\left (1-p'_i^{(k)} \right )} \right )$
In other words, this is the usual logistic cost function, except that instead of the output, we're using the probability during the downward pass that an input pixel is 1.
Here are 16 example input samples:
And here are the trajectories of the training and cross-validation costs over the 2000 epochs. Strictly speaking, the cost is a better measure than error in the reconstructed input since it is not as affected by chance pixel flips during reconstruction (output to input) as a direct pixel-to-pixel comparison. For example, if an input pixel should be on, and it is only turned on 90% of the time during reconstruction, then the cost for that pixel is -ln 0.9 = 0.105. If we were to actually reconstruct that pixel, then 10% of the time the error would be 1, and 90% of the time the error would be 0; but we only do a single evaluation. So the cost gives us a better idea of how likely a pixel is to be correct.
Blue is the training cost, while red is the cross-validation cost. We can see that the cross-validation cost is a little higher than the training cost, indicating that there is likely no over fitting or under fitting going on. The sudden acceleration at epoch 1000 is due to changing the momentum at that point. The end cost is about 0.004 while the cross-validation cost is about 0.005.
Here is a view of what the weights for each of the 67 output units encode:
Interestingly, only one output unit seems to encode a single line. The others all seem to encode linear combinations of lines, some much more strongly than others. The data shows that on average, 38 of the 67 output units are active (although not all the same ones), while at most 51 are active (again, not all the same ones).
Varying the number of output units affects the final cost, apparently with order less than log N. The end cost for 200 units is about 0.002, as is the cross validation cost. The average number of activated outputs appears to be a little over half.
We can learn a second layer of output units by running all the input samples through to the first output layer, and then using their binary outputs as inputs to another RBM layer. We would be using probabilistic binary outputs, so it is important to have enough samples that the next layer gets a good idea of what the input distribution is. We can use the probability outputs directly, but I've found, at least with this toy problem, that this doesn't seem to lead to significantly better results.
To try this, I'll use 100 units in the first layer, which could be overkill, and a variable number of units in the second layer, from 10 to 200. To get the cost, I can run the output all the way back to the input layer. Here's the result in log cost per pixel:
So this isn't so good: the error rate for the second layer is much higher than that for the first layer. One possibility is that the first layer is so good that the second layer is not necessary at all. But then I would have thought we would get at least the same error rate.
That's where I'll leave this article right now. Possible future investigations would be more complex inputs, and why layer 2 refuses to be as good as layer 1.
# My Cabinet of Obsolete Technologies
Over the years, I've bagged some technological items from before I was born, and some nostalgic items from the 80s.
A Radio Shack 40-155 "Personal Stereo Speaker System",
a 1985 Sony WM-F12 Walkman with headphones,
and a 1982 Radio Shack PC-2 Pocket Computer in its case.
1980 Sound Gizmo and 1980s Merlin
Arithma Addiator (with its case and stylus), a film sprocket thing,
a Burroughs punched card printing plate for CanTabCo, and small wooden slide rule
Modern fakes, but in the corner is a roll of J. L. Hammett aluminum foil
for a mimeograph
Vacuum tubes, CRTs, voltmeter
Dymo label machine, photomultiplier tube,
some individually wrapped screws for the Air Force
# Machine Learning: Autoencoders
An autoencoding algorithm is an unsupervised learning algorithm which seeks to recreate its input after processing the output. The layer or layers between input and output then become a representation of the input, which may have fewer or more dimensions than the input.
If the internal layer is further restricted so that only a very few of its components are active for any given input, then it is a sparse autoencoder. Generally, if the dimension of the internal layer is less than that of the input layer, then the autoencoder is performing, appropriately enough, dimension reduction. If, however, the number of dimensions is greater, then we enter the realm of feature detection, which, to me anyway, is a much more interesting application of autoencoding. In addition, feature detection appears to be how the brain handles input.
One of the challenges of feature detection is to ensure the internal layers don't degenerate to a trivial representation of the input, that is, simply repeating the input so that each feature is simply an input feature.
I'll start by talking about autoencoding via backpropagation. Before we tackle this, I'd like to rehash the mathematics of backpropagation, but this time in matrix form, which will be much easier to handle. So feel free to skip if you're not really interested.
### Backpropagation, a more thorough derivation
This time, however, we'll use matrix notation. The equation for the vector of activations for layer l is as follows:
\begin{align*} z^{(l)} &= W^{(l-1)}a^{(l-1)} + b^{(l)}\\ a^{(l)} &= g \left ( z^{(l)} \right ) \end{align*}
where:
• a(l) is a column vector of sl elements (i.e. an sl x 1 matrix), the activations of the neurons in layer l,
• b(l) is a column vector of sl elements (i.e. an sl x 1 matrix), the biases for layer l, equivalent to a fixed input 1 multiplied by a bias weight, separated out so we don't have to deal with a separate and somewhat confusing input augmentation step,
• W(l-1) is an sl x sl-1 matrix for the weights between layer l-1 and layer l, and
• g is a squashing function, which we can take to be the logistic function (for range 0 to 1) or the tanh function (for range -1 to 1). Or really any differentiable function.
A quick sanity check for z = Wa + b: W is sl x sl-1, a is sl-1 x 1, so multiplying W x a cancels out the middle, yielding sl x 1, which is consistent with the definitions for z and b.
Now, the cost function for a single data point x(i),y(i) is as follows:
$J^{(i)}(W, b) = \frac{1}{2}\left \| a^{(L,i)} - y^{(i)} \right \|^2$
|| a - y || is simply the Euclidean distance between a and y, otherwise known as the L2 norm. Note also that it is a scalar, and not a vector or matrix.
The cost over all data points, and adding a regularization term, is:
$J(W, b) = \frac{1}{m}\sum_i^m \frac{1}{2}\left \| a^{(L,i)} - y^{(i)} \right \|^2 + \frac{\lambda}{2}\sum_{l,u,v} \left ( W_{uv}^{(l)} \right )^2$
That last term simply means to take every weight between every neuron and every other neuron in every layer, square it, and add. We don't take any of the bias terms into the regularization term, as usual.
Now, first, we want to determine how gradient descent moves W(L-1) and b(L):
\begin{align*} W^{(L-1)} &\leftarrow W^{(L-1)} - \alpha \frac{\partial J(W,b)}{\partial W^{(L-1)}} \\ b^{(L)} &\leftarrow b^{(L)} - \alpha \frac{\partial J(W,b)}{\partial b^{(L)}} \end{align*}
This just says that we move W downhill in "J-space" with respect to W, and the same with b. Note that since W(L-1) is an sL x sL-1 matrix, then so too must the derivative of J with respect to W(L-1) be. And now let's compute those derivatives. First, the derivative with respect to the weights in the last layer:
\begin{align*} \frac{\partial J(W,b)}{\partial W^{(L-1)}} &= \frac{1}{m} \sum_i^m \left ( \left \| a^{(L,i)} - y^{(i)} \right \| \frac{\partial a^{(L,i)}}{\partial W^{(L-1)}} \right ) + \lambda W^{(L-1)} \\ \frac{\partial a^{(L,i)}}{\partial W^{(L-1)}} &= \frac{\partial g\left (z^{(L,i)} \right )}{\partial W^{(L-1)}} \\ &= \frac{\partial g\left (z^{(L,i)} \right )}{\partial z^{(L,i)}} \left ( \frac{\partial z^{(L,i)} }{\partial W^{(L-1)}}\right )^\top \\ \frac{\partial g\left (z^{(L,i)} \right )}{\partial z^{(L,i)}} &= g'\left (z^{(L,i)} \right ) \\ \frac{\partial z^{(L,i)} }{\partial W^{(L-1)}} &= a^{(L-1, i)} \\ \therefore \frac{\partial J(W,b)}{\partial W^{(L-1)}} &= \frac{1}{m} \sum_i^m \left ( \left \| a^{(L,i)} - y^{(i)} \right \| g'\left (z^{(L,i)} \right )(a^{(L-1, i)})^\top \right ) + \lambda W^{(L-1)} \end{align*}
Note that we just called the derivative of g with respect to its argument, g'. For the logistic and tanh functions, these are nice, compact derivatives:
\begin{align*} g'_{\text{logistic}}(z) &= g(z) \left ( 1-g(z) \right ) \\ g'_{\text{tanh}}(z) &= 1-g^2(z) \end{align*}
Since the argument of g (being z(L,i)) is an sL x 1 matrix, so too is its derivative. a(L-1,i) is an sL-1 x 1 matrix, its transpose is a 1 x sL-1 matrix, and thus g' x a is an sL x sL-1 matrix, which is consistent with what we wanted the size of the derivative of J with respect to W(L-1) to be.
And now with respect to the bias on the last layer:
\begin{align*} \frac{\partial J(W,b)}{\partial b^{(L)}} &= \frac{1}{m} \sum_i^m \left ( \left \| a^{(L,i)} - y^{(i)} \right \| \frac{\partial a^{(L,i)}}{\partial b^{(L)}} \right ) \\ \frac{\partial a^{(L,i)}}{\partial b^{(L)}} &= \frac{\partial g\left (z^{(L,i)} \right )}{\partial b^{(L)}} \\ &= \frac{\partial g\left (z^{(L,i)} \right )}{\partial z^{(L,i)}} \left ( \frac{\partial z^{(L,i)} }{\partial b^{(L)}}\right )^\top \\ \frac{\partial g\left (z^{(L,i)} \right )}{\partial z^{(L,i)}} &= g'\left (z^{(L,i)} \right ) \\ \frac{\partial z^{(L,i)} }{\partial b^{(L)}} &= 1 \\ \therefore \frac{\partial J(W,b)}{\partial b^{(L)}} &= \frac{1}{m} \sum_i^m \left ( \left \| a^{(L,i)} - y^{(i)} \right \| g'\left (z^{(L,i)} \right ) \right ) \end{align*}
Let us define:
$\delta^{(L,i)} = \left \| a^{(L,i)} - y^{(i)} \right \| g'\left (z^{(L,i)} \right )$
Note that this is an sL x 1 matrix. It is the contribution to the weight or bias gradient due to an "error" in output. We can now define our derivatives more compactly:
\begin{align*} \frac{\partial J}{\partial W^{(L-1)}} &= \frac{1}{m}\sum_i^m \delta^{(L,i)} (a^{(L-1,i)})^\top + \lambda W^{(L-1)}\\ \frac{\partial J}{\partial b^{(L)}} &= \frac{1}{m}\sum_i^m \delta^{(L,i)} \end{align*}
Now, what about the derivatives with respect to the previous layer weights and bias? The key insight in backpropagation is that we can generalize these derivatives as follows. For l from L to 2 (we start from L because these are recursive equations) we have:
\begin{align*} \frac{\partial J}{\partial W^{(l-1)}} &= \frac{1}{m}\sum_i^m \delta^{(l,i)} (a^{(l-1,i)})^\top + \lambda W^{(l-1)}\\ \frac{\partial J}{\partial b^{(l)}} &= \frac{1}{m}\sum_i^m \delta^{(l,i)} \\ \delta^{(l,i)} &= \begin{cases} & \left \| a^{(L,i)} - y^{(i)} \right \| g' \left ( z^{(L,i)} \right )\text{ if } l=L \\ & \left ( (W^{(l)})^\top\delta^{(l+1,i)} \right ) g' \left ( z^{(l,i)} \right ) \text{ if } l
A rigorous mathematical treatment for this is so completely outside the scope of this article as to be invisible :) But the general argument is that delta represents the contribution of a layer to the gradient based on the error between desired output and generated output. For the final layer, this is straightforward, and we can directly calculate it. However, for an internal layer, it is as if the errors from the next layer have propagated backwards through the weights, and so we can calculate, from output to input, the contributions of each layer.
### Backpropagation, the algorithm
First, zero out an accumulator for each layer. The accumulators have the same dimensions as the weight and bias matrices. So for l from 2 to L:
\begin{align*} D_w^{(l-1)} &\leftarrow 0 \\ D_b^{(l)} &\leftarrow 0 \\ \end{align*}
Second, compute all the forward activations a for a single data point. So, for l from 2 to L, we have:
\begin{align*} z^{(l)} &= W^{(l-1)}a^{(l-1)} + b^{(l)}\\ a^{(l)} &= g \left ( z^{(l)} \right ) \end{align*}
Compute the delta terms for l from L to 2, and add to the accumulators:
\begin{align*} \delta^{(l,i)} &= \begin{cases} \left \| a^{(l,i)} - y^{(i)} \right \| g' \left ( z^{(l,i)} \right ) & \text{ if } l=L \\ \left ( (W^{l})^\top \delta^{(l+1,i)}\right ) g' \left ( z^{(l,i)} \right ) & \text{ if } l
Next, after doing the above two steps for each data point, we compute the gradients for l from 2 to L:
\begin{align*} \frac{\partial J}{\partial W^{(l-1)}} &= \frac{1}{m} D_w^{(l-1)} + \lambda W^{(l-1)} \\ \frac{\partial J}{\partial b^{(l)}} &= \frac{1}{m} D_b^{(l)} \end{align*}
Finally, we use these gradients to go downhill, for l from 2 to L:
\begin{align*} W^{(l-1)} &\leftarrow W^{(l-1)} - \alpha \frac{\partial J}{\partial W^{(l-1)}} \\ b^{(l)} &\leftarrow b^{(l)} - \alpha \frac{\partial J}{\partial b^{(l)}} \\ \end{align*}
That is one round of updates. We start from zeroing out the accumulators to do the next iteration, and continue until it doesn't look like the cost is getting any lower.
Instead of the above, we could provide a function which, given W and b, computes the cost and the derivatives. Then we give that function to a library which does minimization. Sometimes minimization libraries do a better job at minimizing than manually doing gradient descent, and some of the libraries don't need a learning parameter (alpha).
The whole reason for going through the derivation and not going straight to the algorithm was so that we could add a sparseness measure in the cost function, and see how that affects the algorithm.
First, if we have d dimensions in the input, then an autoencoder will be a d:1:d network.
We will first determine the average activation of layer 2 over all data points:
$\hat{\rho} = \frac{1}{m}\sum_i a^{(2)} ( x^{(i)} )$
Note that this is an s2 x 1 matrix. To be sparse, we want the values of each element to be very low. If we're using a logistic function, this means near to zero. If we're using the tanh function, near to -1, but we will rescale the average activation to lie between 0 and 1 by adding 1 and dividing by 2.
Let us denote our target sparsity for each element as ρ, so that we want our measured sparsity to be close to that. Clearly we don't want ρ=0, because that would give us a trival solution: zero weights everywhere.
For a sparsity cost, we will use the following measure, known as the Kullback-Leibler divergence:
$J_{\hat{\rho}} = \sum_k^{s_2} \rho \ln \frac{\rho}{\hat{\rho}_k} + (1-\rho) \ln \frac{1-\rho}{1-\hat{\rho}_k}$
Note that the sum applies element-by-element to the measured sparsity vector, and so the cost is a scalar. This cost is zero when each measured sparsity element is equal to the desired sparsity, and rises otherwise.
We add this cost to our main cost function as follows:
$J_\text{sparse}(W,b) = J(W,b) + \beta J_{\hat{\rho}}$
where β is just a parameter whereby we can tune the importance of the sparsity cost.
Without going through the derivation, we use the following altered delta for layer 2 during backpropagation:
$\delta^{(2,i)} = \left ( (W^{(2)})^\top \delta^{(3,i)} + \beta \left ( -\frac{\rho}{\hat{\rho}} + \frac{1-\rho}{1-\hat{\rho}} \right )\right ) g'(z^{(2,i)})$
That scalar term added due to sparsity is computed only after all data points have been fed forwards through the network, because that is the only way to determine the average activation of layer 2. It is independent, therefore, of i. So the modification to backpropagation would require this:
1. Going through the data set, compute all the way up to layer 2, and accumulate the sum of the activations for each neuron in layer 2.
2. Divide the sums by m, the number of points in the data set.
3. Perform one iteration of backpropagation.
4. Go back to step 1.
### Why I don't like this
It is said that backpropagation is not biologically plausible, that is, it cannot be the algorithm used by the brain. There are several reasons for this, chief among which is that errors do not propagate backwards in the brain.
A sparse backpropagating autoencoder is doubly implausible, because not only does it rely on backpropagation, but it also requires that we wait until all data points are presented before determining the average activation. It would be much nicer if we had something more biologically plausible, if only because I have the suspicion that any algorithm that is not biologically plausible cannot lead to human-level intelligence.
So in the next article, I'll talk about a biologically plausible algorithm called the reverse Boltzmann machine.
# Machine Learning: K-Means Clustering
K-means clustering is the first unsupervised learning algorithm in this series. Unsupervised means that the answer is not available to the learning algorithm beforehand, just the cost of a potential solution. To me, unsupervised learning algorithms are more exciting than supervised learning algorithms because they seem to transcend human intelligence in a way. An unsupervised learning algorithm will seek out patterns in data without any (or with few) hints. This seems especially important when, as the human, we don't know what the hints could possibly be.
The Google "Visual Cortex" project shows how powerful unsupervised learning algorithms can be: from millions of unlabeled images, the algorithm found generalized categories such as human faces and cat faces. It is easy to see that if the same thing could be done with an audio stream or a text stream, the streams could be combined at a high enough level for association to produce sounds and text for images, images for text and sounds, and at a high enough level, reasoning.
The K-means clustering algorithm treats data as if it were in clusters centered around some number of points k, one cluster per point. Conceptually, the algorithm picks k centroid points, assigns each point in the data to a cluster based on how close it is to which cluster's centroid, moves each centroid to the center of its cluster, and repeats. The result is a set of centroids which minimizes the distances between each point and its associated cluster's centroid.
The cost function is:
$J = \frac{1}{m}\sum_i^k \sum_{j \in C_i} (x_j - \mu_i)^2$
where Ci is cluster i, and μi is the centroid for cluster i.
There are a few methods for picking the initial centroids. One method, the Forgy method, involves picking k random points from the data set to be the initial centroids. Another method, the Random Partition method, assigns each data point to a random cluster, then produces the initial centroids for each cluster. Regardless of the initial method, the algorithm proceeds by repeating the following two steps:
First, produce the clusters by assigning each data point to one cluster. This means comparing the distance of a point to each centroid, and assigning the point to the cluster whose centroid yields the lowest distance.
Second, calculate the centroid of each resulting cluster.
Repeat these steps until the total cost does not change.
### A Concrete Example
I implemented the above algorithm in Java and ran it on the usual concrete strength data set. As usual, I set aside 20% of the data set as a cross-validation. But a problem quickly became apparent: how many clusters should I use? Clearly the more clusters, the less the overall cost would be simply because there would be more centroids.
One solution is to try different numbers of centroids and ask if there is an obvious point where there is not a lot of improvement in the cost. Here is what I found from k=2 through 10:
Blue is the training cost, while red is the cross-validation cost. Interestingly, the cross-validation cost was always below the training cost, indicating that the cross-validation points represent well the training points. There is clearly no overfitting because there is no large gap between costs. However, there is no obvious point at which increasing the number of clusters doesn't help much.
The other solution to the number of clusters relies on evaluating different numbers of clusters only after later processing. If downstream processing works better with a certain number of clusters, then that number of clusters should be chosen. So, for example, if I put each cluster's data through a neural network, how good is the error for each number of clusters?
I trained an 8:10:10:1 neural network on each cluster of points, so k=2 had 2 networks, and k=10 had 10 networks. I used fewer hidden neurons than before, on the theory that each cluster has less data, meaning that I can probably get away with a smaller parameter space. Here are the results:
Clearly the more clusters and the more networks, the better the output. Perhaps because more networks means smaller clusters, which in turn means less variation to account for. Interestingly, 8 clusters works about as well as 5 clusters, and it's only with 9 and 10 clusters that more advantage is found. In any case, choosing k=10, here are the errors:
Compared to training a single 8:20:20:1 network on the entire data set, clustering has definitely reduced the errors. Most errors in the training set are now under 5% (down from 10% before), and even the one troubling point from before (error 100%) has been knocked down to an error of 83%. The low errors in the cross-validation points -- which, remember, the network has never seen -- all lead us to believe that the networks trained are not overfit.
I would still want to look at those high-error points, perhaps even asking for the experimental data for those points to be rechecked or even rerun. But for now, I would be happy with this artificially intelligent concrete master.
For the next article, I'm going to go off the syllabus of the Machine Learning course, and talk about one of my favorite unsupervised learning algorithms, the autoencoder.
# Machine Learning: Feedforward backpropagation neural networks
If we take a logistic function as in logistic regression, and feed the outputs of many logistic regressions into another logistic regression, and do this for several levels, we end up with a neural network architecture. This works nicely to increase the number of parameters as well as the number of features from the basic set you have, since a neural network's hidden layers act as new features.
Each non-input neuron in a layer gets its inputs from every neuron from the previous layer, including a fixed bias neuron which acts as the x0 = 1 term we always have.
Rather than θ, we now call the parameters weights, and the outputs are now called activations. The equation for the output (activation) of neuron p in layer l is:
\begin{align*} z^{(l)}_q &= \sum_{p=0}^{s_{l-1}} w_{pq}^{(l-1)}a_p^{(l-1)}\\ a^{(l)}_q &= g\left (z^{(l)}_q \right ) \end{align*}
Breaking it down:
• w(l-1)pq is the weight from neuron p in layer l-1 to neuron q in layer l
• a(l-1)pq is the activation of neuron p in layer l-1, and of course when p=0, the activation is by definition 1.
• z(l)is the usual sum, specifically for neuron q in layer l.
• g is some function, which we can take to be the logistic function.
So we see that the output of any given neuron is a logistic function of its inputs.
We will define the cost function for the entire output, for a single data point, to be as follows:
$J^{(i)} = \frac{1}{2}\sum_{p=1}^{s_L} \left ( y_p^{(i)} - a_p^{(i, L)} \right )^2$
Note that we are using the linear regression cost, because we will want the output to be an actual output rather than a classification. The cost can be defined using the logistic cost function if the output is a classification.
Now, the algorithm proceeds as follows:
1. Compute all the activations for a single data point
2. For each output neuron q, compute:
$\delta^{(L)}_q = -(y_q^{(i)} - a_q^{(i, L)})(1 - a_q^{(i, L)})a_q^{(i, L)}$
3. For each non-output neuron p, working backwards in layers from layer L-1 to layer 1, compute:
$\delta^{(l)}_p = (1 - a_p^{(i, l)})a_p^{(i, l)}\sum_{q=1}^{s_{l+1}} w^{(l)}_{pq}\delta^{(l+1)}_q$
4. Compute the weight updates as follows:
$w^{(l)}_{pq} \leftarrow w^{(l)}_{pq} + \alpha a^{(l)}_p \delta^{(l+1)}_q$
The last step can, in fact, be delayed. Simply present multiple data points, or even the entire training set, adding up the changes to the weights, and then only update the weights afterwards.
Because it is extraordinarily easy to get the implementation wrong, I highly suggest the use of a neural network library such as the impressively expansive Encog as opposed to implementing it yourself. Also, many neural network libraries include training algorithms other than backpropagation.
### The Concrete Example
I used Encog to train a neural network on the concrete data from the earlier post. I first took the log of the output, since that seemed to represent the data better and led to less network error. Then I normalized the data, except I used the range 0-1 for both the days input and the strength output, since that seemed to make sense, and also led to less network error.
Here's the Java code I used. Compile it with the Encog core library in the classpath. The only argument to it is the path to the Concrete_Data.csv file.
The network I chose, after some experimentation checking for under- and overfitting, was an 8:20:10:1 network. I used this network to train against different sizes of training sets to see the learning curves. Each set of data was presented to the network for 10,000 iterations of an algorithm called Resilient Backpropagation, which has various advantages over backpropagation, namely that the learning rate generally doesn't have to be set.
As before, the blue line is the training cost, the mean squared error against the training set, and the red line is the cross-validation cost, the mean squared error against the cross-validation set. This is generally what I would expect for an algorithm that is neither underfitting nor overfitting. Overfitting would show a large gap between training and cross-validation, while underfitting would show high errors for both.
If we saw underfitting, then we would have to increase the parameter space, which would mean increase the number of neurons in the hidden layers. If we saw overfitting, then decreasing the parameters space would be appropriate, so decreasing the number of neurons in the hidden layers would help.
Since the range of the output is 0-1, over the entire training set we get an MSE (training) of 0.0003, which means the average error per data point is 0.017. This doesn't quite tell the whole story, because if an output is supposed to be, say, 0.01, and error of 0.017 means the output wasn't very well-fit. Instead, let's just look at the entire data set, ordered by value, after denormalization:
The majority of errors fall under 10%, which is probably good enough. If I were concerned with the data points whose error was above 10%, I might be tempted treat those data points as "difficult", try to train a classifier to train data points as "difficult" or "not difficult", and then train different regression networks on each class.
The problem with that is that I could end up overfitting my data again, this time manually. If I manually divide my points into "difficult" and "not difficult" points, then what is the difference between that and having more than two classes? How about as many classes as there are data points?
What would be nice is if I could have an automatic way to determine if there is more than one cluster in my data set. One clustering algorithm will be the subject of the next post. | {"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": 30, "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": 0.823729932308197, "perplexity": 1479.0914374770662}, "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-2016-36/segments/1471982968912.71/warc/CC-MAIN-20160823200928-00131-ip-10-153-172-175.ec2.internal.warc.gz"} |
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$'...-T'vi f^SH^#^ < GRi^TIOT COUNTY, MICH. gOF^TI^AITS AND BlOGl^APHIGAL Sl^BHiGHBS ppoginent and I^epPe^qtatiVe ditizeq^ of tp (JountJ TOGETHER WITH FORTH AITS AND UlOdRAPIUES OF ALL THE (iOVERXORS OF MICHJGA N AND OF THE PRESIDENTS O? THE UNITED STATES. ALSO CONTAINING A COMPLETE IlISTOUY OF THE COUNTY, I'ltOM ITS EAKI.IKST SETTLEJIEN' TO THE PRESENT TIME. CHICAGO: AI'MAN l?ROiril.l< 1SS4. :<■■> \ c- %{ *^ •: -V: <--DD>:DDr:> L. uvm ^^'j Digitized by V^OOQlC k . -t 'i- \ ^ac^' ■• ■■ .■•?i .V '.c^:(- ■>>''- '^^ ' ;^ t « •v. *- •< « * J 1 V "J. - • "': . "• ■■/' Digitized by Google :> ^ iCi?^^: rrr7<^DIl^|]D^>v^ >->\i>vt/^ ^^'-^iAi/-'^^-^ ^^=5-?^ Si-' T (#'< &< ^ A 1. ' V- ^ r> ^?^r' ;n!l^:ilti;>^ 4r^^f.^N Digitized by VjOOQlC V r >^-5r"-r T<^:DQ:<::DDr:>v ■^^j-'C^ -i-3f.> f; V V /»> '•'^-?^ -=<^nii:^tiiir>^ ^^•i5r>^<'* J. Digitized by Google Hi- i \ *' Digitized by Google .-^ tO^/^yC^^i^^ -4f-, Digitized by Google •o /\ "^^ ) 4 '^i> ^-T) FIRST PRESIDENT. 1 ■ % i^(^^'f^<^(^i^,^f^^f^f^<^<^?sg:m^t^^^c^/^j^^'m^^^^^^ GEOBOE WASHIKGTOK SS**- HE Father of our Country was born in Westmorland G>., Va., Feb. 2 2, 1732. His parents were Augustine and Mary (Ball) Washington. The family to which he belonged has not been satisfactorily traced in England. His great-grand- father, John Washington, em- igrated to Virginia about 1657, N J iJi"^ I ^^^ became a prosperous planter. He had tveo sons, Lawrence and John. The former married Mildred Warner and had three children, John, Augustine and Mildred. Augus- tine, the father of George, first married Jane Butler, who bore him four children, two of whom, Lawrence and Augustine, reached maturity. Of six children by his second marriage, George was the eldest, the others being Betty, Samuel, John Augustine, Charles and Mildred. Augustine Washington, the father of George, died in 1743, leaving a large landed property. To his eldest son, Lawrence, he bequeathed an estate on the Patomac, afterwards known as Mount Vernon, and to George he left the parental residence. George received only such education as the neighborhood schools aObrded, save for a short time after he left scIkwI, when he received private instruction in ^ .^ mathematics. His spelling was rather defective. ^"^^^ ^y^M Remarkable stories are told of his great physical strength and development at an early age. He was an acknowledged leader among his companions, and was early noted for that nobleness of character, fair- ness and veracity which characterized his whole life. When George was 1 4 years old he had a desire to go to sea, and a midshipman's warrant was secured for him, but through the opposition of his mother the idea was abandoned. Two years later he was appointed surveyor to the immense estate of Lord Fairfax. In this business he spent three years in a rough frontier life, gaining experience which afterwards proved very essential to him. In 1751, though only 19 years of age, he was appointed adjutant with the rank of major in the Virginia militia, then being trained for acrive service against the French and Indians. Soon after this he sailed to the West Indies with his brother Lawrence, who went there to restore his health. They soon returned, and in the summer of 1752 Lawrence died, leaving a large fortune to an infant daughter who did not long survive him. On her demise the estate of Mount Vernon was given to George, Upon the arrival of Robert Dinwiddie, as Lieuten- ant-Governor of Virginia, in 1752, the militia was reorganized, and the province divided into four mili- tary districts, of which the northern was assigned to Washington as adjutant general. Shortly after this a very perilous mission was assigned him and ac- cepted, which others had refused. This was lo pro- ceed to the French post near Lake Erie in North- western Pennsylvania. The distance to be traversed was between 500 and 600 miles. Winter was at hand, and the journey was to be made without military escort, through a territory occupied by Indians. The 9 s 0: Digitized by Google Z^-i^"-^ GEORGE <i>mmhw TT WASHINGTON. ^^.^A- ) > M^) Y a trip was a perilous one, and several times he came near losing his life, yet he returned in safety and furnished a full and useful report of his expedition. A regiment of 300 men was raised in Virginia and put in com- mand of Col. Joshua Fry, and Major Washington was . commissioned lieutenant-colonel. Active war was then begun against the French and Indians, in which Washington took a most important part. In the memorable event of July 9, 1755, known as Brad- docks defeat, Washington was almost the only officer of distinction who escaped from the calamities of the day with life and honor. The other aids of Braddock were disabled early in the action, and Washington alone was left in that capacity on the field. In a letter to his brother he says : " I had four bullets through my coat, and two horses shot under me, yet I escaped unhurt, though death was leveling my companions on every side." An Indian sharpshooter said he was not bom to be killed by a bullet, for he had taken direct aim at him seventeen times, and failed to hit him. After having been ^>it, years in the military service, and vainly sought promotion in the royal army, he took advantage of the fall of Fort Duquesne and the expulsion of the French from the valley of the Ohio, to resign his commission. Soon after he entered the Legislature, where, although not a leader, he took an active and important part. January 17, 1759, he married Mrs. Martha (Dandridge) Custis, the wealthy widow of John Parke Custis. When the British Parliament had closed the ix)rt of Boston, the cry went up throughout the provinces that "The cause of Boston is the cause of us all." It was then, at the suggestion of Virginia, that a Con- gress of all the colonies was called to meet at Phila- delphia,Sept. 5, 1774, to secure their common liberties, peaceably if ix)ssible. To this Congress Col. Wash- ington was sent as a delegate. On May 10, 1775, the Congress re-assembled, when the hostile intentions of England were plainly apparent. The battles of Con- cord and Lexington had been fought. Among the first acts of this Congress was the election of a com- mander-in-chief of the colonial forces. This high and responsible office was conferred upon Washington, who was still a member of the Congress. He accepted it on June 19, but upon the express condition that he receive no salary. He would keep an exact account of expenses and expect Congress to pay them and nothing more. It is not the object of this sketch to trace the military acts of Washington, to whom the fortunes and liberties of the people of this country were so long confided. The war was conducted by him under ever}' possible disadvantage, and while his forces often met with reverses, yet he overcame every obstacle, and after seven years of heroic devotion and matchless skill he gained liberty for the greatest nation of earth. On Dec. 23, 1783, Washington, in a parting address of surpassing beauty, resigned his commission as commander-in-chief of the army to to the Continental Congress sitting at Annapolis. He retired immediately to Mount Vernon and resumed his occupation as a farmer and planter, shunning all connection with public life. In February, 1 7 89, Washington was unanimously elected President. In his presidential career he was subject to the peculiar trials incidental to a new government ; trials from lack of confidence on the part of other governments; trials from want of harmony between the different sections of our own country ; trials from the impoverished condition of the countr)% owmgto the war and want of credit; trials from the beginnings of party strife. He was no partisan. His clear judgment could discern the golden mean ; and while perhaps this alone kept our government from sinking at the very outset, it left him exposed to attacks from both sides, which were often bitter and very annoying. At the expiration of his first term he was unani- mously re-elected. At the end of this term many were anxious that he be re-elected, but he absolutely refused a third nomination. On the fourth of March, 1797, at the expiraton of his second term as Presi- dent, he returned to his home, hoping to pass there his few remaining years free from the annoyances of public life. Later in the year, however, his repose seemed likely to be interrupted by war with France. At the prospect of such a war he was again urged to take command of the armies. He chose his sub- ordinate officers and left to them the charge of mat- ters in the field, which he superintended from his home. In accepting the command he made the reservation that he was not to be in the field until it was necessary. In the midst of these preparations his life was suddenly cut off. December 1 2, he took a severe cold from a ride in the rain, which, settling in his throat, produced inflammation, and terminated fatally on the night of the fourteenth. On the eigh- teenth his body was borne with military honors to its final resting place, and interred in the family vault at Mount Vernon. Of the character of Washington it is impossible to speak but in terms of the highest respect and ad- miration. The more we see of the operations of our government, and the more deeply we feel the difficulty of uniting all opinions in a common interest, the more highly we must estimate the force of his tal- ent and character, which have been able to challenge the reverence of all parties, and principles, and na- tions, and to win a fame as extended as the limits of the globe, and which we cannot but believe will be as lasting as the existence of man. The person of Washington was unusally tall, erect and well proportioned. His muscular strength was great. His features were of a beauriful symmetry. He commanded respect without any appearance of haughtiness, and ever serious without being dull. ^■.'"^. T^<:^Dfl^iit]>>^ m^y'^r!/^ -l>^^:7- Digitized by Google Digitized by Google /'^M, am Digitized by Google ^■1 SECOND PRESIDENT. ■>^^' yi^^^\^i^ *3 fe'-1^fJ^■n^ . ^^^'CUf^ ^ '&•, i -^^p<&- JOHN ABAMS, ^ V^ A >2 V OHN ADAMS, the second President and the first Vice- President of the United States, was born in Braintree ( now Quincy),Mass., and about ten ^' miles from Boston, Oct. 19, 735. His great-grandfather, Henry Vdams, emigrated from England x)ut 1640, with a family of eight sons, and settled at Braintree. The parents of John were John and Susannah (Boylston) Adams, His father was a farmer of limited means, to which he added the bus- iness of shoemaking. He gave his eldest son, John, a classical educa- tion at Harvard College. John graduated in 1755, and at once took charge of the school in Worcester, Mass. This he found but a "school of affliction," from which he endeavored to gain relief by devoting himself, in addition, to the study of law. For this purpose he placed himself under the tuition of the only lawyer in the town. He had thought seriously of the clerical profession but seems to have been turned from this by what he termed " the frightful engines of ecclesiastical coun- cils, of diabolical malice, and Calvanistic good nature," of the operations of which he had been a witness in his native town. He was well fitted for the legal profession, possessing a clear, sonorous voice, being ready and fluent of speech, and having quick percep- > tive powers. He gradually gained practice, and in \ 1764 married Abigail Smith, a daughter of a minister, 'K and a lady of superior intelligence. Shortly after his jf marris^e, (1765), the attempt of Parliamentary taxa- ^^ tion turned him from law to politics. He took initial V^^ stcpstoward holding a town meeting, and the resolu- ^ tions he offered on the subject became very ix)pular throughout the Province, and were adopted word for word by over forty different towns. He moved to Bos- ton in 1768, and became one of the most courageous and prominent advocates of the popular cause, and was chosen a member of the General Court (the Leg- lislature) in 1770. Mr. Adams was chosen one of the first delegates from Massachusetts to the first Continental Congress, which met in 1774. Here he distinguished himself by his capacity for business and for debate, and ad- vocated the movement for independence against the majority of the members. In May, 1776, he moved and carried a resolution in Congress that the Colonies should assume the duties of self-government. He was a prominent member of the committee of five appointed June 11, to prepare a declaration of inde- pendence. This article was drawn by Jefferson, but on Adams devolved the task of battling it through Congress in a three days debate. On the day after the Declaration of Independence was passed, while his soul was yet warm with the glow of excited feeling, he wrote a letter to his wife, which, as we read it now, seems to have been dictated by the spirit of prophecy. "Yesterday," he says, "the greatest question was decided that ever was debated in America; and greater, perhaps, never was or will be decided among men. A resolution was passed without one dissenting colony, * that these United States are, and of right ought to be, free and inde- pendent states.* The day is passed. The fourth of July, 1776, will be a memorable epoch in the history of America. I am apt to believe it will be celebrated by succeeding generations, as the great anniversary festival. It ought to be commemorated as the day of deliverance by solemn acts of devotion to Almighty God. It ought to be solemnized with pomp, shows* ( < '^: ^A^ ^^s' ^#«*- ■^^^^€^^ ^^Dii^niif^ ^. -ff^^Ci!>^^i Digitized by V^OOQlC ^))«§^^-«-" "3^«?»sr & > •^ ^ b JOHN ADAAfS. ■^2A&er-i -^■S'J^i^J^ Vi games, sports, guns, bells, bonfires, and illuminations from one end of the continent to the other, from this time forward for ever. You will think me transported with enthusiasm, but I am not. I am well aware of the toil, and blood and treasure, that it will cost to maintain this declaration, and support and defend these States; yet, through all the gloom, I can see the rays of light and glory. I can see that the end is worth more than all the means; and that posterity will triumph, although you and I may rue, which I hope we shall not.** In November, 1777, Mr. Adams was appointed a delegate to France^ and to co-operate with Bemjamin Franklin and Arthur Lee, who were then in Paris, in the endeavor to obtain assistance in arms and money from the French Government. This was a severe trial to his patriotism, as it separated him from his home, compelled him to cross the ocean in winter, and ex- posed him to great peril of capture by the British cruis- ers, who were seeking him. He left France June 17, 1779. In September of the same year he was again chosen to go to Paris, and there hold himself in readi- ness to negotiate a treaty of peace and of commerce with Great Britian, as soon as the British Cabinet might be found willing to listen to such proposels. He sailed for France in November, from there he went to Holland, where he negoriated important loans and formed important commercial treaties Finally a treaty of peace with England was signed Jan. 21, 1783. The re-action from the excitement, toil and anxiety through which Mr. Adams had passed threw him into a fever. After suffering from a con- tinued fever and becoming feeble and emaciated he was advised to go to England to drink the waters of Bath. While in England, still drooping and despond- ing, he received dispatches from his own government urging the necessity of his going to Amsterdam to negotiate another loan. It was winter, his health was delicate, yet he immediately set out, and through storm, on sea, on horseback and foot,he made the trip. February 24, i785,Cx)ngress appointed Mr. Adams envoy to the Court of St. James. Here he met face to face the King of England, who had so long re- garded him as a traitor. As England did not condescend to ap|X)int a minister to the United States, and as Mr. Adams felt that he was accom- plishing but little, he sought permission to return to his own country, where he arrived in June, 1788. When Washington was first chosen President, John Adams, rendered illustiious by his signal services at home and abroad, was chosen Vice President. Again at the second election of Washington as President, Adams was chosen Vice President. In 1796, Wash- ington retired from public life, and Mr. Adams was elected President,though not without much opix)sition. Serving in this office four years,he was succeeded by Mr. Jefferson, his opponent in polirics. While Mr. Adams was Vice President the great S) French Revolution shook the continent of Europe, and it was upon this point which he was at issue with the majority of his countrymen led by Mr. Jefferson. Mr. Adams felt no sympathy with the French people in their struggle, for he had no confidence in their power of self-government, and he utterly abhored the class of atheist philosophers who he claimed caused it. On the other hand Jefferson's sympathies were stix>ngly enlisted in behalf of the French people. Hence or- iginated the alienation between these disdnguished men, and two powerful parties were thus soon organ- ized, Adams at the head of the one whose sympathies were with England and Jefferson led the other in sympathy with France. The world has seldom seen a spectacle of more moral beauty and grandeur, than was presented by the old age of Mr. Adams. The violence of party feeling had died away, and he had begun to receive that just appreciation which, to most men, is not accorded till after death. No one could look upon his venerable form, and think of what he had done and suffered, and how he had given up all the prime and strenj^th of his life to the public good, without the deepest emotion of gratitude and respect. It was his i)eculiar good fortune to witness the complete success of the institution which he had been so active in creating and supporring. In 1824, his cup of happiness was filled to the brim, by seeing his son elevated to the highest station in the gift of the people. The fourth of July, 1826, which completed the half century since the signing of the Declararion of Inde- pendence, arrived, and there were but three of the signers of that immortal instrument left upon the earth to hail its morning light. And, as it is well known, on that day two of these finished their earthly pilgrimage, a coincidence so remarkable as to seem miraculous. For a few days before Mr. Adams had been rapidly failing, and on the morning of the fourth he found himself too weak to rise from his l)ed. On being requested to name a toast for the customary celebration of the day, he exclaimed " In- dependence FOREVER," When the day was ushered in, by the ringing of bells and the firing of cannops, he was asked by one of his attendants if he knew what day it was? He replied, "O yes; it is the glor- ious fourth of July — God bless it — God bless you all." In the course of the day he said, "It is a great and glorious day." The last words he uttered were, "Jefferson survives." But he had, at one o'clock, re- signed his spirit into the bands of his God. The j>ersonal appearance and manners of Mr. Adams were not particularly prepossessing. His face, as his portrait manifests,was intellectual ard expres- sive, but his figure was low and ungraceful, and his manners were frequently abnipt and uncourteous. He had neither the lofty dignity of Washington, nor the engaging elegance and gracefulness which marked the manners and address of Jefferson. m^vg^ w. ^V^ ^^^-g-S- ■^y^^^ u:^ A<3n n^ titiv>M^ — iti^x^ -■^I'S^ Digitized by Google e ca: i 5- *^ - I m Digitized by Google m i. ii>/l^^r|'»- z:^^ — e^m%M^ -5^^ ST THIRD PRESIDENT. 27 THOMAS JBFFERSON. HOMAS JEFFERSON was born April 2, 1743, at Shad- well, Albermarle county, Va. His parents were' Peter and Jane ( Randolph) Jefferson, the former a native of Wales, and the latter bom in Lon- don. To them were bom six daughters and two sons, of whom Thomas was the elder. When 14 years of age his father died. He received a most liberal education, hav- ing been kept diligently at school from the time he was five years of age. In 1760 he entered William and Mary College. Williamsburg was then the seat of the Colonial Court, and it was the obode of fashion and splendor. Young Jefferson, who was then 17 years old, lived somewhat expensively, keeping fine horses, and much caressed by gay society, yet he was earnestly devoted to his studies, and irreproacha- able in his morals. It is strange, however, under such influences,that he was not ruined. In the sec- ond year of his college course, moved by some un- explained inward impulse, he discarded his horses, society, and even his favorite violin, to which he had ^ previously given much time. He often devoted fifteen "j hours a day to hard study, allowing himself for ex- *\^ ercise only a run in the evening twilight of a mile out of the city and back again. He thus attained very / high intellectual culture, alike excellence in philoso- phy and the languages. The most difficult Latin and Greek authors he read with facility. A more finished ■'s. there was not to be found, perhaps, in all Virginia, a more pureminded, upright, gentlemanly young man. Immediately upon leaving college he began the study of law. For the short time he continued in the practice of his profession he rose rapidly and distin- guished himself by his energy and accuteness as a lawyer. But the times called for greater action. The policy of England had awakened the spirit of resistance of the American Colonies, and the enlarged views which Jefferson had ever entertained, soon led him into active political life. In 1769 he was chosen a member of the Virginia House of Burgesses. In 1772 he married Mrs. Martha Skelton, a very beauti- ful, wealthy and highly accomplished young widow. Upon Mr. Jefferson's large estate at Shadwell, there was a majestic swell of land, called Monticello, which commanded a prospect of wonderful extent and beauty. This spot Mr. Jefferson selected for his new home; and here he reared a mansion of modest yet elegant architecture, which, next to Mount Vernon, became the most distinguished resort in our land. In 1775 ^^ was sent to the Colonial Congress, where, though a silent member, his abilities as a writer and a reasoner soon become known, and he was placed upon a number of important committees, and was chairman of the one appointed for the draw- ing up of a declaration of independence. This com- mittee consi^ed of Thomas Jefferson, John Adams, Benjamin Franklin, Roger Sherman and Robert R. Livingston. Jefferson, as chairman, was appointed to draw up the paper. Franklin and Adams suggested a few verbal changes before it was submitted to Con- gress. On June 28, a few slight changes were made in it by Congress, and it was passed and signed July 4, 1776. What must have been the feelings of that c>j * .0) / scholar has seldom gone forth from college halls ; and ^f^v^-Sl Digitized by Google ms^'-^^o-- <myM^>r ^ ^L -^ ■^^^'S 38 f A V THOMAS JEFFERSON. % man — what the emotions that swelled his breast — who was charged with the preparation of that Dec- laration, which, while it made known the wrongs of America, was also to publish her to the world, free, soverign and independent. It is one of the most re- markable papers ever written ; and did no other effort of the mind of its author exist, that alone would be sufficient to stamp his name with immortality. In 1779 Mr. Jefferson was elected successor to Patrick Henry, us Governor of Virginia. At one time the British officer, Tarleton, sent a secret expedition to Monticello, to capture the Governor. Scarcely five minutes elapsed after the hurried escape of Mr. Jef- ferson and his family, ere his mansion was in posses- sion of the British troops. His wife's health, never very good, was much injured by this excitement, and in the summer of 1782 she died, Mr. Jefferson was elected to Congress in 1783. Two years later he was appointed Minister Plenipo- tentiary to France. Returning to the United States in September, 1789, he became Secretary of State in Washington's cabinet This position he resigned Jan. J, 1794. In 1797, he was chosen Vice Presi- dent, and four years later was elected President over Mr. Adams, with Aaron Burr as Vice President. In 1804 he was re-elected with wonderful unanimity, and George Clinton, Vice President. The early part of Mr. Jefferson's second adminstra- tion was disturbed by an event which threatened the tranquiUty and peace of the Union; this was the con- spiracy of Aaron Burr. Defeated in the late election to the Vice Presidency, and led on by an unprincipled ambition, this extraordinary man formed the plan of a military expedition into the Spanish territories on our southwestern frontier, for the purjwse of forming there a new republic. This has been generally supposed was a mere pretext ; and although it has not been generally known what his real plans were, there is no doubt that they were of a f:ir more dangerous character. In r8o9, at the expiration of the second term for which Mr. Jefferson had been elected, he determined to retire from political life. For a period of nearly forty years, he had been continually before the pub- lic, and all that time had been employed in offices of the greatest trust and responsibility. Having thus de- voted the best part of his life to the service of his country, he now felt desirous of that rest which his declining years required, and uiX)n the organization of the new administration, in March, 1809, he bid fare- well forever to public life, and retired to Monticello. Mr. Jefferson was profuse in his hospitality. Whole families came in their coaches with their horses, — fathers and mothers, boys and girls, babies and nurses, — and remained three and even six months. Life at Monticello, for years, resembled that at a fashionable watering-place. The fourth of July, 1826, being the fiftieth anniver- — ^ (?^i sary of the Declaration of American Independence, V great preparations were made in every part of the •' Union for its celebration, as the nation's jubilee, and the citizens of Washington, to add to the solemnity of the occasion, invited Mr. Jefferson, as the fraraer, and one of the few surviving signers of the Declara- tion, to participate in their festivities. But an ill- ness, which had been of several weeks duration, and had been continually increasing, compelled him to decline the invitation. On the second of July, the disease under which he was laboring left him, but in such a reduced state that his medical attendants, entertained no hope of his recovery. From this time he was perfectly sensible that his last hour was at hand. On the next day, which was Monday, he asked of those around him, the day of the month, and on being told it was the third of July, he expresied the earnest wish that he might be permitted to breathe the air of the fiftieth anniversary. His prayer was heard — that day, whose dawn was hailed with such rapture through our land, burst upon his eyes, and then they were closed for- ever. And what a noble consummation of a noble life! To die on that day, — the birthday of a nation,- - the day which his own name and his own act had rendered glorious; to die amidst the rejoicings and festivities of a whole nation, who looked up to him, as the author, under God, of their greatest blessings, was all that was wanting to fill up the record his life. Almost at the same hour of his death, the kin- dred spirit of the venerable Adams, as if to bear him company, left the scene of his earthly honors. Hand in hand they had stood forth, the champions of freedom ; hand in hand, during the dark and desper- ate struggle of the Revolution, they had cheered and animated their desponding countrymen; for half a century they had labored together for the good of the country; and now hand in hand they depart. In their lives they had been united in the same great cause of liberty, and in their deaths they were not divided. In person Mr, Jefferson was tall and thin, rather above six feet in height, but well formed; his eyes were light, his hair originally red, in after life became white and silvery; his complexion was fair, his fore- head broad, and his whole countenance intelligent and thoughtful. He possessed great fortitude of mind as well as personal courage ; and his command of tem- per was such that his oldest and most intimate friends never recollected to have seen him in a passion. His manners, though dignified, were simple and un- affected, and his hospitality was so unbounded that all found at his house a ready welcome. In conver* sation he was fluent, eloquent and enthusiastic ; and his language was remarkably pure and correct. He was a finished classical scholar, and in his writings is discemable the care with which he formed his style upon the best models of antiquity. A i '^ -L <iD!l>^DI];>-^ v:v>- Digitized by Google ■•w ■f.;::^ -^ / ^«^*^ -t^^-A.^ P'S^ Digitized by Google r- \ 'Z^^^'^ -T<i>mmi<> T ->-. FOURTH PRFSIDENT. ^ V }>^ ^ ^ I AMES MADISON, "Father of the Constitution/* and fourth ^President of the United States, was born March i6, 1757, and died at his home in Virginia, June 28, 1836. The name of James Madison is inseparably con- nected with most of the important events in that heroic period of our country during which the founda- tions of this great republic were laid. He was the last of the founders of the Constitution of the United States to be called to his eternal reward. The Madison family were among the early emigrants to the New World, landing upon the shores of the Chesa- peake but 15 years after the settle- ment of Jamestown. The father of James Madison was an opulent planter, residing upon a very fine es- tate called "Montpelier," Orange Co., Va. The mansion was situated in the midst of scenery highly pictur- j esque and romantic, on the west side of South-west Mountain, at the foot of Blue Ridge. It was but 25 miles from the home of Jefferson at Monticello. The closest personal and ix>litical attachment existed between these illustrious men, from their early youth until death. The early education of Mr. Madison was conducted mostly at home under a private tutor. At the age of 18 he was sent to Princeton College, in New Jersey. Here he applied himself to study with the most im- t 1 prudent zeal; allowing himself, for months, but three hours' sleep out of the 24. His health thus became so seriously impaired that he never recovered any vigor of constitution. He graduated in 177 i, with a feeble body, with a character of utmost purity, and with a mind highly disciplined and richly stored with learning which embellished and gave proficiency to his subse- quent career. Returning to Virginia, he commenced the study of law and a course of extensive and systematic reading. This educational course, the spirit of the times in which he lived, and the society with which he asso- ciated, all combined to inspire him with a strong love of liberty, and to train him for his life-work of a statesman. Being naturally of a religious turn of mind, and his frail health leading him to think that his life was not to be long, he directed especial atten- tion to theological studies. Endowed with a mind singularly free from passion and prejudice, and with almost unequalled powers of reasoning, he weighed all the arguments for and agaihst revealed religion, until his faith became so established as never to be shaken. In the spring of 1776, when 26 years of age, he was elected a member of the Virginia Convention, to frame the constitution of the State. The next year (1777), he was a candidate for the General Assembly. He refused to treat the whisky-Hovir.g voters, and consequently lost his election ; but those who had witnessed the talent, energy and public spirit of the modest young man, enlisted themselves in his behalf, and he was appointed to the Executive Council. Both Patrick Henry and Thomas Jefferson were Governors of Virginia while Mr. Madison remained member of the Council ; and their appreciation of his A (T^ ii vr)^ri- <^^Dii::^:iiilv>^ Digitized by Google ;| ^ ) ^ ;'^ . f intellectual, social and moral worth, contnbuted not a little to his subsequent eminence. In the year 1780, he was elected a member of the G>ntinental Congress. Here he met the most illustrious men in our land, and he was immediately assigned to one of the most conspicuous positions among them. For three years Mr. Madison continued in Con- gress, one of its most active and influential members. In the year 1784, his tenn having expired, he was elected a member of the Virginia Legislature. No man felt more deeply than Mr. Madison the utter inefficiency of the old confederacy, with no na- tional government, with no power to form treaties which would be binding, or to enforce law. There was not any State more prominent than Virginia in the declaration, that an eflkient national government must be formed. In January, 1786, Mr. Madison carried a resolution through the General Assembly of Virginia, inviting the other States to appoint commis- sioners to meet in convention at Annapolis to discuss this subject. Five States only were represented. The convention, however, issued another call, drawn up by Mr. Madison, urging all the States to send their delegates to Philadelphia, in May, 1787, to draft a Constitution for the United States, to take the place of that Confederate League. The delegates met at the time appointed. Every State but Rhode Island was represented. George Washington was chosen president of the convention ; and the present Consri- turion of the United States was then and there formed. There was, perhaps, no mind and no pen more ac- tive in framing this immortal document than the mind and the pen of James Madison. The Constitution, adopted by a vote 81 to 79, was to be presented to the several States for acceptance. But grave solicitude was felt. Should it be rejected we should be left but a conglomeration of independent States, with but little power at home and little respect abroad. Mr. Madison was selected by the conven- tion to draw up an address to the peopleof the United States, expounding the principles of the Constitution, rj and urging its adoption. There was great opposition ^ to it at first, but it at length triumphed over all, and ^ went into effect in 1789. Mr. Madison was elected to the House of Repre- sentatives in the first Congress, and soon became the avowed leader of the Republican party. While in New York attending Congress, he met Mrs. Todd, a young widow of ftmarkable power of fascination, whom he married. She was in person and character queenly, and probably no lady has thus far occupied so prominent a position in the very peculiar society which has consrituted our republican court as Mrs. Madison. Mr. Madison served as Secretary of State under Jefferson, and at the close of his administration was chosen President. At this time the encroach- ments of England had brought us to the verge of war. JAMES MADISON. ^ British orders in council desttoyed our commerce, and our flag was exposed to constant insult. Mr. Madison was a man of peace. Scholarly in his taste, retiring in his disposition, war had no charms for him. But the meekest spirit can be roused. It makes one's blood boil, even now, to think of an American ship brought to, upon the ocean, by the guns of an English cruiser. A young lieutenant steps on board and orders the crew to be paraded before him. With great nonchal- ance he selects any number whom he may please to designate as British subjects ; orders them down the ships side into his boat; and places them on the gun- deck of his man-of-war, to fight, by compulsion, the battles of England. This right of search and im- pressment, no efforts of our Government could induce the British cabinet to relinquish. On the 1 8th of June, 181 2, President Madison gave his approval to an act of Congress declaring war against Great Britain. Notwithstanding the bitter hostility of the Federal party to the war, the country in general approved; and Mr. Madison, on the 4th of March, 18 13, was re-elected by a large majority, and entered upon his second term of office. This is not the place to describe the various adventures of this war on the land and on the water. Our infant navy then laid the foundations of its renown in grap- pling with the most formidable power which ever swept the seas. The contest commenced in earnest by the appearance of a British fleet, early in February, 18 1 3, in Chesapeake Bay, declaring nearly the whole coast of the United States under blockade. The Emperor of Russia offered his services as me ditator. America accepted ; England refused. A Brit- ish force of five thousand men landed on the banks of the Patuxet River, near its entrance into Chesa- peake Bay, and marched rapidly, by way of Bladens- burg, upon Washington. The straggling little city of Washington was thrown into consternation. The cannon of the brief conflict at Bladensburg echoed through the streets of the metropolis. The whole population fled from the city. The President, leaving Mrs. Madison in the White House, with her carriage drawn up at the door to, await his speedy return, hurried to meet the officers in a council of war. He met our troops utterly routed, and he could not go back without danger of being captured. But few hours elapsed ere the Presidcnrial Mansion, the Capitol, and all the public buildings in Washington were in flames. The war closed after two years of fighting, and on Feb. 13, i8i5,the treaty of peace was signed at Ghent. On the 4th of March, 18 17, his second lerm of office expired, and he resigned the Presidential chair to his friend, James Monroe. He retired to his beau- tiful home at Montpelier, and there passed the re- mainder of his days. On June 28, 1836, then at the age of 85 years, he fell asleep in death. Mrs. Madi- son died July la, 1849. -rt. 1, < c^: ^ ( f Digitized by Google Digitized by Google Digitized by Google ]^rm^^^ ^^!^(^vMi ^ 1 ^ o ^'l AMES MONROE, the fifth jL President of The United States, '^ was born in Westmoreland Co., Va., April 28, 1758. His early life was passed at the place of nativity. His ancestors had for many years resided in the prov- ince in which he was born. When, at 17 years of age, in the process of completing his education at William and Mary College, the Co- lonial Congress assembled at Phila- delphia lo deliberate upon the un- just and manifold oppressions of Great Britian, declared the separa- tion of the Colonies, and promul- gated the Declaration of Indepen- Had he been born ten years before it is highly dence probable that he would have been one of the signers of that celebrated instrument. At this time he left school and enlisted among the patriots. He joined the army when everything looked hoj^e- less and gloomy. The number of deserters increased from day to day. The invading armies came inuring in ; and the tories not only favored the cause of the mother country, but disheartened the new recruits, who were sufficiently terrified at the prospect of con- tending with an enemy whom they had been taught lo deem invincible. To such brave spirits as James Monroe, who went right onward, undismayed through difficulty and danger, the United States owe their political emancipation. The young cadet joined the ranks, and esjx)used the cause of his injured country, with a firm determination to live or die with her strife «:^(^<|^ for liberty. Firmly yet sadly he shared in the mel- ancholy retreat from Harleam Heights and White Plains, and accompanied the dispirited army as it fled before its foes through New Jersey. In four months after the Declaration of Independence, the patriots had been beaten in seven battles. At the battle of Trenton he led the vanguard, and, in the act of charg- ing upon the enemy he received a wound in the left shoulder. As a reward for his bravery, Mr. Monroe was pro- moted a captain of infantry ; and, having recovered from his wound, he rejoined the army. He, however, receded from the line of promotion, by becoming an officer in the stafl* of Lord Sterling. During the cam- paigns of 1777 and 1778, in the actions of Brandy- wine, Germantown and Monmouth, he continued aid-de-camp; but becoming desirous to regain his position in the army, he exerted himself to collect a regiment for the Virginia line. This scheme failed owing to the exhausted condition of the State. Upon this failure he entered the office of Mr. Jefl*erson, at that period Governor, and pursued, with considerable ardor, the study of common law. He did not, however, entirely lay aside the knapsack for the green bag; but on the invasions of the enemy, served as a volun- teer, during the two years of his legal pursuits. In 1782, he was elected from King George county, a member of the Leglislature of Virginia, and by that body he was elevated to a seat in the Executive Council. He was thus honored with the confidence of his fellow citizens at 23 years of age ; and having at this early period displayed some of that ability and aptitude for legislation, which were afterwards employed with unremitting energy for the public good, i Digitized by Google I <1J J > >^ V s 36 ^2Sn 1 / JAMES MONROE. A>\'f ^i^^^^^^(<^^,g; he was in the succeeding year chosen a member of the Congress of the United States. Deeply as Mr. Monroe felt the imperfections of the old Confederacy, he was opposed to the new Constitution, thinking, with many -others of the Republican parly, that it gave too much power to the Central Government, and not enough to the individual States. Still he re- tained the esteem of his friends who were its warm supporters, and who, notwithstanding his opposition secured its adoption. In 1789, he became a member of the United States Senate ; which office he held for four years. Every month the line of distinction be- tween the two great parties which divided the nation, the Federal and the Republican, was growing more distinct. The two prominent ideas which now sep- arated them were, that the Republican party was in sympathy with France, and also in favor of such a strict construction of the Constitution as to give the Central Government as little power, and the State Governments as much power, as the Constitution would warrant. The Federalists sympathised with England, and were in favor of a liberal construction of the Con- stitution, which would give as much power to the Central Government as that document could possibly authorize. The leading Federalists and Republicans were alike noble men, consecrating all their energies to the good of the nation. Two more honest men or more pure patriots than John Adams the Federalist, and . James Monroe the Republican, never breathed. In building up this majestic nation, which is destined to eclipse all Grecian and Assyrian greatness, the com- bination of their antagonism was needed to create the right equilibrium. And yet each in his day was de- nounced as almost a demon. Washington was then President. England had es- poused the cause of the Bourbons against the princi- ples of the French Revolution. All Europe was drawn into the conflict. We were feeble and far away. Washington issued a proclamation of neutrality be- tween these contending powers. France had helped us in the struggle for our liberties. All the despotisms of Europe were now combined to prevent the French from escaping from a tyranny a thousand-fold' worse than that which we had endured Col. Monroe, more magnanimous than prudent, was anxious that, at whatever hazard, we should help our old allies in their extremity. It was the impulse of a generous and noble nature. He violently opposed the Pres- ident's proclamation as ungrateful and wanting in magnanimity. Washington, who could appreciate such a character, developed his calm, serene, almost divine greatness, by appointing that very James Monroe, who was de- nouncing the policy of the Government, as the minister of that Government to the Republic of France. Mr. Monroe was welcomed b/ the National Convention in France with the most enthusiastic demonstrations. Shortly after his return to this country, Mr. Mon- roe was elected Governor of Virginia, and held the office for three years. He was again sent to France to co-operate with Chancellor Livingston in obtaining the vast territory then known as the Province of Louisiana, which France had but shortly before ob- tained from Spain. Their united efforts were suc- cessful. For the comparatively small sum of fifteen millions of dollars, the entire territory of Orleans and district of Louisiana were added to the United Slates. This was probably the largest transfer of real estate which was ever made in all the history of the worid. From France Mr. Monroe went to England to ob- tain from that country some recognition of our rights as neutrals, and to remonstrate against those odious impressments of our seamen. But Eng- land was unrelenting. He again returned to Eng- land on the same mission, but could receive no redress. He returned to his home and was again chosen Governor of Virginia. This he soon resigned to accept the position of Secretary of State under Madison. While in this office war with England was declared, the Secretary of War resigned, and during these trying rimes, the duties of the War Department were also put upon him. He was truly the armor- bearer of President Madison, and the most efficient business man in his cabinet. Upon the return of peace he resigned the Department of War, but con- tinued in the office of Secretary of State until the ex- piration of Mr. Madison s adminstrarion. At the elec- tion held the previous autumn Mr. Monroe himself had been chosen President with but little opposition, and upon March 4, 1817, was inaugurated. Four years later he was elected for a second term. Among the important measures of his Presidency were the cession of Florida to the United States; the Missouri Compromise, and the ** Monroe doctrine,'* This famous doctrine, since known as the ** Monroe doctrine," was enunciated by him in 1823. At that time the United States had recognized the independ- ence of the South American states, and did not ^lish to have European powers longer attempting to sub- due portions of the American Continent. The doctrine is as follows: "That we should consider any attempt on the part of European powers to extend their sys- tem to any jx)rtion of this hemisphere as dangerous to our peace and safety," and "that we could not view any interposition for the purpose of oppressing or controlling American governments or provinces in any other light than as a manifestation by European powers of an unfriendly disposition toward the United States.** This doctrine immediately affected the course of foreign governments, and has become the approved sentiment of the United States. At the end of his second term Mr. Monroe retired to his home in Virginia, where he lived until 1830, when he went to New York to live with his son-in- law. In that city he died,on the 4th of July, 1831. I 3 ^Am^:^ ^.■■^s ^mmm>^. .r<--*==^^c^ Digitized by Google «i-5?1ftsv? ^t ci. efiU^O/Ty^ Digitized by CnQOQlC m-r^^^^t >.i?^r../- iX -T^->IlIl-^IlDs>r^ ^ /\ V ^ -•< SIXTH PRESIDENT, 39 OHN QUINCY ADAMS, the sixth President of the United ^States, was born in the rural home of his honored father, John Adams, in Quincy, Mass., on the I ith cf July, 1767. His mother, a woman of exalted worth, watched over his childhood during the almost constant ab- sence of his father. When but eight years of age, he stood with his mother on an eminence, listen- ing to the booming of the great bat- tle on Bunker 5 Hill, and gazing on upon the smoke and flames billow- ing up from the conflagration of Charlestown. When but eleven years old he took a tearful adieu of his mother, to sail with his father for Europe, through a fleet of hostile British cruisers. The bright, animated boy spent a year and a half in Paris, where his father was associated with Franklin and Lee as minister plenipotentiary. His intelligence attracted the notice of these distinguished men, and he received from them flattering marks of attention. Mr. John Adams had scarcely returned to this country, in 1779, ere he was again sent abroad. Again John Quincy accompanied his father. At Paris he applied himself with great diligence, for six months, to study; then accom pained his father to Holland, where he entered, first a school in Amsterdam, then the University at Leyden. About a year from this time, in 178 1, when the manly boy was but fourteen years of age, he was selected by Mr. Dana, our min- ister to the Russian court, as his private secretary. In this school of incessant labor and of enobling culture he spent fourteen months, and then returned to Holland through Sweden, Denmark, Hamburg and Bremen. This long journey he took alone, in the winter, when in his sixteenth year. Again he resumed his studies, under a private tutor, at Hague. Thence, m V^ :#Vl-^^r^'' in the spring of 1782, he accompanied his father 10 Paris, travehng leisurely, and forming acquaintance with the most distinguished men on the Continent; examining architectural remains, galleries of paintings, and all renowned works of art. At Paris he again became associated with the most illustrious men of all lands in the contemplations of the loftiest temporal themes which can engross the human mind. After a short visit to England he relumed to Paris, and consecrated all his energies to study until May, 1785, when he returned to America. To a brilliant young man of eighteen, who had seen much of the worid, and who was familiar with the etiquette of courts, a residence with his father in London, under such cir- cumstances, must have been extremely attractive; but with judgment very rare in one of his age, he pre- ferred to return to America to complete his education in an American college. He wished then to study law, that with an honorable profession, he might be able to obtain an independent support. Upon leaving Harvard College, at the age of twenty, he studied law for three years. In June, 1794, be- ing then but twenty-seven years of age, he was ap- pointed by Washington, .resident minister at the Netherlands. Sailing from Boston in July, he reached London in October, where he was immediately admit- ted to the deliberations of Messrs. Jay and Pinckney, assisUng them in negoriating a commercial treaty with Great Britian. After thus spending a fortnight in London, he proceeded to the Hague. In July, 1797, he left the Hague to go to Portugal as minister plenipotentiary. On his way to Portugal, upon arriving in Ix)ndon, he met with despatches direcUng him to the court of Berlin, but requesting him to remain in London unril he should receive his instructions. While waiting he was married to an American lady to whom he had been previously en- gaged, — Miss Louisa Catherine Johnson, daughter of Mr. Joshua Johnson, American consul in London ; a lady endownd with that beauty and those accom- plishment which eminently fitted her to move in the elevated sphere for which she was destined. % 'm>^^ — ^;!'i*= F A .,.|l:?>^;iy^; •r m Digitized by Google :V^')^>^^*' ">^<?r''S -^MnD>:Dn^>r-r "^^jQC ^:^ -i^ ^ V 40 /OlfJV^ QUINCY ADAMS. He reacl)^ Berlin with his wife in November, 1797 ; where he remained until July, 1799, when, having ful- filled all the purposes of his mission, he solicited his recall. Soon after his return, in 1802, he was chosen to the Senate of Massachusetts, from Boston, and then was elected Senator of the United States for six years, from the 4th of March, 1804. His reputation, his ability and his experience, placed him immediately among the most prominent and influential members of that body. Especially did he sustain the Govern- ment in its measures of resistance to the encroach- ments of England, destroying our commerce and in- sulting our flag. There was no man in America more . familiar with the arrogance of the British court upon these points, and no one more resolved to present a firm resistance. In 1809, Madison succeeded Jefferson in the Pres- idential chair, and he immediately nominated John Quincy Adams minister to St. Petersburg. Resign- ing his professorship in Harvard College, he embarked at Boston, in August, 1809. While in Russia, Mr. Adams was an intense stu- dent. He devoted his attention to the language and history of Russia; to the Chinese trade; to the European system of weights, measures, and coins ; to the climate and astronomical observations ; while ke kept up a familiar acquaintance with the Greek and Latin classics. In all the universities of Europe, a more accomplished scholar could scarcely be found. All through life the Bible constituted an important part of his studies. It was his rule to read five chapters every day. On the 4th of March, 1817, Mr. Monroe took the Presidential chair, and immediately appointed Mr. Adams Secretary of State. Taking leave of his num- erous friends in public and private life in Europe, he sailed in June, 1819, for the United States. On the 1 8th of August, he again crossed the threshold of his home in Quincy. During the eight years of Mr. Mon- roes administration, Mr. Adams continued Secretary of State. Some time before the close of Mr. Monroe s second term of office, new candidates began to be presented for the Presidency. The friends of Mr. Adams brought forward his name. It was an exciring campaign. Party spirit was never more bitter. Two hundred and sixty electoral votes were cast. Andrew Jackson re- ceived ninety-nine ; John Quincy Adams, eighty-four; William H. Crawford, forty -one; Henry Clay, thirty- seven. As there was no choice by the people, the question went to the House of Representatives. Mr. Clay gave the vote of Kentucky to Mr. Adams, and he was elected. The friends of all the disappointed candidates now combined in a venomous and persistent assault \\\)ow Mr. Adams. There is nothing more disgraceful in the past history of our country than the abuse which i was poured in one uninterrupted stream, upon this high-minded, upright, patriotic man. There never was an administration more pure in principles, more con- scientiously devoted to the best interests of the coun- try, than that of John Quincy Adams ; and never, per- haps, was there an administration more unscrupu- lously and outrageously assailed. Mr. Adams was, to a very remarkable degree, ab- stemious and temperate in his habits; always rising early, and taking much exercise. When at his home in Quincy, he has been known to walk, before breakfast, seven miles to Boston. In Washington, it was said that he was the first man up in the city, lighting his own fire and applying himself to work in his libraiy often long before dawn. On the 4th of March, 1829, Mr. Adams retired from the Presidency, and was succeeded by Andrew- Jackson. John C. Calhoun was elected Vice Presi- dent. The slavery question now began to assume portentous magnitude. Mr. Adams returned to Quincy and to his studies, which he pursued with un- abated zeal. But he was not long permitted to re- main in retirement. In November, 1830, he was elected representative to Congress. For seventeen ^ years, until his death, he occupied the post as repre- N^ sentative, towering alx>ve all his peers, ever ready to ^^ do brave battle* for freedom, and winning the title of ^ "the old man eloquent." {J\x)n taking his seat in the House, he announced that he should hold him- self bound to no party. Probably there never was a member more devoted to his duties. He was usually the first in his place in the morning, and the last to leave his seat in the evening. Not a measure could be brought forward and escape his scrutiny. The battle which Mr. Adams fought, almost singly, against the proslavery party in the Government, was sublime in Its moral daring and heroism. For i>ersisting in presenting petitions for the al)olition of slavery, he was threatened with indictment by the grand jury, with expulsion from the House, with assassination : but no threats could intimidate him, and his final triumph was complete. It has been said of President Adams, that when his body was bent and his hair silvered by the lapse of fourscore years, yielding to the simple faith of a little child, he was accustomed torei)eat every night, before he slept, the prajer which his mother taught him in his infant years. On the 2ist of February, 1848, he rose on the floor of Congress, with a paper in his hand, to address the speaker. Suddenly he fell, again stricken by paraly- sis, and was caught in the arms of those around him. For a time he was senseless, as he was conveyed to the sofa in the rotunda. With reviving conscious- ness, he opened his eyes, looked calmly around and said " TAis ts Ihe end of earth ."then after a moment s pause he added, ^' I am eontetti!' These were the last words of the grand "Old Man E1oc|uent.** 9 y^i^. \^,¥^''^ ^■^^ — 9^^Dii:^.nD;i>A- >^^^vri^^ Digitized by Google - !i-*"py Digitized by Google ?■ SEVENTH PRESIDENT. #i^^f(Fv|| V ■'.) -'N«i2rfi/f9i@'»*Q^*A£ft! ^^^^ cK>4atNffka^ggv> ^ 1 «^:> -NfiiZfijg/rH®"*^^'''**' "55^^•'e>»*.^|^5i/I7^^^;>^^ / t «-J^^il^^ NDREW JACKSON, the ^L/Mm^ mW^^^^Ui seventh President of the United States, was born in VVaxhaw settlement, N. C, March 15, 1767, a few days after his father s death. His parents were poor emigrants from Ireland, and took up their abode in Waxhaw set- tlement, where they lived in deepest poverty. Andrew, or Andy, as he was universally called, grew up a very rough, rude, turbulent boy. His features were coarse, his form un- gainly; and there was but very little in his character, made visible, which was at- tractive. Wlien only thirteen years old he joined the volun- teers of Carolina against the British invasion. In i7»i, he and his brother Robert were captured and imprisoned for a time at Camden. A British officer ordered him to brush his mud-spattered boots. ** I am a prisoner of war, not your servant," was the reply of the dauntless boy. The brute drew his sword, and aimed a desjjerate blow at the head of the helpless young prisoner. Andrew raised his hand, and thus received two fear- ful gashes, — one on the hand and the other upon the head. The officer then turned to his brother Robert with the same demand. He also refused, and re- ceived a blow from the keen-edged sabre, which quite disabled him, and which probably soon after caused his death. They suffered much other ill-treatment, and were finally stricken with the small-pox. Their \^ mother was successful in obtaining their exchan^^e. ^^^^^^ ^7^-^ and took her sick boys home. After a long illness Andrew recovered, and the death of his mother soon left him entirely friendless. Andrew supported himself in various ways, such as working at the saddler^s trade, teaching school and clerking in a general store, until 1784, when he entered a law office at Salisbury, N. C. He, however, gave more attention to the wild amusements of the times than to his studies. In 1788, he was appointed solicitor for the western district of Nonh Carolina, of which Tennessee was then a part. This involved many long and tedious journeys amid dangers of every kind, but Andrew Jackson never knew fear, and the Indians had no desire to repeat a skirmish with the Sharp Knife. In 17 91, Mr. Jackson was married to a woman who supposed herself divorced from her former husband. Great was the surprise of both parties, two years later, to find that the conditions of the divorce had just been definitely settled by the first husband. The marriage ceremony was performed a second time, but the occur- rence was often used by his enemies to bring Mr. Jackson into djsfavor. During these years he worked hard at his profes- sion, and frequently had one or more duels on hand, one of which, when he killed Dickenson, was espec- ially disgraceful. In January, 1796, the Territory of Tennessee then containing nearly eighty thousand inhabitants, the people met in convention at Knoxville to frame a con- stitution. Five were sent from each of the eleven counties. Andrew Jackson was one of the delegates. The new State was entitled to but one member in the Nadonal House of Representatives. Andrew Jack- son was chosen that member. Mounting his horse he rode to Philedelphia, where Congress then held its % m Digitized by Google /* 44 ^^^ <^iiii/^nii^> T -^r^^^y^^ ANDREW JACKSON, I (h i \^ V r^ >( sessions, — a distance of about eight hundred miles. Jackson was an earnest advocate of the Demo- cratic party. Jefferson was his idol. He admired Bonaparte, loved France and hated England. As Mr. Jackson took his seat, Gen. Washington, whose second term of office was then expiring, delivered his last speech to Congress. A committee drew up a complimentary address in reply. Andrew Jackson did not approve of the address, and was one of the twelve who voted against it. He was not willing to say that Gen. Washington's adminstration had been *• wise, firm and patriotic." Mr. Jackson was elected to the United States Senate in 1797, but soon resigned and returned home. Soon after he was chosen Judge of the Supreme Court of his State, which ix)sition he held for six years. When the war of 181 2 with Great Britian com- menced, Madison occupied the Presidential chair. Aaron Burr sent word to the President that there was an unknown man in the West, Andrew Jackson, who would do credit to a commission if one were con- ferred upon him. Just at that time (ien. Jackson offered his services and those of twenty-five hundred volunteers. His offer was accepted, and the troops were assembled at Nashville. As the British were hourly expected to make an at- tack iijxin New Orleans, where Gen, Wilkinson was in command, he was ordered to descend the river with fifteen hundred troops to aid Wilkinson. The expedition reached Natchez ; and after a delay of sev- eral weeks there, without accomplishing anything, the men were ordered back to their homes. But the energy Gen. Jackson had displayed, and his entire devotion to the comrfort of his soldiers, won him golden opinions ; and he i)ecame the most popular man in the State. It was in this expedition that his toughness gave him the nickname of **01d Hickory." Soon after this, while attempting to horsewhip Col. Thomas H. Benton, for a remark that gentleman made about his taking a part as second in a duel, in which a younger brother of Benton's was engaged, he received two severe [)istol wounds. While he was lingering upon a bed of suffering news came that the Indians, who had combined under Tecumseh from Florida to the Lakes, to exterminate the white set- tlers, were committing the most awful ravages. De- cisive action became necessary. Gen. Jackson, with his fractured bone just beginning to heal, his arm in a sling, and unable to mount his horse without assis- tance, gave his amazing energies to the raising of an army to rendezvous at Fayettesville, Alabama. The Creek Indians had established a strong fort on one of the bends of theTallaixjosa River, near the cen- ter of Alabama, about fifty miles below Fort Strother. With an army of two thousand men, (xen. Jackson traversed the pathless wilderness in a march of eleven days. He reached their fort, called Tohopeka or Horse-shoe, on the 27th of March. 1814. The bend of the river enclosed nearly one hundred acres of tangled forest and wild ravine. Across the narrow neck the Indians had constructed a formidable breast- work of logs and brush. Here nine hundred warriors, with an artiple suply of arms were assembled. The fort was stormed. The fight was utterly des- perate. Not an Indian would accept of quarter. When bleeding and dying, they would fight those who en- deavored to spare their lives. From ten in the morn- ing until dark, the battle raged. The carnage was awful and revoking. Some threw themselves into the river; but the unerring bullet struck their heads as they swam. Nearly everyone of the nine hundred war- rios were killed A few probably, in the night, swam the river and escaped. This ended the war. The ix)wer of the Creeks was broken forever. This bold plunge into the wilderness, with its terriffic slaughter, so appalled the savages, that the haggard remnants of the bands came to the camp, begging for peace. This closing of the Creek war enabled us to con- centrate all our militia upon the British, who were the allies of the Indians No man of less resolute will than (ien. Jackson could have conducted this Indian campaign to so successful an issue Immediately he was appointed major-general. Late in August, with an army of two thousand men, on a rushing march, Gen. Jackson came to Mobile. A British fleet came from Pensacola, landed a force upon the beach, anchored near the little fort, and from both ship and shore commenced a furious assault. The battle was long anddoubtful. At length one of the ships was blown up and the rest retired. Garrisoning Mobile, where he had taken his little army, he moved his troops to New Orleans, And the battle of New Orleans which .soon ensued, was in reality a very arduous campaign. This won for (ren. Jackson an imperishable name. Here his troops, which numbered about four thousand men, won a signal victory over the British army of alx)ut nine thousand. His loss was but thirteen, while the loss of the British was two thousand six hundred. The name of (»en. Jackson soon began to be men- tioned in connection with the Presidency, but, in 1824, he was defeated by*Mr. Adams. He was, however, successful in the election of 1828, and was re-elected for a second term in 1832. In 1829, just before he assumed the reins of the government, he met with the most terrible affliction of his life in the death of his wife, whom he had loved with a devotion which has perhaps never been surpassed. From the shock of her death he never recovered. His administration was one of the most memorable in the annals of our country; applauded by one party, condemned by the other. No man had more bitter enemies or warmer friends. At the expiration of his two terms of office he retired to the Hermitage, where he died June 8, 1845. The last years of Mr. Jack- son's life were that of a devoted Christian man. <^lll]:^liii;> /■ r~\ ^m:- u- Digitized by Google ■:%., /7'^^^^^'^'^^"^^^^^^^^^^ Digitized by Google w- . -'A V r _______ <>;x_ T^^^^"^ t:? -7<>llll^nns>r-e J) EIGHTH PRESIDENT. ^mm^^l -^ ^ ARTIN VAN BUREN, the eighth President of the United States, was lx)rn at Kinderhook, N. Y., Dec. 5, 1782. He died at the same place, July 24, 1862. His body rests in the cemetery at Kinderhook. Above it is a plain granite shaft fifteen feet high, bearing a simple inscription about half way up on one face. The lot is unfenced, unbordered or unbounded by shrub or flower. There is but little in the life of Martin Van Buren of romantic interest. He fought no battles, engaged in no wild adventures. Though his life was stormy in political and intellectual conflicts, and he gained many signal victories, his days passed uneventful in those incidents which give zest to biography. His an- cestors, as his name indicates, were of Dutch origin, and were among the earliest emigrants from Holland to the banks of the Hudson. His father was a fanner, residing in the old town of Kinderhook. His mother, also of Dutch lineage, was a woman of superior intel- ligence and exemplary piety. He was decidedly a precocious boy, developing un- usual activity, vigor and strength of mind. At the age of fourteen, he had finished his academic studies in his native village, and commenced the study of law. As he had not a collegiate educarion, seven years of study in a law-office were required of him before he could be admitted to the bar. Inspired with a lofty ambition, and conscious of his powers, he pur- sued his studies with indefatigable industry. After spending six years in an office in his native village, t t ^ 4 r he went to the city of New York, and prosecuted his studies for the seventh year. In 1803, Mr. Van Buren, then twenty-one years of age, commenced the practice of law in his native vil- lage. The great conflict between the Federal and Republican party was then at its height. Mr. Van Buren was from the beginning a politician. He had, perhaps, imbibed that spirit while listening to the many discussions which had been carried on in his father's hotel. He was in cordial sympathy with Jeff'erson, and earnestly and eloquently espoused the cause of State Rights ; though at that rime the Fed- V eral party held the supremacy both in his town and State. His success and increasing ruputation led him, after six years of practice, to remove to Hudson, the county seat of his county. Here he spent seven years, constantly gaining strength by contending in the courts with some of the ablest men who have adorned the bar of his State. Just before leaving Kinderhook for Hudson, Mr. Van Buren married a lady alike distinguished for beauty and accomplishments. After twelve short years she sank into the grave, the vicrim of consump- tion, leaving her husband and four sons to weep over her loss. For twenty-five years, Mr. Van Buren was an earnest, successful, assiduous lawyer. The record of those years is barren in items of public interest. In t8i 2, when thirty years of age, he was chosen to .the State Senate, and gave his strenuous support to Mr. Madison s adminstration. In 1815, he was ap- pointed Attorney-General, and the next year moved to Albany, the capital of the State. While he was acknowledged as one of the most prominent leaders of the Democratic party, he had I 'Vj~'>-^^tt-«'^ JL <:>nii:<^:nilv>v ^ii^ Digitized by V^OOQ IC K- ^jN^^W^^' i ) 1 > (^ 48 -cTV<4Dll^;CD^i> v ^ MARTIN VAN BVREN. ratf^ s'^ir the moral courage to avow that true democracy did not require that " universal suffrage ** which admits the vile, the degraded, the ignorant, to the right of governing the State. In true consistency with his democratic principles, he contended that, while the path leading to the privilege of voting should be open to every man without distinction, no one should be invested with that sacred prerogative, unless he were in some degree qualified for it by intelligence, virtue and some property interests in the welfare of the State. In 182 1 he was elected a member of the United States Senate; and in the same year, he took a seat in the convention to revise the constitution of his native State. His course in this convention secured the approval of men of all parties. No one could doubt the singleness of his endeavors to promote the interests of all classes in the community. In the Senate of the United States, he rose at once to a conspicuous position as an active and useful legislator. In 1827, John Quincy Adams being then in the Presidential chair, Mr. Van Buren was re-elected to the Senate. He had been from the beginning a de- termined opposer of the Administration, adopting the "State Rights*' view in opposition to what was deemed the Federal proclivities of Mr. Adams. Soon after this, in 1828, he was chosen Governorof the State of New York, and accordingly resigned his seat in the Senate. Probably no one in the United States contributed so much towards ejecting John Q. Adams from the Presidential chair, and placing in it Andrew Jackson, as did Martin Van Buren. Whether entitled to the reputation or not, he certainly was re- garded throughout the United States as one of the most skillful, sagacious and cunning of politicians. It was supposed that no one knew so well as he how to touch the secret spiings of action; how to pull all the wires to put his machinery in motion ; and how to organize a political army which would, secretly and stealthily accomplish the most gigantic results. By these powers it is said that he outwitted Mr. Adams, Mr. Clay, Mr. Webster, and secured results which few thought then could be accomplished. When Andrew Jackson was elected President he appointed Mr. Van Buren Secretary of State. This position he resigned in 1831, and was immediately appointed Minister to England, where he went the same autumn. The Senate, however, when it met, to ratify the nomination, and he returned x, refused home, apparently untroubled; was nominated Vice President in the place of Calhoun, at the re-electbn of President Jackson ; and with smiles for all and frowns for none, he took his place at the head of that Senate which had refused to confirm his nomination as ambassador. His rejection by the Senate roused all the zeal of President Jackson in behalf of his repudiated favor- ite ; and this, probably more than any other cause, secured his elevation to the chair of the Chief Execu- tive. On the 2oth of May, 1836, Mr. Van Buren re- ceived the Democratic nomination to succeed Gen. Jackson as President of the United States. He was elected by a handsome majority, to the delight of the retiring President. " Leaving New York out of the canvass," says Mr. Parton, "the election of Mr. Van Buren to the Presidency was as much the act of Gen. Jackson as though the Constitution had conferred upon him the power to appoint a successor." His administradon was filled with exciting events. The insurrection in Canada, which threatened to in- volve this country in war with England, the agitation of the slavery question, and finally the great commer- cial panic which spread over the country, all were trials to his wisdom. The financial distress was at- tributed to the management of the Democratic party, and brought the President into such disfavor that he failed of re-election. With the exception of being nominated for the Presidency by the "Free Soil" Democrats, in 1848, Mr. Van Buren lived quietly upon his estate until his death. He had ever been a prudent man, of frugal habits, and living within his income, had now fortunately a competence for his declining years. His unblemished character, his commanding abilities, his unquestioned patriotism, and the distinguished positions which he had occupied in the government of our country, se- cured to him not only the homage of his party, but the respect ot the whole community. It was on the 4th of March, 1841, that Mr. Van Buren retired from the presidency. From his fine estate at Lindenwald^ he still exerted a powerful influence upon the politics of the country. From this rime until his death, on the 24th of July, 1862, at the age of eighty years, he resided at Lindenwald, a gentleman of leisure, of culture and of wealth; enjoying in a healthy old age, probably far more happiness than he had before experienced amid the stormy scenes of his active life. t V i ^\ c V ?■ \mi \^>^cz. .->^«-v ^:^ ■K^^iiii^niiit> ^^^ j^.^.^'^.f^^ _*4i<^?5^^^y<^, :;,- Digitized by Google y^ J9r/^a^i^v^('>t^ Digitized by Google «f?'£^^C(®V§g ■; ) A V5 V > .^9 ':S ILLIAM HENRY HARRI- SON, the ninth President of the United States, was born at Berkeley, Va., Feb. 9, 1773. His father, Benjamin Harri- son, was in comparatively op- ulent circumstances, and was one of the most distinguished men of his day. He was an intimate friend of George Washington, was early elected a member of the Continental Congress, and was conspicuous among the patriots of Virginia in resisting the encroachments of the British crown. In the celebrated Congress of 1775, Benjamin Har- rison and John Hancock were both candidates for the office of speaker. Mr Harrison was subsequently chosen Governor of Virginia, and was twice re-elected. His son, William Henry, of course enjoyed in childhood all the advantages which wealth and intellectual and cuUivated society could give. Hav- ing received a thorough common-school education, he entered Hampden Sidney College, where he graduated with honor soon after the death of his father. He then repaired to Philadelphia to study medicine under the instructions of Dr. Rush and the guardianship of Robert Morris, both of whom were, with his father, signers of the Declaration of Independence. Upon the outbreak of the Indian troubles, and not- withstanding the remonstrances of his friends, he abandoned his medical studies and entered the army, ^ having obtained a commission of Ensign from Presi- dent Washington. He was then but ig years old. From that time he passed gradually upward in rank until he became aid to General Wayne, after whose death he resigned his commission. He was then 3l\>- pointed Secretary of the North-western Territory. This Territory was then entitled to but one member in Congress and Capt. Harrison was chosen to fill that position. In the spring of 1800 the North-western Territory was divided by Congress into two portions. The eastern portion, comprising the region now embraced in the State of Ohio, was called ** The Territory north-west of the Ohio." The western portion, which included what is now called Indiana, Illinois and Wisconsin, was called the "Indiana Territory." Wil- liam Henry Harrison, then 27 years of age, was ap- lX)inted by John Adams, Governor of the Indiana Territory, and immediately after, also Governor of Upper Louisiana. He was thus ruler over almost as extensive a realm as any sovereign upon the globe. He was Superintendent of Indian Affairs, and was in- vested with powers nearly dictatorial over the now rapidly increasing white population. The ability and fidelity with which he discharged these resiXDnsible duties may be infened from the fact that he was four times appointed to this office — first by John Adams, twice by Thomas Jefferson and afterwards by Presi- dent Madison. When he began his adminstration there were but three white settlements in that almost boundless region, now crowded with cities and resounding with all ftie tumult of wealth and traffic. One of these settlements was on the Ohio, nearly opposite Louisville; one at Vincennes, on the Wabash, and the third a French settlement The vast wilderness over which Gov. Harrison reigned was filled with many tribes of Indians. About i (V m\ ^r<^. ;%>.i.^ S<..:^ -««S«r^ m(^J^ Digitized by Google y^vwr^-^ TT- •) A . s t I WILLIAM HENRY HARRISON, >^'\!Aif'' the year 1806, two extraordinary men, twin brothers, of the Shawnese tribe, rose among them. One of these was called Tecumseh, or "The Crouching Panther;" the other, Olliwacheca, or "The Prophet.** Tecumseh was not only an Indian warrior, but a man of great sagacity, far-reaching foresight and indomit- able perseverance in ai>y enterprise m which he might engage. He was inspired with the highest enthusiasm, and had long regarded with dread and with hatred the encroachment of the whites ui)on the hunting- grounds of his fathers. His brother, the Prophet, was anorator, who could sway the feelings of the untutored Indian as the gale tossed the tree-tops beneath which they dwelt. But the Prophet was not merely an orator : he was, in the superstitious minds of the Indians, invested with the superhuman dignity of a medicine-man or a magician. With an enthusiasm unsurpassed by Peter the Hermit rousing Europe to the crusades, he went from tribe to tribe, assuming that he was specially sent by the Great Spirit. Gov. Harrison made many attempts to conciliate the Indians, but at last the war came, and at Tippe- canoe the Indians were routed with great slaughter. October 28, 18 12, his army began* its march. When near the Prophet's town three Indians of rank made their appearance and inquired why Gov. Harrison was approaching them in so hostile an attitude. After a short conference, arrangements were made for a meet- ing the next day, to agree upon terms of peace. But Gov. Harrison was too well acquainted with the Indian character to be deceived by such protes- tations. Selecting a favorable spot for his night's en- campment, he took every precaution against surprise. His troops were posted in a hollow square, and slept upon their arms. The troops threw themselves upon the ground for rest; but every man had his accourtremenis on, his loaded musket by his side, and his bayonet fixed. The wakeful Governor, between three and four o'clock in the morning, had risen, and was sitting in conversa- tion with his aids by the embers of a waning fire. It was a chill, cloudy morning with a drizzling rain. In the darkness, the Indians had crept as near as possi- ble, and just then, with a savage yell, rushed, with all the desperation which superstition and passion most highly inflamed could give, upon the left flank of the litde army. The savages had been amply provided with guns and ammunition by the English. Their war-whoop was accompained by a shower of bullets. The camp-fires were instantly extinguished, as the light aided the Indians in their aim. With hide- ous yells, the Indian bands rushed on, not doubting a speedy and an entire victory. But Gen. Harrison's troops stood as immovable as the rocks around them unril day dawned : they then made a simultaneous charge with the bayonet, and swept every thing be- fore them, and completely routing the foe. I X Gov. Harrison now had all his energies tasked to the utmost. The British descending from theCan- adas, were of themselves a very formidable force ; but with their savage allies, rushing like wolves from the forest, searching out every remote farm-house, burn- ing, plundering, scalping, torturing, the wide frontier was plunged into a state of consternation which even the most vivid imagination can but faintly conceive. The war-whoop was resounding everywhere in the forest. The honzon was illuminated with the conflagra- tion of the cabins of the setders. Gen Hull had made the ignominious surrender of his forces at Detroit. Under these despairing circumstances. Gov. Harrison was appointed by President Madison commander-in- chief of the North-western army, with orders to retake Detroit, and to protect the frontiers. It would be diflicult to place a man in a situation demanding more energy, sagacity and courage; but General Harrison was found equal to the position, and nobly and triumphantly did he meet all the re- sponsibilities. He won the love of his soldiers by always sharing with them their fatigue. His whole baggage, while pursuing the foe up the Thames, was carried in a valise; and his bedding consisted of a single blanket lashed over his saddle. Thirty-five British officers, his prisoners of war, supped with him after the battle. The only fare he could give them was beef roasted before the fire, without bread or salt. In 1 8 16, Gen. Harrison was chosen a member of the National House of Representatives, to represent the District, of Ohio. In Congress he proved an . active member; and whenever he spoke, it was with force of reason and power of eloquence, which arrested the attention of all the members. In 1 81 9, Harrison was elected to the Senate of Ohio; and in 1824, as one of the presidential electors of that State, he gave his vote for Henry-Clay. The same year he was chosen to the United States Senate. In 1836, the friends of Gen. Harrison brought him forward as a candidate for the Presidency against Van Buren, but he was defeated. At the close of Mr. Van Buren 's term, he was re-nomicated by his party, and Mr. Harrison was unanimously nominated by the Whigs, with John Tyler for the Vice Presidency. The contest was very animated. Gen. Jackson gave all his influence to prevent Harrison s election ; but his triumph was signal. The cabinet which he formed, with Daniel Webster at its head as Secretary of State, was one of the most brilliant with which any President had ever been surrounded. Never were the prospects of an admin- istration more flattering, or the hopes of the country more sanguine. In the midst of these bright and joyous prospects. Gen. Harrison was seized by a pleurisy-fever and after a few days of violent sick- ness, died on the 4th of April ; just one month after his inauguration as President of the United States. I X K/ I ■^^ -^^^e<>- ^ <>D!l^il3;>A ^^x^>^^^. Digitized by Google ^yj^"* -'^.\%'-*' ••' V Digitized by Google "4)^ri^-ii^^ ■%** 4^ enr<4BIl^^llPs>^ o A V TENTH PRESIDENT. 55 A "^Sl^ JOHN TYLER. ,_ .ag OHN TYLER, the tenth Presidentof the United States. He was born in Charles-city Co., Va., March 29, 1790. He was the favored child of af- fluence and high social po- sition. At the early age of twelve, John entered William and Mary College and grad- uated with much honor when but seventeen years old. After graduating, he devoted him- self with great assiduity to the study of law, partly with his father and partly with Edmund Randolph, one of the most distin- guished lawyers of Virginia. At nineteen years of age, ne commenced the practice of law. His success was rapid and aston- ishing. It is said that three months had not elapsed ere there was scarcely a case on the dock- i et of the court in which he was not retained. When but twenty-one years of age, he was almost unanimously elected to a seat in the State Legislature. He connected himself with the Demo- cratic party, and warmly advocated the measures of ^ Jefferson and Madison. For five successive years he I was elected to the Legislature, receiving nearly the ^ unanimous vote or his county. When but twenty-six years of age, he was elected a member of Congress. Here he acted earnestly and ably with the Democratic party, opposing a national bank, internal improvements by the General Govern- '.X ^^}^V:5^^^^- raent, a protective tariff, and advocatmg a strict con- struction of the Constitution, and the most careful vigilance over State rights. His labors in Congress were so arduous that before the close of his second term he found it necessary to resign and retire to his estate in Charles-city Co., to recruit his health. He, however, soon after consented to take his seat in the State Legislature, where his influence was powerful in promoting public works of great utility. With a reputation thus canstantly increasing, he was chosen by a very large majority of votes. Governor of his native State. His administration was signally a suc- cessful one. His popularity secured his re-election. John Randolph, a brilliant, erratic, half-crazed man, then represented Virginia in the Senate of the United States. A portion of the Democratic party was displeased with Mr. Randolph's wayward course, and brought forward John Tyler as his opponent, considering him the only man in Virginia of sufficient popularity to succeed against the renowned orator of Roanoke. Mr. Tyler was the victor. In accordance with his- professions, upon taking his seat in the Senate, he joined the ranks of the opposi- tion. He opposed the tariff; he s[X)ke against and voted against the bank as unconstitutional ; he stren- uously opposed all restrictions upon slavery, resist- ing all projects of internal improvements by the Gen- eral Government, and avowed his sympathy with Mr. Calhoun's view of nullification ; he declared that Gen. Jackson, by his opposition to the nuUifiers, had abandoned the principles of the Democratic party. Such was Mr. Tyler's record in Congress, — a record in perfect accordance with the principles which he had always avowed. Returning to Virginia, he resumed the practice of his profession. There was a split in the Democratic ( I <^iiii^:nni>^ ^^1 ^ Digitized by Google 36 4 Vf party. His friends still regarded him as a true Jef- ^'\ fersonian, gave him a dinner, and showered compli- /^ ments upon him. He had now attained the age of *'^* forty-six. His career had been very brilliant. In con- T sequence of his devotion to public business, his pri- ^ vate affairs had fallen into some disorder; and it was not without satisfaction that he resumed the practice of law, and devoted himself to the culture of his plan- tation. Soon after this he removed to Williamsburg, for the better education of his children ; and he again took his seat in the Legislature of Virginia. By the Southern Whigs, he was sent to the national convention at Harrisburg to nominate a President in 1839. The majority of votes were given to Gen. Har- rison, a genuine Whig, much to the disappointment of the South, who wished for Henry Clay. To concili- ate the Southern Whigs and to secure their vote, the convention then nominated John Tyler for Vice Pres- ident. It was well known that he was not in sympa- thy with the Whig party in the Noith : but the Vice President has but very little power in the Govern- ment, his main and almost only duty being to pre- side over the meetings of the Senate. Thus it hap- pened that a Whig President, and, in reality, a Democratic Vice President were chosen. In 1 84 1, Mr. Tyler was inaugurated Vice Presi- dent of the United States. In one short month from that time. President Harrison died, and Mr. Tyler thus found himself, to his own surprise and that of the whole Nation, an occupant of the Presidential chair. This was a new test of the stability of our institutions, as it was the first time in the history of our country that such an event had occured. Mr. Tyler was at home in Williamsburg when he received the unexpected tidings of the death of President Harri- son. He hastened to Washington, and on the 6th of April was inaugurated to the high and responsible office. He was placed in a position of exceeding delicacy and difficulty. All his long life he had been op|X)sed to the main principles of the party which had brought him into power. He had ever been a con- sistent, honest man, with an unblemished record, (jen. Harrison had selected a Whig cabinet. Should he retain them, and thus surround himself with coun- sellors whose views were antagonistic to his own? or, on the other hand, should he turn against the party which had elected him and select a cabinet in har- mony with himself, and which would oppose all those views which the Whigs deemed essential to the pub- lic welfare? This was his fearful dilemma. He in- vited the cabinet which President Harrison had selected to retain their seats. He reccommended a day of fasting and prayer, that God would guide and bless us. The Whigs carried through Congress a bill for the incorporation of a fiscal bank of the United States. The President, after ten days' delay, returned it with his veto. He suggested, however, that he would <itlD>:llIls>r "yt^iv*; "■"Sv- -4^^>>^:A' JOHN TYLER. -N A :^ / # H ^ trAVA.-- w^^:'^^<m^ approve of a bill drawn up upon such a plan as he '/ proix>sed. Such a bill was accordingly prepared, and ' • privately submitted to him. He gave it his approval. ;' It was passed without alteration, and he sent it back with his veto. Here commenced the open rupture. ! It is said that Mr. Tyler was provoked to this meas- \ ure by a published letter from the Hon. John M. Botts, a distinguished Virginia Whig, who severely touched the pride of the President. The opposition now exultingly received the Presi- dent into their arms, y The party which elected him denounced him bitterly. AH the members of his cabinet, excepting Mr. Webster, resigned. The Whigs ^ of Congress, both the Senate and the House, held a meeting and issued an address to the people of the United States, proclaiming that all political alliance between the Whigs and President Tyler were at an end. Still the President attempted to conciHate. He appointed a new cabmet of distinguished Whigs and Conservatives, carefully leaving out all strong party men. Mr. Webster soon found it necessary to resign, forced out by the pressure of his Whig friends. Thus the four years of Mr. Tyler's unfortunate administra- tion passed sadly away. No one was satisfied. The land was filled with murmurs and vitu])eration. Whigs and Democrats alike assailed him. More and more, however, he brought himself into sympathy with his old friends, the Democrats, until at the close of his terra, he gave his whole influence to the supjwrt of Mr, Polk, the Democratic candidate for his successor. On the 4th of March, 1845, he retired from the harassments of office, to the regret of neither j)arty, and probably to his own unspeakable lelief. His first wife. Miss Letitia Christian, died in Washington, in 1842; and in June, 1844, PresidentTyler was again married, at New York, to Miss Julia Gardiner, a young lady of many personal and intellectual accomplishments. The remainder of his days Mr. Tyler passed mainly in retirement at his beautiful home, — Sherwood For- est, Charles -city Co., Va. A polished gentleman in his manners, richly furnished with mformation from books and expaience in the world, and possessing brilliant powers of conversation, his family circle was the scene of unusual attractions. With sufficient moans for the exercise of a generous hospitality, he might have enjoyed a serene old age with the few friends who gathered around him, were it not for the storms of civil war which his own principles and policy had helped to introduce. When the great Rebellion rose, which the State- rights and nullifying doctrines of Mr. John C. C7al- houn had inaugurated, President Tyler renounced his allegiance to the United States, and joined the Confed- erates. He was chosen a meniber of their Congress : and while engaged in active measures to destroy, by force of arms, the Government over which he had once presided, he was taken sick and soon died. ^4^^- Digitized by Google ar0*^*-'»<.^ <^ Digitized by Google \ ■ ^ 7<cillIl>:in^>T^ "T^s^.-^ v' /^ t:=T V ELEVENTH PRESIDENT. Ik-.*-'. JAMES K. POLK. AMES K. POLK, the eleventh President of the United States, was born in Mecklenburg Co., N. C.,Nov. 2, 1795. His par- ents were Samuel and Jane (Knox) Polk, the fornjer a son of Col. Thomas Polk, who located at the above place, as one of the first pioneers, in 1735. In the year 1S06, with his wife and children, and soon after fol- lowed by most of the members of the Polk fainly, Samuel Polk emi- grated some two or three hundred miles farther west, to the rich valley of the Duck River. Here in the midst of the wilderness, in a region which was subsequently called Mau- ry Co., they reared their log huts, and established their homes. In the hard toil of a new farm in the wil- derness, James K. Polk si)ent the early years of his childhood and youth. His father, adding the pur- suit of a surveyor to that of a farmer, gradually increased in wealth until he became one of the leading men of the region. His niother was a superior woman, of strong common "S sense and earnest piety. Very early in life, James developed a taste for reading and expressed the strongest desire to obtain a liberal education. His mother s training had made him methodical in his habits, had taught him punct-r uality and industry, and had inspired him with lofty principles of morality. His health was frail ; and his father, fearing that he miglit not be able to endure a I sedentary life, got a situation for him behind the counter, hoping to fit him for commercial pursuits. . This was to James a bitter disappointment. He had no taste for these duties, and his daily tasks were irksome in the extreme. He remained in this uncongenial occupation but a few weeks, when at his earnest solicitation his father removed him, and made arrangements for him to prosecute his studies. Soon after he sent him to Murfreesboro Academy. With ardor which could scarcely be surpassed, he pressed forward in his studies, and in less than two and a half years, in the autumn of 181 5, entered the sophomore class in the University of North Carolina, at Chapel Hill. Here he was one of the most exemplary of scholars, punctual in every exercise, never allowing himself to be absent from a recitation or a religious service. He graduated in 1818, with the highest honors, be- ing deemed the best scholar of his class, lx)th in mathematics and the classics. He was then twenty- three years of age. Mr. Polk s health was at this time much impaired by the assiduity with which he had prosecuted his studies. After a short season of relaxation he wentf to Nashville, and entered the office of Felix Grundy, to study law. Here Mr. Polk renewed his acquaintance with Andrew Jackson, who resided on his plantation, the Hermitage, but a few miles from Nashville. They had probably l)een slightly acquainted before. Mr. Polk's father was a Jeffersonian Republican, and James K. Polk ever adhered to the same politi- cal faith. He was a popular public speaker, and was constantly called ui)on to address the meetings of his party friends. His skill as a speaker was such that he was popularly called the Napoleon of the stump. He was a man of unblemished morals, genial and m m\o -^^^c^^ _^*H-^-43r < Digitized by Google y.yv y^'^ii A. 60 G) ^ : — \ : ""." vj^ courteous in his bearing, and with that sympathetic f •? nature in the joys and griefs of others which ever gave t:;, him troops of friends. In 1823, Mr. Polk was elected to the Legislature of Tennessee. Here he gave his J strong influence towards the election of his friend, JARfES K. POLK. Mr. Jackson, to the Presidency of the United States. In January, 1824, Mr. Polk married Miss Sarah Childress, of Rutherford Co., Tenn. His bride was altogether worthy of him, — a lady of beauty and cul- ture. In the fall of 1825, Mr. Polk was chosen a member of Congress. The satisfaction which he gave to his constituents may be inferred from the fact, that .^ for fourteen successive years, until 1839, he was con- A tinned in that office. He then voluntarily withdrew, only that he might accept the Gubernatorial chair of Tennessee. In Congress he was a laborious member, a frequent and a popular speaker. He was always in his seat, always courteous ; and whenever he spoke it was always to the point, and without any ambitious rhetorical display. During five sessions of Congress, Mr. Polk was ^ Speaker of the House Strong passions were roused, and stormy scenes were witnessed ; but Mr. Polk per- formed his arduous duties to a very general satisfac- ^ tion, and a unanimous vote of thanks to him was ^ passed by the House as he withdrew on the 4th of S March, 1839. In accordance with Southem usage, Mr. Polk, as a candidate for Governor, canvassed the State. He was elected by a large majority, and on the 1 4th of Octo- ber, 1839, took the oath of office at Nashville. In 184 1, his term of office expired, and he was again the can- didate of the Democratic party, but was defeated. On the 4th of March, 1845, Mr. Polk was inaugur- ated President of the United States. The verdict of the country in favor of the annexation of Texas, exerted its influence upon Congress ; and^the last act of the administration of President Tyler was to affix his sig- nature to a joint resolution of Congress, passed on the 3d of March, approving of the annexation of Texas to the American Union. As Mexico still claimed Texas as one of her provinces, the Mexican minister, Almonte, immediately demanded his passports and left the country, declaring the act of the annexation to be an act hostile to Mexico. In his first message, President Polk urged that Texas should immediately, by act of Congress, be re- r ' V ceived into the Union on the same footing with the N^ other States. In the meantime. Gen. Taylor was sent ) :oj ) \ r^ 4^^:^vi) with an army into Texas to hold the country. He was sent first to Nueces, which the Mexicans said was the western boundary of Texas. Then he was sent nearly two hundred miles further west, to the . Rio Grande, where he erected batteries which commanded the Mexican city of Matamoras, which was situated on the western banks. The anticipated collision soon took place, and war was declared against Mexico by President Polk. The war was pushed forward by Mr. Polk's administration with great vigor. Gen. Taylor, whose army was first called one of "observation," then of "occupation," then of " invasion, "was sent forward to Monterey. The feeble Mexicans, in every encounter, were hopelessly and awfully slaughtered. TJje day of judgement alone can reveal the misery which this war caused^ It was by the ingenuity of Mr. Polk's administration that the war was brought on. * To the victors belong the spoils." Mexico was prostrate before us. Her capital was in our hands. We now consented to peace upon the condition that Mexico should surrender to us, in addition to Texas, all of New Mexico, and all of Upper and Lower Cal- ifornia. This new demand embraced, exclusive of Texas, eight hundred thousand square miles. This was an extent of territory equal to nine States of the size of New York. Thus slavery was securing eighteen majestic States to be added to the Union. There were some Americans who thought it all right : there were others who thought it all wrong. In the prosecution of this war, we expended twenty thousand lives and more than a hundred million of dollars. Of this money fifteen millions were paid to Mexico. On the 3d of March, 1849, Mr. Polk retired from office, having served one term. The next day was Sunday. On the 5th, Gen. Taylor was inaugurated as his successor. Mr. Polk rode to the Capitol in the same carriage with Gen. Taylor; and the same even- ing, with Mrs. Polk, he commenced his return to Tennessee. He was then but fifty-fgur years of age. He had ever been strictly temperate in all his habits, and his health was good With an ample fortune, a choice library, a cultivated mind, and domestic ties of the dearest nature, it seemed as though long years of tranquility and happiness were before him. But the cholera — that fearful scourge — was then sweeping up the Valley of the Mississippi. This he contracted, and died on the 15th of June, 1849, i" ^^^ fifty-fourth year of his age, greatly mourned by his countrymen. ! v/ / 1 4r^^^?iy^ Digitized by Google <^ Digitized by Google ^...'^'^rty^x^ r rss^S^ T<^:nil:^IlB^> ^/^ TWELFTH PRESIDENT. 1'^ J ^y ACHARY TAYLOR, twelfth President of the United States, ^was bom on the 24th of Nov., 1784, in Orange Co., Va. His father, Colonel Taylor, was a Virginian of note, and a dis- tinguished patriot and soldier of the Revolution. When Zachary was an infant, his father with his wife and two children, emigrated to Kentucky, where he settled in the pathless wilderness, a few miles from Louisville. In this front- ier home, away from civilization and all its refinements, young Zachary could enjoy but few social and educational advan- tages. When six years of age he attended a common school, and was then regarded as a bright, active boy, rather remarkable for bluntness and decision of char- acter He was strong, fearless and self-reliant, and manifested a strong desire to enter the army to fight the Indians who were ravaging the frontiers. There is little to be recorded of the uneventful years of his childhood on his father's large but lonely plantation. In 1808, his father succeeded in obtaining for him the commission of lieutenant in the United States army ; and he joined the troops which were stationed at New Orleans under Gen. Wilkinson. Soon after this he married Miss Margaret Smith, a young lady from one of the first families of Maryland. Immediately after the declaration of war with Eng- land, in 18 1 2, Capt. Taylor (for he had then been promoted to that rank) was put in command of Fort Harrison, on the Wabash, about fifty miles above Vincennes. This fort had been built in the wilder- ness by Gen. Harrison,on his march to Tippecanoe. It was one of the first points of attack by the Indians, led by Tecumseh. Its garrison consisted of a broken company of infantry numbering fifty men, many of whom were sick. Early in the autumn of 181 2, the Indians, stealthily, and in large numbers, moved upon the fort. Their approach was first indicated by the murder of two soldiers just outside of the stockade. Capt. Taylor made every jxissible preparation to meet the antici- pated assault. On the 4th of September, a band of forty painted and plumed savages came to the fort, waving a white flag, and informed Capt. Taylor that in the morning their chief would come to have a talk with him. It was evident that their object was merely to ascertain the state of things at the fort, and Capt. Taylor, well versed in the wiles of the savages, kept them at a distance. The sun went down; the savages disappeared, the garrison slept upon their arms. One hour before midnight the war whoop burst from a thousand lips in the forest around, followed by the discharge of musketry, and the rush of the foe. Every man, sick and well, sprang to liis jxjst. Every man knew that defeat was not merely death, but in the case of cap- ture, death by the most agonizing and prolonged tor- ture. No pen can describe, no immagination can conceive the scenes which ensued. The savages suc- ceeded in setting fire to one of the block-houses* Until six o'clock in the morning, this awful conflict continued. The savages then, baffled at every point, and gnashing their teeth with rage, retired. Capt. Taylor, for this gallant defence, was promoted to the rank of major by brevet. Until the close of the war, Major Taylor was placed in such situations that he saw but little more of active service. He was sent far away into the depths of the wilderness, to Fort Crawford, on Fox River, which empties into Green Bay. Here there was but little to be done but to wear away the tedious hours as one best could. There were no books, no society, no in- C; 4) I 5 Digitized by Google > 64 .•■j'*C»« ^~-7<:aIl>;liIlr>^--r ZACHARY TAYLOR, :^^:- *^^r>^,A' V >* I tellectual stimulus. Thus with him the uneventful years rolled on Gradually he rose to the rank of colonel. In the Black-Hawk war, which resulted in the capture of that renowned chieftain, Col Taylor took a subordinate but a brave and efficient part. For twenty -four years Col. Taylor was engaged in the defence of the frontiers, in scenes so remote, and in employments so obscure, that his name was unknown beyond the limits of his own immediate acquaintance. In the year 1836, he was sent to Florida to comi)el the Seminole Indians to vacate that region and re- tire beyond the Mississippi, as their chiefi by treaty, had promised they should do. The services rendered here secured for Col. Taylor the high appreciation of the Government; and as a reward, he was elevated to the rank of brigadier-general by brevet ; and soon after, in May, 1838, was appointed to the chief com- mand of the United States troops in Florida. After two years of such wearisome employment amidst the everglades of the peninsula, Gen. Taylor obtained, at his own request, a change of command, and was stationed over the Department of the South- west. This field embraced Louisiana, Mississippi, Alabama and Creorgia. Establishing his headquarters at Fort Jessup, in Louisiana, he removed his family to a plantation which he purchased, near Baton Rogue. Here he remained for fist. years, buried, as it were, from the world, but faithfully discharging every duty imposed upon him. In 1846, Gen. Taylor was sent to guard the land between the Nueces and Rio Grande, the latter river being the boundary of Texas, which was then claimed by the United States. Soon the war with Mexico was brought on, and at Palo Alto and Resaca de la Palnia, Gen. Taylor won brilliant victories over tlie Mexicans. The rank of major-general by brevet was then conferred upon Gen. Taylor, and his name was received with enthusiasm almost everywhere in the Nation. Then came the battles of Monterey and Buena Vista in which he won signal victories over forces much larger than he commanded. His careless habits of dress and his unaffected simplicity, secured for Gen. Taylor among his troops, yki^ sobriquet of "Old Rough and Ready.' The tidings of the brilliant victory of Buena Vista spread the wildest enthusiasm over the country. The name of Gen. Taylor was on every one's lips. The Whig party decided to take advantage of this wonder- ful popularity in bringing forward the unpolished, un- lettered, honest soldier as their candidate for the Presidency. Gen. Taylor was astonished at the an- nouncement, and for a time would not listen to it; de- claring that he was not at all qualified for such an office. So little interest had he taken in jx>litics that, for forty years, he had not cast a vote. It was not without chagrin that several distinguished statesmen who had been long years in the public service found their claims set aside in behalf of one whose name ^:'^'^-^f^^ had never been heard of, save in connection with Palo Alto, Resaca de la Palma, Monterey and Buena Vista. It Is said that Daniel Webster, m his haste re- marked, *' It is a nomination not fit to be made," Gen. Taylor was not an elo(]uent si)eaker nor a fine wnter His friends took possession of him, and pre- < pared such few communications as it was needful should be presented to the public. The popularity of the successful warrior swept the land. He was tri- umphantly elected over two opix>sing candidates, — Gen. Cass and Ex-President Martin Van Buren. Though he selected an excellent cabinet, the good old man found himself in a very uncongenial position, and was, at times, sorely perplexed and harassed. His mental sufferings were very severe, and probably tended to hasten his death. The pro-slavery party was pushing its claims with tireless energy , exi>edi- tions were fitting out to capture Cuba ; California was pleading for admission to the Union, while slaver)' stood at the door to bar her out. Gen. Taylor found the political conflicts in Washington to be far more trying to the nerves than battles with Mexicans or Indians. In the midst of all these troubles, Gen. Taylor, after he had occupied the Presidential chair but liule over a year, took cold, and after a brief sickness of but little over five days, died on the 9th of July, 1850. His last words were, " I am not afraid to die. I am ready. I have endeavored to do my duty." He died universally respected and beloved. An honest, un- pretending man, he had been steadily growing in the affections of the people ; and the Nation bitterly la- mented his death. Gen. Scott, who was thoroughly acquainted with Gen. Taylor, gave the following graphic and truthful description of his character: — " With a good store ot common sense, Gen. Taylor's mind had not been en- larged and refreshed by reading, or much converse with the world. Rigidity of ideas was the conse- quence. The frontiers and small military posts had been his home. Hence he was quite ignorant for his rank, and quite bigoted in his ignorance. His sim- plicity was child-like, and with innumerable preju- dices, amusing and incorrigible, well suited to the tender age. Thus, if a man, however respectable, chanced to wear a coat of an unusual color, or his hat a little on one side of his head; or an officer to leave a corner of his handkerchief dangling from an out- side pocket, — in any such case, this critic held the offender to be a co.xcomb (perhaps something worse), whom he would not, to use his oft repeated phrase, 'touch with a pair of tongs.* "Any allusion to literature beyond good old Dil- worth s spelling-book, on the part of one wearing a sword, was evidence, with the same judge, of utter unfitness for heavy marchings and combats. In short, few men have ever had a more comfortable, labor- saving contempt for learning of every kind.** ■^:tlli:^:iin;->^-^ Digitized by Google Digitized by Google X ^^^■/^^i>^^^.:'^ ^ ^^^^<!T€!^ia4^ '^cSu^ti^n? Digitized by Google '^;^/^^))ft®?l^ » ^ THTRTEENTH PRESIDENT. ■S • ■/ » /\ V f ^MILLflHn FILLfflOHE.^ ILLARD FILLMORE, thir- teenth President of the United States, was born at Summer Hill, Cayuga Co., N. Y ., on the 7th of Januar}', 1800. His father was a farmer, and ow- ing to misfortune, in humble cir- cumstances. Of his mother, the daughter of Dr. Abiathar Millard, of Pittsfield, Mass., it has been said that she possessed an intellect of very high order, united with much personal loveliness, sweetness of dis- position, graceful manners and ex- quisite sensibilities. . She died in 1831 ; having lived to see her son a young man of distinguished prom- ise, though she was not permitted to witness the high dignity which he finally attained. Tn consequence of the secluded home and limited means of his father, Millard enjoyed but slender ad- vantages for education in his early years. The com- mon schools, which he occasionally attended were very imperfect institutions; and books were scarce and expensive. There was nothing then in his char- acter to indicate the brilliant career upon which he was about to enter. He was a plain farmer's boy ; intelligent, good-looking, kind-hearted. The sacred influences of home had taught hira to revere the Bible, and had laid Ihe foundations of an upright character. When fourteen years of age, his father sent him some hundred miles from home, to the then wilds of Livingston County, to learn the trade of a clothier. Near the mill there was a small villiage, where some enterprising man had commenced the collection of a village library. This proved an inestimable blessing to young Fillmore. His evenings were spent in read- ing. Soon every leisure moment was occupied with books. His thirst for knowledge became insatiate; and the selections which he made were continually more elevating and instructive. He read history, biography, oratory, and thus gradually there was en- kindled in his heart a desire to be something more than a mere worker with his hands; and he was be- coming, almost unknown to himself, a well-informed, educated man. The young clothier had now attained the age of nineteen years, and was of fine personal appearance and of gentlemanly demeanor. It so happened that there was a gentleman in the neighborhood of ample pecuniary means and of benevolence, — Judge Walter Wood, — who was struck with the prepossessing ap- pearance of young Fillmore. He made his acquaint- ance, and was so much impressed with his ability and attainments that he advised him to abandon his trade and devote himself to the study of the law. The young man replied, that he had no means of his own, no friends to help him and that his previous educa- tion had been very imperfect. But Judge Wood had so much confidence in him that he kindly offered to take him into his own office, and to loan him such money as he needed. Most gratefully the generous offer was accepted. There is in many minds a strange delusion about a collegiate education. A young man is supposed to be liberally educated if he has graduated at some col- lege. But many a boy loiters through university halls and then enters a law office, who is by no means as \^y^i%- u:i^ IlDv->A!§- j:^j^^^ €^^ "'i' --V/V v^ A (i' / i I Digitized by Google ■^X- -ry V<>I1 11^:11 Il^>r ■^^i-i -•ev-^rs^ 68 MILLARD FILLMORE. > :-^ V > .^ ^ % '^ well prepared to prosecute his legal studies as was Millard Fillmore when he graduated at the clothing- mill at the end of four years of manual labor, during which every leisure moment had been devoted to in- tense mental culture. In 1823, when twenty-three years of age, he was admitted to the Court of Common Pleas, He then went to the village of Aurora, and commenced the practice of law. In this secluded, peaceful region, his practice of course was limited, and there was no opportunity for a sudden rise in fortune or in fame. Here, in the year 1826, he married a lady of great moral worth, and one capable of adorning any station she might be called to fill, — Miss Abigail Powers. His elevation of character, his untiring industry, his legal acquirements, and his skill as an advocate, gradually attracted attention ; and he was invited to enter into partnership under highly advantageous circumstances, with an elder member of the bar in Buffalo. Just before removing to Buffalo, in 1829, he took his seat in the House of Assembly, of the State of New York, as a representative from Erie County. Though he had never taken a very active part in politics, his vote and his sympathies were with the Whig party. The State was then Democratic, and he found himself in a helpless minority in the Legislature, still the testimony comes from all parties, that his courtesy, ability and integrity, won, to a very unusual degree the respect of his associates. In the autumn of 1832, he was elected to a seat in the United States Congress. He entered that troubled arena in some of the most tumultuous hours of our national history. The great conflict respecting the national bank and the removal of the deposits, was then raging. His term of two years closed ; and he returned to his profession, which he pursued with increasing rep- utation and success. After a lapse of two years he again became a candidate for Congress ; was re- elected, and took his seat in 1837. His past expe- rience as a representative gave him strength and confidence. The first term of service in Congress to any man can be but little more than an introduction. He was now prepared for active duty. All his ener- gies were brought to bear upon the public good. Every measure received his impress. Mr. Fillmore was now a man of wide repute, and his popularity filled the State, and in the year 1847, he was elected Comptroller of the State. Mr. Fillmore had attained the age of forty-seven years. His labors at the bar, in the Legislature, in \ Congress and as Comptroller, had given him very con- \ siderable fame. The Whigs were casting about to find suitable candidates for President and Vice-Presi- , dent at the approaching election. Far away, on the waters of the Rio Grande, there was a rough old soldier, who had fought one or two successful battles with the Mexicans, which had caused his name to be proclaimed in trumpet-tones all over the land. But it was necessary to associate with him on the same ticket some man of reputation as a statesman. Under the influence of these considerations, the namesofZachary Taylor and Millard Fillmore became the rallying-cry of the Whigs, as their candidates for President and Vice-Peesident. The Whig ticket was signally triumphant. On the 4th of March, 1849, Gen. Taylor was inaugurated President, and Millard Fillmore Vice-President, of the United States. On the 9th of July, 1850, President Taylor, but about one year and four months after his inaugura- tion, was suddenly taken sick and died. By the Con- stitution, Vice-President Fillmore thus became Presi- dent. He appointed a very able cabinet, of which the illustrious Daniel Webster was Secretary of St^te. Mr. Fillmore had very serious difficulties to contend with, since the opposition had a majority in both Houses. He did everything in his power to conciliate the South ; but the pro-slavery party in the South felt the inadequacy of all measures of transient conciliation. The population of the free States was so rapidly in- creasing over that of the slave States that it was in- evitable that the power of the Government should soon pass into the hands of the free States. The famous compromise measures were adopted under Mr. Fillmore s adminstration, and the Japan Expedition was sent out. On the 4th of March, 1853, Mr. Fill- more, having served one term, retired. In r 85 6, Mr. Fillmore was nominated for the Pres- idency by the " Know Nothing " party, but was beaten by Mr. Buchanan. After that Mr. Fillmore lived in retirement. During the terrible conflict of civil war, he was mostly silent. It was generally supposed that his sympathies were rather with those who were en- deavoring to overthrow our institutions. President Fillmore kept aloof from the conflict, without any cordial words of cheer to the one party or the other. He was thus forgotten by both. He lived to a ripe old age, and died in Buffalo. N. Y., March 8, 1874.. A vj / 1 f. mr\lB^(^'^^ St-?53^ "A-i<y- ^;:-JL <-^D!lgDI];.>A ^T-,.j^Xfy^ -^!xy- ^^m^^^ Digitized by Google 4 ' ^ 1^/^^^^ Digitized by Google I- ) ;?!«<►- -^k€ ^ 6V 4?llll^Ptlr> ■^%<sr"^^^ r>;;^:^ FOURTEENTH PRESIDENT ^1 ilt^tfLftjt*^. ■»^>^! r^ft-Obv^ ►irr*^'*^;'*^i»i?*:n'^ l^» ^FHflHKLIN PIERCE.^ :<^ V ■ ) ^ RANKLIN PIERCE, the fourteenth President of the '' United States, was bom in Hillsborough, N. H., Nov. 23, 1804. His father was a Revohitionary soldier, who, with his own strong arm, hewed out a home in the wilderness. He was a man of inflexible integrity; of strong, though uncultivated mind, and an uncompromis- ing Democrat. The mother of Franklin Pierce was all that a son could rlrsiio, :in intelligent, pru- dent, affectionate, Christian wom- an. Franklin was the sixth of eight children. Franklin was a very bright and handsome boy, gen- erous, warm-hearted and brave. He won alike the love of old and young. The boys on the play ground loved him. His teachers loved him. The neighbors looked upon him with pride and affection. He was by instinct a gentleman; always speaking kind words, ! doing kind deeds, with a peculiar unstudied tact which taught him what was agreeable. Witliout de- veloping any precocity of genius, or any unnatural devotion to books, he was a good scholar ; in body, in mind, in affections, a finely-developed boy. When sixteen years of age, in the year 1820, he entered Bowdoin College, at Brunswick, Me. He was one of the most popular young men in the college. The purity of his moral character, the unvarying courtesy of his demeanor, his rank as a scholar, and genial nature, rendered him a universal favorite. There was something very peculiarly winning in his address, and it was evidently not in the slightest de- gree studied : it was the simple outgushing of his own magnanimous and loving nature. Uix)n graduating, in the year 1824, Franklin Pierce commenced the study of law in the office of Judge Woodbury, one of the most distinguished lawyers of the State, and a man of great private worth. The eminent social qualities of the young lawyer, his father's prominence as a public man, and the brilliant jKjlitical career into which Judge Woodbury was en- tering, all tended to entice Mr. Pierce into the faci- nating yet perilous path of ix)litical life. With all the ardor of his nature he espoused the cause of Gen. Jackson for the Presidency. He commenced the practice of law in Hillsborough, and was soon elected to represent the town in the State Legislature. Here he served for four yeais. The last two years he was chosen speaker of the house by a very large vote. In 1833, at the age of twenty-nine, he was elected a member of Congress. Without taking an active part in debates, he was faithful and laborious in duty, and ever rising in the estimation of those with whom he was associatad. In 1837, being then but thirty-three years of age, he was elected to the Senate of the United States; taking his seat just as Mr. Van Buren commenced his administration. He was the youngest member in the Senate. In the year 1834, he married Miss Jane Means Appleton, a lady of rare beauty and accom- plishments, and one admirably fitted to adorn every station with which her husband was honoied. Of the ^^Vi?))«^^ ^pti;^z^ ^>^^ < ( -^^i^^^^^M^ Digitized by VjOOQlC t€^ ti'SSa ^<f* T24;^ <iilii:<5:iin^> 7« ■^rrr FRANKLIN PIERCE. Ta^^Ks^s" -^|?^7Jf5"^,- (,'> ^ A ■^ three sons who were bom to them, all now sleep with their parents in the grave. In the year 1838, Mr. Pierce, with growing fame and increasing business as a lawyer, took up his residence in Concord, the capital of New Hampshire. President Polk, upon his accession to office, appointed Mr. Pierce attorney-general of the United States ; but the offer was declined, in consequence of numerous professional engagements at home, and the precariuos state of Mrs. Pierce s health. He also, about the same time declined the nomination for governor by the Democratic party. The war with Mexico called Mr. Pierce in the army. Receiving the appointment of brigadier-general, he en^barked, with a portion of his troops, at Newport, R. I., on the 27 th of May, 1847. He took an important part in this war, proving him- self a brave and true soldier. When Gen. Pierce reached his home in his native State, he was received enthusiastically by the advo- cates of the Mexican war, and coldly by his oppo- nents. He resumed the practice of his profession, very frequently taking an active part in political ques- tions, giving his cordial support to the pro-slavery wing of the Democratic party. The compromise measures met cordially with his approval ; and he strenuously advocated the enforcement of the infa- mous fugitive-slave law, which so shocked the religious sensibilities of the North. He thus became distin- guished as a "Northern man with Southern principles.*' The strong partisans of slavery in the South conse- quently regarded him as a man whom they could safely trust in office to carry out their plans. On the 1 2th of June, 1852, the Democratic conven- tion met in Baltimore to nominate a candidate for the Presidency. For four days they continued in session, and in thirty-five ballotings no one had obtained a two-thirds vote. Not a vote thus far had been thrown for Gen. Pierce. Then the Virginia delegation brought forward his name. There were fourteen more ballotings, during which Gen. Pierce constantly gained strength, until, at the forty-ninth ballot, he received two hundred and eighty-two votes, and all other candidates eleven. Gen. Winfield Scott was the Whig candidate. Gen, Pierce was chosen with great unanimity. Only four States — Vermont, Mas- sachusetts, Kentucky and Tennessee — cast their electoral votes against him Gen. Franklin Pierce was therefore inaugurated President of the United States on the 4th of March, 1853. His administtation proved one of the most stormy our country had ever experienced. The controversy l>e- tween slavery and freedom was then approaching its culminating point. It became evident that there was an " inepressible conflict " between them, and that this Nation could not long exist " half slave and half free." President Pierce, during the whole of his ad- ministration, did every thing he could to conciliate the South ; but it was all in vain. The conflict every year grew more violent, and threats of the dissolution of the Union were borne to the North on every South- ern breeze. Such was the condition of aff*airs when President Pierce approached the close of his four-years' term of office. The North had become thoroughly. alien- ated from him. The anti-slavery sentiment, goaded by great outrages, had been rapidly increasing; all the intellectual ability and social worth of President Pierce were forgotten in deep reprehension of his ad- ministrative acts. The slaveholders of the South, also, unmindful of the fidelity with which he had advo- cated those measures of Government which they ap- proved, and perhaps, also, feeling that he had rendered himself so unix)pular as no longer to be able acceptably to serve them, ungratefully dropped him, and nominated James Buchanan to succeed him. On the 4th of March, 1857, President Pierce re- tired to his home in Concord. Of three children, two had died, and his only surviving child had been killed before his eyes by a railroad accident ; and his wife, one of the most estimable and accomplished of ladies, was rapidly sinking in consumption. The hour of dreadful gloom soon came, and he was left alone in the world, without wife or child. When the terrible Rebellion burst forth, which di- vided our country into two parties, and two only, Mr. Pierce remained steadfast in the principles which he had always cherished, and gave his sympathies to that pro-slavery party with which he had ever been allied. He declined to do anything, either by voice or pen, to strengthen the hand of the National Gov- ernment. He continued to reside in Concord until the time of his death, which occurred in October, 1869. He was one of the most genial and social of men, an honored communicant of the Episcopal Church, and one of the kindest of neighbors. Gen- erous to a fault, he contributed liberally for the al- leviation of suff"ering and want, and many of his towns- people were often gladened by his material bounty. I^vs^^^ 1.:^- ^<^i]!]-^ntift> A O- j;;^J>^*:-^a^ -^fSf^ J Digitized by Google ^ ^Z^Tne^ Digitized by Google ^J* FIFTEENTH PRESIDENT r.-;;''.-l 75 <. -4 5|iN^-^ VCSAAMj ^ AMES BUCHANAN, the fif- teenth President of the United States, was born in a small frontier town, at the foot of the eastern ridge of the Allegha- nies, in Franklin Co., Penn., on the 23d of April, 1791. The place where the humble cabin of his father stood was called Stony Batter. It was a wild and ro- mantic sppt in a gorge of the moun- tains, with towering summits rising grandly all around. His father was- a native of the north of Ireland ; a poor man, who had emigrated in 1783, with little prot>erty save his own strong arms. Five years afterwards he married Elizabeth Spear, the daughter of a respectable farmer, and, with his young bride, plunged into the wilder- ness, staked his claim, reared his log-hut, opened a clearing with his axe, and settled down there to per- form his obscure part in the drama of life. In this se- cluded home, where James was born, he remained for eight years, enjoying but few social or intellectual advantages. When James was eight years of age, his father removed to the village of Mercersburg, where his son was placed at school, and commenced a course of study in English, Latin and Greek. His progress was rapid, and at the age of fourteen, he entered Dickinson College, at Carlisle. Here he de- veloped remarkable talent, and took his stand among the first scholars in the institution. His application to study was intense, and yet his native powers en- abled him to master the most abstruse subjects with facility. In the year 1809, he graduated with the highest honors of his class. He was then eighteen years of age; tall and graceful, vigorous in health, fond of athletic sport, an unerring shot, and enlivened with an exuberant flow of animal spirits. He immediately commenced the study of law in the city of Lancaster, and was admitted to the bar in 18 12, when he was but twenty-one years of age. Very rapidly he rose in his profession, and at once took undisputed stand with the ablest lawyers of the State. When but twenty-six years of age, unaided by counsel, he suc- cessfully defended before the State Senate one of the judges of the State, who was tried upon articles of impeachment. At the age of thirty it was generally admitted that he stood at the head of the bar; and there was no lawyer in the State who had a more lu- crative practice. In 1820, he reluctantly consented to run as a candidate for Congress. He was elected, and for ten years he remained a member of the Lower House. During the vacations of Congress, he occasionally tried some important case. In 1 831, he rerired altogether from the toils of his profession, having ac- quired an ample fortune. Gen. Jackson, upon his elevation to the Presidency, appointed Mr. Buchanan minister to Russia. The duties of his mission, he performed with ability, which gave satisfaction to all parties. Uix)n his return, in 1833, he was elected to a seat in the United States Senate. He there met, as his associates, Webster, Clay, Wright and Calhoun. He advocated the meas- ures proposed by President Jackson, of making repri- r* A '>: y t i I '•'-:^ m ^f^ .c:^ r^mm\i^>^. -^^5t^^^^ .^l^jyv:^ Digitized by VjOOQlC ,#Kii^^^l^ -^^- ^^■■o^ 76 JAMES BUCHANAN. -^■im^' \ r) A c^:- V ) / \ ^ sals against France, to enforce the payment of our claims against that country ; and defended the course of the President in his unprecedented and wholesale removal from office of those who were not the sup- porters of his administration. Upon this question he was brought into direct collision with Henry Clay. He also, with voice and vote, advocated expunging from the journal of the Senate the vote of censure against Gen. Jackson for removing the deposits. Earnestly he opposed the abolition of slavery in the District of Columbia, and urged the prohibition of the circulation of anti-slavery documents by the United States mails. As to petitions on the subject of slavery, he advo- cated that they should be respectfully received ; and that the reply should be returned, that Congress had no power to legislate upon the subject. " Congress," said he, " might as well undertake to interfere with slavery under a foreign government as in any of the States where it now exists." Upon Mr. Polk s accession to the Presidency, Mr. Buchanan became Secretary of State, and as such, took his share of the resix)nsibility in the conduct of the Mexican War. Mr. Polk assumed that crossing the Nueces by the American troops into the disputed territory was not wrong, but for the Mexicans to cross the Rio Crande into that territory was a declaration of war. No candid man can read with pleasure the account of the course our Government pursued in that movement. Mr. Buchanan identified himself thoroughly with the party devoted to the perpetuation and extension of slavery, and brought all the energies of his mind to bear against the Wilmot Proviso. He gave his cordial approval to the compromise measures of 1S50, which included the fugitive-slave law. Mr. Pierce, upon his election to the Presidency, honored Mr. Buchanan with the mission to England. In the year 1856, a national Democratic conven- tion nominated Mr. Buchanan for the Presidency. The political conflict was one of the most severe in which our country has ever engaged. All the friends of slavery were on one side ; all the advocates of its re- striction and final abolition, on the other. Mr. Fre- mont, the candidate of the enemies of slavery, re- ceived 114 electoral votes. Mr. Buchanan received 174, and was elected. The ix>i)ular vote stood 1,340,618, for Fremont, 1,224,750 for Buchanan. On March 4th,* 1857, Mr. Buchanan was inaugurated. Mr. Buchanan was far advanced in life. Only four years were wanting to fill up his threescore years and ten. His own friends, those with whom he had been allied in ix>litical principles and action for years, were seeking the destruction of the Government, that they might rear w\ioxi the ruins of our free institutions a nation whose corner-stone should be human slavery. In this emergency, Mr. Buchanan was hopelessly be- wildered. He could not, with his long-avowed prin- ciples, consistently oppose the State-rights party in their assumptions. As President of the United States, bound by his oath faithfully to administer the laws, he could not, without perjury of the grossest kind, unite with those endeavoring to overthrow the repub- lic. He therefore did nothing. 1^ The opponents of Mr. Buchanan s administration nominated Abraham Lincoln as their standard bearer in the next Presidential canvass. The pro-slavery party declared, that if he were elected, and the con- trol of the Government were thus taken from their hands, they would secede from the Union, taking with them, as they retired, the National Capitol at Washington, and the lion s share of the territoi}' of the United States. Mr. Buchanan s sympathy with the pro-slaver^' party was such, that he had been willing to offer them far more than they had ventured to claim. All the South had professed to ask of the North was non- intervention upon the subject of slavery. Mr. Bu- chanan had been ready to offer them the active co- operation of the Government to defend and extend the institution. As the storm increased in violence, the slaveholders claiming the right to secede, and Mr. Buchanan avow- ing that Congress had no ix)wer to prevent it, one of tlie most pitiable exhibitions of governmental im- becility was exhibited the world has ever seen. He declared that Congress had no ix>wer to enforce its laws in any State which had withdrawn, or which was attempting to withdraw from the Union. This » was not the doctrine of Aitdrew Jackson, when, with his hand w\xm his sword-hilt, he exclaimed, " The Union must and shall be preserved!" South Carolina seceded in December, i860; nearly three months before the inauguration of President Lincoln. Mr. Buchanan looked on in listless despair. The rebel flag was raised in Charleston: Fort Sumpter was l)e>'ieged; our forts, navy-yards and arsenals were seized; our de|X)ts of military stores were jilun- dered ; and our custom-houses and post-offices were api^ropriated by the rebels. The energy of the rebels, and the imbecility of our Executive, were alike marvelous. The Nation looked on in agony, waiting for the slow weeks to glide away, and close the administration, so terrible in its weak- ness At length the long-looked -for hour of deliver- ance came, when Abraham Lincoln was to receive the scepter. The administration of President Buchanan was certainly the most calamitous our country has ex- perienced. His best friends cannot recall it with pleasure. And still more deplorable it is for his fame, that in that dreadful conflict which rolled its billows of flame and blood over our whole land, no word came from his lips to indicate his wish that our country V banner should triumph over the flag of the rebellion. He died at his Wheatland retreat, June i, 186S. -■y^-- -Vf \0 - -^::Il!l^t^nDr> s^:-!:. isx>^ Digitized by Google iy/7$is^^k7u!*^
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^1 BR AH AM LINCOLN, the
1^ sixteenth President of the
¥^United States, was lx)rn in
Hardin Co., Ky., Feb. 12,
I S09. About the year 1 7 80, a
man by the name of Abraham
'"^ Lincoln left Virginia with his
family and moved into the then
wildsof Kentucky. Only two years
after this emigration, still a young
man, while working one day in a
field, was stealthily approached by
an Indian and shot dead. His widow
was left in extreme ix)verty with ^so.
little children, three boys and two
girls. Thomas, the youngest of the
boys, was four years of age at his
father's death. This Thomas was
the father of Abraham Lincoln, the
President of the United States
whose name must henceforth forever be enrolled
with the most prominent in the annals of our worW.
Of course no record has been kept of the life
of one so lowly as Thomas Lincoln. He was among
the poorest of the poor. His home was a wretched
log -cabin; his food the coarsest and the meanest.
or write. As soon as he was able to do anything for
himself, he was compelled to leave the cabin of his
starving mother, and push out into the world, a friend-
less, wandering boy, seeking work. He hired him-
self out, and thus spent the whole of his youth as a
laborer in the fields of others.
When twenty-eight years of age he buil! a log-
cabin of his own, and married Nancy Hanks, the
daughter of another family of poor Kentucky emi-
grants, who had also come from Virginia. Their
second child was Abraham Lincoln, the subject of
this sketch. The mother of Abraham was a noble
woman, gentle, loving, pensive, created to adorn
a palace, doomed to toil and pine, and die in a hovel.
" All that I am, or hope to be," exclaims the grate-
ful son "I owe to my angel-mother. "
When he was eight years of age, his father sold his
cabin and small farm, and moved to Indiana. Where
two years later his mother died.
Abraham soon became the scribe of the uneducated
community around him. He could not have had a
better school than this to teach him to put thoughts
into words. He also became an eager reader. The
books he could obtain were few ; but these he read
and re-read until they were almost committed to
memory.
As the years rolled on, the lot of this lowly family
was the usual lot of humanity. Thore were joys and
griefs, weddings and funerals. Abraham s sister
Sarah, to whom he was tenderly attached, was mar-
ried when a child of but fourteen years of age, and
soon died. The family was gradually scattered. Mr.
Thomas Lincoln sold out his squatter's claim in 1830,
and emigrated to Macon Co., III.
Abraham Lincoln was then twenty-one years of age.
With vigorous hands he aided his father in rearing
another log-cabin. Abraham worked diligently at this
until he saw the family comfortably settled, and their
small lot of enclosed prairie planted with com, when
he announced to his father his intention to leave
home, and to go out into the world and seek his for-
tune. Little did he or his friends imagine how bril-
liant that fortune was to be. He saw the value of
education, and was intensely earnest to improve his
mind to the utmost of his power. He saw the ruin
which ardent spirits were causing, and became
strictly temperate; refusing to allow a drop of intoxi-
Gods word, "Thou shalt not take the name of the
I^rd thy God in vain ;" and a profane expression he
was never heard to utter. Religion he revered. His
morals were pure, and he was uncontaminated by a
single vice.
Young Abraham worked for a time as a hired laborer
among the farmers. Then he went to Springfield,
where he was employed in building a large flat-boat.
In this he took a herd of swine, floated them down
the Sangamon to the Illinois, and thence by the Mis-
sissippi to New Orleans. Whatever Abraham Lin-
coln undertook, he performed so faithfully as to give
great satisfaction to his employers. In this adven-
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ture his employers were so well pleased, that upon
his return they placed a store and mill under his care.
In 1832, at the outbreak of the Black Hawk war, he
enlisted and was chosen captain of a company. He
returned to Sangamon County, and although only 23
years of age, was a candidate for the Legislature, but
was defeated. He soon after received from Andrew
Jackson the appointment of Postmaster of New Salem,
His only post>ofiice was his hat. All the letters he
he chanced to meet. He studied surveying, and soon
candidate for the Legislature, and was elected. Mr.
Stuart, of Springfield, advised him to study law. He
walked from New Salem to Springfield, borrowed of
Mr. Stuart a load of books, carried them back and
began his legal studies. When the Legislature as-
sembled he trudged on foot with his pack on his back
one hundred miles to Vandalia, then the capital. In
1836 he was re-elected to the Legislature. Here it
was he first met Stephen A. Douglas. In 1 839 he re-
moved to Springfield and began The practice of law.
His success with the jury was so great that he was
soon engaged in almost every noted case in the circuit.
In 1854 the great discussion began between' Mr.
Lincoln and Mr. I>>uglas, on the slavery question.
In the organization of the Republican party in Illinois,
in 1856, he took an active part, and at once became
one of the leaders in that party. Mr. Lincoln's
speeches in opposition to Senator Douglas in the con-
test in 1858 for a seat in the Senate, form a most
notable part of his history. The issue was on the
slavery question, and he took the broad ground of
the Declaration of Independence, that all men are
created equal. Mr. Lincoln was defeated in this con-
test, but won a far higher prize.
The great Republican Convention met at Chicago
on the 1 6th of June, i860. The delegates and
strangers who crowded the city amounted to twenty-
five thousand. An immense building called ** The
Wigwam," was reared to accommodate the Conven-
tion. There were eleven candidates for whom votes
were thrown. William H. Seward, a man whose fame
as a statesman had long filled the land, was the most
prominent. It was generally supposed he would be
the nominee. Abraham Lincoln, however, received
the nomination on the third ballot. Little did he then
dream of the weary years of toil and care, and the
bloody death, to which that nomination doomed him :
and as little did he dream that he was to render services
to his country, which would fix upon him the eyes of
the whole civilized world, and which would give him
a place in the affections of his countrymen, second
only, if second, to tl\at of Washington,
Election day came and Mr. Lincoln received 180
electoral votes out of 203 cast, and was, therefore,
constitutionally elected President of the United States.
The tirade of abuse that was poured ui^n this good
and merciful man, especially by the slaveholders, was
greater than upon any other man ever elected to this '
high position. In February, 1861, Mr. Lincoln started
for Washington, stopping in all the large cities on his
way making speeches. The whole journey was frought
with much danger. Many of the Southern States had .
already seceded, and several attempts at assassination
were afterwards brought to light. A gang in Balti-
more had arranged, upon his arrival to" get up a row,"
and in the confusion to make sure of his death with
revolvers and hand-grenades. A detective unravelled
the plot. A secret and special train was provided to
take him from Harrisburg, through Baltimore, at an
unexi)ected hour of the night. The train started at
half-past ten ; and to prevent any possible communi-
cation on the part ot the Secessionists with their Con- ,
federate gang in Baltimore, as soon as the train hud
started the telegraph-wires were cut. Mr. Lincoln
reached Washington in safety and was inaugurated,
although great anxiety was felt by all loyal people.
In the selection of his cabinet Mr. Lincoln gave
to Mr. Seward the Department of State, and to other
prominent opponents before the convention he gave
important positions.
During no other administration havi the duties
devolving upon the President been so manifold, and
the responsibilities so great, as those which fell tu
the lot of President Lincoln. Knowing this, and
feeling his own weakness and inability to meet, and in
his own strength to cope with, the difficulties, he
learned early to seek Divine wisdom and guidance in
determining his plans, and Divine comfort in all his
trials, both personal and national. Contrary to his
own estimate of himself, Mr. Lincoln was one of the
most courageous of men. He went directly into the
rebel capitakjust as the retreating foe was leaving,
with no guard but a few sailors. From the time he
made for his assassination,and he at last fell a victim
to one of them. April 14, 1865, he, with Gen. Grant,
was urgently invited to attend Fords' Theater. It
was announced that they would Le present. Gen.
Grant, however, left the city. President Lincoln, feel-
ing, with his characteristic kindliness of heart, that
it would be a disappointment if he should fail them,
very reluctantly consented to go. While listening to
the play an actor by the name of John Wilkes Booth
entered the lx)x where the President and family were
seated, and fired a bullet into his brains. He died the
next morning at seven o clock.
Never before, in the history of the world was a nation
plunged into such deep grief by the death of its niler.
Strong men met in the streets and wept in speechless
anguish. It is not too much to say that a nation was
in tears. His was a life which will fitly become a
model. His name as the savior of his country will
live with that of Washington s, its father; hiscouritr>'-
mcn being unable to decide which is the greater.
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S£ ^ENTEENTH PRES/BEiVT.
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NDREW JOHNSON, seven-
teenth President of the United
States. The e;irly life of
Andrew Johnson contains but
the record of ix>verty, destitu-
tion and friendlessness. He
was lx)rn December 29, 1808,
in Raleigh, N. C. His parents,
belonging to the class of the
''\)oox whites '* of the South, were
in such circumstances, that they
could not confer even the slight-
their child. When Andrew was five
years of age, his father accidentally
lost his life while heiorically endeavoring to save a
friend from drowning. Until ten years of age, Andrew
was a ragged boy about the streets, supported by the
labor o{ his mother, who obtained her living with
her own hands.
He then, having never attended a school one day,
and being unable either to read or write, was ap-
prenticed to a tailor in his native town. A gentleman
was in the habit of going to the tailor's shop occasion-
ally, and reading to the boys at work there. He often
read from the speeches of distinguished British slates-
men. Andrew, who was endowed with a mind of more
than ordinary native ability, became much interested
in these speeches ; his ambition was roused, and he
was inspired with a strong desire to learn to read.
He accordingly applied himself to the alphabet, and
with the assistance of some of his fellow- workmen,
learned his letters. He then called upon the gentle-
man to borrow the book of speeches. The owner,
pleased with his zeal, not only gave him the book,
but assisted him in learning to combine the letters
into words. Under such difficulties he pressed on-
ward laboriously, spending usually ten or twelve hours
at work in the shop, and then robbing himself of rest
and recreation to devote such time as he could to
He went to Tennessee in 1826, and located at
Greenville, where he married a young lady who pos-
sessed some education. Under her instrucrions he
learned to write and cipher. He became prominent
in the village debating society, and a favorite with
the students of Greenville College. In 1828, he or-
ganized a working man*s party, which elected him
alderman, and in 1830 elected him mayor, which
position he held three years.
He now began to take a lively interest in political
affairs ; identifying himself with the working-classes,
to which he belonged. In 1835, he was elected a
member of the House of RepresentaUves of Tennes-
see. He was then just twenty-seven years of age.
He became a very active member of the legislature,
gave his adhesion to the Democratic party, and in
1H40 '* stumped the State,** advocating Martin Van
Buren's claims to the Presidency, in opposition to those
of Gen. Harrison. In this campaign he acquired much
readiness as a sf)eaker, and extended and increased
his reputation.
In 1841, he was elected State Senator; in 1843, he
was elected a member of Congress, and by successive
elections, held that important post for ten years. In
1853, he was elected Governor of Tennessee, and
was re-elected in 1855. In all these resi)onsible posi-
tions, he discharged his duties with distinguished abil-
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ANDREW JOHNSON.
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ity, and proved himself the warm friend of the work-
ing classes. In 1857, Mr. Johnson was elected
United States Senator.
the annexation of Texas, stating however, as his
reason, that he thought this annexation would prob-
ably prove " to be the gateway out of which the sable
sons of Africa are to pass from bondage to freedom,
and become merged in a population congenial to
themselves." In 1850, he also supported the com-
promise measures, the two essential features of which
were, that the white people of the Territories should
be permitted to decide for themselves whether they
would enslave the colored people or not, and that
South persons who attempted to escape from slavery.
Mr. Johnson was never ashamed of his lowly origin :
on the contrary, he often took pride in avowing that
he owed his distinction to his own exertions. " Sir,"
said he on the floor of the Senate, " I do not forget
that I am a mechanic ; neither do I forget that Adam
was a tailor and sewed fig-leaves, and that our Sav-
ior was the son of a carpenter."
In the Charleston- Baltimore convention of i860, he
was the choice of the Tennessee Democrats for the
Presidency. In 1861, when the purjwse of the South-
ern Democracy became apparent, he took a decided
stand in favor of the Union, and held that " slavery
must be held subordinate to the Union at whatever
cost." He returned to Tennessee, and repeatedly
imperiled his own life to protect the Unionists of
Tennesee. Tennessee having seceded from the
Union, President Lincoln, on March 4th, 1862, ap-
pointed him Military Governor of the State, and he
established the most stringent military rule. His
numerous proclamations attracted wide attention. In
1864, he was elected Vice-President of the United
States, and upon the death of Mr. Lincoln, April 15,
1865, became President. In a speech two days later
he said, " The American people must be taught, if
they do not already feel, that treason is a crime and
must be punished ; that the Government will not
always bear with its enemies ; that it is strong not
only to protect, but to punish. * * The people
must understand that it (treason) is the blackest of
crimes, and will surely be punished." Yet his whole
administration, the history of which is so well known,
was in utter inconsistency with, and the most violent
opposition to, the principles laid down in that speech.
In his loose policy of reconstruction and general
amnesty, he was opposed by Congress ; and he char-
acterized Congress as a new rebellion, and lawlessly
defied it, in everything possible, to the utmost. In
the beginning of 1868, on account of "high crimes
and misdemeanors,** the principal of which was the
removal of Secretary Stanton, in violation of the Ten-
ure of Office Act, articles of impeachment were pre-
ferred against him, and the trial began March 2y
It was very tedious, continuing for nearly three
months. A test article of the impeachment was at
length submitted to the court for its action. It was
certain that as the court voted upon that article so
would it voteui3on all. Thirty-four voices pronounced
the President guilty. As a two-thirds vote was neces-
sary to his condemnation, he was pronounced ac-
quitted, notwithstanding the great majority against
him. The change of one vote from the no( guilty
side would have sustained the imi^eachment.
The President, for the remainder of his term, was
but little regarded. He continued, though im potently,
his conflict with Congress. His own party did not
think it expedient to renominate him for the Presi-
dency. The Nation rallied, with enthusiasm unpar-
alleled since the days of Washington, around the name
of Gen. Grant. Andrew Johnson was forgotten.
The bullet of the assassin introduced him to the
President's chair. Notwithstanding this, never was
there presented to a man a better opportunity to im-
mortalize his name, and to win the gratitude of a
nation. He failed utterly. He retired to his home
in Greenville, Tenn., taking no very active part in
politics until •187 5. On Jan. 26, after an exciting
struggle, he was chosen by the Legislature of Ten-
nessee, United States Senator in the forty-fourth Con-
gress, and took his seat in that body, at the special
session convened by President Grant, on the 5th of
March. On the 27th of July, 1875; ^^^ ex-President
made a visit to his daughter's home, near Carter
Station, Tenn. When he started on his journey, he was
apparently in his usual vigorous health, but on reach-
ing the residence of his child the following day, was
stricken with paralysis, rendering him unconscious.
He rallied occasionally, but finally passed away at
2 A.M., July 31, aged sixty-seven years. His fun-
eral was attended at Geenville, on the 3d of August,
with every demonstration of respect.
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EIGHTEENTH PRESIDENT.
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V
LYSSES S. GRANT, the
eighteenth President of the
^United States, was born on
the 29th of April, 1822, of
Christian parents, in a humble
home, at Point Pleasant, on the
banks of the Ohio. Shortly after
his father moved to George-
town. Brown Co., O. In this re-
mote frontier hamlet, Ulysses
cation. At the age of seven-
teen, in the year 1839, he entered
Point. Here he was regarded as a
solid, sensible young man of fair abilities, and of
sturdy, honest character. He took respectable rank
middle in his class, and was sent as lieutenant of in-
fantry to one of the distant military posts in the Mis-
souri Territory. Two years he past in these dreary
solitudes, watching the vagabond and exasperating
Indians.
The war with Mexico came. Lieut. Grant was
sent with his regiment to Corpus Christi. His first
battle was at Palo Alto. There was no chance here
for the exhibirion of either skill or heroism, nor at
Resacade la Pal ma, his second battle. At the battle
of Monterey, his third engagement, it is said that
he performed a signal service of daring and skillful
munition. A messenger must be sent for more, along
a route exposed to the bullets of the foe. Lieut.
Grant, adopting an expedient learned of the Indians,
grasped the mane of his horse, and hanging upon one
side of the animal, ran the gauntlet in entire safety.
From Monterey he was sent, with the fourth infantry,
to aid Gen. Scott, at the siege of Vera Cruz. In
preparation for the march to the city of Mexico, he
was appointed quartermaster of his regiment. At the
battle of Molino del Rey, he was promoted to a
first lieutenancy, and was brevetted captain at Cha-
pultepec.
At the close of the Mexican War, Capt. Grant re-
turned with his regiment to New York, and was again
sent to one of the military posts on the frontier. The
discovery of gold in California causing an immense
tide of emigration to flow to the Pacific shores, Capt.
Grant was sent with a battalion to Fort Dallas, in
Oregon, for the protection of the interests of the im-
migrants. Life was wearisome in those wilds. Capt.
Grant resigned his commission and returned to the
States ; and having married, entered upon the cultiva-
tion of a small farm near St. Louis, Mo. He had but
little skill as a farmer. Finding his toil not re-
munerative, he turned to mercantile life, entering into
the leather business, with a younger brother, at Ga-
lena, 111. This was in the year i860. As the tidings
of the rebels firing on Fort Sumpter reached the ears
of Capt. Grant in his counting-room, he said, —
"Uncle Sam has educated me for the army; though
I have served him through one war, I do not feel that
I have yet repaid the debt. I am still ready to discharge
my obligations. I shall therefore buckle on my sword
and see Uncle Sam through this war too."
He went into the streets, raised a company of vol-
unteers, and led them as their captain to Springfield,
the capital of the Stale, where their services were
offered to Gov. Yates. The Governor, impressed by
the zeal and straightforward executive ability of- Capt.
Grant, gave him a desk in his office, to assist in the
volunteer organization that was being formed in the
State in behalf of the Government. On the 15th of
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i;'$(>t^^ <-^nDi^:iiii^>r ULYSSES S. GRANT. June, 1 86 1, Capt. Grant received a commission as Colonel of the Twenty-first Regiment of Illinois Vol- unteers. His merits as a West Point graduate, who had served for 15 years in the regular army, were such that he was soon promoted to the rank of Brigadier- General and was placed in command at Cairo. The rebels raised their banner at Paducah, near the mouth of the Tennessee River. Scarcely had its folds ap- peared in the breeze ere Gen. Grant was there. The rebels fled. Their banner fell, and the star and stripes were unfurled in its stead. He entered the service with great determination and immediately began active duty. This was the be- ginning, and until the surrender of Lee at Richmond he was ever pushing the enemy with great vigor and effectiveness. At Belmont, a few days later, he sur- prised and routed the rebels, then at Fort Henry won another victory. Then came the brilliant fight at Fort Donelson. The nation was electrified by the victory, and the brave leader of the boys in blue was immediately made a Major-General, and the military' district of Tennessee was assigned to him. Like all great captains, Gen. Grant knew well how to secure the results of victory. He immediately pushed on to the enemies* lines. Then came the terrible battles of Pittsburg Landing, Corinth, and the siege of Vicksburg, where Gen. Pemberton made an unconditional surrender of the city with over thirty thousand men and one-hundred and seventy-two can- non. The fall of Vicksburg was by far the most severe blow which the rebels had thus far encountered, and opened up the Mississippi from Cairo to the Gulf. Gen. Grant was next ordered to co-operate with Gen. Banks in a movement upon Texas, and pro- ceeded to New Orleans, where he was thrown from his horse, and received severe injuries, from which he was laid up for months. He then rushed to the aid of Gens. Rosecrans and Thomas at Chattanooga, and by a wonderful series of strategic and tactical meas- ures put the Union army in fighting condition. Then followed the bloody battles at Chattanooga, Lookout Mountain and Missionary Ridge, in which the rebels were routed with great loss. This won for him un- bounded praise in the North. On the 4th of Febru- ary, 1864, Congress revived the grade of lieutenant- general, and the rank was conferred on Gen. Grant. He repaired to Washington to receive his credentials and enter upon the duties of his new office. Gen. Grant decided as soon as he took charge 4 4 the army to concentrate the widely-dispersed National troops for an attack upon Richmond, the nominal capital of the Rebellion, and endeavor there to de- stroy the rebel armies which would be promptly as- sembled from all quarters for its defence. The whole continent seemed to tremble under the tramp of these majestic armies, rushing to the decisive battle field. Steamers were crowded with troops. Railway trains were burdened with closely packed thousands. His plans were comprehensive and involved a series of campaigns, which were executed with remarkable en- |^ ergy and ability, and were consummated at the sur- k render of Lee, April 9, 1865. The war was ended. The Union was saved. The almost unanimous voice of the Nation declared Gen. Grant to be the most prominent instrument in its sal- vation. The eminent services he had thus rendered the country brought him conspicuously forward as the Republican candidate for the Presidential chair. At the Republican Convention held at Chicago, May 21, 1868, he was unanimously nominated for the Presidency, and at the autumn election received a majority of the popular vote, and 214 out of 294 electoral votes. The National Convention of the Republican party which met at Philadelphia on the 5 th of June, 1872, placed Gen. Grant in nomination for a second term by a unanimous vote. The selecrion was emphati- cally indorsed by the people five months later, 292 electoral votes being cast for him. Soon after the close of his second term, Gen. Grant started upon his famous trip around the world. He visited almost every country of the civilized world, and was everywhere received with such ovations and demonstrations of respect and honor, private as well as public and official, as were never before bestowed upon any citizen of the United States. It is not too much to say that his modest, courteous, and dignified demeanor in the presence of the most dis- tinguished men in the different nations in the world, reflected honor upon the Republic which he so long and so faithfully served. The country felt a great pride in his reception. Upon his arrival in San Fran- cisco, Sept. 20, 1879, the city authorities gave him a fine reception. After lingering in the Golden State for a while, he began his tour through the States, which extended North and South, everywhere mark- ed by great acclamation and splendid ovations. c~ i *< > <l mA^^^^ ^^^^^^>^;7lm .^ rJ<inii^i]ii;i>-^ .^xf^Xjrr;::. r^X Digitized by Google /<^^ / Digitized by Google ^-<'-.-v- ^tt/XBaJ^vis T 4>HD^Dni'> T" r^^"^ J Y ^ NINETEENTH PRESIDENT. '^r^ ^V^ 91 I ..^-a ^ib$<-«-
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1
UTHERFORD B. HAYES,
the nineteenth President of
the United States, was bom in
Delaware, O., Oct. 4, 1822, al-
most three months after the
death of his father, Rutherford
Hayes. His ancestry on both
the paternal and maternal sides,
was of the most honorable char-
acter. It can be traced, it is said,
as far back as 1 280, when Hayes and
Rutherford were two Scottish chief-
tains, fighting side by side with
Baliol, William Wallace and Robert
Bruce. Both families belonged to the
nobility, owned extensive estates,
and had a large following. Misfor-
tune overtaking the family, George Hayes left Scot-
land in 1680, and settled in Windsor, Conn. His son
George was bom in Windsor, and remained there
during his life. Daniel Hayes, son of the latter, mar-
ried Sarah Lee, and lived from the time of his mar-
riage until his death in Simsbury, Conn. Ezekiel,
son of Daniel, was bom in 1724, and was a manufac-
turer of scythes at Bradford, Conn. Rutherford Hayes,
son of Ezekiel and grandfather of President Hayes, was
bom in New Haven, in August, 1756. He was a farmer,
blacksmith and tavern-keeper. He emigrated to
Vermont at an unknown date, settling in Brattleboro,
where he established a hotel. Here his son Ruth-
erford Hayes, the father of President Hayes, was
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born. He was married, in September, 18 13, to Sophia
Birchard, of Wilmington, Vt., whose ancestors emi-
grated thither from Connecticut, they having been ^
among the wealthiest and best famlies of Norwich.
Her ancestry on the male side are traced back to
1635, to John Birchard, one of the principal founders
of Norwich. Both of her grandfathers were soldiers
in the Revolutionary War.
The father of President Hayes was an industrious,
frugal and opened-hearted man. He was of a me-
chanical turn, and could mend a plow, knit a stock-
ing, or do almost anything else that he choose to
undertake. He was a member of the Church, active
in all the benevolent enterprises of the town, and con-
ducted his business on Christian principles. After
the close of the war of 181 2, for reasons inexplicable
to his neighbors, he resolved to emigrate to Ohio.
The joumey from Vermont to Ohio in that day,
when there were no canals, steamers, nor railways,
was a very serious affair. A tour of inspection was
first made, occupying four months. Mr. Hayes deter-
mined to move to Delaware, where the family arrived
in 1817. He died July 22, 1822, a victim of malarial
fever, less than three months before the birth of the
son, of whom we now write. Mrs. Hayes, in her sore be-
reavement, found the support she so much needed in
her brother Sard is, who had been a member of the
household from the day of its departure from Ver-
some time before as an act of charity.
Mrs. Hayes at this period was very weak, and the
PVJ)$«€^^ 7^>ll!l^lllli^ ^^c^ .S5^^^ Digitized by VjOOQlC 9* \,- - /•v ■7<:il3;l-".^j^j>v RUTHERFORD B. HAYES. A :^^y V < subject of this sketch was so feeble at birth that he was not expected to live beyond a month or two at most. As the months went by he grew weaker and weaker, so that the neighlx>rs were in the habit of in- <}uiring from time to lime " if Mrs. Hayes* baby died last nights" On one occasion a neighbor, who was on familiar tenns with the family, after alluding to the boy's big head, and the mother's assiduous care of him, said in a bantering way, ** That's right ! Stick to him. You have got him along so far, and I shouldn't wonder if he would really come to something yet." •* You need not laugh, said Mrs. Haves. " You wait and see. You can't tell but I shall make him President of the United States yet." The boy lived, in spite of the universal predictions of his speedy death; and when, in 1825, his older brother was drowned, he became, if possible, still dearer to his mother. The boy was seven years old before he went to school. His education, however, was not neglected. He probably learned as much from his mother and sister as he would have done at school. His sports were almost wholly within doors, his playmates being his sister and her associates. These circumstances tended, no doubt, to foster that gentleness of dispo- sition, and that delicate consideration for the feelings of others, which are marked traits of his character. His uncle Sardis Birchard took the deei>est interest in his education ; and as the l)oy*s health had ini- piDved, and he was making good progress in his studies, he proposed to send him to college. His pre- paration commenced with a tutor at home; but he was afterwards sent for one year to a professor in the Wesleyan University, in Middletown, Conn. He en- tered Kenyon College in 1838, at the age of sixteen, and was graduated at the head of his class in 1842. Immediately after his graduation he began the study of law in the office of Thomas Sparrow, Esq., in Columbus. Finding his opportunities for study in Columbus somewhat limited, he determined to enter the Law School at C'ambridge, Mass., where Vie re- mained two years. In 1845, after graduatmg at the Law School, he was admitted to the bar at Marietta, Ohio, and shortly afterward went into practice as an attorney-at-law with Ralph P. Buckland, of Fremont. Here he re- mained three years, acquiring but a limited practice, and apparently unambitious of distinction in his pro- fession. In 1849 he moved to Cincmnati, where his ambi- tion found a new stimulus. For several years, how- ever, his progress was slow. Two events, occurring at this period, had a ix)werful influence uix)n his subse- quent life. One of these was his marrage with Miss Lucy Ware Webb, daughter of Dr. James Webb, of Chilicothe; the other was his introduction to the Cin- cinnati Literary Club, a body embracing among its members such men as Chief Justice Salmon P.Chase, Gen. John Pope, Gov. Edward F. Noyes, and many others hardly less distinguished in after life. The marriage was a fortunate one in ever)- respect, as ever> body knows. Not one of all the wives of our Presidents was more universally admired, reverenced and beloved than was Mrs. Hayes, and no one did more than she to reflect honor uix>n American woman- hood. The Literary Club brought Mr. Hayes into constant association with young men of high char- acter and noble aims, and lured him to display the (Qualities so long hidden by his bashfulness and modesty. In 1856 he was nominated to the ofl[ice of Judge of the Court of Common Pleas; but he declined to ac- cept the nomination. Two years later, the office of city solicitor becoming vacant, the City Council elected him for the unexpired term. In 1 86 1, when the Rebellion broke out, he was at the zenith of his professional life. His rank at the bar was among the the first But the news of the attack on Fort Sumpter found him eager to take up arms for the defense of his country. His military record was bright and illustrious. In C>ctol)er, 186 1, he was made Lieutenant-Colonel, and in August, 1862, promoted Colonel of the 79th Ohio regiment, but he refused to leave his old comrades and go among strangers. Subsequently, however, he was made Colonel of his old regiment At the battle of South Mountain he received a wound, and while faint and bleeding displayed courage and fortitude that won admiration from all. Col. Hayes was detached from his regiment, after his recovery, to act as Brigadier-General, and placed in command of the celebrated Kanawha division, and for gallant and meritorious services in the battles of Winchester, Fisher's Hill and Cedar Creek, he was promoted Brigadier-General. He was also brevettcd Major-General,*Hbr gallant and distirguished ser\ices during the campaigns of 1864, in West Virginia." In the course of his arduous services, four horses were shot from under him, and he was wounded four times. In 1864, Gen. Hayes was elected to Congress, from the Second Ohio District, which had long been Dem- ocratic. He was not present during the campaign, and after his election was importuned to resign his commission in the amiy ; but he finally declared, ** I shall never come to Washington until I can come by the way of Richmond." He was re-elected in 1866. In 1867, Gen Hayes was elected Governor of Ohio, over Hon. Allen G. Thurman, a popular Democrat. In 1869 was re-elected over George H. Pendleton. He was elected Governor for the third term in 1875. In 1876 he was the standard bearer of the Repub- lican Party in the Presidential contest, and after a hard long contest was chosen President, and was in auf;urated Monday, March 5, 1875. He served his full term, not, however, with sarisfacrion to his party, but his administration was an average one y V •.^^*: -K-na:<-i]n;>^ ^7y> Digitized by Google i Digitized by Google 4^llll^lll]^>r /- TWENTIETH PRESIDENT *f^'S ^^xn^^^^^ 1 AMES A. GARFIELD, twen- tieth President of the United States, was born Nov. 19, 1 83 1, in the woods of Orange, Cuyahoga Co., O His par- ents were Abram and Eliza (Ballou) Garfield, both of New England ancestry and from fami- lies well known in the early his- tory of that section of our coun- try, but had moved to the Western Reserve, in Ohio, early in its settle- ment. The house in which James A. was l>orn was not unlike tht? houses of f poor Ohio farmers of that day. It was about 20 x 30 feet, built of logs, with the spaces be- twecn the logs filled with clay. His father was a hard working farmer, and he soon had his fields cleared, an orchard planted, and a log barn built. The household comprised the father and mother and their four children — Mehetabel, Thomas, Mary and James. In May, 1823, the father, from a cold con- tracted in helping to put out a forest fire, died. At this time James was about eighteen months old, and Thomas about ten years old. No one, perhaps, can tell how much James was indebted to his biother s toil and self-sacrifice during the twenty years suc- ceeding his fathers death, but undoubtedly very much. He now lives in Michigan, and the two sis- ters live in Solon, O., near their birthplace. The early educational advantages young Garfield enjoyed were very limited, yet he made the most of them. He labored at farm work for others, did car- penter work, chopped wood, or did anything that would bring in a few dollars to aid his widowed mother in her struggles to keep the little family to- gether. Nor was Gen. Garfield ever ashamed of his origin, and he never forgot the friends of his strug- gling childhood, youth and manhood, neither did they ever forget him. When in the highest seats of honor, the humblest fjiend of his boyhood was as kindly greeted as ever. The jxxjrest laborer was sure of the sympathy of one who had known all the bitterness of want and the sweetness of bread earned by the sweat of the brow. He was ever the simple, plain, modest gentleman. . The highest ambition of young Garfield until he was about sixteen years old was to be a captain of a vessel on Lake Erie. He was anxious to go aboard a vessel, which his mother strongly opposed. She finally consented to his going to Cleveland, with the understanding, however, that he should try to obtain some other kind of employment. He walked all the way to Cleveland. This was his first visit to the city. After making maifey applications for work, and trying to get aboard a lake vessel, and not meeting with success, he engaged as a driver for his cousin, Amos Letcher, on the Ohio & Pennsylvania Canal. He re- mained at this work but a short time when he went home, and attended the seminary at Chester for about three years, when he entered Hiram and the Eclectic Institute, teaching a few terms of school in the meantime, and doing other work. This school was started by the Disciples of Christ in 1850, of which church he was then a inember. He became janitor and bell-ringer in order to help pay his way. He then became both teacher and pupil. He soon ** exhausted Hiram " and needed more ; hence, in the fall of 1854, he entered Williams College, from which he graduated in 1856, taking one of the highest hon- ors of his class. He afterwards returned to Hiram College as its President. As above stated, he early united with the Christian or Diciples Church at Hiram, and was ever after a devoted, zealous mem- ber, often preaching in its pulpit and places where he happened to be. Dr. Noah Porter, President of Yale College, says of him in reference to his religion : f < c^: ( ^ ^ A'><^fV ^^•71. <-^i]!ir4Diif> rNA^:- ^^-'T^iJ^ iJ--. -'J i^oogle Digitized by ^ 96 >5 > '5) W> ■I i JAMES A. GARFIELD. ">«^i«'^ r C ** President Garfield was more than a man of strong moral and religious conrictbns. His whole history, from boyhood to the last, shows that duty to man and to God, and devotion to Christ and life and faith and spiritual commission were controlling springs of his being, and to a more than usual degree. In my judgment there is no more interesting feature of his character than his loyal allegiance to the body of Christians in which he was trained, and the fervent sympathy which he ever showed in their Christun communion. Not many of the few 'wise and mighty and noble who are called ' show a similar loyalty to the less stately and cultured Christian comnmnions in which they have been reared. Too often it is true that as they step upward in social and political sig- nificance they step upward from one degree to another in some of the many types of fashionable Christianity. President Garfield adhered to the church of his mother, the church in which he was trained, and in which he served as a pillar and an evangelist, and yet with the largest and most unsec- tarian charity for all *who love our Lord in sincerity.*" Mr. Garfield was united in marriage with Miss Lucretia Rudolph, Nov. ii, rSsS, who proved herself worthy as the wife of one whom all the world loved and mourned. To them were born seven children, five of whom are still living, four boys and one girl. Mr. Garfield made his first political speeches in 1856, in Hiram and the neighboring villages, and three years later he began to speak at county mass-meet- ings, and became the favorite speaker wherever he was. During this year he was elected to the Ohio Senate. He also began to study law at Cleveland, and in 1861 was admitted to the bar. The great Rebellion broke out in the early part of this year, and Mr. Garfield at once resolved to fight as he had talked, and enlisted to defend the OTd flag. He re- ceived his commission as Lieut. -Colonel of the Forty- second Regiment of Ohio Volunteer Infantry, Aug. 14, 1861. He was immediately put into active ser- vice, and before he had ever seen a gun fired in action, was placed in command of four regiments of infantry and eight companies of cavalnr, charged with the work of driving out of his native State the officer (Humphrey Marshall) reputed to be the ablest of those, not educated to war whom Kentucky had given to the Rebellion. This work was bravely and speed- ily accomplished, although against great odds. Pres- ident Lincoln, on his success commissioned him Brigadier-General, Jan. 10, 1862; and as "he had been the youngest man in the Ohio Senate two years before, so now he was the youngest General in the army.** He was with Gen. Buell s army at Shiloh, in its operations around Corinth and its march through Alabama. He was then detailed as a member of the General Court-Martial for the trial of Gen. Fitz-John Porter. He was then ordered to report to Gen. Rose- crans, and was assigned to the "Chief of Staff." The military history of Gen. Garfield closed with ^-■j-^* 'V^^^f?- ^^^ft^ V <^tltl his brilliant services at Chickamauga, where he won the stars 01 the Major-General. Without an effort on his part Gen. Garfield was elected to Congress in the fall of 1862 from the Nineteenth District of Ohio. This section of Ohio had been represented in Congress for sixty years mainly by two men — Elisha Whittlesey and Joshua R. Giddin^. It was not without a struggle that he resigned his place in the army. At the time he en- tered Congress he was the youngest member in that body. There he remamed by successive re- elections until he was elected President in 1880. Of his labors in Congress Senator Hoar says : " Since the year 1864 you cannot think of a question which has been debated in Congress, or discussed before a tribunel of the American people, in regard to which you will not find, if you wish instruction, the argu- ment on one side stated, in almost every instance belter than by anybody else, in some speech made in the House of Representatives or on the hustings by Mr. Garfield." Upon Jan. 14, 1880, Gen. Garfield was elected to the U. S. Senate, and on the eighth of June,«of the same year, was nominated as the candidate of his party for President at the great Chicago Convention. He was elected in the following November, and on March 4, 1881, was inaugurated. Probably no ad- ministration ever opened Us existence under brighter auspices than that of President Garfield, and every day it grew in favo.* with the people, and by the first of July he had completed all the initiatory and pre- liminary work of his administration and was prepar- ing to leave the city to meet his friends at Williams College. While on his way and at the depot, in com- pany with Secretary Blaine, a man stepped behind him, drew a revolver, and fired directly at his back. The President tottered and fell, and as he did so the assassin fired a second shot, the bullet cutting the left coat sleeve of his victim, but inflicting no further injury. It has been very truthfully said that this was " the shot that was heard round the world " Never before in the history of the Nation had anything oc- curred which so nearly froze the blood of the people for the moment, as this awful deed. He was smit- ten on the brightest, gladdest day of all his life, and was at the summit of his power and hojie. For eighty days, all during the hot months of July and Au^st, he lingered and suffered. He, however, remained master of himself till the last, and by his magnificent bearing was teaching the country and the world the noblest of human lessons — how to live grandly in the very clutch of death. Great in life, he was surpass- ingly great in death. He passed serenely away Sept. 19, 1883, at Elberon, N. J, on the very bank of the ocean, where he had been taken shortly previous. The worid wept at his death, as it never had done on the death of any other man who had ever lived upon it. The murderer was duly tried, found guilty and exe- cuted, in one year after he committed the foul deed. ^ .^^ Digitized by Google : .'«©^,:JV. ':mir ) Digitized by Google ';^/^')^t§^ ■:2^:sr ?VC>l]ll5^:llIlf>r^ J -:2^' ^ir;:^. <sr TWENTY^FIRST PRESIDENT. 99 ^ T HESTER A. ARTHUR, twenty-first President of the United States, was bom in Franklin County, Vermont, on theiifthof October, 1830, andis the oldest of a family of two sons and five daughters. His father was the Rev. Dr. William Arthur, a Baptist clergyman, who emigrated to this countr)* from the county Antrim, Ireland, in his 1 8th year, and died in 1875, in Newtonville, near Albany, after a long and successful ministry. Young Arthur was educated at Union College, Schenectady, where he excelled in all his studies. Af- ter his graduation he taught school in Vennont for two years, and at the expiration of that tim^came to New York, with J500 in his ^xxiket, and entered the office of ex- Judge E. D. Culver as student. After being admitted to the bar he formed a partnership with his intimate friend and room-mate, Henry D. Gardiner, with the intention of practicing in the West, and for three months they roamed about in the Western States in search of an eligible site, but in the end returned to New York, where they hung out their shingle, and entered upon a success- ful career almost from the start General Arthur soon afterward married the daughter of Lieutenant ■^^^i T QJ' ^\ 9 Hemdon, of the United States Navy, who was lost at sea. Congress voted a gold medal to his widow in recognition of the bravery he displayed on that occa- sion. Mrs. Arthur died shortly before Mr. Arthur's nomination to the Vice Presidency, leaving two children. Gen. Arthur obtained considerable legal celebrity in his first great case, the famous Lemmon suit, brought to recover possession of eight slaves who had been declared free by Judge Paine, of the Superior Court of New York City. It was in 1852 that Jon- athan Lemmon, of Virginia, went to New York with his slaves, intending to ship them to Texas, when they were discovered and freed. The Judge decided that they could not be held by the owner under the Fugitive Slave Law. A howl of rage went up from the South, and the Virginia Legislature authorized the Attorney General of that State to assist in an appeal. Wm. M. Evarts and Chester A. Arthur were employed to represent the People, and they won their case, which then went to the Supreme Court of the United States. Charles O'Conor here espoused the cause of the slave-holders, but he too was beaten by Messrs. Evarts and Arthur, and a long step was taken toward the emancipation of the black race. Another great service was rendered by General Arthur in the same cause in 1856. Lizzie Jennings, (o) a respectable colored woman, was put off a Fourth Avenue car with violence after she had paid her fare. General Arthur sued on her behalf, and secured a h) verdict of$500 damages. The next day the compa- ^
ny issued an order to admit colored persons to ride (^.
on their cars, and the other car companies quickly v^
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General Arthur was a delegate to the Convention
at Saratoga that foj^nded the Republican party.
Previous to the war he was Judge- Advocate of the
Second Brigade of the State of New York, and Gov-
ernor Morgan, of that State, appointed hira Engineer-
in-Chief of his staff. In 1861, he was made Inspec-
tor General, and soon afterward became Quartermas-
ter-General. In each of these offices he rendered
great service to the Government during the war. At
the end of Governor Morgan s term he resumed the
practice of the law, forming a partnership with Mr.
Ransom, and then Mr. Phelps, the District Attorney
of New York, was added to the firm. The legal prac-
tice of this well-known firm was very large and lucra-
tive, each of the gentlemen composing it were able
lawyers, and possessed a splendid local reputation, if
not indeed one of national extent.
He always took a leading part in State and city
politics. He was appointed Collector of the Port of
New York by President Grant, Nov. 21 1872, to suc-
ceed Thomas Murphy, and held the office until July,
20, 1878, when he was succeeded by Collector Merritt.
Mr. Arthur was nominated on the Presidential
ticket, with Gen. James A. Garfield, at the famous
National Republican Convention held at Chicago in
June, 1880. This was perhaps the greatest political
convention that ever assembled on the continent. It
was composed of the leading politicians of the Re-
publican party, all able men, and each stood firm and
fought vigorously and with signal tenacity for their
respective candidates that were before the conven-
tion for the nomination. Finally Gen. Garfield re-
ceived the nomination for President and Gen. Arthur
for Vice-President. The campaign which followed
was one of the most animated known in the history of
our country. Gen. Hancock, the standard-bearer of
the Democratic party, was a popular man, and his
party made a valiant fight for his election.
Finally the election came and the country's choice
was Garfield and Arthur. They were inaugurated
March 4, 1881, as President and Vice-President.
A few month? only had passed ere the newly chosen
President was the victim of the assassin s bullet. Then
came terrible weeks of suffering, — those moments of
anxious suspense, when the hearts of all civilized na-
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tionswere throbbing in unison, longing for the le- ^
covery of the noble, the good President The remaxk- /
able patience that he manifested during those hours ^
and weeks, and even months, of the most terrible suf-
fering man has often been called upon to endure, was
seemingly nK>re th<an human. It was certainly God-
like. During all this period of deepest anxiety Mr.
Arthur s every move was watched, and be it said to his
credit that his every acdon displayed only an earnest
desire that the suffering Garfield might recover, to
serve the remainder of the term he had so auspi- \
ciously begun. Not a selfish feeling was manifested \
in deed or look of this man, even though the most t
honored position in the world was at any moment
likely to fall to him.
At last God in his mercy relieved President Gar-
field from further suffering, and the world, as never
before in its history over the death of any other
man, wept at his bier. Then it became the duty of
the Vice President to assume the responsibilities of
the high office, and he took the oath in New Yorit,
Sept. 20, 1 88 1. The position was an embarrassing
one to him, made doubly so from the facts that all
eyes were on him, anxious to know what he would do,
what policy he would pursue, and who he would se-
greatly neglected during the President s long illness,
and many important measures were to be immediately
decided by him ; and srill farther to embarrass him he
did not fail to realize under what circumstances he
became President, and knew the feelings of many on
this point. Under these trying circumstances President
Arthur took the reins of the Government in his own
hands ; and, as embarrassing as were the condition of
affairs, he has happily surprised the Nation, acting so
justly, so wisely, so well, that but few have criticised
his administration. Should he continue during the
remainder of his term to pursue the wise policy he
has followed thus far, we believe President Arthur's
administration will go down in history as one of the
wisest and most satisfactory our country has ever
enjoyed. His highest ambition seems to be to do his
duty to the whole Nation, even to the sacrifice of his
warmest personal friends. \Vith the good of the
people at heart, and guided by the wisdom already
displayed, he will surprise his opponents, gratify his
friends, and bless the American Republic, during
the years he occupies the Presidential chair.
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GOVERNORS OF MICHIGAN.
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TEPHEN T. MASON, the
first Governor of Michigan, was
a son of Gen. John T. Mason,
of Kentucky, but was born in
Virginia, in 1812. At the age
of 19 he was appointed Secre-
tary of Michigan Territory, and
served in that capacity during the
Porter. Upon the death of Gov.
Porter, which occurred on the 6th of
July, 1834, Mr. Mason became Act-
ing Governor. In October, 1835, he
was elected Governor under the St ate
organization, and immediately en-
tered upon the performance of the
' duties of the office, although the
State was not yet admitted into the Union. After
the State was admitted into the Union, Governor
Mason was re-elected to the position, and served with
credit to himself and to the advantage of the State.
He died Jan. 4, 1843. The principal event during
Governor Mason *s official career, was that arising from
the disputed southern boundary of the State.
Michigan claimed for her southern boundary a line
running east across the peninsula from the extreme
southern point of Lake Michigan, extending through
Lake Erie, to the Pennsylvania line. This she
claimed as a vested right — a right accruing to her by
compact. This compact was the ordinance of 1787,
the parties to which were the original 13 States, and
the territory northwest of the Ohio ; and, by the suc-
cession of parties under statutory amendments to the
oidinance and laws of Congress — the United States on
the one part, and each Territory northwest of the
Ohio, as far as affected by their provisions, on the
other. Michigan, therefore, claimed it under the prior
grant, or assignation of boundary.
Ohio, qn the other hand, claimed that the ordinance
had been superseded by the Constitution of the
United States, and that Congress had a right to regu-
late the boundary. It was also claimed that the
Constitution of the State of Ohio having described- a
different line, and Congress having admitted the State
under that Constitution, without mentioning the sub-
ject of the line in dispute. Congress had thereby given
its consent to the line as laid down by the Constitu-
tion of Ohio. This claim was urged by Ohio at
some periods of the controversy, but at others she ap-
peared to regard the question unsettled, by the fact
that she insisted upon Congress taking action in re-
gard to the boundary. Accordingly, we find that, in
18 1 2, Congress authorized the Surveyor-General to
survey a line, agreeably to the sfct, to enable the people
of Ohio to form a Constitution and State government.
Owing to Indian hostilities, however, the line was not
run till 1 818. In 1820, the question in dispute
underwent a rigid examination by the Committee on
Public Lands. The claim of Ohio was strenuously
urged by her delegation, and as ably opposed by Mr.
Woodbridge, the then delegate from Michigan. The
result was that the committee decided unanimously
in favor of Michigan ; but, in the hurry of business,
no action was taken by Congress, and the question
remained open till Michigan organized her State gov-
ernment.
The Territory in dispute is about five miles in
width at the west end, and about eight miles in width
at the east end, and extends along the whole north-
ern line of Ohio, west of Lake Erie. The line claimed
by Michigan was known as the ** Fulton line," and
that claimed by Ohio was known as the" Harris line,"
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r\^.^''Vi'''"$^'^^l^" -SBS^^jSKl .^^-1 <.^ll!l^:iItlr1>A £:^ .555^^)^ #^^^^^' I ,^' m^ Digitized by Google /^ io6 .•>^<t>~- T<:DIl^:i]D>>v "^^THiT-V v > u i ^^^ s STEPHEN T. MASON. from the names of the surveyors. The territory was valuable for its rich agricultural lands ; but the chief value consisted in the fact that the harbor on the Maumee River, where now stands the flourishing city of Toledo, was included within its limits The town originally bore the name of Sw^n Creek, afterwards Port Lawrence, then Vestula, and then Toledo. In February, 1835, the Legislature of Ohio passed an act extending the jurisdiction of the State over the territory in question; erected townships and directed them to hold elections in April following. It also directed Governor Lucus to appoint three com- missioners to survey and re-mark the Harris line ; and named the first of April as the day to commence the survey. Acting Governor Mason, however, anticipated this action on the part of the Ohio Legislature, sent a special message to the Legislative Council, appris- ing it of Governor Lucas' message, and advised imme- diate action by that body to anticipate and counteract the proceedings of Ohio. Accordingly, on the 1 2th of February, the council passed an act making it a crimmal offence, punishable by a heavy fine, or im- prisonment, for any one to attempt to exercise any official functions, or accept any office within the juris- dicrion of Michigan, under or by virture of any au- thority not derived from the Territory, or the United States. On the 9th of March, Governor Mason wrote General Brown, then in command of the Michigan militia, directing him to hold himself in readiness to meet the enemy in the field in case any attempt was made on the part of Ohio to carry out the provisions of that act of the Legislature. On the 31st of March, Governor Lucus, with his commissioners, arrived at Perrysburgh, on their way to commence re-surveying the Harris line. He was accompanied by General Bell and staff, of the Ohio Militia, who proceeded to muster a volunteer force of about 600 men. This was soon accomplished, and the force fully armed and equipped. The force then went into camp at Fort Miami, to await the Governor s orders. In the meantime. Governor Mason, with General Brown and staff, had raised a force 800 to 1200 strong, and were in possession of Toledo. General Brown's Staff consisted of Captain Henry Smith, of Monroe, Inspector; Major J. J. UUman, of Con- stantine. Quartermaster; William E. Broadman, of Detroit, and Alpheus Felch,of Monroe, Aids-de- camp. When Governor Lucas observed the deter- mined bearing of the Michigan braves, and took note t ^^.m of their number, he found it convenient to content himself for a time with '* watching over the border." Several days were passed in this exhilarating employ- ^ mentf and just as Governor Lucas had made up his mind to do something rash, two commissioners ar- v,: rived from Washington on a mission of peace. They remonstrated with Gov. Lucus, and reminded him of the consequences to himself and his State if he per- sisted in his attempt to gain possession of the disputed territory by force. After several conferences with both governors, the commissioners submitted proposi- tions for their consideration. Governor Lucas at once accepted the propositions, ^ and disbanded his forces. Governor Mason, on the other hand, refused to accede to the arrangement, and declined to compromise the rights of his people by a surrender of possession and jurisdiction. When Gov- ernor Lucus disbanded his forces, however, Governor Mason partially followed suit, but sUll held himself in readiness to meet any emergency that might arise. Governor Lucus now supposed that his way was A clear, and that he could re-mark the Harris line with- ^ out being molested, and ordered the commissioners to proceed with their work. In the meantime. Governor Mason kept a watch- ful eye upon the proceedings. General Brown sent scouts through the woods to watch their movements, and report when operations were commenced. When the surveying party got within the county of Lena- wee, the under-sheriff of that county, armed with a warrant, and accompanied by a posse, suddenly made his appearance, and succeeded in arresUng a portion of the party. The rest, including the commissioners, took to their heels, and were soon beyond the dis- puted territory. They reached Perrysburgh the fol- lowing day in a highly demoralized condition, and reported they had been attacked by an overwhelm- ing force of Michigan malitia, under command of General Brown. This summary breaking up of the surveying party produced the most tremendous excitement throughout Ohio. Governor Lucas called an extra session of the Legislature. But little remains to be said in reference to the " war." The question continued for some time to agitate the minds of the opposing parties ; and the action of Congress was impatiently awaited. Michigan was admitted into the Union on the condition that she give to Ohio the disputed territory, and accept io return the Northern Peninsula, which she did. O i^ f ( i Digitized by Google 'Vj^^r^z^-t/^^^^^^yc? /Cv i Digitized by Google \ c<^x% 0*- <^:BD^nn^>r J •'^ Y SECOND GOVERNOR OF MICHIGAN. ILLIAM WOODBRIDGE, ^second Governor of Michigan, was born at Norwich, Conn., Aug. 20, 1780, and died at Detroit Oct. 20, i86i. He was of a family of three brothers and two sisters. His father, Dudley Woodbridge, removed to Marietta, Ohio, about 1 7 90. The life of Wm. Woodbridge, by Chas. Lauman, from which this sketch is largely com piled, mentions noth- ing concerning his early education beyond the fact that it was such as was afforded by the average school of the time, except a year with the French colonists at GalUpolts, where he acquired a knowledge of the French language. It should be borne in mind, however, that home education at that time was an indispensable feature in the training of the young. To this and and to a few studies well mastered, is due that strong mental discipline which has served as a basis for many of the grand intellects that have adorned and helped to make our National history. Mr. Woodbridge studied law at Marietta, having as a fellow student an inrimate personal friend, a young man subsequently distinguished, but known at that time simply as Lewis Cass. He graduated at the law school in Connecticut, after a course there of nearly three years, and began to practice at Marietta in 1 806. In June, 1 806, he married, at Hartford, Con- necticut, Juleanna, daughter of John Trumbell, a distinguished author and judge ; and author of the (i peom McFingal, which, during a dark period of the Revolution, wrought such a magic* change upon the spirits of the colonists. He was happy in his domes • tic relations until the death of Mrs. W., Feb. 2, 19, i860. Our written biographies necessarily speak more fully of men, because of their active participation in public affairs, but human actions are stamped upon the page of time and when the scroll shall be unrolled the influence of good women upon the history of the world will be read side by side with the deeds of men. How much success and renown in life many men owe to their wives is probably little known. Mrs. W. en- joyed the best means of early education that the country afforded, and her intellectual genius enabled her to improve her advantages. During her life, side by side with the highest type of domestic and social graces, she manifested a keen intellectuality that formed the crown of a faultless chaiacter. She was a natural poet, and wrote quite a large number of fine verses, some of which are preserved in a printed memorial essay written upon the occasion of her death. In this essay, it is said of her '*to contribute even in matters of minor importance, to elevate the reputation and add to the well being of her husband in the various stations he was called upon to fill, gave her the highest satisfaction " She was an invalid during the latter portion of her life, but was patient and cheerful to the end. In 1807, Mr. W. was chosen a representative to the General Assembly of Ohio, and in 1809 was elected to A^ the Senate, continuing a member by re-election until his removal from the State. He also held, by ap- pointthent, during the rime the office of Prosecuting Attorney for his county. He took a leading part in the Legislature, and in 181 2 drew up a declaration and 'Vi>^-^^'<K resolutions, which passed the two houses unaminously ^ Digitized by VjOOQlC <: -r- -X r i II > WILLIAM WOODBRIDGE. r/-, :: ■>;/ iy' / ^ •'A and attracted great attention, endorsing, in strongest and most emphatic terms, the war measures of Presi- dent Madison. During the period from 1804 to 18 14 the two law students, Woodbridge and Cass, had be- come widely separated. The latter was GovcTiK>r of the Territory of Michigan under the historic **(*ovemor and Judges" plan, with the mdisi)ensable rwjuisitc of a Secretary of the Terrilorry. This latter position was, in 18 1 4, without solicitation on his part, tendered to Mr. W. He accepted the position with some hesita- tion, and entered upon its duties as soon as he could make the necessary arrangements for leaving Ohio. The office of Secretary involved also the duties of collectorof customsatthe portof I>etroit, atwi during the frequent absences of the Governor, the dischargeof of his duties, also including those of Superintendent of Indian Affairs. Mr. W. officiated as (Governor for about two years out of the eight years that he held the office of Secretary I - nder the administration of "Gov- ernor and Judges," which the people of the Territory preferred for economical reasons, to continue some time after their numbers entitled them to a more popular representative system, they were allowed no delegate in Congress. Mr. W., as a sort of informal agent of the people, by correspondence and also by a visit to the National capital, so clearly set forth the demand for representation by a delegate, that an act was passedin Congress in 18 19 authorizing one to be chosen. Under this act Mr. W. was elected by the concurrence of all parties. His first action in Congress was to secure the passage of a bill recognizing and confirming the old French land titles in the Territory according to the terms of the treaty of peace with Great Britain at the close of the Revolution ; and another for the construction of a Government road through the "black swamps" from the Miami River to Detroit, thus open- ing a means of land transit between Ohio and Mich- igan. He was influential in securing the passage of bills for the construction of Government roads from Detroit to Chicago, and Detroit to Fort Gratiot, and for the improvement of La Plaisance Bay. The ex- pedition for the exploration of the country around Lake Superior and in the valley of the Upper Mis- sissippi, projected by Governor Cass, was set on foot by means of representations made to the head of the department by Mr. W. While in Congress he stren- uously maintained the ri^t of Michigan to the strip of territory now forming the northern boundary of Ohio, which formed the subject of such grave dispute between Ohio and Michigan at the time of the ad- mission of the latter into the Union. He served but one term as delegate to Congress, de- clining further service on account of personal and family considerations. Mr. VV. continued to discharge the duties of Secretary of the Territory up to the time its Government passed into the *'second grade.** In 1824, he was appointed one of a board of commissioners for adjusting private land claims in r. f, the Territory, and was engaged also in the practice of his profession, having the best law library in the Ter- ritory. In 1828, upon the recommendation of the Governor, Judges and others, he was appointed by the President, J. <^. Adams, to succeed Hon. James VVith- erell, who had resigned as a Judge of what is conven- tionally called the **Suprerae Court** of the Territory. This court was apparently a continuation of the Terri- torial Court, under the "first grade" or **(k)vemor and Judges" system. Although it was supreme in its ju- dicial functions within the Territory-, its powers aind dudes were of a very general character. In 1832, the term of his appointment as Judge ex- piring, President Jackson appointed a successor, it is supposed on politica] grounds, much to the disappoint- ment of the pubBc and the bar of the Territory. The partisan feeling of the time extended into the Terri- tory, and its people began to think of assuming the dignity of a State government. Party lines becom- ing very sharply drawn, he identified himself with the Whigs and was elected a member of the Conven- tion of 1835, which formed the first State Constitution. In 1837 he was elected amember of tFe State Senate. This sketch has purposely dealt somewhat in detail with what may be called Judge W*s. earlier career, because it is closely identified with the early his- tory of the State, and the development of its politi- cal system. Since the organization of the State Gov- ernment the history of Michigan is more familiar, and hence no review of Judge W s career as Governor and Senator will be attempted. He was elected Gov- ernor in 1839, under a popular impression that the affairs of the State had not been prudently adminis- tered by the Democrats. He served as Governor but ' little more than a year, when he was elected to the Senate of the United States. His term in the Senate practically closed his polit- ical life, although he was strongly urged by many prominent men for the WTiig nomination for Vice President in 1848. Soon after his appointment as Judge in 1828, Gov- ernor W. took up his residence on a tract of land which he owned in the township of Spring Wells, a short distance below what was then the corporate lim- its of Detroit, where he resided during the remainder of his life. Both in his public papers and private communications, Governor W. shows himself a mas- ter of language; he is fruitful in simile and illustra- tion, logical in arrangement, happy in the choice and treatment of topics, and terse and vigprous in expres- sion. Judge W. was a Congregationalist. His opinions on all subjects were decided; he was earnest and energetic, courteous and dignified, and at times ex- hibited a vein of fine humor that was the more at- tractive because not too often allowed to come to the surface. His letters and addresses show a deep a.nd earnest affection not only for his ancestral home, l>ut the home of liis adoption and for friends and family. ^ /: -:?!l. -^<;^[l!l:^;tli;>^ 'i\r;r\ -^4^>5^ci^l>r-,! Digitized by Google r Digitized by Google ^r^^«s^^> ^v<^tin^nii^> r GOVERNORS OF MICHIGAN. ■^J^^Hj^L ^ 113 ^ Y V V ) -^«ie ►-• ] ) » )»> tJOHN S. BARRY OHN STEWARD BARRY, I Governor of Michigan from Jan. 3, 1842, to Jan. 5, 1846, and from Jan. 7, 1850, to Jan. I, 1852, was born at Amherst, N. H., Jan. 29, 1802. His par- ents, John and Ellen (Steward) Barry, early removed to Rocking- ham, Vt., where he remained until he became of age, working on his father's farm, and pursuing his studies at the same time. He mar- ried Mary Kidder, of Grafton, Vt., and in 1824 went to Georgia, Vt,, where he had charge of an academy for two years, meanwhile studying law. He afterward practiced law in that State. While he was in Georgia he was for some time a member of the Governor s staff, with the title of Governor's Aid, and at a somewhat earlier period was Captain of a company of State militia. In 183 1 he removed to Michigan, and settled at White Pigeon, where he engaged in mercantile business with I. W. WiUard. Four years after, 1834, Mr. Barry removed to Con- r c stantine and continued his mercantile pursuits. He became Justice of the Peace at White Pigeon, Mich.i in 1831, and held the office until the year 1835. Mr. Barry's first public office was that of a member of the first constitutional convention, which assembled and framed the constitution upon which Michigan was admitted into the Union. He took an important and prominent part in the proceedings of that body, and showed himself to be a man of far more than ordinary ability. Upon Michigan being admitted into the Union, Mr. Barry was chosen State Senator, and so favorably were his associates impressed with his abilities at the first session of the Legislature that they looked to him as a party leader, and that he should head the State ticket at the- following election. Accordingly he re- ceived the nomination for Governor at the hands of his party assembled in convention. He was elected, and so popular was his administration that, in 1842, he was again elected. During these years Michigan was embarrassed by great financial diffi- culties, and it was through his wisdom and sound judg- ment that the State was finally placed upon a solid financial basis. During the first year of Gov. Barry s first term, the University at Ann ATlx)r was opened for the reception :V 4 ( 'Vir->§W''~ .,::s^ <.in!l^|]Dr> r:viup- 4^5^'^ifc' Digitized by Google if: ■A ^: f'-r f /I "4 ■>^^> >:v O ^V <•illIl>:llIl^.>r ,/is^f Cm- J :0 \ :^ V JOHN STEWARD BARRY. ^5 of students. The Michigan Central and Michigan Southern railroads were being rapidly constructed, and general progress was everywhere noticeable. In 1842, Uie number of pupils reported as attending the public schoob was nearly fifty-eight thousand. In 1843, ^ State land office was established at Marshall, which was invested with'tiie charge and disposition of all the lands belonging to the State. In 1844, the tax- able property of the State was imaod to be over twenty-eight millbns of dollars^ the tax being at the rate of two mills on the dollar. The expenses of the State were only seventy thousand dollars, while the income from the railroads was nearly three hundred thousand dollars. At this time the University of Michigan had become so prosperous that its income was ample to pay the interest on the University debt; and the amount of money which the State was able to loan the several progressing railroads was one hundred and twenty thousand dollars. Efforts were made to increase the efficiency of the common schools with good results In 1845, when Gov. Barry's sec- ond term expired, the population of the State was more than three hundred thousand. The constitution of the State forbade more than-two consecutive terms, but he was called upon to fill the position again in 1850 — the only instance of the kind in the history of the State. He was a member of the Territorial Legislature, of the Constitutional Conven- tion, and afterward of the State House of Represent- atives. During Mr. Barry's third term as Governor the Nor- mal School was established at Ypsilanti, which was endowed with lands and placed in charge of a board of educarion consisting of six persons. A new con- stitution for the government of the State was also adopted and the ** Great Railway Conspiracy Case " was tried. This grew out of a series of lawless acts which had been committed upon the property of the Michigan Central Railroad Company, along the line of their road, and finally the burning of the depot at Detroit, in 1850. At a setting of the grand jury of Wayne County, April 24, 185 1, 37 men of the 50 under arrest for this cnme were indicted. May 20, following, the accused parties appeared at the Circuit Court of Wayne, of which Warner Wing was resident judge. The Rail- road Company employed ten eminent lawyers, in- cluding David Stuart, John Van Arman, James A. Van Dyke, Jacob M. Howard, Alex, D, Fraser, Dan- iel Goodwin and William Gray. The defendants were represented by six members of the State bar, led by William H. Seward, of New York. The trial occupied four months, during which time the plaintiffs exam- ined 246 witnesses in 27 days, and the defendants 249 in 40 days. Mr. Van Dyke addressed the jury for the prosecution; William H. Seward for the defense. The great lawyer was convinced of the innocence % t: of his clients, nor did the verdict of that jury and the sentence of that judpe remove his firm belief thai his clients were the victims of purchased treachery, rather than so many sacrifices to justice. The verdict of ** guilty ** was rendered at 9 o'clock p. M., Sept. 25, 1851. On the 26th the prisoners were put forward to receive sentence, when many of them protested their entire iniK)cence, after which the pre- siding judge condemned 12 of the number to the fol- lowing terms of imprisonment, with hard labor, within the State's prison, situate in their county: Ammi Filley, ten years ; Orlando L. Williams, ten years; Aaron Mount, eight years ; Andrew J. Freeland, eight years; Eben Faniham, eight years; William Corvin, eight years; Richard Price, eight years; Evan Price, eight years; Lyman Champlin, five years; Willard W. Champlin, five years; Erastus Champlin, five years; Erastus Smith, five years. In 1840, Gov. Barry became deeply interested in the cultivation of the sugar beet, and visited Europe to obtain information in reference to its culture. He was twice Presidential Elector, and his last public service was that of a delegate to the National Democratic Convention held in Chicago in 1864. He was a man who, throughout life, maintained a high character for integrity and fidelity to the trusts bestowed upon him, whether of a public or a private ^ nature, and he is acknowledged by all to have been v one of the most efficient and popular Governors the ^ Slate has ever had. ^ Gov. Barry was a man of incorruptible integrity. Si His opinions, which he reached by the most thorough < investigation, he held tenaciously. His strong con- ( victions and outspoken honesty inade it impossible for him to take an undefined position when a principle was involved. His attachments and prejudices were strong, yet he was never accused of favoritism in his administration of public affairs. As a speaker he was not remarkable. Solidity, rather than brilliancy, char- acterized his oratory, which is described as argument- ^ ative and instructive, but cold, hard, and entirely wanting in rhetorical ornament. He was never elo- { quent, seldom humorous or sarcastic, and in manner rather awkward. Although Mr. Barry's educational advantages were so limited, he was a life-long student. He mastered both ancient and modem languages, and acquired a thorough knowledge of history. No man owed less to political intrigue as a means of gaining posi- tion. He was a true statesman, and gained public es- teem by his solid worth. His political connections were always with the Democratic party, and his opin- ions were usually extreme. Mr. Barry reUred to private life after the beginnin^^ of the ascendency of the Republican party, and. car- ried on his mercanrile business at Constantine. - He died Jan. 14, 1870, his wife's death having occurre<i a year previous, March 30, 1869. They left nochilciren. i DD^J^ -^^■^T^-^z::- -^f^^-T^fO^J^^^ Digitized by Google ^>ffeu\/*;:->: > '1. d/l^U^^ Digitized by Google t -^^ — erv^iti n SI nfi>^ ">a^%^-^^ -^^¥m^^\m:^ GOVERNORS OF MICHIGAN. 117 f y^ V^ '^ I ^f • X LPHEUS FELCH, the thiid Governor of Michigan, was ^bomin Limerick, Maine, Sep- tember 28, 1806. His grand- father, Abijah Felch, was a sol- dier in the Revolution ; and when a young man, having with others obtained a grant of land be- tween the Great and Little Ossipee Rivers, in Maine, moved to that re- gion when it was yet a wilderness. The' father of Mr. Felch embarked in mercantile life at Limerick. He was the first to engage in that business in that section, and continued it until his death. The death of the father, ■ followed within a year by the death of the mother, left the subject of this sketch, then three years old, to the care of relatives, and he found a home with his paternal grandfather, where he re- Tuained until his death. Mr Felch received his early education in the district school and a neighboring academy. In 182 1 he became a student at Phillips Exter Academy, and, subsequently, entered Bowdoin College, graduated with the class of 1827. He at once began the study of law and was admitted to practice at Bangor, Me., in 1830. He began the practice of his profession at Houlton, Me., where he remained until 1833. The severity of the climate impaired his health, never very good, and he found it necessary to seek a change of climate. He disposed of his library and started to seek a new home. His intention was to join his friend, Sargent S. Prentiss, at Vicksburg, Miss., but on his arrival at Cincinnati, Mr. Felch was attacked by cholera, and when he had recovered sufficiently to permit of his traveling, found that the danger of the disease was too great to permit a journey down the river. He therefore determined to come to Michi- gan. He first began to practice in this State at Mon- roe, where he continued until 1843, when he removed to Ann Arbor. He was elected to the State Legisla- ture in 1835, and continued a member of that body during the years 1836 and 1837. While he held this office, the general banking law of the State was enact- ed, and went into operation. After mature delibera- tion, he became convinced that the proposed system of banking could not prove beneficial to the public interests ; and that, instead of relieving the people from the pecuniary difficulties under which they were laboring, it would result in still further embarrass- ment. He, therefore, opposed the bill, and pointed out to the House the disasters which, in his opinion, were sure to follow its passage. The public mind, however, was so favorably impressed by the measure that no other member, in either branch of the Legisla- ture, raised a dissenting voice, and but two voted with him in opposition to the bill. Early in 1838, he was appointed one of the Bank Commissioners of the State, and held that office for moie than a year. Dur- ing this time, the new banking law had given birth to that numerous progeny known as "wild-cat" banks. Almost every village had its bank. The country was flooded with depressed "wild-cat" money. The ex- aminations of the Bank Commissioners brought to light frauds at every point, which were fearlessly re- c^ ^ ;^ -Q^ <> fi>-^ ^-?t^3^$@7Si^
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ported to the Legislature, and were followed by crim-
inal prosecutions of the guilty parties, and the closing
of many of their institutions. The duties of the of-
fice were most laborious, and in 1839 Mr. Felch re-
signed. The chartered right of almost every bank
had, in the meantime, been declared forfeited and
the law repealed. It was subsequently decided to
be constitutional by the Supreme Court of the State.
In the year 1842 Governor Felch was appointed
to the office of Auditor General of the State; but
after holding the office only a few weeks, was com-
missioned by the Governor as one of the Judges of the
Supreme Court, to fill a vacancy caused by the resig--
nation of Judge Fletcher. In January, 1843, he was
elected to the United States Senate for an unexpired
term. In 1845 he was elected Governor of Michigan,
and entered upon his duties at the commencement of
the next year. In 1847 he was elected a Senator
in Congress for six years ; and at once retired from
the office of Governor, by resignation, which took
effect March 4, r847, when bis Senatorial term com-
menced. While a member of the Senate he acted on
the Committee on Public Lands, and for four years
was its Chairman. He filled the honorable position
of Senator with becoming dignity, and with great
credit to the State of Michigan.
During Governor Felch *s administration the two
railroads belonging to the State were sold to private
corporations, — the Central for $2,000,000, and the Southern for$500,000. The exports of the State
amounted in 1846 to $4,647,608. The total capacity of vessels enrolled in the collection district at Detroit was 26,928 tons, the steam vessels having 8,400 and the sailing vessels 18,528 tons, the whole giving em- ployment to 18,000 seamen In 1847, there were 39 counties in the State, containing 435 townships ; and 275 of these townships were supplied with good libra- ries, containing an aggregate of 37,000 volumes. At the close of his Senatorial term, in March, 1853, Mr. Felch was appointed, by President Pierce, one of the Commissioners to adjust and settle the Spanish A % and Mexican land claims in California, under the V treaty of Gaudalupe Hidalgo, and an act of Congress % (>assed for that purpose. He went to California in *; May, 1853, and was made President of the Comrais- ^ sion. The duties of this office were of the most ira- ' portant and delicate character. The interest of the new State, and the fortunes of many of its citizens, both the native Mexican population and the recent American immigration ; the right of the Pueblos to their common lands, and of the Catholic Church to k the lands of the Missions, — the most valuable of the % r. Sute, — wereinvolved in the adjudications of this Com- mission. In March, 1856, their labors were brought to a close by the final disposition of all the claims which were presented. The record of their proceed- ings, — the testimony which was given in each case, and the decision of the Commissioners thereon, — consisting of some forty large volumes, was deposited in the Department of the Interior at Washington. In June of that year. Governor Felch returned to ^ Ann Arbor, where he has since been engaged piinci- =1 pally in legal business. Since his return he has ^ been nominated for Governor and also for U. S. Sen- -^ ator, and twice for Judge of the Supreme Court. But the Democratic party, to which he has always been attached, being in the minority, he failed of an elec- tion. In 1873 he withdrew from the active practice of law, and, with the exception of a tour in Europe, I in 1875 has since led a life of retirement at his home Vj in Ann Arbor. In 1877 the University of Michigan |: conferred upon him the degree of LL. D. For many years he was one of the Regents of Michigan University, and in the spring of 1879 was ap[x>inted Tappan Professor of Law in the same. Mr. Felch is the oldest surviving member of the Legislature from Monroe Co., the oldest and only surviving Bank Com- missioner of the State, the oldest surviving Auditor General of the State, the oldest surviving Governor of the State, the oldest surviving Judge of the Supreme Court of Michigan, and the oldest surviving United States Senator from the State of Michigan. / <^ crAl-^^HT^ ■•wr-, /71O. -.-*' ^^i]!i:^:ca^> Digitized by Google Digitized by Google '^;^ >^\5<sr -r^-t-^ J^ % GOVERNORS. n^^i ^ ^""§^1^ 121 ILLIAM L. GREENLY Governor of Michigan for the year 1847 , was bom at Hamil- ton, Madison Co., N. Y., Sept. 1 8, 1 8 1 3. He graduated at Un- ion College, Schenectady, in 1 83 1, studied law and was ad- mitted to the bar in 1834. In 1836, having removed to Michi- gan, he settled in Adrian, where he has since resided. The year following his arrival in Michigan he was elected State Senator and served in that capacity until 1839. In 1845 he was elected Lieut. Gov- ernor and became acting Governor by the resignation of Gov. Felch, who was elected to the United States Senate. The war with Mexico was brought f^ to a successful termination during Gov. Grecnly's administration. We regret to say that there are only few records extant of the action of Michigan troops / in the Mexican war. That many went there and fought well are points conceded ; but their names and v^ nativity arc hidden away in United States archives and where it is^ almost impossible to find ihem. The soldiers of this State deserve much of the credit of the memorable achievements of Co. K, 3d Dragoons, and Cos. A, E, and G of the U. S. Inf. The two former of these companies, recruited in this State, were reduced to one-third their original num- ber. In May, 1846, the Governor of Michigan was noti- fied by the War Department of the United States to enroll a regiment of volunteers, to be held in readi- ness for service whenever demanded. At his sum- mons 13 independent volunteer companies, 11 of infantry and two of cavalry, at once fell into line. Of the infantry four companies were from Detroit, bear- ing the honored names of Montgomery, Lafayette, Scott and Brady upon their banners. Of the re- mainder Monroe tendered two, Lenawee County three, St. Clair, Berrien and Hillsdale each one, and Wayne County an additional company. Of these alone the veteran Bradys were accepted and ordered into ser- vice. In addition to them ten companies, making the First Regiment of Michigan Volunteers, springing from various parts of the State, but embodying to a great degree the material of which the first volunteers was formed, were not called for until October follow- ing. This regiment was soon in readiness and pro- ceeded by orders from Government to the seat of war. 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HE HON. EPAPHRODI-
TUS RANSOM, the Seventh
Governor of Michigan, was a
native of Massachusetts. In
that State he received a col-
legiate education, studied law,
and was admitted to the bar.
the time of its admission to the
Union, he took up his residence
at Kalamazoo.
Mr. Ransom served with marked
ability for a number of years in the
State Legislature, and in 1837 he was appointed As-
sociate Justice of the Supreme Court. In 1843 he
was promoted to Chief Justice, w\jich office he re-
tained until 1845, when he resigned.
Shortly afterwards he became deeply interested in
the building of plank roads in the western portion of
the State, and in this business lost the greater portion
of the property which he had accumulated by years
of toil and industry.
Mr. Ransom became Governor of the State of
Michigan in the fall of 1847, and served during one
temi, performing the duties of the office in a truly
statesmanlike manner. He subsequently became
President of the Michigan Agricultural Society, in
which position he displayed the same ability that
shone forth so prominently in his acts as Governor.
He held the office of Regent of the Michigan Univer-
sity several times, and ever advocated a liberal policy
in its management.
Subsequently he was ap[X)inted receiver of the
land office in one of the districts in Kansas, by Pres-
ident Buchanan, to which State he had removed, and
where he died before the expiration of his term of
office.
We sum up the events and affairs of the State un-
der Gov. Ransom's administration as follows: The
Asylum for the Insane was establised, as also the
Asylum for the Deaf, Dumb and Blind. Both of
these institutes were liberally endowed with lands,
and each of them placed in charge of a board of five
trustees. The appropriation in 1849 for the deaf and
dumb and blind amounted to $81,500. On the first of March, 1848, the first telegraph line was com- pleted from New York to Detroit, and the first dis- patch transmitted on that day. The following figures show the progress in agriculture : The land reported as under cultivation in 1848 was 1,437,460 acres; of wheat there were produced 4,749,300 bushels; other grains, 8,197,767 bushels; wool, 1,645,756 pounds; maple sugar, 1,774,369 pounds; horses, 52,305; cat- tle, 210,268; swine, 152,541; sheep, 6ro,534; while the fiour mills numbered 228, and the lumber mills amounted to 730. 1847, an act was passed removing the Legislature from Detroit to Lansing, and tempo- rary buildings for the use of the Legislature were im- mediately erected, at a cost of$12,450.
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:<$V > ) t 'J S.V ! ! I T/ V r;::;^ W- .:.-j -;c ■»■ v»^*^ X--'^^*!?^ — -.-»^^ ■^<-^(]!];<^:gQv->a^ .;^./«Xi>V5^ Digitized by J, Google Digitized by Google ^iCi^ ^ '-*^-^ T7 ^^7mmm> GOVERNORS OF MICHIGAN. MSaiBd OBERT Mc CLELLAN 1), ^(iovernor of Michigan from Jan. I, 1852, to March 8,1853, was born at Grcencastle, Frank- vj^ lin Co., Penn., Aug. i» 1807. Among his ancestors were several officers of rank in the Revolution- ary war, and some of his family con- nections were distinguished in the war of 1812, and that with Mexico. Fiis father was an eminent physiciau and surgeon who studied under l>r. Benj. Rush, of Philadelphia, and practiced his profession successfully until six months before his death, at the age of 84 years. Although Mr. family had been in good circum- stances, when he was 17 years old he was thrown upon his own resources. After taking the usual pre- liminary studies, and teaching school to obtain the means, he entered Dickinson College, at Carlisle, Penn., from which he graduated among the first in his class, in 1829. He then resumed teaching, and having completed the course of study for the legal profession, was admitted to the bar at Chambersburg, Pcnn., in 1831. Soon afterward he removed to the Qty of Pittsburgh, where he practiced for almost a year. *^ 1S33, ^^^' McClelland removed to Monroe, in the Territory of Michigan, where, after a severe ex- amination, he became a member of the bar of Michi- gan, and engaged in practice with bright prospect of success. In 1835, a convention was called to frame a constitution for the proposed State of Michigan, of which Mr. McClelland was elected a member. He took a prominent part in its deliberations and ranked among its ablest debaters. He was appointed the first Bank Commissioner of the State, by Gov. Mason, and received an offer of the Attorney Generalship, but decHned both of these offices in order to attend to his professional duties. In 1838, Mr. McClelland was elected to the State legislature, in which he soon became distinguished as the head of several important committees. Speaker pro tempore^ and as an active, zealous and efficient member. In 1840, Gen. Harrison, as a candidate for the Presidency, swept the country with an overwhelm- ing majority, and at the same time the State of Michi- gan was carried by the Whigs under the popular cry of " Woodbridge and reform *' against the Democratic l)arty. At this time Mr. McClelland stood among the acknowledged leaders of the latter organization ; was elected a member of the State House of Representa- tives, and with others adopted a plan to regain a lost authority and prestige. This party soon came again into power in the State, and having been returned to the State Legislature Mr, McClelland's leadership was acknowledged by his election as S[)eaker of the House of Representatives o ^ I <^D!i;^dd;>^ -^5S^^ Digitized by Wh^^'^ im^ 'T<my.m>T « T 4 \ . ) A :^5 V > ■'■) »30 t!T ROBERT McClelland. ^ t±- ^V.' 9^:A^S ■.7:v.- <^ in 1843. Down to this time Michigan had consti- tuted one congressional district. The late Hon. Jacob M. Howard had been elected against Hon. Alpheus Felch by a strong majority ; but, in 1 843, so thoroughly had the Democratic party recovered from its defeat of 1840 that Mr. McClelland, as a candidate for Con- gress, carried Detroit district by a majority of about 2,500. Mr. McClelland soon took a prominent posi- lion in Congress among the veterans of that body. During his first term he was placed on Committee on Commerce, and organized and carried through what were known as the " Harbor bills.** The continued confidence of his constituency was manifested in his election to the 29th Congress. At the opening of this session he had acquired a National reputation, and so favorably was he known as a parlimentarian that his name was mentioned for Speaker of the House of Rep- resentatives. He declined the offer in favor of J. W. Davis, of Indiana, who was elected. During this terni he became Chairman of Committee on Comiiierce, in which position his reports and advocacy of important measures at once attracted public attention. The members of this committee, as an evidence of the es- teem in which they held his services and of their personal regard for him, presented him with a cane which he retains as a souvenir of the donors, and of his labors in Congress. In 1847, ^^' McClelland was re-elected to Con- gress, and at the opening of the 30th Congress be- came a member of the Committee on Foreign Rela- rions. While acUng in this capacity, what was known as the " French S|X)liation Bill" came under his si>e- cial charge, and his management of the same was such as to command universal approbation. While in Congress, Mr. McClelland was an advocate of the right of petition as maintained by John Q. Adams, when the petition, was clothed in decorous language and presented in the proper manner. This he re- garded as the citizens'consUtutional right which should not be impaired by any doctrines of temporary expe- diency. He also voted for the adoption of Mr. Gid- dings s bill for the abolishing of slavery in the District of Columbia. Mr. McClelland was one of the few Democrats associated with David Wilmot, of Penn- sylvania, in bringing forward the celebrated "Wilmot Proviso," with a view to prevent further extension of slavery in new territory which might be acquired by the United States. He ar^d Mr. Wilmot were to- gether at the time in Washington, and on intimate and confidential terms, Mr, McClelland was in sev- eral National conventions and in the Balrimore con- vention, which nominated Gen. Cass for President, in 1848, doing valiant service that year for the elec- rion of that distinguished statesman. On leaving Congress, in 1848, Mr. McClelland returned to the practice of his profession at Monroe. In 1850 a convention of the State of Michigan was called to the State constitution. He was elected a revise member and was regarded therein as among the ablest V and most experienced leaders. His clear judgment ^ and wise moderation were conspicuous, both in the ^, committee room and on the fk)or» in debate. In 1850, ; he was President of the Democratic State convention [^ which adopted resolutions in support of Henry Qay s v^ famous compromise measures, of which Mr. McClel- land was a strong advocate. He was a member of the Democratic National convention in 1852, and in that year, in company with Gen. Cass and Governor Felch, he made a thorough canvass of the State. He continued earnestly to advocate the Clay com- promise measures, and took an active part in the canvass which resulted in the election of Gen. Pierce to the Presidency. In 185 1, the new State oonstitution took effect and it was necessary that a Governor should be elected for one year in order to prevent an interre^um, and to bring the State Government into operation under the new constitution. Mr. McQelland was elected Governor, and in the fall of 1852 was re-elected for a term of two years, from Jan. r, 1853. His admin- istration was regarded as wise, prudent and concilia- tory, and was as popular as could be expected at a time when party spirit ran hi^h. There was really no opposition, and when he resigned, in March, 1853, the State Treasury was well filled, and the State otherwise prosperous. So widely and favorably had Mr. McClelland become known as a statesman that on the organization of thecabinet by President Pierce, in March| 1853, he was made Secretary of the Interior, in which capacity he served most creditably during four years of the Pierce administration. He thoroughlv re-organized his department aftd reduced the expend- itures. He adopted a course with the Indians which relieved them from the impositions and annoyances of the traders, and produced harmony and civilization among them. During his administration there was neither complaint from the tribes nor corruption among agents, and he left the department in perfect order and system. In 1867, Michigan again called a con- vention to revise the State constitution. Mr. McClel- land was a member and here again his long experi- ence made him conspicuous as a prudent adviser, a sagacious parliamentary leader. As a lawyer he was terse and pointed in argument, clear, candid and im- pressive in his addresses to the jury. His sincerity and earnestness, with which Was occasionally mingled a pleasant humor, made him an able and effective advocate. In speaking before the people on political subjects he was especially forcible and happy. In 1870 he made the tour of Europe, which, through his extensive personal acquaintance with European dip- lomates, he was enabled to enjoy much more tha^n most travelers, Mr. McClelland married, in 1837, Miss Sar&H E. Sabin, of Williamstown, Mass. They have haul six children, two of whom now survive. A \ .^--^^J?Zl- -^^nor^TDo^^A- ;=>5^^ Digitized by Google J Digitized by Google :^ ^^^7<cMm^f> GOVERNORS OF MICHIGAN. i 5$
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NDREVV PARSONS, Gover-
nor of Michigan from March
8, 1853 to Jan. 3, 1855, was
born in the town of Hoosick,
County of Rensselaer, and
State of New York, on the 2 2d
c) day of July, 1817, and died June
6, 1855, at the early age of 38
years. He was the son of John
Parsons, born at Newburyix)rt,
Mass., Oct. 2, T782, and who was the
son of Andrew Parsons, a Revolutionary
soldier^ who was the son of Phineas
Parsons, the son of Samuel Parsons,
a descendant of Walter Parsons, born
in Ireland in 1290.
Of this name and family, some one hundred and
thirty years ago, Bishop (iilson remarked in his edi-
tion of Camden's Britannia: "The honorable family
of Parsons have been advanced to the dignity of
Viscounts and more lately Earls of Ross."
The following are descendants of these families :
Sir John Parsons, born 148 1, was Mayor of Hereford;
Robert Parsons, born in 1546, lived near Bridgewater,
England. He was educated at Ballial College, Ox-
ford, and was a noted writer and defender of the
Romish faith. He established an English College at
Rome and another at Valladolia. Frances Parsons,
bom in 1556, was Vicar of Rothwell, in Notingham;
Bartholomew Parsons, born in 1618, was another
tooted member of the family. In 1 634, Thomas Parsons
was knighted by Charles I. Joseph and Benjamin,
bri>ihers, were born in Great Torrington, England,
and accompanied their father and others to New
England about 1630. Samuel Parsons, born at Salis-
bury, Mass., in 1707, graduated at Harvard College in
1730, ordained at Rye, N. H.,Nov. 3, 1736, married
Mary Jones, daughter of Samuel Jones, of Boston,
Oct. 9, 1739, died Jan. 4, 1789, at the age of 82, in
the 53rd year of his ministry. The grandfather of Mary
Jones was Capt. John Adams, of Boston, grandson
of Henr)', of Braintree, who was among the first set-
tlers of Massachusetts, and from whom a numerous
race of the name are descended, including two Presi-
dents of the United States. The Parsons have be-
come very numerous and are found throughout New
England, and many of the descedants are scattered
in all parts of the United States, and especially in
the Middle and Western States. Covernor Andrew
Parsons came to Michigan in 1835, at the age of 17
years, and spent the first summer at Lower Ann
Arbor, where for a few months he taught school which
he was compelled to abandon from ill health
He was one of the large number of men of sterling
worth, who came from the East to Michigan when it
was an infant State, or, even prior to its assuming
the dignity of a State, and who, by their wisdom,
enterprise and energy, have developed its wonderful
natural resources, until to-day it ranks with the proud-
est States of the Union. These brave men came to
Michigan witli nothing to aid them in the conquest
of the wilderness save courageous hearts and strong
and willing hands. They gloriously conquered, how-
ever, and to them is due all honor for the labors
so nobly performed, for the solid and sure foundation
which they laid of a great Commonwealth.
9
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$>: 0) ■a^»«s gj^jBjSllllij, Digitized by Google 134 Tr^mnh>T AN£>REVi^ PARSONS i :^:. /l\ w In the fall of 1835, he explored the Grand River >|j Valley in a frail canoe, the whole length of the river, ^ from Jackson to Lake Michigan, and spent the following winter as clerk in a store at Prairie Creek, in Ionia, ^ County, and in the spring went to Marshall, where he resided with his brother, ihe Hon. Luke H. Parsons, also now deceased, until fall, when he went to Shia- wasse County, then with Clinton County, and an almost unbroken wilderness and constituting one organized township. In 1837 this territory was organized into a county and, at the age of only 19 years, he (An- \ drew) was elected County Clerk. In 1840, he was elected Register of Deeds, re-elected in 1842, and also in 1844. In 1846, he was elected to the State Senate, was appointed Prosecuting Attorney in 1848, and elected Regent of the University in 185 1, and Lieutenant Governor, and became acting Governor, in 1853, elected again to the Legislature in 1854, and, . V? overcome by debilitated health, hard labor and the responsibilities of his office and cares of his business, retired to his farm, where he died soon after. He was a fluent and persuasive speaker and well calculated to make friends of his acquantances. He was always true to his trust, and the whole world could not persuade nor drive him to do what he con- ceived to be wrong. When Governor, a most power- ful railroad influence was brought to bear upon him, to induce him to call an extra session of the Legisla- ture. Meetings were held in all parts of the State for that purpose. In some sections the resolutions were of a laudatory nature, intending to make him do their bidding by resort to friendly and flattering words. In other places the resolutions were of a demanding nature, while in others they were threatening beyond measure. * Fearing that all these influences might fail to induce him to call the extra session, a large sum of money was sent him, and liberal offers ten- dered him if he would gratify the railroad interest of the State and call the extra session, but, immovable, he returned the money and refused to receive any favors, whether from any party who would at- tempt to corrupt him by laudations, liberal ofl*ers, or :^ V ) by threats, and in a short letter to the people, after V giving overwhelming reasons that no sensible man | could dispute, showing the circumstances were not *♦' ** extraordinary," he refused to call the extra session. ^ This brought down the wrath of various parties upon his head, but they were soon forced to acknowledge the wisdom and the justice of his course. One of his greatest enemies said, after a long acquaintance : 'though not always coinciding with his views I never doubted his honesty of purpose. He at all times sought to perform his duties in strict accordance, with the dictates of his conscience, and the behests of his oath. " The following eulogium from a politcal op- ponent is just in its conception and creditable to its author: ^ Gov. Parsons was a politician of the Dem- ocratic school, a man of pure moral character, fixed and exemplary habits, and entirely blameless in every public and private relation of life. As a politician he was candid, frank and free from bitterness, as an ex- ecutive officer firm, constant and reliable." The highest commendations we can pay the deceased is to give his just record, — that of being an honest man. In the spring of 1854, during the administration of Governor Parsons, the Republican party, at least as a State organizadon, was first formed in the United States " under the oaks " at Jackson, by anti-slavery men of both the old parties. Great excitement pre- vailed at this time, occasioned by the settling of Kansas, and the issue thereby brought up, whether slavery should exist there. For the purpose of permif- ting slavery there, the ** Missouri compromise '* (which limited slavery to the south of 36^ 30^) was re- repealed, under the leadership of Stephen A, Douglas. This was repealed by a bill admitting Kansas and Nebraska into the Union, as Territories, and those "who were opposed to this repeal measure were in short called ** anti-Nebraska ** men. The epithets, " Ne- braska** and "anti-Nebraska,** were temporally em- ployed to designate the slavery and anti-slavery parties, pending the desolution of the old Democratic and Whig parties and the organization of the new Democratic and Republican parties of the present. 1 f" 1 .-'; /VV-- ■c?a^ j1^ <^i]i]:v^tir^ -^ '^-^e^ -s,^^ ■ ,^^.V3i>^f^ Digitized by Google Digitized by Google ■■■J r -^^wsr ■r:?-7 4:nD^DD^>: r^ ^i-'-jsf-X i. J A f '^ / GOVERNORS OF MICHIGAN. ■-m^JJ\^^^ 137 KlNSLKY ©. BiNQHAM, INSLEY S. BINGHAM, Governor of Michigan from 1855 to 1859, and United States Senator, was born in Camillus, Onondaga County, N. Y., Dec. 16, 1808. His father was a fanner, and his own early life was consequently de- voted to agricultural pursuits, but notwithstanding the disadvan- tages related to the acquisition of knowledge in the life of a fanner he managed to secure a good aca- demic education in his native State and studied law in the office of Gen. James R. Lawrence, now of Syracuse, N. Y. In the spring of 1S339 he married an estimable lady who had recently arrived from Scot- land, and obeying the impulse of a naturally enterprising disposition, he emigrated to Michigan and purchased a new farm in company with his brother-in-law, Mr. Robert Worden, in Green Oak, Livingston County. Here, on the border of civilization, buried in the primeval for- est, our late student commenced the arduous task of preparing a future home, clearing and fencing, put- ting up buildings, etc, at such a rate that the land chosen was soon reduced to a high state of cultivation. Becoming deservedly prominent, Mr. Bingham was elected to the office of Justice of the Peace and Post- master under the Territorial government, and was the first Probate Judge in the county. In the year 1836, when Michigan became a State, he was elected to the first Legislature. He was four times re-elected, and Speaker of the House of Representatives three years. In 1846 he was elected on the Democratic ticket. Rep- resentative to Congress, and was the only practical farmer in that body. He was never forgetful of the interest of agriculture, and was in particular opposed to the introduction of " Wood s Patent Cast Iron Plow " which he completely prevented. He was re- elected to Congress in 1848, during which time he strongly opposed the extension of slavery in the territory of the United States and was committed to and voted for the Wilmot Proviso. In 1854, at the first organization of the Republican party, in consequence of his record in Congress as a Free Soil Democrat, Mr. Bingham was nominated and elected Governor of the State, and re-elected in 1856. Still faithful to the memory of his own former occupation, he did not forget the farmers during his administration, and among other profits of his zeal in their behalf, he became mainly instrumental in the establishment of the Agricultural College at Lansing. In 1859, Governor Bingham was elected Senator in Congress and took an active part in the stormy cam- paign in the election of Abraham Lincoln. He wit- (r ii' I 'V^-: i^-"3y^K^^- ^::s^^%^ JL. ^M>mmi^;^ j^^ %fr^j. Digitized by V^OOQlC ^> 138 ■r-7<t:m:m>^-^ rz.'^ 4 i (0 v) KINSLEY S. BINGHAM. nessed the commencement of the civil war while a member of the United States Senate. After a cora- ls paratively short life of remarkable promise and pub- ;'^ lie activity he was attacked with appoplexy and died I suddenly at his residence, in Gteen Oak, Oct 5, 1861. ^ The most noticable event in Governor Bingham's first term was the completion of the ship canal, at the Falls of St. Mary. In 1852, Angust 26, an act of Congress was approved, granting to the State of Mich- igan seven hundred and fifty thousand acres of land for the purpose of constructing a ship canal between Lakes Huron and Superior. In 1853, the Legislature accepted the grant, and provided tor the apix>intment .^ of commissioners to select the donated lands, and to iJj arrange for building the canal. A company of enter- prising men was formed, and a contract was entered into b^ which it was arranged that the canal should be finished in two years, and the work was pushed rapidly forward. Every article of consumption, ma- chinery, working implements and materials, timber for the gates, stones for the locks, as well as men and supplies, had to be transported to the site of the canal from Detroit, Cleveland, and other lake ports. The rapids which had to be surmounted have a fall of ^ seventeen feet and are about one mile lone. The ^ length of the canal is less than one mile, its width one ^ hundred feet, depth twelve feet and it has two locks »^ of solid masonary. In May, 1855, the work was com- ^ pleted, accepted by the commissioners, and formally p=i delivered to the State authorities. "^ The disbursements on account of the construction S of the canal and selecting the lands amounted to one million of dollars ; while the lands which were as- signed to the company, and selected through the agency at the Sault, as well as certain lands in the Upper and Lower Peninsulas, filled to an acre the Government grant. The opening of the canal was an important event in the history of the improvement of the State. It was a valuable link in the chain of . lake commerce, and particularly important to the y V interests of the Upper Peninsula. ^ -^ There were several educational, charitable and re- formatory institutions inaugurated and opened during Gov. Bingham's administrations. The Michigan Ag- ricultural College owes its establishment to a provision of the State Constitution of 1850. Article 13 says, " The Legislature shall, as soon as practicable, pro- vide for the establishment of an agricultural school." For the purpose of caryinginto practice this provision, A^ legislation was commenced in 1855, and the act re- quired that the school should be within ten miles -of Lansing, and that not more than$15 an acre should
be paid for the farm and college grounds. The col-
'^ lege was opened to students in May, 1857, the first of
^/ existing argricultural colleges in the United States.
fA> Until the spring of 1 861, it was under the control
*^ of the State Board of Education; since that time it
^\
1
^ has been under the management of the State Board
r ■ ■ ^
of Agriculture, which was created for that purpose.
In its essential features, of combining study and
labor, and of uniting general and professional studies
in its course, the college has remained virtually un-
changed from the first. It has a steady growth in
number of students, in means of illustration and
efficiency of instruction.
The Agricultural College is three miles east of
Lansing, comprising several fine buildings ; and there
are also very beautiful, substantial residences for the
professors. There are also, an extensive, well-filled
green-house, a very large and well-equipped chemical
laboratopv 9"^^ of ^^^ "*<^^ scientific apiaries in the
United States, a general museum, a meseum of me-
chanical ihventions, another of vegetable products,
extensive bams, piggeries, etc., etc, in fine trim for
the purposes designed. The farm consists of 676
acres, of which about 300 are under cultivation in a
systematic rotation of crops.
Adrian College was established by the Wesleyan
Methodists in 1859, now under the control of the
Methodist Church. The grounds contain about 20
acres. There are four buildings, capable of accom-
modating about 225 students. Attendance in 1875
was 179; total number of graduates for previous year,
121 ; ten professors and teachers are employed. Ex-
clusive of the endowment fund ($80,000), the assets of the institution, including groimds, buildings, furni- ture, apparatus, musical instruments, outlying lands, etc., amount to more than$137,000.
Hillsdale College was established in 1855 by the
Free Baptists. The Michigan Central College, at
Spring Arbor, was incorporated in 1845 It was kept
in operation until it was merged into the present
Hillsdale College. The site comprises 25 acres,
beautifully situated on an eminence in the western
part of the city of Hillsdale. The large and impos-
ing building first erectqd was nearly destroyed by fire
in 1874, and in its place five buildings of a more
modem style have been erected. They are of brick,
three stories with basement, arranged on three sides
of a quadrangle. The size is, respectively, 80 by 80,
48 by 7 2, 48 by 7 2, 80 by 60, 5 2 by 7 2, and they con-
tain one-half more room than the original building.
The State Reform School. This was established
at Lansing in 1855, in the northeastern portion of the
city, as the House of Correction for Juvenile Of-
fenders, having about it many of the features of a
prison. In 1859 the name was changed to the State
Reform School. The government and dicipline, have
undergone many and radical changes, until all the
prison features have been removed except those that
remain in the walls of the original structure, and
which remain only as monuments of instructive his*
tory. No bolts, bars or guards are employed. The
inmates are necessarily kept under the surveillance of
officers, but the attempts at escape are much fein^er
than under the more rigid regime of former days.
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GOVERNORS OF MICHIGAN.
^
OSES WISNER. Governor of
Michigan from 1859 to 1861,
was born in Springport, Cayu-
ga Co., N Y., June 3, 1815.
His early education was only
what could be obtained at a
(jiiiinon school- Agricultural labor
' and frugality of his parents gave
i him a physical constitution of unus-
^i> Lial strength and endurance, which
was ever preserved by temperate hab-
its. In 1837 he emigrated to Michi-
V/^ gan and purchased a farm in Lapeer
County It was new land and he at
once set to work to clear it and plant
crops. He labored diligently at his
task for two years, when he gave up
the idea of 'Deing a farmer, and removed to Pontiac,
Oakland Co. Here he commenced the study of law
in the office of his brother, George W. Wisner, and
Rufus Hosmer In 1841 he was admitted to the bar
and established himself in, his new vocation at the
village of Lapeer. While there he was apptx)inted
by Gov. Woodbridge Prosecuting Attorney for that
county, in which capacity he acquitted himself well
and gave promise of that eminence he afterward at-
tained in the profession. He remained at Lapeer but
a short time, removing to Pontiac, where he became
a member of a firm and entered fully upon the
practice.
In politics he was like his talented brother, a Whig
of the Henry Clay stamp, but with a decided anti-
slaver) bias. His practice becoming extensive, he
took little part in politics until after the election of
Mr. Pierce to the Presidency in 1852, when he took an
active part against slavery. As a lawyer he was a
man of great ability, but relied less upon mere book
learning than upon his native good sense. Liberal
and courteous, was he yet devoted to the interest of
his client, and no facts escaped his attention or his
memory which bore upon the case. He was no friend
of trickery or artifice in conducting a case As an ad-
vocate he had few equals. When fully aroused by the
merits of his subject his eloquence was at onca grace-
ful and powerful. His fancies supplied the most
original, the most pointed illustrations, and his logic
became a battling giant under whose heavy blows the
stowed upon him rare qualities, and his powers as a
popular orator were of a high order.
On the passage of the Kansas-Nebraska Act of
1854, repeahng the Missouri compromise and opening
the Territories to slavery, he was among the foremost
in Michigan to denounce the shamful scheme. He
actively participated in organizing and consolidating
the elements opposed to it in that State, and was a
member of the popular gathering at Jackson, in July,
1854, which was the first formal Republican Conven-
tion held in the United States. At this meeting the
name " Republican " was adopted as a designation of
the new party consisting of Anti-slavery, Whigs,
Liberty men. Free Soil Democrats and all others op-
posed to the extension of slavery and favorable to its
expulsion from the Territories and the District of
Columbia. At this convention Mr. W. was urged to
accept the nomination for Attorney General of the
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State, but declined. An entire State ticket was nom-
inated and at the annual election in November was
elected by an average majority of nearly io,ooo.
Mr. W. was enthusiastic in the cause and brought to
its support all his personal influence and talents. In
his views he was bold and radical. He believed from
the beginning that the political power of the slave-
holders would have to be overthrown before quiet
could be secured to the country. In the Presidential
canvass of 1856 he supported the Fremont, or Re-
publican, ticket. At the session of the Legislature of
1857 he was a candidate for United States Senator,
and as such received a very handsome support. •
In 1858, he was nominated for Governor of the
State by the Republican convention that met at De-
troit, and at the subsequent November election was
chosen by a very large majority. Before the day of
every county and his majority was greater even than
that of his popular predecessor, Hon. K. S. Bingham.
He served as Governor two years, from Jan. i, 1859,
to Jan. I, 1 86 1. His first message to the Legislature
was an able and statesman-like production, and was
read with usual favor. It showed that he was awake
to all the interests of the State and set forth an en-
lightened State policy, that had its view of the rapid
settlement of our uncultivated lands and the devel-
opment of our immense agricultural and mineral re-
sources. It was a document that reflected the highest
credit upon the author.
His term having expired Jan. i, 1861, he returned
to his home in Pontiac, and to the practice of his
profession. There were those in the State who
counselled the sending of delegates to the peace con-
ference at Washington, but Mr. W. was opposed to all
such temporizing expedients. His counsel was to
send no delegate, but to prepare to fight.
After Congress had met and passed the necessary
legislation he resoh ed to take part in the war. In
the spring and summer of 1862 he set to work to
raise a regiment of infantry, chiefly in Oakland
County, where he resided. His regiment, the 2 2d
Michigan, was armed and equipped and ready to
march in September, a regiment whose solid quali-
ties were afterwards proven on many a bloody field.
Col. Ws. commission l)ore the date of Sept. 8, 1862.
Before parting with his family he made his will. His
regiment was sent to Kentucky and quartered at
Camp Wallace. He had at the breaking out of the X
war turned his attention to military studies and be- f'
came proficient in the ordinary rules and discipline, h
His entire attention was now devoted to his duties. |
His treatment of his men was kind, though his disci- ih
pline was rigid. He possessed in an eminent degree
the spirit of command, and had he lived he would
no doubt have distinguished himself as a good
officer. He was impatient of delay and chafed at
l>eing kept in Kentucky where there was so little
prospect of getting at the enemy. But life in camp,
his incessant labors, cx)upled with that impatience
which was so natural and so general among the vol-
unteers in the early part of the war, soon made their
influence felt upon his health. He was seized with
typhoid fever and removed to a private house near
Uxington. Every care which medical skill or the
hand of friendship could bestow was rendered him.
In the delirious wanderings of his mind he was dis-
ciplining his men and urging them to be prepared for -.
an encounter with the enemy, enlarging upon the jus- ^
tice of their cause and the necessity of their crush-
ing the Rebellion. But the source of his most ix>ig-
nant gnet was the prospect of not being able to come
to a hand-to-hand encounler with the "chivalry."
He was proud of his regiment, and felt that if it could ^
find the enemy it would cover itself with glory, — a
distinction it afterward obtained, but not until Col. W.
was no more. The malady baffled all medical treat-
ment, and on the 5th day of Jan., 1863, he breathed
his last. His remains were removed to Michigan and
interred in the cemetery at Pontiac, where they rest
by the side of the brave Gen. Richardson, who re-
ceived his mortal wound at the battle of Antietam.
Col. W. was no adventurer, although he was doubtless
ambitious of military renown and would have striven
for it with characteristic energy. He went to the war
to defend and uphold the principles he had so much
at heart. Few men were more familiar than he with
the causes and the underlying principles that led to
the contest. He left a wife, who was a daughter of
Gen. C. C. Hascall, of Flint, and four children to
mourn his loss. Toward them he ever showed tbe
tenderest regard. Next to his duty their love axxci
welfare engrossed his thoughts. He was kind, gen^
erous and brave, and like thousands of others lie
sleeps the sleep of the martyr for his country.
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GOrERNORS OF MICHIGAN.
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LFSTIN BLAIR, Governor
of Michigan from Jan. 2,
1 86 1, to Jan. 4, 1H65, and
kown as the War Governor, is
and illustration of the benifi-
ct^nt influence of republican in-
stitutions, having inherited neith-
er fortune nor fame. He was horn
in a log cabin at Caroline, Tomp-
kins Co., N. v., Feb. 8, 18 18.
His ancestors catne from Scot-
land in the time of (ieorge I, and
for many generations followed the
pursuit of agriculture. His f^ither,
I George Blair, settled in Tompkins
County in 1809, and felled the trees and erecled the
first cabin in the county. The last 60 of the four-
score years of his life were spent on that six)t. He
married Rhoda Beackman, who now sleeps with him
in the soil of the old homestead. The first 17 years
of Mr. Blair's life were spent there, rendering his
father what aid he could nix^n the farm. Fie then
spent a year and a half in Cazenovia Seminary pre-
paring for college; entered Hamilton College, in
Clinton, prosecuted his studies until the middle of
♦he junior year, when, attracted by the fame of Dr.
Noit, he changed to Union College, from which he
graduated in the class of 1839. Upon leaving col-
lege Mr. Blair read law two years in the office of Sweet
^ t>avis, Oswego, N Y., and was admitted to jiractice
^ '^4^ and the same year moved to Michigan, locat-
ing in Jackson. During a temporary residence in
Eaton Rapids, in 1842, he was elected Clerk of Eaton
County. At the close of the official term he returned to
Jackson, and as a Whig, zealously espoused the cause
of Henry Clay in the campaign of 1844. He was chosen
Representative to the Legislature in 1845, at which
session, as a member of the Judiciary Committee, he
rendered valuable service in the revision of the gen-
eral statutes ; also made an able supix)rt in favor of
abolishing the color distinction in relation to the elec-
rive franchise, and at the same session was active in
securing the abolition of capital punishment. In 1848
Mr. Blair refused longer to affiliate with the Whig
party, liecause of its refusial to endorse in convention
any anti-slavery sentiment. He joined the Free-soil
movement, and was a delegate to their convention
which nominated Van Buren for President that year
Upon the birth of the Republican party at Jackson,
in 1854, by the coalition of the Whig and Free-soil
elements, Mr. Blair was in full sympathy with the
movement, and acted as a member of the Committee
on Platform. He was elected Prosecuting Attorney
of Jackson County in 1852 ; was chosen State Senator
two years later, taking his seat with the incoming Re-
publican administration of 1855, and holding the
position of parliamentary leader in the Senate. He
was a delegate to the National Convention which
nominated Abraham Lincoln in i860. Mr. Blair
was elected Governor of Michigan in i860, and re-
elected in 1862, faithfully and honorably discharging
the nrduoii'^ dutJo^ of the office during that most mo-
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AUSTIN BLAIR.
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mentous and stormy period of the Nation s life. Gov.
i^ Blair ix>ssessed a dear comprehension of the perilous
* situation from the inception of the Rebellion, and his
policy and the administrative ability which charac-
terized his gubernatorial career.
Never perhaps in the history of a nation has a
brighter example been laid down, or a greater sacri-
fice been made, than that which disringuished Mith-
igan during the civil war. All, from the " War Gov-
ernor/* down to the poorest citizen of the State, were
animated with a patriotic ardor at once magnificiently
sublime and wisely directed.
Very early in 1861 the coming struggle cast i^s
shadow over the Nation. Governor Blair, in his mes-
sage to the Legislature in January of that year, dwelt
very forcibly upon the sad prospects of civil war; and
/^ as forcibly pledged the State to support the principles
= of the Republic. After a review of the conditions
^ of the State, he passed on to a consideration of the
° relations between the free and slave Stales of the
Republic, saying: " While we arecitizensof the State
of Michigan, and as such deeply devoted to her in-
terests and honor, we have a still prouder title. We
are also citizeas of the United States of Amenca. By
this title we are known among the nations of the earth.
In remote quarters of the globe, where the names of
the States are unknown, the flag of the great Republic,
the banner of the stars and stripes, honor and protect
her citizens. In whatever concerns the honor, the
prosperity and the perpetuity of this great Govern-
ment, we are deeply interested. The people of Mich-
igan are loyal to that Government — faithful to its con-
stitution and its laws. Under it they have had peace
and prosperity ; and under it they mean to abide to
the end. Feeling a just pride in the glorious history
of the past, they will not renounce the equally glo-
rious hopes of the future. But they will rally around
the standards of the Nation and defend its integrity
and its constitution, with fidelity." The final para-
graph being:
** I recommend you at an early day to make niani-
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fest to the gentlemen who represent this State in the
two Houses of Congress, and to the country, that
Michigan is loyal to the Union, the Constitution, and
the laws and will defend them to the uttermost; and
to proffer to the President of the United States, the
whole military power of the State for that purpose.
Oh, for the firm, steady hand of a Washington, or a
Jackson, to guide the ship of State in this perilous
storm ! Let us hope that we will find him on the 4th
of March. Meandme, let us abide in the faith of our
fathers — * Liberty and Union, one and inseparable,
now and forever.* "
How this stirring appeal was responded to by the
people of Michigan will be seen by the statement
that the State furnished 88,1 1 1 men during the war.
Money, men, clothing and food were freely and abun-
dantly supplied by this State during all these years of
darkness and blood shed. No State won a brighter
record for her devotion to our country than the Pen-
insula State, and to Gov. Blair, more than to any
other individual is due the credit for its untiring zeal
and labors in the Nations behalf, and for the heroism
manifested in its defense.
Gov. Blair was elected RepresentaUve to the
Forrieth Congress, and twice re-elected, to the Forty-
first and Forty-second Congress, from the Third Dis*
trict of Michigan. White a member of that body he
was a strong supporter of reconstruction measures,
and sternly opposed every form of repudiation. His
speech upon the national finances, delivered on the
floor of the House March 21, 1868, was a clear and
convincing argument Since his retirement from Con-
gress, Mr. Blair has been busily occupied with his ex-
tensive law practice. Mr. Blair married Sarah L.
Ford, of Seneca County N. Y., in February, 1 849.
Their family consists of 4 sons — George H., a la'w
partner of A. J. Gould ; Charles A., a law partner inrith
hir father, and Fred. J. and Austin T. Blair, at home.
Governor Blair s religion is of the broad type, and
centers in the "Golden Rule." In 1883, Gov. Blair
was nominated for Justice of the Supreme C7ourt
of the State by the Republican party, but was defeated.
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GOVERNORS OF MICHIGAN.
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ENRY ROWLAND CRAPO,
Governor of Michigan from
1865 to 1869, was born May
24, 1804, at Dartmouth, Bris-
tol Co., Mass., and died at
Flint, Mich., July 22, 1869.
was the eldest son of Jesse
and Phoebe (Rowland) Crapo.
His father was of French descent
and was very poor, sustaining his
family by the cultivation of a farm in
Dartmouth township, which yielded
nothing beyond a mere livelihood.
His early life was consequently one
of toil and devoid of advantages for
I intellectual culture*, but his desire for
an education seemed to know no bounds. The in-
cessant toil for a mere subsistence upon a compara-
tively sterile farm, had no charm for him ; and, longing
for greater usefulness and better things, he looked for
them in an education. His struggles to secure this
end necessitated sacrifices and hardships that would
liave discouraged any but the most courageous and
persevering. He became an ardent student and
worker from his boyhood, though the means of carry-
ing on his studies were exceedingly limited. He
sorely felt the need of a dictionary; and, neither having
» money wherewith to purchase it, nor being able to
procure one in his neighborhood, he set out to compile
' , one for himself. In order to acquire a knowledge of
the English language, he copied into a book every
word whose meaning he did not comprehend, and
upon meeting the same word again in the newspapers
and books, w^hich came into his hands, from the
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jji^j^Vl>$«^i^^^ <-«•- j^^^ — ^r^^n !i^niir>^T^^ — ^€S^ y^ context, would then record the definition. Whenever unable otherwise to obtain the signification of a word in which he had become interested he would walk from Dartmouth to New Bedford for that purpose alone, and after referring to the books at the library and satisfying himself thoroughly as toitsdetinition, would walk back, a distance of about seven miles, the same night. This was no unusual circumstance. Under such difficulties and in this manner he com- piled quite an extensive dictionary in manuscript which is believed to be still in existence. Ever in pursuit of knowledge, he obtained posses- sion of a book upon surveying, and applying himself diligently to its study became familiar with this art, which he soon had an opportunity to practice. The services of a land surveyor were wanted, and he was called upon, but had no compass and no money with which to purchase one. A compass, however, he must and would have, and going to a l)lacksmith shop near at hand, upon the forge, with such tools as he could find in the shop, while the smith was at dinner, he constructed the compass and commenced life as a surveyor. Still continuing his studies, he fitted him- self for teaching, and took charge of the village school at Dartmouth. When, in the course of time and un- der the pressure of law, a high school was to be oix:ned, he passed a successful examination for its principalship and received the appointment. To do this was no smatl task. The law required a rigid examination in various subjects, which necessitated days and nights of study. One evening, after con- cluding his day s labor of teaching, he traveled on foot to New Bedford, some seven or eight miles, called upon the preceptor of Friend s Academy and passed ^. O Cl Digitized by Google > «5o ■7<:D3:■•-:aQ^:>rT- -v.:^^ HENRY HOWLAND CRAPO. •i* ^ a severe examination. Receiving a certi6cate that ^ he was qualified, he walked back to his home the same night, highly elated in being possessed of the acquirements and requirements of a. master of the high school. ^. In 1852, at the age of 28 years, he left his native ^ town and went to reside at New Bedford, where he followed the oc* upation of land surveyor, and oc- casionally acted as an auctioneer. Soon after becom- ing a citizen of this place, he was elected Town Clerk, Treasurer, and Collector of taxes, which office he held until the municipal government was changed, — about fifteen years, — when, upon the inauguration of the city government, he was elected Treasurer and Collector of taxes, a |>osilion which he held two or three years. He was also Justice of the Peace for many years. He was elected Alderman of New Bedford; was Chaimian of Council Committee on Education, and as such prepared a report upon which was based the order for the establishment of the free Public Library of New Bedford. On its organization, Mr. Crapo was choien a member of the Board of Trustees. This was the first free public library in Massachusetts, if not in the world. The Boston Free Library' was es- tablished, however, soon afterwards. While a resident in New Bedford, he was much interested in horticul- ture, and tft obtain the land necessary- for carrying out ^ his ideas he drained and reclaimed several acres of ^ rocky and swampy land adjoining his garden. Here S he started a nursery, which he filled with almost every '^ description of fruit and ornamental trees, shrubs, flowers, etc. In this he was very successful and took great pride. He was a regular contributorto the New England Horticultural Journal, a position he filled as long as he lived in Massachusetts. As an indica- tion of the wide reputation he accjuired in that field of lalx)r, it may he mentioned that after his death an affecting eulogy lo his memory was pronounced by the President of tiie National Horticultural Society at its meeting in Philadelphia, in 1869. During his resi- dence in New Bedford, Mr. Cra|x> was also engaged in the whaling l)usiness. A fine barque built at Dart- mouth, of which be was part owner, was named the "H. H. Crapo*' \\\ compliment to him. Mr. C. also took part in the State Militia, and for several years held a commission as Colonel of one of the regiments. He was President of the Bristol County Mutual Fire Insurance Co., and Secretary' of the Fkxlford Commercial Insurance Company in New Bedford; and while an officer of the municipal gov- (^ ernment he com piled and published, between the years [836 and 1845, ^^'*^ numbers of the New Bedford Directory, the first work of the kind ever published there. \^d Mr. C. removed to Michigan in 1856, having been ^f^ induced to do so by investments made principally in pine lands, first in 1837 and subsequently in 1856. ;;) He touk u[> liis residence in the city of Flint, and en- gaged largely in the manufacture and sale of lumber ^ at Flint, Kenton ville. Holly afid Detroit, becoming \ one of the largest and most successful business men of the State. He was mainly instrumental in the construction of the Fhnt & Holly R. R., and was President of that corporation nniil its consolidation \ with the Flint & Pere Marquette R. R. Comi>any. He was elected Mayor of that city after he had been a resident of the place only ^st. cr six years. In 1862 he was elected State Senator. In the fall of 1864 he received the nomination on the Rei)ublican ticket for Governor of the State, and was elected by a large majority. He was re-elected in 1866, holding the office two terms, and retiring in January, 1869, having given the greatest satisfaction to all parties. While serving his last term he was attacked with a disease which terminated his life within one year afterwards. During much of this time he was an in- tense sufferer, yet often while in great pain gave his attention to public matters. A few weeks previous to his death a successful surgical operation was per- formed which seemed rapidly to restore him, but he overestimated his strength, and by too much exertion in business matters and State affairs suffered a relapse from which there was no rebound, and he died July 33, 1869. In the early part of his life. Gov. Crapo affiliated with the Whig party in politics, but became an active member of the Republican party after its organization. He was a meml>er of the Christian (sometimes called the Disciples') Church, and took great interest in its welfare and prosperity. Mr. C. married, June 9, 1825, Mary K. Slocum, of Dartmouth. His marriage took place soon after he had attained his majority, and before his struggles with fortune had been rewarded with any great meas- ure of success. But his wife was a woman of great strength of character and |K)ssessed of courage, hope- fulness and devotion, (jualities which sustained and encouraged her husband in the various pursuits of his early years. For several years after his marriage he was engaged in teaching school, his wife living with her parents at the time, at whose home his two older children were bom. While thus situated he was accustomed to walk home on Saturday to see his family, returning on Sunday in order to be ready for school Monday morning. As the walk for a go6d part of the time was 20 miles each way, it is evident that at that period of his life no common obstacles deterred him from |)erfonning what he regarded as a duty. His wife was none the less consci- entious in her sphere, and with added resix>nsibilities and increasing requirements she labored faithfully in the ]x;rfo''mance of all her duties. They had ten children, one son and nine daughters. His son, Hon. Wm. W. Crajx), of New Bedford, is now an honored Representative to Congress from the First Congressional District of Massachusetts. K>^ ^vy> Digitized by Google k ''-'. >••> • ^v'< Jt^^^>/^ ^ d^et^^^a^ Digitized by Google GO VKRXORS OF MICHIGAN. HENRY p. BAIIPWIN. '^ . v'^ ^-'^cXM^I^a^TZTZr^w ^, i ENRY P. BALDWIN, Ciov- ernor of Michigan from Jan. 4, 1869, to Jan. I, 1873, is a lineal descendant of Nathan- iel Baldwin, a Puritan, of Buck- inghanishire, England, who set- ded at Milford, Conn., in 1659. His father was John Baldwin, a graduate of Dartmouth Col- lege. He died at North Provi- dence, R. I., in 1826. His paternal grandfather was Rev. Moses Baldwin, a graduate of Princeton College, in 1757, and the first who received collegiate hon- ors at that ancient and honored institution. He died at Parma, .Mass., in 18 13, where for more than 50 years he had been pastor of the Presl)yterian Church. On his mother's side Governor B. is descended from Robert Williams, also a Puritan, who settled in Ro.x- bur\', Mass., about 1638. His mother was a daughter of Rev. Nehemiah Williams, a graduate of Harvard College, who died at Brimfield, Mass., in 1796, where lor 21 years he was pastor of the Congregationalist Church. The subject of this sketch was born at Coventry, R. I., Feb. 22, 1^14. He received a New England common-school education until the age of 12 years, when, both his parents having died, he be- came a clerk in a mercantile establishment. He re- mained there, employing his leisure hours in study, until 20 years of age. At this early period Mr. B. engaged in business on his own account. He made a visit to the West, in ^^37 ♦ which resulted in his removal to Detroit in the spring of 1838. Here he established a mercantile nouse which has been successfully conducted until e present time. Although he successfully conducted a large business, he has ever taken a deep interest in all things affecting the prosperity of the city and Stale of his adoption. He was for several years a Director and President of the Detroit Young Men's Society, an institution with a large library designed for the benefit of young men and citizens generally. An Episcopalian in religious belief, he has been prominent in home matters connected with that de- nomination. I'he large and flourishing parish of St. John, Detroit, originated with Governor Baldwin, who gave the lot on which the parish edifice stands, and also contributed the larger share of the cost of their erection. Governor B. was one of the foremost in the establishment of St. Luke s Hospital, and has always been a liberal contributor to moral and relig- ious enterprises whether connected with his own Church or not. There have been, in fact, but few public and social improvements of Detroit during the past 40 years with which Governor B.'s name is not in some way connected. He was a director in the Michigan State Bank until the expiration of its char- ter, and has been President of the Second National Bank since its organization. In i860, Mr. Baldwin was elected to the State Senate, of Michigan ; during the years of i86i-*2 he was made Chairman of the Finance Committee, a member of Committee on Banks and Incorix)rations, Chairman of the Select Joint Committee of the two Houses for the invesrigation of the Treasury Depart- ment and the official acts of the Treasurer, and of the letting of the contract for the improvement of Sault St. Marie Ship Canal. He was first elected Governor in jS68 and was re-elected in 1870, serving from 1869 to 1872, inclusive. It is no undeserved eulogy to say that Governor B.'s happy faculty of es- timating the necessary means to an end — the knowing of how much effort or attention to bestow upon the thing in hand, has been the secret of the unifonn S3 1 ^ (^ ^^^^^^--- <^DrA^iiiiv> ^.^^ ■^N^y^ Digitized by ibgle V > A ^ 154 HENRY P BALD WIN. A >£^^^^r■^ t success that has attended his efforts in all relations of life. The same industry and accuracy that dis- tinguished him prior to this term as Governor was manifest in his career as the chief magistrate of the State, and while his influence appears in all things with which he has had to do, it is more noticeable in the most prominent position to which he was called. With rare exceptions the important commendations of Governor B. received the sanction of the Legislat- ure. During his administration marked improve- ments were made in the charitable, penal and reforma- tory institutions of the State. The State Public School for dependent children was founded and a permanent commission for the sui)ervision of the several State institutions. The initiatory steps toward building the Eastern Asylum for the Insane, the State House of Correction, and the establishment of the State Board of Health were recommended by Governor B. in his message of 1873. The new State Capitol also owes its origen to him. The appropriation for its erection was made upon his recommendation, and the contract for the entire work let under this administration. Governor B. also appointed the commissioners under whose faithful sui)ervision the building was erected in a manner most satisfactory to the people of the State. He advised and earnestly urged at different times such amendments of the constitution as would per- mit a more equitable compensation to State officers and judges. The law of 1 869, and prior also, permitting municipalities to vote aid toward the construe- tion of railroads was, in 1870, declared unconstitu- tional by the Supreme Court. Many of the munici- palities having in the meantime issued and sold their bonds in good faith, Governor B. fell that the honor and credit of the State were in jeopardy. His sense of justice im|)elled him to call an extra session of the Legislature to propose the submission to the people a constitutional amendment, authorizing the payment of such bonds as were already in the hands of bona^ fide holders. In his special message he says : '*The credit of no State stands higher than that of Michigan, and the people can not afford, and I trust will not consent, to have her good name tarnished by the repu- diation of either legal or moral obligations." A spe- cial session was called in March, 1872, principally for the division of the State into congressional districts. A number of other important suggestions were made, however, and as an evidence of the Governors la- borious and thoughtful care for the financial condition r ^ c i of the State, a series of tables was prepared and sub- mitted by him showing, in detail, estimates of receipts, expenditures and appropriations for the years 1872 to 1 87 8, incl usi ve. Memorable of Governor B. s admin- istration ,were the devastating fires which swept over many portions' of the Northwest in the fall of 1871. A large part of the city of Chicago having been re- duced to ashes. Governor B. promptly issued a proc- lamation calling upon the people of Michigan for liberal aid in behalf of the afflicted city. Scarcely had this been issued when several counties in his State were laid waste by the same destroying element. ^^ A second call was made asking assistance for the suf- % fering people of Michigan. The contributions for these objects were prompt and most lil^eral, more than$700,000 having been received in money and supplies
for the relief of Michigan alone. So ample were
these contributions during the short period of about
3 months, that the Governor issued a proclamation
expressing in behalf of the people of the State grate-
ful acknowldgment, and announcing that further
aid was unnecessary.
Governor B. has traveled extensively in his own ==
country and has also made several visits to Europe 5r»
and other portions of the Old World. He was a pas- ==
senger on the Steamer Arill, which was captured and *
bonded in the Carribean Sea, in December, 1862, by *
Capt. Semmes, and wrote a full and interesting ac-
count of the transaction. The following estimate of
Governor B. on his retirement from office, by a leading
newspaper, is not overdrawn: **The retiring message
of Governor B., will be read with interest. It is
a characteristic document and possesses the lucid
statement, strong, and clear practical sense, which
have been marked features of all preceding documents
from the same isource. Governor B. retired to private
life after four years of unusually successful adminis-
tration amid plaudits that are universal throughout the
State. For many years eminent and capable men
have filled the executive chair of this State, but in
painstaking vigilance, in stem good sense, in genuine
public spirit, in thorough integrity and in practical
capacity, Henry P. Baldwin has shown himself to be
the peer of any or all of them. The State has been un-
usually prosperous during his two terms, and the Stale
administration has fully kept pace with the needs of
the times. The reriring Governor has fully eamed
the public gratitude and confidence which he to-<iay
possesses to such remarkable degree.**
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GOVERNORS OF MICHIGAN.
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OHN JUDSON BAGLEY,
^Governor of Michigan from
1873 to 1877, was bom in
Medina, Orleans Co., N. Y.,
July 24, 1 832. His father, John
Bagley, was a native of New
Hampshire, his mother, Mary M.
Bagley, of Connecticut. He at-
tended the district school of Lock-
port, N. Y., until he was eight years
old, at which time his father moved
to Constantine, Mich., and he at-
tended the common schools of that
village. His early experience was
|\| like that of many country boys whose
parents removed from Eastern States
to the newer portion of the West.
His father being in very poor circum-
stances, Mr. B. was obliged to work
as soon as he was able to do so.
Leaving school when 13 years of age
he entered a country store in Constan-
tine as clerk. His father then re-
moved to Owosso, Mich., and he again
f engaged as clerk in a store. From
early youth Mr. B. was extravagantly fond of reading
and devoted every leisure moment to the perusal of
such books, papers and periodicals as came within
his reach. In 1847, he removed to Detroit, where he
secured employment in a tobacco manufactory and
remained in this position for about five years.
In 1853, he began business for himself in the man-
ufacturing of tobacco. His establishment has become
one of the largest of the kind in the West. Mr. B.
has also been greatly interested in other manufactur-
ing enterprises, as well as in mining, banking and in-
surance corporations. He was President of the
Detroit Safe Company for several years. He was one
of the organizers of the Michigan Mutual Life Insur-
ance Company of Detroit, and was its President from
1867 to 1872. He was a director of the Amer-
ican National Bank for many years, and a stock-
holder and director in various other corporations.
Mr. B. was a member of the Board of Education two
years, and of the Detroit Common Council the same
length of time. In 1865 he was appointed by Gover-
nor Crapo one of the first commissioners of the
Metropolitian police force of the city of Detroit, serv-
ing six years. In November, 1872, he was elected
Governor of Michigan, and two years later was re-
elected to the same officj, retiring in January, 1877.
He was an active worker in the Republican party, and
for many years was Chairman of the Republican
State Central committee.
Governor Bagley was quite liberal in his religious
views and was an attendant of the Unitarian Church.
He aimed to be able to hear and consider any new
thought, from whatever source it may come, but was not
bound by any religious creed or formula. He held
in respect all religious opinions, believing that no one
can be injured by a firrh adherence to a faith or de-
nomination. He was married at Dubuque, Iowa, Jan.
16, 1855, to Frances E. Newberry, daughter of Rev.
Samuel Newberry, a pioneer missionary of Michigan,
who took an active part in the early educational mat-
ters of the State and in the establishment of its ex-
cellent system of education. It was principally
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JOHN J, BAG LEY,
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through his exertions that the State University was
founded. Mr. B. s family consists of seven children.
As Governor his administration was charac-
terized by several important features, chief among
which were his efforts to improve and make popular
the educational agencies of the State by increasing
the faculty of the University for more thorough in-
struction in technical studies,by strengthening the hold
of the Agricultural College upon the public good will
and making the general change which has manifested
itself in many scattered primary districts. Among
others were an almost complete revolution in the
management of the penal and charitable institutions
of the State; the passage of the liquor-tax law, taking
the place of the dead letter of prohibition; the estab-
lishing of the system of dealing with juvenile offend-
ers through county agents, which has proved of great
good in turning the young back from crime and plac-
ing the State in the attitude of a moral agent ; in se-
curing for the militia the first time in the history of
Michigan a systematized organization upon a service-
able footing. It was upon the suggestion of Gov. B.
in the earlier part of his administration that the law
creating the State Board of Health, and also the law
creating a fish commission in the inland waters of the
State, were passed, both of which have proved of great
benefit to the Slate. The successful representation
of Michigan at the Centennial Exhibition is also an
honorable part of the record of Gov. B. s adminis-
tration.
As Governor, he felt that he represented the State
— not in a narrow, egotistical way, but in the same
sense that a faithful, trusted, confidential agent rep-
resents his employer, and as the Executive of the
State he was her " attorney in fact" And his intelli-
gent, thoughtful care will long continue the pride of
the people he so much loved. He was ambitious —
ambitious for place and power, as every noble mind
is ambitious, because these give opportunity. How-
ever strong the mind and powerful the will, if there
be no ambition, life is a failure. He was not blind to
the fact that the more we have the more is required
of us. He accepted it in its fullest meaning. He
his ideas of what they should be. With a heart as
broad as humanity itself; with an intelligent, able and
cultured brain, the will and the power to do, he
asked his fellow citizen to give him the opportunity to
labor for them. Self entered not into the calculation.
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His whole life was a battle for others; and he entered V
the conflict eagerly and hopefully. ^
His State papers were models of compact, busi- #??*
ness-like statements, bold, original, and brimful of ^
practical suggestions, and his administratbns will long ^
be considered as among the ablest in this or any
other State.
His noble, generous nature made his innumerable
benefactions a source of continuous pleasure. Liter-
ally, to him it was ^ more blessed to give than to
His greatest enjoyment was in witnessing the com-
fort and happiness of others. Not a tithe of his char-
ities were known to his most intimate friends, or even
to his family. Many a needy one has been the recipi-
ent of aid at an opportune moment, who never knew
the hand that gave.
sponse to some charitable request, and said to him :
**Govemor, you give away a large sum of money ; about
how much does your charities amount to in a year.^**
He turned at once and said : ** I do not know, sir ; I
do not allow myself to know. I hope I gave more
this year than I did last, and hope I shall give more
next year than I have this." This expressed his idea
of charity, that the giving should at all times be free
and spontaneous.
During his leasure hours from early life, and espe-
cially during the last few years, he devoted much time
to becoming acquainted with the best authors. Biog-
raphy was his delight; the last he read was the **Lifc
and Wotk of John Adams," in ten volumes.
In all questions of business or public affairs he
seemed to have the power of getting at the kernel of V
the nut in the least possible time. In reading he
would spend scarcely more time with a volume than
most persons would devote to a chapter. After what
seemed a cursory glance, he would have all of value
the book contained. Rarely do we see a business
man so familiar with the best English authors. He
was a generous and intelligent patron of the arts, and
his elegant home was a study and a pleasure (^
to his many friends, who always found there a
hearty welcome. At Christmas time he would spend }
days doing the work of Santa Qaus. Every Christmas ^
eve he gathered his children about him and, taking \
the youngest on his lap, told some Christmas ' story, ^
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closing the entertainment with **The Night
Christmas," or Dickens's "Christmas Carol.
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GOVERNORS OF MICHIGAN.
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HARLES M. CROSWELL,
Governor of Michigan from
Jan. 3, 1877 to Jan. i, 1881,
was bom at Newburg, Orange
County, N. Y., Oct. 31, 1825.
He is the only son of John and
Sallie (Hicks) CroswelL His
father, who was of Scotch-Irish
extraction, was a paper-maker,
and carried on business in New
York City. His ancestors on
his mothers side were of Knicker-
bocker descent. The Croswell
family may be found connected
with prominent events, in New York
and Connecticut, in the early exis-
tence of the Republic. Harry Cros-
President Jefferson, published a pa-
per called the Balance^ and was
prosecuted for libeling the President
under the obnoxious Sedition Law.
He was defended by the celebrated
Alexander Hamilton, and the decis-
ion of the case establised the important ruling that
the truth might be shown in cases of libel. Another
member of the family was Edwin Croswell, the fam-
ous editor of the Albany Argus; also, Rev. William
Cxoswell, noted as a divine and poet.
When Charles M. Croswell was seven years of age,
his father was accidentally drowned in the Hudson
River, at Newburg ; and, within three months preced-
ing that event, his mother and only sister had died, —
thus leaving him the sole surviving member of the
family, without fortune or means. Upon the death
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of his father he went to live with an uncle, who, in
1837, emigrated with him to Adrain, Michigan. At
sixteen years of age, he commenced to learn the car-
penter s trade, and worked at it very diligently for
four years, maintaining himself, and devoting his spare
time to reading and the acquirement of knowledge.
In 1846, he began the study of law, and was ap-
pointed Deputy Clerk of Lenawee County. The du .
ties of this office he performed four years, when he /*s
was elected Register of Deeds, and was re-elected
in 1852. In 1854, he took part in the first movements
for the formation of the Republican party, and was a
member and Secretary of the convetion held at Jack-
son in that year, which put in the field the first Re-
publican State ticket in Michigan. In 1855, he
formed a law partnership with the present Chief- Jus-
tice Cooley, which continued until the removal of
Judge Cooley to Ann Arbor.
In 1862, Mr. Croswell was appointed City Attorney
of Adrian. He was also elected Mayor of the city
in the spring of the same year ; and in the fall was
chosen to represent Lenawee County in the State
Senate. He was re-elected to the Senate in 1864,
and again in 1866, during each term filling the posi-
tions above mentioned. Among various reports made
by him, one adverse to the re-establishment of the
death penalty, and another against a proposition to
pay the salaries of State officers and judges in coin,
which then commanded a very large premium, may
be mentioned. He also drafted the act ratifying the
Thirteenth Amendment to the Federal Constitution,
for the abolishment of slavery, it being the first
amendment to the instrument ratified by Michigan.
In 1863, from his seat in the State Senate, he de-
livered an elaborate speech in favor of the Proclama-
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CHARLES M.
CRO SWELL.
don of Emancipation issued by President Lincoln,
and of his general policy in the prosecution of the
war. This, at the request of his Republican associ-
ates, was afterwards published. In 1867, he was
elected a member of the Constitutional Convention,
and chosen its presiding officer. This convention
was composed of an able body of men ; and though,
in the general distrust of constitutional changes
which for some years had been taking possession of
the people, their labors were not accepted by the pop-
ular vote, it was always conceded that the constitu-
tion they proposed had been prepared with great care
and skill.
In 1868, Mr. Croswell was chosen an Elector on
the Republican Presidential ticket; in 1872, was
elected a Representative to the State Legislature
from Lenawee County, and was chosen Speaker of
the House of Representatives. At the close of the
session of that body his abilities as a pariiamentarian,
and the fairness of his rulings were freely and form-
ally acknowledged by his associates ; and he was pre-
sented with a superb collection of their portraits
handsomely framed. He was, also, for several years.
Secretary of the State Board for the general supervis-
ion of the charitable and penal institutions of Michi-
gan ; in which position, his propositions for the amel-
ioration of the condition of the unfortunate, and the
reformation of the criminal classes, signalize the be-
nevolence of his nature, and the practical character
of his mind.
In 1876, the general voice of the Republicans of
the State indicted Mr. Croswell as their choice for
Governor; and, at the State Convention of the party
in August of the same year, he was put in nomination
by acclamation, without the formality of a ballot. At
the election in November following, he was chosen to
the high position for which he had been nominated,
by a very large majority over all opposing candidates.
His inaugural message was received with general
favor ; and his career as Governor was marked with
the same qualities of head and heart that have ever
distinguished him, both as a citizen and slatesaian.
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Governor Groswell has always prepared his ad- ^
dresses with care ; and, as his diction is terse, clear, ^
and strong, without excess of ornament, and his de- i
livery impressive, he is a popular speaker; and many )v
of his speeches have attracted favorable comment in
the public prints, and have a permanent value. He
has always manifested a deep interest in educational
matters, and was for years a member and Secretary of
the Board of Education of Adrain. At the formal
opening of the Central School building in that city,
on the 24th day of April, 1869, he gave, in a public
Schools."
In his private life. Governor Croswell has been as
exemplary as in his public career he has been suc-
cessful and useful. In February, 1852, he was mat-
ried to a daughter of Morton Eddy, Lucy M. Eddy,
a lady of many amiable and sunny qualities. She j.
suddenly died, March 19, 1868, leaving two daugh- ^
ters and a son. Governor Croswell is not a member ^^^
of any religious body, but generally attends the Pres- 1=3
byterian Church. He pursues the profession of law, ^
but of late has been occupied mainly in the care of his «^
own interests, and the quiet duties of advice in C
business difficulties, for which his unfailing pru-
dence and sound judgment eminently fit him. Gov-
ernor Croswell is truly |x>pular, not only with those of
like political faith with himself, but with those who
differ from him in this regard.
During Gov. Croswell's administration the public f
debt was greatly reduced; a policy adopted requiring ^
the State insritutions to keep within the limit of ap«
propriations; laws enacted to provide more effectually
for the punishment of corruption and bribrery in elec-
tions; the State House of Correction at Ionia and the
Eastern Asylum for the Insane at Pontiac were opened, /^
and the new capital at Lansing was completed and
occupied. The first act of his second term was to pre- '
side at the dedication of this building The great riot (
at Jackson occured during his administration, and it
was only bv his promptness that great distrucrion of
both life and propert) V .w invented at tha* time. "
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GOVERNORS OF MICHIGAN.
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DAVID H. JEROME, Gover-
aior of from Jan. i, 1881, to
Jan. I, 1883, was born at De-
troit, Mich,, Nov. 17, 1829.
His parents emigrated to
Michigan from Trumansburg,
Tompkins Co., N. Y., in 1828,
locating at Detroit. His father
died March 30, 1831, leaving
twice married, and four of the
children living at the time of his
death were grown up sons, the off-
spring of his first union. Of the
five children by his second marriage, David H. was
the youngest. Shortly after Mr. Jerome's death, his
widow moved back to New York and settled in
Onondaga County near Syracuse, where they remained
until the fall of 1834, the four sons by the first wife
continuing their residence in Michigan. In the fall
of 1834, Mrs. Jerome came once more to Michigan,
locating on a farm in St. Clair County. Here the
Governor formed those habits of industry and ster-
ling integrity that have been so characteristic of the
man in the active duties of life. He was sent to the
district school, and in the acquisition of the funda-
mental branches of learning he displayed a precocity
and an application which won for him the admiration
of his teachers, and always placed him at the head
of his classes. In the meantime he did chores on
the farm, and was always ready with a cheerful heart
and willing hand to assist his widowed mother. The
heavy labor of the farm was carried on by his two
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older brothers, Timothy and George, and when 13
years of age David received his mother's permission to
attend school fit the St. Clair Academy. While attend-
ing there he lived with Marcus H. Miles, now de-
ceased, doing chores for his board, and the following
winter performed the same service for James Ogden,
also deceased. The next summer Mrs. Jerome
moved into the village of St. Clair, for the purpose of a>'.
continuing her son in school. While attending said
academy one of his associate students was Sena-
tor Thomas W. Palmer, of Detroit, a rival candidate
before the gubernatorial convention in 1880. He
completed his education in tlfe fall of his i6th- year,
and the following winter assisted his brother Timothy
m hauling logs in the pine woods. The next summer
he rafted logs down the St. Clair River to Algonac.
In 1847, M. ^' Miles being Clerk in St. Clair Coun-
ty, and Volney A. Ripley Register of Deeds, David
H. Jerome was appointed Deputy to each, remaining
as such during 1848-49, and receiving much praise
from his employers and the people in general for the
ability displayed in the discharge of his duties. He
spent his summer vacation at clerical work on board
the lake vessels.
In 1 849-^5 o, ^^ abandoned office work, and for the
proper development of his physical system spent
several months hauling logs. In the spring of 1850,
his brother "Tiff" and himself chartered the steamer ^
"Chautauqua," and "Young Dave" became her mas- Y
ter. A portion of the season the boat was engaged
in the passenger and freight traffic between Port
Huron and Detroit, but during the latter part was
used as a tow boat. At that time there was a serious
obstruction to navigation, known as the "St. Clair
Flats,** between Lakes Huron and Erie, over which
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vessels could carry only about 10,000 bushels of grain.
Mr. Jerome conceived the idea of towing vessels
from one lake to the other, and put his plan into
operation. Through the influence of practical men, —
among them the subject of this sketch, — Congress
removed the obstruction above referred to, and now
vessels can pass them laden with 60,000 or 80,000
bushels of grain.
During the season, the two brothers succeeded
in making a neat little sum of money by the sum-
mer s work, but subsequently lost it all on a contract
to raise the "Gen. Scott," a vessel that had sunk in
Lake St. Clair. David H. came out free from debt,
but possessed of hardly a dollar of capital. In the
spring of 185 1, he was clerk and acting master of the
steamers "Franklin Moore" and "Ruby," plying be-
tween Detroit and Port Huron and Goderich. The
following year he was clerk of the propeller "Prince-
ton," running between Detroit and Buffalo.
In January, 1853, Mr. Jerome went to California,
by way of the Isthmus, and enjoyed extraordinary
success in selling goods in a new place of his selec-
tion, among the mountains near Marysville He re-
mained there during the summer, and located the
Live Yankee Tunnel Mine, which has since yielded
millions to its owners, and is still a paying investment.
He planned and put a tunnel 600 feet into the mine,
but when the water supply began to fail with the dry
season, sold out his interest. He left in the fall of
1853, and in December sailed fwm San Francisco for
New York, arriving at his home in St. Clair County,
about a year after his departure. During his absence
his brother "TifT* had located at Saginaw, ana in
1854 Mr. Jerome joined him in his lumber operations
in the valley. In 1855 the brothers bought Black-
mer & Eaton's hardware and general supply stores,
at Saginaw, and David H. assumed the management
of the business. From 1855 to 1873 he was also ex-
tensively engaged in lumbering operations.
Soon after locating at Saginaw he was nominated
for Alderman against Stewart B. Williams, a rising
young man, of strong Democratic principles. The
ward was largely Democratic, but Mr. Jerome was
elected by a handsome majority. When the Repub-
iican party was bom at Jackson, Mich., David H.
Jerome was, though not a delegate to the convention,
one of its "charter members.*" In 1862, he was com-
missioned by Gov. Austin Blair to raise one of the
six regiments apportioned to the State of Michigan. V
Mr. Jerome immediately went to work and held v'
meetings at various points. The zeal and enthusiasm 1^;
displayed by this advocate of the Union awakened a ^
feeling of patriotic interest in the breasts of many .J
brave men, and in a short space of time the 23d
Regiment of Michigan Volunteer Infantry was placed
in the field, and subsequently gained for itself a bril-
liant record.
In the fall of 1862, Mr. Jerome was nominated by
the Republican party for State Senator from the 26lh
district, Applcton Stevens, of Bay City, being his op- \
ponent. The contest was very exciting, and resulted ^
in the triumphant election of Mr. Jerome. He was ^
twice renominated and elected both times by in-
creased majorities, defeating George Lord, of Bay
City, and Dr. Cheseman, of Gratiot County. On tak-
ing his seat in the Senate, he was appointed Chair-
man of the Committee on State Affairs, and was ac-
tive in raising means and troops to cany on the war.
He held the same position during his three terms of '
service, and introduced the bill creating the Soldiers* '
Home at Harper Hospital, Detroit.
He was selected by Gov. Crapo as a military aid,
and in 1865 was appointed a member of the Stale
Military Board, and served as its President for eight
consecutive years. In 1873, he was appointed by
Gov. Bagley a member of the convention to prepare
a new State Constitution, and was Chairman of the
Committee on Finance.
In 1875, Mr. Jerome was appointed a member of
the Board of Indian Commissioners. In I876 he was
Chairman of a commission to visit Chief Joseph, the
Nez Perce Indian, to arrange an amicable settlement
of all exisring difficulties. The commission went to
Portland, Oregon, thence to the Blue Hills, in Idaho,
a distance of 600 miles up the Columbia River.
At the Republican State Convention, convened at
Jackson in August, 1880, Mr. Jerome was placed in
the field for nomination, and on the 5th day of the
month received the highest honor the convention
could confer on any one. His opponent was Freder-
ick M. Holloway, of Hillsdale County, who was su|>-
ported by the Democratic and Greenback parties.
The State was thoroughly canvassed by both parties,
and when the polls were closed on the evening of
election day, it was found that David H. Jerome bad
been selected by the voters of the Wolverine State to
occupy the highest position within their gift.
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GOVERNORS OF MICHIGAN
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OSIAH W. BEGOLE, the
present (1883), (iovernor of
Michigan was born in Living-
ston, County, N. Y., Jan. 20,
18 1 5. His ancestors were of
French descent, and settled at
an early period in the Slate of
Maryland. His grandfather, Capt.
Bolles, of that State, was an offi-
cer in the American army during
the war of the Revolution. About
the beginning of the present cent-
ury both his grandparents, having
become dissatisfied with the insti-
tution of slavery, although slave-
holders themselves, emigrated to
Livingston County, N. Y., then
a new country, taking with them a
number of their former slaves, who
volunteered to accompany them.
His father was an officer in the
American army, and served during
the war of 181 2.
Mr. B. received his early education in a log school-
house, and subsequently attended the Temple Hill
Academy, at Geneseo, N. Y. Being the eldest of a
family of ten children, whose parents were in moder-
ate though comfortable circumstances, he was early
taught habits of industry, and when 2 1 years of age,
being ambitious to better his condition in life, he re-
solved to seek his fortune in the fur West, as it was
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then called. In August, 1836, he left the parental
roof to seek a home in the Territory of Michigan
then an almost unbroken wilderness. He settled in
Genesee County, and aided with his own hands in
building some of the early residences in what is now
known as the city of Flint. There were but four or
fiVQ houses where this flourishing city now stands
when he selected it as his home.
In the spring of 1839 he married Miss Harriet A.
Miles. The marriage proved a most fortunate one ,
and to the faithful wife of his youth, who lives to en-
joy with him the comforts of an honestly earned com-
petence, Mr. Begole ascribes largely his success in
life. Immediately after his marriage he commenced
work on an unimproved farm, where, by his jjcrse-
verance and energy, he soon established a good home,
and at the end of eighteen years was the owner of a
well improved farm of five hundred acres.
Mr. Begole being an antr-slavery man, became a
member of the Republican party at its organization.
He served his to^vnsmen in various offices, and was
in 1856, elected County Treasurer, which office he
held for eight years.
At the breaking out of the Rebellion he did not
carry a musket to the front, but his many friends will
bear witness that he took an active part in recruiting
and furnishing supplies for the army, and in looking
after the interests of soldiers* families at home. The ^,.
death of his eldest son near Atlanta, Ga., by a Confed- ^
rate bullet, in 1864, was the greatest sorrow of his life. * j
When a few years later he was a member in Congress ^
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JOSIAH W.
BBGOLB.
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Gov. Begole voted and worked for the soldiers'
bounty equalization bill, an act doing justice to the
soldier who bore the burden and heat of the day, and
who should fare equally with him who came in at the
eleventh hour. That bill was defeated in the House
on account of the large appropriation that would be
required to pay the same.
In 1870, Gov. Begole was nominated by acclama-
tion for the office of State Senator, and elected by a
large majority. In that body he served on the Com-
mittees of Finance and Railroads, and was Chairman
of the Committee on the Institute for the Deaf and
Dumb and Blind. He took a liberal and public-
spirited view of the importance of a new capitol
building worthy of the State, and was an active mem-
ber of the Committee that drafted the bill for the
same He was a delegate to the National Republi-
can Convention held at Philadelphia in 1872, and
was the chosen member of that delegation to go to
Washington and inform Gen. Grant and Senator
Wilson of their nominations. It was while at that
convention that, by the express wish of his many
friends, he was induced to offer himself a can-
4«date lor the 4KH«iinaiiioa of ^aeniber 4o tfae 43d Cm-
gress, in which he was successful, after competing for
the nomination with several of the most worthy, able
and experienced men in the Sixth Congressional Dis-
trict, and was elected by a very large majority. In
Congress, he was a member of the Committee on
Agricultural and Public Expenditures. Being one of
the 17 fanners in that Congress, he took an acrive
part in the Committee of Agriculture, and was ap-
pointed by that comrailtee to draft the most impor-
tant report made by that committee, and upon the
only subject recommended by the President in his
message, which he did an^ the report was printed in
records of Congress ; he took an efficient though an
unobtrusive part in all its proceedings.
He voted for the currency bill, remonetization of
silver, and other financial measures, many of which,
though defeated then, have since become the settled
k policy of the country. Owing to the position which
Mr. Begole occupied on these questions, he became a
"Greenbacker."
In the Gubernatorial election of 1882, Mr. Begole
was the candidate of both the Greenback and Dem-
-A ocratic parties, and was elected by a vote of 154,269,
>C. the Republican candidate, Hon. David H. Jerome,
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receiving 149,697 votes. Mr. Begole, in entering
upon his duties as Governor, has manifested a spirit
that has already won him many friends, and bids fair
to make his administration both successful and pop-
ular.
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The very best indications of what a man is, is what
his own townsmen think of him. We give the foK
lowing extract from the Flint GMe, the leading Re-
publican paper in Gov. Begole s own county, and it«
too, written during the heat of a political campaign,
which certainly is a flattering testimonial of his ster- ^
ling worth : C^
" So far, however, as Mr. Begole, the head of the /.
ticket, is concerned, there is nothing detrimental to
his character that can be alleged against him. He
has sometimes changed his mind in politics, but for
sincerity of his beliefs and the earnestness of his pur-
pose nobody who knows him entertains a doubt. He
is incapable of bearing malice, even against his bit-
terest political enemies. He has a warm, generous
nature, and a larger, kinder heart does not beat in
the bosom of any man in Michigan. He is not much x=:
given to making speeches, but deeds are more signif- « j
leant of a man*s character than words. There arc r:
many scores of men in all parts of the State where ^
Mr. Begole is acquainted, who have had practical ^
demonstrations of these facts, and who are liable to
step outside of party lines to show that they do not
forget his kindness, and who, no doubt, wish that he
was a leader in what would not necessarily prove a
forlorn hope. But the Republican party in Michigan
is too strong to be beaten by a combination of Demo-
crats and Greenbackers, even if it is marshaled by so ]
good a man as Mr. Begole." ^"
This sketch would be imperfect without refemng *'
to the action of Mr. B. at the time of the great calamity *
that in 1881 overtook the people of Northeastern
Michigan, in a few hours desolating whole counties
by fire and destroying the results and accumulations
of such hard work as only falls to the lot of pioneers.
While the Port Huron and Detroit committees were
quarreling over the distribution of funds, Mr. Begole
wrote to an agent in the "[burnt district " a letter, from
which we make an extract of but a single sentence : '
" Until the differences between the two committees
from them, draw on me. Let no man suffer while I
have money." This displays his true character.
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GRATIOT COUNTY.
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INTRODUCTORY.
■ »^0OBfr« - -
N THE strength of the his-
tory of a section of country
lies the biographical rec-
ord of its seitlers and later
residents. The annals of
the one class delineate its
pioneer period ; those of the
other represent its progress and the
status of the generation whose experien-
ces constitute the period closed by the
era of its collated records. Gratiot
County is fortunate in its day. Its won-
derful pioneer era laps on its present
period and the registration is complete.
Many of those whose efforts gave the
county its earliest impetus may still be
seen in its thoroughfares. Many of the
characters in the day of its first things are still on
the stage and watch with keen-eyed alertness the
manipulating of the present, still jealous for the
repute of Gratiot, and eagerly solicitous for her sub-
stantial and permanent progress.
The projectors of these records strive to establish
but one claim for its biographical integrity. It is
prepared from the stand-point of no man's prejudice
or biased opinion. To demonstrate the exact rela-
tion of every individual represented to the genera-
full
scope in
tions of the past and present is its
personal record.
Succeeding ages sweep away the debris of human
errors and perpetuate the real greatness of a com-
munity. Character stands out statuesque and events
cluster about individuals forming the grandest and
truest historical structure of which any age is capa-
ble. Only biography can fitly represent the founda-
tion, progress and ultimatum of local history and
portray with perfect justice the precise attitude and
relation of men to events and to circumstances.
Gratiot County is justly proud of her pioneer
record, and, so far as possible, the compilers of the
biographical sketches have striven to honor the rep-
resentatives of that period as well as those of to-day.
Labor and struggle, performed in the light of hope
and the earnestness of honest endeavor, established
the county on a permanent basis, and is rounding up
a period of glorious completeness. Her villages are
creditable and her agricultural community is com-
posed of the best grades of humanity.
In the following sketches but one purpose has been
kept in view — to collect floating threads of personal
record, through which the enterprise of decades to
follow may complete a perfect and continuous histor-
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OR A T/O T CO UNTY,
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EN. NATHAN CHURCH,
senior member of the bank-
ing house of Church, Bills &
Co., Ithaca, was born in
Ionia Co.» Mich., Nov. 22
1840. He is of English an-
•^^$-V»** W cestiy, and is the son of ^(1^ Lafayette and Sophronia ( Benjamin ) Church. His father was born July 5, 18 16, in Niagara Co., N, Y., near the shore of Lake Ontario, and was the youngest of nine children — seven sons and two daughters. Four of the sons and one daughter are yet living, their ages ranging from 84 to 68, and the average age being 74. The name of Church is quite a prominent one. Some of the family have rendered service to the Gov- ernment, to literature, theology or science, in almost every decade of the history of this country. The father of Lafayette, Willard Church, was a soldier of the Revolutionary war, serving gallantly under ** Mad Anthony " Wayne, and was one of the few survivors of the hardships endured by the prisoners of war on the prison ship Jersey. He was a near relative of Col. Benjamin Church, famous in the King Philip war. Four of the seven sons above referred to be- came ministers in the Baptist Church, and PharcelUis Charch, D. D., now living at Tarrytown, N. Y., is v^&^tr ^> well-known in theological circles as the author of a number of able and useful religious works. He was for a number of years editor of the New York Chron- icle^ which was afterwards merged with the Exam- iner^ and became The Examiner and Chronicle, I'wo of his sons founded the Galaxy (since bought out by the Century\ and now publish the Army ami Navy Journal. Leroy Church, another of the seven broth- ers, was for some years editor and publisher of the Chicago Standard, a Baptist newspaper well-known throughout the West. Lafayette Church (who has a more detailed sketch elsewhere in this work) came to Michigan in 1836, and was one of the pioneers of Ionia County. In 1847, he removed to Wheatland Township, Hillsdale County, and in 1854 he made his final location in Arcada Township, this county, ujxyn land purchased of the Government, where he resides, being oiie of the earliest pioneers of the county. While engaged in agriculture, he was also a worker for Christianity, having been ordained a minister in the Baptist Church. He was thus doubly occupied until the fall of 1862, when his patriotic impulses led him to offer his services to the Government, receiv- ing authority from the Governor of the State. He, with his son Nathan, and Mr. Turck, of Alma, raised a company of volunteers from among the best people in the count), and this was made Co. D, 26th Mich. Vol. Inf., of which he was commissioned Captain. > X.^ 1 4 ^ Digitized by Google W§^r't^-i-i- ?" »'* > > GRATIOT COUNTY. "^i^f-xs^f^ ^i^±^'\.l.\ '^ it t \\'^.'*^:i ^•^■■A The regiment rendezvoused at Jackson, Mich., where it was the recipient of much attention from the pat- riotic citizens and press. (Before leaving for the front, it was presented by the ladies of Jackson with a beautiful blue silk banner, which was carried into many a hard-fought engagement during the war. The blood-stained remnant is now preserved among the battle-flags in the State Military Museum at Lan- sing.) On reaching Washington, the regiment was assigned to provost duty at Alexandria, and it was thus engaged until the following spring, when it was ordered to Suffolk to aid in resisting the advance of Gen. Longstreet. Its signally gallant services in the field from that time until the close of the war — no- tably from the Wilderness to Appomattox — made it one of the best-known organizations in the service, being particularly famous as " skirmishers." Capt. Church served with his company until April 2, 1864, when he was appointed Chaplain of the regiment, and held that position until the close of the war. Since his muster-out, he has led a quiet life at his home in Arcada Township. The subject of this biography, Nathan Church, at- tended the common schools of Hillsdale and Gratiot Counties unril he was 16 years old, when he entered Kalamazoo College. After a partial course of study in that institution, he became assistant in the office of his father (who had been elected County Treas- urer), and for som^ time had entire charge of the business of that office. After three years with his father, he taught school for a time at Ithaca and St. Louis, one term in each village. He was also for a short time clerk in the store of John Jeffrey, one of the earliest in the county, in which was also located the village postoffice. It was, however, in the late civil war that he found the opportunities for which he was most naturally fitted. An eager, ambitious youth, the series of events before the firing on Sumter had deeply interested his ardent mind, and three months before he was of age he was enrolled in the volunteer army. Aug. 12^ 1 861, he enlisted in Co. C, 8th Mich. Vol. Inf., and when the organization of the company was perfected he was made Sergeant. He served in that company until Jan. 17, 1862, when, suffering terribly from rheumatism, he was discharged for disability at Beau- fort, S. C, coming home upon crutches. The next summer, having partially recovered his health, he, his father and William S. Turck raised a company by their joint efforts, which was mustered in as Co. D, 26th Mich. Vol. Inf., and of this company Lafay- ette Church was, as above mentioned, commissioned Captain, Nathan Church First Lieutenant, and Wm. '^ S. Turck Second Lieutenant. Lieut. Church's com- • mission was dated Sept. i, 1862. On the arrival of the regiment at the seat of war, it was assigned to ' provost duty at Alexandria, Va., and soon after Lieut. Church was detailed as Aid-de-camp upon the staff of Gen. Slough, Military Governor of Alexandria, which position he held until his regiment was ordered to Suffolk. April 15, 1863, he was promoted Adju- tant of his regiment, and one year from that date was , commissioned Captain. He served with his regiment ! at the siege of Suffolk, Va., in the Blackwater expedi- tions, the second campaign on the Peninsula in 1863, and in the Second Army Corps (Hancock's) through ' the memorable campaigns of 1864 and 1865. ^ In the great battle of Spottsylvania Court-House, , Va., May 12, 1864, in which 4,500 prisoners, 25 flags y, and 22 pieces of artillery were captured, his regiment • was in the front line in the assault, and was the first to reach the enemy's works — at the deadly " angle" — . which were carried after a desperate hand-to-hand fight. Adjutant Church (not having yet been mus- tered in as Captain) was with two or three non-com- nJssioned officers, the first to scale the works. His regiment lost about one-third of its men in this bat- ^ tie, seven of the nine color-guards being killed or wounded. His conduct on this occasion attracted the attention of Gen. N. A. Miles, then commanding the I St Brigade, ist Division, 2d Corps, who detailed . him at once upon his staff. He served upon this gallant Generals staff until the close of the war, except some portions of the time when in command of his regiment, holding successively the positions of Aid-de-camp, Brigade Inspector, Division Inspec- tor, Engineer Officer ist Division, and Adjutant General of the Military District of Fortress Monroe. He was appointed to the rank of Major SepL 12, 1864, having previously been brevetted as Major of ' United States Volunteers " for gallant services before Petersburg, Va, ;" and Lieutenant-Colonel, March 7, 1865, for "conspicuous gallantry and meritorious services " in the campaign terminating in Lee's sur- render at Appomattox. The 26th, under his com- mand, occupied intrenchments before Petersburg, and. ■K^^D!]:^Cn^>^ — ^4.^»f ••, Digitized by Google r-;.^ K ■■■■ J > -^^^si — 6v<4nii^nDi^v^ ->tf€^^ -«* GRATIOT COUNTY. \ 4) ,) > "> / Ax » 's during the closing months of 1864 and the early part of 1865, was engaged in almost daily fighting, except while in winter quarters. It was in the skirmish line on the 9th of April, when Lee surrendered, 'and through its lines, Gen. Grant, with a flag of truce, carried out part of the important ceremony. His regiment was mustered out June 4, 1865, but he was retained in the service of the United States by spe- cial order of the War Department, and assigned to duty as Assistant Adjutant General of the Military District of Fortress Monroe. This positon he held until Nov. 7, 1865, when he was relieved, at his own request. While here, his duties brought him frequent- ly in contact with Jefferson Davis, at that time a pris- oner in that fortress. Gen. Church was not only a brilliant officer of un- usually quick perceptions and commanding presence, but was distinguished for beiug reckless of his per- sonal safety. A newspaper account by an eye witness states that at Sailor s Creek, Col. Church, mounted upon a white horse, led two regiments, his own and the 140th Pa. Vol., in an assault upon entrenchments occupied by a superior force of the enemy, and that, being the only mounted officer, he reached the works several yards in advance of his men. The prisoners captured in the works outnumbered the attacking party. His gallant conduct in this affair elicited much comment. On the suggestion of Gen. Miles, he was appointed a Captain in the regular army at the close of the war, but this commission he declined. Returning to the employments of peace. Gen. Church formed a partnership with Wilbur Nelson, and the two opened a general merchandise store at Ithaca. This connection was prosperous and lasted until 1872, when, having become interested in lum- bering and real-estate speculations, he sold his inter- est in the store to Gilbert C. Smith. In 1866, soon after entering mercantile life, he founded the Gratiot Journal^ of which for one year he was editor, and joint proprietor with Daniel Taylor. In December of 1872, he purchased a saw-mill in Arcada Town- ship, four miles north of Ithaca. This is still owned by him, together with 1,200 acres of timheredl and in that vicinity and a large amount of other land through- out the county. He employs at present 30 men, in sawing, planing and manufacturing lumber, shingles, hoops and staves. The banking house of Church, Bills & Co. was organized in 1877, the first of the two firms doing a banking business at Ithaca. Gen. Church still deals largely in real estate, and this, with his other interests, make him one of the busiest men in the community. He has been an earnest supporter of the various railroads projected for Gratiot County. He has de- voted both time and money to bring Ithaca into rail communication with the outer world, and his friends truly say that without his efforts Gratiot's county-seat would to-day be without a railroad. He held the position of Postmaster at Ithaca for seven years, and County Clerk two terms, or four years. He was largely instrumental in organizing the Gratiot County Agricultural Society, and was its first President. Dec. 25, 1866, at Tecumseh, Lenawee County, he was united in marriage to Miss Mary H., daughter of Hon. Perley and Caroline (Brown) Bills. She was bom May 17, 1848, in that village, and graduated at the State Normal School, at Ypsilanli, in the class of 1866. To this marriage five children have been bom: Carrie Helen, Jan. 5, 1868; Leroy B., July 20, 1869; Clarence N. and Gaylord P. (twins), Aug. 12, 187 1 ; and Edgar N., Aug. i, 1874. Gaylord P. died when about a year old. Gen. Church is politically a Republican, but while he is influential in his party, he is in no sense a wire- puller or office-seeker. His title as General is given him by reason of his being appointed Quartermaster General on the staff of Governor Jerome, in 1881, which rank he held for two years. He is a remarka- bly active, clear-headed and successful business man, a public-spirited citizen, and has worked effectively for the welfare of Ithaca and Gratiot County. His many good qualities are so universally esteemed that all will be pleased to see his portrait, given opposite the beginning of this sketch. ^f©<OTWv» o V ^ ^ C9 MiiCfi/®^ ]^ohn L. Biohard, farmer, section 33, New- (^ ark Township, was born July 7, 1844, in vj.^ Pennsylvania. He is a son of John and ^ik? Rachel (Fiy) Richard, both of whom were iir natives of the Keystone State, were there mar- \ ried and resided 14 years. In 1846 they removed to Qhio, and there belonged to the farming c'^-V^>)$§i^^--
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class. In the spring of 187 1 they came to Gratiot
County and settled in the township of Newark, where
they still reside.
Mr. Richard was a child of two years when his
parents located in the Buckeye State, where he grew
to the age of 18 years, engaged in assisting on the
farm, and acquiring a fair education in the common
schools. Roused to a sense of the necessity pressing
upon the authorities of the United States Government
under the stringencies of civil war, he yielded to his
convictions of duty and enlisted Aug. 6, 1862, in the
I nth Reg. Ohio Vol. Inf., and served his country
under that enrollment three years. He was in the
battle of Hough's Ferry, Tenn., and, while on picket
guard at Lenoir Station, he, with 5 1 of his comrades,
was captured by the rebels, and conducted to
Atlanta, Ga., where they were held two weeks, and
then removed to Pemberton Castle, Richmond, and
a month later were incarcerated at Belle Isle. They
became inmates of the latter place on the first day
of January, 1864, and there remained until March 1 2,
when they were transferred to the stockade prison at
Andersonville, where their sufferings were in no sense
or degree less than those of the myriads who suc-
cumbed to the horrors of the place, or of those whose
endurance proved equal to such frightful experiences
as cannot be equaled on the recorded pages of
human suffering. The very name of Andersonville
must cause a shudder while time endures! After
seven months of horror they were sent to Savannah,
and later to Milan, whence, after a month, they
were ordered to be transferred to Blackshear, Ga.
While on their way thither the train was intercepted,
and 250 starved, ragged, forlorn human creatures, of
whom Mr. Richard was one, were paroled and sent
to the camp at Annapolis. Two weeks later they
were furloughed, and Mr. Richard returned to his
home in Ohio. In six weeks he was exchanged and
rejoined his regiment. His health was too much im-
paired for active service, and he was on detached
duty until the close of the war. On the expiration of
his term of enrollment he was discharged, at Cleve-
land, Ohio, whence he returned home.
Mr. Richard was married Dec. 28, 1865, ^^ Sarah
D., youngest daughter of Asa and Jane (Staples)
Richardson. The father was a native of Vermont,
the mother of Maine. Of this marriage, four chil-
dren have been born : Earl C, Alice I., Tacie A.,
and Laura M.
After his becoming a family man, Mr. Richard
continued to reside in Ohio until 1870. In that year,
he removed his family and interests to Gratiot Co.,
Mich., and bought 40 acres of land in Newark Town-
ship. On this he has already cleared and placed 35
acres under creditable cultivation. He is a Repub-
lican of unmistakable type, and has served his town-
ship in several official positions to which he has been
elected. He received an appointment in r88o to fill
a vacancy as Township Clerk, and has been since
twice elected to the same incumbency, which he now
holds. A branch of the body known as the Union
Prisoners of War Association, designated the Camp
of Gratiot County, has been established therein, of
which Mr. Richard is President. Himself and wife
are members of the United Brethren Church
^^^iOfinfwy^
[j,lmon Townsend, farmer, section 31, North
I Shade Township, is a son of Josiah and
Dolly (Parker) Townsend, natives of Mas-
sachusetts and Connecticut respectively. They
i both died in the State of New York, the father
in Wayne and the mother in Jefferson County.
Almon was born in Jefferson Co., N. Y., Jan. 7,
1804, and remained under the parental care until he
was 2 1 years of age, when he bought 200 acres of
land in his native county. He improved 160 acres
of this land, and there made his home for a period
of 28 years, when he sold it and moved to Wayne
County, same State. There he remained, farming
and stock-raising, for five years, until 1865, when he
again sold out and came to Hubbardston, Ionia
County, this State, and lived for about one year.
From this point he moved to Clinton County, this
State, and entered upon the arduous task of clearing
and improving a new farm, which he successfully ac-
complished, and erected a house and barn thereon,
at a cost of some $2,000. Mr. Townsend was united in marriage to Miss Chloe, daughter of Gad and Sally Chapin, residents of Jefferson Co., N. Y., Sept. 28, 1828. The father and mother died in their native county at an early day, and the wife passed away from earth in Aug- ust, 1880. 'VI )'v^ ': -^<-^C!i:^:il!]>>>A _^-.ip«\<;K_ -l^^f.'>'- Digitized by Google :=;N^i.X^t> .<Xv._ T3V<^^^Illi:^nil>>T- ^ GRATIOT COUNTY. i8i J In 1 88 1, Mr. Townsend removed from Clinton to this county and settled on 80 acres of Government land on section 31, on which he is now residing. Mr. Townsend was again married, his second wife being Mrs. Emma S. Myers, daughter of John and Lorinda (Wales) Robbins, natives of Massachusetts and New York respectively. The father has constantly followed the occupation of farming, and is at present living in Clinton County, this State. The mother died in Jefferson Co., N. Y., in 1845. Mrs. Emma Townsend, the wife of our subject, was born in Lewis Co., N. Y., April 17, 1834, and is the mother of four children, namely, Ardella I., Dempster E., Jerome W. and Orrin A. The hus- band and wife are members of the Methodist Epis- copal and Christian Churches, respectively. Mr. Townsend is a man of iron constitution, hale, hearty and enjoying life at 80 years of age. In po- litical opinion and belief he is a staunch Republican. '^ ^34=4-^hH^ 'ohn Lewis, farmer and stock-raiser, section 9, Sumner Township, was born in Salem Township, Washtenaw Co., Mich., Feb. 21, 1833, and is probably one of the oldest natives of Michigan now living in Gratiot County. His parents, John and Jane (Lewis) Lewis, were natives of Steuben Co., N. Y., and of Dutch ancestry. They followed farming, and coming to Michigan in 1828, were among the first settlers in Washtenaw County. Ann Arbor and Ypsilanti were then small villages. The first newspaper, the Emigrant^ was started a year after their arrival. Indians were nu- merous. John was a strong young fellow, and as he grew up he helped fell the timber and clear their farm of 160 acres. It is likely that these pioneer experi- eflces have had their effect on his after life, in mak- ing him better able to face the cold world. Losing his father when he was 16 yearsold, he was obliged to look out for himself; and he worked out by the month in the woods and among the neighboring farmers. Jan. i, 1855, in his native county, he mar- ried Miss Theda M. Noble, born in Wayne Co., Mich., Sept. 25, 1837. She was reared and educated in Washtenaw County. Mr. and Mrs. Lewis then settled on the farm which he had purchased when 22 years old. He af- terward purchased a larger farm, which he had to give up in the hard times that existed about the open- ing year of the war. In 1863, he moved to Living- ston County, where he rented a farm for three years ; and in February, 1866, he settled on 60 acres on section 9, Sumner Township, which he had purchased the previous fall. To this farm he has added 60 acres, and more than half of his farm is well improved and cultivated. He has also a suitable residence and bams. Mr, Lewis has been in every sense an active man. For 14 seasons he ran a threshing-machine ; and he purchased the first machine ever brought into his native township. He has also lumbered extensively, putting in 1,000,000 feet one winter. He has held various offices in his school district, and politically is a Republican. His wife has for 20 years been an active member of the United Brethren Church. Mr. and Mrs. L. are the parents of two children: Her- bert H., born Feb. 21, i860; Cora M., born March 2, 1867. v^ ames T. Hall, resident at St. Louis, was a son of Abraham and Hannah (Jones) Hall. The parents were both of pure English ex- traction, and emigrated to the New World about 1832 or 33. They first located in Herkimer Co., N. Y., and from there moved to Oneida County, same State, where the father followed the occupation of a farmer until his death in 1856. The mother died in the same county in 1841. James T. Hall, the subject of our biographical notice, was born in Herkimer Co., N. Y., Feb. 8, 1836. When one year of age he was taken by his parents to Oneida County, same State. He resided in that county, working on his father's farm and at- tending the common schools, until 1868, when his parents had both deceased, and he came to this coun- ty and located at Alma. Oh his arrival at Alma he associated himself with a Messrs. Pierce and Ward, under the firm name of Pierce, Hall & Ward, in the lumber business. The firm had a lumber-yard at Alma and also a mill, and shipped the product of the c ^: Y Digitized by Google$«^#
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latter to Saginaw. They were also engaged in the
purchase of tracts of timber land on Pine River.
The partnership lasted until 1875, when it was mutu-
ally dissolved.
Politically, Mr. Hall is a Democrat. In the fall
of 1874 he was elected County Register of Deeds,
running against Joseph H. Seaver, of Ithaca, and, al-
though the county was conceded to be 800 Republi-
can, Mr. Hall was elected by a majority of 104 votes.
In 1876 he again ran for the same position, but was
defeated.
After his retirement from office, Mr. Hall engaged
conductor, and followed that occupation until 1880,
when he became Superintendent of the road. He
served in that capacity from June, 1880, to June,
1883, when the road was sold to the Detroit, Lan-
sing & Northern Railroad. After quitting the above
business he commenced the manufacture of patent
hoops, at Alma. His machine was one of three in
the United States, and cut the hoops from the solid
log, at the rate of 100 per minute. They ship to
Chicago, New York city, St. Louis (Mo.), and Sagi-
naw City, and are meeting with signal success in the
Mr, Hall was united in marriage, June 6, 1867, at
Holland Patent, Oneida Co., N. Y., to Miss Catherine
L. Hamlin (daughter of Joseph and Delia Hamlin),
born in Holland Patent, April i, 1841. Their union
has been blessed with two children : Jessie W., bom
at Alma, March 10, 1870; and Nina A., born at
Alma, in October, 1871.
Mr. Hall held the position of Supervisor of Ar-
cada Township fourterms — 187 1-72-74-77. Socially
he is a member of the Order of Masonry, Knights
Templar, A. O. U. W., and K. of H., and has been
Trustee of the village of St. Louis one term — 187 1-2.
illiam J. Marshall, farmer, section ^;^^
North Star Township, was born in the
county of Livingston, State of New York
March 30, 1833. He is a son of William and
Elizabeth (Chase) Marshall, natives of the
Empire State. They moved to Allegany Co., same
State, in 1841, and after remaining there two years,
in 1843, ^^^ when our subject was but ten years old.
came to this Slate and settled in Ingham County. ;
Here William remained attending the common
schools, assisting his father in the support of the *
family and developing into manhood. In 1856, ',
when 23 years of age, Mr. Marshall left the parental -^
home in Ingham County and came to this county.
He first settled on section 9, North Star Township,
and now owns 100 acres of good agricultural land on
section 33. Nov. 26, of this year, he was unitedin
marriage to Sarah, daughter of Abijah L. and Phebe
(Driggs) Clark. The father is deceased, and the V
mother is still living in Bunker Hill, Ingham County, .^
this State. Mrs. M. was born in Batavia, Genesee )
Co., N. Y. She received a good education in the
common schools of her native county and attending
Michigan Central College, then located at Spring
Arbor and now being at Hillsdale, Mich. Her desire
and aim was to become proficient as a teacher, and
so studiously did she apply herself to the accom-
plishment of that end that, while but 14 years of
age, her knowledge was considered sufficient to
enable her to enter upon her labors of imparting
knowledge to the young, which occupation she has
successfully followed for a number of years, receiving
numerous encomiums upon her competency, pro-
ficiency and the success of her work. She has
taught in Genesee Co., N. Y. ; Jackson, Ingham and
Gratiot Counties, this State. She taught eight terms
in District No. 5, North Star Township, this county,
the last term being in the winter of 188 1-2.
When the cloud of rebellion arose and threatened
the Nation with dissolution, and when every loyal
heart beat with a throb of sorrow at the injustice of
their brothers in dishonoring the ** Flag of our Fa-
thers " by their attack on Sumter, our subject joined
the ranks of the defenders of the Nation's honor and
enlisted in Co. D, 26th Mich. Vol. Inf., Aug. 9, 1862.
He was on detail service most all the time during his
term of enlistment and was discharged June 5, 1865,
after serving almost three years.
Mr. Marshall has cleared for himself and others
over 150 acres of land. When he began in this
county he had no team and he had to work two days
for the use of an ox team one day. He finally got
possession of a yoke of calves and soon had a team
of his own. He went to Maple Rapids to purchase
flour, a distance of 20 miles, and his conveyance was
a two-wheeled cart with a wood-rack on it; he
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walked all the way, and two-thirds of the way he was
compelled to go on logs to keep out of the water; and
the money he paid for the flour he earned by chop-
ping a road four rods wide and clearing two and a
half rods wide, at six cents a rod, through a heavy
timber. In fact, Mr. M. experienced all the trials so
well known to the old pioneers of the county.
Mr. and Mrs. M. have one child living and one
dead Phebe E. (Mrs. George Belding, of North
Star Township) is the living child, and William L.
died at five years of age. They also have an adopted
son, Benjamin J. Mr. M. is a member of the Ma-
sonic Order.
i— <-S€ij4H^«-*---*- —
I homas R. Payne, farmer, section 28, Fulton
Township, is a son of Arnold and Loana
(Parker) Payne, natives of Rhode Island
and New York State. They first settled after
marriage in New York, and afterwards came
to Michigan, locating at Green Oak, Living-
ston County. They afterwards removed to Ingham
County, and several years later, in 1846, they came
to Fulton Township, this county. She died in 1850,
and he followed Nov. 23, 1879.
Their family was composed of eight sons and ^yt
daughters. Thomas R., the youngest, was born in
Ingham Co., Mich., Jan. 14, 1845, and was one year
old when his parents removed to Gratiot County.
He remained at home attending the common schools
and working on the parental farm until 21 years old,
except a year and a half spent in the service of his
country. He enlisted, in December, 1863, in the 4th
Mich. Vol. Cav., and served till July, 1865. May
18, 1864, in a fight at Kingston, Ga., he was wounded
in the abdomen. In consequence of this he was
transferred to the Veteran Reserve Corps, where he
served until his discharge.
Returning from the army he worked his fathers
farm on shares until the latter s death. He has
owned at diflferent times various tracts of land and
in 1879 he bought 80 acres on section 28, Fulton,
where he now resides. He now owns 90 acres of land,
70 of which are nicely cultivated. He has built a
modern residence and barn, which will compare
favorably with any in Fulton Township.
He was first married in Fulton Township, Oct. 23,
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1865, to Maggie, daughter of John and Sarah (Covert)
Potes, natives of Pennsylvania and New York State.
Mrs. Payne was born in Seneca Co., N. Y., Feb. 5,
1844, and died Aug. 22, 1874, leaving three children :
Newton B., Frank J. and Maggie M. Mr. P. was
again married, in Lenawee Co., Mich., Dec. 31, 1874,
to Sarah J. Potes, youngest sister of his first wife.
She was born in Lyons, Fulton Co., Ohio, Dec. 10,
1856, and is now the mother of one daughter, Myrtie
A. Mr. and Mrs. P. are members of the Christian
Church. Politically, he is a Republican.
obert Smith, editor and proprietor of the
^ Gratiot Journal^ published at Ithaca, was
^(^^' bom April 13, 1 84 1. At the age of 14
A^ years he entered a printing office, with a pur-
pose to master a knowledge of the " art pre-
servative of all arts." He has worked in
every sphere known to that business, and is thoroughly
versed in all its various details. In i860 he removed
from his home in Syracuse, N. Y., to New York city,
where he passed six months as a journeyman printer.
He then returned to Syracuse and after a brief stay
there proceeded to Rochester, in the same State,
where he remained till the winter of 1863. He then
came to Lansing, Mich., and obtained employment
in the State printing office. In the summer of 1864
he and H. S. Hilton went to St. John s and pur-
chased the Clinton Republican, They continued the
publication of 'that journal till 1869. During this
period Messrs. Hilton & Smith, in company with C.
F. Smith, established the Flint Globe ^ the latter and
Mr. Hilton managing the Globe^ while Robert Smith
remained at St. John's and controlled the destiny of
the Republican^ making it one of the handsomest and
best weeklies in Michigan. *
In 1869, as above stated, these gentlemen disposed
of both journals, H. S. Hilton and Robert Smith
subsequently going to Jackson, Mich., where they
purchased a two-thirds interest in the Daily Citizen.
They remained there some eight months, when they
severed their connection with that journal. Mr.
Smith then returned to St. John's again, where he
temporarily established his home. The following
winter he was induced to take the management of the
job department of the Lansing State Republican
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calmly, he determined to proceed with his business,
and before he left Detroit he purchased a new office
equipment, and so expedited his movements that he
issued his paper without the loss to his patrons of a
single copy. He bought the ground property where
he is now located, on which a building was in pro-
cess of erection, the lower story being well nigh com-
pleted, and re-established himself in his business,
which he has continued to conduct, with success.
He manages a heavy job-printing business. The list
of subscribers to his paper numbers upwards of 1,700.
Mr. Smith was married Oct. 5, 1869, at St. John s,
Mich., to Miss H. Carrie Scattergood. She is a native
of Plymouth, Wayne Co., Mich., where she was born
Feb. 8, 1846, and is the daughter of Joshua and
Caroline (Barker) Scattergood. To Mr. and Mr.
Smith three children have been born : Robert, Jr., at
St. Johns, Oct. 18, 1870; Maud, at Mankato, Minn.,
Aug. 15, 1872, and Harry M., at Ithaca, Oct. 17, 1876.
[illlam H Sibley, farmer, section 18, Se-
ville Township, was born June 9, 1833, in
Columbia Co., N. Y. His parents, Will-
iam and Ruth (Vincent) Sibley, were natives
of the same county where their son was
born. The father engaged in farming in his
native State for a number of years, and in 1839 he
removed his family to Jackson Co., Mich. They
went later to Calhoun County, where, in 1864, the
father died, and the de mise of the mother occurred
in 1872.
Mr. Sibley was 11 years old when he came to
Michigan. He commenced to work by the month as
a farm laborer at 14 years old, at (5 per month, and
worked for various parties from that time on. He
was employed for (20 a month for about two years
in Branch County. He then went to Calhoun Coun-
ty, where he remained the same length of time, re-
turning thence to Branch County. He went again,
four years later, to Calhoun County, where he re-
mained four years, and then in Branch County again
until 1876, when he came to Gratiot County and lo-
cated again as stated, and has since been engaged
in farming.
Mr. Sibley was married, in 1856, to Laura M.,
daughter of Solomon and Lydia (Warner) White.
She was born June 4, 1838, in Branch Co., Mich.,
and is the second of a family of two daughters and
one son. Her parents were farmers, and her father
died in 1849 in Branch County. Her mother lives
in the city of Cold water. Mr. and Mrs. Sibley are
the pafents of three children ; Eva M., George J. and
Clara L. Mrs. Sibley is a. member of the Baptist
Church. Mr. Sibley is a Republican in polirical con-
nection, and has held the school offices of the district
where he resides.
homas T. Newton, farmer on section 31,
Fulton Township, is a son of Harris and
Eliza A. (Perrin) Newton, natives of Ver-
mont and New York. Eliza A. Perrin first
married George Chipman. After her second
marriage, Mr. and Mrs. Newton settled in Oak-
land Co., Mich., where they lived until Mr. N. s
death, Sept. 18, 1863. Mrs- N. then removed to
Lebanon, Clinton County, where she now lives.
Their family numbered nine — five sons and four
daughters.
The second son was Thomas T., born in Oakland
County, Jan. i, 1842. Educated in the common
schools, he remained at home until 21 years old, and
then went to Whitewater, Wis., and lived six months.
He then removed to Michigan. March 20, 1865, he
enlisted in the 22d Mich. Vol. Inf., being afterwards
transferred to the 29th. He was honorably dis-
charged Aug. 20, 1865. In December of the same
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187
year, he came to Clinton County and lived until
1 868, when he again went to Wisconsin, and also to
Iowa. After an absence of eight months, he bought
120 acres of wild land in Clinton County, and built a
log house. Two years later he sold, and for three
years he managed his mothers farm. In September,
1874, he purchased 200 acres, partly improved, on
section 34, North Shade, which he worked for ^s^
years. Selling this place, he then bought 160 acres
in Fulton Township, on section 31. He also owns
80 acres on section 36, North Shade, and has alto-
gether 180 acres improved.
March 17, 1870, in Lebanon, Clinton Co., Mich.,
he married Miss Martha, daughter of Benjamin and
Mary (Postle) Graham. She was born in Oakland
County Dec. 26, 1842. This marriage has been
blessed with two children : Maidie, born March 15,
187 1, and Georgiana, June 29, 1873.
Mr. Newton has been Justice of the Peace for three
years. He was elected Supervisor of North Shade
in the spring of 1879, and resigned after serving
three months. He is a member of the A. O. U. W.,
and is politically a Republican. He and wife are
members of the Christian Church, and of Essex
Grange, P. of H.
Ibridge G. Trtiver, of the firm of E. W.
Travcr & Co., manufacturers of, and deal-
ers in, coopers' supplies at St. Louis, was
bom in Columbia Co., N. Y., Nov. 16, 1833.
His parents, John J. and Catherine (Coons)
Traver, removed to Ann Arbor, Mich., in 1837,
where his father bought two farms — one of 56 acres,
situated partly within the village corporation; the
other, located near by, consisted of 80 acres. His
father s occupation was that of a remover of build-
ings, in which business the son was for several years
engaged.
Mr. Traver went to Tyrone, Livingston Co., Mich.,
in 1867, and passed the succeeding four years in
farming. He removed to Fenton, Genesee County,
from there, and engaged in the manufacture of round
hoops. He was thus employed till November, 1882,
when, in company with his son, E. W. Traver, he re-
moved to St. Louis. Continuing in the round-hoop
trade till the following spring, he and his son, as the
firm of E. W. Traver & Co., purchased of Wm. Rose
the Shook mill, known as the **St. Louis Cooperage."
They completely refitted and equipped the buildings
with new machinery, and in the winter of 1883-4
further increased their facilities for manufacturing by
setting up a saw mill of large capacity. They man-
ufacture each year millions of patent coiled hoops ;
each month they turn out hundreds of thousands of
round hoops ; and another important branch of their
business is the manufacture of soft and hard wood
staves. They handle yearly hundreds of thousands
of racked hoops; keep constantly on hand barrels
and kegs of all sizes and descriptions, and solicit cor-
respondence for all kinds of slack and tight cooper-
age. They employ upwards of a hundred men the
year round. The capacity of their mill and auxiliary
shops is about 20,000 patent coiled hoops, 10,000
round hoops and 5,000 sawed staves each day. They
have recently improved, as well as increased the
capacity of, their mill by putting in round-hoop ma-
taking advantage of the aid of each new invention in
the way of labor-saving machinery, and may reason-
ably expect, at no distant day, to be one of the lead-
ing firms of Gratiot County.
E. G. Traver, the subject of this sketch, was mar-
ried at Ann Arbor Jan. 3, 1856, to Minerva, daughter
of Jacob and Nancy Snapp. She was born June 8,
1832, in the State of New York. Of their union, two
sons were born : Edgar W., Nov. 24, 1^56, and Will-
iam H., June 19, 1863.
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dward Lake, farmer, Bethany Township,
occupies the southeast quarter of the south-
west quarter of section 20, and owns also
the 30 acres adjoining on the east. Mr. Lake
was born in Charlotte, Chittenden Co., Vt.,
Sept. 24, 1823, and grew up as a farmers son.
When six years of age his parents, Heman and Bet-
sey (Morgan) Lake, moved to Hamburg Township,
Livingston (3o., Mich., locating, in agricultural pur-
suits, upon a farm of 160 acres. When 22 years of
age he went to Iowa, with no capital, and followed
teaming, etc., there about two years ; next, he fol-
lowed lumbering a year at the mouth of the Manis-
tee River, in this State; next, in 1847, the family
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moved to Bengal Township, Clinton Co., Mich.,
bought a farm and for about two years engaged in
the manufacture of brooms.
At the last mentioned place, Dec. 7, 185 1, Mr.
Lake married Miss Harriet, a daughter of Ebenezer
and Mary A. (Sanford) Bliss, who was born in Broome
Co., N. Y., Aug. 28, 1830. They have one daughter,
Ellen, who was born in Arcada Township, this county,
March 5, 1859, and is now the wife of Allen H.
Reed, a farmer in Bethany Township, and they also
have one daughter, Gertie, who was born in that
township, March 29, 1882.
Mr. Lake remained in Clinton County about two
years after his marriage, then moved into Arcada
Township and pre-empted a quarter of section 25,
but soon sold it and bought 80 acres of timber land
adjoining, one mile north of Ithaca. Of this he
Aug. 28, 1866, he moved to his present farm, where
he purchased 120 acres, mostly timber. Of this he
has cleared 70 acres and sold 40. His son-in-law
has 40 acres adjoining on the north.
Mr. L. has built a^ nice residence here, besides
barns, etc., and has a good orchard. He is a pro-
gressive and prosperous agriculturist. When he first
settled in Arcada his nearest neighbor was a Mr.
Climer, eight miles distant, near St. Louis. He
erected a log house, and himself and family endured
the privations and trials incident to pioneer life.
In this family is an adopted son, Willie H., born
Dec. 14, 1856, in Indiana, who was taken into this
family when 14 months of age.
iUiam Greaser, farmer on section 17, Ful-
ton Township, is a son of William and
Emily (Leerett) Creaser, natives respect-
ively of England and Canada. They set-
tled in the latter country after marriage, and
in the spring of 1868 came to Michigan. A
year later they came to Fulton Township, this county,
where the father died, Sept. 17, 1873, and the mother
March 11, 1881. Their family comprised 13 chil-
dren.
The second son, William, was born in Canada
East, Aug. 24, 1827. In his early life he attended
the common schools, and worked for his father. On
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gaining his legal freedom, at the age of 21, he worked
out by the month for one year, and then went to Ver-
mont for a year. Returning to the Dominion, he
bought a farm of ^bout 50 acres, which he worked
a year and a half, and then sold. A year later he
removed to Canada West, where he purchased a farm
and lived for 16 years. In October, 187 i, he sold
out, and, coming to Gratiot County, bought half a
section. Having since disposed of a portion of his
land, he now has 150 acres, of which 1 10 are well
improved. In 1880, he built his fine residence.
Jan. 22, 1850, in Canada East, he married Miss
Elizabeth, daughter of Thomas and Elizabeth
(Brooks) McCombs, natives of Ireland. They emi-
grated to Canada, where the father died, March 12,
1863, and the mother, in June, 1868. Their daugh-
ter Elizabeth was born in Canada East, Aug. 12,
1828. Mr. and Mrs. Creaser have had 10 children,
eight of whom survive : Thomas W. B., Emily E.,
Susan S., Philip W., George A., Lucy A. J., Wilhelra-
ina E. and Violet A. Sophia and John R, are de-
ceased.
Mr. C. has held the offices of School Treasurer
and Inspector, and is politically a Democrat. He
and wife are members of the Methodist Episcopal
Church.
volin Church, farmer, section 23, Arcada
Township, was born in Wheatland Town-
f^ ship, Hillsdale Co., Mich., Dec. 22, 1853, and
is a son of Lafayette and Sophronia (Benja-
min) Church (see sketch). When one year
old he was brought by his parents to Gratiot
County. They settled on section 11, Arcada Town-
ship, and here the subject of this biographical notice
was reared and educated, working on his father's
farm until 17 years old. He then devoted one year
to the acquisition of some of the more advanced
branches of learning, attending the college at Fen-
ton ville, Genesee County. When 19 years of age
he left home, and for two years traveled through the
Scuth and West. Returning home, he remained with
his father unril 24 years old.
Dec. 9, 1877, ^^ was married to Miss Carrie,
daughter of Francis and Hattie (Hurd) Nelson, na-
tives of Michigan. Carrie was bom in Lenawee
Co., Mich., and died in Arcada Township, this
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v^ county, Aug. 2, 1879, leaving a wide circle of friends
/^^ to sympathize with her husband. Nov. 22, 1880, he
;Vj was^ again married, at St. Louis, to Miss Julia, daugh-
* terof Patrick and Bridget (Rhyne) Fitzgerald, na-
A. tives of the Emerald Isle. They follow farming, and
now reside in Arcada Township, aged respectively
76 and 54. Their daughter Julia was born in Roch-
ester, N. Y., July 5, 1859, and was there reared and
educated.
Shortly after marriage, Mr. and Mrs. Church set-
tled on 80 acres of wild land on section 23, Arcada,
which he had purchased the previous year. He has
since added 60 acres to his farm, making 140, of
which 80 acres are under cultivation. Mr. and Mrs.
C. have one son. Maxwell, bom Oct. 5, 1881. Mr.
C. is an enterprising and genial young man, and
commands the respect of all who know him. In
politics he is a Republican.
GRATIOT COUNTY.
X-A^
191
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^on. Archibald Bard Darragh, Representa-
tive from Gratiot County, resident at St.
Louis, was born Dec. 23, 1840, in La Salle
Township, Monroe Co., Mich. He is a son of
Benjamin F. and Catherine B. Darra^h. The
family legends preserve the patronymic through
its descent and trace it unmistakably to its fountain
head, which was that of one of the Scottish clans.
It is immortalized by the pen of Sir Waller Scott in
one of his historical romances.
The progenitors of the Darragh families of this
connecrion and generation, founded by inter-marriage a
line of Scotch-Irish descendants, — a race signally dis-
tinguished for meritorious traits, inherently honest,
intelligent and possessing the most valuable charac-
teristics incident to humanity. The line of Mr.
Darragh s descent on the paternal side is obscure,
from the fact patent in the nature of the race origin.
It is well known that a peculiar feature of one class
of Scotch is its utter contempt for, and abnegation of,
precedents and types. A man is what he makes
himself, is the canon of its existence; and tradi-
tionary observances and recollections are only " auld
wives' fables." The present generation is traceable
only to its immediate ancestors, who inhabited the
eastern and southeastern portions of Pennsylvania,
-^<-;]!i;
with whose interest and affairs they were promi-
nently identified. Henry and Ann (Jamison) Darragh,
great-grandparents, were natives of the North of
Ireland, and emigrated to America prior to the
Revolutionary war, settling in that part of Pennsyl-
vania now known as Bucks County. Henry Darragh
became a Captain in the Continental Army, and died
in Bucks County in 1782, at the age of 45 years.
His wife died in Bedford Co., Penn., aged 73 years.
Their family comprised seven children. George W.
Darrah, thtir youngest son (grandfather of Mr.
Darragh), was born July 12, 1778, in Bucks Co.,
Penn. He married Rebekah More Jan. 7. 1803, and
removed with his family from Fulton Co., Penn., to
Michigan, in 1834. The children were, Lewis, Benj.
F., Mary A., Geo. W., James, John and Martha.
The paternal grand-parents of the subject of
this sketch were residents of Fulton County in the
Keystone State, and came to Michigan in 1834,
where they passed the remainder of their lives.
The name of George W. Darrah (who found
it expedient to drop the letter that forms the
distinguishing link in the name), is indissolubly con-
nected with the history of the Peninsula State, from
the fact that he was an officer in the 2d Regiment
Infantry, organized and called out by Gov. Mason,
to resist the attempted jurisdiction of Ohio over
Michigan territory. He died in Monroe Co., Mich.,
in 1839, aged 61 years.
Benjamin F. Darragh was born in Fulton Co., Pa.,
in 1808, and was married to Catherine Bard, Dec.
4, 1834. She was bom Nov. 12, 1804, near Mercers-
burg, Pa., and died in April, 1863. In the ma-
ternal line the descent of Mr. Darragh of this sketch
is traceable for several generations, as his mother
came of a race just as signally distinguished for firm,
sturdy traits of character as that of her husband,
though of a tyi>e widely at variance. On the 29th
of October, 1830, Archibald Bard, her father, re-
corded his genealogy in this wise: "Archibald Bard,
who is the son of Richard Bard, who was the son of
Archibald Bard, the son of William Bard, the son of
John Bard. Richard Bard married Catherine Poe,
Dec. 22, 1756. Archibald Bard, the younger, mar-
ried Elizabeth Beatty, who had children : Richard,
Maria, William Beatty, Catherine, Margaret, Eliza-
beth, Archibald, Eliza Jane and Martha Olivia."
The record is made in the first volume of " Henry's
Exposition," now in Mr. Darragh s possession, and
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GRATIOT COU.VTY.
containing explicit and full recoids of the births,
deaths and marriages of the generation to which his
grandfather belonged. John Bard came from Ireland
in the early part of the 17th century and settled in
Maryland, whence his descendants dispersed. Rich-
ard Bard, great-grandfather of Mr. Darragh and third
in descent from John Bard, was born near Philadel-
phia, Dec. 26, 1726, and settled in that part of York
County which was afterwards set off and named
Adams County, in the State of Pennsylvania, In
1744, the war between England and France termi-
nated the historic peace established by the Quakers
between the colonists and Indians, and Braddock's
campaign, with its disastrous results, seemed to let
loose upon the borders many of the possibilities of
savage warfare. As!«aults on the frontier settlements
were frequent and resulted in murder of the whites,
or what was in most instances worse, — capture.
These hostilities grew less frequent as time pro-
gressed, but did not wholly cease until 1759.
In 1758, the Indians sent their marauding parties
into York County, and killed and abducted the fron-
riersmen and their families. On the 13th of April,
in that year, 19 ** Delawares " invested the home of
Richard Bard. The inmates were Mr. Bard, his
wife, Lieut. Potter (brother of Gen. Potter), a babe
of six months, and a bound boy. The Indians made
an entry into the house and were repulsed. But
they were too numerous to be successfully resisted,
and capitulation was determined on by the whites.
They surrendered on promise of their lives being
spared; the house was rifled of all valuables and the
other buildings fired. Lieut. Potter was murdered
soon after they had taken up their line of march, and
not long after the infant child shared the same fate.
On the fifth day Mr. Bard resolved to escape, as the
brutality of his captors and the hardships he en-
countered were fast disabling him and incapacitating
him from travel. He was sent to a spring for water,
but a short time after his resolurion was formed and
communicated to his wife ; he took advantage of the
opportunity his errand afforded, vo make his escape.
The character of the wife may be inferred from the
fact that she not only approved of his determination,
but diverted the attention of the Indiana until her
fleeing husband was beyond the reach of their ven-
geance. Can the women of this period adequately
picture to their understandings the qualities of a
woman who could deliberately ch6ose to be left to
such chances as lay before Mrs. Bard, isolated and
alone in the ijower of the most implacable of savages,
— the Delawares, This volume is honored in record-
ing her name and |)erpetuating the fame of her act
of self-sacrificing, womanly devotion. It is probable
that her native strength of character and superiority
inspired her savage captors with resi^ect, for her life
was spared and she was subjected to no indignities
beyond the hardships of the march and its incidental
privations. She was formally adopted by the tribe,
but refused to learn or use their language, 2s she
would have been obliged, in that event, by their cus-
toms, to choose or accept a husband. She was in
captivity two years and five months, and was ran-
somed by the payment of $200 by her husband, who never ceased his efforts to find her after he attained his own freedom. The story of his escape would grace the pages of romance. His sufferings rivaled those of the Unionists who came "out of the jaws of de^h " in making their escape from the stockade prison at Andersonville. He subsisted on buds and raw rattlesnakes, and finally reached Fort Pitt (Pitts- burg) where he began his search and negotiations for his wife. After their re-union, they settled in Frank- lin Co., Pa., where they reared their family. The foregoing account is abstracted from the detailed record written by Archibald, the second son, and compiled in a volume now in the possession of Mr. Darragh, entitled " Mirror of Olden-Time Border Life." Richard Bard died Feb. 22, 1799. The de- mise of his wife occurred Aug. 30, 181 1. Archibald Bard (2d) was born June 27, 1765, near Green Castle, Pa. He engaged extensively in agri- culture and oflftciated for a number of years as Judge of the County Court of Franklin Co., Pa. He >vas prominent in public life and gained some notoriety in literary circles through his biographical writings and essays on religious topics. He was married to Elizabeth Beatty, July 2, 1799, and died Oct. 18, 1832. His wife was born Jan. 17, 1774, and died in January, 1852. Mr. Darragh is the second child and elder son of his parents, to whom were l)orn five children, three of whom survive : Maria E. is the wife of William S. McDowell, a farmer of Du Page Co., 111.; James C. is Secretary and Treasurer of the Stockwell & Darragh Furniture Company of Grand Rapids* Until C.:^^ •■-vTl. ■^<^[i:i>-[ii];i>A ^'-<^^^'-7^ ^^■i> Digitized by Google A. GRA TIO T CO UN 7' K. ^ / /S V ^ he was 12 years old Mr. Darragh was a pupil in the common schools of his native county. In 1852, his parents removed to the city of Monroe, where he had the advantage of the academy there located, and he prepared for a collegiate course under the instruction of Hon. Edwin Willits, then at the head of a select school at Monroe. In the fall of 1857, Mr. Darragh entered the Classical Department of the University of Michigan at Ann Arbor, where he remained two years. Through the medium gf ^ friend, William E. Crume, he obtained a position as private tutor in Claiborne Co., Miss. He was in one of the most disloyal sections of the seditious South when the key note of the Rebellion transfixed the civilized world. The loyal blood in his veins, and the sturdy patriotism he inherited from the races to which he belongs, as- serted themselves too strongly for him to remain quiescent, even if he had not been already marked as a Yankee school-master ; but when he took the initiatory toward a speedy retreat to the North, his departure was made possible only through th*e inter- vention of the friend through whose instrumentality he went South. The latter, though true to his heart's instincts, was prominent in his own disloyalty to his country's flag; but, with cocked revolver, he protected his friend until the train, which he boarded with difficulty, bore him away toward safety. The route was made under harassing perplexities, and only by strategy and justifiable misleading did Mr. Darragh elude the rebel officials and escape deten- tion, and more probably death. He reached home and again entered the University of Michigan, where he remained a year, and was graduated in the Classical Department, receiving the degree of A. B. in 1868, after the close of the war. The influences that were abroad permeated every element and involved every class in Michigan. The inmates of her educational institutions, pupils and professors, one by one, laid aside their books and their duties and enrolled in the defense of the Union flag. Students, approaching the finale of their edu- cational career, grew impatient over the slow march of the succeeding days and received the credentials of their scholarship without a vestige of the pride and gratification which had seemed the only thing worth living for when they began tHfeir curriculum of study. But one thought ruled the hour, — men were needed at the front. Their years of effort were vain and their futures of promise only pulseless, tideless seas of baffled hopes, ambitions and energies, if the nation died in the throes of mortal agony that were nearing its vitals. The tide of Northern student life that surged toward the vortex of battle through the succeeding years of the war, was one of the sublim- est spectacles the world ever saw, and bore a weight of significance worthy the consideration of kings and prime ministers. A double incentive actuated Mr. Darragh in his views of the situation and his relation to the duties of his manhood. The same impulses that swayed others held mastery over him and the memory of the indignities to which he had been subjected, from the simple fact that accident, so to speak, gave him being under a Northern sky, brought home to him with a sharp significance the realities of the case. On the 14th of August, 1862, he enlisted as a private in Co. H, 1 8th Mich. Vol. Inf. The regiment joined the United States forces opposing the command of Kirby Smith on the fifth of April. On the 25th of the same month, private Darragh, with 62 others belong- ing to his regiment and to the " Tenth Kentucky " and " Fourth Indiana Cavalry," were captured while on picket duty near Walton, Boone Co., Ky., in a sudden charge of rebel cavalry, under John Morgan. The prisoners were marched on the double quick to Falmouth, Ky., and on the day following their arrival they were paroled by Major Dick Morgan, a nephew of the celebrated guerrilla chief The notice of ex- change of paroled prisoners was issued early in Jan- uary, 1863, and private Darragh immediately joined Co. D, Ninth Mich. Cav., having received a commis- sion as Second Lieutenant. His regiment achieved its first triumph in the spring of 1863, in the rout and capture of Everett's guerrillas, a portion of Buck- ner's command at Triplett's Bridge, Ky. It took a prominent part in the pursuit and capture of Mor- gan, the celebrated ** raider," making first acquaint- ance with the devastating rebel hordes under his command, on the fifth of July, when a detachment from its organization cut off and captured Col. Robert Alston, Morgan's Chief of Staflf, with 5 1 prisoners. The regiment was in the advance when Morgan was brought to bay on the banks of the Ohio, at Buffing- ton s Island, and made the attack with a vigor t.hat secured the capture of Col. Basil Duke and most of his immediate command. While Duke struggled to VS" f 'Vj.->«^#- ^^^f^ 9-^<->Il!i;^:i]Di1>A^ -Sjr^^i W- Digitized by LnOOQ IC V r ^ /:• K O 194 GRATIOT COUNTY. "Zi^jR^'^ -^^t>^:^m hold the field, Morgan fled north with his main body of troops. A detachment from the regiment participated in the engagement of July 20th, which resulted in the capture of the command of Morgan with the excep- tion of the rebel chief and about 500 men, who were taken prisoners with Morgan himself six days later by Cos. D, I. C. H and E, of the " Ninth," under command of Major W. B. Way, who reported offi- cially to Gen. Burnside, from Salineville, Ohio, under date of July 26, 1863 : "After a forced march yes- terday and last night, with almost continued skir- mishing, we succeeded this morning, at eight o'clock, in pressing Morgan to an engagement about half a mile from this town. After more than an hour of severe fighting, we scattered his forces in all direc- tions. The following is the result of our engage- ment: from 20 to 30 killed ; about 50 wounded; 255 prisoners. Our loss slight. My command is 250 strong." Within a month, Lieut. Darragh marched with his regiment, under Burnside, over the moun- tains into East Tennessee. The " Ninth " did good service at Loudon Bridge, Knoxville, Cumberland Gap, and aided in driving the enemy through Straw- berry Plains, Morristown, Russellville, Blue Springs, Greenville, Jonesborough and Wautaga, to the very gates of the Old Dominion. It had watered its horses in every stream from the Cumberland range to the Blue Ridge. The campaign of the winter of '63-4, in the mountains of East Tennessee, is with- out precedent in the annals of the war. The cold was extreme, and supplies, which at first were insuf- ficient, were at last wholly cut off. The soldiers were in rags ; East Tennessee, so often traversed by both armies, was destitute of provisions and forage, and the effort to keep the cavalry forces mounted was a failure. The line of daily march was marked by dead horses and abandoned equipments, and the situation well nigh rivaled the bitter recitals of Val- ley Forge. The men's feet were, many of them, des- titute of covering, save the swathings of pieces of blankets and cloth, in which they were enveloped. By the middle of February, there were but 50 service able horses in the entire command, and on the 25th of that month, Lieut. Darragh, in charge of 50 picked men, was ordered to report direct to Gen. Garrard, Brigade Commander, and until March 25th was en- gaged in scouting and reconnoitering expeditions; ^ and the command was frequently involved in skir- mishes with detachments of Confederate cavalry. In April the regiment was ordered to Kentucky to remount, and in Jutie was a prominent factor in routing Morgan at Cynthiana and driving him from the State. It was in the advance and was deployed on the right of the Union line opposed to Morgan's left. The day was won by a brilliant sabre charge, which made a complete rout. The official report of the commanding General Burbridge claimed 1,100 rebels killed, wounded and captured. During the month of July, the regiment marched through Ken- tucky and Tennessee, into Georgia, joining Sherman's conquering legions at Marietta in their advance on Atlanta. The cavalry was engaged in protecting the flanks, keeping open communications, in scouting, re- connoitering and raiding, till after the fall of Atlanta. 1 1 participated in the successful raid around At- lanta, under Kilpatrick. On the 14th day of Novem- ber, 1864, the " General" was sounded, the regiment marched out of its camp near Atlanta and took its x {position in Sherman's grand army in the first day's ^^ " March to the Sea." The progress through Georgia ^ was one continuous skirmish with the rebel cavalrj*, '\i under Gen. Wheeler. The regiment distinguished ^\ itself at Lovejoy's Station, at Macon, at Waynesboro, ^'' and at Cypress Swamp, and won the following special *' mention from Gen. Kilpatrick, in his official report to Gen. Sherman : " It has at all times behaved most handsomely and attracted my special attention." It was the escort of Gen. Sherman in the investment of Savannah, and made a gallant charge at Aiken, S. C, and was in hot action at Averysboro and at Benton- ville. The Ninth was the only Michigan cavalry regi- • ment that marched with Sherman to the ocean, and . it fired the last volley at the rebels, in behalf of the National standard, prior to the surrender of Gen. Johnston's army. The commission of Mr. Darragh as First Lieutenant was dated Feb. 12, 1864; that of Captain was conferred June 9, 1865. He was mus- , tered out of service July 21, 1865, and w^as honor- '^^ ably discharged at Jackson. I After leaving the military service, Mr. Darragh re-\\ solved to fit himself for the legal profession, and, , with that intent, went to Jackson to engage in the ;\ proper course of study under the direction of Gov. ♦ Blair. But the experiences of the years which had •^ v; > Digitized by Google J r- 'X y ^ / GRATIOT COUNTY. Vv-^ ^•A 195 s, intervened since his student days, had made havoc with his mental habits, and he found it difficult to concentrate his attention sufficiently to render his readings profitable. He obtained a position in the West-Side union school at Jackson, and had chaige of the Grammar Department two years. In 1867 he was elected the first Superintendent of Jackson County, and discharged the duties of the office two years. Mr. Darragh came to Gratiot County in 1870, and soon after established his banking business at St. Louis, where he has since prosecuted the matters common to such institutions. He has been inti- mately connected with the prominent interests of the village since he became a resident, and has officiated continuously as a member of the Village Board of Education. The perfect organization of the union school is largely due to his eflfoits and views, made practical by his own experience as an educator. He is a P.epoblican to the core, and has been active in local politics. In 1872, he was elected County Treasurer, and in 1882 was nominated and 'elected Representative of Gratiot County, receiving 62 ma- jority on the popular vote over the Fusion candidate. The canvass was spirited and the entire Fusion ticket was ele':ted with the exception of Representa- tive and Circuit Court Commissioner. Both candi- dates are residents at St. Louis, and Mr. Darragh s majority in his home township (Pine River) was 36. Mr. Darragh was active in his capacity of Assem- blyman. He served as Chairman of Committee on Private Corporations, a position for which he was pe- culiarly fitted, and he also acted on Committees on Stale Affairs and on State University. The character of Mr. Darragh needs no elabora- tion at theliands of the biographer. From the sim- ple recital of the successive events of his career the future generations who may be interested in tracing his influence and position in Gratiot County, will be at no loss to form a just estimate of his deserts. His portrait appears on page 190, and will prove a satisfaction to his friends, as it is one of the most valuable of the large collection in this volume. He was married June 8, 1875, to Annie P. Cul- bertson, of Monongahela City, Pa. She was born May 14, 1848, at Allegheny City, Pa., and is a daugh- ter of Albert and Emily (Brown) Culbertson. Mary, only child, was bom Sept. 15, 1879, at St. Louis. '' i'":' .% -^v^ ?^.\rX_ -<-Mi[i: _SS'x>.-.^ ~0250" v^ ;• atrick Brewer, farmer on section 15, Emer- iT^^^ son Township, was born in Wicklow Co., 4lfe> Ireland, Jan. i, 1825, and is the son of [;!;[ Richard and Ann (Kenney) Brewer, natives ' * ^ of the Emerald Isle, where they were small farmers. In 1850 they emigrated to Canada, setding near Kingston, Ont., and farmed there. Patrick, at the age of 27, left his parents and "worked in San- y dusky (^o , Ohio, until the summer of 1856. He ^\ then came to this State and county, and settled on ; his present farm in Fmerson Township. In this county, March 31, 1867, he was united in marriage to Mrs. Ruth Decker {nee Convis), daughter of John D. and Submitte (Graves) Convis, natives of Rhode Island and Vermont, respectively. They were married in the State of New York, and after a number of years removed to Emerson Township, this county, where they died, the father in 1867, and the mother in r86i. Ruth was born in Ontario, Wayne Co., N. Y., March 22, 1835 ; came at the age ria of nine to Shiawassee Co., Mich., and later to Gra- ;-; tiot County, where she was married. ^ Mr. and Mrs. Brewer have had four children, two >^/ of whom are living: Richard S.,born Nov. 21, 1870: Emma L., born Dec. 17, 1874; Mittie A., born Sept. 3, 1868, and died Oct. 3, 1868; Joseph A., born Sept. 16, 1869, and died Sept. 30, 1869, Mr. Brewer is ix)litically a faithful Republican. He has held the offices of Overseer of Highways and School Di- rector. /N ^^Ai^s^V >. I f ohn S. Parker, farmer, section 8, Newark , Township, was born March 25, 1841, in '" Wayn^Co., Mich. His father, John Par- ker, was a native of Vermont, and married Mary Berry, who was born in the State of New York, where they settled for a time. They afterwards removed to Ohio, and later to Michigan, ' which was then in its pioneer period, locating in Wayne County. In 1854 they settled in Newark, Gratiot County. Their family consisted of eight sons and three daughters. Mr. Parker is the fourth son, and actpiired his edu- cation in the common schools At 16 he became ^ 7- Digitized by Google 'k!m •«ti" ^^DD;^!!!!^^)^ <5j t 196 GRATIOT COUNTY, ^2*NiA2> :r^^.7r- ^ 425 master of his own fortunes, and has spent all his life thus far in the Peninsula State, with the excep- tion of two months, which were mostly passed in Missouri. In March, 1873, he bought 120 acres of land, under partial improvements, and erected there- on suitable and convenient farm buildings. He now owns 160 acres in Newark Township, of which 120 acres are under good cultivation, and 90 acres in Fulton Township, 55 of which are improved. Mr. Parker was married Dec. 24, 1873, to Mary, third daughter of John and Nancy (Dravenstot) Greer, natives of Pennsylvania. Mrs. Parker was born in Clinton County, Sept. 19, 1854. Her parents were natives of Ohio. Two children are now in- cluded in the household: Jane A., born April 23, 1876, and Roscoe B., bom July 14, 1879. In political matters Mr. Parker votes independ- ently. He is a member of the Order of Masonry. oseph A. Guthrie, physician and farmer, on section 15, Emerson Township, was born in Chenango Co., N. Y., Dec. 12, 18 15, and is the son of Nathan and Abbie (Richard- son) Guthrie, natives of New England, and of Scotch and English extraction. The Guthries for several generations back have been physicians and surgeons. Nathan Guthrie practiced in Genesee Co., N. Y., when that county was very new, and he had to contend with most of the hardships of pio- neer life. He deserves the credit of being one of the foremost in developing that now rich country, and his children were the first white children born there. The subject of this sketch was scarcely one year old when he lost his mother, and he was taken care of by his aunt and uncle. He Igst his father by death four years later, and was then left entirely to his relatives. They treated him kindly, and enabled him to obtain a practical education in the common schools. At the age of 19 he began teaching in the common schools, and by spending his earnings in better informing himself, he progressed rapidly. He studied in select schools, and then gave himself to the art of medicine, under Dr. L. Tucker, of Earl- ville, Madison Co., N. Y. He remained with that gentleman four years, and attended a course of lec- tures at Geneva, N. Y. In the spring of 1842, he secured his diploma, and he has since acquired, by a long and successful practice, the reputation of a very skillful physician. July 16, 1844, at Sandy Hill, Washington Co., N. Y.^he was married to Eunice Town, a native of Washington Co., N. Y. She died in Shiawassee Co., Mich., in September, 1846, and March 16, 1847, in Shiawassee County, he was again married, to Emma M. Convis, daughter of John D. and Submitte (Graves) Convis, natives of Vermont. She was bom in Ellisbiirg, Jefferson Co., N. Y., April 29, 1829, and when a year and a half old went with her parents to Wayne County, that State, where she received a cdmmon-school education. At the age of 16 she came to Shiawassee County, this State, and taught for a short time previous to her marriage. In 1857, Dr. and Mrs. Guthrie came to this county and set- tled on f2o acres, 80 on section 15 and 40 on sec- tion 14, to which he has since added 80 acres, and he now follows farming in connection*with the prac- tice of his profession. Their first experiences here were such as most pioneer, families undergo, though perhaps they were even more severe. The Doctor was the first regular medical graduate to practice in Gratiot County. The Dr. and Mrs. Guthrie have a family of three: Justus N., born May 21, 1848; Jesse L., born Sept. 9, 1850; and Ella C, born March 26, i860. They are members of the Baptist Church. He was one of the first four Justices of the Peace chosen in Emer- son Township, and he has held that office 12 years. He was also for some time Assistant Revenue As- sessor. Politically he is an active Republican. v^ i ^{M^harles S. Harmon, general farmer, section ^^^"^ 28, New Haven Township, is a son of ^r^i^ Walter Harmon, a native of Connecticut and a farmer by occupation, who came to this State in 1844, and located in Ionia County, as one of the first settlers in Sebewa Town- ship. He subsequently moved into Clinton County, and died November, 1861, aged about 63. His wife, Mary, nee Dicks, was also a native of Connecti- cut, and died in this county Dec. 22, 1858, aged 59. Charles S., the subject of this sketch, worked with C P ;^rvg^ ^€^^ -t ^>n % Wv>^^> — =^5€S5^ Digitized by Google r ^ •>"$$§t#®^ r .- N mmmor v'y r G^^y^ TIO T CO UNJ Y. J A y Si ^ his father on the farm in Ionia County until 19 years of age, when he returned to his native State, New York, where he was born, Sept. 16, 183 1, in Chautau- qua County. Residing in Genesee County, that State, for three years, he returned to Clinton County, where he remained with his parents until hf^ mar- riage, Oct. 15, 1854, to Miss Frances Z. White, daugh- ter of Moses H. and Miranda (Wheelock) White. (See sketch.) She was born in Jackson Co., Mich., March 13, 1839, moving afterward to Ingham County, and next to Clinton County, where she lived till her marriage. She' is the mother of five children, three of whom are dead, namely : Phebe R. and Florence M., living; and Worth H., Mary M.and Effie J., de- ceased. A year after marriage, Mr. H. bought 40 acres of land in Watertown Township, Clinton County, which he afterward sold and bought another " 40 " in the same township, where he followed agriculture for eight years. Both these places he found in a state of wild natur^ On leaving the latter place he went to Lansing, Mich., and followed teaming nearly a year. In 1864 he came to this county and lived the first year with his father-in-law ; he then purchased a 40-acre piece of land, where he now dwells, mov- ing upon it three y^rs after the purchase. To this tract he has added 40 acres more, and of the total 80 acres he has 75 acres in fine cultivation. Mr. Harmon has held the school offices of his dis- trict, and in political affairs he is a Republican. rohn M. Everden, farmer and teacher, section 30, Emerson Township, was born in Ingham Co., Mich., Oct. 5, 1852, and is a son of O. A. and Harriet Jane (Phelps) Everden, natives of Pennsylvania and New York, respectively. They were married in the latter State, and two years after came to Michigan. They located on a farm in Ingham County, where their son John was bom. He came with his parents to this county in the spring of 1854, and has since lived in Emerson Township, section 30. Being the eldest of three children, it early came to his lot to be a sort of fore- man around the farm ; but, in spite of hard work and limited advantages, he found time to obtain a fair education in the common schools of his time, so that by perseverance he qualified himself for teaching. I — = (^ I 1 At the age of 20, he began teaching, and has since taught in the winters, and farms in the summers. Of the 80 acres, .50 are well cultivated. He is con- sidered a skillful farmer and a competent teacher. He still resides on the old homestead, with his mother, a woman of sterling worth. April 19, 1883, in Saginaw City, he was united in the bonds of matrimony to Jennie, daughter of Ira and D. A. (Westcott) Van Buskirk, natives of New York. She was born in Syracuse, N. Y., Sept. 20, 1862, and came to this county in her childhood. He is connected with the Baptist Church, of Ithaca, and she, with the M. E. Church, at the same place. Mr. Everden is a member of Ithaca Lodge, No. 123, F. & A. M., and now holds the office of J. W., in that lodge. He has held I he township offices of Superintendent of Schools, Supervisor and School Inspector. Politically, he is a strong supporter of Republican principles. I illiam N. Rogers, farmer on section 33, ^ .^--^ Pine River Township, is a son of William ^'p T. and Lydia M. (Beckwith) Rogers, natives of New York State. They married and set- tled in that State, afterwards removing to Medina Co., Ohio, where they resided until their death. William N., the subject of this bio- graphical narrative, was born in New York State, Sept. 16, 1820. He was two years old when his par- ents removed to Ohio, and in that State he was edu- cated and grew to manhood. At the age of 18, he was apprenticed to the blacksmith's trade for three years at Ashland, Ohio. This business he followed most of the rime unul 1877. He came to this county in October, 1854, and set- tled on the farm which he had entered the June pre- vious, on section 33, Pine River Township. He built the first blacksmith shop in Grat»ot County, on his farm. He and four others, among them Col. Ely, Mr. Porter and J. H. Clark, cut through the woods what was known as the " middle trail." He built a log house 28 X 16, and afterwards sold his whole fann, trading 40 acres for the place on which he now resides, one yoke of steers, one cow and one barrel of pork. His present farm is all nicely under culti- ^ / c 'V • '» 'Vl:')^^^ '^^ — eA<?il!l:<DDi>^ rr w?% Digitized by VjOOQlC ■l) /^V -r<:PD:>:llD>>v GRATIOT COUNTY, > T V ^ vation. He has at different times owned various farms in Arcada and Pine River Townships. April 1 8, 1843, in Homer Township, Medina Co., Ohio, he was married to Lydia, daughter of Peter and Hannah (Taylor) Clark. They first settled in New Jersey, and afterwards removed to New York State. Thence they went to Ohio, and lived there 14 years ; and in 1854 they came to Ionia Co., Mich., where they died. Their daughter Lydia was born in Tioga Co., N. Y., Aug. 2, 1822. Mr. Rogers enlisted in the 8th Mich. Vol. Inf., and served in the Union army 16 months. He was honorably discharged May 24, 1865, at Detroit. During the first part of his service, he was em- ployed as blacksmith; and when Ralph Ely was promoted Colonel, he was detailed as cook for that popular leader. Mr. and Mrs. R. have had fivt children: Han- nah S., Roxana E., Mary C, Phebe U. R. and Will- iam H. Hannah S. was married to Henry Adams, and died April 28, 1876. Roxana E. was married to George M. Simonson, of Saginaw, and died Feb. 20, 1867. Mr. Rogers has held the various school offices, and has been a Trustee of Alma village for six years. In political sentiment, he is a Democrat. ^'^tium/fM^ S|^g)<2f999v ^f fe ddison G. Fraker, farmer, section 8, Wash- ^I^MLng ^ ington Township, is a son of Napoleon B. S|t^ and Rebecca (Merrills) Fraker, natives of New 'Jlsr York State. They followed farming, and in 1 86 1 came to Gratiot County, locating on 160 acres on section 8, Washington Township. Mr. Fraker afterwards added 20 acres, and brought 1 25 acres to a good state of improvement. He lived on this farm until 1879, when he removed to his present home in Ithaca. The subject of this sketch was born July 18, 1847, in St. Lawrence Co., N. Y., and at the age of 23 he was married to Amelia Campbell, the daughter of Cornelius and Pamelia (Amadon) Campbell, who live on a farm in Washington Township. She was born Oct. 9, 1852. Mr. and Mrs. Fraker lived first one year on section 7, Washington Township, then on their present place four years, then on another farm on the same section for four years, then set- tling permanently on their present farm. Mr. Fraker ■ ■■■J Vv -<: nn' u J • has 260 acres of land, and is extensively engaged in stock-raising, as well as farming. They have five children, named : Jennie R., Howard C, Ernest K. (died June 20, 1879), N. B. and Kittie (twins). Mr. Fraker was chosen Township Treasurer in i88i,<nd again in 1882. He has been School Di- rector, and is at present Assessor of fractional school district No. 3, Washington and Fulton Townships. ^M -^3 i^philip P. Allen, farmer, section 29, Emerson iT^^^ Township, was born in Delaware Co., N. Y., JliSr April 21, 1829, and is the son of Isaiah and }^( Elsie (Peck) Allen, natives of New York, and "f^ descendants of the Puritan fathers. They followed farming, and died in this State, some years ago. Philip, when quite young, moved vdih his father to Seneca County and afterwards to Steuben County. In these two counties he received a pretty fair education, and at the age of 19 he engaged in teach- ing in the district schools of Steuben County. This he followed until his marriage in that county, July 22, 1850, to Mary A., daughter of Richard Sawtell, a native of New England. Mary A. was born in New York, July 2, 1830. Five years after their marriage they came to this county and settled on section 29, Emerson Township. Here his wife died, Jan. 8, 1855, leaving two children to comfort her husband: Ozema F., born Nov. 14, 1852, and George H., born Feb. 4, 1855. He was again married, April 17, 1865, to Emma G., daughter of Ralph and Jane (Terry) Bellows, natives of New York and Michigan, respectively, and of English and Scotch extraction. They resided most of their lives in this State, and died here, the father Feb. 11, 1863, and the mother March 2, 1869. Emma G. Bellows was t)orn in Marshall, Mich., Jan. 25, 1846, and remained with her parents till her marriage, coming with them to Gratiot County, in 1861. Mr. and Mrs. Allen have a family of four children, as follows : Leland W., bom Feb. 5, 1866, Cecil W., Oct. I, 1870, Tessie M., June 2, 1877, and Rexford E., Oct. 6, 1882. They are members of the Baptist Advent Church. Mr. Allen is a man who is respected by all who •V ;.>^ Digitized by Google Digitized by Google i Ar^^^>A4f [ .^^'' ') Digitized by Google •:'''^>r<^ f ' \a/(/i4^ -e7^ 4s^cA.></^ Digitized by Google Digitized by Google ;- '^^ GRATIOT COUNTY, -X id — Ks0 ^ 201 t know him. He has held the office of Township Treasurer for a number of years, and has also been Township Clerk. He is now Moderator of his school district. Politically he is a Democrat. ^M£Cl2^®i^ X A / 'A SS^^997»v Fon. Charles H. Morse, farmer, stock-raiser and real-estate dealer, residing on section 29, New Haven Township, and one of the representative and energetic business men of the county, is a native of Orangeville, Wyoming Co., N. Y., where he was born Jan. 27, 1838. The parents of Mr. Morse were Harvey and Lydia (Watkins) Morse, and natives of Green and Madison Counties, N. Y. From a " History of the Morse family,** owned by the Buffalo Historical Society, we learn that the fam- ily history is of very ancient origin. It is quite clearly traced to a little town in Norway, south of Christiana. This town was named Moss, because it was a mossy country. The family took the name of Moss, and in course of succeeding generations and centuries, as in almost all names which come down to us through centuries, it has changed in form and * orthography, appearing as Moss, Morss and Morse, and some lesser variations. It is quite clear that the family accompanied Will- iam the Conqueror when he subdued England, or came soon after, as the name appears in England, and is more easily traced from about that date. The first official account is in the time of Edward III, A. D. 1327, when the records show an official ap- pointment dated 1358. This probably accounts for the fact that they had a crest or semblance of a coat- of-arms. This consisted of an open shield, sur- mounted by two battle axes, crossed, and one ax and three pellets in the body of the shield. The motto in Latin, ^n Deo^ non artnis^ fido^ — " In God I trust, not in arms." The Morse family in America descended from seven families, who came from England about 1635, ^^^ heads of these families named Samuel, Joseph, An- thony and William Morse, all settling in Massachu- setts. Later, Robert Morse landed in New Jersey, Joshua, ** somewhere in New England," and " John Moss," in New Haven, Conn. It seems to be a his- ^^ " ^^" V -J"^ torical fact that these are the seven families whence the Morses in early days sprang. Samuel Morse, the progenitor of the branch of the family to which Charles H. Morse belongs, was born in 1585, in Eng- land, probably at Ipswich, came to Massachusetts with his wife Elizabeth and son John, in the ship ** Increase," in the year 1635, and settled "south of Charles River/' near Boston, and named the place Dedham. He, with twelve others, owned a large tract of land, built the first " meeting-house " and school-house. The " compact " drawn up by himself and his 12 associates, under which they were to live, is marked by all that severe piety and intolerance that characterized the " Blue Laws "of Connecticut. The whole history of the family indicates that they have generally been men of sterling integrity and noted for puritanism. Some have been minis- ters in the Episcopal Church, but generally they have been Presbyterians. They fought in the Revolution and in every war since to the Rebellion. Some were eccentric. John Morse, born in 17 12, built his chimney in the hall of his house. He shut himself in his room and resolved to fast 40 days, but after trying it three or four days came out, saying the Lord had excused him from the other days! He also chiseled his own tombstone, and asked to be buried with his head to the north. The genealogy of the family, from Samuel Morse to the subject of the sketch, Charles H. Morse, is as follows: Samuel Morse, born 1585, came to America 1635, died 1654; son John, bom 161 1, came to America with his father 1635, died 1657; John's son Ezra, bom 1643, died 1697; Ezras son Seth, born 1686, died 1783; he settled in Connecti- cut; Seths son John, bom in 17 12, date of death unknown; John's son David, born about 1755, died about 1830; David's son Simeon, born Oct. 4, 1781, died August, 1867 ; Simeon's son Harvey, born June 22, 1802, died May i, 1878; and Harvey's son Charles H., bom Jan. 27, 1838. Mr. Morse had three brothers and three sisters, viz: Evaline, born Dec. 24, 1826, and married to H. H. Beers; Electa, born Sept. 28, 1828, and mar- ried to Lafayette Winchester; Catharine, bom July 4, 1 83 1, and married to Horace Briggs; Lucius, born Oct. 13, 1833, married Rose Cutter and died May 15, 1875 ; John, bom April 26, 1835, married Sarah Holly, murdered Aug. i, 1867 ; Myron, born Fel». 20, 1840, married to Elizabeth Chittle. r v,> I K/ / ]v>-^ J^ Digitized by Google ^^^- ■>■- ^rr^>nii>:nni-> lA- -^ IT'^ -^^7^ 4 GRA TIO T CO UISTT Y. ^ i / The parents of the subject of this biography were hard-working, industrious and energetic people, and C'harles H. was educated in the school of labor, on the farm, necessity preventing his developm'int into manhood in idleness or wealth. He labored on the farms in the neighborhood, contributing his earn- ings to the support of the family, and attending the common schools as opportunity would permit until he attained the age of 17 years. Possessing a determi- nation to succeed in the battles of the world, he de- voted his idle moments to his books ; and at the age of 16 he was thoroughly capable of entering on the profession of a teacher, which he did with credit. ^'^ '^SSf Mr. Morse accompanied his parents to this State, where they located in Orleans Township, Ionia County. He then engaged in teaching during the winter months, and assisted the father on the farm during the summer. Here his father and mother died, the former May i, 1878, at the advanced age of 76 years; and his mother Dec. 3, 1881, at the home of our subject, aged 73 years. They were iden- tified with this State since 1855. When the nation was aroused from her peaceful slumber of years by the flashing of the terrible news along the wires from State to State that Sumter had fallen, and our martyr President had called for strong arms and brave hearts to battle for the perpetuity of our flag and Government, our subject halted not to consider, hut was among the first to offer his services. He enlisted Sept. 14, 1 861, as a private in Co. D, jd Mich. Vol. Cav., and on the organization of the company was appointed Sergeant. He served with the company as Sergeant until Dec. 15, 1862, when he was promoted to Commissary Sergeant of the regiment, and he always had personal charge of the subsistence of the regiment during the time he held the office. During his service with the regiment, he was pres- ent at the siege and capture of New Madrid and Island No. 10. At New Madrid, under Gen. Pope, he first "smelled powder burned in anger." Soon after the battle of Pittsburg Landing, his regiment was ordered to Tennessee, and participated in the siege of Corinth, Miss., and after the evacua- tion did hard service all through the summer of 1862, in Northern Mississippi and Alabama, and West Tennessee, participating in the battles of luka, Sept. 19, 1862, and Corinth, Oct. 3 and 4, 1862, — two as severely contested and decisive engagements, consid- ering number engaged, as were fought during the war. In November, 1862, he accompanied his regiment in advance of Gen. Grants army, which moved nearly down to Grenada, Miss., engaged daily with the enemy in severe skirmishing, particularly at Cof- feeville, where the cavalry advance were confronted by the entire rebel army of Northern Mississippi. This campaign of Gen. Grant's was apparently broken up by Van Dorn's raid on his communications and the destruction of his supplies. Van Dorn struck Gen. Grant's communication at Holly Springs, Miss., Dec. 20, 1862, destroyed a large amount of army supplies of all kinds and raided north into Tennessee, destroying the railroad as he nwved. Mr. Morse was taken prisoner at Holly Springs, by Van Dorns forces, while absent from his regiment after supplies. He was paroled the same day and as a result was sent North until exchanged, which took place in April, 1863. During the remainder of his service with the regiment he participated with it in all its arduous service, scouting in West Tennessee and Northern Mississippi. Their battles, though termed skirmishes, were numbered by scores. Few cavalry regiments saw harder service than his and few indeed were the marches it made when Mr. Morse was not with it. After re-enlistment, Mr. M. was ordered to report to Gen. W. A. Pile, at Benton Barracks, St. Louis, Mo., who was charged with the organization of regi- ments of colored troops at that place. He remained on duty with Gen. Pile until August, 1864, when he was commissioned Captain in the 117th U. S. Col- ored Infantry, and ordered to report at Covington, Ky., where his regiment was then organizing. He was the senior Captain in the regiment, taking rank from Aug. 16, 1864. During August and September he assisted in recruiting and organizing his regiment to its maximum number, and in October it was or- dered to Virginia, and assigned to the ist Brigade, I St Division, 25th Army Corps, Gen. Godfrey Weit- zel commanding. The 24th and 25th Army Corps constituted the Army of the James. When Richmond was evacuated, Mr. Morses company led the advance of the 25th Corps, and his regiment was probably the first infantry that entered the capital of the Southern Confederacy. A <^ii!i:<^:Da>^ z. -S^-T^MS:!. -^^^^^f®^" Digitized by Google s^n^^^^ -:2s€^ ■trV 4iDn:i;iiDv> I I 4 A GRATIOT COUNTY. \ i Remaining at Richmond and Petersburg until June 2, 1865, he was, with the 25th Corps, ordered to the Mexican border, to aid in enforcing the famous " Monroe Doctrine." Louis Napoleon saw the " hand- writing on the wall," and called the French troops home from Mexico, leaving Maximilian to his sad fate. In the fall of 1865, the mustering-out of troops began. The 117th Regiment, to which Mr. M. still belonged, was occupied in garrison duty on the bor- der, and in October of the same year Mr. M., then Captain, assumed command of the regiment, which he retained most of the time until the end of its service. Jan. 12, 1866, Mr. M. was promoted from Captain to Lieutenant-Colonel of the regiment. Subsequently, owing to the muster-out of other regiments, the 1 17th was the only infantry on the border, and was scat- tered from Galveston to Fort Mcintosh, 500 miles up the Rio Grande. Mr. Morse commanded the |)Osts of Brazos de Santiago, Fort Brown and Ringgold Barracks. While at the latter post his jurisdiction ex- tended over 300 miles of the border. Here he had a chance to observe much of Mexican life, and pro- nounces them (save a small educated class), the most degraded human beings in the world making a claim to civilization. In June, 1867, Mr. Morse was brevetted Colonel of U. S. Volunteers, to date from March 13, 1865, " for faithful and meritorious conduct during the war;" his commission being signed by President Andrew Johnson and Secretary Edwin M. Stanton. The 117th was the last volunteer regiment in the service, and their " three years, or during the war," was nearly completed July i, 1867. They were or- dered to assemble in New Orleans for muster-out, and on the 23d day of August Mr. Morse was mus- tered out of the military service of the United States, after a continuous service of 5 years, 1 1 months and 9 days. Soon after Mr. M. received his discharge, he came to this county and purchased 320 acres of heavily timbered land, located on sections 20 and 29, New Haven Township. There was at the time 40 acres under improvement. The farm was originally owned by Richard Crispel. After making this purchase, Mr. M. at once entered on the task of improving his land, at times engaged in lumbering and in real estate, and now owns 400 acres, 270 acres of which are well improved, supplied with good stock and adorned with handsome and complete farm buildings, and is considered the most valuable farm in the towftship. Mr. Morse was united in maniage, Feb. 14, 1864, to Miss Julia, daughter of Nathaniel and Chloe (Thompson) Sessions, late of Ionia County. The father was born Aug. 20, 1790, and died March 15, 1880, age nearly 90. The mother was bom in 1798, and died in 1879, aged 81. They were natives of Connecticut and New York, respectively ; and came to this State in 1837, since which time they have been identified with the prosperity of Ionia County from its earliest settlement, always living in the vi- cinity of Matherton. It was there Julia was born, Dec. 13, 1838. She was reared and educated under the watchful care of fond and loving parents. Pos- sessing a mind capable of rapid cultivation and a large amount of energy and determination, she soon attained a point in her studies which thoroughly qualified her to enter upon the duties of a teacher, which she performed with great credit. After a few years of successful teaching she gave up the school room for the home and entered on the duty of wife and mother. She has had fiwt children, four of whom are living, namely : John C, bom March 8, 1870; Mark C, born Oct. 27, 1872; Noel M., born Jan. 10, 1874, and Katie M., bom July 18, 1878. One child died in infancy. Mrs. Morse is a dutiful and loving wife, a kind mother and a generous and esteemed neighbor, al- ways working for the social* and intellectual improve- ment of the community in which she may be found. She was a twin daughter in a family of 15 chil- dren, 10 of whom are living. Her membership and identity with the M. E. Church extends over a long period of time, and her religious zeal ranks her among the Christian workers of the county. The official record of Mr. Morse in the County and Congressional District in which he lives has been an honorable and creditable one. He has held the office of Supervisor eight terms, since 1870, and also other township and school offices in the gift of the people of the township. He was elected Representative on the Republican ticket in 1872, and the interest he manifested in the welfare of his constituency procured him a speedy return in 1874. These two terms spent in the Leg- A % s G «t#»- '^^ — 9:M>mtm^ \f^^ Digitized by VjOOQlC ■ ■J r^ 204 y^>. GRATIOT COUNTY. ^- 1-'. ^^3^^^^ ^ r. ^ \ islature extended his reputation as a man of ability and integrity, and at the close of his last tenn he was put forth as the nominee of the Republican party for Senator from the 28th District. His record had been marked with such manly ac- tion, ability and integrity that the people rallied around him even as he had rallied around the old flag in its time of peril, and elected him by a hand- some majority. Mr. Morse has been closely allied with the inter- ests of the Republican party in this State, and as a representative of the party stands forth unaccused, without a blemish. Mr. Morse is an Officer of the Day in the Post of the Grand Army of the Republic at Carson City. As a representative man of the State and county, and one in every way worthy the confidence and esteem of the people, we take great pleasure in presenting the portrait of Mr. Morse, together with that of his most estimable lady, in this work. />. ^ 1^4- Joseph B. Davidson, farmer, section 48, Elba '^ Township, is a son of John and Mary R. (Marriott) Davidson, natives of Pennsylva- nia and Maryland. Mr. Davidson, Sr., was a farmer, and his home was in Ohio until his death, in the autumn of 1872. Joseph was born May, 2, 1841, in Licking Co., Ohio. At the age of 28 he married Lilly Kneeland, who was born in Howell, Livingston County, May 28, 1852, the daughter of John B. and Lucena S. (Sickles) Knee- land. Mr. Kneeland was a native of Tompkins Co., N. Y., and followed farming. Mr. and Mrs. Davidson settled at their present residence on 65 acres of section 28. They are the parents of two children : John W. and Frank E. Mr. Davidson enlisted in the service of his country at Cleveland, Ohio, in Co. D, 41st Ohio Vol. Inf. He was in the battle of Stone River ; was wounded at Chickamauga, and. at Missionary Ridge : was wound- ed both in the hips and in the wrist. On account of these honorable wounds he was discharged from the army. He was Highway Commissioner of his township for one term, and School Superintendent two terms. He has also held the office of Moderator of his school district for a number of years. He is a thorough Republican in his political views. He is a^ member of Elsie Lodge, No. 238, F. & A. M., and also of the G. A. R. -h ihlfred Finch, farmer, section 24, Arcada Township, was born in Orleans Co., N. Y.^ SejH 26, 1852, and is the son of Linas Finch, a native of New York, and of English de- scent. The father was by occupation a ma- chinist; and, enlisting in the service of his country, fell a victim to some rebel bullet. Alfred's mother died in Orleans Co., N. Y., in March, 1861, and at the age of nine Alfred found himself under the care of a Mr. Hall, of Orleans County. Two years later they all came to Eaton Co., Mich., where Alfred lived, working summers and attending school in the winters, until 16 years old. He then went to live with Levi Bartlow, in Clinton County, remaining with him till 21 years old. For the next five years he was variously engaged. Aug. 6, 1878, at St. Johns, he was united in the bonds of matrimony to Nancy, daughter of Erastus and Jimima (Packard) Farrington, natives of New England and of English descent. Mr. Farrington s occupation has been a shoemaker, and he is now a farmer. Nancy was bom June 11, 1857, in Emerson Township; was there educated, and there lived until her marriage. One year after marriage, Mr. and Mrs. Finch settled on 40 acres in Arcada Township, He now has 15 acres under cultivation. They have a family of three children, as follows : Alice, bom March 5, 1879; Bertha, June 27, 1880; and Charles, Oct. 20, 1883. In politics, Mr. Finch is a Republican. ohn T. Botsford, farmer, section 15, New Haven Township, is a son of Reuben and Martha (Lambson) Botsford (see sketch), and was born in Whitby Township, Ontario, Feb. 27, 1849. On leaving his native home, when seven years of age, he came with his par- ents to Michigan, setthng in the village of Reuby, Clyde Township, St. Clair County, for four years; Digitized by Google . .-J V^-DDKI1D;> ^V GRATIOT COUNTY. Y. was then four years with his father on a farm near that village, attending school during the winter sea- sons. In the fall of 1865 they moved to this county, where John T. remained, working in agricultural pursuits and attending school until his marriage. His wife, Sarah, is a daughter of George and Alice (Fisher) Cross, natives of England, who came to America early in life, ultimately settling in Newark Township, this county. Mrs. B. was born July 7, 1857, one of the first white children born in that township. Here she was reared and educated. Mr. and Mrs. B. have one child, Ettie E., who was born Dec. I, 1884. They are members of the Baptist Church, and in politics he is a Republican. -s ¥-' illiam J. Courter, farmer, section 7, Ar- cada Township, was born in Orleans Township, Ionia County, Sept. 25, 185 1. His parents are natives of New York State, moved to this county in 1854, and are now living on a farm in Arcada Township. Coming with his parents to an unsettled country, William had no school advantages during his early youth, but he was endowed with a desire to learn, and as he be- came older he developed quite a taste for books. When 16 years old, he commenced earning his own livelihood, going for a time to the lumber woods of Mecosta County. Returning home, he passed 13 years in working at farming in the summers and in the wocxis winters. The last four years of that period he was in the employ of Bradley Hayes, of Ionia County, an extensive farmer and lumberman. During these four years he lost but 13 days* time, and so highly were his services appreciated that he was paid for that lost time. On leaving Mr. Hayes* employ he was married to Jeannette, daughter of Ira and Ann (Mcintosh) Bar- low, natives of New York State and of English and Scotch ancestry. They followed farming, and re- nwved from New York State to the vicinity of Detroit, Mich., and thence to Sydney Township, Montcalm County, where they now reside. Jeannette was born in that county, Nov. 11, 1857, where she was edu- cated in the district schools, and lived until her mar- riage. Mr. and Mrs. Courter came to this county and located on 80 acres of his father's homestead. He has now 60 acres nicely improved, and good farm buildings. They have two children : Ira Albert, bom Aug. 22, 1878, and Fred S., bom Nov. 15, 1882. Politically, he is a Democrat. He has been Overseer of Roads for some time. ^<HJh*^ -i^ ♦ ->4^ >r c^y'^^^fp^ ^^m: ■^1 !{piS:harle8 W. Bayley, farmer, section 25, Elba '"^ife*^!^ lownship, is a son of W. H. and Jane ^{'^' (VV^ilson) Bayley, natives of England, and ^^ residents of Canada. He was bom near To- A rontn, < anada, July 7, 1849. On setting out to make his own way in the world, he went to Lorain Co., Ohio, where he was engaged in farm- ing until 1879. Sept. 23, 1879, he was united in marriage to Catharine Eschtnith, the eldest daughter of John and Sophia (KeicYi) Eschtruth. They were natives of Germany, and emigrated to the Great Re- public in 1847, settling in Lorain Co., Ohio. Mr. Eschtruth is there engaged in farming and operating a stone quarry. Mrs. Bayley was born in Lorain County, Dec. 28, 1852. Politically, he votes with the Republican party. In Elyria, Ohio, he was an active worker in the temperance union, and he is srill interested in that cause. t ewis B. Wolford, farmer, section 29, New Haven Township, is a son of David and Laverna (Conger) Wolford, natives of New York. He was bom in Cayuga Co., N. V., ^ Nov. II, 1837 ; when six years old he was taken to Huntington Co., Ind., and two years later to his native county; in 1858 he came and settled on section 21, New Haven Township, this county; in 1867 he moved into Sumner Township, where he lived for six years, during which time he followed lumbering in Montcalm County. In the spring of 1876 he moved into New Haven Township. Jan. 14, 1 88 1, Mr. Wolford married Mrs. Ellen M. Wiles, daughter of Peter D. and Mary (Babcock) Pendell. Mr. P. was a native of Saratoga, N. Y., of (ierman-Knglish descent, came to Michigan in 1847, and to this county in 1858; he was a farmer. He and his wife both died in New Haven Township. Mrs. W. was born in Wayne Co., N. Y., July 14, '^n'\J. :- ^j-,r^.^ _•'. vv-^ , /., ^ y'l * Digitized by Google m -:i^^^ ferv<^DD^;flU>i>v -«a 2 206 GRA TIO T CO UNTY, 1845. When two years old she came to this State, since which time she has been a. resident of Ionia and Gratiot Counties. She was first married in 1862, to George Bennett, a native of Michigan, who died June 20, 1870. She afterward married David Wiles, who was bom Jan. 22, 1832, in Ohio, and died April 20, 1877. By another wife he had been the father of seven children, and she, by her former marriage, had two children. By the present union there has been one child, Mary L., born Aug; 12, 1882. Mrs. W. has a farm of 80 acres, most of which is well im- proved. Mr. W., a Republican, has been honored with office in his school district. illiam C. Wooloy, farmer, section 33, Elba Township, is a son of John K. and Fanny (Crose) Wooley, natives of New Jersey. Mrs. Wooley was the first white settler of Elba Township, locating on section 34 Jan. 4, 1855. In March of the same year, she re- moved across the line into Clinton County, where she still resides. William C. was born June 14, 1840, in Kalamazoo Co., Mich., and left home at the age of 14 to care for himself. He worked on a farm until 1867, when he married Martha Harrison, daughter of John S. and Louisa (Baker) Harrison, natives of Ohio, where they followed farming. Mr. and Mrs. Wooley have a family of three children : John H., Claude D. and Cora P. Mr. Wooley first purchased 80 acres in Elba Town- ship, but has added 160 acres to^his nucleus. Of his whole farm, 180 acres are well improved. In 1873 he built his large barn. His was the first fam- ily to settle permanently in the township, and when he came he found a dense wilderness. He enlisted in Co. H, 25th Mich. Inf., Aug. 27, 1862, and served his country faithfully during the remainder of the war. His company was engaged under Col. Moore at Green River Bridge July 4, 1863, with the notorious John Morgan's command, and killed more men than there were in the company engaged. He was mustered out at Salisbury, N. C, and finally discharged at Ja'^.kson, Mich. Mr. Wooley is a member of Elsie I^odge, No. 238, F. & A. M. He was Deputy Sheriff under George Patch. He is one of the representative citizens of Gratiot County. 0C>o ^ "o<55~ t i rank Manecke, farmer, section 22, New "^ Haven Township, was bom in Mecklen- > burg, Germany, in 1830. His mother died Sr when he was three years old, and then until- he was eight he lived with his grandmother. His father having married again he returned to him, who was then superintendent of large land tenants in that country. He was carefully educated, and before he left his native land at the age of 15 he was well versed in French as well as in his native tongue. At the age mentioned he came to the Unifed States with his father, settling in Wood Co., Ohio, near Fostoria. Here the father bought a farm and pro- ceeded to teach his only two children, Frank and Frederick, in the art of agriculture. On attaining legal age, Frank began as a common laborer for farmers in Seneca Co., Ohio, and two years later he came to Michigan, locating, in Novem- ber, 1854, 120 acres of wild forest land, on sections ^ 21 and 22, New Haven Township, under the Grad- uation Act. In the spring following he set about improving this place, spending the winters for sev- eral years in this work, while the summers he worked in East Plains, Ionia County. In i860 he settled on this farm, where he has since made a comfortable home. Under the last call for recruits in 1864, Mr. Man- ecke was drafted, and placed in Co. E, 15th Mich. Inf. His regiment was with Sherman in North Car- olina, but before it was called into action the war closed, and Mr. M. returned home without participa- ting in any engagement. Resuming work on his farm, he has prospered until he has reduced 100 acres under the plow and added by purchase 40 acres more. It is one of the most productive farms in the township. He has produced per acre as high as 38 bushels of wheat, 80 bushels of corn and 6 bushels of clover seed. His residence, recently built, is a beautiful and convenient structure, and his farm buildings are first-class. Mr. M. has held the school office of his township, and in political issues he is a Republican. Mr. Manecke was first married April 27, i860, to Miss Adaline Burt; she was born in New York, about 1 83 1, and died at her home in New Haven Township, Oct. 28, 1863, leaving one child, Burt. 4 r % Digitized by Google r z^^ — 6vc>ti net; n lo^ r-^T- GRATIOT COUNTY. '':^^' '^ 4^^a^fsv^|| 207 V/ She was a member of the Regular Baptist Church. /, ' Mr. M. was again married Jan. 15, 1864, in Newark *^ Township, this county, to Mrs. Susanna Ridenour, ^ rue Munson, who was born in Medina Co., Ohio, Aug. 22, 1830, where she resided until her first mar- riage, in April, 1851. Since that time she has lived in this State, and, except three years, in Clinton County. The children of Mrs. M., by her former husband, were : Polly S. and Aminda J., both mar- ried, in this and Ionia Counties; and George, who died in infancy. J —k=^ ^ •<>' X enry K. Betan, senior proprietor of the Retan House, Ithaca, was born in Sussex Co., N. J., Aug. 27, 181 7, and is a son o^ John and Margaret (Smith) Retan, natives of INova Scotia and New Jersey, and of Dutch and New England descent. The father was a far- /\^ mer, and died in Waterford, Oakland Co., Mich., in 1843. The mother died in Owosso, Mich., in 1867. When the subject of this sketch was seven years old, his father removed to Oakland County, this State, and settled on a farm near Pontiac. Henry here worked on the farm, occasionally attending school, and developed into manhood. At the age of 26 he left home, and started a store at Commerce, Oakland County. He was in mercantile life about 15 years, and then went into the hotel business. He was first at Owosso one year, then at Ovid 1 2 years, and then lived at Ovid three years without other occupation than caring for his wife, who was then an invalid. In May, 1883, he came to Ithaca, and started the Retan House in company with his son-in-law, Dennis T. Covert. This hotel has a very large patronage, and has acquired an enviable reputation as a home-like, well managed house. Nov. 17, 1842, at Pontiac, he formed a life partner- ship with Miss Catharine Voorheis, daughter of Jacob and Rachel (Powelson) Voorheis, natives of New '^ Jersey, and of Dutch and English descent. She was born at Peapack, Somerset Co., N. J., Sept. 20, 1820, " , and came to Michigan with her parents when 13 years old, living in Oakland County until her mar- riage. Mr. and Mrs. Retan have had a family of eight, four surviving : Harrison L., Harriet E. (Mrs. D. T. Covert), Jay V. and Addie. The two first are in Ithaca, the two last at Ovid. The deceased are George, Margaret, Frank and Lily. Mr. Retan is politically a Democrat. r§|IUexander T. Bice, farmer, section 32, Elba K Township, is a son of Clark and Sarah A. ijJI^S" (Coonley) Rice, natives of Massachusetts :ind New York respectively. They emigrated lo Michigan in 1840, and settled on a farm. Alexander was born Dec. 10, 1834, in Jasper, Steuben Co., N. Y. At the age of 25, he was mar- ried to Clara J. Armstrong, daughter of Elias and Eunice (Hewitt) Armstrong, natives of Connecticut. She was bom May 20, 1835, *" Wheatland, Monroe Co., N. Y. Mr. Armstrong came to Livingston Co., Mich., and lived there until his death, Sept. 19, 1863. Mrs. Armstrong died Feb. 17, 1872, at Eaton Rapids, Mich. In 1876, Mr. Rice located on 100 acres on sections 29 and 32, Elba Township, and he has creditably improved 60 acres of this farm, besides erecting a neat farm house, barn and granaries. In 1876, he was elected School Superintendent of his township, and the following year he was elected Supervisor. This latter office he filled continuously until the spring of 1883, except the year 1881. He is a mem- ber of St. John s Lodge, No. 105, F. & A. M. Po- litically, he has always been a Democrat. He is one of the truly representative men of the county, and stands highly with all parties. ^iPrancifl J. Corey, farmer on section 2, New- \ ark Township, was born in Nankin Town- ^^'n\ ship, Wayne Co., Mich., Dec. 18, 1836, and is the son of John D. and Roxie (Fergu- M^ son) Corey, natives of Rhode Island and Ver- l niont. They have followed farming, and now reside on section 29, Arcada Township. Francis lived with his parents and worked on their farm until of age, moving with them when 18 years old to Ingham Co., Mich. Jan. I, 1858, at Lansing, he was married to Rachel, daughter of George and Eliza (Carter) Brown, natives of New York and of English and ^7^>I1!1 m\i<> / (V Digitized by VjOOQlC m I f 208 GRATIOT COUNTY, r^: ■^- German ancestry. The father died in Ingham County in 1864, aged 55. The mother still lives in this county. Rachel was born in Williams Co., Ohio, May 26, 1839, and came to Michigan when 17 years old. After marriage, Mr. and Mrs. Corey lived in Ingham County until the winter of 1866, when they came to this county and purchased 80 acres on sec- tion 32, Arcada Township. While living on that place, they improved 44 acres. Selling out Dec. 7, i8?3, they have just become well settled on their new home of 40 acres of well-improved land near Ithaca, formerly owned by William Hutchins. Mr. and Mrs. Corey have a family of four, as fol- lows : Lorada E., born Jan. 21, i860; Ellsworth D., Aug. 14, 1861; Lorena F., Feb. 3, 1864; and Eliza J., Nov. 3, 1868. Oct. 28, 1863, he enlisted in Co. H,4th Mich. Vol. Cav., and served in the Army of the Cumberland under Gen. Minty. He fought at Kingston, Look- out Mountain, Stone Mountain and Cottonwood Creek, and in many skirmishes, such as cavalrymen always meet with. He was in Kilpatricks raid through Georgia in 1864, and in Wilson's raid from Eastport, Miss., to Macon, Ga., the same year. He was honorably discharged Aug u;, 1865, after 23 months of active service. In civil life, Mr. Corey has been a worker in the ranks of the Democratic party. He has been Constable for two terms. -^^m^^^^ srael W. Hause, farmer on section 15, Ful- ton Township, is the son of Simon and Sally (Coats) Hause, natives of the State of New York. They resided first in Chemung Co., N. Y., then in Steuben Co., Mich., and in 1853 they removed to Clinton Co., Mich. They came to Gratiot County in March, 1858, and returned to Clinton County in May, 1870. Here he died, June 11, 1877. She survives him, and resides in St. John s. Their family comprised two sons and five daughters. The subject of this notice, the elder son, was born in Steuben Co., N. Y., Sept. 21, 1841, and was 12 years old when his parents removed to Michigan. He received a common-school education, and made his home with his parents until he attained his ma- jority. He came to Gratiot County with his parents and lx)ught 40 acres of partly improved land on ^ section 15, Fulton Township; and m January follow- ■ ing he settled with his family there. He has built a comfortable residence and barns, and has 30 acres under cultivation. Dec. 2, 1862, in Fulton Township, he married Miss Harriet A., daughter of William J. and Sarah A. (Sornberger) Carr, natives of New York. They came to Fulton Township, Gratiot County, in i860. Mrs. Carr died here May 13, 1863. Mr. Carr survives. Their daughter Harriet was born in Madison Co., N. Y., March 31, 1843. She is a member of the Meth- odist Episcopal Church. Politically, Mr. Hause is a Republican. — «- #^ ''\^£X2i^^A illiam Alpaugh, farmer on section 5, Ful- 5L ton Township, is a son of Philip and Eva ^ * Alpaugh, natives of the State of New York. In 1846, they left that State and ^ came to Hillsdale Co., Mich., where they . died, he Oct. 10, 1874, and she Dec. 16, 1880. \ The subject of this sketch was born in Montgomery - Co., N. Y., Jan. i, 1830, and received a fair com- mon-school education. At the age of 16 he came with his parents to Michigan. At the age of 22, he started out to make his own way in life. He learned the trade of carpenter and joiner, which he followed much of the time until 1882. He came to this county in January, 1865, and bought 40 acres on section 2, North Shade Township. Here he lived about seven years, when he sold and bought 40 acres on section 5. Fulton Township, his present home. He has since added 40 acres, and has about one-half of his farm under cultivation. Sept. 3, 1862, he married Mary E., daughter of Joseph H. and Margaret (Clement) Salisbury, natives of Montgomery Co., N. Y. Mrs. Alpaugh was bom in Pittsfcrd, Hillsdale Co., Mich., Sept. 22, 1841. This marriage has been blessed with two children : Evie A. and Edwin G. The latter died when two years old. Mr. A. is a member of the Masonic Order, and, with his wife, of the Christian Church. In polidcs he is a Republican. He is a strong tem- perance man, and takes a deep interest in all tern iter- ance movements. VJ -^<-[!li:v:l!r>-^ Digitized by Google Digitized by Google ir- Digitized by Google ^ €& Digitized by Goog^ ^ Digitized by Google ^"Ti^^-i^ -^C:tltl^IlIl^>v ^■^X^. >^'l^C! GRATIOT COUNTY, > 211 *N^ _or<>_ J; >: V / "^ ;^ ^^ ■02:0 illiam Siokels, one of the leading business men of Sickels, and representative men of the county, and whose portrait we are pleased to present in this work as a meritorious rep- resentation of one of Gratiot's self-made men, was born in Palmyra, Wayne Q)., N. Y., May 30, 1824, and is a son of John F. Sickels, native of the same State, whose Holland ancestors settled on the Mohawk River over 200 years ago. Mr. Sickels attended the common schools of his native State until he attained the age of 1 2 years, when, in com- pany with the family, he came to Wayne County, this State, where they arrived in 1836. Here William attended the Northville Academy, assisting pn the farm at times until the fathers death in 1839, when he assumed control of the farm and successfully cul- tivated it for one year. He then resumed his studies at Northville Academy and completed his education. After the completion of that arduous though pleas- ant task, he went back on the farm and remained until 1849, when he moved to Howell Township, Livingston County, this State, and occupied his time in farming until 1854, then went to what is now Wyandotte, Wayne Count}', built the first store and dwelling house in the village proper and established the first postoffice there. In 1856 he removed to what is now Elsie, Clinton County, and also estab- lished the first postoffice in that village, and was Deputy Postmaster. He remained at Elsie until 1 86 1, when he removed to St. Johns, same county, and there held the position of Register of Deeds until 1863, and Deputy Register from 1863 to 1865; was also Judge of Probate from 1865 to 1869. From 1869 to 1 88 1 he held a position in the Postoffice Department at Washington, D. C. In May, 1881, Mr. S. resigned his position at Washington and joined his family at Sickels, this county, whither he had removed them in September, 1873. In 1883 Mr. Sickels built a large steam flouring mill at Sickels and thoroughly equipped it with the best and roost modern improved machinery, with boilers 4j4 x 12 feet and a 40-horse-power engine, which is recognized as one of the best flour-produc- ing mills in the county. His residence is undoubt- edly the finest in Hamilton Township ; and, remarka- Wa. •K^^^ ri^:^^ ^<mv- ble as it may appear, it is nevertheless true, the structure is composed mostly of native wood which grew on his own farm. The building is supplied with hot and cold water throughout, and is elegantly furnished. The library, of which he is justly proud, required an outlay of over$2,000 in its selection and
purchase, and comfort, happiness and plenty sur-
round the family hearthstone.
Mr. Sickels was married Nov. 8, 1846, to Isabel B.,
daughter of Dennis Kingsley (deceased), a native of
Vermont, and one of the early pioneers of Wayne
County. She was bom in Orleans Co., N. Y., March
13, 1828. Four children have been born to their
union, viz.: Dennis K., Annie I., Hettie E. and
William C.
Dennis is living in Washington, D. C, and was
married to Alice M. Hugely. Annie I. married John
H. Winton, of Ithaca, this county. Hattie E. was
married to Warren Abbott, who died in 1880, leaving
two children to the care of the mother, who lives
with them at home. William C. is unmarried and
living with the family in their pleasant abode.
The credit of their prosperity, of their happy home
and the fine appearance of their large farm of 640
acres, is not all claimed by the father; each one
nobly did his part ; and of the mother, for her untir-
ing labors, all unite in highest praise. That " the
the hill of difficulty is one of the strongest * consti-
tutionals * for strengthening the financial backbone of
a struggling family," was, undoubtedly, fully corrob-
orated in her energetic labors. She superintended
the clearing of the land (Mr. S. being in Washington
a great portion of the time attending to his duties in
the Postoffice Department), and the building of their
fine residence and barn, with the assistance of her
daughter Annie as architect, and also the clearing of
another farm of 100 acres, which they own; and to
her good judgment and fine management their pros-
perity in a great measure is indebted. Tmly we
may say, she is one of those women who are too
often ignored and too little appreciated by biograph-
ical writers of the day.
Mr. S. owns the store building in Sickels, besides
considerable other village property. He was a soldier
in the late civil war, enlisting in Co. E, 23d Mich.
Vol. Inf. : was appointed First Lieutenant and had
command of the company most of the tmie for about
six months, when, contracting typhoid pneumonia, he
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was compelled to resign. The Captain of the com-
pany was O. T.. Spaulding.
ent devoting considerable time to the propaga-
tion of fine stock, and is handling, with good success,
a species of the Shorthorn breed of cattle known as
the " Rose of Sharon." He has one two-year old
from the herd of H. M. Vale, of Independence,
Mo., which is considered one of the finest and most
celebrated herds in the United States.
Mr. Sickels and his entire family, with the excep-
tion of his youngest son, are members of the Method-
ist Episcopal Church. He is a member of the
Masonic Order and the I. O. O. F.
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bharles H. Webster, superintendent of
Church's mill, and residing on section 7^
Emerson Township, was born at Wellington,
Lorain Co., Ohio, May 28, 1844, and is the
son of Joseph and Elizabeth (Magraugh)
Webster, natives of Pennsylvania and Connecticut,
respectively, and of Dutch and Irish extraction.
The father was by trade a tailor, and died April 2,
1845, before Charles H. was a year old. The latter
lived until 12 years of age with his mother and a
step-father, whom she married in 1854.
While but a mere boy he resix)nded to his country's
call for volunteers, and enlisted Aug. 25, 186 1, in
Co. H, 2d Ohio Vol. Cav. He served first under
Gen. Blunt, then under Gen. Burnsides, and finally
under Gen. G. A. Custer. He was engaged in all
battles in which his company was involved, among
them being the battles of the Wilderness, Peters-
burg and Richmond, at the close of the war. He
was often detailed for special and important duties,
and was made a Corporal towards the close of the
war. Being wounded in the knee and thereby dis-
abled, June 28, 1864, he was captured the following
day at Reams* Station, near Petersburg. He was
taken to Libby prison and confined for four weeks in
that iniquitous pen. Being then paroled, he found
his way to his company and remained with it until
he was honorably discharged, Sept. 18, 1865. He
served four years and 25 days, and his arduous and
interesting experiences would fill a volume.
Mr. Webster has a copy of the congratulatory order
issued by Gen. Custer to his division, on Lee's sur-
render.
Returning home he shortly started for Michigan,
arriving at Ithaca Oct. 22, 1865. He purchased of
the State 200 acres of land in Emerson Township.
For about three years longer he was a bachelor, im-
proving his farm summers, and in the winters acting
as clerk, at first in the dry-goods store of Nelson &
Church, and later in JefTery's store. Dec. 28, 1868,
he was married to Marie E. Church, daughter of
Lafayette and Sophronia (Benjamin) Church (see
sketch), who was born in Hillsdale Co., Mich., Oct
9, 185 1. She came to this county when three years
old, and was here educated, and here lived until her
marriage. Some months after that event Mr. and
Mrs. Webster moved from Ithaca to section 27, Emer-
son Township. They afterwards moved to section
28, and in 1874 they settled on section 7. Here he
owns 80 acres, and has the management of Church's
mill.
They have had five children, only two of whom,
Addie E. and Albert H., survive. Arthur, Alta and
a baby are dead. They are members of the Baptist
Church. Mr. Webster has been Township Gerk
two years; has been chosen Justice of the Peace
twice, but did not qualify. Politically he is a stanch
Republican.
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eorge J. Butcher, cabinet-maker, furniture
^^ dealer and undertaker. Elm Hall, was bom
near Norwich, Eng., June 8, 1833, and is
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of English descent. His father was a gardener,
r and came to the United States when George
f was four years old, locating first at Buffalo, N.
Y. Eight years later they removed to Chippewa,
Ont., where Mr. Butcher followed his trade as
gardener. Afterwards, removing to Elgin Co., Ont.,
he secured a tract of 200 acres of wild land.
On this farm the subject of this narrative lived and
worked under his father's guidance, until 18 years old.
He was then apprenticed for three years to a Mr.
Maxwell Hamilton, of Simcoe, Ont., to learn carpen-
try. After serving out his time, he worked for the
same gentleman one year as a journeyman carpenter
He then planned an extended tour to California and
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the West Indies ; but, laying off for a period at
Dubuque, Iowa, he became homesick, and returned
to work once more for Mr. Hamilton.
Jan. 14, 1856, he was united in marriage to Miss
Frances E. Webb, bom in Canada, July 14, 1840.
Working at his trade in that country for three years
more, Mr. and Mrs. B. then came to this State and
county, and located with her uncle, Nathaniel Strayer,
of Seville Township. Mr. B. here built a house four
miles away, making two trips daily. He worked 103
days at $3 per day, and lost no time whatever. The following summer, with the money thus earned, he erected the first frame building in the township, which he ran as a hotel until 1 869. He then resumed his trade, and, after following that for three years, he started his present cabinet shop. He now has a stock worth$1,000, and his annual business
is t3,ooo.
July 17, 187 1, in Canada, his second marriage
occurred, he taking this time as the partner of his
sorrows and joys Miss Alice Hayward, a native of
Ontario, where she was bora, July 2, 1850.
Mrs. B. is a member of good standing in the M. E.
Church. Mr. Butcher has held the office of Constable
for several years. He is a member of North Star
Lodge No. 306, 1. O. O. F., has passed all the chairs,
and is now D. D. G. M. of the order. Politically, he
is a Democrat.
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f heron Finney, farmer, section 19, Emerson
Township, was born in Essex Co., N. Y.,
March 24, 1807, and was the son of Scotch
and Welsh parents. They were natives of
Connecticut, and were farmers by occupation.
Most of their lives they resided in Essex
County, where they died many years ago. Theron
remained on his father's farm until 19 years of age,
when he began to battle for himself. When 28 years
old; he came to Hillsdale Co., Mich., and was there
married to Harriet Butler, daughter of Zebina and
Polly (Porter) Butler, and born July 20,1817. Mr.
and Mrs. Finney resided on a farm in Hillsdale
County until 1859, when they came to Gratiot County
and entered 320 acres of unimproved land on section
19, Emerson Township. Mr. Finney has improved
a considerable acreage, and sold all but 60 acres,
upon which he now lives.
They have had a family of nine children : Melvina
R., Mary L., Josephine D., WilmerT., Dora A., Butler
J., Frank L., Rarason P. and Arza A. The last four
named are dead. Mr. Finney has held the offices of
School Inspector and Township Treasurer for several
years. In political faith, he is a Republican.
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eorge H. Oliver, druggist and groceryman,
-, -^ Elm Hall, was born in DeWitt, Clinton
"Me^ Co., Mich., Jan. 3, 1845. His parents were
^y^^ natives of New York, of English and Scotch
descent, and his father was a carpenter. When
he was four years old, his parents removed to
where the village of Grand Ledge now stands, in
Eaton County. It was then an unbroken forest, and
his father built one of the first houses there. The
first school-house was also raised by his father and
a few neighbors. Here our subject lived, grew up
and was educated.
In February, 1865, at the age of 20, he enlisted
in Co. C, 1 2th Mich. Vol. Inf., and was assigned to
the Army of the West. He was in no active engage-
ments, and was honorably discharged in July, 1865.
His health failed him ; and on arriving home he was
confined to his bed until September. He then went
to Poughkeepsie, N. Y., and took a course in East-
Returning to Grand Ledge, he was for a time engaged
in book-keeping. For the ensuing four years he was
learning the painter s trade. Then assuming control of
a good business in that line, he associated with him-
self a Mr. Deering. This partnership lasted until the
spring of 1 87 1, when he left Grand Ledge and came
to Gratiot County, to join his father in the grocery
business. His health not being the best, he has not
resumed his trade, but has continued in the drug and
grocery business at Elm Hall. In October, 1881, he
became sole proprietor of the business. He has a
amounting to $3,000 annually. March 4, 1874, in Montcalm County, he was married to Miss Laura A. Van Leuvan, who was bom in Sumner Township, July 30, 1856. She lived for I < 1 Digitized by LnOOQ IC r . • • . ^ -T<:llD:<^ODr.>r-T :^^^^ ^^^•^^.^C^ J sy N- 214 G/^.4 TIO T CO UNT Y, some time in Salem, Washtenaw County, and then came to Montcalm County, where she was married. She is the mother of two children : Inez E. and Floyd E. Mr. and Mrs. O. are members of the M. E. Church. He has held the office of Constable, and politically is a Republican. lilas Hill, farmer, section 3, Hamilton Town- ship, is a son of Stephen Hill (deceased), a native of Vermont, and who emigrated from that State to Otsego Co., N. Y., where the subject of our sketch was born, July 6, 1830. Three years after the birth of Silas, in 1833, the family removed to Cuyahoga Co., Ohio, where they lived for four years, until 1837, when they moved to Erie County, the same State. Here young Hill remained, attending the common schools of the county and developing into manhood. In 1856 he went to Bureau Co., 111., and after remaining there some six months, during which time he was variously employed, he came to Eaton Co., Mich., where he arrived in the spring of 1857. Mr. Hill purchased the farm on which he is now living in November, 1873, and located upon it in January following, and has constantly resided thereon. The farm consists of 80 acres, and is under a good state of cultivation. He was married March 18, 1857, to Lucy, daughter of Edward Bracy, of Eaton Co., Mich., and three children have been bom to their union, two of whom, George F. and Edwin, are living, and one is deceased. Mr. Hill has held the offices of Highway Commis- sioner and Supervisor and is at present Treasurer of Hamilton Township. -fr- #^ -> ^ dward Y. Kelley, merchant at Bridgeville, Washington Township, is a son of Joseph and Esther C. (Hockens) Kelley. The former was an employe of the Government, being engaged on Indian affairs and also fol- lowed farming. He died in the State of New York, in the spring of 1834. Mrs. Kelley died in the same State, in 1867. Edward was born Jan. 14, 1832, at Danville, Caledonia Co., Vt. On the death of his father, he was taken by an old acquaintance of the family and kept for three years. He was then kept by another family until he was 13, since which time he has made his own way in life, working at the blacksmith s trade and at other emplgyments. In the autumn of 1866 he purchased 30 acres on sec- tion 20, Washington Township, and engaged in farm- ing. He is now in mercantile life at Bridgeville ; has a full line of drugs, groceries had hardware, and a large trade. In i860 he was married to Betsy C. Woodcock, daughter of Asa and Mary (Ryan) Wood- cock, residents of New York State. She was bom in 1828, and died in Gratiot County, in 1868, leaving five children, — Mary F., Edna J., Eddie J., Esther A. and Henry L. Mr. Kelley was subsequently mar- ried to Eliza Woodcock, a sister of his first vrife. This marriage has been blessed with two children — Cora B. and Floyd. Mr. Kelley is a member of the Masonic Order and of the I. O. O. F. Politically he votes with the Republican party. / V^ -^—4^ 44.-H /N Charles C. Qilmore, editor and proprietor I^SA cf ihe Corner Local. Elm Hall, was bom in Old Town, Maine, April 15, 1850; and is W the son of Solomon and Abigail E. (Stewart) Gil more, natives of Maine and of Scotch descent. Solomon Gilmore was a lumberman in his native State until 32 years of age, when he went to Pennsylvania. Here he lived until death, about 1862, aged ^2. His wife died in the same State a year previous, at the age of 5 1 . The subject of this biography left his native State when very young, and went with his parents to Penn- sylvania, where they lived in the lumber regions of the mountains. Owing to their peculiar surroundings, his opportunities for education were very limited, and he had but one year schooling. His desire for learn- ing was however such that he would, after working hard all day, spend hours by himself over his book. In this manner he mastered Davies* Algebra, and the rudiments of other branches taught in the high schools. At the age of 19, he set out to earn his own living. By accident he got to using the tools in the camp, and soon found that he was a natural black- smith. He was therefore employed by the proprietor to do all such work as came along in that line. He ^'^ ■^<-^ai!:<GD^> Digitized by >v> Google V r -.-<^-T''.. ^•:tlll>:iins>r >^>^ GRA TIOT CO UNTY, J V V was thus employed until the spring of 1874, when he came to Saginaw, this State. Six months later, he came to Gratiot County, and located at Elm Hall. Soon he built a stumping machine, and pulled stumps in the sumn^r, following his trade in the winter. Since coming to the county, he has been a regular correspondent of the Gratiot Journal^ and has thus secured a good idea of newspaper writing. From 1880 to the close of 1883, his occupation has, how- ever, been well-driving, in prosecuting which he has used appliances of his own invention. Nov. 17, 1883, he purchased and assumed control of the Corner Locals and his first issue appeared Nov. 24. He has a growing circulation, already reaching 350, and his paper has constantly improved. Dec. 3, 1878, at Elm Hall, he was united in marriage to Miss Lizzie Fox, bom at Leslie, Ingham Co., Mich., in 1855. She came to Gratiot in 1877. She is the mother of two children : Edna and Frederick. She is a member of the M. E. Church. Mr. jG. is a member of Elm Hall Lodge No. 257, F. & A. M., Elm Hall, and has for some time held the office of Secretary of the lodge. He has held the office of Justice of the Peace for three years, and in politics is a Republican. -%^ -•— j -s dwin Meaoham, farmer, section 35, Elba Tp., is a son of Almon and Polly (Kel- ly) Meacham, natives of Massachusetts and New York, respectively. They emigrated to Ohio in an early day, and resided in Cuya- hoga County until their death, in 1852. Edwin was bom Nov. 30, 1845, in Cuyahoga Co., Ohio, and at the tender age of seven was left an orphan by the death of both his parents. He was cared for by his uncle and aunt, with whom he lived until he was 21. With some money which they gave to him, he came to Gratiot Co., Mich., and purchased 80 acres of land on section 35, in the township of Elba. He has now improved 50 acres of his farm. March 21, 1870, he was married to Alice A. Crego, the only daughter of Lorin M. and Eliza O. (Stone) Crego, natives of New York. This marriage has been blessed with two children, — Jessie A. and Jennie A. Mr. Meacham is one of the most respected citizens of his township, and has held various local offices. In 1 87 1 he was elected Township Clerk, and to that office he was re-elected in 1872 and 1873. He was elected Supervisor in 1881 and 1883, and now repre- sents Elba Township in the Board of Supervisors. He has also been School Director for the past 12 years. He is a member of the Masonic Order, and of the I. O. O. F. Politically he is a strong Re- publican. II : 3< HJ i %i : t I avid Muffly, farmer, section 3, Hamilton Township, was born in Washington Town- ship, Westmoreland Co., Pa., Dec. 20, 1830. The family removed to Stark Co., Ohio, while David was quite young, and there he resided on the parental farm, attending the common schools and developing into manfiood. In 1850, when 20 years of age, Mr. Muffly left the parental home to fight life s battles alone, and went to Seneca Co., Ohio. He remained in that county five years, until 1855, when, desiring a home for him- self and family, having in the meantime married, he came to this State and settled in Hamilton Township, this county. His experiences were those of many others of Michigan's pioneer settlers. Hardship, deprivation and want were his to battle with, and successfully did he wage the war against and van- quish them. He built his log cabin in the woods, and in the erection of the same used only one single sawed board, and that for the door. Here he lived and amid the howling of wolves, the crying of panthers, and with ** prowling Indians for neighbors " he en- tered on the task of clearing his land. Although he had many trials and difficulties to overcome, he ex- perienced some of the joys and pleasures of those pioneer days. He was at the first township election, when almost every man in the township was elected to office. Mr. Muffly, like many others when the flag of our country was dishonored by the rebel shot at Fort Sumter, went forth to meet the enemy and battle for its maintenance. He enlisted in Co. F, 2gth Mich. Vol. Inf. He was in the battle of De- catur (Ala.) and Murfreesboro ; and shortly after the last-named battle, while packing and preparing for a V >: v/ V r r ]1];>-^ ^V^ Digitized by Google V r f 2[6 v<:iiii>;uus> V >^M-! GRATIOT COUNTY. V > ./ ^i 1 S-. forced march, he was accidentally precipitated into a railroad ditch, and, striking his breast upon the iron which happened to be piled there, so lacerated it and crippled him he was transferred to the hospital. Here his wounds were un professionally treated, and he finally received his discharge on account of disa- bility and returned to his family. Mr. Muffly was married Jan. ii, 1854, to Miss Delilah Street. Seven children have been bom to the union, namely : Rufus S., Martha J., James C, Vilda, Arminia, David S. and Francis M. The father and mother are both members of the Christian Church. 'ames Qriffith, farmer, section 5, Emerson Township, was born in Chemung Co., N. Y., Dec. 3, 1837, aniis the son of Lewis and Hannah (Boyer) Griffith, natives of New York State. The father is now a resident of Lenawee Co., Mich., and the mother died in New York Slate in 1839, when James was only two years old. Two years after that event he came with his father to Michigan and settled in Lenawee County. Being among the early settlers of that part of the State, they had to perform the toilsome work of clearing and improving a new farm, and James passed many more days at work than at school. At 19 years of age, obtaining his father s permission to look out for himself, he commenced as a common laborer. In i860 he came to Gratiot County and located 120 acres of wild land on section 5, Emerson Township. Aug. 17, 1862, he enlisted as a private in Co. G, 5th Mich. Vol. Cav., and went to the Army of the Potomac, where he served under Gen. Phil. Sheri- dan. He was an eye-witness of the famous ride to Winchester by that commander. He fought at Cold Harbor, Winchester, Cedar Creek, and numerous lesser engagements. He was honorably discharged in June, 1865, having served in the field nearly three years. Returning home to his farm he kept bache- lor's hall for seven and a half years. March 6, 1873, he formed a life partnership with Emeline Decker, born in Ontario Co., N. Y., May 16, 1844. This union has been blessed with four children, — Sarah P., Lewis, Maud and James K. Mr. Griffith has im- proved 70 acres of his farm, and has a fine dwelling and barn. He is considered a skillful farmer, and as a citizen is very popular. He has been Assessor for 1 2 years, and has also been Overseer of High- ways. Politically he is a Republican. K >;^ayid Beichard, farmer, section 6, Ithaca Hytptl Township, was bom in Ashland Co., Ohio, jy^^ Nov. 28, 1847, ^'^^ ^s a son of John A, Reichard, deceased, a native of Pennsylvania, fhere our subject lived, assisted his father on the farm, attended the common schools and de- veloped into manhood. In 1865 Mr. R. left the parental home, to battle against the trials of life single-handed and alone, and came to this county, where he anived in the spring of that year, and where he has ever since resided. He first settled in Fulton Township, where he remained 1 1 years, and then went to Ithaca Township, where he is now living, the occupier and owner of 115 acres of fine land. Mr. Reichard was married March 9, 1869, to Miss Mary, daughter of Edward Waggoner, of Ithaca, and two children have been born to their union, namely : John E. and Orill. Mrs. Reichard was bom in Springfield, Jefferson Co., Ohio. 4-^AAA^ ^~ ^' orman L. Higbie, M. D., physician and farmer, section 35, Elba Township, is a son ^^ of Oliver H. and Esther (Randall) Higbie, "1^ natives of New York. They lived in that ]L State, on a farm, till the endof their lives, which came for Mr. Higbie in 1848, and his wife in 1S58. Norman L. was born in Delaware Co., N. Y., Feb. 16, 1832. At the age of 18 he left home, and for the ensuing eight years he was engaged in teach- ing school, with the exception of two years, during which he attended at Rondout Seminary, Ulster Co., N. Y., and two years at New York Confercnce Sem- inary, at Charlotteville, Schoharie Co., N. Y. During this time, too, he was studying the profession of medicine. In May, 1854, he came to Ann Arbor, % \y ^/J^ -- \ <->Da:^[ia;> L, r Digitized by -*4it^:il>:{0 Google \ r XJ^i^y*^: -X GRATIOT COUNTY. ^m ^ a V ^ Mich., and afterwards he went to Iowa; then returned to Ann Arbor. Thence he went to Plymouth, Wayne County, and practiced medicine for two years. In the practice of his profession, he also spent one year at Jackson ^nd one year at Howell. He then spent two years in the South for his health. Returning to Michigan, he practiced medicine in Jackson County from 1861 to 1874. His health then failed him, and he was compelled to retire from active practice. Jan. 12, 1875, he arrived in Gratiot County, and located on the southeast quarter of section 35, Elba Township. He has since added 40 acres to his farm. In 1856, he was united in marriage to Jane Hor- ton, who was born in Rensselaer Co., N. Y., May 31, 1832. She was the daughter of Joseph and Elmira (Marks) Horton. Mr. Horton was born in New Leb- anon, Columbia Co., N. Y., April 7, 1807 ; and Mrs. Horton was born July 13, 1808. Dr. and Mrs. Hig- bie are the parents of six children, — George L., Joseph E., Alice J., William H., Myra A. and Alfred. They are active members of the M. E. Church. Dr. Higbie was chosen Superintendent of Schools in his township in ^875, and again in 1877, and he is now the health officer of his township. In poli- tics he is a Republican. ^<HJH5|e^ I illiam Martin, farmer, section 1 3, Wash- ington Township, is a son of Henry and Sarah (Bugg) Martin,* who Were of English descent, and who came to America in 1835. They landed at New York July 3, and came \J direct to Washtenaw Co., Mich. They located on 80 acres in Dexter Township, where Mr. Martin died Nov. 26, 1844; and Mrs. Martin in December, 1859. At the age of 2 1, William Martin commenced to make his own way in life, and engaged in farming. The same year, he was married to Fanny, daughter of Michael and Fanny McCabe, natives of Ireland. They came to America at an early day, and are now both dead. Mr. Martin came to Gratiot County in 1856, and settled on 32 acres on section 13, Washington Town- ship. He married for his second wife Harriet Miles. Dy his first marriage he has four children, and by his second, 11. In his township Mr. Martin has been 217 -N^ 1 Constable five terms. Justice of the Peace two terms, and School Assessor three terms. Politically, he has always been a supporter of the Democratic party. illiam D. Letts, farmer, section 35, Elba Township, is a son of Edward and Mary (Galligan) Letts, natives of >Iew York and Michigan. They were married in Clin- ton County in 1 85 1. In 1856 they located on 80 acres on section 35, Elba Township, then in its primitive wildness. They now have 70 acres well improved. During their first years here, almost their only companions were the wolf, the wild-cat, and other denizens of the forest. They often built fires to keep the bears away from their calves and pigs, and occasionally they would take the dinner horn and call the wolves to their door. Mrs. Letts was the first white persoif to go from her neighbor- hood to Chesaning. making the trip of 18 miles through the wilderness alone. The subject of this sketch was married at the age of 24, to Vora Dunlap, the eldest daughter of Andrew and Mary (Coryell) Dunlap, and who was born April 4, 1855. Mr. and Mrs. Letts are the parents of two children, — Leroy D., born Nov. 16, 1880, and Floyd L., born Aug. 2, 1883. Mr. Letts is politically a Republican. He has held the office of School In- spector for a number of terms, and is one of the en- ergetic young men of the county. Tob C. Wolford, farmer on section 33, Sumner Township, is a son of David and Laverna (Conger) Wolford, natives of New York. The father was a mason and shoe- maker while in New York State. Aftet moving to Michigan in April, 1858, he engaged in farming, which he followed until his death in 1867. His wife is still living in this county. Job C, the subject of this biography, was born in Cayuga Co , N. Y., Sept. 19, 1843. When he was 12 years old, the family movgd to Indiana, and two years later returned to Cayuga County. After an- other year, they came to this county and settled in New Haven Township. Here Job worked for his ; r r ^t; ,^^ __J.<;(|t|>:||[]v.>L •c<>^ %(^J Digitized by LnOOQ IC V w r 218 -7<iDli:v:Dll>->-r Vv/ GRATIOT COUNTY. r /N V f.y father until the spring of 1864. March 24 of that year, he enlisted in Co. K, 21st Mich. Vol. Inf. He served as a private in the Army of the Cumberland under Gen. Sherman, for 14 months, and fought at Chattanooga, Bentonville and Goldsborough. At the last named place, March 29, 1865, he was wounded, while on a charge, by a ball which penetrated his right thigh. By this he was not permanently injured. He was honorably discharged May 23, 1865. Returning home, he purchased 80 acres on section 33, Sumner Township, heavily timbered, and set about making himself a home. March 25, 1866, in North Shade Township, he was married to Miss Emily A. Dean, daughter of Amos and Betsy (Grant) Dean. She was born Aug. i, 1843, in Yates Co., N. Y. Her father was a farmer and died June 26, 1858. Her mother resides with her daughter, enjoy- ing good health and being quite active, although 76 years old. Mr. and Mrs. Wolford have a family of three: Judson E , born Oct. 28, 1867; Jessie E., April 3, 1874; Cora V., Nov. 26, 1877. Mr. W. has nicely improved 60 acres of his original 80, and has added 40 acres, also improved. He is a member of Elm Hall Lodge No. 257, F. & A. M. He has held the office of School Director, and in political sentiment is a Republican. -«^^ ^r«- : rin J Sprague, merchant at Martins Cor- ners, Washington Township, is a son of Beriah and Maria (Sweet) Sprague. Beriah Sprague was born in St. Lawrence Co., N. Y., in 1815, and died in this county, Dec. 9, 1883. Maria (Sweet) Sprague was born in Jefferson Co., N. Y., in 181 9, and is still living, in Gratiot County. The subject of this sketch was born in St. Law- rence Co.. N. Y., July 12, 1 841, and remained with his parents until 2 1 years old' He then taught, and worked on a farm for a time. He taught altogether 10 terms of school, six of which were in Gratiot County. Nov. 27, 1867, he was married to Emeline L Noble, daughter of James and Isabella (Laid- low) Noble, of Scotch descent. They came to Amer- ica and located in St. Lawrence Co , N. Y., where they followed farming, and \vhere their daughter Emeline was born Au^^ 5, 1845- In i8^>9» ^^r. V- Sprague came to Gratiot County and purchased 40 ^ acres on section 16, Washington Township. This ' farm he afterwards sold, and for one year he was out , of employment. In 188 1, he started the store he now has, at Martin's Corners. He has been School , Superintendent for five years, and in 1882-3 was Supervisor of his township. Politically, he is a zeal- ous Republican. rederick L. C088, merchant at North Star, o and resident on section 15, North Star " '^ Township, was bom in Delaware Co., N. Y., Aug. 27, 1842. He is a son of Peter Coss^ of North Star Township, who came here with f -H in 1867. Mr. Coss came to this county the same year as his father, but located at Pompei, where he was engaged in the mercantile business until 1869, when he moved to Ithaca, where he lived 1 1 years ; thence to North Star, and established himself in the same business. He carries on a general mercantile business, has a stock sufficient to meet the requirements of the neighborhood and is having a good trade. Mr. Coss enlisted in the late civil war, enrolling in Co. A, 56th Pa. Vol. Inf, and participated in the bat- tles of second Bull Run, South Mountain, Anrietam, Fredericksburg (both battles), Chancellorsville, Get- tysburg and others. Mr. Coss has been united in marriage twice. He was first married Feb. 14, 1867, to Mrs. Louisa Swift, of North Star Township, who had by her first husband two children, Emma J. and Adelaide (Sav- age), deceased. He was again married July 4, 1883, to Alice J. Craun, of North Star. Politically, Mr. Coss is a staunch Republican. ♦e^^^^^ *- ri^^W"-^' :n ^aniel Qower, farmer, section 30, Elba Township, is a son of John and Polly (Bowker) Grower, natives of Pennsyl- vania and New York. They are residents of Tompkins Co., N. Y., where Mr. Gower is a t inner. Daniel was bom Sept. i, 1843, in Tompkins County. Leaving home in the second year of the war, he enlisted Sept. i, 1862, in Co, K, -<:'.u\'.:::\^^- J- Digitized by Google Digitized by Google f ^"-^f t i\ Digitized by Google V r ^ ■ST G/^A TIOT CO UN TV, J /\ V Third New York Artillery, and was first sent to New- bern, N. C. He then served in South Carolina for three months, and then returned to Newbem. In March, 1864, he came home on a furlough, after which he reported again at Newbem. He was in the battle at Ross* Mill, N. C, Nov. 2, 1862; Kingston, Dec. 14, 1862; White Hall, Dec. 16, 1862. In the latter engagement he was wounded in the chest by a shell. He was mustered out at Richmond, June i, 1865, and finally discharged at Syracuse, N. Y. After leaving the service he worked on a farm by the month, and also by the year. In 1868, he was united in marriage to Mary A., daughter of John and Elizabeth ( Chester ) Allen, natives of Steuben County, and Cayuga Co., N. Y., respectively. Mr. Allen is a farmer and resides in Illinois. Mrs. Allen lives in New York State. Mr. and Mrs. Gower came to Ingham County, this State, immediately after marriage, and a year later they moved to this county, locating on section 30, Elba Township. After seven months they went into the pine woods of Hamilton, where they lived three years. They then lived four years in New York State and one year in Cook Co., 111., when they re- turned to their farm in this county. They have a family of three children : Edward W., Henry A. and Bertha I. Mr. Gower has held the office of Drain Commissioner, Assessor and Director. Politically he is bound to no party, but votes for the best man. •SS^^^^Tjryvk ^lisha C. Cook, farmer, section 31, North Star Township, was born in Steuben Co., N. Y., March 3, 18 18. His parents were Na- than and Chloe (Cobb) Cook, natives also of that State. The latter dying in 1824, the bereft hus- j band came to Michigan, settling in Livingston County, and afterward in Gratiot County, where he made his home with his son Elisha until his death, in the former county, while on a visit there, at the age of 88 years. While residing in this county he hewed the timber for the Presbyterian church which now stands on section 31. In his early life Mr. Cook, the subject ot this sketch, attended school, one year of the time the 221 Groton Academy, in Tompkins Co., N. Y. He ac- quired the trade of carpentry, mostly by working with his father, who was a millwright. Mr. C. fol- lowed his trade for 20 years. At the age of about 23 he left home and pursued his vocation a number of years in Clinton Co., Mich. In 1852 he went overland to California, where he remained three years, with great benefit to his health, though not meeting with the pecuniary success which he had expected. Returning to Clinton Co., Mich., he followed his occupation several years, teaching school during the winter seasons. In the spring of 1858, he came with his family — which, then comprised a wife and one child — to Gratiot County, and purchased 100 acres of wild land, on section 31, North Star Township, where he now resides. He has since added 80 acres to his estate, and now has 1 00 acres in a good state of cul- tivation. On his arrival here he built a rough board house, which the family occupied until January, 187 1, when they moved into their present fine residence. Mr. C. has also a fine equipment of barns, etc., upon his farm, and his present circumstances give evidence of industry, economy and prosperity. Mr. Cook was married July 19, 1855, in Clinton Co., Mich., to Miss Margaret, second daughter ol Peter and Elizabeth (Berdan) Lott, natives of New York State who settled in Wayne County, this State, in an early day, and three years afterward moved to Clinton County, where they resided the remainder of their life. Mr. and Mrs. Cook have had five chileren, three of whom survive, as follows: Fremont H., born April 19, 1856; Harriet L., Feb. 4, 1867; and Carrie V., July 22, 1870. Milan, born Aug. 4, 1862, died Feb. 24, 1863; and Ida E., bom Jan. 8, i860, died March 13, 1883. Politically, Mr. C. is a Republican ; and he has held the offices of Sheriff, 1868-72, Supervisor ot North Star Township, one year, and Township Clerk, and takes considerable interest in school affairs. He is a member of the M. E. Church and of the Masonic Order. We take pleasure in giving Mr. Cook s portrait on a preceding page, as he is not only a representative man and worthy citizen of the county of Gratiot, but also one who has proved faithful in all the public official relations in which his fellow citizens have seen fit to place him. 5, T s> / s A ^>'V \^i^^l^ N^ -^-^iia>:noi:> ^^'J^ (T Digitized by VjOOQlC ' 4 A 0^ OWp'MO rz-. 44vf,*g7^W-v» GRATIOT COUNTY. - o<r>o coo lamuel M. Soott, merchant, resident on sec- tion 22, North Star Township, was bom in Essex Township, Clinton Co., Mich., Feb. 13, 1849; his father, named also Samuel M., was a native of the State of New York, and is now deceased. The subject of this sketch was brought up on a farm and educated at the common school and at Eastman's Commercial College at Poughkeepsie, New York. He afterward clerked for about 12 years in Nelson & Barbers store at Ithaca, and came to his present location in June, 1883, and established a store, where he keeps a full line of general merchandise, and has a successful trade. He is a member of the I. O. O. F., and was for two terms Clerk of Newark Township. Mr. Scott was married Nov. 10, 1878, to Miss Celia J., daughter of A. W. Belding, of this township. Their three children are, Lelo A., Grace R. and Ola A. [ ewel Smith, grocer, Wheeler village, Wheeler Township, was born May i, 1852, and is J^g* ^ the son of John H. and Jane (Castimore) "^ "V Smith, natives of New Jersey. The father 1(5 was by profession a millwright, and removed to Trumbull Co., Ohio, in 1845. He came to Gratiot County in February, 1 863, and located on section 34, Wheeler Township. He entered 160 acres of land, of- which he had improved 50 at the time of his death, March 6, 1872. Mrs. Smith died Feb. 14, 1882. Newel was married at the age of 18 to Sarah, the daughter of Richard and Sarah A. Ellsworth, natives of New York. She died March 16, 1880, leaving two children, — Nina J. and Amy E. Oct. 12, 1881, he was again married, to Jane, the third daughter of Thomas and Ellen (Thurlow) Wordel, natives of England, but now resident of Canada. By this sec- ond marriage Mr. Smith has one child, — Nellie M. Mr. Smith drove the first ox team to Saginaw from this part of the country. He has been very popular among his fellow citizens, has held several local of- fices, and has never been defeated for any office for ^<:;r,n u u . which he has been nominated. In the spring of 1875, he was elected Justice of the Peace, which of- fice he held two terms. He was chosen Supervisor in 1876, to which office he was also re-elected sev- eral times, and he has been Supervisor altogether six years. In politics he is a Democrat. He is a mem- ber of St. Louis Lodge, No. 188, F. &. A. M. f. -f-HeJ-^-^^H—t^ ohu W. Smith, farmer, section 28, Elba Township, is the second son of Dewey and Phebe (Davis) Smith, natives of Vermont and Ohio, respectively. He was bom March 5, 1846, in Wells Co., Ind., and at the age of 22 he left his father's farm to make his own way in life. ~ For about 10 years he worked at lum- bering. He was married in 1873 to Belle, daughter of John W. and Christina (Covert) Sutphin. She was born Dec. 27, 1856, in Livingston Co., Mich., and came to Elba Township in 1874. They are the parents of one son, — Dewey D. Smith, bom Feb. 20, 1878. Mr. Smiths father purchased 160 acres in Elba Township, in 1858, of which he, John W., now owns 80 acres. In 1879, he erected his large and well ar- ranged barn. He is now actively engaged in farming and stock-raising. He was elected Township Clerk in 1877, and held that position for four years in suc- cession. In 1880, he was chosen Township Treas- urer, which office he filled two terms. He is a mem- ber of Maple River Lodge, No. 76, I. O. O. F. Po- litically, he votes the Republican ticket. ^14- g? A v/ uther J. I>eaD, farmer, section 15, North Star Township, is a native of the Empire State, where he was bom Dec. 11, 1831. His father, Sether, was a native of Pennsylvania, and removed with his family from Allegany Co., N. Y., to Hillsdale Co., Mich., in the fall of 1842. Mr. Dean came to Gratiot County in 1855, en- tered 1 60 acres of land, and assisted his brothers to clear a piece of land and build a house for their fathers family. He taught school the first winter, returned to Hillsdale County in the spring of 1856, r: ^ i!^^-^ 4^->^:|y. Digitized by LnOOQ IC A r^^<^i> X T <>[lll>^tll]v> V -ir^^^^ r I s -Os GRA TIO T CO UNTY, 223 "S and May 13 following married Miss Lucy, daughter of John McBride, now deceased. " He came with his bride into this wilderness and commenced housekeep- ing amid the privations and untoward obstacles of pioneer life. He finished his house and continued hard work until he made for himself and family a comfortable home. He owns at present 82 acres of good land, and is engaged in general farming. Within one year after he was married he lost his house and all the contents by fire. This was a severe blow, but he was not the man to give up the ship of life on that account. By his first wife Mr. Dean had three children, name- ly : Herbert E., deceased ; Effie M., now the wife of Frank P. Walker, of Ithaca ; and Arthur J. For his present wife Mr. Dean married Mrs. Elizabeth Row- ley, Oct. 16, 1882, who had had by her former hus- band two children, namely : Erastus A. and Ida M. Mr. Dean, in religious views, is a Baptist; he has been School Inspector several years, and at present is Township Clerk. saac Wooley, farmer, section 34, Elba Town- ship, is a son of James and Margaret (Chan- dler) Wooley, natives of New Jersey. James Wooley was by occupation a shoemaker. He came to Gratiot County in 1855, and entered 320 acres of Government land on section 34, Elba Township He subsequently gave each of his sons 80 acres, and he is yet alive, at the advanced age of 93. Isaac Wooley was bom Feb. 17, 1829, in the State of New York. At the age of 20 he left home to work for himself, and, going to New York State, he was engaged in farming for six years. Sept. 4, 1855, he was united in marriage to Martha Whitney, daughter of William E. and Mary (Scott) Whitney, natives of New York. Mr. Whitney was bom in Ontario County, and was a minister of the gospel. Mrs. Whitney was born in Niagara County. Mr. and Mrs. Wooley remained in Ingham County, where they were married, until 1859, and then re- moved to Gratiot County. They settled first on 100 acres, but, afterwards selling 20 aijd buying 15, they now have 95 acres, of which 57 are well improved. - 'Vi ¥^^ ^-^f" — 9-^<i}n They are the parents of one daughter, bom Dec. 18, 1856. Mr. Woqley has been Highway Commissioner in his township for three years. He is a member of Maple River Lodge No. 76, I. O. O. F.; and politi- cally he votes with the Republican party. Mrs. Wooley is an active member of the Free-Will Bap- tist Church. A«i2£C;©i^ ^^^^uinnr^ mm^.. r eneca Sly, Postmaster, and member of the mercantile firm of Glass & Sly, Elm Hall, is a son of George J. and Samantha (Riggs) Sly, natives respectively of New York and Connecticut. George J. Sly came to Michigan in 1839, and died at Elm Hall, this county, at the advanced age of 72. Mrs. Sly is yet living, at Elm Hall. The subject of this biography, Seneca, was bom at White Oak, Ingham County, this State, Jan. 20, 1842. He worked on the farm, and received a good common- school education, under the care ol his parents, until 20 years old. Oct. 18, 1862, he enlisted in Co. B, 26th Mich. Vol. Inf., under the command of Col. Nathan Church, and was sent to the Army of the Potomac. His corps was occupied in the defense of Suffolk, Yorktown and Washington, at which latter place he was discharged for disability caused by disease of the lungs. He was confined to his bed a year. Hearing reports of the healthfulness of Gratiot County, he came here in the hope of improving his physical condition, and engaged as cook in the woods for Fowler & Cleverdon. He was to work "for his board, if he earned it, and more, if he earned it." This work proving beneficial to his health, he began as teamster for the same company. Retuminghome for a while, he came again to Sumner Township, this county, and carried on farming. In 1877, he engaged as clerk in the store of Blair & Houck, of Elm Hall, which position he held four years. During this time he was elected Township Clerk, which oflice he filled with credit four years. For a year more he was in the store of Mr. Beeson. In 1882, he established a grocery of his own, being about the same time Justice of the Peace. He has recently taken a partner, and the firm is now Glass & r ;• r. T \y r Digitized by Goog le ■;>i/\'. J'. C" f. J 0^\ GRATIOT COUNTY. ^^ / Sly. He was appointed Postmaster in July, 1882. He IS also a Notary Public, having been appointed soon after he came to Elm Hall. Feb. 22, 1866, at Elm Hall, he was married to Miss Mary I. Boyd, daughter of John and Elizabeth Boyd, natives of Pennsylvania, where also the daughter was born, in February, 1846. She afterwards came to Ohio, and then to this State, where she was married. Mr. and Mrs. Sly have a family of five: Ettie A., Hattie B., Libbie, Fred A. and an infant. Mr. S. has been an active Republican since the organization of the party. He is J. V. C. in the G. A. R. post at Elm Hall, and he and wife are attached to the faith of the United Brethren Church. ^ ohn MuU, farmer on section 5, Emerson Township, was born in Yates Co., N. Y., May 26, 1 810, and is a son of Christopher and Catharine (Bussard) Mull, of German de- scent and natives of Pennsylvania. They followed farming, and died in Livingston Co., N. Y., in 1864, the father aged 90, and the mother aged 88. John came, when very young, with his parents, to Canandaigua, Ontario Co., N. Y., and three years later they removed to Mt. Morris, Livingston Co., N. Y. In 1826 he went to Nunda, Allegany County, where, Sept. 18, 1832, he was married to Eliza, daughter of Joel and Patty (Tuttle) Knapp, natives of Connecticut, and of New England parent- age. The former was a tailor by trade. They died in Livingston Co., N. Y., the one Aug. 12, 1855, aged 73, and the other April 11, 1864, aged 88. Eliza was born in Rockland Co., N. Y., on the banks of the Hudson, Jan. 29, 1807. When seven years old she went with her parents to Phelps, Ontario Co., N. Y., and later to Ossian, Livingston County, where she was educated and married. Shortly after that event they went to Trumbull Co., Ohio, where he engaged in turning wood plates, at that time very fashionable in that country. Two years later, in the fall of 1833, he returned to New York and farmed for nine years. Going once more to Ohio, he resumed his former employment of mak- ing wooden dishes. In the fall of 1846 they came to Lenawee Co., Mich., and farmed for five years. Their next move was to Mason, Ingham County, and in March, 1861, they came to Gratiot County and settled on 40 acres on section 5, Emerson Township. Mr. Mull has since added 40 acres, and has made excellent improvements. March 25, 1864, he enlisted in Co. C, 2d Mich. Vol. Inf., and was sent to the Army of the Potomac. He participated in ^^t. active engagements, among them Cold Harbor, June 3, 1864. While supporting the battery he was compelled to sit within a few feet of the cannon s mouth, which caused the loss of hearing in the right ear, and seeing in the right eye. He was also in the battle of ^cllowhouse Station, Aug. 19, 1864, and in the battles in front of Peters- burg, where he was captured March 25, 1865, just one year from his enlistment Five days later he was paroled, and he received an honorable discharge June 12, 1865. Returning home, he has since de- voted his time to his farm and family. Mr. and Mrs. Mull have had eight children, of whom fist^ are living, — Ann A., born Aug. 11, 1837 ; Harriet N., Jan. 21, 1842; Mariah E., March 17, 1844; Jennie M., Jan. 3, 1847; John S., Oct. 13, 1849. The three not living are as follows: Joel F., born Nov. 25, 1833, and died July 10,1858; William H., bom April 23, 1840, and died in the service of the United States, at Farmington, Miss., Aug. 14, 1862; and Edwin E., born July 14, 1837, and died Aug. 8, 1883. Mr. Mull has held the office of Justice of the Peace for a number of years, and Highway Commissioner for six years. In politics he is an adherent of the Republican party. r K ■> i ♦ lo « » i <- %\. eorge Smith, manufacturer of brick and tile, section 22, North Star Township, was born in Onondaga Co., N. Y., Feb. 22 1 837 ; his father, James Smith, was a native of Cayuga Co., N. Y., and is now a resident tf Kalkaska, Mich. He moved with his fam- ily to Hillsdale Co., Mich., when his son George was only six years of age, settling upon a farm, where the latter was reared and educated. The subject of this sketch came to Gratiot County in September, 1869, and, until about five years ago, followed farming. He is now driving a prosperous business in the manufacture of brick and tile, in connection with farming. His land property com- prises 1 16 acres. A K^ Digitized by Google r A^/ .^'^ V -^i^^ /.N ^ .< 7<c>iitiJi^nii>>^ GRATIOT COUNTY. '^■:^ i:^^:i\^i 225 ^ Mr. Smith was married Aug. 18, i860, to Miss At- lanta L., daughter of Erastus Shaw (deceased), who was a native of Rutland Co., Vt. She was born in Tompkins Co, N. Y., in 1840, and came to Michi- gan, with her husband, in April, 1861. Their chil- dren are: Rosa B., deceased, Emma A., Eugene J., Flora v., Addie L., Frank J. and Grant O. Emma A. is the wife of Foshen Hoffman. Mr. Smith has been Township Clerk, Justice of the Peace a few years, is a member of the Order of Patrons of Husbandry, and, with his wife, is in re- ligious belief a sympathizer with the Baptist Church. iharlOB B. Slaughter, manufacturer and re- pairer of wagons, Breckenridge village* Wheeler Township, was born in the State of New York, April 13, 1829, and is the son of James and Mary (Voak) Slaughter, natives of New York. The father was a farmer, and also practiced medicine. He moved to Seneca Co., Ohio, in 1841, and died therein 1844. Mrs. Slaugh- ter died in 1 87 1. The son was 15 years old when he left home as an apprentice to the carpenter's trade, which he has always followed for a liveUhood. At the age of 22, he was united in marriage to Ebaline, third daughter of Michael and Hepsoby (Famulinger) Long, natives of Ohio, in which State they followed farming until their death. Mrs. Slaughter died Dec. 27, 1856. He afterwards married Maria A., daughter of Silas T. and Harriet H. Jewell, natives of Massachusetts and New Hampshire. Both are now deceased, Mrs. Jewell dying March 14, 1852, and Mr. Jewell April 6, 1869, in Ohio. Mr. Slaughter came to Gratiot County with his wife in 1 86 1, and settled on section 22, Wheeler Town- ship. He first entered 320 acres, but has now 160 acres. He was the eighth white man in Wheeler Township. His first home was a 10 x 10 shanty, when wild animals were abundant. He often went to Saginaw and fetched on his back provisions for his family. They were obliged to go four miles to church. In spite of such trials they enjoyed to a high degree the peculiar pleasures of pioneer life. Mr. Slaughter has one child by his first marriage, and four by his second: Del L., Ida H., Sarah L., Charlie B. and Nellie M. He is a member of North- ern Light Lodge, No. 40, F. & A. M., at South To- ledo, Ohio. In politics he affiliates with the Repub- lican party. Mrs. Slaughter is an active member of the M. E. Church. t -S-wx/x^S^.^S'X/vv.- r.^^.^' ^%:f Mj^orydon Cronkhite, retired farmer, section nJ, 1 2, Emerson Township, was born in Hoosac, Y., Oct. 17, 1803, and with his parents went to Otsego County two years later. When about 14 years old, the family moved to the " Holland purchase " in Western New York, and he lived there until 1856, when he came to Ionia, Mich. From 1868 till 1881 he lived in Saranac; and then he came to this county to live with his nephew, Albro Curtiss. March 12, 1825, at Middlebury, N. Y., he was married to Melinda Fisk. She was a native of War- saw, N. Y., in which State she was educated. Mr. Cronkhite was the oldest of 12 children, and had himself four children, two of whom are living: Jerome, married and living in Illinois; George, a res- ident of Pullman, III., and an overseer in the car-shops of that place. He is a member of the Baptist Church at Saranac, Ionia County. Politically, he was always a Whig, during the life-time of the Whig party *; and now he is a firm Republican. ilUam H. Morrison, farmer, section 31, Elba Township, is a son of William F. and Rebecca (Smith) Morrison, natives of Cayuga Co., N. Y. Mr. Morrison was by occupation a cabinet-maker, and resided in the Slate of New York until his death, in 1840. Mrs. Morrison removed to Michigan, and died in Eaton County in 1876. The son, William H., was born Jan. 14, 1 831, in Orleans Co., N. Y. His father dying when he was nine years of age, he went to live with his uncle, remaining Xivt, years. For the next few years he attended school and worked for his board in the winters and labored on the Erie Canal in the summers. He then went to Tompkins Co., N. Y., and learned the blacksmith trade. In 1869, ^ f S 9 c> %mo -3^' y<y' •?^ ^^^ Digitized by V^OOQlC f i V 226 GRATIOT m^^^ — COUNTY. he came to Gratiot County, and located on the east half of the southeast quarter of section 31, Elba Township. This was at that time all wild land, but he has now 65 acres well improved. At the age of 23 he married Mary E. Luttenton, daughter of Almon and Livonia (Blanchard) Lutten- ton, natives of Orleans Co., N. Y. They came to Wayne Co., Mich., in 1839, and located on a farm, where Mr. Luttenton died April 10, 1844. Mrs. Lut- tenton died in the Slate of New York, Sept. 12, 1869. Mary E. was their third daughter, and was bom March 9, 1834. Mr. and Mrs. Morrison have had nine children, as follows : William J., Dwight S., Der J., Rebecca M., Almon L. (drowned in a barrel July 6, 1869), John W., Alma L., David F. and Mary E. Aug. 19, 1861, Mr. Morrison enlisted in Co. F, Third New York Cavalry. With ^his regiment he participated in the engagements of ^^al^s Bluff and Edwards' Ferry, and was with Banks' expedition into the Shenandoah Valley. At Elizabeth City, N. C, he was wounded by a musket ball, which he still car- ries in his body. He also fought at Roanoke Island, and other places, and was finally discharged Aug. 28, 1865. In 1869, he was elected Supervisor of Elba Town- ship ; and he has been School Director for a number of terms. He is a member of Genesee Lodge, No. 24, I. O. O. F., and affiliates with the Republican party. iheldon Wight, of the firm of S. & M. Wight, of Sickels, and whose biography we are pleased to give as a representative man of Hamilton Township, was born in Lorain Co., Ohio, April 22, 1847, and is a son of Leonard Wight, of Van Buren Co., Mich., a native of Rochester, New York. Mr. Wight's education was acquired in the common schools of his native county, which he attended, and lived at home, developing into manhood. At the age of 20 years, in the fall of 1867, he left the parental hearthstone and went forth to battle against the trials and troubles of life alone, or rather in company with the life companion he had chosen a year previous, and came to this county. He settled 1 ■;> <" on the west half of the southwest quarter of section 16 4, Hamilton Township, where he has resided years, and is at present living. ( Mr. W. established his present business in the fall * of 1 88 1, and in 1883 admitted his brother as a full partner. The business, a planing mill and repair V. shop, is a prosperous one; it is run by steam power; they have a large single surfacer and matcher, and a small surfacer for moulding and siding; and they prin- cipally manufacture sleighs, and do a general repair business. Mr. Wight was united in marriage to Miss Mary, \ daughter of Abraham Weaver, deceased. Five | children have been bom to Mr. and Mrs. W., namely : ^ Charley, Alma, Florence, Freddie and Bertie. In addition to his business, Mr. W. devotes con- siderable of his time to the cultivation of his farm, consisting of 80 acres, less six acres incorporated in the village of Sickels, and also to an apiary, and prides himself on his success in the last named '" business. ^ Mr. Wight was a soldier in the late civil war, ^ enlisting in Co. F, 6th Mich. Cav., was in Kilpatricks ^ raid toward Richmond, battles of the Wilderness, ^ Cedar Creek, Fisher's Hill, Five Forks, and others, J and likewise in all the charges immediately preced- ,^ ing Lee's surrender. After the grand review at *; Washington, D. C, his regiment was ordered to Powder River, Montana, and built Fort Reno. While at Fort Reno, he was sent as a herder up a ravine about a mile from the fort, mounted on a mule. Seeing a wolf prowling around the herd, he tried his revolver on the animal, but only succeeded in breaking a hind leg. Following the wolf, he > emptied his revolver in the chase, and was led about ( a half a mile over a hill into another ravine. His ^ attention was then suddenly drawn to three mounted redskins, who were undoubtedly hostile in their intentions. Being unarmed, and perceiving that the ravine he was in led to the fort, he took the shortest cut home. He asserts that if he had not had a good mule on that occasion, he would not now he conducting a wagon shop at Sickels. Later in the fall the regiment was ordered to Salt Lake, Utah, but Mr. W. and a few others were sent to Fort Bridger, where he wintered. He was one of the 53 who marched back "as a command" and were discharged at Detroit, Mich., July 5, 1866. Mr. W. recollects many reminiscences of the '* soldier Digitized by Google i{ /\ ^==— — — viz life;" and records " that while on Tongue River, in ' ' Montana, they were * corralled * by the Indians. ;*\ Henry Evans, one of their number, volunteered to I attempt the hazardous undertaking of stealing his A way through the line of the enemy to the command, ' "^ for the purpose of procuring aid. He and Sergeant Hall stole forth in the night time, successfully eluded the watchfulness of the redskins, and by traveling in the night, and concealing themselves in the day-time, they reached the command on the third day. Re- inforcement soon reached them, and after being cor- ralled for 12 days, they were rescued from their perilous condition." He also relates that while at Detroit, waiting for his discharge, and stopping at the Wesson Hotel, at about two o'clock in the morning of the 4th of July, 1866, he found himself on the floor of his room, shouting **fire!" He and Henry Evans attempted to escape down the stairs ; but these were on fire, and they were forced to jump from the first-story window. This was a narrow escape, and a poor way to celebrate the national holiday. Mr. Wight is a member of the I. O. O. F., and also of the Grand Army of the Republic. Mason Wight, brother and business partner of our s;y subject, was born in Lorain Co., Ohio, March 2, 1850. He followed the occupation of a farmer until 1 883, when he came to this county and engaged with his brother in the business they are now jointly con- ducting. He was married, Dec. 16, 1874, to Miss Edith I Wright, and five children have been born to the union, four of whom are now living, namely : Lydia U A., Laura L., Irvin and Nettie. V He also is a member of the L O. O. F. ^enry W. Myers, farmer, section 19, Wash- ington Township, is a son of Jacob and Magdalena (Walburn) Myers» natives of Maryland and Pennsylvania. Mr. Myers yet lives, in De Kalb Co., Ind. Mrs. Myers died in I Seneca Co., Ohio, in 1850. Henry was born Oct. 3, 1844, in Seneca Co., Ohio, and left home at the age of 18. He was variously employed until Nov. 5, 1865, when he married Mrs. Lovina E. Mc- Entaffer, the widow of Timothy McEntaffer, and the GI^A TIO T CO UNTY, 227 ^ daughter of Jacob and Catharine (Kountz) Echelbar- ger, natives of Pennsylvania, where they followed farming. They afterwards removed to Ohio, locating in Columbiana County. Their next move was to De Kalb Co., Ind., where they died, both in April, 1878. Mr. and Mrs. Myers came to this State and county, and located on 5 1 acres on section 1 9, Washington Township. He has a fine residence, and a substan- tial barn. Politically, he has always supix)rted the Democratic party. Mrs. Myers has by her first mar- riage ^st children, — Isabel, Lorinda, Byron B., Oli ver and Olive (twins). % ^ y indrew J. Hatfield, farmer, section 15, Em- erson Township, was born in Medina Co., Ohio, July 1 1, 1839, and was the son of Jacob and Roxie (Houghton) Hatfield, natives of Pennsylvania and Cortland Co., N. Y. The former went to Ohio when seven years old, and lived on a farm in Medina County until 1862, when he moved to Michigan, and came to Gratiot County. He settled first in Newark Township, and then in Bethany Township, where he died Sept. 28, 1870. Mrs. Hatfield was of Puritan ancestry, and when (piite young was taken to Medina Co., Ohio, where she was married at the age of 16. She died March 22, 1841, at the age of 20 years, 10 months and 29 days, leaving two children, — Andrew J. (our subject), and L. Catharine (Shelly), who died in Charlotte, this State, in November, 1881. Andrew worked on his father s farm and obtained an academic education at Seville, Ohio. When 22 years old, he engaged for a short time in teaching. Nov. 25, i860, in his native county, he was married to Julia, daughter of John and Barbara (Geisinger) Wydeman, natives of Northumberland Co., Pa., and of German descent. They emigrated to Canada, where they were married, and 15 years later they removed to Medina Co., Ohio, where Julia was born, March 28, 1836. She was educated in that county, and lived at home (her father dying April 26, 1850) until her marriage. Two years after that event Mr. and Mrs. Hatfield came to this State and county and lo- cated in Newark Township. He purchased 40 acres in that township. May 25, 1864, he engaged with J. M. Kidd, of Ionia, as agent and collector for their V/ r p^V:^^^f^- -^<^i]!l::-l]ii;>-^ Digitized by Google f 228 (9^y^ T/0 T CO UNTY. >t>\^ -^^ V J \ fanning-mill establishment. This business he fol- lowed for 12 years. In April, 1877, he moved to Emerson Township and located on a farm of 80 acres, partly improved. He has it now nearly all in good cultivation, and has a very fine residence, which cost$3,000.
Mr. and Mrs. Hatfield have a family of three, —
Emma E., bom May 25, 1861 (married and residing
in Grand Rapids); William Forest, bom Aug. 24,
1862, and Arthur H., born July 21, 1864. They are
members of the M. E. Church. He is a member of
Ithaca Lodge, No. 123, F. & A. M. Politically he is
a staunch Republican. He has held the office of
Deputy Sheriff.
I
enry Qrover, an enterprising farmer, resi
dent on section 2, Arcada Township, was
bora in Hull, Yorkshire, Eng., Dec. 10,
1844; and is the son of Thomas and Maria
(Sherwood) Grover, natives of Yorkshire, Eng.
Thomas Grover was by occupation a carriage
smith, and came to this country in 1850, locating in
New York State. Two years later, he came to Len-
awee County, this State, and after a few years there
he came to Gratiot County, where he died, at his
home on section 2, Arcada Township, Aug. 27, 1877,
at the age of 65. His wife now resides at St. Louis,
in this county, at the age of 68.
The subject of this sketch came with his parents
to New York. State, and thence to Lenawee Co.,
Mich., where he was married. Nov. 28, 1867, to Ame-
lia, daughter of Joseph and Eliza (Clark) Barber,
narives of New York. They followed farming, and
came to this county, where Mr. Barber now lives, on
section 2, Arcada Township. Mrs. Barber is de-
ceased. Amelia was born in Hancock Co., Ohio, and
came when five years old with her parents to Lena-
wee Co., Mich.
Two years after marriage, Mr. and Mrs. Grover
went to Manistee County, where they farmed for
seven years. They returned to Adrian, and three
years later came to Gratiot County, settling down on
90 acres of his father s homestead. He is a progress-
ive farmer, and has about half his farm nicely
improved. They have five children, as follows : Char-
lie O., born Aug. 25, 187 1; Eliza M., Sept. 24, Vf
1873; Clara E., Dec. 31, 1875 ; Rose A., March 11, ^:
1878; Maria B., Oct. 6, 1883. Politically, Mr. Gro- ,;.
ver is a staunch Republican. '
^4 avid D. Stoddard, farmer, section 10,
■R^ Washington Township, is a son of Orson
and Bathia (Hulbert) Stoddard, natives of
Connecticut and New York. Mr. Stoddard,
Sr , \\.is born Jan. i, 1804, while Mrs. Stod-
» dard was born in July, 18 10. In 1854, they
came to Michigan and located in Wayne County.
Soon after, they removed to Gratiot and located on
section 1 1 , Washington Township, where Mr. Stod-
dard died, June 15, 1870, and Mrs. Stoddard, April
21, 1870.
The subject of this sketch was born in Allegany
Co., N. Y., April 24, 1830. At the age of 20, he en-
gaged as a farm hand, and worked as such for five
years. Nov. 9, 1854, he married Mary Ryan, daugh-
ter of Adam and Betsy (McNett) Ryan. In 1856,
Mr. and Mrs. Stoddard came to Gratiot, and located
on section 11, Washington Township. They after-
wards removed to section 10, on a fami of 20 acres.
They were among the first settlers of the township,
and found no improvements when, amid the snows
of winter, they first arrived among the forests of this
part of Michigan. They have two children, named
Alice F. and Freeman O. In politics, Mr. Stoddard
is a Republican. He and wife are members of the
U. B. Church.
^
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ames Bemaley, farmer, section 2, Hamilton
Township, is a son of Jacob and Elizabeth
(Nonnemaker) Remaley, natives of Penn-
sylvania, and of German and Welsh extraction,
both of whom are deceased.
James was born in Northampton Co., Pa.,
May 19, 1826, and in 1834 accompanied his parents
to Trumbull Co., Ohio, where they located. Here he
attended the common schools of the county, acquired
an education and developed into manhood. In the
year 1846, he determined to battle against the
trials and stmggles of life alone, and came to Eaton
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GRATIOT COUNTY.
231
County, this State, and entered 80 acres of Govern-
ment land, for which he paid $roo. This land lies two miles north of Charlotte, Eaton County this State, and is now valued at$106 per acre.
Mr. Remaley remained in Eaton County until the
year 1854, when he removed to Hillsdale County,
and there lived for 23 years, until 1877, when he
came to this county, since which time he has con-
stantly resided here. He owns 250 acres of land,
and besides attending to his farming devotes a portion
of his winters to lumbering.
Mr. Remaley was married, Feb. 13, .1853, to
Susanna, daughter of Eli Foglesang, of Hamilton
Township, of German descent, and one of the old
settlers of Southern Michigan. Of this marriage
seven children were bom, six of whom are living, viz.:
Elizabeth (Watkins), Mary (Wilber), Geo. A., Alice
R., Clara L. and Clarence A. One son, Eli, died in
December, 1877, in his sixteenth year.
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j3f— »*$l^i/^OTfiv* illiam E. Winton, attorney, Ithaca, is a son of William Winton, who was the son of James and Ann Winton, and was bom June 10, 1779, in the parish of Dunning, Perthshire, Scotland. After the death of both his parents, which occurred about the year 1800, having a desire to visit the New World, he took passage at Greenock, May 12, 1802, on board the ship ** Draper," of New York, for America; ar- 1/ rived at New York July 4, 1802. He came West - into Madison Co., N. Y. ; became acquainted with and married Desdemona Leach, of Chittenango, in 18 1 7. He then purchased and settled on a farm at Bridgeport, in the town of Sullivan, Madison Co., N. Y., and about 12 miles northeast from Syracuse, at which place his wife died, April, 1823. To them were born three sons, — James Winton, born Jan. — , 1 i8r9, now living at Manchester, Washtenaw Co., s Mich.; William E. Winton, the subject of this sketch, J bom Dec. r7, 1820; and David L. Winton, bom Jan. V 2r, 1823, now deceased, having died at Cohoctah, y Livingston Co., Mich., Dec. 17, r853. He afterwards ''> married a lady by the name of Lana Houser, by * whom he had one son and four daughters, all of ^ whom are now dead except Mary, who was born Oct. 13 :^^ — —^ i D H : I'V -X' 31, 1830, and now living between Chelsea and Man- chester, Washtenaw Co, Mich.; and Ann, bom March 15, 1833, and now of Fairmont, 111. He came to Michigan in December, 1845, ^"^ ^^^^ ^^ Man- chester, Mich., Jan. 21, 1858. His second son, William E. Winton, enjoyed the advantages of the village school at Bridgeport, dur- ing his childhood, his father keeping him during the school vacations at the Chittenango Sulphur Springs for his health. At the age of 13 he went to Albany on a tour of sight-seeing, visiting the museum, thea- ter and places of amusement, and where for the first time he saw a steamboat, as she passed up the Hud- son, bound for Troy. In the winter of 1837, being then 16 years of age, he obtained the consent of his parents, and came to Michigan with the family of Daniel Boutell, and after a journey of 2 1 days reached their destination, on section 30, in town 4 north, of range 5 east, after- wards organized as the township of Deerfield, Liv- ingston County, Mr. Winton remained in the family of, and worked for, Mr. Boutell until the age of 21. In the fall of 1839 he returned to the State of New York to trans- act some business for Mr. Boutell, giving him an op- ix)rtunity of visiting his fathers family, but so changed in personal appearance as not to be recog- nized by any one of them. On his return to Michigan, after a month s absence, he induced his younger brother, David L. Winton, to come West with him. He became acquainted with Sarah Ramsdell in 1840, to whom he was married Nov. 27, 1842. She was the daughter of Noah and Polly (Mary) Rams- dell, then of the township of Tuscola, afterwards changed to Cohoctah, Livingston County. She was born Oct. 2, 182 1, at Fairix)rt, some 10 miles east of Rochester, N. Y., from which place her father, in 1828, moved to Waterford, Plymouth Township, Wayne Co., Mich., and built the first flouring mill there. In 1839 her father exchanged his mill property for a farm of 640 acres in said township of Tuscola (now Cohoctah), where Mr. Winton became ac- quainted with the family. At the time of his marriage, his father-in-law, being considerably involved in debt, induced Mr. Winton to take charge of the farm, pay off the debts and save the property, which he accomplished in the ::i!D^>-^^— ■ — -^'-r- -.:• ^">C 'J- V^ v.-' , r \ Digitized by Google <:nD:o:Dnv>^ K-^': ■:2/-i, (0 i i GRATIOT COUNTY, course of ten years of hard labor and strict economy, receiving for such services about 200 acres of the farm; during which time he held various township offices. On the 22d of June, 1852, he was left a widower by the death of his wife, by whom he had three children : Sarah J. born Dec. 9, 1843; Mary D., born Oct. 10, 1845, and John H., born May 31, 1852. After the death of his wife, he leased his farm and made pro- visions for the care of his two children then living, — Sarah J. having died of croup Sept. 23, 1844, — and, having had only the advantages of a common-school education, he si>ent six years teaching, attending school and reading law. August, 1858, he graduated at the State and National Law School at Poughkeep- sie, N. Y. Armed with his diploma, he went to New York, purchased a law library, and returned to Mich- igan, and was, Sept. 10, 1858, at Howell, Mich., ad- mitted to practice in the courts of law and equity in this Slate. He visited the World s Exhibition at the Crystal Palace in New York, 1853. He visited the United States Military Academy at West Point, July, 1858, where he was introduced to Gen. Winfield Scott, at his headquarters. He attended the celebration of the laying of the first Atlantic cable at New York City in August, 1858. He received, October, 1858, the nomination for Prosecuting Attorney, on the Republican ticket, in Livingston County, and was, with the rest of the ticket, defeated, the Democrats, who were in the ascendancy, carrying the county. March 3, 1859, he sold his farm. April 4, 1859, he was married to Mariette Thomp- son, daughter of Joseph R. and Mary J. Thompson, of Corunna, Mich. She was born March 15, 1831, in the town of Columbia, Herkimer Co., N. Y. Her father came to Michigan in 1834, and settled on a farm at South Lyon, Oakland County. Mr. Winton started June 11, 1859, on a prospect- ing tour, visiting St. Johns, Maple Rapids, Ithaca, St. Louis, Midland City and St. Charles, and returned home. He moved into Gratiot County, and arrived at Ithaca, March 28, i860, then the county seat, boasting of 15 families all told, and having a weekly mail ; a dense forest covered the greater part of the present village, not a road opening to it from any di- rection. He was elected Circuit Court Commissioner No- vember, i860, and was appointed Deputy County Clerk in January, 1861. Having received his com- mission therefor, he enrolled all persons liable to military duty in the south half of Gratiot County in 1863, and continued in the conscripting business to the close of the war ; and was, during the same period. Superintendent of the County Poor, and, as such, had to make provisions for the support of quite a large number of families of the patriotic citi- zens who had gone to the front to defend the liber- ties of the country. Such families were provided for at their homes. Mr. Winton made arrangements with John Hicks, of St. Johns, who filled his orders for supplies. He was elected to the offices of Circuit Court Commissioner and Prosecuting Attorney in Novem- ber, 1864. He was re-elected Prosecuting Attorney in November, 1866, and was a delegate to the Con- gressional Convention held at Flint the same year, at which Hon. Randolph Strickland received the nomination. Mr. Winton was also a delegate to the Congressional Convention at Flint in 1868, at which Hon. John F. Driggs received the nomination, and, as was believed by many of the delegates, unfairly; and for that and other reasons, whether founded or unfounded. Judge Isaac Marston, then of Bay City, and William E. Winton, of Ithaca, took the field against Mr. Driggs, defeated him, and Hon. Jabez G. Sutherland was elected to Congress over Mr. Driggs. Oct. 19, 1868, Mr. Winton, wife and his wife's sis- ter, Mrs. Gilbert, visited the prairies of Wisconsin, Illinois and Iowa, and enjoyed the hospitalities of Milwaukee, Chicago, Davenport, Muscatine, Sigour- ney, Oskaloosa, Dcs Moines, and returned via Iowa City. He was elected Judge of the Probate Court No- vember, 1872, for the term of four years. On the 28th day of June, 1876, Mr. Winton and wife, in company with Hon. Wilbur Nelson and wife, left Ithaca for Philadelphia, via Detroit, Cleveland, Pittsburg, Harrisburg, Washington, D. C, and Balti- more; and on the 4th of July witnessed the nations grand display. After spending 12 days visiting the Centennial Exhibition, the thermometer vary- ing from 95 ^^ to 100^, they returned via New York Central & Canada Southern, \isiting all places of in- terest, and reached home in August ^'V5^<s % ^mv?m^{^ -^.^ ^rr' , _^^^c|zv^;vy>. Digitized by Google '•■•>/^* ><v-S'€?' c r u GRATIOT COUNTY. <rf>)^A># ^^\- 233 A V' Y ^ Mr. Winton h^s been successfully connected with many of the most important suits in the county, both of law and equity. He has an interest in the new bank building known as the " Jeffery, Winton Bank Block," in which he has as good, if not the best law office and library in the county. He was a proprie- tor of Turck, Winton & Co s. Bank, at Alma, and is now a stockholder in Steel, Turck & Co s. Bank at Ithaca. He was elected the first President of the village of Ithaca, in November, 1869, and has been a mem- ber of the Common Council most of the time since the village was incorporated. He is strictly temperate, and is a member of the Presbyterian Church. He was brought up a Demo- crat, but identified himself with the Whigs soon after arriving at the age of 21; became a Free-Soiler, and represented that party in convention at Pontiac, September, 1848, and was chosen Secretary of the Convention. He became a Republican on the or- ganization of that party in 1856, and as such attended the mass convention at Kalamazoo that same year, at which many of the Northern States were repre- sented, and where for the first time he had the pleasure of meeting Abraham Lincoln, our late President. Mr. Winton relates two incidents occurring on his way to Michigan in 1837. They came overland, via Syracuse, Rochester, the Ridge road to Youngstown, crossed into Canada and took the Mountain road. A sudden change to extreme cold, after a rainy thaw, left the road a bed of ice ; the vehicle, a covered emigrant wagon ; Mr. and Mrs. Boutell and three children seated back, and their oldest son, John, seat- ed in front with Mr. Winton, the driver. Advan- cing in this condition, six emigrant teams and two loads of Indians following close in the rear, ap- proached the foot of Battle Hill. The road up this was cut into the side of the mountain on the left, a precipice 200 feet deep on the right, with logs laid along the edge, a trifle higher than the dirt line ; the snow and ice, then as smooth as a skating rink, had raised the road bed above these logs. The emigrant teams and Indians remained at the foot of the hill, to witness the attempted ascent, which proved nearly successful * but, on reaching the summit, both horses slipped down, the wagon ran back, dragging the horses after it; and as the off hind wheel passed over the edge of the precipice, with immediate destruction V / m^-^^^} apparent, young Winton made a desperate leap for- ward, to avoid entanglement with the horses, down this awful gulf, rushing through the shrubs, plunging down the steep declivity with such momentum that his downward course was contmued for a hundred feet or more before he had the power to effect a halt. He was greatly surprised, on looking op, to see the wagon above him hanging on the edge of that dreftd^U pit, in the exact position as when he made that '* loip for life." Hurriedly clambering up the steep, on reaching the road, he was further surprised to find the wagon py- cillating on two wheels only; the off front wheel, having dropped slightly in between the log at the edge and the ice, became bound sufficient to hold all fast; the off hind wheel hung over, while the near fore wheel was raised up clear from the road, waidng to go over on the least stir of a horse or person in- side. The horses lay as if dead, the family re- maining in the same position. Not an emigrant or Indian had stirred. All sat spell-lxmnd, as silent as the chamber of death, until Mr. Winton beckoned (not daring to speak for fear a Jiorse would stir) for help from the foot of the hill. At this, some 20 white men and Indians came rushing franticly to the spot, surrounded the wagon and held it fast, while Mr. Winton assisted the family therefrom; and tak- ing the horses by the bits, they sprang to their feet, and, with the help of men and Indians, took it to the top of the hill in safety ! On arriving at Windsor, opposite Detroit, just as the ferry had made its last trip, a delay was caused of about three days, for the river to freeze over, it being then jammed full of broken ice from shore to shore, slowly moving down the stream from the upper lakes, during which lime over 200 families arrived on their way to Michigan. The ice a little below Windsor parted, all above remaining stationary, while that below moved on down to Sandwich before coming to rest, leaving the river oj^n between. The crossing was effected near Sandwich on the new ice formed in this open space, on the afternoon of the third day, the forenoon having been occupied in get- ting the women and children over from Windsor to Detroit, on foot, the broken ice from the lakes having been thrown into so many strange, fantastic heaps and windrows, reaching up the river for miles, as to render crossing therewith teams impossible, and very t tk A K/ y >L .^ Digitized by LnOOQ IC L ■■■■■A T <i'm%m>T -5i^-...' GRATIOT COUNTY. ^ '< { ^ ■ .--J V 's '.\ ^ difficult to be effected on foot. The ice at and be- low Sandwich was thrown into heaps similar to that at and above Windsor. The new-formed ice ex- tended from Sandwich up the river about three-quar- ters of a mile, where the channel was still open. The new ice over the channel was thin and slippery. Great precaution was used by the ferrymen who had charge of the crossing. The ice near the shore being of sufficient strength, the teams were distrib- uted thereon from Sandwich up to within 30 rods of the open channel to avoid two crossing in the same place. The teams were unhitched and the horses led over singly. The loads were got over by hitch- ing a single horse, with about 200 feet of rope, to the end of a tongue. The rider, with hatchet in hand, to cut the rope in case a load broke through, put spur to his horse and crossed at full speed. Mr. Boutells wagon being uppermost, brought his crossing nearest the open channel, increasing the peril. He led one horse and Mr. Winton fol- followed with the other some 20 rods behind. On reaching a point opposite this open channel, the wagon went spinning past, when two wheels broke through the new ice ; dropping on a large cake of lake ice that had floated under, they bounded to the sur- face again and passed on ; at the same time a violent gust of wind came sweeping up the river, sending young Winton sliding over the smooth ice, at the halter's end, the horse following for some considera- ble distance towards this open sea, with no power to stop, except by ordering the horse to stand, which the dumb brute obeyed, and by means of the halter got himself back to the obedient animal ; and by keeping the horse between himself and the open river, passed beyond danger. They stayed over night at the " New York and Ohio House," situated on the southwest corner, where Woodward Avenue crosses Jefferson Avenue, which, with the " National Hotel," the " Eagle Tavern,*' and " Detroit Cottage" (all wood buildings), were the leading inns of that city. Detroit, then the capital of the State, and one of the oldest cities of the Union, was but the embryo city of to-day. It contained more log buildings than brick ; the streets were entirely destitute of pave- ments, and nearly so of sidewalks, and the place had no railipad communication whatever. William E. Winton's great-great-grandfather was * •V' the Earl of Winton, whose estate and strong castle was west of Edinburgh. The Earl of Winton, in 1715, thenof the age of 25 years, very reluctantly espoused the cause of the son of James H, known as the " Chevalier de St. George," the pretended heir to the English throne: Earl Winton commanded the cavalry and had great influence with the Highlander Infantry. He was, with many other Scottish noble- men, taken prisoner at Ix>ndon, February, 17 16; and while many of those Scotch noblemen pleaded guilty to the charge of high treason. Lord Winton pleaded not guilty. He received sentence of death after trial, but made his escape from the Tower. He is frequently referred to in the "Tales of a Grandfather," by Sir Walter Scott, Vol. Ill, Chap- ters VIII and IX. The Wintons are supposed to be of English origin, as their history in Scotland is of modem date, and as the " Statute of Winton " is repeatedly referred to by Mr. Chitty in his Notes to Blackstones Commen- taries on the Laws of England; also by Mr. Green- leaf in his " Law of Evidence," Vol. I, § 349, and by other text writers on the English law. But whatever history may furnish relating to Mr. Win ton's ancestr}-, nothing gives him more pleasure than to know that he is a citizen of the United States of America. He is now making arrangements to visit Europe soon, and especially Scotland, the land of his fathers. John H. Winton, the only son of William E. Win- ton, was born May 31, 1852, atCohoctah, Livingston Co., Mich. He came to Ithaca, Mich., March, i860, with his father's family. He was kept at school until the age of 18, after which he taught several terms, and attended the State Normal School at Ypsilanti, Mich. He visited the Centennial Exhibition at Phil- adelphia in the fall of 1876. He read Jaw in his father's office, and was admitted at Ithaca, Mich., April 8, 1881, to practice as an atlorney-at-law and solicitor in chancery. He was appointed Village At- torney in March, 1882. He has successfully prose- cuted and defended several important suits in law and in equity, and has his office with his father, in the Jeffery, Winton Bank Block, south of the bank, on first floor, Ithaca, Mich. He became acquainted with Annie Sickels, daugh- ter of William and Isabel B. Sickels, to whom he was married, at the residence of her parents in the village of Sickels, Gratiot (x)., Mich., on the 31SI r h ^ A :-:!I !!>•>- X' r .^% ;<<* Digitized by VjOOQlC ■%^n ^.:f? v,<^'Viu, v<^|]tl:<^I]ll^>T' X-^Ci ^ /N T '^ • 'V GI^A TIO T CO UNTY, > 235 day of May, 1881. She was born at Northville, Wayne Co., Mich., Aug. 10, 1854. By this raarriage he has one son, William Winton, born July 21, 1882. On a previous page appears a portrait of Judge Winton. dolphuB Willert, farmer, section 31, New- Ij^M^ ark Township, was born Aug. 29, 1844, in Py^ Germany. His parents came to the United >&f States when he was 15 years old and settled '^ in Clinton Co., Mich. When he reached his * majority, in 1865, he came to Gratiot County and bought 40 acres of unimproved land in Fulton Township. On this he labored three years and ex- changed with his brother for another farm in the same township, which he afterward sold and l)Ought 53 acres in Newark Township where he now lives. About 35 acres are under good improvements. Mr. Willert is a Democrat in political principle. He was married Dec. 3, 1865, in Newark Town- ship, to Louisa, daughter of Lawrence and Mary W. Smith. She was born Sept. 2, 1848, in Livings- ton Co., Mich. The children born to Mr. and Mrs. Willert are Mary W., Frederick A., Alfred T., Law- rence G. and Ira E. -^^ ^ndrew Call, farmer, section 28, Elba Town- jfv^'>» IP ship, is a son of Sherman and Susan (Ran- ^V^ dall) Call, natives of New York. Sherman "fcr Call was a farmer, and came from New York r to Michigan in 1854. Twenty years later he was again induced to travel westward, and ac- cordingly went to Iowa, and thence to Minnesota, where he died, in 1876. His wife died in Wayne Co., Mich., in 1863. The subject of this sketch was born Dec. 5, 1825, in Onondaga Co., N. Y. At the tender age of nine he commenced to work for himself, and earned the first pair of boots he ever owned. Sept. 15, 1850, in Clinton Co., N. Y., he was married to Mary J. Brad- ford, the daughter of William and Dorothy (Call) Bradford, natives of Vermont and New York, re- spectively. This marriage resulted in six children : Mary J., Charlotte M , John H., Elba, Susan M. (died Aug. 29, 1853), and Sherman (died March 17, 1857). Mrs. Call died Sept. 4, 1877, in Elba Township, this county. Mr. Call located on 80 acres on section 28, Elba Township, in 1855. He has cultivated 75 acres of this. His substantial dwelling-house was erected in 18^5. In 1863, he felt himself Called into the service of his country, and he accordingly enlisted in Co. F, 2d Mich. Vol. Cav. He participated in all the en- gagements of that regiment, and was mustered out at Macon, Ga., though his final discharge was re- ceived at Jackson, Mich. Since the war he has been continuously engaged in farming. In January, 1884, he sold his farm, and he has since removed to Elsie, Clinton County. March 20, 1878, he married Mrs. Fannie A. Eddy, a daughter of Silas Reynolds, a farmer and wagon- maker in the State of New York, where she M'as bom Feb. 26, 1 83 1. She was a widow, and the mother of two children, — Alice Eddy, born April 18, 1857, and Ira A. Eddy, bom Jan. 24, 1861. Mr. Call is a mem- ber of Maple River Lodge, No. 76, I. O. O. F., and is a straight Republican. VL r /N ibsalom L. Ward, of Ithaca, formerly of ^ North Star Township, was born in Gallia Co., Ohio, March 24, 1832, and was the son of Allen and Sarah (White) Ward, natives of Virginia and North Carolina. He was brought up on a farm and educated at the common school. When a young man he leamed the black- smith's trade, which he followed until 1854, when he came to this county and settled on his present farm, the northwest quarter of section 11. He also owned and improved the north half of the north half of section 10. Subsequently he erected his resi- dence on the northeast quarter of section 10. He has thus, with true pioneer hardihood and industry, made for himself a comfortable home and accumu- lated a handsome amount of property, although com- ^ mencing in the wild woods of frontier life. Mr. Ward was a soldier in the late war, enlisting in Co. E, 2d Mich. Cav., and serving two years. He participated in the battles of Franklin, Nashville, Lost Mountain, Buzzard's Roost, Resaca, Kenesaw Mountain, Mossy Creek, etc. r '^yi^^^>- ■^m:<m-^> z. ^^^'M .71 Digitized by LnOOQ IC .■>T«,-- N^^t^t/'* r 2i A V > ') ^ ,•) V, GRATIOT COUNTY. >^^ii- - -^rf>^'i^.:0 ^ I f Feb. 9, 1854, the year of his settlement in this county, Mr. Ward married Miss Clara Criner, a a daughter of George Criner and a native also of Gallia Co., Ohio. Of their 11 children seven are living, viz: George A., Lina J., John W., Clara D., Sarah A., Ada A and Maud A. One daughter, Orpha E., died April 4, 187 1, at the age of 16 years. The other deceased were, Dennis L. and a pair of twins, — Elda and Etta. In regard to religion, Mr. Ward is a member of the Free Methodist Church. illiam Oliver Watson, farmer on section 7, Arcada Township, was born in Livings- ton Co., Mich., Dec. 15, 1848; and is the son of John T. and Harriet (Wilcox) Wat- son, natives of Genesee Co., N. Y., and Ba- tavia, N. Y., respectively. The falher was in mercantile life in New York, and came to Michigan in 1834, while it was yet a Territory. Relocated at Howell, Livingston County, which was then but a " shanty town," and had but a few inhabitants. He first taught school, then filled several county offices in succession, and later became a farmer. He fin- ally removed to Oakland County, where he died, July 15, 1864, at the age of 55, leaving a large fam- ily, of which our subject was the seventh. Harriet (Wilcox) Watson came to this State in 1834, after her marriage, and still lives, at Breckenridge, Wheeler Township, this county. William O. left home at the early age of nine, and went on a farm in Milford Township, Oakland County and afterwards on a farm in Highland Township, same county. He was there educated in the district schools. After nine years, he came to Ithaca. Here he clerked in different stores. Dec. 31, 1874, at Ithaca, he was united in marrige to Ella F., daugh- ter of Dewitt C. and Edna F. (Utley) Chapin, na- tives of New York State. Dewitt C. Chapin was a prominent citizen of Allegan, Mich., and while there held the office of Probate Judge. He came to this county and lived at Ithaca, where he was Reg- ister of Deeds at the time of his death, June 29, 1873. After that sad event, the whole duties of the office devolved upon Ella F., who performed them for two years, until the expiration of the term for which her father had been elected. She had previ- ously been her fathers clerk for two years. Her mother still resides in Pine River Township, at the age of 56 years. Ella R was bom in AWegan, Mich., April 10, 1851 ; moved to Dewitt, Qinton County, three years later; and at the age of 13 came with her parents to Alma, this county. Here she at- tended the common schools, and she afterwards pur- sued a course of study at the State Normal School at Ypsilanti. She commenced teaching at* the age of 15, and taught for a number of years. Mr. and Mrs. Watson located on a farm in Pine River Township; and four years later removed to Arcada Township. They purchased 80 acres on sec- tions 7 and 8, and now have 70 acres well improved. They have re'^ently built a neat bam, at a cost of$500. They have had four children, one now not liv-
ing: John C, born Jan. 28, 1878; Charles E., born
March 17, 1881 ; Byron, bom Nov. 10, 1882 ; Fred.
C, born Jan. 3, 1876, and died March 25, 1876.
Mrs. Watson is a member of the Baptist Church at
Ithaca. Mr. Watson is a Royal Arch Mason, be-
longing to Ithaca Chapter, No. 70, and has held
several offices in the order. He has been School
Director for four years, and is now serving his second
term as Township Treasurer. In politics he is an
uncompromising Republican. He and wife are peo-
ple of refinement and education, and stand very
high in their community.
onathan Qidley, farmer, section 21, Em-
erson Township, was bom in Morrow Co.,
xi-^ Ohio, Jan. 31, 1842 ; and is a son of Moses
i-? and Ruth (Wood) Gidley, natives of New York.
1|l They emigrated to Ohio, where they were mar-
\ ried and followed farming in Morrow County.
When Jonathan was bom the country was very new,
and as he was the oldest of the family, it was his lot
to bear the brunt of the farm work. He was, however,
able to attend school to some extent, and hard work,
aided by a natural bent, gave him a good grounding,
especially in mathematics.
Aug. 30, 1861, he enlisted in Co. C, 15th Ohio
Infantry, and was assigned to the Army of the Cum-
berland, under Gen. Thomas. He participated in
the battles of Pittsburg Landing, Stone River, Chick-
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amauga and Chattanooga, and other engagements.
He was unhurt during his service, but his clothing
was several times penetrated by rebel bullets. He
was discharged at San Antonio, Tex., Nov. 25, 1865,
and returned to Lansing, whither his parents had re-
moved. He settled near that city, and farmed for a
number of years. While there, his father died, Dec.
10, 1866, at the age of 51. His mother still resides
near Grand Ledge.
Nov. 15, 1868, in Morrow Co., Ohio, he was mar-
ried to Sarah A., daughter of George and Nancy
(Odell) Green, natives of Virginia. They were of
German descent, and followed farming. The daugh-
ter was born in Marion Co., Ohio, Aug. 4. 1840, and
at the age of 15 went to Mi^rrow County to reside
with a married sister. Mr. and Mrs. Gidley came to
Lansing, and in the spring of 1880 to Gratiot County,
settling on 80 acres of timbered land on section 21,
Emerson Township. He has now 20 acres cleared,
and has built a comfortable house, at a cost of $800. They have a family of three children : George O., born Sept. 18, 1869; Cora E., Oct. 28, 1870; and Nellie M., Aug. 22, 1883. Mr. and Mrs. Gidley arc members of the M. E. Cnurch. He is a member of Emerson Lodge No. 375, L O. O. F., and is now Secretary of that body ; and he is also a member of Moses Wisner Post No. loi, G. A. R.,at Ithaca. He holds the office of Drain Commissioner in his town- ship, being elected in 1881. In politics he is an earnest Republican. -f-^ »♦■■ \* [eDjamin F. Benson, farmer, section 19, Lafayette Township, is a son of Benjamin H. and Rachel (Brown) Benson, natives of New York and New Jersey, respectively, lie died in February, 1869, and she April 6, 1880, in New York State. The subject of this sketch was born in Niagara Co., N. Y., May 15, 1830. He remained on his father 's farm until he was 23, when he went to Ohio and engaged in lumbering for about six months. Returning for a short time to his home, he then came to Michigan and worked for a time at various things. The winter of 1855-6 was passed at home in New York. Thence he returned lo Michigan. The year 1856 found him in the Slate of Iowa, where he lived eight years. In 1864, he was united in matrimony to Malisa C. Holstead, who died the following year. Two years later he came again to Michigan and located in Clin- ton County, on 1 20 acres of wild land, of which he improved 80 acres. In 1877 ^^ came to Gratiot County and purchased 149 acres on section 19, La- fayette Township. He has now 80 acres well im- proved, and the timber chopped from 20 acres more. He married his present wife April 29, 1866. Her maiden name was Rose Wilhelm, and she was the daughter of Ernest and Fredrica {Curts) Wilhelm, natives of Germany, who emigrated to the New Worid at an early day. Mr. and Mrs. Benson are the parents of three children, — William P., Ernest E. and Rosa. Mr. Benson stands very high in his community. He has been Moderator of his school district several terms. As to politics he votes for the best men, re- gardless of ticket. H«- :ert Woodward, farmer section 30, Arcada Township, is a son of John and Priscilla (Goodspeed) Woodward, natives of New York and of English descent. They carried on farming in the Empire State until 1840, and then emigrated to this State, being among the very first settlers of Allegan County. The subject of this sketch was bom in Leighton Township, Allegan County, June 12, 1848, and re- mained under the 'parental roof until 22 years of age. He was educated in the common school, and in his leisure time was employed on his fathers farm. Sept. 7, 1869, in Plainwell, Allegan County, he was united in the bonds of matrimony to Miss Helen V. Hays, daughter of Alexander and Harriet (Watson) Hays, natives of New England and of English and Irish descent. Mr. Hays' occupation was* that of a blacksmith, and he died in April, 1869. The daughter Helen was bom in Waymouth Town- ship, Medina Co., Ohio, and was there reared and educated, living with her parents until her maniage. Mr. and Mrs. Woodward followed farming in Alle- gan County for six years. They then came to Gratiot. After buying and selling several times, he purchased in July, 1882, his present farm of 40 acres, then all timber. He has now under cultivation nine I T V s' s^ ^ (t r "J i^4^f> ^.^x^ J^ <?ll!l>:ill]s> JL ': r^L- ''^::J-^^ Digitized by VjOOQlC r'^^i>- -r-r<:llD>:i]Il>:>-r Vn/ G/^A TIO T CO UNT V. ■'■>j f V ; v-"^ ^ 1 acres and has erected a comfortable dwelling and stables. Mr. and Mrs. W. are the parents of eight children, four of whom survive,— Floyd, Gracie B., Hattie E. and Blanche. The deceased are Minnie, Glennie and two babies which died in infancy. The follow- ing epitaph was composed by an uncle, for Glennie s grave : " Over the river so still and cold, Glennie, our angel has gone to the fold ; Sweet little sleeper, your walking will be By the river of life and the beautiful tree." Mr. Woodward is a member of Alma Lodge, No. 244, F. & \. M. He has held the offices of Over- seer and School Director, and is now Justice of the Peace in Arcada Township. Politically he is a Re- publican. = I^Mjl^avid C. Bounds, farmer, section 2, Lafay- ij^P^ ette Township, is a son of Joseph and jjf^y^ Mary (Remington) Rounds, natives of j^ Rhode Island. The father was a sailor and i^ passed 30 years of his life on the sea. He after- wards vvent to Massachusetts, where he died Aug. 6, 1862. His wife died Sept. 23, 1866. David C. was bom Sept. 19, 1836, in Dartmouth, Mass., and was 18 years old when he began to care for him- self. For seven years he was employed in getting out live-oak timber in the Southern States. In 1861 he came to Gratiot County and located on section ^6y in what is now Wheeler Township, but was at that time unorganized. He lived there eight years, and then came to Lafayette Township and entered 160 acres on section 2. He has now 40 acres of well improved land. He built a neat dwelling house in 187 1, and his substantial barn in 1877. He was married Aug. 22, 1870, to Matilda Mc- Kenna, who unfortunately died the following Octo- ber. He subsequently, June 4, 1871, married Sarah V. Cornell, the widow of Daniel P. Cornell. She was born Aug. 9, 1841, in Steuben Co., N. Y., and was the daughter of Bernard and Dorinda (Ken- nedy) Fox, natives of New York. She bore to Mr. Cornell three children, — Bertha A., Ray and Daniel O. She has lived in Gratiot County since 1857, and is one of the pioneer school-teachers of the county. Mr. Rounds is one of the most respected citizens of the township in which he lives. Politically he is a Democrat. :^|^|Cohn W. Smith, farmer, section 28, Wheeler ^l^ig^ Township, was born Jan. 25, 1846, in liw"'' Trumbull Co., Ohio, and was the son of fl^ Noah and Lucinda (Hudson) Smith, natives of ^iF New Jersey and Trumbull Co., Ohioi Mr. \ ^mhh was by occupation a carpenter and joiner, and lived in Ohio until March, 1883. He then came to Gratiot County, and now makes his home with his son. Mrs. Smith died May i, 1875, in Trumbull Co., Ohio. At the age of 14, John left home and commenced working on a farm. This he followed three years, and then enlisted in the Trumbull Guards, an inde- pendent company. They were on duty in the Eastern army, were engaged three times, and after a service of three years and three months, were discharged at Gallipolis, Ohio. Mr. Smith came first to Ionia Co., Mich., and then to Gratiot County, settUngon 40 acres, section 28, Wheeler Township. In 1864, he was married to Charlotte A. Pickett, who was born Feb. 23, 1845, in Trumbull Co., Ohio. Her parents came to Gratiot in 1865, locating on section 2, Lafayette Township. Mr. Pickett was accidentally killed in 1867, while breaking roll-ways on Bad River. Mr. and Mrs. Smith have two adopted children : Jennie E. and Wesley O. Mr. Smith is a highly respectable citizen. He has held the office of Highway Commissioner and School Inspector of Wheeler Township. Politically, he is an adherent to th^ National party. t r/j^(||5^(iinund A. Goodhall, farmer, section 10, North Star Township, son of Edmund Goodhall of Hamilton Township, a native of England, was born in the native land of his father, March 10, 1852. His father, with his fimily, emigrated to the United States in 1854 and settled in New York. Here Mr. Goodhall re- mained, assisting in the care of the family, until the X > Digitized by Google Digitized by Google Digitized by Google '^^.- y^'XiAb''^'^ ^mmh>^ ^is^^^^^M I GRATIOT COUNTY. 241 A :<? V Si ^ i year 1865, when he accompanied them to this county. He follows the vocation of farmer, combined with that of working in a saw-mill. Mr. Goodhall was united in marriage, Dec. 22, 1878, to Emma, daughter of Frederick Homister, and to their union have been born one child, Nellie V. Mr. G. is yet a young man, and being possessed of that element so necessary to success and the accom- plishment of aim, has a future not darkened with despair but brightened by pleasant contemplations. amuel Wheeler, farmer, section 18, Lafay- ette Township, is a son of Amos and Har- riet (Hubbell) Wheeler. They were na- tives of Connecticut, and followed farming in that State until 1855, when they came to Ing- ham Co., Mich. They resided in that county 24 years, when Mr. Wheeler died. Mrs. Wheeler died Feb. 15, 1874, in Illinois, at the age of 70 years, 9 months and 15 days. The subject of this sketch was born Jan. 31, 1826. At the age of 2 1 he left home, and worked in a cheese factory and on a farm until 1851, when he married Nancy Barger, She was born in Medina Co., Ohio, Feb. 3, 1832, and was the second daughter of Sam- uel and Barbara E. (Holler) Barger, natives of Penn- sylvania. Mr. and Mrs. Wheeler came to Ingham County, this State, in the autumn of 1851, and he was there engaged in farming until May 12, 1857. On that date he came to Gratiot County and settled on 143 acres of wild land. Of this he has cleared 100 acres. In 1867 he erected a large bam, — the third in the township. He also has a fine, large dwelling-house on his place. Mr. and Mrs. Wheeler are the parents of six children, — Benjamin F., Clar- ence L., Dora J., Harriet J., Lucy E. and Amos S. Politically, Mr. Wheeler has always been a staunch Republican. He was elected Township Treasurer in 1859, and served four years. In 1864 he was chosen Supervisor, and in that office he was retained for six successive years. He is a member of the Masonic Order, belonging both to the blue lodge and to the chapter. As a representative man of the county, and one deserving the respect, esteem and commemoration of its citizens, we give place to Mr. Wheeler s portrait in this work. -.$<r>o_
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fftllen Curtis, farmer, section 4, Hamilton
1^ Township, was bom in the County of Cay-
State of New York, Nov. 4, 1804. His
^jN^ uga, Mate ot iNew York, iNov. 4, 1804. Mis
'•Jjlr father, Ashbel Curtis, died while Allen was
^ quite young and he was thrown upon the mercy
of others. He lived with his half-brother,
Israel Curtis, for a short time and then made his
home with his sister, working out for or ^st dollars a
month, for two or three years. In 1825 he went in
company with his brother Daniel to Livingston
County, his native State, and there entered upon the
occupation of a farmer. Here he remained, pursu-
ing his vocation, until 1854, when he came to this
State and settled in Oakland County.
In the fall of 1856, Mr. Curtis came to this County
and entered 320 acres of land in La Fayette Town-
ship. He remained on the land long enough to con-
struct the usual " log cabin " of the pioneer ; and in
the fall of the same year, when listening to the im-
portunities of his son-in-law he returned to Oakland
County and remained until the following spring, 1857,
when, accompanied by his family, he returned to La-
fayette Township. His experience in establishing a
home, clearing and improving the land was similar
to those of many others of Gratiot's pioneer settlers.
His house was erected in the woods ; wild animals
and prowling Indians were his visitors. On one oc-
casion, while en route to a " raising," Mr. C killed
two bears, and all the men in the neighborhood, after
assisting to dress them, were allotted their portion.
At another rime he was compelled to mortgage his
farm to procure a barrel of flour. In fact, trials en-
compassed him on every hand, yet nobly did he meet
and conquer them. He was compelled to cut a road,
through the woods, to the location he had selected
for his house, and his was the first team that came up
the river on the south side from St. Charles, and his
settlement was the first made in the neighborhood.
Mr. Curtis was united in marriage Feb. 21, 1833,
to Sophia, daughter of Daniel Hamilton. To this
union one child, Abigail, was born. Mrs. C, after
sharing his trials in the establishment and improve-
ment of their home, died April 4, 1867, mourned as a
loving mother, a devoted wife and kind friend.
Mr. C. is a man possessed of a constitution which
in earlier days enabled him to encounter an almost
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unlimited amount of physical labor. His endurance
was exceedingly remarkable, and even now, with 79
winters and summers of wear upon his system, he is
not void of activity. In October, 1866, he fell from
a house and broke one wrist, and in 187 i he crippled
his other hand while fighting fire, which has caused
him considerable annoyance in pursuing his vocation.
Mr. Curtis was again married, April 4, 1868, this
time to Miss Helen Clunas, daughter of Thomas
Clunas, deceased, a native of Scotland. She was
born in Upper Canada, Jan. 5, 1833. He settled on
his present farm in Hamilton Township, in Novem-
ber, 1868. The township (Hamilton) in which his
farm was located was named in honor of Franklin
Hamilton, a nephew of our subject and who was
** brought up " from the age of seven years by Mr.
Curtis.
Mr. Curtis owns 40 acres of land where his home
is located, and for over 40 years has been a member
of the Methodist Episcopal Church.
fa^lBton H. Maurer, farmer, section 16, New-
^^ ark Township, was born March 14, 1850, in
Hancock Co., Ohio. His falher, John Maurer,
was a native of Germany ; his mother, Louisa
(Sage) Maurer, was born in the State of New
York. The father died in Hancock Co., Ohio,
where he settled after his marriage. The mother re-
sides in Wood Co., Ohio.
At the age of 14, Mr. Maurer began life on his own
account, as a farm laborer, and spent six years as an
assistant at several points. He then took a farm to
work on shares for.one year, when he decided to ex-
pend his efforts wholly in his own behalf, and in 1872
bought 40 acres of land in Williams Co., Ohio. He
retained its possession four years, sold out and in the
fall of 1876 came to Gratiot County and bought 40
acres of partly improved land in Newark Township.
On this property he has since resided and has nearly
all his acreage under cultivation. Mr. Maurer is in
sympathy with the Republican party and supports its
issues.
He was married Jan. 26, 187 1, in Seneca Co.^Ohio,
to Susan, youngest daughter of Wesley and Sarah
(Rber.sole) Bradford. Her father was born in Penn-
sylvania, became a soldier in the Union army and
yielded up his life on the battle field. The mothei
was bom in Ohio and now resides in Kansas. Mrs.
Maurer was born Sept. 25, 1854, in Hancock Co.,
Ohio. Of her marriage one child was born Dec. 9,
1872 — Charles O. Maurer.
,harles M. Chaffin, teacher and farmer,
resident on section 30, North Star Town-
''^ shi[>, was born in Hancock Co., Ohio, Aug.
29, 1849, and his parents removed with him
10 Graiiot County in 1854, settling in North
^rir Township, where he now lives, on part o(
the homestead ; was educated in the common schools
and at the State Agricultural College at Lansing; he
also attended school at Ithaca several seasons. He
has since become a prominent teacher in this county,
having now taught school during the winter for the
last 12 years, by the most improved nomial methods.
He also attends normal institutes, and is a membei
of the Gratiot County Teachers* Association. During
the summer he follows agricultural pursuits.
June 25, 1876, Mr. Chaffin was married to Sarah
Barnes, daughter of John Barnes. By this maniage
one child has been born, Bessie A. Mrs. C. was bom
in England, and was brought to America by hei
parents when young, who settled first in Jackson Co.,
Mich., and came to Graiiot County in August, 1854,
settling in North Star Township. Mrs. Chaffin is
also a teacher ot many years* experience. She
attended the Ypsilanti Nonnal School, and has taught
22 terms in this county.
Mr. Chaffin s father, John W. Chaffin, now deceased,
was a native of Virginia, and was bom in 1822; was
brought by his parents to Wayne Co., Ohio, when six
months old, and in 1854, after a residence in different
counties, he settled in North Star Township, and
therefore was a pioneer here. He was well known
as a dealer in live stock and in furs. He married
Clara A. Evitts, daughter of Bela Evitts, and had
eight children, six of whom are living : Charles M.,
Homer W., Theodore A., Clara L., Perry F. and
Edith L.
Mr. C. died Nov. 10, 1873, a highly resj>ectcd
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member of the United Brethren Church, a generous
and charitable citizen, judiciously distributing of his
means for the support of benevolent institutions.
J
saao D. Crippin, farmer, section 23, Elba
Township, is a son of Stephen and Lucy
(Bums) Crippin, natives of New York. Mr.
Crippin's business was lumbering. He died
in Illinois, and his wife in Michigan. The
subject of this sketch was born in Warren Co.,
Pa., Sept. 28, 1822, and has followed the noble occu-
pation of farming all his life. In 1838, he came to
Branch County, this State, where he lived 18 years.
In that county he was married to Martha Havens,
the daughter of Thomas and Polly Havens. She died
about 1855, leaving one child: Mary J.
He enlisted in Co. D, First Mich. Light Art., Aug.
10, 1864, and was most of the time of his service
stadoned at Murfreesboro, Tenn., on fortress duty.
He was discharged at Jackson, Aug. 3, 1865. After
one year passed in the southern part of Michigan,
he came to Gratiot County. In 1867, he was married
to Miranda, the fourth daiughter of Thos. and Rachel
A. Davidson. She was born Feb. 22, 1837. Her
parents were bom in Pennsylvania and Maryland,
and were engaged in farming.
Mr. and Mrs. Crippin have two children: Freddie
E. and Eva P.
Mr. Crippin is Assessor of his school district, and
in politics is a National. He is a member of Elsie
Lodge No. 238, F. & A. M., Maple River Lodge No.
76, I. O. O. F., and Major Lusk Post No. 167, G.
A. R.
[Ivin P. Bamaby, deceased, late resident of
North Star Township, was born near San-
dusky, Erie Co., Ohio Oct. 17, 1821. He
was a son of Alvin P. Bamaby, deceased, who
moved his family from Ohio to this State and
settled in Ciss County in 1825. Here our
subject lived and developed into manhood, receiving
the advantage afforded by the common schools of
the county. His inclination being of a mechanical
turn, he early applied himself to learning thecarpen-
%
ter's trade, which he soon accomplished, and followed
for the greater portion of his life.
Mr. Bamaby was married Oct. 3, 1853, to Miss
Esther, daughter of Daniel Bleacher (deceased), and
to their union there were born ten children, nine of
whom are living: Mary A., Francis E, Flora A.,
Ezra A., Ulysses S., Perry I., James H., Bertha M.
and Daniel V.
Mr. B. enlisted in the late civil war in Co. M, ist
Mich. Cav., and was stricken with disease a few
days previous to the battle of the Wilderness and
did not convalesce until after the war. Mr. B. and
his family came to this county in 1869, and on March
13, 1881, the father died, leaving the mother and her
nine children and a host of friends and relatives to
mourn his loss.
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eorge W. Zimmerman, farmer and stock-
raiser, section 25, Arcada Township, was
in Lower France, Dec. i6> 1831, and is
the son of Michael and Catharine Zimmerman,
natives of France and of German ancestry.
Michael followed faraiing, and died in France,
at an unknown date. His wife came to the Great
Republic in 1847, ^^^ ^s still living, well and strong,
at the age of 77, in Jackson County, this State.
When 14 years old, the subject of this sketch set
out to learn the harness-maker's trade, being appren-
ticed near home. After working at this 18 weeks, he
came with his mother and relatives to this country,
landing at New York. He then went to Philadelphia,
and afterwards to Syracuse, N. Y., where he remained
two years. He was apprenticed here to a blacksmith,
and worked with him until the latter failed. Going
to his mother in Buffalo, he lived there with her until
she was married, when they all went to live on a farm
in the vicinity of Buffalo. Three years later he came
to Jackson Co., Mich. Returning to New York after
one year, he was united in marriage, in Erie County,
Nov. 15, 1853, to Elizabeth, daughter of Martin and
and Magdalen a Marcolf, natives of France and of
German descent. The former followed farming, and
died in Erie County, Oct. 15, r882, aged 76. The
latter is still living in the same county, at the age of
70. Elizabethwas born Jan. 27, 1836, at Weisen-
burg, in that part of France now possessed by
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Prussia, and when a year and a half old was brought
by her parents to America. They settled in Erie Co.,
N. Y., where she lived until her marriage.
Mr. and Mrs. Zimmerman came to this State and
located near Brooklyn, Jackson County. July 31,
1862, he enlisted in Co. F, 20th Mich. Vol. Inf., under
Capt. Warner, and served in the Army of the Potomac.
He fought in 16 engagements. He was made a
Corporal in 1863, and a Sergeant in 1864, which latter
rank he held till the close of the war. He was
wounded at Cold Harbor, Va., by a gunshot in the
right limb near the ankle. Otherwise he escaped
unhurt. He was often honored with special duty,
and was honorably discharged in June, 1865. Re-
turning to his home in Jackson County, he shortly
after removed to this county, locating on a farm of
160 acres, heavily timbered, in Hamilton Township.
After improving 35 acres, he sold, and in August,
1879, he settled on 160 acres of improved land, a
mile and a half from Ithaca, in Arcada Township.
He has since sold 80 acres to his eldest son, William
H., who is married and lives on that tract. He has a
fine orchard of 1 2 acres, mostly in apples.
Mr. and Mrs. Zimmerman are the parents of seven
children, one dead : William H., bom March 15,
1855, Barbara M., Oct. 16, 1856, Lena M., July 22,
1858, David W., May 10, 1866, Emma E., Aug. 27,
1868, James Walter, April 21, 1873, George B., bom
Aug. 13, 1861, and died May 21, 1880.
Mr. Zimmerman is in politics a Republican. He
has held the offices of Township Treasurer, and
Overseer of Highways. He is a Protestant, and his
wife a Mennonite.
Irich Wermuth, farmer and stock-raiser,
section 24, New Haven Township, was
-j^.-^ t)orn in district of Berne, Switzerland, Aug.
/•]>S 10, 1815, and was reared on a small farm
1^ and educated in the public school among the
] mountain fastnesses of his native country.
When 15 years old his father died; and as he was
the eldest of the orphaned children, much care de-
volved upon his immature years. By economy and
perseverance they accumulated sufficient means to
bring them over to the " land of opportunity," in the
spring of 185 1, when they located in Fulton Co.,
Ohio. Three years later Mr. W. came and ** located "
40 acres of land on the section where he now re-
sides. Subsequently he purchased 80 acres more,
and of the total 1 20 acres he has improved 90, re-
ducing it to a good state of cultivation and placing
thereon good farm buildings, etc. He is an enter-
prising and prosperous farmer. In polirics he is a
member of the Democratic party, and he has held
the school offices of his district for x 2 years.
In June, 1862, Mr. W. married, in Newark Town-
ship, this county. Miss Mary Willet, a German lady
who was born in Tellen, Germany, Jan. 22, 1843,
and came to this country in 1869, settling with her
parents in St. John s, Clinton Co., Mich.; two years
later she came to Newark Township, this county.
The four children in this family are : Adolphus,
born May 21, 1865; Ellen, May 11, 1868; Frank,
April 25, 1872; and Charles, May 15, 1876.
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^|V1[| saao N. Coleman, farmer, sec. 30, Emerson
^ Rfl l Township, was born in Dayton, Ohio, Dec.
M^T 2, 1832 ; and is the son of Isaac and Emma
Vi5^ (Piper) Coleman, natives of Gemiany and New
rp England, respectively. The father was by trade
^ 1 mechanic, and used tools nearly all his life.
Isaac, junior, spent his boyhood days, until he was
12 years of age, in Dayton, when his parents removed
to Seneca County and located on a farm in the vi-
cinity of Tiffin. Here he leamed the art of arts,
farming, and he has followed that continuously until
the present time. January, 1853, he removed to
Michigan and located in Lenawee County.
Sept. 8, 1853, he was united in marriage, in Litch-
field, Hillsdale County, to Louisa J., daughter of
David and Louisa (Ketch) Moon, natives of New
England. She was born in Niagara Co., N. Y., Nov.
8, 1836; and, her mother dying shortly afterwards,
she was adopted by George Perry. She lived with
him (he died in 1846) and his wife until her mar-
riage. She had lost all track of her father, and she
was 25 years old when, by an accident, she first
learned something of her relatives, and found that
she was one of a large family of children.
In the spring of 1855 Mr. and Mrs. Coleman came
to Gratiot County and settled in Emerson Township.
He was one of the organizers of the township. At
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that time there were but few families to assist in sub-
stituting civih'zation for the unbroken forest which
surrounded them for miles in every direction. Mr.
Coleman assisted once in a very romantic and exciting
bear hunt, and the party succeeded in despatching a
bear that weighed nearly 500 pounds.
July 31, 1862, he enlisted in Co. D, 26th Mich.
Vol. Inf., commanded by Lafayette Church, of this
county, and joined the Army of the Potomac. Owing
to physical disability brought on by sunstroke and
rheumatism, he became permanently crippled, and
was honorably discharged March 25, 1865. He had
been promoted as Corporal, and had the credit of
capturing a fierce rebel by his own efforts.
Mr. and Mrs. Coleman have had seven children,
six of whom are living : George J., born Sept. 22,
1854; Charlie W., Dec. 9, 1858; Ozro E., Oct. 5,
1861 ; Sadie E., Dec. 27, 1866; Frank A., July 25,
1869; Ray N., Jan. 31, 1877; Earl, born Sept. 22,
1879, and died July i, 1883. They are members of
the Seventh-Day Adventist society. Mr. Coleman
is an energetic and popular man, and has held vari-
ous local offices. He was the first Justice of the
Peace of the township, was Supervisor five years and
Treasurer ten years. He has also been Township
Clerk, and is now School District Assessor. Politi-
cally he has always been identified with the Repub-
lican party.
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Tohn Brauher, general farmer, section 24,
New Haven Township, was born in Berne,
Switzerland, Nov. 9, 1846, of Swiss and
German descent. When two years of age his
father died and he went to live with his grand-
mother, and when eight years of age they
emigrated to America and went to reside with his
mother in Fulton Co., Ohio, who had previously re-
married and settled there.
Mr. Brauher received a good common-school edu-
cation, and at the age of 14 he accompanied his
mother and step-father to this county, locating in
Newark Township. They subsequently removed to
New Haven Township, where the subject of this
sketch lived until his marriage, in Montcalm County,
to Miss Maggie, daughter of William A. and Nancy
(Stiiller) Miller, natives respectively of Maryland
and Ohio and of English, Irish and German descent.
Mrs. B. was born in Hancock Co., Ohio, Dec. 17,
1856; when nine years old she came with her parents
to Montcalm County, Mich., where she lived until
her marriage, soon after which she settled with her
husband on 80 acres where they now reside. Mr.
B. purchased this tract in 1867, when it was nearly
all covered with heavy timber; but he has since
cleared and improved 50 acres of it, subduing it to
the plow in a fine tillable condition. His prosperity
as a farmer is manifest. In regard to national is-
sues Mr. B. is a Democrat.
The living children in this family are Francis,
Rosetta, William and Byron A. The deceased is
Calvin.
p enry A. Shaw, farmer section 11, Washing-
K^^H ton Township, is a son of Alvin and Jane
^^ (Fuller) Shaw, natives of Connecticut and New
^ York. Alvin Shaw has followed farming all his
I life, and he and his wife still reside in Wales,
Erie Co., N. Y. Their son, Henry, was bom July i,
1836, in Java, Wyoming Co., N. Y. He lived with
his parents, working and attending district school,
until 20 years old, when he commenced working by
the month, also attending school a portion of the
time. He then bought a farm and commenced
farming on his own account.
June 27, 1858, in Wyoming. Co., N. Y., he was
united in marriage to Louisa, youngest daughter of
Spencer and Mary (Trickey) Bryant, natives of Ver-
mont and Canada. They moved to New York, in
which State they died, Mrs. Bryant, Oct. 16, 1875,
and Mr. Bryant, April 27, 1877. In 1861, Mr. and
Mrs. Shaw came to Clinton County, this State, and
lived 20 months in Greenbush Township. Return-
ing to New York State, they lived there for nearly
three years. Coming to Gratiot County they pur-
chased 80 acres of wild land on section 1 1, Washing-
ton Township. Mr. Shaw has now 65 acres im-
proved. Ever since coming to the county he has
been, to some extent, interested in bee culture, and
since 1880 he has built up a wide reputation in that
business. He has a fine apiary of his own, and,
being looked upon as an expert, he is called upon by
people from eight to ten miles away to attend to their
apiaries. During 18 years he has taken 196 swarms
out of the woods.
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Mr. and Mrs. Shaw have had six children, one of
whom is dead, and two are married. These latter
are: Mrs. Winfield Strouseand Mrs. Herman Hoffer.
The three residing at home are : Grant, Archie and
Bertie. Esther died Sept. 7, 1876. Mr. Shaw is po-
litically a zealous Republican. He has been Justice
of the Peace for eight years, and has also been School
Inspector of his township. He and wife are mem-
bers of the U. B. Church.
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rs. Laverna B. (Conger) Wolford, resid-
ing on the southwest quarter of section
22, New Haven Township, is the wife of
David Wolford, deceased, who was bom in
Schoharie Co., N. Y., Jan. 5, 181 2.
Mr. Wolford was brought up under the care
^ of fond and loving parents, and remained under the
parental roof-tree until he attained the age of 23
= years. He then set forth upon " the ship of trouble "
A' to fight the battles of adversity which so often are
=3 encountered by the ambitious and energetic young
sJ^ men in their journey to prosperity. He left his na-
^ tive county and went to Cayuga County, same State,
and was there united in marriage to the subject of
our sketch, Dec. 7, 1835.
Mr. and Mrs. W. remained in that county for 15
years, when they moved to Huntington Co., Ind.
They remained in the latter county some two years
and then returned to New York. Two years after-
ward they came to this Slate and located on 160
acres of land on section 22, New Haven Township,
arriving here and settling on the land in 1859. At
that time the land was in a wild state of nature, and
Mr. W. experienced the trials and overcame the ob-
stacles so abundantly met with in the lives of the
early pioneers. He was a mason by occupation, and
always followed that vocation until he came to this
State, when he entered on the arduous though pleas-
ant task of clearing his land and preparing a home
for his family, and prior to his death had cleared and
improved 40 acres. He died Nov. 10, 1866, leaving
a wife and five children, besides many warm-hearted
and affectionate friends to mourn his loss. He went
out to work one Saturday morning, and did not re-
turn. He was found Sunday noon, and the physi-
cians pronounced his death to be caused by heart
disease.
Mr. W. was warmly esteemed as a father, friend
and neighbor. He was honored with positions of
trust, and at the date of his death held the (TflSce ot
Justice of the Peace. Mr. W. was a member of the
M. E. Church, also of the I. O. O. F., and in politi-
cal belief and opinion was a staunch and active Re-
publican.
Laverna R. was born in Cayuga Co., N. Y., May
12, 18 1 6, and was reared and educated under the
care of her parents, with whom she remained until
she was married. Her parents were of German ex-
traction, and lived and died in the State of New
York.
Mrs. Wollord retains the original 120-acTe home-
stead in her own name, and is still residing on the
same.
The five children born to Mr. and Mrs. W. are as
follows : Margaret and Job C, both married ; Lucre-
tia, Lewis B. and John W. Lucrelia and John W.
are living with their mother on the farm which the
latter cultivates.
Mrs. W. is a member of the M. E. Church. She
is in her 66th year, and enjoying fair health.
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Norton Smith, farmer, section 20, Washington
Township, is a son of Parmer and Betsy
(Pullman) Smith, natives of the State of New
York. Mr. Smith was by trade a cooper. He
came to Michigan, but remained only a short
time, and then returned to New York State. He
died Dec. 3, 1843. Betsy (Pullman) Smith is now a
resident of St. T^ouis, Mich.
The subject of this sketch was bom Oct. 18, 1826,
in the State of New York. Losing his father when
14 years old he was the main support of the family,
including four girls, until he was 30 years old. March
4, 1856, he married Adeline, daughter of Erastus and
Julia A. (Coon) Berry, natives of New York. They
came to Branch Co., Mich., but after one year re-
turned to New York State, where Mrs. Berry died in
1851, and Mr. Berry in 1859. Dec. 31, r857, Mr.
and Mrs. Smith came to Gratiot County and located
on 79^ acres on section 20, Washington Township.
This was then wild land, and they were among the
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first settlers of the township. Most of their early
neighbors are long since dead. At first they located
a half mile from any house, but new dwellings have
sprung up within a stOiie s throw of the house. He
had to cut a road to his place, and for many years
deer could be seen running with his cattle, when he
went to bring them home.
Mr. and Mrs. Smith have six children: Fred E.
and Fanny E. (twins), bom in 1857; Frank, born in
1862; Emma, bom in i860; William H., born in
1866; and Clara A., born in 1875. Mrs. Smith is a
member of the United Brethren Church. Mr.
Smith has been Justice of the Peace, Treasurer and
Clerk of his township, one term each, and has held
school offices a number of times. Politically he is a
Republican.
lohn Sweet, farmer, section 29, Emerson
Township, was born in Sparta, N. Y., Feb.
26, 1825, and is the son of Amos and Polly
(Blighton) Sweet, natives of New England.
John wsis early left an orphan, his father dying
when he was very young, and his mother fol-
lowing her husband when the lad was but 12 years
old. At this tender age he was left alone to battle
with the world, and he went to work for an old friend
of his father, in Medina Co., Ohio, where his mother
had moved with some friends previous to her death.
In 1845, he was married, in Medina County, to
Narina N. White, born in the State of Vermont, July
2, 1827. She died in Spencer, Medina County, in
March, 1864, leaving four children, — Lucius B.,
Lucia A., Isaac and Sophronia E. He was again
married in July, 1864, to Mrs. Sophronia Snyder («<f<f
White), daughter of William and Polly (Curtis)
White, natives of New Hampshire, and descended
from New England stock. She was born in Chitten-
den Co., Vt , Nov. 7, 1826, and at the age of 19 came
to Medina Co., Ohio, where she was married the sec-
ond time. She had four children by her first mar-
riage, two living: Emma E., born Oct. 19, 1843;
George N., bom July 8, 1845. Hester A. was born
Sept. 8, 1 84 1, and died March 15, 1863; Florence I.
died Feb. 15, 1858.
Mr. Sweet is a minister in the Baptist Church, be-
ginning early in life, and has always been an earnest
worker for that denomination. His wife is also a
member of the Church. He has held the office of
Overseer, and is a supporter of the Republican party.
He has been a resident of this county for 13 years,
and has 60 acres of improved land.
^
illiam J. Fitzgerald, famier, section 26,
Elba Township, is a son of John and
Mary (Berry) Fitzgerald, natives of Ireland,
who emigrated to New York in an early
day, and engaged in farming. Their son,
William J., came to Michigan in 187 1. For
six years he was engaged with a Mr. Hays, of Ionia
County, in the summer as overseer of a large farm,
and in the winter as foreman of a crew of hands in
the pine woods. In 1881 he came to Elba Town
ship and located on 80 acres on section 26, of which
40 acres are nicely improved.
In 1870 he was united in marriage to Emily, fourth
daughter of Oliver and Julia (Miller) Richards, na-
tives of New Yoik. She was born Feb. 4, 1853.
Mr. and Mrs. Fitzgerald are the parents of three
children: Anna M., Emma B. (deceased), and Will-
i?im F. Mr. Fitzgerald enjoys the confidence and
esteem of his fellow-citizens, and was chosen High-
way Commissioner for Elba Township in 1883. Po-
litically he is a Republican.
ohn A. Pasinger, farmer, section 24, New
Haven Township, was born in Lawrence
'^^^ Co., N. v., April i, 1825. His parents were
of Dutch descent and lived and died in the
State of their son's nativity. The occupation
of the father was that of a mechanic, which
vocation the son followed in after years.
Our subject remained under the parental roof-tree
assisting his father until he attained the age of 13,
when he began to learn the trade of a carpenter and
joiner, under the instruction of his father, and worked
with him at the trade until 18 years of age. He
then set out to battle with the trials of life alone,
gaging a portion of his time in a saw-mill and lum-
ber interests in Ontario, in the vicinity of the Ottawa
River.
Returning to his native county, he engaged m van
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ous occupations for a period of four years, when he
was married in that county, June 17, 1849, to Miss
Lucy A. North, a native of the same county as Mr.
Pasinger, where she was born June 16, 1829, and
where she lived with her grandparents until her
marriage.
Six children have been born to their marriage,
four of whom, Henry W., Eugene C, Hannah M.
and Anna L., are livmg, and two, Franklin and Orson,
are deceased.
After their marriage in New York, Mr. P. followed
his trade for some 18 years, also being engaged in
the lumber business. In 1865 he came to this State
and purchased 80 acres of wild land in Clinton
County. He made some improvement on this land
and returned to New York. In 1873 he returned to
his land in Clinton County, and made a permanent
settlement. He added 80 acres to his original pur-
chase and then sold 40 acres, leaving him 120 acres.
Of this, he improved 70 acres, erected a house and
in x88i sold the entire tract preparatory to going
West to start a new home. Before moving his fam-
ily, he changed his mind, and came to this county
and purchased 140 acres of land on section 24, for-
merly owned by a Mr. Shepherd. His farm has a
large orchard, which is in fine bearing condition.
Mr. Pasinger has held the office of Highway Com-
missioner and is 'identified with the best interests of
the township. Politically, he is a staunch Democrat.
aniel F. Muscott, retired farmer, on section
12, Emerson Township, was born in
5J|r^ Western, Oneida Cx)., N. Y., March 19,
^■^Tiw 181 1. In this town Gen. Halleck was born,
and Gen. Floyd, of the Revolution, one of the
signers of the Declaration of Indej^endence, is
buried in the same township. Daniel's father,
Nehemiah Muscott, was a native of New Jersey, of
Hollander parentage, and was by trade a tanner.
A portion of his life, however, was spent on the seas.
The mother of Daniel, Hannah (Felton) Muscott,
was a native of New York, and of Puritan stock.
Both died in Washtenaw Co., Mich., at the age
of 67.
The subject of this sketch attended district school
and worked for his father until he was 21, when he
began to clear a farm for himself in his native county.
He was thus engaged for five years, but during this
time, in Rome, N. Y., Sept. 19, 1832, he formed a
life partnership with Sobrina Walsworth. She was
born in Rome, June 28, 181 1, and was the daughter
of Asa and Hannah (Dickerson) Walsworth, natives
of Rome. A few years after marriage, Mr. and Mrs.
Muscott went to Sherman Township, Huron Co.,
Ohio, where they lived until 1854. Then they came
to Michigan and lived ten years in Ingham County.
In February, 1864, they came to Gratiot County and
purchased 160 acres in Emerson Township, shortly
after buying 80 acres more. He now has one of the
finest farms in the county, 240 acres in extent, 130
of which are excellently improved. He has also a
comnoodious dwelling and other farm buildings.
And now, as his active and eventful life is drawing
to a close, he and his wife, both 73 years old, pass
the time in quiet enjoyment of the fruits of their
They have had a family of six, all of whom are
alive, married, and have families : Sobrini, born Dec.
22, 1833, Ralph, April 28, 1839, Theodore W., July
25, 1843, Hannah, July 22, 1846, Ellen A., April 7,
1849, and Merriti, Dec. ?, 1854.
Mr. and Mrs. Muscott are active members of the
Presbyterian Church. He has held the office of
Supervisor for two terms, and Township Treasurer for
two terms.
Politically, he has been a stalwart Republican
since the organization of the party.
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I<^Iitewart Edg^ar. farmer, on section 2, Emer-
- tfeii V ^" Township, was born in Dumfrieshirc,
' V ^'^ Keir Parish, Scotland, May 8, 181 9; and
f\^ is the son of John and Jane (Nicholson) Edgar,
\ natives of Scotland. John Edgar was ot
( Scotch ancestry for at least ^s^ centuries back.
He was a farmer at first, but spent the latter part of
his life weighing metal at the iron mines of England,
where he moved about 1853. He died in Cletnir
Moor, Eng., in March, 1855. Jane Nicholson lived
with her parents in her native county, and was there
reared, educated, married and died.
The subject of this sketch was educated in the
parish schools of his native couniy, and at the age of
19 began to ^ork as a common laborer in the mines
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of his native county and Gal way County. In th^
latter, Oct. 18, 1844, he was united in marriage to
Margaret, daughter of Anthony and Mary (McQueen)
Dunn, natives of Galway, Scotland. He was a saw-
Margaret was bom in Galway County, nearCanmore
Castle, May i, 1830, and was bred and educated
there. Nine years after marriage, Mr. and Mrs.
Edgar removed to Cumberland Co., £ng., where he
worked in the mines. In the summer of 1855, they
came to London, Ontario, Can., where he was em-
ployed as a railroad section foreman. Later he was
stationed in the same capacity at St. Thomas, and
remained there seven years. In December, 1862,
he came to Michigan with his family, and settled on
122 acres in Emerson Township, purchased two
years previously. He has 70 acres well improved,
and good farm buildings. He has also purchased
1 20 acres additional, which is worked by his two
oldest sons.
Mr. and Mrs. Edgar have a family of seven : El-
len, Jane, Stewart, James, William George Thomas,
Mary and John, Politically, Mr. Edgar is a staunch
Republican. He and wife are life-long members of
the Presbyterian Church of Scotland. .They are
among the most respected citizens of the township.
fames Henry, proprietor of the St. Louis
Flouring Mills, manufacturer and dealer in
lumber, shingles, flour, feed, etc., was born
in County Tyrone, Ireland, Feb. 24, 1825. He
is a son of William and Sarah A. (Gilmore)
Henry, and both parents were natives of the
Emerald Isle. His father died there, at the age of
84 years, in the same house in which he was born.
His mother died previously, when she was about 42
years old.
Mr. Henry was brought upon a farm and obtained
a fair education. At 18 he learned the business of
a wagon-maker, and in 1849 left his native country
for the United States. He spent two summers on a
farm in Yates Co., N. Y-, and in 1851 proceeded to
Allegany Co., N. Y., where he learned engineering,
which he followed three years and then came to Bay
City, Mich., and operated in the same capacity one
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summer, after which he proceeded to St. Charles, v^
Saginaw County, where he was similarly employed';
six years. In 1861 he went to Grant Co., Wis., and /* .
became proprietor of 160 acres of land by purchase,
Three years after he returned to Michigan and fol-
lowed his trade of engineer in Saginaw County three
years. He went to Hemlock City and bought a saw
and shingle mill, which the operated 10 years with
satisfactory success, and in 1879 went to Cedar Lake,
Montcalm County, where he built a saw and shingle
mill and engaged vigorously in the prosecution of \
lumbering interests. Two years later, the steam
boiler exploded, destroying the mill and killing two
men. At the moment of the explosion, Mr. Henry
was in the mill, standing near the stove, which was
about 20. feet from the boilef. The roof fell upon
him, but the stove kept it from crushing him to death.
He hastened the re-building of the mill and in 60
days it was again running.
In the fall of 1882, Mr. Henry moved to St. Louis,
where he had purchased one and a half acres of land,
and built a residence. In September of the same
year he bought his mill site, which includes about 15 -
acres, and is largely engaged in the manufacture of £j^
mill products. He also owns 400 acres of land in p:
Richland Township, Saginaw County. His flouring \/
mills are 30x80 feet, with three stories and base-
ment. The wing is 22 x 40 feet in size and two
stories high. The mills are fitted with the most
modern style of machinery for the production of first-
class work, and the power is supplied by six Leff"-
well turbine water wheels. The fixtures include six
run of stones, and the capacity of the workt is 1 25
barrels per day. The flouring and saw mills were
owned 24 years by H. L. Holcomb, of whom Mr.
Henry purchased them in September, 1882. In De-
cember following, the saw-mill burned, entailing a
loss of j(3,ooo, without insurance.
Mr. Henry was married in St. Charles, Saginaw
County, Feb. 24, 1859, to Jane, daughter of William
and Mary Boyst, a native of New York. Four
children have been born of their marriage, two of (^
^hom are living, — Fred Cook and Myra J. The f
deceased were William B. and Nellie M. Mr. Henry ^} .
is a Republican in political sentiment, and, while re- , '
siding in Saginaw County, held the positions of Town- v/
ship Clerk and Treasurer. ^
Physically, Mr. Henry is a fine sample of manly ^'
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vigor and energetic effort. He has the hardihood of
a man who has passed his years of prime and yet
retains his powers of strength and endurance to a
degree that proves the correctness of his habits and
course of life. Both he and his wife have reached a
period of existence altogether satisfying from their
part of well-directed effort and their future, which
holds higher and better promise than that of youth s
fresh flush of hope and ambition. They can rest on
the fruition of the years that are gone, which assure
the type of those to come. The portraits of Mr. and
Mrs. Henry are to be found on pages 250 and 251.
eorge Little, blacksmith, at Sickels, was
born in the county of Franklin, and State
of Vermont, Jan. 5, 1850, aiid is a son of
Peter Little, of Sweetsburg, Canada, and a na-
tive of that county. Mr. Little received the
advantages afforded by the common schools of
his native country. He learned his trade in Ver-
mont while quite a young man and has success-
fully pursued it until the present time with the ex-
He came to St. Louis, Mich., in 1880, and after
remaining there eight months, went to Ithaca, where
he lived for six months. He then came to Sickels,
this county, at which place he now carries on his
He was married June 14, 1874, to Miss Katie
Golden, and four children have been born to their
union, namely : Annie, Ettie, George Thomas and
William Henry.
t illiam W. Palmer, farmer, section 28,
North Star Township, is a native of the
Empire State, and was born in Onondaga
County, May 27, 1823. His parents, Gilbert
and Ann (Pitts) Palmer, were natives respect-
ively of Green and Columbia Cos., N. V., who
emigrated to Lenawee Co., Mich., in 1837, settling in
the wild woods, amongst savage animals and Indians.
Mr. Palmer settled where he now lives in this county
in 1854, and whe;e he at present owns 80 acres of
good land. He has given his children 160 acres.
He was a blacksmith by trade when a young man,
but for many years he has been a prosperous
farmer.
July 2, 1845, Mr. Palmer married Miss Lydia M.,
daughter of Chester and Aurelia (Guthrie) Savage,
and of their nine children ^st, only are now living,
viz.: Ida L., Rufus M., Frank G., Roscoe C. and
Vere D. Ida L. married Edwin E. Palmer, and
lives in Mecosta Co., Mich., in Fork Township;
Rufus M. married Charlotte Henry, and lives on part
of the homestead ; Frank G. married Llewella Husen,
and is a prominent teacher; Roscoe C. lives in Chicago;
and Vere D. is at home, attending school winters
and working on the farm during the rest of the
year.
Mr. Palmer, the subject of this biographical notice,
was the first Treasurerof North Star Township, hold-
ing the office five years; has also been Township
Clerk one year. School Inspector one year, and is
Justice of the Peace. He is a member of the Mawnic
fraternity.
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^Jpr|j> ohn H. Bangs, farmer, section 1 1 , Arcada
l^pilt Township, was born in De Kalb Co., Ind.,
)j^' ' May II, r847; and is the son of Heman
and Almira (Chaffee) Bangs, natives of Ver-
mont and New York. Heman Bangs removed
from Vermont to New York ; thence to Michi-
gan ; and lastly to De Kalb Co., Ind., where he was
one of the first settlers.
The subject of this biographical notice remained
at home, working on the farm and attending the com-
mon school, until he attained his majority. He then
came to Gratiot, and kept " bachelor s hall ** on 80
acres his father had purchased a few years before.
Some months later, he returned to his native county,
where, Jan. 21, 1869, he was married to Miss Emma
De Long, daughter of James and Elizabeth (Fair)
De Ix)ng, natives of Maryland and Virginia. Emma
was born in Allen Co., Ind., Oct. 6, 185 1, went when
10 years old to De Kalb Co., Ind., and there was
reared and educated.
Immediately after marriage, Mr, and Mrs. Bangs
came to Gratiot and settled down on his then unim-
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GRATIOT COUNTY.
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proved farm. He has now under cultivation 40
acres, and has erected one of the best barns in the
township.
Mr. and Mrs. B. have a family of four, as follows :
Cora, born Jan. 16, 1870; Stella, Sept. i, 1872;
Leota, Oct. 5, 1873; Raymond, Aug. 5, 1877.' Po-
litically, Mr. Bangs is a Republican. He and wife
are members of the United Brethren Church.
.aoob Schaub, farmer, section 28, Lafayette
^ Township, is a son of George and Sophisf
(Brandan) Schaub, natives of Germany.
They followed farming in the old country until
1852, when they emigrated to America. They
farmed in Lorain and Sandusky Counties, Ohio,
until their death in the latter county in 1869. Jacob
left home at the age of 28, and worked on a farm
until he was married, July 10, 1858, to Mary
Rice.
In 1876 he removed with his family to Gratiot
County, and located on 80 acres of land on section
28, Lafayette Township. He has improved 60 acres.
In 1878 he built his barn, and in 1883 he erected
a large and well-arranged dwelling-house
Mrs. Schaub was born Oct. 13, 1840, in Sandusky
Co., Ohio. She has brought to her husband 14
children: Barney, Anthon G., Christian W., Sophia
E., Jacob, Jane, Emma, Willie and Wilson (twins),
George, Frank, Albert, Bertie and Alice.
Mr. Schaub has been Moderator of his school
district for three years. Politically he is a Democrat.
_^n
braham L. Wight, whose Christian name
was given him in honor of the martyred
Lincoln, who took the oath of office and en-
tered on the duties of Chief Magistrate of the
Nation eight days after the birth of our sub-
ject, is a son of Leonard Wight, who came to Eaton
County, this State, in 1858, and settled in the town-
ship of Benton, where Abraham was born, Feb. 24,
1 86c. He lived with his parents in Benton Town-
5ihip, Eaton County, until 1869, when he accom-
panied them to Chester Township, same county, and
where the mother died in 1874.
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mon schools of his county and followed his inclina-
tion to learn the wagon and carpenter business by
working for his brother, Sheldon Wight. He is now
engaged with his brothers S. and M. Wight, in their
planing-mill ; is present Clerk of Hamilton Town-
ship, and a member of the I. O. O. F.
Mr. Wight owns 40 acres of land on section 5, and
devotes as much of his time to its improvement as is
compatible with the faithful performance of his
other duties. He has four brothers, — Francis, Shel-
don, Reuben and Mason, living. His only sister
and the eldest child of the family, died when she
was 1 2 years of age.
Mr. W. is yet a young man, and, possessing his
portion of that indomitable energy characteristic of
the young men of the county, supported by a large
amount of ambition, is certain to succeed
— ^-«s«$4H6»H-! VWinbrose B. Angell, farmer, on section 28, I Arcada Township, is a son of William and Rhoda (Bonnell) Angell, natives of New York and Connecticut, respectively. They followed farming, and died in Stockbridge, Ingham Co., Mich., the father Jan. 28, 1864, aged 69, and the mother June 6, 1865, aged 64. They were pioneers of Ingham County. Ambrose B. was born in Orange Co., N. Y., April 15, 1834, and at the age of eight came with his parents to Wayne County, this State. Here he lived six years, working on the farm and attending school. When 14 years old, he moved with his parents to Bunkerhill Township, Ingham County, and settled on a farm. Two years later, he went to Jackson, and for two years he attended the High School in that city. He then attended i8 months at Albion College. Returning to Ingham County, he was for the ensuing four years engaged in teaching, in the common schools. Going back to his father s farm, he worked it, in partnership with his brother Malcolm, until the latter s death, in 1866. For the next seven years, he carried on the farm by himself. Going then to Rives, Jackson County, he purchased 80 acres of improved land, and commenced farming there. April 9, 1877, he received a great financial set- back in the form of a fire, that speedily reduced to 1 ( - A >: I.. f :<^:iiiif->^ ^.:' :>.y^ -^re>^^.i>N. I Digitized by Google :-y<'' 256 GRATIOT COUNTY, J '< \y ^ ashes his residence, household goods, barns, live stock, grain and farm implements. His total loss was not less than$4,400. Shortly after this, he sold
his farm, came to Gratiot County and purchased 160
acres of partly improved land on section 28, Arcada
Township, where he has since resided. He has
cleared 60 acres, and now, of his 160 acres, no are
under the plow. He has commodious farm buildings.
Nov. 24, 1864, at Waterloo, Jackson County, he
was married to Elvira J., a daughter ot Hiram and
Martha (McNeal) Drew, natives of New England,
and of Irish descent. She was born at Grass Lake,
Jackson County, Dec. 22, 1840, and lived wiih her
parents in that county until her marriage. She
attended school at Grass Lake and Leoni, and com-
menced teaching school at the age of 16. This she
followed till she was 22, and at 23 she was married.
Mr. and Mrs. Angell have a family of six, as fol-
lows: Mattie R., born Dec. 30, 1865, Edith E., Dec.
8, 1866, Cora A., Dec. 3, 1867, Florence E., Feb. 2,
1869, Edwin F., March 5, 187 i, Willie C, Oct. 19,
1875-
Mr. and Mrs. Angell are active members of the
Patrons of Husbandry. He has held the office of
Drain Commissioner and Highway Commissioner.
Politically, he votes with the Republican party.
ollin W. Maxam, merchant, section 29,
Lafayette Township, is a son of Isaac B.
and Clarissa (Kellogg) Maxam, natives of
New York. Mr. Maxam, Sr., followed farm-
ing in New York State until 1849, when he
removed to Ohio, and engaged there in farm-
ing and stock-raising. Rollin W. was born Feb. 19,
185 1. He remained with his father until 21. He
then worked one season manufacturing cheese.
Coming to Michigan in the fall of 1872, he was for
the ensuing three years manager of a cheese factory.
He then enbarked in farming. In 1878, he came to
this county and located on section 29, Lafayette
Township, spending the next three years clearing his
farm.
Nov. 7, 1 88 1, he was apiX)inted Postmaster of La-
fayette post-office. Jan. i, 1882, he engaged in
mercantile business, which he has followed since.
He has a general stock of dry goods, groceries, boots
and shoes, and miscellaneous goods. He also has an
extensive apiary, and deals in bees and honey.
He was married in 1870, to Ida E. Bissell, daughter
of Warren and Charlotte (Bailey) Bissell. They were
natives of Ohio, and died the mother in Ohio, in
1854, and the father in Kansas, in 1879.
Mr. and Mrs. Maxam are the parents of three
children: Arthur J., Mabel and Arno. Politically,
Mr. Maxam is a Republican.
rancis M. Utter, farmer, section 33, Ar-
cada Township, was bom in Chatham,
f^^ Medina Co., Ohio, March 10, 1833; and
yj^ is the son of Amos and Margery (Hamilton)
yi^ Utter, natives of New York State. Amos Ut-
{ ter was a mechanic and farmer, of English and
German descent, and died in Manistee Co., Mich.,
in October, 1876.
When Francis was six years old, his father re-
moved to Shelby Co., 111., and two years later, in
June, 1 84 1, he came to Michigan, locating in Port-
land, Ionia County. Here he worked on his father s
farm and attended the common school, until he at-
tained his majority. For the ensuing three years he
worked at farming on shares in the summer time, and
at lumbering in the winters.
Jan. I, 1857, in Pine River Township, this county,
he was united in marriage to Miss Sophia C. Roberts,
daughter of Stephen and Rachel (Stuck) Roberts,
natives of New York. They afterwards removed to
this State, where Sophia was born, in Pittsfield, Wash-
tenaw Co., Mich., April 8, 1840. She was reared
and educated in that county, and -there lived and
cared for her fathers household until 17 years old,
when she was married.
Shortly after that event, Mr. and Mrs. Utter re-
moved to Portland, Ionia County, where they carried
on farming for 10 years ; thence to Dallas Township,
Clinton County, where they were similarly engaged
for 12 years. Mr. Utter was also extensively en-
gaged in buying and selling real estate. In March,
1876, they came to this county, where he purchased
80 acres in Lafayette Township. Shortly after, he
sold, and bought 40 acres in New Haven. Here he
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erected a house, and farmed for about three years.
He then purchased 1 60 acres of timbered land on
section 33, Arcada Township, his present home, and
commenced to improve the same. He has 25 acres
carefully improved, and is possessed of sufl5cient
ability and experience to make in time one of the
most successful farmers in the township.
Mr. and Mrs. Utter have had born to them four
children, of whom three are living: Amos D., l)orn
Oct. 14, i860; Francis M., Sept. 24, 1863; Ceylon
A., April 28, 1875. Clara A. was bom Oct. 6, 1857,
and was fatally scalded by falling into a tub of hot
water, March 17, 1861. Mr. Utter has held the of-
fices of Director, Assessor, Inspector and Moderator
in his school district. He is at present Moderator.
Politically he is a Democrat.
lien Oberlin, farmer, section 23, Elba
Township, is a son of George and Esther
(Bowman) Oberlin, natives of Pennsylvania.
They died in 1868 and 1863, respectively.
Allen was born Nov. 15, 1 814, in Lancaster
Co., Pa. Leaving his father s farm at the age
of 21, he worked by the month until he was 26, when
he married Mary, daughter of John and Christina
(Baisler) Wulmoyer. They were natives of Germany,
and emigrated to America at an early day. Mary
Wulmoycr was born April 21, 182 1.
Mr. and Mrs. Oberlin moved to Stark Co , Ohio,
and remained there a period of ten years. He then
went to Medina County, in the same State, living
there eight years. His next move was to Indiana,
but three months more found him in Lansing, Mich.,
where his home was for the next eight years. He
then located on section 23, Elba Township. At that
rime they were surrounded by a perfect wilderness,
and the howl of the wolf and the scream of the wild-
cat became familiar sounds to their ears. Their
nearest neighbor in one direction was three miles
away, in the other eight. They first entered a large
tract of land, but, old age coming on, they have sold
most of their land, and now live on a 20-acre place.
They are the parents of nine children : Eliza, Rachel,
Mary A., Esther (died Dec. 12, 1883), John, George,
Christina, Malcolm and Rebecca.
Mr. Obcriin is one of the most prominent citizens
of Elba Township, and is looked up to by his neigh-
bors. He has held the office of Highway Com-
missioner. He is an acrive member of the Free
Methodist Church, and has always been a supporter
of the Republican party.
asper C. Sickels, Postmaster and merchant
at Sickels, was born at Howell, Livingston
Co., Mich., March 27, 1849, and is a son
of Aaron Sickels, an eariy settler of Wayne
Co, Mich., but now of Walton, Grand Trav-
erse County, this Slate. When he was seven
years old the family moved to Wyandotte, Mich.,
and two years afterward they came to Duplain, Clin-
ton Co., Mich., where his father was in turn a mer-
chant, miller and farmer.
Mr. S., the subject of this sketch, was educated in
the common schools, and in 1871 engaged in mer-
cantile business at Elsie, Mich., until in 1873, when
his health failed and he resorted to agricultural em-
ployment until 1880. In November of this year he
purchased his present store at Sickels, where he
keeps a full line of goods in general merchandise,
and is doing a prosperous trade. He also owns a
steam saw-mill in the pineries of this and Saginaw
counties.
May 5, 1870, Mr. Sickels was married to Miss
Mary P., daughter of Elisha Fuller (deceased), and
the three children now comprised in their family are,
Hattie, Claud and Frankie.
Mr. S. is a member of the Orders of Masonry and
Odd Fellowship.
omer Qalehouse, farmer, section 25, Elba
Township, is a son of John W. and Julia
(Wilson) Galehouse, natives of Ohio and
Massachusetts. The father was murdered, at
Doylestown, Ohio, in 184 1 ; and the mother
died in 1843. Homer was born in Wayne Co.,
Ohio, March 24, 1838. Being left an orphan when
only five years of age, he went to live with his grand-
parents. At the age of 13, he was apprenticed to
half years ill health compelled him to abandon that
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occupation. For the next few years he worked at a
number of things, until he finally settled down as a
farmer.
In 1875, in the State of Indiana, he joined his for-
tunes with Mary Pettyjohn, born April 7, 1843, in
Stark Co., Ohio. The same year he removed to Elba
Township, this county, finally locating on 80 acres
of wild land on section 25. He has now comfortable
buildings, and 60 acres of well improved land. Mr.
and Mrs. Galehouse have a family of seven children,
— John D., Charles E., George H., Lucette E., Frank
Z., Sarah L. and Mary J. Mr. Galehouse is a mem-
ber of the U. B. Church, and votes with the Repub-
lican party.
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eorge W. Marshall, farmer, section 17,
Lafayette Township, is a son of Nathan
D. and Hannah E. (Turner) Marshall, natives
of Ohio. They were engaged in farming in
that State until 1865, when they came to
Michigan. They followed farming in Clinton
County unlil 1878, when they came to Lafayette
Township, Gratiot County, and located on section 18,
on their present place of 60 acres.
The subject of this sketch was born in Geauga Co.,
Ohio, Aug. II, 1855. He lived with his parents, at-
tending the common schools a portion of the time,
until he was 18 years old. He then left home to
work on his own account. He was employed on a
farm the first year at $18 per month, and the second at$20, and also attended school occasionally until
Jan. 12, 1882, when he was married to Ella Phelps,
born in Livingston County, Aug. 6, 1865. She is the
eldest daughter of James and Elizabeth (Hodges)
Phelps, natives of New York and Canada, respect-
ively. They came in 1881 to this county, where Mr.
Phelps follows his trade of blacksmith.
Feb. 19, 1882, Mr. and Mrs. Marshall located on
a tract of 80 acres on section 17, Lafayette Township,
where they now reside. Mr. Marshall has improved
40 acres of his farm and erected a neat and commo-
dious dwelling-house.
In the winter of 1883-4, he taught the school in
district No. 3. They are the happy parents of one
child, Allen B, born Dec. i, 1883. In 1882, Mr.
Marshall was chosen School Inspector of his Town-
ship for two years. He is also Pathmasterin his "Y
district. Politically he stands on the platform of >|
"Anti-Monopoly."
V
»ttJ'|ruce Hunter, farmer, section 35, Elba
.P^k- Township, is a son of John and Charlotte
^ (Kenna) Hunter, natives of New York,
where the former died. Bruce left home at
the early age of 13, and went to work driving
team on the New York water-works. Coming
to Detroit in 1842, he worked a year as blacksmith.
The next four years were spent in Canada. Then
he spent a short time in Buffalo, N. Y., 18 months at
Cayuga Creek, Niagara County, and two years in
Erie Co., N. Y. Coming to Michigan in 1856, he
spent 18 months in Jackson County, and then located
in Elba Township, this county. He worked two years
in Elsie, then returned and sold his Elba farm, then
went to Elsie once more. He finally purchased 40
acres on section 35, Elba Township, where he now
resides.
In 1853 he was married to Miranda, daughter of
Ralph and Margaret Sutphin. Mr. and Mrs. Hunter
have a family of six children : William H., Frank,
Fred, George, Eva and Florence. In politics Mr.
Hunter is a Republican. He has been Justice of the
Peace, and has been a school officer for eight years.
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^orace Spear, farmer, section 35, Lafayette
1^ Township, is a son of Calvin and Charlotte
(Stone) Spear, natives of Vermont and Can-
ada, respectively, and was bom Feb. 23, 1832.
At the age of 17, he left home, and began to
care for himself. In 1849, he came to Sanilac
Mich., where he remained a short time. He
then went to St. Clair Co., Mich., after a year return-
ing to Sanilac County. Thence he removed to Ionia
County, in 1863. His next move after a number of
years, was to Lawrence Co., Tenn., where he re-
mained one year, and then, returning to Michigan,
settled in Gratiot County, in the year 1878. He first
located on section 28, Emerson Township, and then,
after three years, removed to his present residence, on
section 35, Lafayette Township.
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In his 2 2d year, he was married to Mary A, West-
ervelt, who was born in Canada, Jan. 15, 1838. She
was the daughter of Garrett and Lucinda (Pollard)
Westervelt, natives of Canada. Mr. and Mrs. Spear
are the parents of six children : Delila J., Minerva,
William A., Ida L., John A. and Alfred H.
Mr. Spear held the office of Highway Commis-
sioner, in St. Clair County, one year, and he has also
held various school offices. He and Mrs. Spear be-
long to the Free Methodist Church, in which they
are active workers. Mr. Spear has a license as a
local preacher of the gospel, and occasionally leads
services for his denomination.
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aoob J. Muffly, farmer, section 9, Hamilton
Township, was born in Stark Co., Ohio,
Nov. 6, 1837. He is a son of John Muffly,
of this Township, who brought his family to
this County in 1855 and settled on the above
named section and where he and our subject
^ njw live. They settled in the woods and were sub-
Tt jected to all the trials encountered by the eariy pio-
neer settlers of the county. Wild animals predomi-
nated in abundance and, " although they were con-
sidered a necessity to supply the craving appetites of
hungry, ambitious and energetic individuals," the
howling of the wolves, the crying of the panther and
wild-cat were no pleasant sounds to listen to, and
grated harshly on the ear, at least of the feminine
portion of the household.
When the shot which started a nation from its
peaceful sleep of years, was thundered from rebel
guns upon Fort Sumter, and our martyred President
called for loyal hearts to battle for the perpetuity of
the " Flag of our Fathers " and the preservation of
our nation s honor, the heart of our subject beat in
unison with the cause and he enlisted in Co. F, 29th
Mich. Vol. Inf. He was in the battles of Decatur,
Murfreesboro and others, and was honorably dis-
charged Sept. 6, 1865.
Mr. Muffly was married Aug. 2, 1866, to Miss
Mary, daughter of 2k>roaster Moss, deceased, and five
children have been born to their union, four of whom,
John L., Birdsey A., Charles H. and Annie are liv-
ing. Mrs. M. was bom in Waterloo, Jackson Co.,
Mich., in 1847, and is a cousin to ex.-Gov. Blair, of
this State. Mr. and Mrs. M. are both members of
the Methodist Episcopal Church. They have a fine
farm of 80 acres, on which they are at present living
and pleasure and happiness surround the family
hearthstone.
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^iOrace S. Taylor, farmer, section 20, Area-
da Township, was born in St. Lawrence Co.,
N. Y., Feb. 7, 18 18; and is the son of James
and Tabitha (Borland) Taylor. James Taylor
was bom in Orange Co., N. Y., of Irish and
English descent, and was by occupation a
farmer. He died in Cleveland, Ohio, at the age ot
87. His wife died in Litchfield, Medina Co., Ohio,
The subject of this sketch remained with his father
on the farm and attended school, first the common
schools, and then the Gouverneur Academy of St.
Lawrence County, and taught until 23 years old.
He commenced teaching at the age of 21, and^ fol-
lowed that for three years. He then removed to
Medina Co., Ohio, where he farmed and taught select
school until 1854. He then became a railroad con-
tractor, and after a time became connected with a
saw-mill. In the spring of 1867 he came to this
State and county, and purchased 120 acres of partly
improved land on section 20, Arcada Township, and
devoted himself to farming. He has made rapid im-
provements, has erected new bams, and now has
about one-half his farm in a state of high cultivation.
Though becoming advanced in years, he is a progress-
ive farmer, and acUvely devdled to building up his
township. He takes an especial interest in all things
pertaining to schools and in all benevolent and econ-
omic projects.
Oct. 5, 1852, at Penfield, Lorain Co., Ohio, he was
united in marriage to Maria, daughter of Orrin and
Abigail (Hickofc) Starr, natives of New York, and ot
English descent. The Starrs have an interesting and
valuable genealogical record, which traces the family
back to Dr. Comfort Slarr, of Kent, England, 1635.
The book is a quarto, and contains 579 pages. Maria
Starr was bom in Harpersfield, Delaware Co., N. Y.
Mr. and Mrs. Taylor have had a family of three,
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two of whom survive, as follows : James L., born
Jan. 19, 1856; Abbie E., born July 29, 1867; Emma
S., bom Sept. 8, 1857, and died May 18, 1870. Mr.
Taylor is a member of the I. O. O. F. lodge at Me-
dina, Ohio. He is highly esteemed by all his num-
erous friends, and has been often asked to hold of-
fice. He has been for some time Superintendent of
Schools. In political sentiment, he is an ardent and
influential Greenbacker, and uncompromisingly op-
posed to any and all monopolies. In 1880, he was
unanimously nominated for Representative, by his
party, — a high compliment to Mr, Taylor s ability and
popularity.
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11 obert Gladson, farmer and stock-raiser,
section 17, North Star Township, was born
in Oakland Co., Mich., June 5, 1844, and
is a son of John Gladson, deceased, a native
of England, who moved with his family to
Clinton Co., this State, in 1854, and a few
years afterward to this county. Mr. Robert Glad-
son was a soldier in the late war for 18 months, being
a member of Co. I, 27th Mich. Vol. Inf., and taking
part in the battles of the Wilderness and Spottsyl-
vania. In the latter engagement he was wounded in
the right shoulder. He was married June 26, 1 870, to
Miss Amanda J., daughter of John Garver (dec),
and they have five children, as follows : William N.,
Ralph E., Ellen M., Altha E. and Edith S.
Mr. G. is a Republican, and has been Constable
two years, and held other offices. He is a member
of the Grand Army of the Republic.
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f homas Derry, farmer, section 3, Hamilton
Township, is a son of Thomas and Mary A.
(Johnson) Derry, natives of England, where
Thomas, Jr., was born, in Cambridgeshire, Jan.
26, 1832.
school education in his native country, and emigrated
to the United States, with his parents, in 1854, settling
in Wayne Co., N. Y.
In 1866, Mr. Derry left the parental home, and,
following the inclination of his ambitious disposition
^V
to better his financial condition in life, came to thu
State, arriving in this county in January of that year
and has resided here ever since. He settled in th<
woods, and had but two acres of land cleared or
which to raise a sufficiency to sustain himself am
family; yet, being endowed with that spirit ot push
pluck and energy so necessary to success, he me
and successfully conquered all difficulties.
Mr. Derry was united in marriage to Miss Mar]
A., daughter of John Swails, deceased. Mrs. D
was born and brought up on the banks of Lak<
Ontario, on the identical farm on which the Britisl
troops landed during the war of 181 2.
Mr. and Mrs. D. are the parents of nine children
namely : Albert, Herbert A., Frank, Emma, Agne
M., Willis, Lewis, Annie and Frederick. Alber
married Miss Mary Williams, and one son, Earl, ha
been born to them, Emma married a brother c
Miss Williams, and to them has been born a son
named George William.
Mr. Derry owns 44 ji acres of land, which is unde
the best of cultivation, with a large bam and com
modious residence. He is a member of the Pres
byterian Church, of which denomination Mrs. D. ha
been a member since she was 16 years of age.
Herbert A. Derry, son of our subject, is one of th
enterprising business men of the township, and i
engaged in lumbering.
Mr. and Mrs. D. made a visit to the old homestea
in Wayne Co., N. Y., in 1883, and spent a pleasar
vacation among their relatives and friends.
eorge B. Andrus, hotel-keeper, Breckei
^ ,_ ridge village, Wheeler Township, was boi
^Av;r in Batavia, N. Y., March 28, 1827; ar
^i\ was the son of James and Hannah (I>odg<
t Andrus, natives of New York. Mr. Andni
' Sr., was engaged in farming and running
saw-mill in New| York until 1856, when he came
Michigan. Mrs. Andrus died in 1857, and Mr. A
drus in i860, both in Kalamazoo County.
The subject of this sketch remained at home un
he was 21, when he commenced to care for himse
He worked on a farm and in saw-mills until he w
26 years old, and then married Elizabeth, daught
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of William and Mary A. (Vandorn) Young. She
died in April, 1862, leaving two sons, — ^Auburt and
Lewis. Mr. Andrus was again married, to Mary P.
Doty, the widow of Benjamin Doty. She was born
Dec. 25, 1 84 1, the daughter of William M. and Annis
Russell, natives of New York and Pennsylvania.
They came to Pompei, this county, in April, 1876,
where he kept a hotel one year. He pursued the
same calling one year at Ithaca, and then removed
to Breckenridge, where he is still in the hotel busi-
ness. Mr. Andrus has four children by his second
marriage : Jewett E., Minnie, James A. and Kittie
A. In politics he is a Republican.
lias Sower, physician, clergyman and far-
mer, section i, North Star Township, is a
native of York Co., Pa., where he was born
5|S. April 5, 18 10. He is a son of Henry Sower,
ik deceased, a native of Frederick Co., Md. ; the
latter was a son of John Sower, who came from
Germany many years ago and settled in Maryland.
The father of our subject was a soldier in the war of
181 2, and moved his family from Maryland to Centre
Co., Pa., in 18 15. Here the son attended the com-
mon schools, assisted on the farm and grew to man-
hood. In 1835 Mr. Sower moved to Holmes Co.,
Ohio, where he remained for one year and then went
to Seneca County, same State. He remained here for
four years, until 1840, when he went to Richland
County, and after remaining there ten years engaged
in various occupations, he returned to Seneca County.
He remained there until 1854, when he came to this
county and entered 320 acres of Goverment land
on which he is now residing. His trials were similar
to those of Michigan's pioneer settlers, and he ener-
getically met them, with all the determination of an
individual whose great ambition was to succeed in
life, and conquered them.
He arrived in this county, after having entered
ois land at the Land Office on Oct. 6, 1854, in the
afternoon of the 9th of December, the same year.
Eight inches of snow was on the ground and he and
his family slept in their wagon for an entire week
before the customary " log cabin " was erected. At
last the round log shanty was completed, 14 x 20,
and he and his family moved into their *' palace."
He began to chop, roll and burn the logs and cleared
a small patch on which to raise a crop, and success-
fully continued his labor until want was driven
from the door, and plenty entered, and, taking her
seat by the side of comfort and happmess looked
back upon the past with satisfaction and content.
The Doctor read medicine for a number of years
before coming to this State, not with the intention of
practicing but more for his own edification, yet his
knowledge of medicine soon became known to his
neighbors and the indisposed would not accept No for
an answer in response to their earnest request to call
and administer to their ailments. He therefore en-
tered on the practice through no desire on hii part,
jind yet, after following the same for a few years, he
became so infatuated with the profession he has con-
tinued it ever since. He had nothing to feed his
horses when he first came here and was compelled
to sell them, and for four years followed the profession
by walking to his patients. He was what might be
called ** the father of the neighborhood." He ad-
ministered to their want?, cured their diseases, made
their coffins, preached their funerals and placed the
dirt uix)n their graves.
Mr. Sower was married May i, 1832, to Margaret
Bitner, who died Aug. i, 1851. They had ten chil-
dren, eight of whom are living, namely: Susan,
Lydia, John H., Catherine, Daniel, Lovina, William
and Samuel. One daughter, Mary J., after reaching
womanhood and marrying, died from the effects of a
sun-stroke, leaving the children to the care of the
husband. Mr. S. was again married, June 8, 1854,
to Miss Elizabeth, daughter of John Klingomon, and
four children have been born to their union, two of
whom, Sarah E. and Almira, are living; one son,
David E., twin brother to Sarah, died in his 20th
year, and another in infancy.
Dr. Sower was licensed as an exhorterin 1840, and
July 27, 1843, was licensed to preach the gospel
from a Methodist standix)int. Aug. 28, 1853, he
was ordained Deacon by Bishop T. A. Morris, of Mt.
Vernon, and received the Elder's ordination at the
hands of Bishop Scott at Grand Rapids, Oct. 5,
1862. He and his wife are both members of the
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]\ Dr. Sower's life-long friends will prize this work
more highly for the portrait of the pioneer, which is
given on a preceding page.
^arley S. Evitts, fanner, section 32, North
Star Township, is a native of Trumbull
Co., Ohio, where he was bom Jan. 10, 1834,
and is a son of Bela Evitts (deceased), a native
of Connecticut. He was brought upon a farm,
receiving his education in the common school.
When only four years old his parents emigrated, with
the family, to this county, settling, in June, 1854, in
North Star Township, where he has since made it
his home. He was a pioneer, witnessing all the
features of a frontier life and having his share of their
experiences. Deer, wolves and bears were plentiful
when he settled here. He now owns 80 acres of fine
farming land, where he humbly wins from the soil
his livelihood.
Mr. Evitts was married Feb. 28, 1861, to Miss
Margaret Bartrim, a native of Ireland who was
brought to this country when six years of age. Her
father was Thomas Bartrim, now deceased, who set-
tled first in Pennsylvania, then, in 1849, in Ohio, and
finally, in 1854, in this county^ Mr. and Mrs. E.
have ^s^ children, viz. : John L., Alva H., Clara
M., George B. and Mary E., — all at home.
.esse Pepple, farmer, section 17, Emerson
I^Silt" Township, was born in Hancock Co., Ohio,
^'^^ Dec. 15, 1842; and was the son of Jesse
rW and Mary (Tipple) Pepple, natives of Pennsyl-
vania and Ohio, and of Pennsylvania German
descent. The former died in Michigan in
1869, and the latter in Ohio in 1857. Jesse, junior,
passed his youth in working on his fathers farm
summers and attending school winters. At the age
of 20 he apprenticed himself to a pump-maker at
Findlay, Ohio. Serving out his term, he formed a
partnership with his employer, and remained in that
business until September, 1867. He then came to
Michigan, and purchased 40 acres of unbroken for-
GRATIOT COUNTY,
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est land, erecting the log house so familiar to pio-
neers. He has since added 40 acres to his farm by
purchase, and has improved 43 acres of the whole.
He has a good residence and farm buildings. For
five years, he also followed pump-making, in connec-
tion with farming.
He was married, Aug. 1 1, 1864, at Findlay, Ohio,
to Susan Beard, daughter of Adam and Delight
(Smith) Beard, natives of New England. They are
farmers, and live in Hancock Co.,- Ohio, where their
daughter was born, Oct. 12, 1842. Mr. and Mrs.
Pepple have had two children, but both died in in-
fancy.
Mr. Pepple is a member of Emerson Center
Lodge, No. 375, 1. O. O. F. He is an enterprising
farmer, and ix)pular in his township. He held the
office of Highway Commissioner for a period of 10
years, and that of School Director for nine years.
In 1880, he was chosen Supervisor of Emerson
Township. He held that office two years, and in
1883 was again elected. Politically, he is a staunch
Republican.
arks Allen, farmer, section 29, Emerson
Township, was born in Delaware Co., N.
t'J|i^ "^ Y., July 13, 1836 ; and is the son of Isaiah
^6 J and Elsie (Peck) Allen, natives of New York,
jk^ and of Yankee and German descent. His
father came to Michigan when about 50 years
old, and located in Emerson Township, where he
died, at the age of 64, and his wife, at the age of
58. Parks Allen left his native county when quite
young, and went with his parents to Seneca Co., N.
Y., then seven years later to Steuben Co., N. Y. He
worked on his fathers farm, and attended thedistiict
schools as much as he could, until the fall of 1854,
when he emigrated to Michigan with his parents, and
helped to make a home on 160 acres o< heavy timber
land in Emerson Township. They were the third
family to settle in Emerson, and the first to sow
wheat. They sowed fxve acres, and from that stumpy
field gathered 40 bushels per acre.
Oct. 22, 1 86 1, the subject of this sketch was mar-
ried, in Emerson Township, to Minerva, daughter of
Ralph and Jane (Terry) Bellows, natives of New
York and Michigan, respectively. She was bom in
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Genesee Co., Mich., Oct. 22, 1843. She afterwards
lived in Calhoun and Eaton Counties, and at the
that she was quahfied to teach in the common schools.
She engaged in teaching in this county, and con-
tinued at it until her marriage.
Mr. and Mrs. Allen settled on 80 acres of the old
homestead on section 19, Emerson Township, and
resided there until the spring of 1882, when they
moved into their magnificent residence on section 29.
This dwelling was planned and built by the owner,
and does credit to his taste. They have been the
parents of seven children, of whom ^st. are living:
Ella J, born April 8, 1863; Ernest R., April 10,
1867; Percy C, Jan. 21, 1877; J. Alton, Feb. 17,
1879; Blanche G., Jan. 21, 1883. Ray P. was born
Feb. I, 1873, and died May 5, 1874; Pearl was born
June 7, 1876, and died July 13, the same year.
Mr. Allen now has 240 acres in his farm, with 170
acres under high cultivation. His place is one of
the model farms in the county. He is personally
popular, and has held the office of Assessor for six
years. In politics he is a liberal Republican.
oseph Scudder, farmer, section 18, Lafay-
ette Township, is a son of Embree and
Rebecca (Every) Scudder, natives of New
Yoik. They were engaged in farming in that
State until the year 1835, when they came to
Lenawee County, this State, and located on 80
acres. They afterwards removed to Ingham County,
where Mr. Scudder died June 11, 1861, and where
Mrs. Scudder still resides. Joseph was born April
13, 1 83 1, in the State of New York. At the age of
2 1 he began farming on his own account, and mar-
ried Mahala Every, who was born in New York, the
daughter of Abram and Charlotte Every, also natives
of New York. In 1853 he removed to Ingham
County, this State. Mrs. Scudder died in 1861, and
in 1863 he married Elizabeth Every. In 1879 he
came to Gratiot County, and purchased 100 acres of
land. He has improved 54 acres of this.
While in Ingham County Mr. Scudder held all the
township offices at different times, except that of
Clerk. He was Supervisor for six years. In Lafay-
ette Township he enjoys the respect and confidence
of all who know him. He is a member of the Ma-
sonic Order, and affiliates with the National party.
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.rederick Homister, farmer, section 10,
o North Star Township, was born 'in Meck-
lenburg, Germany, Oct. 15, 1834. He is a
'*son of Christian Homister, native of the same
counlry in which the son was born, and who,
with his wife and two children, emigrated to
America and located ten miles west of London, Can-
In 1857 the family moved on a farm, in the neigh-
borhood of their first location, and here Frederick as-
sisted his father and attended the common schools
until 1866, when he came to Wyandotte, this State,
and remained 18 months, occupied in hauling the
rock to pave Michigan avenue, and then returned
to Canada. In 1876 he returned to this State and
located in this County, and has constantly resided
here ever since. On his return, he brought a steam
saw-mill with him, erected it on his farm and oper-
ated it continually until the present time. It has a
35-horse-power engine, with boiler 12x4 feet and
containing 10 six-inch flues, and does excellent work.
Mr. Homister was tnarried Dec. 24, 1856, to Miss
Mary L., daughter of James Turner, deceased, and
12 children have been born to their union, namely :
Emma (Goodhall) Charles, John W., Rosa (White),
Sarah A. M., Minnie E. C, Frederick L., Frank W.,
Mary E. L., James H., Nelly A. and Hattie V.
The father of Mrs. H. died in the fall of 1862;
her mother is still living, with the son, at an ad-
vanced age.
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bshua M. Davidson, farmer, section 25,
r- Elba Township, is a son of John L. and
Mary R. (Merritt) Davidson, natives of
Ohio. Mr. Davidson, Sr., was a farmer by oc-
cupation, and died in Ohio, March 12, 1873.
Mrs. Davidson came to Gratiot County the
same year. The son was born April 23, 1837. At
the age of 20 he began to work at the shoemaker s
trade, which he followed for 15 years. At the age
of 25 he was united in marriage to Elizabeth Bell,
daughter of John and Marilda (Mead) Bell. Mr.
Bell was engaged a portion of his life as a minister
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GRATIOT COUNTY,
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of the gospel, and a portJbn in the tannery business.
He died in 1878. Mrs. Bell died in 1867. They
were both natives of Ohio, born in Richland and
Huron Counties, respectively. Mr. Davidson came
to Gratiot County in 1880, and located on a tract of
40 acres, 1 8 of which are now well improved. Mr.
and Mrs. Davidson are the parents of four children,
— Rosa B., Mary V., Allena L. and Minta M.
Mr. Davidson enlisted in Co. C, 65 th Ohio Vol.
Inf., Oct. 12, 1861. After his muster in, he went
with his command to Louisville, Ky., arriving in De-
cember, and was assigned to Gen. Wood's command.
Losing his health and becoming unfit for duty, he was
discharged, Aug. 6, 1862. He was sent to Camp
Chnse, Ohio, and thence went to his home in Huron
County. He is a member of the G. A. R., and of
the L 0.0. F. Politically he is a Republican. Mrs.
Davidson is an active member of the M. E. Church.
^Ibro Curtiss, farmer on section 12, Emer-
son Township, was born in Wyoming Co.,
N. Y., Oct. 17, 1839 ; and is a son of Wat-
erman F. and Sylvia (Cronkhite) Curtiss. The
former was a native of Massachusetts and of
English descent. He followed farming in the
State of New York until 1859, and then came to
Ionia Co., Mich., where he died, six miles from the
city of Ionia, Aug. 2, 1861, at the age of 55. Mrs.
Curtiss, the daughter of Jacob and Basheba (Surdam)
Cronkhite, was bom in Otsego Co., N. Y., Nov. 18,
1806. When 10 years old she came with her parents
to the ** Holland purchase," and lived and was edu-
cated in what is now Wyoming Co., N. Y., where she
was also married. At the age of 77, and in compar-
atively good health, she now lives in Emerson Town-
ship with her children.
The subject of this sketch passed his youth in at-
tending school and working on his father's farm. In
February, 1862, he came with his mother to this
county, and entered 80 acres of land in Emerson
Township. He has since added 120 acres; and of
his whole farm, 140 are well improved. In place of
the dense forest, he has now a fine farm, and very
large and convenient farm buildings, his dwelling
alone costing $2,000. Before making these improve- ments, however, he spent nearly two years in the ser- vice of his country. He enlisted in Co. A, 8lh Mid Vet. Vol. Inf., Dec. 29, 1863, and served under Co Ely, in the Army of the Potomac. He participate^ in all the battles of that army during the campaig of 1864-5. At the battle of the Wilderness, Jun 6, he was wounded in the right arm by a ball ; an( at Petersburg he was struck by two spent balls, on entering the foot, and the other between the shoul ders. He was discharged at Detroit, Aug. 14, 1865 after an honorable service. He was united in marriage, June 29, 1876, at Si Louis, to Lucy L. Woodward, daughter of Allen an< Almira (Lewis) Woodward, narives of New Yorl Mr. Woodward enlisted in a New York regiment i 1862, and served till the close of the war. Lucy wa bom in Erie Co., N. Y., Sept. 20, 1857, and cam with her parents when three years old to Washtenai Co., Mich. One year later her mother died, and he father returned to Erie County. After four yeai they came to Ionia County, and then, in the sprin of 1873, he came to Gratiot County and located on fann of 40 acres. Mr. and Mrs. Curtiss have two children: Blanch A., born April 11, 1877 ; and Roy W., born March i 1882. They are members of the Baptist Cliurcl He has held several school offices in his district, an votes with the Republican party. i eonard H. Bandall, farmer, section \ It Lafayette Township, is the son of Isaac t and Mary (Webster) Randall. They wei natives of Vermont, where they followed farn ing until 1839. Mr. Randall died in Veniion and Mrs. Randall died in Washtenaw Count this State, in 1 849. Leonard H. was born March 1834. He left home when 15, and worked by tl month until June 9, 1857, when he married Eaii J. Burgin. She was born June 9, 1841, and was tl second daughter of Ebenezer H. and Sophronia i (Keneson) Burgin, natives of Vermont. When Mr. Randall first located here, he enten 80 acres, but he has since added 80 acres to tha Of his 160 acres, 60 are now well improved. ] 1875, he built his neat dwelling-house and his laq barn. Mr. and Mrs. Randall are the parents of sevi V- ■X^^O!]>:ti«N>~ .,.^:::>^-i Digitized by Google r^^^ T ■A7/- m r \> children : George W., Eugene A., Fred A., Hattie A., ft Mary S. (died March 7, 1869), Eddie C. and Minnie •; S. Mr. Randall has been Highway Commissioner I in his township, and has been Pathmaster for a A number of years. He is a National, in politics. He ^ and wife are consistent members of the Baptist Church. illiam Kipp, druggist,Brecken ridge village, Wheeler Township, is a son of John and Elizabeth A. (Leamon) Kipp, natives of Dutchess Co., N. Y., and Frederick Co., Md. Mr. Kipp, Sr., was by occupation a farmer, and came to Michigan in 1861. He first located in Genesee County, afterwards coming to Gratiot County, locating in Pine River Township. William Kipp was born March 4, 1846, in Frederick Co., Md., and came with his parents to Michigan. At the age of 16, he commenced teaching school, having received his own education at home. In 1877, he engaged in mercantile life, in Breckenridge, now keeping a full line of drugs and groceries. Feb. 13, 1870, he was united in the bonds of matrimony to Sarah M. Swawze. They have now a family of four children: Edith A., George, Chariie J. and Albert S. Mr. Kipp is an enterprising man, and well liked by all who know him. He was elected School Inspector in 1883, for a term of two years. Polirically he is a Republican. <«I]ll:<DIl^:>r GRATIOT COUNTY. 267 rs -r • ;-5 ^ 1 heron L. Knapp, farmer on section 14, Ar- cada Township, was born in Geneva, Ash- tabula Co., Ohio, Aug. 25, 1853, and is a son of Lucius C. and Mary (Searles) Knapp. Lucius Knapp is now a residetit of Live Oak, Fla., and his occupation in life has been car- pentry. His wife died in Arcada Township, this county, Sept. 17, 1858. When the subject of this narrative was nine months old his father took him to the State of Pennsylvania, afterwards moving to this State and county, where he settled on section 25, Arcada Township, in 1854. They were one of the very first families to locate in Arcada. After the death of his mother, Theron was taken by his father to New York State, where he lived with an UDcle until ^o years old. He then re- turned to his father in Michigan. Two years later the latter moved to St. Louis, where Theron lived with his father until 2 1 years of age, and where he was educated, in the graded schools. At the age of 22 he engaged for two years with J. R. Livingston in the capacity of salesman for his pumps. He then began to cultivate the farm of 92 acres on section 14, Arcada Township, which had been willed to him by his mother in October, 1857. When he began, the land was all wild and covered with timber. He now has 45 acres in good condition for tilling, and good farm buildings. He has con- siderable stock on his place and on the uncleared portion of his farai is some valuable timber. Oct. 23, 1880, he was married, at St. Louis, to Miss Elizabeth Fry, of German descent. She was born in Green Co., Penn., Aug. 11, 1855, and came to Mich- igan, 1865. Mr. and Mrs. Knapp have one son, Al- bert, born June 15, 1882. Mr. K. is in politics a supporter of the National party. He has been Over- seer of Highways, and is now School Director. Mrs. K. is a member of the Christian Church. ohn H. Durkee, farmer, section 11, Arcada 1^ Township, was born in Rutland Co., Vt , Feb. 21, 1820, and is the son of Elias S. and Betsy (Sweet) Durkee, naUves of New York, and of English and German extraction. They followed farming, and lived most of their lives in New York. John's father dying in 1827, he was early left to himself in learning the ways of the cold world, being the oldest of the children. He lived for four years with a gentleman in the neighborhood, and then returned home, working at various things for a time. He then once more worked for a neighbor of his mother's, and his time was thus spent, on a fann in summer and in the mills in winter, until his marriage. Feb. 20, 1840, in Orleans Co., N. Y., he formed a life partnership with Jeannette, daughter of Peter and Sarah Helms, natives of Germany. She was born in New York State, Dec. 17, 1819, and died April 25, 1853, having been married 13 years, and leaving to Mr. Durkee four children, none of whom are now living. He was again married in Lenawee Co., K^ A r ^^-VVi^T^-rr;^ ■^<-D!l^^^DI1v>'^ V>/ V '^^ Digitized by Google ^y^rm<^ 268 GRATIOT COUNTY. rz.-. ^im^^\ ^ 1 Mich., July 26, 1857,10 Mrs. Philena (Nevins) Mont- gomery, daughter of Nathan and Martha (Smith) Nevins, natives of New York State. She was bom in the vicinity of Buffalo, in that State, March 17, 1832. She lived with her parents until her first marriage, and by this she has one daughter: Lillie, born Sept. 21, 1855, Mr. and Mrs. Durkee lived in Lenawee County until the spring of 1883, when they came to Gratiot, and purchased 80 acres. They have during their brief residence here won hosts of friends, and are esteemed as worthy citizens and kind neighbors. They have had four children, two of whom are living: Anna, born Dec. 24, 1867, Fred, bom Nov. 21, 187 1, Clara A., bom March 15, 1859, and died Sept. 20, 1882, Ida M., born Oct. 11, 1863, and died April 22, 1865. They are members of the M. E. Church. Politically, Mr. Durkee is a Republican. Jeremiah Dancer, farmer, section 21, Wheeler Township, was born in Jackson, Mich , July 16, 1849, and is a son of John and Jane (Powell) Dancer, natives of Steuben Co., N. Y. They were farmers, and came to Livingston Co., Mich., in 1843. They after- wards removed to Jackson County, whe«e Mr. Dancer died, in 1867. Mrs. Dancer is still living, in Wash- tenaw County, having married Nor. H. Newton, in 1875. Jeremiah left his home in 1873, and engaged in farming, which he has followed ever since. In the spring of 1877, he came to Gratiot County, locat- ing on 80 acres, on section 10, Wheeler Township. Here he lived three years. Returning to Jackson County, he farmed there for one year, then sold his farm, and came once more to this county, settling on 40 acres on section 34. He was married, Nov. 6^ 1877, to Harriet, daughter of Wni. R. and Cornelia (Vedder) Bradford, natives of Jackson Co., Mich., and of New York, respectively. Mr. Bradford is a farmer by occupation, and came to Gratiot County in 1870. He settled on 160 acres on section 17, but has sold all but 40 acres. Mr. and Mrs. Dancer are the parents of two children : Freddie and Florence. In politics, Mr. Dancer is a Republican. -t3=H=^4-f«- ames Turner, farmer, section 10, North Star Township, and one of the early set- tlers of the township, and whose success is attributable to his own indomitable energ)% was bom in Mecklenberg, Germany, June 4, 1849. He.is a son of Joseph Tumer, deceased, who emigrated to America with his family in 1859, locating in Canada, where they remained until i860, when they moved to this State, and settled in Lyons, Ionia County. In 1864 they moved to this county, and a year afterward, in 1865, the father died. Mr. Tumer can look back with pride at his victory over difficulty and adversity. He encountered in- numerable trials in the establishing of his home in the woods, a half mile from any road, and in clear- ing his land and during the time procuring the nec- essaries of life, yet triumphed over all. He now owns a farm of 120 acres all under fence, and 75 acres cleared and under cultivation. His residence is a two-story brick, with main building 18 x 26 and wing 17 X 24 feet, and, when compared with the "log cabin " in which he formerly lived, is certainly an emblem of perseverance and energy. His barn, 40 X 62 feet, with 20-foot posts, stands as a monument of the work of his own hands, and is another link in the chain of prosperity indicative of his past labors. Mr. Turner was married Oct. 26, 1876, to Nancy E., daughter of Frederick Huntley, and three chil- dren have been born to this union, two of whom are living, namely : Nellie May and Myrtie Belie. Mrs. Turner came from Canada to this county, in 1874, and followed the vocation of teacher and taught eight terms, and was recognized and acknowledged as a very proficient and successful teacher. Mrs. Turner has a sister, Marie E., who came to this county a year later than herself. She also taught school, but, as she was beginning her third term, her health failed her. She has now been an invalid four years, during which time the farthest she has been from home is two and a half miles. Mrs. Tumer r ^ -^<:myiim^'^ '^.-c^ m^ ^^Xx'J- Digitized by Google y<v- r J <N v./ GRATIOT COUNTY. 269 -^ has live other sisters living, and one deceased, and also two brothers. The mother of our subject is still living, with her children, and has attained the advanced age of 86 years. She is the mother of 1 2 children, of whom James is the youngest. Though she has lived to such an advanced age, she is active as a young lady of 18 ; and even now she practices her idiosyncrasies by going into the field and doing the work of a man, and in the fall of 1882 shucked 500 bushels of corn, unaided by any one. She is aware it is unnecessary for her to do manual labor, yet she possesses the spirit of energy inculcated in the minds of her chil- dren, and cannot remain idle, and prefers outdoor labor to indolence in the house or even household labor. Mrs. Turner's father died Jan. 7, 1882, in the township in which they reside. He was well read in the affairs of the day, informed in ancient and modern history, and respected by all who knew him. His widow, Mrs. Turners mother, still resides in the township to which they came eight years ago. ^^ H|^ eorge B. Burgess, farmer, section 24, Arcada Township, is a son of William and Ruth (Hathaway) Burgess, natives of Ohio (see sketch), and was bom Sept. 8, 1856, in the house he now lives in, being probably the first white person born in Arcada Township. He was the sixth of his father s family, and was bom about a year after the family came to this county, in the third log house in the township. For several years after his birth, his parents were obliged to fol- low a trail to get to the nearest town, which was at that time Maple Rapids. It required years of close economy and hard work before they could, through the produce of their farm, obtain many of the comforts of life. Until 23 years old, George worked for his father, and attended the common schools as he best could. March 4, 1879, he was united in marriage to Martha M., daughter of Daniel and Lorana (Silver- thom) Tyrrell, natives of Ontario, Canada. They followed fanning, and came in 1867 to Arcada Town- ship, where Mr. Tyrrell died, March 2, 1872, and Mrs. Tyrrell, July 16, 1878. Martha M. was born in Ontario, Canada, Jan. 29, 1858, and when eight years old came to this county with her parents, Jind lived on section 26, Arcada Township, until their death. She then lived in the family of William Burgess, until her marriage. Mr. and Mrs. Burgess settled down on the old homestead, and now live in the log house built by his father. He now owns 40 acres on section 24. They have two little ones : Elnora, born Jan. 5, 1881, and Ruth L., born June 5, 1882. In politics, he is a Republican. t 7r eorge W. Skinner, farmer oh section 8, Emerson Township, was bom in Morrow Co., Ohio, Feb. 14, 1832; and is a son of David and Abigail (Bewley) Skinner, natives of Ohio, and of English and German extrac- tion. They followed farming, and died, the father in Van Wert Co., Ohio, in 1879, aged 81 ; and the mother in Morrow Co., Ohio, in August, 1852, aged 51. The subject of this sketch passed his youth in at- tending the common schools, and in working on his father's farm. When of age, he came to this State, and for three years was engaged in fishing in Lake Huron and Saginaw Bay. He then went to Livings- ton County, and thence to Denver, Col. For the next 15 months he worked in the gold mines in Cal- ifomia Joe Gulch, Buckskin Joe Gulch, and at the head waters of the Arkansas. Sept. 8, 1 861, he en- listed in Co. €, ist Col. Cav. He served in the westem army, and was engaged generally in skirmish- ing with the enemy, in Texas and all through the Southwest, in guarding the Unionists, and in keeping the Indians quiet. He escaped unhurt, and was honorably discharged Dec. 3, 1864. Returning to this State, he went first to Livingston County, and then to Saginaw, and in the spring of 1865 he came to Gratiot County, and located on 80 acres in Bethany Township, which he had entered in 1856. In that township. May i, 1866, he was united in marriage to Harriet A., daughter of John and Eliza (Knapp) Mull, natives of New York, and of New England parentage. She was born in Ossiar., Liv ingston Co., N. Y., Jan. 21, 1842, and when only two years old she went with her parents toTmmbullCo., Ohio. Two years later they came to I^nawee Co., f c •I r^ I ^X^ x-y y v^ <:Da>:iIIls>-^ '^:»->^ W?^!^ Digitized by Google m ^ ^ >: V 4 <>l \ ^ 370 ■-n^<:iDIl>:DIl^.> ■^N ■-^.€^XA^ GRATIOT COUNTY, Mich., where she commenced attending the public schools, and when she was 10 years old they moved again, to Ingham County, where she completed her education. The family came to this county in i86r. Six years after marriage, Mr. and Mrs. Skinner moved to Emerson Township, where he purchased 80 acres. He has since sold 40 acres, and bought 40 more on section 5. Most of his land is now nicely .improved. He has just completed a large barn. They have two children: Frank, bqrn April i, 1867 ; and Jennie L., born Aug. 5, 1870. Mr. Skin- ner is a member of Emerson Lodge, No. 377, I. O. O. F., and of Moses Wisner Post, No. 101, G. A. R. In politics he is an earnest and influential Repub- lican. ^^^%¥- iilliam W. Wooley, farmer, section 34, Elba Township, is a son of James and Margaret (Chandler) Wooley, natives of New Jersey. Mr. Wooley, Sr., was a shoe- maker by trade, and removed to Gratiot County in 1855. The subject of this sketch was born Sept. 27, 1830. At the age of 14 he left home, and worked at farming and other things, until 1862. August 1 6th of that year, in Clinton County, he was married to Mary M. Dodge. His father, when he came to Gratiot, located 320 acres of Government land on section 34, Elba Township, and he subsequently gave 80 acres to each of his children. Mr. Wooley has brought 65 acres of his farm to a state of good cultivation. In 1877 he erected a substantial barn on his place. He has also a very neat dwelling-hcuse. Mrs. Wooley was the eldest daughter of her father's family, and was bom April 6, 1 841, in the State of Vermont. She was the first school-teacher in Elba Township, and taught in District No. i. She after- wards taught several terms of school. Mr. and Mrs. Wooley are the parents of two children : Maud E. and Maggie D. Another child, Minnie B.,died Aug. 28, 1870, aged two years, three months and one day. Mr. Wooley enlisted in the service of the country during the rebellion, but was discharged for disability before entering the field. In civil life he has held a number of ix)sitions of honor and trust. Soon after his township was organized, he was appointed Treasurer, and he was afterwards elected several times to the same office. He has held the office of Highway Commissioner, and in 1870 he was appointed Supervisor of Elba Township to fill a vacancy. He has also held the office of Assessor in School District No. I. Politically he is a staunch Republican. ferry Shaver, farmer, on section 17, Enier- \ son Township, was born in Delaware Co., N. Y., Nov. 19, 1822, and was a son of Jacob I. and Sally (Kinch) Shaver. The former was a native of Delaware Co., N. Y., and of Dutch descent. He came to this county in 1856, locating a land warrant of 80 acres on section 2, Emerson Township, and remained here till his death, July 21, 1873, at the age of 77 years and three months. Mrs. Sally Shaver was a native of Con- necticut, and of New England parentage. She was married to Mr. Shaver in Delaware Co., N. Y., and died in Emerson Township, at the age of 77 years and two and a half months. At the age of two, Jerry went with his parents to Seneca County, where he lived until 16, attending school and working on his fathers farm. Thence he went to Steuben Co., where. May 30, 1846, he was married to Ursula, daughter of Richard and Cordelia (Reid) Sawtell, natives of New England, and of English descent. Richard Sawtell was a physician, and died in the Slate of New York, in 1842; Mrs. Sawtell died in Gratiot County, in 1865. Ursula was born in Chenango Co., N. Y., Sept. 27, 1826. Receiv- ing her education in her native county, she went to Steuben County in 1842. Six years after marriage, Mr. and Mrs. Shaver came to this State, and settled first in Ingham County, where they lived unul the fall of 1856. They then came to Gratiot County, and located on section 17, Emerson Township, securing 80 acres by the Graduation Act. He has since purchased 40 acres additional, and has 70 acres well improved. They came into a dense wilderness, and suffered severely during the "starving time " of 1857. They are the parents of four children, two of whom are living: Herman D., born March 2, 1848, J. Frank, born June 2, 1864, William, born Jan. 10, 1847, and died Feb. 7, 1847, Mary A., born July 21, 1850, and died Jan. 10, 1870. In politics Mr. Shaver is a liberal Democrat. ^ /Ts s./ ^<:m^my- Digitized by -#f^V^ Google / \ r ■ ; •*• Digitized by Google ^ct^^.^A£l. \^A^0^^ Digitized by Google t ■^v -rW^ ■ST 4)^f^V:|^ sJ» A V > J ■^ ;< V G:^^ no T CO UNTY. '^^ ^ <xy>- ' 0O6 " j^auiel Griffeth, farmer on section 8, Emer- son Township, was born in Montgomery, N. Y., Jan. 9, 1820, and is a son of Dan- iel and Lois (McNeal) Griffeth, natives of Wales and Scotland, respectively. They were married in Canada, and he became a hatter by trade. In 1814 they removed to the State of New York, where the mother died, in 1835. The father afterwards came to this State, and he died in Man- chester, Washtenaw County, in 1847, d^i years old. The subject of this sketch attended school and worked on a farm until 20 years old, when he set out alone for Michigan, and located in Marshall. He afterwards returned to New York for one year. In May, 1846, on the breaking out of the Mexican war, he enlisted as a private in Co. F, 8th New York Inf., under Gen. Worth. He participated in three actions : Cherubusco, Aug. 19, 1847; Molino del Rey, Sept. 8, 1847, and the storming and capture of Mexico, Sept. 12, 13 and 14, 1847. He escaped unhurt in all these engagements, and was honorably discharged with the rank of Orderly Sergeant, in August, 1848, at Jefferson Barracks. Returning to Michigan he engaged in farming in Oakland County. Dec. 19, 1849, he was united in marriage, in Inde- pendence, that county, to Nancy M., daughter of Hiram and Betsy (Placeway) Burgess, natives of New York and Vermont. They came to Oakland Co., Mich., in 1837, and later to this county, where the father died, April 9, 1879, at the age of 77, near St. Louis. Mrs. Burgess still lives, enjoying a ripe old age of 77, and is active and intelligent. Nancy M. was born in Allegany Co., N. Y., Nov. 4, 1830, and came with her parents to this State seven years later. She was educated in Oakland and Livingston Counties. Two years after marriage Mr. and Mrs. Griffeth removed to Wayne County, and Dec. 18, 1856, they came to this county and entered 80 acres in Pine River Township. Five years later, most of which time they lived in the town of St. Louis, they re- moved to Emerson Township and settled on 120 acres of heavily timbered land. Surrounded by miles of unbroken forest, they encountered many hardships before they finally succeeded in making for themselves a comfortable home. He has added 40 acres to his farm, and of his 160, 100 acres are now admirably improved and cultivated. Mr. Grif- feth is an intelligent farmer, and with his kind- hearted wife deserves this happy home. They have had a large family, and of their 12 children nine are living. Their names and the dates of their birth are as follows: Mary J., Oct. 8, 1852 ; James A., Jan. 3, 1854; Emery L., Dec. 28, 1855; Ann Maria, May 26, 1858; Isadore L., Jan. 22, 1861 ; Hattie A., March 24, 1863; Hiram A., Sept. 26, 1865; Nancy M., Oct. 9, 1867 ; Florence A., June 2, 1870. These three are sleeping their last sleep: Hiram Andrew, bom Dec. 2, 1850, and died March 4, 1852; Daniel A., born June 25, 1873, and died July 3, 1879; and a baby, which died in infancy. Mr. and Mrs. Griffeth are active members of the Baptist Church, she being the first person baprized in Pine River. He is one of the old pioneers who have helped to make Gratiot what it is, and deserves to be remembered by posterity. He built the first frame house north of Pine River, and drove the first team from St. Louis to Midland. In politics he is one of the most active supporters of the National Greenback party. Mr. Griffeth s portrait is given on the opposite page. ^? ordis Smith, farmer on section 27, Pine River Township, is a son of Ira and Zada (Hitchcock) Smith, natives of Connecticut. They removed to New York State, and in 1851; came to this State and county, locating in Pine River Township. The mother is still living in that township. The father died there Feb. 22, 1878, at the age of 85. They had a family of seven. The subject of this biography. Cordis, was the third son of the family, and was born Sept. 7, 1832. Starting out at the age of 20 to make his own way in life, he came West and spent three years in differ- ent States, and then returned to New York. In the fall of 1857, he came to Gratiot County; and for nearly six years following, he was employed in the woods and otherwise. By several different payments, he bought 160 acres of land in Pine River Township, where he now resides. He has now nearly 100 acres well improved. t iff'Vg'^e^^* -^^€^^ .i^^a^ <->nii:<nBy:> A-^:^ •#: vs;^ Digitized by Google 4 ^ '^ *74 GRATIOT COUNTY. ^' ^:;.i^Cv^. April 19, 1864, in Pine River Township, he was married to Mrs. Jane M. (Badger) Rice, widow of Elijah B. Rice, who died Nov. 19, 1861. She was born in Washington Co., N. Y., April 13, 1828, and is the daughter of Samuel and Matilda (Freeman) Badger. They were natives of New York State, and died in Washington County, that State, March 15, 1870, and Dec. 2, 1836, respectively. The daughter married Mr. Rice in New York State, and came with him to Pine River Township, this county, in October, 1854. Their first meal of victuals here was eaten in the woods, and they had to cut their own road from Gen. Ely's, two miles away. Mrs. Smith had by this first marriage one child, George T.,born Sept. 4, 1858. Mr. Smith stands high in his neighborhood, as a farmer and a citizen. He is politically a Repub- lican. dward Graham, farmer, section 30, North Shade Township, is the son of John and Rachel (Dean) Graham, native^ of Ver- mont, from whence they moved to York State and located on a farm in Yates County, where the mother died about 1845, and the father in 1871. The subject of our sketch was born in Yates Co., N. Y., Aug. 20, 1828, and remained at home on the farm until he was 16 years of age, and then lived with his brother until he attained his majority. When 26 years of age he came to this State and lo- cated in Coldwater, Branch County, where he re- mained one year ; then went to Calhoun County and remained there about a year, when he removed to Hillsdale County and engaged himself for a period of two years. Mr. Graham, at this period in his life, concluded to visit the famous Pike's Peak, but after making preparations for the journey, and having started on the same and reached Illinois, he abandoned the idea and returned to this State, locating on 40 acres of land on section 30, North Shade Township, this county, to which he has since added 20 acres. Mr. Graham was united in marriage to Miss Rhoda, daughter of Hiram and Hannah (Cornish) Chappel, July 4, 1853. She was born May 20, 1835, in Yates Co., N. Y. Mrs. (iraham has not known tlie where- abouts of her brother for a number of years. Her mother died in Chenango Co., N. Y., in 1870. Mr. and Mrs. G. have had two children, William H., bom Oct. 17, 1866, and John E., born Aug. 21, 1872. Politically Mr. G. is a Republican. V ,/:^f< :t:i: % uther M. Stites, farmer, section 24, North IJ Shade Township, is a son of Benjamin and j^^'"*^ and Phebe (Nickson) Stites, natives of New j' JLTsey and farmers by occupation, who settled in Fulton Co., Ohio, and afterward moved to [ I enawee Co., Mich., where they yet reside. The subject of this sketch was born Feb. 5, 1858, in Fulton Co., Ohio, and was therefore but four years old when the family moved to Michigan. He mar- ried, Sept. 12, 1880, Miss Effie J., daughter of Luther J. and Amanda L. (Townsend) Brink, and bom \pril 25, 1862, in Gratiot Co., Mich., being one of the first bom in the township of North Shade. In political matters Mr. Stites is a Democrat. Mr. Brink was a soldier in the last war, being a member of the loth Mich. Cav. He died at Camp Nelson, Ky. His widow is yet living, and resides in Nashville, Jackson Co., Iowa. She again married, her present husband being Samuel Evans, of Hubbardston, Ionia Co., Mich. r^^ l^aron Sloan, farmer, section 22, Pine River Ei£J|4 Township, is a son of Thomas and Basheba if (Pitcher) Sloan, natives of Massachusetts. f j^" They first settled in New York State, where the father died. The mother afterwards came to Eaton Co., Mich., where^ she died. Aaron was born in Oneida Co., N. Y., Aug. 10, 181 5. Re- ceiving his education in the common schools, he helped his father on the farm until 20 years old, wher he started out for himself. To aid him in the battle of life, he had nothing but willing hands and a lov- ing wife. At the age of 21, Dec. 24, 1836, in Wat- erloo, Seneca Co., N. Y., he had formed a life part nership with Caroline C, daughter of William anc Sally (Hall) Taylor, natives respectively of Nev York State and Vermont. Mr. and Mrs. Taylor set ^nf• X / >—,7«, '- im: ■/ " Digitized by Vx/ 'J Google V /C -r<^I]ti:<lll]s>^- r--::-':^ ^ X ^ y GRA no T CO UNTY. y ^ / tied in New York, and afterwards came to Michigan ; and in 1879, came to Gratiot County, where he died, in the fall of 1880. She still survives, at the age of 85. After marriage, Mr. and Mrs. Sloan removed to Ohio, and in 1846 they came to Eaton Co., Mich. Five years later, they removed to Montcalm County, and in February, 1854, he came with his family to Gratiot County. He bought 160 acres of land in Pine River Township, where he now resides. He has sold part of his farm, and divided part among his children, and now retains 60 acres, all of which is nicely improved. In August, 1862, he enlisted in the 26th Mich. Vol. Inf., and served eight months, on detached ser- vice. He was discharged at Detroit, on account of sickness. Mr. and Mrs. Sloan have had ^vt children, three surviving: William H., Hiram L. (deceased), Almi- ra (deceased), Aaron F> and Rachel E. Hiram L. enlisted in the same regiment with his father, after- wards re-enlisting in the 8th Mich. Vol. Inf., and died at Fairfax Seminary, Va. Mr. Sloan has held the office of Highway Commissioner four years. In politics, he is a supporter of the National party. I : 3» i j i »C : > illiam Towner, farmer, section 24, North Shade Township, is a son of Daniel and Polly (Budlong) Towner, natives of New York State, the latter of New Lebanon. The family were engaged in agricultural >ursuits. The subject of this sketch was bom May 19, 1805, in Steuben Co., N. Y. ; he lived with his parents until his mothers death, which occurred in 1855, in Livingston Co., Mich. His father died in 1864. William came to this county in 1853, locating on section 24, on a tract of 80 acres of wild land, where he now has 60 acres well improved, and furnished with a good residence, a large bam, etc. His house he erected in the summer of 1880, at a cost of nearly$1,000.
Mr. T. married Miss Diana, daughter of Jacob and
Sarah (Kinney) Brink, the former a native of New
Jersey and the latter of Connecticut. He died Sept.
25, 1879, and she, Jan. 5, 1857, both in this county.
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Mr. and Mrs. T.'s two children have been, Herbert ^j>,
M., bom in 1847, and Elvertes, in 1849, and died in (:,^
April, 1863. Mrs. T. is a member of the Second- *;N^
Advent Church, and Mr. T., in politics, is a Repub- J
lican. Herbert has charge of the farm. He married
Miss Mary B., daughter of George and Barbara
Franks. Their two children are, Verna F., born in
September, 1877, and Erma V., Feb. 19, 1881.
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Ifred J. Brooke, farmer and mechanic, sec-
^^ tion 30, Emerson Township, was born in
Wayne Co., Ohio, Jan. 23, 1833; and was the
son of John and Sarah L. (Brenholtz) Brooke,
natives of Lycoming Co., Pa., of English and
German descent. The father was a carpenter and
joiner, but afterwards engaged in farming in Ohio,
in which State he died, at the age of 57, and his wife
at the age of 67. Alfred J. lived the first part of his
life in Wayne and Wood Counties, in Ohio. At the
age of 16 he was apprenticed to the blacksmith s
trade, under his brother. After serving his time he
went into partnership with his brother; and three
years later he bought him out and conducted a large
shop on his own account, until 1864. In the spring
of 1865, he came to this State and county, and pur-
chased 40 acres of wild land on section 30, Emerson
Township. Here he erected a small house and shop
in which to carry on his trade ; but one year later he
was prevailed upon to move to the village of Ithaca.
He worked at his trade there some time, and then,
in the spring of 1878, returned to his farm. He
has since devoted himself to the improvement of his
farm, and now has 80 acres, of which 60 are well
improved.
March 8, 1856, he was united in marriage at Free-
port, Ohio, to Louisa, daughter of Joseph and Sarah
(Tucker) Kelly, natives of Rhode Island, and of
English and Irish extraction. They moved after
marriage to Sandusky Co., Ohio, where Louisa was
born. May 4, 1835. At the age of 16, she removed
with her parents to Wood Co., Ohio, and there lived
until her marriage. Mr. and Mrs. Brooke have had a
large family, — 12 children; but the death roll is
longer than the list of the living, and only five now
survive: Dora S., born Aug. 24, 1858; Louis Am-
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bTX)e, May4, i860; Alfred J., Jan. 30, 1867; Lillie
M., Nov. 15, 1868, and Emma L., Sept. 8, 1873.
Those who are now sleeping their last sleep are as
follows: a baby which died in infancy; Etta B., born
Nov. 28, 1863, died Feb. 18, 1865; Alta L., born
May 13, 1862, died May 18, 1862; Joseph M., born
March 17, 1870, died Aug. i, 1870; Wilson, born Jan.
10, 1872, died April 24, 1872 ; Moody, born Aug. 27,
1875, died Sept. 10, 1875.
Mr. Brooke is a member of Ithaca Lodge, No. 1 140,
K. of H., and in politics is an ardent Republican.
Mrs. Brooke is a conscientious member of the M. E.
Church of Ithaca.
^dwin Hopkinson, farmer, section 20, North
Star Township, is a native of Nottingham-
shire, Eng., and was born April 16, 1835 ;
5 S his father was William Hopkinson, also a na-
ii tive of that country. Mr. H., the subject of
J this sketch, emigrated to this country in 1854,
first locating in Lyons, N. Y., then, in 1865, in Han-
cock Co., Ohio, and finally, in 1870, in this county,
where he has since lived, and where he owns 80
acres of good farming land, following agriculture and
raising stock. He was married Jan. 5, 1865, to Miss
Eleanor, daughter of James Turnbull (deceased), a
native of Scotland. She is a native of Wayne Co.,
N. Y. Their three children are, Mary E., Elmer E.,
deceased, and William V.
Politically, Mr. Hopkinson is a Republican.
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homas Qrover, a prominent farmer, resid-
ing on section 2, Arcada Township, was
born in Southampton, Eng., June 17, 1839;
and is the son of Thomas and Maria (Sher-
wood) Grover, natives of Yorkshire, Eng.
Thomas Grover was by occupation a carriage
smith, and came to this country in 1850, locating in
New York State. Two years later he came to this
State, where he died, at his home on section 2,
Arcada Township, Aug. 27, 1877, at the age of
65. His wife now resides at St. Louis, in this
county, at the age of 68.
The subject of this sketch was 1 1 years old when
I
his parents came to this country, and he came with
them to Lenawee Co., Mich. At the age of 17, he
left the parental roof and worked as a laborer on va-
rious farms until he brought up in Linn Co., Iowa,
where, at Paris, Sept. 29, 1865, he was married to
Margaret, daughter of Alexander and Phebe (Sutton)
Bumham, natives of Ohio. They moved to Kansas,
and Mr. Burnham enlisted in the Mexican war. He
died in April, 1848. His wife now resides in Kan-
sas, aged 58.
One year after marriage, Mr. and Mrs. Grover
came to Michigan, shortly after returning to Linn
Co., Iowa, where he was for a time in the cattle bus-
iness. He bought and sold two or three farms, and
finally, in the winter of 1878, came to Gratiot County
and settled on 90 acres of his father s place. He
afterwards purchased 40 acres, and now has in the
aggregate 1 30 acres of good farming land, partly im-
proved. He has erected a neat residence, and a
substantial barn.
Mr. and Mrs. Grover have had nine children,
eight of whom survive : P. Maria, Howard A.,
Anna M., Mary A., Frank N., Thomas S., Perry M.
and Henry H. (deceased). In political sentiment,
Mr. Grover is not partisan, but at elections he exer-
cises his best judgment.
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Charles C. Proctor, farmer, section 31,
North Shade Township, was the son of
Jeremiah and Marindia (Carnahan) Proctor,
narives of New York, where the mother died.
The father died in Clinton County, this State,
ii^ 1855, at the advanced age^f 76 years.
The subject of our sketch was bor« Dec. 9, 1815,
in Brookfield Co., N. Y., and remained under the
parental roof-tree until he was 29 years of age. He
followed the trade of a cooper until he moved to
Ionia County, this State. Here he remained for
eight years, when he came to this county and located,
in the year 1855, on 85 acres of land on section 31,
North Shade Township, and now has 55 acres of the
same under good improvement.
Mr. Proctor may be considered one of the pioneer
settlers of the county, and as such he has certainly
experienced numerous trials and difficulties in build-
ing a home in the then wilderness and battling and
overcoming all obstacles.
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He was married to Miss Charlotte E., daughter of
John and Julia (McLeod) Nichols, April 18, 1844.
Mr. Nichols was a native of Germany, who emi-
grated to America at an early day. He was captured
by the British and taken to Canada, and escaped by
swimming the Niagara River. He died in the State
of New York. Mrs. Nichols was a native of New
York, and died in the same State.
Mr. and Mrs. Proctor are the parents of two chil-
dren : one son, George W., married Miss Lydia Ka-
nounse, and one daughter, Julia M., now Mrs. Will-
iam Burk.
Mr. Proctor has been Justice of the Peace five
years, and also Supervisor. The wife and husband
are members of the United Brethren organization,
and are respected and esteemed citizens of the town-
ship. Mr. P. is a Republican in political opinion.
iilliam Stonebrook, farmer, section 24,
North Shade Township, is a son of
Frederick and Sarah (Cline) Stonebrook,
natives of Union Co., Penn., who came to
Ohio in the year 1822, settling first in Wayne
County and afterward in Holmes County, where
Mr. S. died. He was a carpenter by trade. Mrs. S.
died in Indiana.
The subject of this sketch was born Aug. 18, 1822,
in Union Co., Penn. When he became of age he
engaged in chopping for about six months in In-
diana ; he then returned to Ohio and married ; he
moved from Wood Co., Ohio, to Gratiot Co., Mich.,
in 1865, locating on section 24, North Shade Town-
ship, on 160 acres of wild land; of this he has now
95 acres in good cultivation. In the summer of
1883 he erected a fine brick house, at a cost of
nearly $2,000. Mr. Stonebrook married Miss Belinda, first daughter of Michael and Hannah (Shotwell) First; her mother was a native of New Jersey, and her father of Penn- sylvania : the latter was a brewer by occupation, but also followed agriculture to some extent. -After the above marriage, Mr. and Mrs. F. moved from Penn- sylvania to Ohio, locating in Wayne County in i8r9 : they are both now deceased. Mrs. F. died in Wayne Co., Ohio, and Mr. F. in Gratiot Co., Mich. The children of Mr. and Mrs. Stonebrook are, m iL''J!5rf ^^^f^ ■^^' James H., Elizabeth, Michael, Sarah, Samuel J., Adolphus A. and Margaret J. The parents are members of the Baptist Church. Mr. S. has always been a Democrat in political views, and he has held T the office of Assessor of his school district. \6) '^^MAon/^^ ^^^i^W^ rs. Catharine A; Walker, residing on sec- tion 25, Arcada Township, was bom in Stark Co., Ohio, Jan. 8, 1828 ; and is the ^)^ ^^ daughter of Abraham and Barbara (Myers) Van Nostrand, natives of Pennsylvania and of German descent. Abraham Van Nostrand re- moved to Stark Co., Ohio, and afterwards to Tuscar- awas County, where he died, in 1843. Mrs. Van Nostrand died in the same county in 1844. Cath- arine was thus left an orphan at 15, and she went to live with her uncle. Sept. 20, 1848, she was united in marriage to John, son of Silas and Margaret (Peo- ples) Walker, natives of New England, and of Irish and English descent. Silas Walker was a mechanic and farmer, and removed to Ohio, where he died a number of years ago, and his wife in 1 87 9, at the advanced age of 81. John Walker was born Sept. 28, 1824, and passed his boyhood days on his father's farm in Tuscarawas Co., Ohio. Here he was mar- ried. Fifteen years after marriage, and eight years after they came to Michigan, he enlisted, Oct. 4, 1864, in Co. C, 29th Mich. Vol. Inf. He died in the service, July 6, 1865, at Anderson, Tenn. He had made a settlement in 1856, on 80 acres on section 25, Arcada Township, and since his death, with the aid of her two sons, she has nicely improved 70 acres. Samuel L. Walker was born April 25, 1857 ; and Joshua C. was bom Aug. 4, 1859. They are energetic and in- telligent young men, and likedby all who know them. Mrs. Walker has three other children living: Celes- tia Pickard, born Sept. 27, 1849, and now residing at Mt. Pleasant, Isabella County ; Henry L., bom Sept. II, 1852, residing at the same place; and J. Albert, born June 12, 1864, also residing at Mt. Pleasant, Mich. She has lost three children : Mary M., born March 31, 1850, and died Sept. 25, 1852; Margaret J., bom Dec. 12, 1854, and died March 26, '^^.- 4^^f Digitized by Google :^t2'* ■t=rv<^?nD>;mi^>^r^^^ :^Z^ > i 278 GRATIOT COUNTY. 1856; and Silas M., born Juue 11, 1861, and died Nov. 19, 1865. Mrs. Walker is a member of the Christian Church, to which also her husband be- longed. He was politically a Republican. f I m jlfred A. Gross, farmer, section 2, Hamilton Township, is a son of Jonah Gross, de- ceased, a native of the State of Massachusetts and where, in the town of Enfield, Hampshire County, Alfred was born, April 14, 1831. The father removed his f«imily to Oakland County, this State, in 1831, and here the son assisted on the farm, attended the common and subscription schools, receiving a fair education and developing into man- hood. Mr. Gross was married April 15, 1857, to Rhoda M., daughter of Anson Dayton, deceased, and in 1 865 came with her husband to this county. They located in the woods and commenced the arduous task, so familiar to the old pioneers of the county, of improving their land for a future home for themselves and children. Their trials and troubles were similar to those of many others identified with the early set- tlement of the county ; energetically did they, each one doing his or her part, battle against all difficul- ties, until at last victory was theirs, and they are now the possessors of 320 acres of land and have four children : Frank J., Warren E., Carrie W., and Lucy, to gladden their hearts in their declining years. In addition to his landed estate Mr. Gross owns and runs a shingle mill on section i, Hamilton Town- ship. Politically, he is a zealous Democrat. I illiam Burgess (deceased) was a farmer on section 24, Arcada Township; was born in New York State March 21, 1828, and died in Arcada Township, March 22, 1880, leaving a mouraing wife and a family of four. His early boyhood was spent on the farm in his native State, and when a young man he went to Lawrence Co., Ohio. He afterward went to Wood County, in the same State, where he was mar- ried, May 20, 1842. He came to Gratiot County in 1854, and was one of the very first settlers in Arcada Township, build- ing the third log house in that township. He was a progressive farmer, an upright citizen, and a pleasant neighbor. He was a member of the Christian Church and a supporter of the Republican party. He was often chosen to office by his fellow citizens, and al- ways gave satisfaction. His wife, Ruth, tiee Hathaway, was the daughter of Daniel and Polly (Marick) Hathaway, natives of Massachusetts, and of English ancestry. Daniel Hathaway was by trade a ship carpenter, learning that work in Massachusetts. He moved to Paines- ville, Ohio, below Cleveland, and afterwards to Wood Co., Ohio, where he died about 1852, at the age of 60. Polly (Marick) Hathaway died in the same county, in 1867. Ruth was bom in Geauga Co., Ohio, April 15, 1824, and when 13 years old her par- ents removed to Wood County, where she was mar- ried. Mr. and Mrs. Burgess had a family of eight, four of whom survive: Mary A., bom July 29, 1843; George B., Sept. 8, 1855 ; Willie B., May 4, 1864; and Lora, Sept. 18, 1867. The deceased are: John William, bom May 21, 1842, and died June 11, 1842 ; Lora A., born April 21, 1846, and died Sept. 15, 1857; Rowena, born May 15, 1850, and died April 18, 1870; John A., born May 15, 1850, and died June II, 1879. Mrs. Burgess still survives, and is a member of the Christian Church. ^^^4— ^ A f- '^VS^ , artin Grill, farmer, sect ion 30, North Shade v Township, was born Sept. 15, 1830, in r; a Pennsylvania. His parents, John and r^ ^ Sarah (Funck) Grill, were also natives of ^ the Keystone State, and the former followed the occupation first of butcher and then of cooper and farmer. In 1839 they left Pennsylvania and came to Ohio and lived for one year in Stark County. In 1840 they moved to Summit County, where they H\ed until their death, Mr. Grill dying in 1867, and Mrs. Grill in 1876. Martin Grill remained under the parental loof until he was about 21 years old, when he went to Illinois and for a time was engaged in farming. He spent one year in a saw-mill at Decatur, 111., after which he went to Indiana and stopped with his — -m^^ij^ r ^•7 <mn'^>^ — ^^^ Digitized by Google Digitized by Google ^.^. dl i. >:.' ;: il Digitized by Google ,..yU^. c^(f^.^^fT^. Digitized by GoogI^<^^^ 1^1 1 fl'l Digitized by Google y^i^^'-' GRATIOT COUNTY. ^-^i.'~ «79 ^ f.^ /^ Y .< brother for a short time, and after this he returned to his home in Ohio. He remained at home helping his father on the farm and in the mill until he was about 25 years of age. In the mill, our subject did some of the hardest work that ever falls to man to perform, as the mill was kept running day and night for a great part of the year. He was married to Rachel Ludwick, daughter of Samuel and Mary E. (Dick) Ludwick, natives of Pennsylvania. Mr. Lud- wick followed farming in his native State, and later in life moved to Summit Co., Ohio, where they both passed the remainder of their days, the former dying in 1855, and the latter in 1856. To Mr. and Mrs. Grill have been born ten chil- dren, as follows: Mary S., Hiram W., Amanda E., Eliza J., Henry D., Emma J., Martha, Martin, Charlie W. and Clara E. Mr. Grill came to Gratiot County in 1868 and lo- cated upon section 30, North Shade Township, where he has a good farm. He is regarded as a man of good judgment by his neighbors, and as being a fair, upright and honorable citizen, as is evinced by the people of his district having chosen him as Assessor for 14 terms in succession. Mr. G. has suffered twice from the enmity of the elements. July 3, 1859, the lightning struck and totally demolished his father s barn, the contents of which belonged to Martin. March 12, 1871, his house was burned, and almost all the household goods were also consumed. ••- -#^ -H < J "> * ■^ i-^'j » ohn L. Bichards, farmer, section 33, New- ark Township, was bom July 7, 1844, in Pennsylvania. He is a son of John and Rachel (Fry) Richards, both of whom were natives of the Keystone State, were there mar- ried and resided 14' years. In 1846 they re- moved to Ohio, and there belonged to the farming class. In the spring of 187 1 they came to Gratiot County and settled in the township of Newark, where they srill reside. Mr. Richards was a child of two years when his parents located in the Buckeye State, where he grew to the age of 18 years, engaged in assisting on the farm, and acquiring a fair education in the common schools. Roused to a sense of the necessity pressing ^ upon the authorises of the United States Government under the stringencies of civil war, he yielded to his convictions of duty and enlisted Aug! 6, 1862, in the I nth Reg. Ohio Vol. Inf., and served his country under that enrollment three years. He was in the battle of Hough s Ferry, Tenn., and, while on picket guard at Lenoir Station, he, with 5 1 of his comrades, was captured by the rebels, and conducted to At- lanta, Ga., where they were held two weeks, and then removed to Pemberton Castle, Richmond, and a month later were incarcerated at Belle Isle. They became inmates of the latter place on the first day of January, 1864, and there remained until March 12, when they were transferred to the stockade prison at Andersonville, where their sufferings were in no sense or degree less than those of the myriads who suc- cumbed to the horrors of the place, or of those whose endurance proved equal to such frightful experiences as cannot be equaled on the recorded pages of human suffering. The very name of Andersonville must cause a shudder while rime endures! After seven months of horror they were sent to Savannah, and later to Milan, whence, after a month, they were ordered to be transferred to Blockshire, Ga. While on their way thither the train was intercepted, and 250 starved, ragged, forlorn human creatures, of whom Mr. Richards was one, were paroled and sent to the camp at Annapolis. Two weeks later they were furloughed, and Mr. Richards returned to his home in Ohio. In six weeks he was exchanged and rejoined his regiment. His health was too much impaired for active service, and he was on detached duty until the close of the war. On the expiration of his term of enrollment, he was discharged at Cleveland, Ohio, whence he returned home. Mr. Richards was married Dec. 28, 1865, to Sarah / D., youngest daughter of Asa and Jane (Staples) Richardson. The father was a native of Vermont, the mother of Maine. Of this marriage, four chil- dren have been born : Earl C, Alice I., Tacie A., and Laura M. After his becoming a family man, Mr. Richards continued to reside in Ohio until 1870. In that year, he removed his family and interests to Gratiot Co., Mich., and bought 40 acres of land in Newark Township. Of this he has already cleared and placed 35 acres under creditable cultivation. He is a Republican of unmistakable type, and has served A (V Ky ^ c? c i^m^r^c^ ^<^my'M^- Xi^^ Digitized by LnOOQ IC ^ ■>i-. x-c^ ^<•:DII>:nII^>v -z^-:. K<^. -^f^ 280 GI^A TIO T CO UNTY, I t 1 t I his township in several official positions to which he has been elected. He received an appointment in 1880 to fill a vacancy as Township Clerk, and has been since twice elected to the same incumbency, which he now holds. A branch of the body known as the Union Prisoners of War Association, desig- nated the Camp of Gratiot County, has been estab- lished therein, of which Mr. Richards is President. Himself and wife are members of rhe United Breth- ren Church. 9nry Simmon, farmer, section 16, Hamil- ton Township, is a son of John Simmon (deceased), who resided in Adams Co., Pa., and where the subject of our sketch was born, Aug. 26, 1826. The father moved to Stark Co., Ohio, while Henry was yet a child, locating on a farm. Here the child remained, developing into manhood while as- sisting the father on the farm and attending the com mon schools, receiving his education in the una- dorned, rudely constructed pioneer log school-house so well remembered by the early settlers of that State. Mr. Simmon came to this County in 1855, and set- tled on section 9, Hamilton Township, since which time he has constantly resided in the township. He has experienced all the trials and struggles as well as some of the pleasures of the early settler. His home was located in the woods, distant from neigh- bors and friends ; the nights were made hideous by the howling of wolves, the crying of the wild-cat and panther, and the more timid portion of the fam- ily were continually in awe of the visitation of prowl- ing Indians ; his cabin contained mother earth for a floor, dry leaves for a bed and the rudely constructed fire-place for cooking; wintered his cattle four years on browse which he procured by chopping down the trees; at one time carried 100 pounds of flour on his back 12 miles to satisfy the hunger of his family. Here he lived and worked and prospered. Mr. Simmon enlisted in the late war, in Co. I, 23d Mich. Inf., and was engaged in the battles of John- sonville, Columbia and Nashville. He has been Townshi]> Treasurer for five years ; is a member of the Methodist Episcopal Church and the G. A. R. Dec. 19, 1848, Mr. Simmon was married to \ Julia A., daughter of John Muffly, of this coui They have had ten children, seven of whom are ing, as follows: Magaret J., Susan, Sarah E., Johi Lacinda, William H. and Eva N. ,mery V. Dean, farmer, section 19, New Township, was bom Dec. 11, 185 1, in State of New York. He is a son of A and Betsey (Ludlow) Dean, the former a na of Vermont, the latter of the State of 1 York, where they settled and resided i] 1857, in which year they came to Michigan and cated in Ionia County, where the father died in following year. Mr. Dean left home to try the world alone at age of 16 years, and passed the ensuing ten year a farm laborer. In 1862 he came to Gratiot Cou and, in the summer of 1877, he purchased 80 a< of land in its original condition on section 1 Newark Township, where he has since resided operated as a farmer. He has placed 40 acre his land under improvements and cultivation, has made creditable progress in placing his fam a state suitable for successful farming during brief period it has been in his possession. In pc cal belief and effort, Mr. Dean is a Republican. He was married in Newark Township, Apri 1882, to Mary M., youngest daughter of Chester Sophronia (Wade) Howland. Her parents were tives respectively of the counties of Oneida and leans, N. Y. The father was a lineal descendar John Howland, one of the Mayflower pilgrims, Mrs. Dean is a member of the ninth generatioi direct descent from her pilgrim ancestor. Mr. Mrs. Howland came to Michigan in its early pei and first settled in Lenawee Connty, where the] sided 20 years, removing thence to Hillsdale Cou and in the summer of 1 87 1 came to Gratiot Cou They bought 40 acres of land in section 20, Ne^ Township. Mr. Howland had placed 25 acres ui improvement, and erected good and suitable f buildings on his farm, where he resided until death, which occurred March 29, 1882. Mrs. H land resides on the homestead. The Howlands a remarkably long-lived race. Chester Howland ^u-^^K^ r^m^M'^ A r-^ 4^^ All Digitized by Google Digitized by Google Digitized by Google ^A^ .V-' t:7 TCitlIi:Y:PIls>v r-'i ■ r ^ GRATIOT COU/^TY, \ V "^ one of seven children, and there was no death in the the family until that of the mother, which occurred on the day the youngest of the family was 50 years old. Mrs. Dean is one of five children born to her parents, four of whom are living. George A. died when three years old. He was the fourth child. The others are: Achsah L., Martha L. and Sarah £. Mrs. Dean was born May 15, 1865, in Hillsdale Co., Mich. ^ichael PoUasky, commission merchant at Alma, was born Nov. 16, 1832, in Hun- gary, of which country his parents, Mi- chael and Rebecca (Blitz) PoUasky, were natives. The son was a Lieutenant in the Hungarian army and engaged in the futile struggle of Hungary for independence. After the failure of the effort to assert the claims of that peo- ple to the right of self-gpvernment, Mr. PoUasky, with his wife and children — Rosa and Max — and ac- companied with his father, mother and sister Han- nah, emigrated to America. On reaching the New World they made a stay of eight months in Newark, N. J., and removed thence to Detroit, where the father is still a resident. The mother died there Dec. 25, 1879. Mr. PoUasky was about 23 years of age when he arrived in the United States. He came to Wayne Co., Mich., where he rented a farm and en- gaged in agricultural pursuits, doing a considerable business as a dairyman. This he followed two and a half years, and subsequently went to Detroit, where he engaged in the manufacture of shoes about a year and a half. This period was a time of trial, as circumstances were unfavorable, and the venture did not prove remunerative. His next business was a9 a merchant in the Lake Superior country, where he operated two years. In the faU of 1863 he came to Alma, and, associated with another man, again em- barked on the sea of trade. His choice of a bus- iness partner was unfortunate, and their affairs be- came so involved that the stock of the concern was surrendered to satisfy creditors. Mr. PoUasky re- ceived a receipt in full for all his liabilities and again opened accounts with the world, with a determined resolution to continue to struggle manfully for suc- cess. His outfit comprised a disposition to make all possible effort, and a faithful, helpful wife. He man- aged to establish himself again in mercantile pur- suits, to which he added lumbering, and conducted his joint business interests with satisfactory results until 1873, when shrinkage of values and the crowd- ing necessities of a large family made heavier de- mand upon his resources than his business warranted, and he began the manufacture of tubs and pails, which promised to be fairly remunerative. He suf- fered heavy losses from fire, his stock and establish- ment being seriously damaged three times in succes- sion with no insurance ; this, coupled with his inex- perience, brought such disaster that he was compelled to sell his interests. His son bought his stock and fixtures and the business was transferred to St. Jo- seph, Mich., where Mr. PoUasky again made an effort to reinstate himself and win success. Disaster again overtook him, despite his efforts to avert it, and he made an assignment for the benefit of his cred- itors. In 1877 he engaged in trade as a produce and commission merchant at Alma, and his final venture . has met with the success which his indom- itable courage and cheerful, hopeful contest with ad- verse fate deserves. He is a member of the Order of Masonry, and also belongs to "The Sons of Covenants." He is a decided Republican in political tendency. Was Vil- lage President three terqis, and has held other local offices. Mr. PoUasky was married in his native country March 15, 1852, to CeUa, daughter of Emanuel and Sarah Wix, all of whom were born in Hungary. Mrs. PoUasky was born April 12, 1831. Of her mar- riage, six children have been born, — Moses, Rosa, Max, Frank, Marcus and Anna. The first- named died in infancy. Rosa died when 13 years of age. The parents are members of the Mosaic Church. The portrait of Mr. PoUasky is presented on an- other page. — • •#•#• 1— • 1 ?^^i^ J^ .amuel Bigelow, druggist, general merchant and dealer in agricultural implements at Estella, was born in Steuben Co., N. Y., March 7, 1827. His father, Samuel L. Bige- low, was a native of New York, and directly fl-.crended from the Puritan fathers. His mother, Catharine (Van Gordon) Bigelow, was also a VV v^ V r V.' X <-0!]:-:'-Df1^>^ Digitized by Google \ r A r-2 • < • V 1 • a84 --r<-ilin:->:ilIl^:X— GRATJOT COUNTY. rz-^r^ -4>t?^I^':f >» > native of New York, and was descended from the first Dutch settlers of Manhattan Island. She is closely connected with the family of Anneke Jans, a German lady who willed or leased to Trinity Church, of New York City, a great part of the land on which the city is situated, including the Astor and Stewart property. The case of the Anneke Jans heirs has become famous in the last few years, and may be unsettled for a generation to came. Several of the ancestral connections of Samuel Bigelow were in the Revolution, and he has a cane cut by an uncle from a hickory tree that grew up within the fortifications of Ticonderoga. It was cut just after Col. Ethan Allen and Benedict Arnold captured that important post from the British. He has also an oil portrait nearly loo years old, of his paternal grandfather, who was a prominent minister in the Baptist Church. The subject of this narrative remained in Steuben County until nearly nine years old, when his father removed to Yates County and settled on Crooked Lake, one of the pleasant bodies of water so numer- ous in that section. Here he grew into manhood, working in his father's mills and stores until 21 years of age, and receiving his education in the Yates County Academy. Leaving home, he was for two years employed as buying and selling agent by the Yates County Linseed Oil Company. Thence he came to Grand Rapids, this State, and for five years he was employed as clerk in a store and as teacher in the common schools of Kent County. Next he went to Ottawa County, and farmed until 1861. Moving to Ravenna, Muskegon County, he was in mercantile life for three years. He then sold out, and, with his wife, spent one year in making a tour of Canada and the New England States. In Decem- ber, 1866, he found himself in Gratiot County, and for a time he taught school. For several years sub- sequent he was in the employ of Mr. Tucker, a mer- chant of Estella, and he then started a store of his own. He carries a moderate stock of goods, and does an annual business of about$1,500.
Oct. 12, 1853, in Kent County, this State, he was
united in marriage to Miss Hannah Walcott. She
was a native of Canada, was born May 14, 1835, and
died at her home in Estella, in February, 1869. He
was again married, at Estella, Jan. 21, 187 1, to Miss
Dora Bell, daughter of George S. Bell. She was a
native of Ohio, and died Nov. 12, 1873, leaving two
children, Alberta and George S.
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Mr. B. is a member of Elm Hall Lodge, No. 257, Si(
F. & A. M., and of Ithaca Chapter, No. 70, R. A. M. ^
He has for some time been Secretary of the lodge. ■■^■
He has held the offices of Justice of the Peace and
Township Clerk for several years each, and is now . -^
Notary Public. Politically, Mr. B. is very lil>eral in
his views, but leans toward the Democratic party.
^aniel W. Altenburg, farmer and County
1^ Surveyor, was bom in Wyoming Co., N.
Y., May 5, 1834; and is a son of Daniel
and Sarah (Latson) Altenburg. His father
was a native of New York, of Holland de-
\ ■, and ha? followed farming all his life.
In the fall of 1839, he moved to Union Township,
De Kalb Co., Ind.; and he was one of the pioneers
of that county. His family was the fifth in the
township. He afterwards removed to the county
seat. Auburn, where, in comfortable circumstances,
he now lives a retired life. He is 74 years old, and
the second oldest pioneer in De Kalb County. He
is an active member of the M. E. Church, and has
been Class-leader for many years. Sarah Latson was
a native of Genesee County, and of New England
ancestry. She moved to De Kalb Co., Ind., in
1834, and died in Union Township May 22, 1863.
She had always been a faithful Christian, and her
death was an example to all unbelievers. She passed
away rejoicing, and admonishing her children to
serve the Lord and keep his commandments. She
left nine children, all of whom are yet living, in good
circumstances, and occupying positions of trust and
honor. One is a prominent attorney at Little Rock,
Ark., and has represented his county in the Arkansas
Legislature. Four served their country during the
Rebellion, and were honorably discharged.
The subject of this sketch, when six months old,
was taken by his parents to Sandusky Co., O., and four
years later to De Kalb Co., Ind., where they settled
in Union Township. They found themselves in a
dense wilderness, and Daniel being the oldest sou,
as he grew up much of the labor of clearing and im-
proving a farm in a new country devolved upon him.
His educational advantages were therefore limited;
but, being of a persevering disposition, he attended
school during his less busy winters, and thus, with
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the help of miscellaneous reading, he acquired a fair
education. During the last two years that he lived
at home, he was an engineer on the Elk River Val-
ley railroad, which runs through De Kalb County.
Feb. i8, 1855, he was married to Sophia, daughter
of Lanslot and Maria (Truman) Ingman, natives
respectively of Fairfield Co., Ohio, and London,
England ; and of English and German descent. Mr.
Ingman followed farming most of his life, but was
also for some time a cabinet-maker. He removed to
De Kalb Co., Ind., in 1836, very early in its history,
he and his brothers being the first two settlers near
Auburn ; and in connection with his brotl^er-in-law,
Wesley Parks, located and platted the present city
of Auburn. He was for many years a prominent
man, and for some time Justice of the Peace. In
that place Mr. Ingman died, Dec. 2, 1874; Mrs.
Ingman May 26, 1883; and their only daughter be-
sides Sophia, but a little later. Sophia (Ingman)
Altenburg was bom Feb. i, 1838, in Auburn, Ind.,
and was the third white child born in that place.
She lived in Auburn with her parents until eight
years of age, when her father traded his cabinet shop
and village property for a farm near by, to which
they all removed. There she was reared and edu-
cated and married.
Mr. and Mrs. Altenburg moved to the county seat :
he having been chosen County Surveyor, resided
there for ten years. For five years of this time he
was County Surveyor, and he surveyed nearly
the whole county. He finally resigned, not wish-
ing to serve under a Democratic administration.
Oct. 18, 1864, he enlisted in Co. M, ist Ind.
Vol. Heavy Art., under Capt. Samuel E. Arm-
strong and Col. Canby. He was at New Orleans
and at the taking of Mobile, and was honorably
discharged at New Orleans, Oct. 24, 1865. Selling
his property in Auburn, he came to this State and
county, and located on 80 acres on section 17, New-
ark Township. Here he resided 17 years, brought
64 acres to a high state of cultivation and drainage,
and built a very fine brick residence. His farm was
known as one of the model farms of Gratiot County.
He made maple sugar very extensively, producing
annually from 3,500 to 4,500 pounds. Aug. 4, 1883,
he sold his farm in Newark Township; and Aug. 10,
he purchased 80 acres on section 25, Arcada Town-
ship, where he now resides. He has a good location,
and is fast making a fine farm, 46 acres being al-
Mr. and Mrs. Altenburg have a family of seven, as
follows: Frank F., born April 10, 1856; Araminta,
April 18, 1858; Henry I., Oct. 4, 1862; Maria E.,
Jan. 19, 1867 ; William L., July 3, 187 1 ; Orville L.,
Dec. 21, 1876; and Daniel T., Dec. 10, 1878. Mr.
and Mrs. A. are members of the Methodist Episco-
pal Church, and active workers for Christianity. All
their family have been brought up under careful re-
ligious influences.
Mr. Altenburg is a member of Ithaca Lodge, No.
216, I. O. O. F. Politically he is a staunch Repub-
lican. He has always commanded the respect of
his fellow citizens, and although he is not an office-
seeker he has occupied many positions of honor. In
1867, he was appointed Deputy County Surveyor, and
the following year he was elected County Surveyor.
Excepting one term, he has held one of these two
offices continuously to the present time. He has
been School Director two years, and Notary Public
for the same length of time. In January, 187 1, the
Board of Supervisors appointed him Drain Commis-
sioner, which office he retained for ten years. He
then positively declined to serve longer.
^f^QfUtnn^
ames Riddle, farmer, section 10, Emerson
^ Township, was born in Ontario, Canada,
Oct. 14, 1826, and is the son of Archibald
^ ^^ and Bethia (Marr) Riddle, natives of Scotland.
They followed farming all their lives, first in
the old country, and then in Ontario, Canada,
where they died, the father in 1873, the mother in
May, 1880. James was brought up near London,
Ontario, and remained as a laborer on his fathers
farm until 30 years of age. He received a fair edu-
cation in the common schools of Middlesex County.
In 1856 he came to this State and county, and lo-
cated 240 acres of land in Emerson Township. He
spent two summers here and then returned to Can-
During this period, March 29, 1866, at London,
Canada, he was married to Isabel, daughter of Will-
iam and Margaret (Beattie) Scott, natives of Scot-
land. She was born in Westminster, Middlesex Co.,
Ont., April 28, 1834, and, receiving her education in
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the district schools of that county, remained at home
until her marriage. One year after that event, Mr.
and Mrs. Riddle came to this county and^setiled on
the farm he had purchased in 1856. He now owns
120 acres, nearly all in an excellent state of cultiva-
tion, and has good buildings for residence, shelter of
stock, etc. Politically he is an earnest and influen-
tial Republican, and he has held the office of Over-
seer of Highways for some years. Mr. and Mrs.
Riddle are members of the Presbyterian Church,
are conscientious readers of the Bible, and actively
devoted to the interests of Christianity.
I illlam Marion CurtisB, farmer, section 1 1,
Emerson Township, was born in Wyoming
Co., N. Y., Jan. 8, 1852, and is the son of
Waterman F. and Sylvia (Cronkhite) Curtiss,
natives of New York and of English descent.
He resided in his native county until six years
old, when he came with his parents to this State, and
located on a farm in Ionia County. Here he received
two years' schooling, and in February, 1861, he came
with his mother (his father having died in Ionia
(bounty in i860) to this county and settled in Emer-
erson Township. From that on he gave his time to
attending school and to farming.
March 15, 1878, in Lafayette Township, he was
married to Catharine Mcintosh, daughter of Funley
and Ellen (Chisholm) Mcintosh, natives of Scot-
land, where they still live, on a farm. Catharine was
bom in Rothshire, March 29, 1859, and when 12
years old came with her brother to this country and
lived with an uncle in Lafayette Township, Grariot
County, until her marriage. Mr. and Mrs. Curtiss
settled on 80 acres on section 11, Emerson Town-
ship, in 1878. It was then heavily timbered, but of
the 40 acres which they now own, 28 acres are now
under the plow, and they have built a cozy little
dwelling-house. They are the parents of two chil-
dren: Nora E., born July 14, 1879; Arthur W., born
Oct. 4, 1 88 1. They are members of the Presby-
terian Church. Mr. Curtiss is a young man of en-
terprise and judgment and stands deservedly high in
his community. In politics he votes with the Repub-
lican party.
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Justin Shoup, farmer, secdon 8, North Shade
^ Township, is a son of Henry and Polly
. i^/ (Hilaiid) Shoup. The former was bom in
'-'■' \ Pennsylvania, in 1795, and died in Sandusky
:' Co., O., Jan. 14, 1875; Mrs. S. was bom in
D1804, and died Jan. 10, 1879, in Sandusky
Co., Ohio.
The subject of this sketch was bom March 2,
1834, in Sandusky Co., Ohio, remaining with his
parents until he was 28 years of age, when he en-
listed in Co. D, 128th Ohio Vol. Inf., and served two
years in the Eastern army. He was on detached
duty at Johnson s Island, guarding prisoners of war.
He was discharged at Camp Chase, Ohio, June 20,
1865. He then lived two years longer with his parents;
next, two years in Kent Co., Mich., then 19 months
in Kansas, then one year again in Kent County, and
finally, in 1871, he came to Gratiot County, locating
on 80 acres of land, on section 8, North Shade
Township, where he has 60 acres in good tillable
condition.
Politically, Mr. S. is a Democrat, and he has been
a school officer of his township a number of terms.
He was married Jan. 5, 1868, to Miss Eunice,
daughter of Edmund and Clarissa (Hoyt) Ring,
who was born April 19, 1850, in Cuyahoga Co., Ohio.
Her parents were natives of the State of New York,
whence they moved to Ohio, then to Ionia, Mich.,
and finally to Kent Co., Mich., where they yet reside.
Mr. and Mrs. Shoup s children are: Flora B., Eki-
mund H. and Clara L.
,^ saac B. Ward, farmer and lumberman, resi-
dent on section 20, Sumner Township," is a
son of Lewis and Isabel (McLeod) Ward,
natives of New England and of English and
Scotch descent. Lewis Ward was by occupa-
tion a miller, and both he and wife are de-
ceased.
The subject of this memoir was born in Galway
Township, Saratoga Co., N. Y., Feb. 21, 1829. Four
years later his father moved to Lorain Co., Ohio,
where he lived 12 years. Thence he came to Eaton
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' State, Isaac B. worked out for himself among the
;*\; neighbors for about six years, and then went to Ionia
^ County. «
In North Plains Township, that county, Oct. 14,
185 1, he was united in marriage to Miss Lovena,
daughter of Harvey and Eliza A. (Freeman) Lewis,
natives of Pennsylvania and of German descent.
She was bom Oct. 8, 1834, and came with her
parents to Livingston Co., Mich., and then to Mont-
calm County. Thence she went to Ionia County and
worked as a domestic until her marriage.
After living in North Plains Township five years,
Mr. and Mrs. Ward came to Gratiot County and lo-
cated on 80 acres on section 20, Sumner Township,
afterwards purchasing 40 acres on section 29. He
has seen many ot the peculiar experiences common
to pioneers. When he came the country was entirely
new, and the only means of getting from place to
place was by the Indian trails. He had to go 20
miles to purchase supplies. He now has a fine farm
with 80 acres well improved.
^ Mr. and Mrs. W. have been the parents of four
/; children, three now surviving: Ackley L., born May
^ 18, 1854; William W., April 18, 1856; Lemuel Jay,
Ny' May 16, 1861. A baby was born July 3, 1852, and
died in infancy. Mr. Ward is a member of Elm
Hall Lodge, No. 257, F. & A. M. He has held the
offices of Supervisor one year, Township Treasurer
three years. Highway Commissioner eight years, and
other minor offices. In politics he is an ardent Re-
publican.
ichard Foster, farmer, section 8, Washing,
ton Township, is a son of Richard and
Fanny (Hines) Foster, natives of Stafford-
shire, England. Richard Foster was a lock
and gun smith, and died in London in 1852.
Richard, junior, was born in Wolverhampton, Staf-
fordshire, England, Oct. 10, 1822. When 21 he was
apprenticed to his fathers trade, and in 1852 he
came to America. He lived three years in New
York City, and then went to New Jersey, where he
enlisted in Co. D, ist U. S. Sharpshooters. He went
to the Army of the Potomac and fought in the seven
days' battle before Richmond, at Fredericksburg,
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Bull Run, Antietam, Frederick City and other places.
He escaped unhurt, and held at the time of his dis-
charge the position of Armory Sergeant of his regi-
ment. He was discharged in front of Petersburg,
Va., Sept. 14, 1864. He keeps as a trophy a sabre
which he captured from a rebel Colonel. On leaving
the service, Mr. Foster went first to New York, and
then came to Gratiot County, locating on 80 acres on
section 8, Waslungton Township. He has improved
35 a»:res, but has also worked at his trade in the
mean tin.e.
In August, 1847, he was married to Elizabeth,
daughter of Wilh'am and Martha (Dunch) Fletcher,
natives of Kent and Middlesex, England. They
both died in the old country, Mr. Fletcher having
been a hotel-keeper until his death. Mr. and Mrs.
Foster have had seven children, four of whom are
living: Joseph, Richard, William and George. Mr.
Foster has been Roadmaster in his township. Polit-
ically he is a Republican. He and wife are mem-
bers of the M. E. Church.
.nos n. Kimmel, farmer on section 33, Pine
River Township, is a son of Christopher
C. and Phebe (Spears) Kimmel, natives of
Pennsylvania and Ohio. The father settled in
Ohio in 1833, and came to Michigan in 1855,
settling in North Star Township, this county,
where he died, Jan. 20, 1873. His wife is still a res-
ident of that township. Their family numbered 14,
13 of whom lived to be adults.
Enos H., the subject of this notice, was the second
child and first son of the family, and was born in
Hancock Co., Ohio, Aug. 15, 1841. He was 14
years old when his parents came to Gratiot County,
and he remained with them three years longer.
Then for two years he worked out by the month.
Aug. 12, 1861, he enlisted in the Eighth Mich. Vol.
Inf. He served four years, and fought in 13 heavy
engagements. At James Island, he was wounded by
a shell, and in consequence lost from the right hand
one finger and temporarily the use of two others.
He was also slightly wounded in the thigh at Cold
Harbor, Va. From this he was only off duty for
three weeks. He was discharged at Washington,
D. C.
Returning to Gratiot County, from the service, he
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bought 80 acres of wild land in Hne River Town-
ship, which he has since converted into a valuable
farm and a comfortable home.
In Clinton County, Dec. 24, 1865, he was married
to Elmira A., daughter of Zebina and Ann Rice, na-
tives of New England. She was bom in Clinton
County, Dec. 7, 1844, and died Aug. 12, 1873, leav-
ing three children, George C, Rosa A. and Orrin R.
He was again married, at St. Louis, Mich., July 4,
1875, to Lydia, daughter of John and Lucy Frank-
lin. To this union came one child, Archie, who was
carried away by the hand of death when two years
old. Jan. 4, 1878, he married for his present wife,
at Saginaw, Mich., Mrs. Alice Hale, daughter of
Henry and Sarah Waymire, natives of Ohio, and
widow of George Hale. She was also born in Ohio,
Jan. 5, 1 86 1. They have had one child, James G.,
which died at the age of two weeks. Mr. Kimmel
is one of the enterprising, intelligent farmers of Pine
River Township. Politically, he is a Republican.
Tohn Mulholland, farmer, section 24, New-
ark Township, was bom in Seneca Co.,
Ohio, Nov. 6, 1839. He is a son of
William and Eliza (Dillon) Mulholland. They
were natives of Ireland, and became residents
of the United States in 1828, settling in Ohio.
Their family included three sons and four daughters.
Mr. Mulholland is the second son of his parents,
and resided in the county where he was bom until he
was 28 years of age. He spent his early life as as-
sistant of his father on the farm and in attendance
at school, and, after reaching manhood, had the man-
agement of his father's farm six years. In the fall of
1864 he was drafted, but instead of entering the
service himself he sent a substitute, to whom he
paid $1,000. He was married in Hancock Co., Ohio, March 14, 1867, to Sarah, daughter of George and Catherine (Krable) Graham, both natives of Ohio. Mrs. Mulholland is the second daughter, and one of seven children. Of her marriage three sons have been born — Homer G., Everett W. and Arthur M. The mother was born Nov. 21, 1842, in Hancock Co., Ohio. The family removed to Gratiot County in the autumn of 1868, where Mr. M. bought 80 acres of land in Newark Township. It was wholly in i original state, and the family took possession of a k house, which was their abode until the winter ( 1 88 1, when they moved into a fine frame hous newly erected. Mr. Mulhollar.d proceeded with tl improvements on his farm after the manner of mc of his calling who fortify their possessions in wii judgment. In 1878 be built an excellent bam as 2 accessory to his careful and prosperous farming. K is an adherent to the principles of the Republica party, and his wife belongs to the Methodist Episo pal Church. enjamin Burton, farmer, section 25, A cada Township, was born in Crawford Cc Ohio, Feb 27, 1853, and is the son < David and Sarah (Dewell) Burton, natives < Ohio. David Burton is a farmer by occi pation, and resides in Pine Piver Townshi two miles from Alma. Until of age, Benjamin live on his fathers farm in Crawford Co., Ohio, and a tended the common schools, receiving a very fair ec ucation. In the spring of 1874, he went with h father to Wyandot County, same State, and ei gaged in farming. He also did an extensive thresl ing business. Two years later, they removed I Seneca County, and located on a beautiful farm i Eden Township, where our subject remained ti marriage. Dec. 30, 1878, in Springfield Township, Jefferso Co., Ohio, he was united in the bonds of matrimon to Sarah E., daughter of John and Elizabeth (Rol ertson) Blythe, natives of Pennsylvania and Ohu and of Irish extraction. John Blythe was a farme and died in Jefferson Co., Ohio, July 2, 187$, at th
age of 72 ; his wife died in the same county. Ma
10, 1850, aged 42. Sarah E. Blythe was born i
Springfield Township, Jefferson County, April 3^
1848. When three years old, her mother died, lea^
ing her the youngest of three children. Her fath<
married again. She obtained a good education i
the schools of her county, and cared for her father
household until his death. Five years later, she wj
married. For a little more than two years, Mr. an
Mrs. Burton resided in Seneca County, on their fan
of 60 acres. He then sold, and came to Michigai
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farm is nicely located, and 107 acres are well im-
proved. It has one of the finest orchards in the
county.
They have a family of two daughters: Ada M.,
born Aug. 7, 1880; and Hattie E., born May 28,
1882. Mr. Burton has made many friends during
his short residence in this county. Politically he is
an ardent Republican.
eorge Chandler, farmer, on section 28,
Pine River Township, is a son of Charles
and Alcrnda (Fletcher) Chandler ; the for-
mer born in Pomfret, Conn., Dec. 2, 1780, and
the latter born in Windsor, Conn., in 1784.
They had a family of nine, three sons and six
daughters. George, the second son, was born in
Pennsylvania, April 16, 18 *6. He received a com-
^ mon-school education, and also acquired much valu-
able knowledge by private reading. At the age of
21, he learned the trade of millwright, which occupa-
tion he followed for over 20 years. He had charge
of building the first grist-mill in Gratiot County, at
Alma. It was afterwards destroyed by fire.
Previous to that, in 1852, he went by steamer to
California, and for four years was most of the time
engaged in mining. Returning to the Mississippi
valley, he came in the summer of 1856 to Gratiot
County, of which he has been one of the pioneers.
He bought 160 acres of wild land on section 4, Ar-
cada Township, improved the same, and after 16
years' residence sold out for the handsome sum of
^,000. He then purchased 80 acres on section 28,
Pine River Township, where he now resides, having
60 acres nicely under cultivation.
Sept. 24, 1845, at Jamestown, N. Y., he was mar-
ried to Nancy Woodin, a native of Pennsylvania.
This union was blessed with three children, — Martha,
Jeremiah B. and Charles S. The first and last
named are deceased. March 19, 1877, at St. Louis,
he was again married, to Mrs. Eunice (Van Burren)
Hubbelly widow of Dennis A. Hubbell, who was
killed on Morris Island, S. C, in the late war. Mr.
Chandler has been for six years Highway Commis-
sioner, five years TownshipTreasurer, one year Super-
visor, and three years Justice of the Peace, in Arcada
Township. He is now Justice of the Peace in Pine
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River. He has also held numerous school offices. He
is in every sense a representative citizen. In political
sentiment, he is a " through and through " Repub-
lican.
enry J. Bentley, farmer, section 29, Newark
^ Township, was born July 8, 1842, in Canada.
>^*^ His parents, Wilson and Miriam (Jackson)
^ Bentley, were also natives of the Dominion
j where they passed the entire period of their
lives.
Mr. Bentley came to Michigan when he was 22
years of age, and first settled in Clinton County,
where he passed fvst years, engaged in the manu-
facture of wooden bowls. In the spring of 1869 he
bought 80 acres of land in a primeval condition,
where he has since resided.' He has cleared and im-
acres by purchase, 30 acres being improved. In
political faith and action, Mr. Bentley assimilates
with the Democratic party, and has been School
Director in District No. 6, Newark Township, six
years.
He was married in St. Johns, Clinton Co., Mich.,
Sept. 2, 1864, to Deborah E., daughter of Asa W. and
Rhoda (Day) Ellsworth. The parents were natives
of Canada, where Mrs. Bentley was born, Apiil 16,
1842. The four children belonging to the household
were born as follows: Oscar L., March 10, 1866;
Melvina E., April 6, 1869; Charles A., July 3, 1876,
and William J., April 8, 1880.
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illiam O. Johnson, farmer, section ^^^ Pine
River Township, is a son of Otis and Sarah
C. (Plumstead) Johnson. Otis Johnson •
was born on the Atlantic Ocean, while his
parents were tn route from Ireland to the
great republic. Sarah Plumstead was a na-
tive of New York. William O. Johnson was the
sixth son of a family of 14, seven sons and seven
daughters. He was born in Ohio, but came with his
parents when quite young to Michigan, settling in
Oakland County. His father, with two of the sons,
Robert and James, served through the Mexican war l^
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and some time after returning, moved to Ionia
County, where he resided until his death.
While living in Ionia County and attending the
common school, the subject of this biography " took
French leave " of home and started out to make his
own way in life. He went to Oakland County, and
hired out to a farmer for 40 days at 12 J^ cents per
day. The five dollars thus earned, he immediately
put at interest. He afterwards worked for six dol-
lars per month, and next was employed in a hotel at'
$13 per month. In the spring of 1854, he came to Gratiot County, and the following fall he deposited the money for 160 acres of wild land on section 33, Pine River Township. He at once sold 80 of this for$25 more than it cost him ; and the remaining
80 is his present farm. He built a log house and
while living alone chopped the wood and timber from
35 acres. After living on the place nine months, he
went to Missouri, where' he was variously employed
for three or four years before returning to his farm.
He was in the meantime married to Mary R.,
daughter of Thomas and Sarah Hale, natives of
North Carolina. She was born in Cape Girardeau
Co., Mo. Mr. and Mrs. Johnson have had two chil-
dren : Emma L , born March 4, 1862; Alonzo P.
(deceased), born May 20, 1865, and died Dec. 24,
1866. Mr. J. lived in his first log house two or three
years, and then erected his present dwelling. His
80 acres are now all underdrained and in cultivation.
He is a member of the Masonic Order, and in polit-
ical sentiment is a Democrat.
Lylvester Wheeler, farmer, section 13, New-
ark Township, was born April i, 1816, in
Swantoii, Vt. His parents, Jesse Wheeler,
Jr., and Sally (Morgan) Wheeler, were also
born in the Green Mountain State, and, when
the son was but three years old, removed to
Onondaga Co., N. Y. Later on, they removed to
Batavia, N. Y., and after a stay there of two years
they went to Oswego County in that State, where the
father bought and improved a farm, and resided
thereon nearly 40 years.
On reaching his majority, Mr. Wheeler commenced
his life's contest single-handed. In 1852 he went to
Kane Co., III., and a little more than a year later he
came to Michigan. After a brief residence in Ingham
County, he came, in the winter of 1854, to Gratiot
County, where he bought 120 acres of land under the
Graduation Act. He subsequently bought 40 acres
additional, and later disposed of 80 acres by sale.
He holds 80 acres at present, with 65 acres in a
finely advanced state of cultivation. Mr. Wheeler
endorses and supports the principles and issues of
the Republican party, and has been active in the
school interests of his township.
He was married March 31, 1837, in Oswego Co.,
N. Y., to Hannah, daughter of William G. and
Lavinia (Bristol) Peck. She was born Jan. 10, 1817,
in Oswego County, and has become the mother of
nine children, all but one of whom still survive.
They are named Amanda J., William H., Edmund
J., Almira M., Jesse C, Lavinia C, John W., George
W. and Eliza A. Jesse C, the fifth child, died when
he was 26 years of age.
I^i ovell J. Puller, farmer, section 9, Newark
Township, was bom April 16, 1827. His
parents, Calvin and Bethana Fuller, were
natives of Vermont and New York respect-
ively, and their family included three sons and
1^ three daughters.
Mr. Fuller was the second son, and passed the
years of his boyhood, previous to the age of 1 8, in
obtaining his education. His parents removed to
Ohio when he was five years old, and the Buckeye
State was his home until 1872. In 1845 he began to
" do for himself," and spent some time as a woods-
man, after which he became a carpenter, and followed
that business for 12 years. In March, 1872, he set-
tled in Ionia Co., Mich., and there resided two and
one-half years. In the same year he bought 200
acres of land in Newark Township, this county,
whither he removed his family in 1875. His farm
now comprises 160 acres, cleared and cultivated.
Mr. Fuller belongs to the National Greenback party,
and in the spring of 1883 was elected Supervisor,
which post he resigned a short time after his
election.
He was first married in 1848, in Medina Co., Ohio,
to Elizabeth Inhan, a native of the Buckeye State.
Three children were bom to them« Julia, bom in
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1852, is the only survivor. Amelia and Samuel are
deceased. The wife and mother died in 1854. Mr.
Fuller was a second time married May 8, 1856, to
Mary Coolman, who was bom in Ohio, June 8, 1838.
Of their ten children but two survive. EvalM., bom
Jan. 28, 1867, and Varo C, born July 16, 1869, are
living. The following is the record of the dead :
Lovell D., bom Jan. 25, 1857, died Feb. 21, 1862;
Clara E., born June 10, 1859, died Feb. 3, 1862;
Joseph E., born Dec. 12, 1862, died April 23, 1864;
G>ra v., born March 27, 1865, died Sept. 19, 1866;
Gracie B,, born May 27, 1871, died Sept. 23, 187 1;
Ionia D.,born Mays, 1873, died in September, 1873;
TJlly D., bom Sept. 25, 1876, died Feb. 6, 1877 ;
Myrtie A., born Jan. 20, 1878, died Feb. 15, 1878.
Aug. 28, 1878, the mother crossed the river to the
land of eternal life, where her eight sons and daugh-
ters awaited her coming. Mr. Fuller was a third
time married April 3, 1879, to Harriet E. Hayes,
who was born Aug. 8, 1833, in the State of Vermont.
f heron A. Johnson, farmer, section 29, Pine
River Township, is a son of Matthew and
and Mary (Robinson) Johnson, natives of
Nova Scotia. TJiey first settled, after mar-
riage, in New Brunswick, afterward removing
to Canada. In 1862, they came to this State
and county, and settled in Pine River Township,
where they now reside. Their family comprised
seven children : Matilda, Sarah, Theron A., Bradley,
Amanda, Mary and Lydia. Theron A., Bradley and
Mary are yet living.
The subject of this biographical narrative, the
oldest son of the family, was bom in New Brunswick,
April 12, 1834. At the age of 14, he came with his
parents to Canada, and at 18 he engaged in carriage
smithing. This occupation he followed for six years,
and then went to Winneshiek Co., Iowa, where he
worked at blacksmithing for four years. In June,
1862, he came to Gratiot County, and followed the
same business at Alma, for thr^e years.
In 1S65, he was appointed Postmaster at Alma
under President JohnsOn. After one year, on ac^
count of ill health, he resigned, and bought 160 acres
of wild land in Pine River Township, where he now
resides. In the summer of 1883, he erected a large
and commodious residence. He now has 100 acres
of his farm under cultivation, and his surroundings
all betoken thrift and industry.
July 23, 1856, at Bradford, Ont., he formed a life
partnership with Miss Julia, daughter of David and
Phoebe Lloyd, natives of Canada. Mr. Lloyd was
killed in the Canadian rebellion. Mrs. Lloyd came
with her daughter to Michigan, and died March 28,
1866. The daughter, Julia, was bom in Canada,
March 25, 1837.
Mr. and Mrs. Johnson have a family of eight chil-
dren, bom in the following order: Sarah A., June 13,
1857; Lily, May 29, 1859; Charles El, June 4,1861 ;
Ella, July 31, 1865; Alice, Nov. 9, 1868 ; Theron L.,
July 29, 1873; D'Arcy Lloyd, Dec. 31, 1875; and
Ethel, April 25, 1878. Mr. Johnson is a prominent
man, and has filled numerous offices of tmst and
honor, showing both his ability and his popularity.
He was Supervisor from Arcada Township in 1864-5,
and was Chairman of the Board. In 1881, he was
the National candidate for State Senator, and was
defeated by Hon. Giles T. Brown, the Republican
nominee. He was editor of the Gratiot Journal
most of the time from 1868 to 1872. In 1877, he
was chosen Secretary of the Farmers' Mutual Fire
Insurance Company, which office he has since filled.
Politically, he is now a zealous and influential mem-
ber of the National Greenback party.
The portrait of Mr. Johnson is presented on page
292, and is that of a prominent and representative
citizen and agriculturist of Gratiot County.
:rank Smith, deceased, was a farmer on
section 24, New Haven Township. He
was born in Prussia, Sept. 27, 1820. He
worked as a common laborer in his BAdr«
\^ country until 1853, when he emigrated to Xht
land of freedom and prosperity, settling first in
Ohio and a year later on an 8o-acre tract in tbie
county, where he lived the remainder of his days.
Thi^ country was then perfectly ivild. Here he
cleared and put in good arable condition 25 aCitt ;
was industrious, honest and prosperous, and a high-
minded, consistent Catholic. His death — which was
from dropsy — occurred Dec. 10, 1864, just after hav-
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ing been drafted for army service. Having gone, on
this military duty, as far as Flint, where the doctors
pronounced him unfit for a soldier s life, he return-
ed home, and in four weeks he was dead ! He had
been a soldier in the Prussian army for five years, a
portion of that time an officer of rank.
Mr. Smith was married, in Newark Township, this
county, May i, 1855, to Miss Mary Wermuth, who
was born in Baden, Switzerland, in March, 1833.
When 17 years of age she came with her parents to
this country, settling first in Fulton Co., Ohio, and
afterward in Newark Township, this county, where
she lived until marriage.
July 27, i86§, she married George P. Steadman, her
present husband, who was born in New York State,
Oct. 2, 1826, and emigrated to this State in 1842.
He was a soldier in the last war, and, being shot in
the left leg, at the second battle of Bull Run, he was
incurably wounded. He, with his wife, spent the
years 1879-81 in the gold regions of California. In
politics Mr. S. is a Democrat, and he has held the
office of School Moderator for nine years.
Mrs. S. is a noble woman, and is recognized as
such by her neighbors. Her children by her first
husband are : Caroline, born Aug. 30, 185 1; Fred,
born April 23, 1859; and Louis B., born Dec. 23,
1 86 1, and died Dec. 8, 1864. By her present hus-
band : Adaline, born Nov. 29, 1867; and Edgar,
born April 2r, 1871, and died Dec. 19, 1873.
Barnes S. Lance, farmer on section r i, Ful-
ton Township, is a son of James and Mary
(Johnson) Lance, natives of New Jersey
and Ohio. They settled in Wayne Co., Ohio,
where they lived all their lives. James was
bom in that county Sept. 30, 1837. He re-
ceived a limited education, and was about r9 when
he left home to make his own way in life. For five
years he worked on farms for others ; and then he
bought a farm in his native county. After a short
time he sold out and bought a farm in Medina Co.,
Ohio. Soon hie sold again, and returned to Wayne
County.
In November, 1865, he came to Gratiot County
and bought 80 acres, partly improved, on section 11,
Fulton Township. Here he has been .content to
stay. He has since added 40 acres, and now has
65 acres cleared. Dec. r2, r86r, in Milton, Wayne
Co., Ohio, he was married to Amanda M., daughter
of William and Clara (Lee) Lance, natives of New
Jersey and Ohio. She was born also in Wayne Co.,
Ohio, Feb. 27, 1S43.
born Oct. 23, 1863; Edward E., Jan. 17, 1866;
Clara A., Jan. 11, 1868; Alfred S., July 30, 1871;
Dewey W., Oct. 31, 1877 ; and one which died in in-
fancy. Politically, Mr. Lance votes the Democratic
ticket.
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tf ii:;lbert Smith, farmer, section 20, Emerson
y^^ Township, was bom in Baden, Germany,
March 22, 1842, and is a son of Ignatius arul
Catharine (Kline) Smith, natives of Germany.
> At the age of eight years he came with his
' parents to the United States, and settled in
Seneca Co., Ohio. His father died in Michigan in
1874, and his mother residfs in Sumner Township,
this county. When 15 years old he left home to
learn the cabinet-makers* trade, with an uncle.
Leaving him he spent one year on a farm, and then
enlisted in Co. A, 49th Ohio Inf., under a Capt. Lang-
worthy. He joined the 4th- Corps of the Army of
the Cumberland, and participated in the battles of
Pittsburg Landing and Stone River, and in numerous
lesser engagements. At Stone River he was taken
prisoner and detained about two weeki. He was
then paroled, went to Columbus, Ohio, was taken
sick and went home on furlough. On regaining his
health he engaged in the lumber business in this
State, following that until 1869.
Nov. 4, of that year, he was married, at Alma,
Gratiot County, to Josephine, daughter of Daniel
and Nancy (Burgess) Griffeth, natives of the State of
New York. She was born in Wayne Co., Mich., Oct.
8, 1852, and when she was two years old her parents
removed to St. Louis, this county. They afterwards
settled in Emerson Township, where she lived until
her marriage. Mr. and Mrs. Smith settled on a farm
of 80 acres in 1869, which he had purchased in 1865,
and he has now 140 acres, of which 60 are well im-
proved. They are the parents of three living children,
and one dead : Lewis, bom Feb. 6^ 1^72; Bert A.^
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bom Feb. lo, 1879; Emma, born June 23, 1880;
James, born May 14, 1877, and died May 17, 1877.
Mrs. Smith is connected with the Baptist Church.
Mr. Smith is a member of Emerson Lodge, No. 375,
I. O. O. F. He has held the office of Highway Com-
missioner, and votes with the Democratic party.
limeon Gray, deceased, late resident of sec-
tion II, Fulton Township, was a son of
Semy Gray, and was bom in New York
State, in January, 1825. He came with his
parents to Oakland Co., Mich., when quite
young, and lived in that county until the spring
of 1854, He then came to Gratiot County, and
bought 80 acres in Fulton Township. He afterwards
sold that place, and purchased 60 acres on section
II, where he resided until his death, in October,
1874.
Feb. 23, 1852, in Oakland County, he married
Miss Susan, daughter of John C. and Amelia Grace,
natives of Massachusetts and Maine respectively.
She was born in Oakland County, March 4, 1834.
Mr. and Mrs. Gray had nine children, six of whom
survive : John H., Edna, Rachel, Wallace, Guy and
Pearl A. The deceased are Capitola, Norma and
Freddie. Mr. Gray was Highway Commissioner one
term, and in politics was a Republican.
— *»'>^§ ^*' —
illiam A. Krom, farmer, section 26, Elba
Township, is a son of Andrew and Huldah
(Skinner) Krom, natives of Orange Co.,
N. Y. The father was by occupation a black-
smith. He came to Michigan and settled in
Kalamazoo County in 1849. Mrs. Krom
died in 1858. The son, William A., came to Elba
Township in 1867, and engaged in farming and
speculating in land. He now owns an excellent
farm on sections 23, 24 and 25, 160 acres in extent.
His lumber business, which he has carried on for 17
years past, is very extensive.
In 1868 he was united in the bonds of matrimony
to Hattie Oberlin, daughter of Allen and Esther
Oberlin, natives of Pennsylvania and Germany re-
spectively. Two children resulted from this union :
Julia A., born Dec. 2, 1870, and Mary, bom April 26,
wife Dec. 11, 1883.
He has held the confidence and good will of his
neighbors ever since he began his residence in this
county, and has been honored with a number, of
local offices. He has been State Road Commissioner
for a number of years, and Township Treasurer for
the last nine years. When he entered upon the
duties of the latter office, he found the financial con-
dition of the township very unsatisfactory, but he has
now greatly improved the condition and management
of the treasury. Politically, he is a " true blue "
Republican. He is a member of Elsie Lodge, No.
238, F. & A. M.
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eorge Noll, farmer and mechanic, section
31, New Haven Township, is a son of
William and Betsy (Hart) Noll ; the for-
mer, of German ancestry, was a native of
Pennsylvania, where he lived until his death,
at the age of 56. His wife, a native of Ire-
land, died in Pennsylvania.
Mr. George Noll, the subject of this sketch, was
born in Greenwich Township, Berks Co., Pa.; when
nine years of age his father died ; from the age of
eight years to 19, and from 20 to 22 he was a laborer
for Jonathan Beaver, in his native county. He then
(1835) engaged to learn the trade of blacksmith, and
soon became a skillful workman, earning good wages;
but his zeal in his calling led him to over-work and
he broke down. In 1843 ^^ went to Canada, where
quit blacksmithing. He accordingly went upon a
farm, in Ontario, and pursued agriculture until 1867,
when he came to this State and purchased 80 acres
of wild land where he now resides. He first stopped
at Carson City six weeks, preparatory to erecting a
house in which to dwell. He now has 72 acres of
well improved land and a comfortable residence.
In politics he is a Republican, and has held some of
the township offices.
May 20, 1847, at Smith ville, Niagara Co., Ont.,
Mr. Noll married Miss Margaret H. Carpenter, a na-
tive of Ontario, where she was bom July 27, 1824.
She is a woman of considerable physical strength and
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executive ability. Mr. and Mrs. N. are the parents of
ten living children and four deceased. The living
are: Joseph W., born Jan. 22, 1848; Charles H.,
Nov. 4, 1850; Gershon M., Sept. 14, 1852; Jonathan
A., April 18, 1855; James L., Feb. 7, 1857; Albert
G., March 6, 1859; John B., Sept. 25, i860; Sarah
A., Aug. 8, 1862; Reneldo B., Sept. 3, 1864; and
Mary Jane, Nov. 8, 1867.
Mr. and Mrs. Noll are active members of the
Methodist Episcopal Church.
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[arlow Worthing, retired farmer, section
10, Sumner Township, was bom Nov. 29,
1812, in Waitesfield Township, Washing-
ton Co., Vt. His parents, Abner and Sallie
(Barloiv) Worthing, were natives of New
England and of New England ancestry, and
both died in Northport, Vt. His father was a car-
When three years of age, the subject of this sketch
was moved with the family to Addison Co., Vt.,
where they lived until he was 12 years old; then
they moved lo Windsor County, and when 14 years
old he went to live with an uncle, a tanner, in a dif-
ferent part of that State, but two years later he left
him and returned home. He soon went to Canada,
learned of his uncle. While in the French settle-
ments of the Dominion he learned the French lan-
guage, which he learned to speak readily. On leav-
ing Canada he went to Plattsburg, N. Y., on Lake
Erie, where he worked a year at his trade ; next he
was a ssailor on Lake Champlain for a year; then at
home for a few months; then was on a whaling ex-
pedition 14 months. While on his return home from
this voyage he visited St. Helena, and saw the first
burial place of Napoleop Bonaparte. He also visited
the curious island of Madagascar; then, crossing
over to South America, he remained awhile in Brazil.
He also stopped at the volcanic island of Amster-
dam, southeast of the Cape of Good Hope. Their
search for whales was principally in the Indian
Ocean, going as far south as the 49th parallel.
On returning to his native country, he resumed
tanning for two years ; then for a year he worked in
a morocco factory in Albany, N. Y. ; then two years
at the tanning business again at his old home in
Vermont; next, in 1839, he went to Wisconsin and
Illinois, selling Yankee notions; then joined a boat
crew at Peoria, III., and went to Memphis, Tenn.;
then he visited Cincinnati and Pittsburg, when he V
enlisted in the Mexican war, near its close, and was j
not therefore called into active service. Spending '
one year in Madison, Ind., he worked at masonry 18
months in Illinois ; was then two years and a half in
Iowa, and finally, in 1855, he came to the land office
at Ionia, and, under the Graduation Act, took posses- ^ '
sion of a half of section 10, where he still resides.
Yet unmarried, he boarded with one of the settlers, ,
and set out to improve his wilderness home. He |
successfully reduced a goodly portion of the land to \
a tillable condition, when rheumatism attacked him, I
and for the last 1 5 years he has done but little work. 1
He was Supervisor of this township at the first,
and during the yeats 1856-7, 1861, 1864 and 1868, >
Justice of the Peace eight years, Notary Public, High-
way Commissioner, etc., etc. In politics, he is a /
substantial Republican, and in religion a member of i
the United Brethren Church.
Oct. 17, 1862, Mr. Worthing was married to Mrs.
Sybil Metcalf, nee Kellogg, who was bom in Bradford
Co., Pa., July 4, 1831. By her former husband, her '
children are: Clara S. P., James H., Francis E. and
Levi F. By her present husband, the children are :
Sybil L., Mary L. and Barlow A. Mrs. W. is a mem-
ber of the Free Methodist Church.
eorge Whitman, farmer, section 29, North
Shade Township, is a son of Jacob and
Elizabeth (Case) Whitman, natives of Adams
Co., Pa., the father being bom in 1794 and the
f mother in 1795. The former died in 1869 and
the latter in 1844. The father of Mr. Whitman fol-
lowed the occupation of a farmer until his death.
The subject of our sketch was born May 25, 1832,
in Wayne Co., Ohio, where the parents had moved
at an early day. He remained under the parental
roof-tree until he attained the age of 19 years, when
to battle against the trials strewn along its pathway.
Mr. Whitman was married to Miss Mary Righley,
daughter of John and Rachel (Grcenhoe) Righley,
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natives of the Keystone State, where the father was
bom in 1812 and the mother in 181 6. Both are de-
ceased, the father dying in Summit Co., Ohio, in 1856,
and the mother in Erie County, same State, in 1882.
Mrs. Whitman, the wife of our subject, was bom
May 7, 1835, in Wayne Co., Ohio. After their mar-
riage the husband and wife moved to Indiana, where
they remained for seven years, then returned to Ohio
and remained three years, from which State they
emigrated to this county, arriving here Nov. 10, 1869 ;
they locate4 on section 29, North Shade Township,
securing 80 acres of wild and unbroken land. By
good management, coupled with energy and industry,
he has placed his land under such a state of culti-
vation that he looks back upon the past and wonders
how the improvement was ever accomplished. In
1883 he erected a large barn, 40x60 feet, which is
one of the best in the township.
Mr. and Mrs. W. are the parents of four children,
three sons and one daughter. John A., Joseph A. S.,
Douglas, and Amanda A.
Mr. Whitman has been honored with the position
of Constable of his township for two terms; has
been Moderator of his school district two terms, and
Postmaster six terms. He is also one of the Direc-
tors of the County Fair Association, of Gratiot, Clin-
ton, Ionia and Montcalm Counties, serving now his
second term.
The grandfather of Mrs. W. was a giant in stature,
being six feet and eleven inches in height. He was
a soldier of the war of 181 2, and died in Marshall
Co., Ind., Dec. 15, 1867.
Mr. Whitman in political action, belief and senti-
ment is a staunch Democrat.
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avid H. Payne, farmer on section 31, Ful-
ton Township, is a son of Arnold and
Loana (Parker) Payne, natives respectively
of Rhode Island and New York. They set-
^ tied after marriage in the Empire State, and in
\S^9 came to Washtenaw Co., Mich. After a
residence there of about four years, they removed to
Livingston County, and thence to Ingham County.
In the winter of 1846, Arnold Payne, with his wife
and 13 children, came to Gratiot County and took
up a large tract of land on section 31, Fulton. He
set about cleanng his land, and built a log house.
On this place he lived until his death, Nov. 24, 1879.
His first wife died Feb. 25, 1850. In 1853 he was
again married to Mrs. Mary (Bussell) Dickerman,
who died Aug. 31, 1865. He owned at the time of
his death 120 acres in Fulton Township, the old
Their family comprised 13 children, the following
eight of whom survive : Abigail, James L., Day and
Dwight (twins), Eliza, David H., Albert B. and
Thomas P . The deceased are : Alma, Lucy, Mary,
Perry and Arnold. The subject of this biographical
notice, the nth of the family, was bom in Livingston
Co., Mich.. Dec. 5, 1839, and was about seven years
old when his parents came to Gratiot County. He
received a common-school education, and remained
at home until 2 1 years of age, when he began to im-
prove 40 acres given him by his father. After clear-
ing 30 acres he sold out, and bought 40 acres on sec-
tion 31. This he worked two years, when he again
sold, and bought 80 acres on section 32. Two years
later he removed to Clinton County, and bought 60
acres in Essex Township, where he lived about eight
years. He then sold, and invested in village prop-
erty in Maple Rapids, where he erected good build-
ings and lived one year, and then traded for a farm
in Ionia County, where he lived from February, 1877,
to 1880. He then made his last move, coming to
120 acres, 100 of which are nicely improved.
Feb. 22, 1868, in Lyons, Ionia Co., Mich., he was
married to Miss Elizabeth, daughter of James and
Bethie (Walling) Youdan, natives of England and
New York State respectively. Mr. and Mrs. Y. came
to Michigan and settled in Clinton County in 1844,
where they lived until 1879, and then removed to
Clare County, where they lived until his death,
March 17, 1883. Mrs. Y. yet survives. Mr. and
Mrs. Payne have four children : Harlan, O. D., Verne
and Edith H.
Mr. P. has held the various school offices, and has
been Township Clerk in Fulton one year. He has
been Highway Commissioner in Clinton County. He
is a Democrat, and is a member of the Masonic Or-
der, being a Knight Templar. He is also a member
of the G. A. R., and he and wife are members of
Essex Grange, No. 429, P. of H.
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i<$^ V / 4 A 298 GRATIOT COUNTY. r:^\'.£- ^r In the fall of 1861, Mr. Payne enlisted in the 3d Mich. Vol. Cav., and served one year. He was in the engagement at Island No. 10, and at New Mad- rid, Mo. At the last named place he was thrown from his horse, and received severe injuries about the spine, in consequence of which he was honorably discharged. A portrait of Mr. Arnold Payne, the father of the subject of the foregoing sketch, is given in this work. eorge Crooks, farmer and mason, resident on section 27, Newark Township, was bom Sept. 19, 1835, in Fairfield Co., Ohio. Andrew and Sarah (Arnold) Crooks, his parents, were natives of the Buckeye State. At the age of 21 years, Mr. Crooks went to learn his trade and spent 18 months in completing a perfect practi- cal knowledge of its details. He has combined the callings of mason and agriculturist ever since. He became a soldier for the Union within tjie first year of the war, enlisting Feb. 20, 1862, in the 49th Ohio Vol. Inf., and, after three years of service, was honorably discharged at Huntsville, Ala., Feb. 2, 1865. He was in the battle of Peach Creek, and his command was attached tp the force of Gen. Sher- man, under whom it made the historic march to the sea. Mr. C. was disabled for a time, by hardships and exposure, and was cared for in the hospitals at Mur- freesboro, Nashville, New Albany, Jeffersonville, Louisville, Cincinnati, Camp Dennison and Cleve- land. At the last place he narrowly escaped death from strychnine placed in the food by the steward of the hospital. In the fall of 187 1, Mr. Crooks bought 160 acres of unimproved land in Newark Township. He erected a dwelling, took possession, and entered upon the labor of clearing and improving, and now has 65 acres under tillage. He was married April 6, 1858, in Wyandot Co., Ohio, to Sarah, daughter of Wal- lace and Catharine Greer. Mrs. Crooks was born Sept. 4, 1838, in Columbiana Co., Ohio. Her parents were born in the same State. The household in- cludes five children : Alwilda M., Dora M., Minnie M., Eugene G. and Alice D. Both parents are active members of the United Brethren Church, and Mr. Crooks is an ardent Republican. -5S22_ r \ <Lm ^enry W. Kinsel, farmer, section 15, Newark Township, was born March 7, 1847, in Han- cock Co., Ohio. He is the son of William and Catherine (Damon) Kinsel, who were na- tives of Germany. In the early period of their 1 lives they came to the United States, and, after staying a few years in Ohio, they came to Newark Township, Gratiot Co., Mich. The father enlisted in the 26th Regt. Mich. Vol. Inf., and after a year's service died at Norfolk, Va. The mother is still living. Mr. Kinsel was a lad of seven years when his parents came to Gratiot County. When his father became a soldier he returned to his native State and remained there three years, after which he came back to Gratiot County to engage in farming. He now owns 120 acres of land, with 75 acres under im- provement. He is a Republican in political faith, and has discharged the duties of several local offices to which he has been elected. Mr. Kinsel was married Aug. 21, 1870, in Newark Township, to Theda, eldest daughter of Jacob S. and Catherine (Baker) Beechler. The parents were born in Ohio, and are now residents of Newark. Mr. Beechler was the first Supervisor of the township. Mrs. Kinsel was born Nov. 28, 1847, ^" Ohio. She is a lady of creditable educational attainments, and has been a popular and successful teacher in Gratiot County. To herself and husband five children have been born, four of whom are living. They are named : Nora E., Myrtie C, Orin H. and Orpha M. omer Roberts, farmer, section 29, North ^ Shade Township, is a son of Joseph and Deborah (Wood) Roberts. They were both natives of Vermont, where the father followed the occupation of a carpenter and joiner. The parents moved from Vermont to Livingston Co., N. Y., and from there they came to this State and located on section 29, North Shade Township, this county, in 1853, securing 160 acres, upon which they lived and toiled, and on which our subject lives. He has added 40 acres, and by the united efforts of him. A Digitized by Google GRATIOT COUNTY. 299 s^ >'>^ ^ \ /On self and wife, 75 acres of the land has been placed under gpod improvement. The father was born in Orange Co., Vermont, Dec. 5, 1798. He enlisted in the U. S. Army in 181*1, and served until Aug. 15, 1815, and returned to his native State, and, after coming to this country, died, Nov. 5, 1880, leaving four children, namely: Josiah, George F., Sarah and Homer. Homer, the subject of our sketch, was born June I, 1834, in Livingston Co., N. Y., and has constantly resided on the old homestead ever since his parents located on it. His mother died in 1869, in North Shade Township, this county. Oct. 4, i860, Mr. Roberts was united in marriage to Mary Jane, daughter of Julia A. (McCurdy) Dob- son, natives of the State of New York. They moved to Jackson Co., this State, and remained there for a number of years, thence removed to Hillsdale County, from which place they came to this county and are now living in North Shade Township. Mr. and Mrs. Roberts are the parents of three children : Anna E., Effie A. and Libbie A. Mr. R. has held the position of Township Treas- urer, and in political opinion is a Republican. Both Mr. and Mrs. R. are members of the Con- gregational Church. ^ ^>;^ .--'s-' ^ :■ ;">> Frederick B. Segward, farmer, Fulton Township, section 2, was born Aug. 15, 1 84 1, in Buffalo, N. Y. His parents, Clemens and Catherine (Myers) Segward, were natives of Germany. They came to the United States in early life, and settled in the State of New York, where the father died, about the year 1870. The mother yel survives, in the Empire State. Mr. Segward was bred to the business of a farmer, and followed agriculture in his native State until he was 22 years old. In the fall of 1863, he came to Gratiot County and bought 46 acres of wild land in Newark Township, on section 35. He there resided and made good advance in the improvement of his land during the next 12 years, when he removed to Fulton Township and bought 40 acres of land, to which he has since added by purchase dd acres. That of his land now under improvement and in progi'^ssive cultivation, is estimated at 75 acres. Mr. Segward is a Republican in political sentiment and action. He was married Oct. 16, 1863, in Niagara Co., N. Y., to Emma, daughter of Peter and Charity Deline. Her parents were natives of the Slate of New York, and her father is now a citizen of Newark Township. Her mother died in 1868. Mrs. Segward was born June 13, 1843, i'^ t^c Empire State. The household includes three children — Catherine A., Mary L. and Frances M. v^ apoleon B. Frakeir, retired farmer, residing at Ithaca, was born in Saratoga Co., N. Y., June 25, 1 8 15, and was of New England parentage and English ancestry. At the age of 15, he moved with his parents to St. Law- rence County, same State ; and here he worked on his father's farm until of age. For the ensuing eight years he was employed as a farm laborer in the vicinity, and he was then united in marriage with Miss Rebecca Merrill, who was born in St. Lawrence Co., N. Y., Sept. 4, 18 17. They at once settled on a 50-acre farm purchased by Mr. F., and there lived until 1 86 1. He added 120 acres, and improved the whole farm of 170 acres, erecting suitable buildings. Selling out in the spring of the year mentioned, he purchased 240 acres of land in the State of Iowa, and started for the new home. While on his way, he fell in with parties coming to Michigan, who induced him to change his course. He came to Gratiot County, and shortly traded 120 acres of his Iowa land for 160 acres on section 8, Washington Town- ship. He soon after brought his family here from Ohio. He has added 20 acres, and of the whole 180 acres, 130 are improved ; and the two large stock and grain barns and suitable residence show the results of his labor. He retired from active business in 1880, and came to Ithaca, where he has since re- sided. He owns there two and a half acres of land, and a good dwelling. He and wife have been the parents of four chil- dren, — Addison and Ransom, living, and Ansel and Charles, dead. Ansel died in the service of his country, and Charles from the effects of exposure during the .service. Politically, Mr. Fraker is a.Re* r v.-^rL -^<:Q3>:Gav>-^ A;^. -, J r r i J Digitized by Google •.Va>'.- r- r i 300 GRATIOT COUNTY. f V V publican. He has been Supervisor of Washington eight years. Clerk three years and Justice of the Peace six years. He has also been Highway Com- missioner, and has held various other offices. ^rastus C. Farrington, farmer, section 30, Emerson Township, was born in Norfolk Co., Mass., Aug. 4, 1824, and was the son 5S. of Harvey and Nancy (Tilson) Farrington, -^ natives of Massachusetts, and of old New England stock. They both died in the Bay State, at an advanced age, about 1868. Erastus worked at home until 16 years old, and was kept so busy with work that his school advantages were very limited. At the age mentioned, he was apprenticed to one Erastus Dupey, of Wrentham, Mass., to learn the trade' of making shoes. After one year he re- turned home, and engaged with his father in this business, which they carried on together until he was of age. At that age, he was united in marriage to Jimima Packard, a native of Maine. Eight years later they removed to Fulton Co., Ohio, and in the fall of 1854 they came to this State, locating on the present homestead, section 30, Emerson Township. For six or eight years after he came here, he followed his trade winters, and fanned during the summers. March 10, 1866, his wife died, leaving six chil- dren, a seventh dying previous to her demise. Their names are as follows: Eugene E., bom Oct. 29, 1853; Nancy E., bom June 11, 1857; Nellie M., born Aug. 13, 1859; Charles W.,born July 18, 1864; Alice, born March 26, 1851, and died Sept. 1 1, 1862 ; Elmer E., born March 15, 1862, and died Aug. 29, 1873 ; Willie, born Feb. 19, 1866, and died Aug. 4, March 25, 1867, he was again married, in Wood Co., Ohio, to Laura, daughter of Jonas and Mary (Carpenter) Carter, natives of New England. She was born in Delaware Co., O., May 16, 1832, but at the age of one year her parents removed to Wood County, where she received a good education. At the age of 17, she began teaching district school, which she followed unril 1864, and then devoted herself to the study of art. In 1865 she moved with her parents to this State and county, keeping up her work as an artist until her marriage, since which time she has lived on the farm. Mr. Farrington arrived in Emerson Township before an acre of wood had been cleared away, and after securing 40 acres he began to open up the country and make roads through the forest, then un- broken for miles in every direction. He has now 60 acres of very valuable land, most of it well improved. Beginning in a small log hut, he has lived to be able to have a large, well arranged and comfortable resi- dence. He is a member of Ithaca Lodge, No. 123, F. & A. M.; and has been a Master Mason for nine years. In the lodge he has held the offices of J. D., S. D., J. W., S. W. and Tyler. In politics, he is an ardent and influential Republican. He belongs to the Baptist Church, and his wife to the Methodist Episcopal Church. They are socially popular, and few citizens of Gratiot County are more highly esteemed by their neighbors. -4- \ OBwell Danly, farmer, on section 36, Fulton Township, is a son of Ingalls and Electa (Angell) Danly, narives of the State of New York. The parents first settled in Jefferson Co., N. Y., where they followed the occupation of farming until their death. The father departed this life May 7, r838; the mother, July 15, 1864. Their family included four sons and three daughters. The eldest of the family was Roswell, born in Jefferson Co., New York, Oct. 24, 1827. He received a common-school education, and remained at home unril 23 years old. After the death of his father, the labor and responsibility of managing the home farm largely devolved upon him. Although his home was with his mother unril he was 23, yet at the age of 17 he embarked as a sailor on the lakes, which business he followed 14 years, i. e., from 1844 to 1858. Shipping before the mast as a common sailor, he gradually worked his way up to the post of mate, then pilot, and for four years commanded a vessel, thus earning the title of Captain, by which he is com- monly known in the community in which he resides. He has a high place in the confidence and esteem of a wide circle of friends. In the fall of 1854, he located 80 acres of land in Clinton County, this V .>v>/ Digitized by Google Digitized by Google Digitized by Google <• T <:Iltl><:lia>> T ^ GRATIOT COUNTY. ; '^ 1^ State, and worked during the subsequent winteis at clearing the same. In the summer of 1858, he bought 80 acres of partly improved land in Fulton Township, on section 36, where is his present resi- dence. He has since 'added 40 acres opposite his farm in Clinton County, and has 100 acres well cultivated. Jan. 29, 185 1, in Jefferson Co., N. Y., he was united in marriage to Nancy Brougham. Her parents, William and Nancy (Rilyea) Brougham, were narives of the Empire State. Mrs. Danly was born in that State, May 24, 1829. Mr. and Mrs. D. are the parents of four children : William W., Viola J. (deceased September, 1864), James B. and Charles R. William W.,the eldest, is at Boyne City, Charlevoix County, engaged in lumbering. He is married, and has two daughters. Capt. Danly was the enrolling officer of Fulton Township during the war, and has held the office of Supervisor two terms. He is politically an ardent supporter of the Democratic party, and he is a mem- ber of the Masonic Order. ^chuyler W. Ambler, real-estate and loan agent at Ithaca, was born July 24, 1826, in Nassau, Rensselaer Co., N. Y. His father, Peter W. Ambler, was born in January, 1802, in Columbia Co., N. Y. The parents of the latter went in his infancy to Nassau. He was of English descent and was reared to the vocation of agriculture, which he made the pur- suit of his early manhood, and later engaged in mercantile life. He went in ^833, to Yates, Orleans Co., N. Y., and in 1839 returned to Nassau, where he was interested a few months in the manufacture of woolen goods. He was a man of deep religious convictions, and in the winter of 1840 was licensed to preach ; he was regularly ordained a minister of the Baptist Church in 1843. In 1846 he bought 60 acres of land in Nassau Township, which he man- aged about eight years and sold in 1854. A few years later he bought the property whereon he died, Oct. 5, 1873. He labored in the interests of religion in Columbia and Rensselaer Counties, in the State of New York. His wife, Polly (Waterbury) Ambler, was of English descent and was bom in jNassau, where she died, in April, 1871. Mr. Ambler was a diligent student in the early years of his life, and, at the age of 16, was placed at Transylvania Institute for the purpose of making a thorough preparation for college ; but the plan of his education was never consummated, as his health failed and he was compelled to abandon the project. He was employed. for a time on the farm and taught school a number of winters. In 1851 Mr. Ambler bought 200 acres of land in Nassau, and devoted his energies to the pursuit ot agriculture until 1858, when he engaged in general mercantile pursuits at Brainard's Bridge, Nassau Township. Soon after the inception of the project he became associated with an individual named Hasting Kellogg, which rela- tion existed and was managed successfully until the spring of 1869. At that date, Mr. Ambler sold his interest to his partner. He had sold his farm in 1863, and the disposal of his sole remaining business interest left him free to select a new location, which he was desirous of doing. He came to Jackson, Mich., and spent the summer of 1869, there examin- ing the comparative claims of new districts in the Peninsula State, relative to the choice of a location. He fixed upon Gratiot County and arrived at St. Louis Nov. 6, 1869. He engaged in teaching the winter ensuing, and in the spring of 1870 he became a salesman in the mercantile establishment of Hi- ram Harrington, and continued in that vocation be- tween two and three years. Meanwhile he was elected President of the village and served in that capacity one year (1872). In January, 1873, he came to Ithaca as Deputy County Treasurer, for A. B. Darragh, and discharged the duties of the posi- tion two years. In the fall of 1874 he was elected Treasurer and held the position four years. During the period of his official term he became interested in buying and selling real estate and in negotiating loans. On the expiration of his official obligations, he opened an office for the regular and systematic transaction of business in the avenues named, and has since been engaged in attention to his private af- fairs. He is dealing extensively in real estate, and now owns 700 acres of valuable farming lands in Gratiot County. He also owns town property, in- cluding a fine residence and a dwelling with two lots. Mr. Ambler has been President of Ithaca three successive years and Trustee for two years. He has also served one year as Justice of the Peace of Em-* eraon Township. K^ :7\ /^v. y<^ ^m:- IvV- ,y> //.N vl >. r Digitized by Google 7- <^^llll^nily> V ":^^<s'- -^^si ^(5^^ ^ f i f :■ >) '•h (^ 304 GJ^A TIO T CO UNTY. His marriage with Miss Charlotte M. Knapp, of Nassau, N. Y., occurred Sept. 14, 1850. She was born in the same place, April 2, 1832, and is the daughter of Isaac and Melinda Knapp. (The mother resides with the daughter.) Mr. and Mrs. Ambler have had eight children, as follows : Mary E., wife of Robert Banwell, a merphantof Belvidere, 111. (They are the parents of three children — Fred- die, Charlie and Irvine.) Sarah M. was married to Julius E. Lyon, who is now deceased and left two children — Florence and Ix)throp M. She is now the wife of Isaac M. Sayles, of Ithaca, and has an in- fant child. Eva S. was born Aug. 29, 1856, and died Dec. 9, 1864. Irvin S. was born Sept. 27, 1858, and died Nov. 15, 1877. The remainder of those surviving are Nettie L., Inis, Willie and Fanny. Mr. Ambler is a fair type of the substantial ele- ment of Gratiot County. He has conducted his bus- iness on a basis of integrity and uprightness, and guided his life in a manner that secures to him, at its later meridian, the comfort and content he has earned. His portrait, on another page, is a credita- ble acquisition to the list of similar representarive men in this volume. ^dward Downs, farmer, on section 13, Ful- ton Township, is a son of John and Mar- garet (Foreman) Downs, natives of Ohio 5^ S. and Pennsylvania. They first settled in Holmes ^ Co., Ohio, and afterward removed to Hancock County, same state, where they at present reside. Edward was born in Holmes Co., Ohio, May 18, 1840. He received a common-school edu- cation, and remained at home until 2 1 years of age. In May, r 861, he responded to the first call of President Lincoln for troops to suppress the Southern rebellion, and enlisted in the 21st Ohio Vol. Inf., which was a three-months regiment. In August, 1862, he again enlisted, this time in the 99th Ohio Vol. Inf., and he served from that time on to the close of the war. He was in 32 regular engagements, besides numerous skirmishes. In October, 1865, he came to Gratiot County and bought 65 acres on section 23, Fulton Township. He afterward purchased 40 acres on section 13, where he now resides, and where he has put up a good dwelling and other farm buildings. He has 80 acres under cultivation. April 10, 1863, in Hancock Co., Ohio, he was united in marriage to Lucinda, daughter of John and Margaret (Gibson) Chaffin, natives of Virginia and Pennsylvania. Mrs. Downs was born in Hancock Co., Ohio, Aug. 18, 1839, and is the mother of ^s^ children: James E., Ella M., Mary E., John L. and Milo V. Mr. and Mrs. D. have adopted as their own child Marcia Cole, and she is known as Marcia C. Downs. Politically, Mr. D. is a Republican. saiah Hatfield, farmer, section 36, Newark Township, is the son of Jacob and Catherine (Franks) Hatfield, the former a native of New Jersey, the latter of Pennsylvania. After their marriage, they located in Wayne Cx)., Ohio, where they resided more than 30 years. Their family comprised fvvt sons and two daughters, named as follows: William, Michael, George, Jacob, Isaiah, Charlotte and Sally. Late in life, the parents moved to Medina Co., O., to reside with their young- est son, and there lived till the fathers death. The mother returned to Wayne County, where she died. Mr. Hatfield was born in Wayne Co., Ohio, Apnl 28, 1822. He left home at the age of 16, and en- gaged in farming, afterwards becoming interested in managing threshing-machines, which business he pursued nearly six years. In 1853, associated with his brother Jacob, he went to the State of Iowa and bought 590 acres of land, which they sold after one season, and returned to Ohio. They bought 170 acres of land in Medina County, and held its pro- prietorship seven years. Mr. Hatfield sold his in- terest therein in the spring of 1 861, and came to Michigan. He bought 80 acres of unimproved land in Newark Township, and disposed later of 40 acres. All but eight acres of the remaining moiety are cleared and under cultivation. He is mdependent in political sentiment and action, and has occupied the various school offices in his district. He is con- nected by membership with the Masonic fraternity. Mr. Hatfield was married Aug. 30, 1848, to Mrs. Polly (Weidman) Shank, widow of Michael Shank, and daughter of John and Barbara Weidman. Her parents were natives of Pennsylvania, and after their /.N -^<^[!'l^^'I;[i;>>-^ J3'^-'^:^yTL^ Digitized by Google r ^r'-'% '7<m':>:m>^-^ ^\ A ^ GRATIOl COUNTY. 305 marriage removed to Canada, where the daughter was born Feb. 27, 1821. But one of three children bom of her first marriage survives, Mariette. The others were named John and Henry. Three chil- dren have been born of her marriage with Mr. Hat- field : Teresa, May 16, 1856; Adam P., born July 18, 1849, and died March 24, 1850; George, born Feb. 2, 1850, and died Sept. 16, 1856. Mr. and Mrs. Hatfield are members of the Church of United Brethren. Mr. H. was for 30 years a member of the Methodist Episcopal Church, and has for four years been a minister in the Church to which he now be- longs. [ oah Sooy, farmer on section i, Fulton Town- ship, is the son of Samuel and Rebecca (Tailor) Sooy, who were of Welsh and Hol- land descent and settled in New Jersey. rlG Noah was born in Wayne Co., Ohio, June 10, 1816, and received a common-school education in that county. When 1 8 years old he removed to Me- dina County, same State, and in the fall of 1866 he made his last, long move to this county, buying 100 acres on section 3, Fulton Township. After residing there 14 years he sold and purchased 77 acres on section i, same township, where he now resides. He has 60 acres under cultivation. Aug. 12, 1 84 1, in Medina Co., Ohio, he married Miss Sarah Driskell, who was born in Wayne Co., Ohio, Feb. 5, 1822. They have had seven children, of whom four survive: Elizabeth, Jemima, Avery and Corlis S. The deceased are : Perry, Joseph C. and Benjamin F. Mr. Sooy has been School Di- rector two years, and in politics is a National. ^enry Bodfish, farmer, section 12, Bethany Township, is a son of Oliver and Sarah (Walker) Bodfish, who were natives respect- ively of Massachusetts and Maine, first settled in New Bedford, Mass., and afterward in Onon- daga Co., N. Y., where Mr. B. followed agricul- tural pursuits and resided the remainder of his life, his death taking place .\pril 8, 1883. His wife died Aug. 27, 1851. -'?^,'- -^<:C The subject of this sketch was born in Onondaga Co., N. Y., April 18, 1843. When 20 years of age he enlisted in the loth N. Y. Cav., and served a year and a half, participating in the battles of the Wild- erness, Spottsylvania Court-House, Cold Harb6r, Weldon Railroad, Vaughn Road, Five Forks, etc. ; was at the surrender of Gen. Lee. He was then at his home in Onondaga County a year, and next, in April, 1866, he came to Midland Co., Mich., where he followed milling and lumbering nearly 12 years. In the spring of 1878 became to his present place, which he had bought eight years previously. At first it comprised 120 acres, but Mr. B. subsequently dis- posed of 40 acres, and a half of the remainder is now in a good tillable condition. Sept. 6, 1874, Mr. Bodfish was married to Miss Emma, daughter of Seth and Julia A. (Crandall) Gould, natives of Canada. She was bom in Cana da, Aug. 18, 1852. The children of Mr. and Mrs. B. are John H., George, Sarah M., Mary G. and Frank L. Mr. Bodfish is a member of the Masonic Order, and in politics is a " National." I^iram Townsend, farmer, section 31, North Shade Township, is the son of Josiah and ^1^ Dolly (Parker) Townsend, and was born in O Jefferson Co., N. Y., Sept. 23, 1806. His parents ( were natives of Connecticut, where they were engaged in farming. They moved to Jefferson Co., N. Y., where they spent the remainder of their days. At the age of 2 1 years, Hiram left the home of his parents and embarked on the voyage of life for him- self. He learned the trade of carpenter and joiner, which he followed for about 14 years. During this period he spent much time of the winters in the manufacture of joiners* tools. In the year 1854, Mr. Townsend married Miss Louisa, daughter of Amasa and Luna (Townsend) Page. Mr. Page was a native of New Hampshire, and the mother of New York State. Both of them have long since closed life's labors, the former dying in i860, and the latter in 1858, both in New York. Mrs. Townsend died in 1847, in Jefferson Co., N. Y. Sept. 28, 1848, he was married to Miss Luna Page, a younger sister of his first wife. ft r: -i 2_ : h 9 Digitized by Google GRATIOT COUNTY, J \/ Mr. Townsend moved from New York to Michigan in 1865, and located on section 31, North Shade Township, on a tract of 87 acres of land, of which 65 acres are in a good state of cultivation. The farm is well improved and has upon it good farm buildings. Mr. Townsend is the father of eight chil- dien, viz.: Luna, Erastus, Ambrose E., Eber L., Harlan, Orville H., Frank E. and Ida A. The first four were by his first wife. Politically, Mr. Townsend is a Republican. ■ I "Hoj^ g ^^o^ ! ■ ^ ilton H. Davis, fanner on section 1 6, Ful- ton Township, is a son of William and Sally M. (Cast) Davis, natives of New York State. He was bom in Medina Co., t Ohio, March 19, 1851, and at the age of 13 came with his parents to Gratiot County. He remained at home until 22 years old, and then pur- chased 80 acres of Government land in Otsego Co., Mich. Six years later he sold, and bought 85 acres in Fulton Township, this county, where he now re- sides. He has 70 acres under cultivation. Feb. 22, 1873, at Ithaca, this county, he married Sarah, daughter of Peter and Nancy I^ddick, She was born in Seneca Co., N. Y., Nov. 6, 1850. This marriage has been blessed with three children: James E., William T. and Nela M. Mr. Davis is a member of the M. E. Church, and in politics is a Republican. oseph B. Holton, farmer, section 1 4, Beth- yl^^lf- any Township, is a son of Joseph and Eliz- ?^ & '"^ abeth (Barnes) Holton, who emigrated from T|v, England to America in 1849 and first settled W in Jackson Co., Mich., and in 1866 where they y now reside, in Bethany Township, this county. Joseph E., the eldest son, was born Aug. i, 1842, in England ; remaining with his parents until the war of the rebellion commenced, he enlisted, in August, 1861, in the 8th Mich. Inf.; but, being under 18 years of age, he was soon discharged, by request of his father. In August, 1862, he again enlisted, in the same regiment, and remained in the service until July, 1865, participating in 13 engagements. When -v.- :. ^:- •■ before Petersburg, Va., in April, 1865, he received gunshot wound in his left thigh. After his discharge he came to Jackson Co., Mich and soon entered the commercial college at Albioi Mich., where he graduated. Since 1866 he has re sided on his present place, where he is the owner c 120 acres of good land, with 57 acres cleared an subdued to a fine tilth. In the spring of 1880 h was elected Justice of the Peace, which oflice h still holds. Has been also School Director for si years and Commissioner of Highways. He belong to the " National " party. March 19, 1868, in Bethany Township, Mr. Ho ton married Miss Dorinda, daughter of Bernard an Dorinda Fox. (See sketch of Bernard Fox.) Mr H. was bom in Steuben Co., N. Y., April 4, 184J The children in this family are : Harvey B., Id M., Carrie L., Jessie E., George W. and Fred. I Jessie died when about three years old. rederick S. Kelly, retired farmer an stock-raiser, section 36, Ithaca Townshi] was bom in Wood Co., Ohio, May i( 1832. His father, John A. Kelly, was a nati\ of Ohio, and was the first settler in Mon gomery Township, Wood County. When h went there, the Indians were very numerous, an numbers of them would occasionally spend the nigl at his hospitable home. When he '* raised" h cabin, he had to go 14 miles for help. In th pioneer home, the subject of this sketch passed h early childhood, and it was but natural for him to ai quire that pluck and energy with which all successf pioneers are endowed. Frederick Kelly's mother, Rachel Shawn, was native of Virginia, came to Ohio when very youn and there lived until her death, in 1840. Her fath was a soldier in the Revolution, serving seven yeai Frederick attended the first school in his nati^ township. The school-house was a log stractui 14 X 18, covered with "shakes." The benches coi sisted of the roughest son of bass wood logs, split, ac the legs inserted therein so as to form a half-ronn seat. The fire-place was made of sticks and daul and the prominence of the comers admitted of it children climbing to its top, which was a fine reso Digitized by Google '. C' r<> ^:IlU:^:tlIl>^-r- r GRA no T CO UNTY. 307 for the urchins of that pioneer school. The familiar trick of fastening the door, and then calling out, ** Teacher, stay out or treat," was occasionally prac- ticed on Christmas by the mischievous pupils ; but on one occasion the master beat them at their game. He took advantage of the peculiar style of the chim- ney, and, by covering its top, smoked them out; Frederick passed the first 22 years of his life in at- j tending school, and in assisting his father to clear their farm and make a comfortable home. Feb. 17, 1853, he was married to Mary Davis, a native of Ohio. Two years later, they came to this State and entered 280 acres of land in Newark Township, this j county. June 17, 1866, his wife died at her home in ! this county, leaving two children: Ella, born Aug. I 25, 1857 ; and John, bom Nov. 25, 1858. Mr. Kelly was a second time married, April 18, i 1867, to Mrs. Emma Jenner(«<r<r Humphrey), daugh- ter of John and Ann (Best) Humphrey, natives of I . England. She was born in Sussex, England, April , , 13, 1 84 1. Her parents were farmers, and she lived _: at home and attended school in England until 15, " when her parents brought her to the United States. -.1 Their passage across the Atlantic occupied six '" weeks. From New York city they went to Levanna, Y Cayuga Co., N. Y., thence to Springport ; and in the j fall of 1863 they came to this county and located in ^ Newark Township. Emma s first husband, Henry Jenner, enlisted Sept. 3, 1862, was taken prisoner at Newbern, N. C, Feb. 2, 1864, and died in the prison pen at Anderson ville, April 18, 1864, of small- pox. Mr. Kelly enlisted, Aug. 12, 1862, in Co. D, 26th Mich. Vol. Inf., commanded by Capt. Lafayette Church, of this county. He enlisted as wagoner, and was soon made "boss" wagoner, which post he held until he was honorably discharged, June 15, 1865, after serving nearly three years. Jan. II, 1 88 1, he left his well improved farm of 280 acres in Newark township in care of his son, and purchased his present home of 40 acres on section 1 36, Ithaca Township, near the village of Ithaca. Here he lives a retired life, devoting a portion of his time to dealing in stock. He has by his second mar- riage one daughter, Fanny, born June 8, 1877, the I namesake of her aunt, Fa"hny Kelly, who was for five r\ months a capdve among the Indians of Idaho. Mrs. Kelly's first marriage occurred Dec. 14, 1859; "' and by this marriage she has two sons: Thomas C, born Feb. 12, 1862, and Edward H., born Junes, 1863. Mr. and Mrs. Kelly are not members of any Church, believing that a high morality, as taught by our conscience, is the best religion. He has held the office of Highway Commissioner for six years, and Township Treasurer for two years, besides minor offices. He was the second Treasurer of New- ark Township. Polirically, he is a zealous member of the National Greenback party. A^HJiO/®^ 'SS^)^3'79Vw -K-^oo:- |: eter Myer, farmer, section 9, Bethany Town |,Mp,fe ship, was bom in Prussia, Feb. 23, 1821 J [irV^. His parents were natives of the same country j\^.^ and there followed the occupation of farming 'fC until the year 1841, when they emigrated to the United States and settled in Dhio, where they both died, the former in 1875, and the latter in 1870. Mr. Myer remained at home, in his native land, assisting his father on the farm and accompanied them to the States. On arrival in Ohio he engaged himself as a farm laborer for two years to a gentleman in the vicinity of Cleveland, afterward working in a brick-yard two summers and cutting wood in the winters. His next move was to Huron County, where he remained two years working on a farm, and then moved to Williams County, same State, and purchased 40 acres of land. He labored on this land for nine years, when he sold it and came to this county, arriving here in the year 1867. On arriving here, he purchased 80 acres of land on section 9, Bethany Township, and turned his undivided atten- tion to the cultivation of the same. He has suc- cessfully cleared 62 acres of this land and placed it under good improvement, on 40 acres of which there is not a stump to be seen. Mr. Myer was united in marriage June 20, 1850, in Cleveland, Ohio, to Miss Julia N. Midlle, bom in Germany, Aug. 31, 182 1. She came to the United States in 1850, the year she was married. Mr. and Mrs. Nfyer are the parents of six children, only two of whom survive, namely : Catherine, who was united in marriage to John Schultes, and is at present living on section 8, Bethany Township; and <v^ V izn r ^ / Digitized by Google 308 y^^'»/<-'-^ GRATIOT COUNTY. ^i-'tKir^ -■^i2-V^/■•.-"^ ^i V A ^ 3 Mary, the wife of Frank Peach, living on section 4, in the same township. Mr. and Mrs. Myer are both members of the Ger- man Lutheran Church, and Mr. M. has held an of- fice in the Church for many years. In political opinion Mr. M. is a Democrat. ^1 ^-4$. \^
;ame8 M. MoKee, farmer, section 6, Ithaca
Township, was born in Niagara Co., N. Y.,
Jan. 14, 1836. His father was Anthony
McKee, a native of Orange Co., N. Y., and o^
Scotch and German extraction. James was
reared on a farm and educated in the common
schools of his native county. In 1867 he came to
Washtenaw Co., Mich., where he worked at his trade
of carpenter and joiner during the summer and
taught school during the winter. He came to Gratiot
County in 1873, taught one winter, and has since
been engaged in agriculture, now owning 85 acres of
well improved land.
Oct. 22, 1873, Mr. McKee married Miss Mary
Killin, daughter of Patrick Killin, and their children
are : Belle and Berenice.
Mr. McKee is a Freemason in good standing,
having taken nine degrees in the mystic art.
iilliam H. Wheeler, farmer, section 12,
Newark Township, was born Oct. 9, 1839,
in Oswegp Co., N. Y. His parents, Sylvester
and Hannah (Peck) Wheeler, were natives
respectively of Vermont and New York. (See
sketch.) In 1852, when he was but 13 years old,
his family went to Kane Co., III., and after a stay of
more than a year they came to Michigan. He re-
mained with them until 1863. They came to Gratiot
County in 1855, after a stay of six months in Ingham
County. Since that date, Mr. Wheeler has contin-
ued a resident of Gratiot County. He owns 160
acres of land and has 108 acres under fine improve-
ments and in advanced cultivation. Mr. Wheeler is
a Republican, and acts for the issues and interests of
that party. He has been Director of School District
No. 2 ten successive years, and has served four years
as School Assessor.
He was married in Greenbush, Clinton C^., Mich.,
Aug. 6, 1863, to Mrs. Ann L., widow of George
Hawkes, and daughter of John and Ann L. Cook.
She is a native of England, and was born Nov. 5,
1839, near Canterbury. Her parents brought her to
the United States when she was 1 2 years old. Her
first husband died March 14, 1861, leaving two chil-
dren, — Samuel J., born Dec. 11, 1859, and Thomas
E., Sept. 6, 1 86 1. Following is the record of the
births of six children born to Mr. and Mrs. Wheeler:
Alfred W., July 3, 1864; George E., Aug. 29, 1866;
Mary J., Dec. 5, 1868; Warren W., April 8, 1870;
Cora E., July 29, 1873; Frederick H., July 8, 1876.
The family attend the United Brethren Church, ol
which the parents are zealous members.
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ranklin Miller, the first resident lawyer of
Gratiot County, was born in Lodi, Seneca
Co., N. Y., March 13, 1833. His ances-
tors, back to an indefinite date previous to the
Revolution, were farmers, and formerly resided
in the township of Goshen, Orange Co., N. Y.,
emigrating to the " lake country " at the close of the
war for independence.
He received the rudiments of a common English
education in the district schools of the neighborhood,
and, commencing at 1 6, pursued for three years a
course of academic studies. The ensuing three years
he studied law at Elmira, N. Y., and in 1855 he was
admitted to practice in the courts of the Empire
State. The same year, he came to this State and
county, arriving previous" to the first election of county
officers, when he was elected Prosecuting Attorney, —
the first to hold that office in Gratiot. He was the
first resident licensed attorney, and at the next elec-
tion was re-elected for a second term. Before the
conclusion of this term, however, ill health compelled
his resignation; and in the spring of 1859 he made
the overland trip to California, going the next year to
Oregon. On the discovery of the gold fields of Ida-
ho, he was among the first to settle in that little-known
Territory.
In 1871, he returned to Michigan, married, and
remained a resident of Gratiot County until 1882,
when he went once more to Idaho. He will be long
remembered as one of the pioneers of this county.
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He was among those who secured the location of the
county offices at Ithaca, and he was the first Post-
master of the county seat, which he named in re-
membrance of Ithaca, N. Y. He purchased and
and brought into Gratiot County its first printing
press. He was the original projector of the Michi-
gan Central Union Fair Association, and was in var-
ious ways instrumental in the progress of the county
and county seat.
^ohn P. Buppert, farmer on section 27, Ful-
ton Township, is a son of John P. and
Christine (Sholler) Ruppert, natives of Ger-
T7A many, in which country they died. He was
W^ also born in Germany, Sept. 15, 1815, and in
\ 1853 came with his wife and one child to the
United States. For three years he lived in the State
of Ohio. In the autumn of 1856, known as the
*' smoky fall," he came to Gratiot County and bought
80 acres of wild land on section 27, Fulton Town-
ship, where he has since resided. He has now 40
acres under the plow.
He was married in the " Fatherland," in Septem-
ber, 1843, to Miss Anna B., daughter of Frederick
and Mary B. (Christine) Buttner, natives also of the
old country. She was born there Sept. 8, 18 14. Mr.
and Mrs. Ruppert have one son, George M., a sketch
of whom is given in this work. They have formerly
been members of the Evangelical Lutheran Church.
Politically, Mr. R. is a Democrat.
rohn Biohard, Sr., farmer on section 34, New-
ark Township, is a son of John and Mary
(Poorman) Richard, natives of Franklin
Co., Pa. They followed farming all their lives
and died in Westmoreland Co., Pa., whither
they had removed. The father departed this
life in May, 1833, and the mother Dec. 19, 1845.
The subject of this biography was born March 16,
1 8x1, in Westmoreland Co., Pa., and alternately
worked on the farm and attended school until 21
years old. At this age he was united in marriage
with Rachel Fry, daughter of Michael and Regina
(Spillman) Fry, natives of Luzerne Co., Pa. Mr. and
Mrs. Fry followed farming, and died in their native
county, the father in 1853, and the mother in 1866.
Their daughter Rachel was born May 27, 1815, in
Westmoreland Co., Pa., and was the third daughter
of a family of 13 children, all of whom are now dead
but three.
Mr. and Mrs. Richard moved in 1846 to Ashland
Co., Ohio, and in 1854 they went to Wood County,
same State. Here he worked out a comfortable
home from the dense forest. He is a man of iron
constitution, and nothing in the way of hardship or
toil could daunt him. In the spring of 1871, he
moved with his family to Gratiot County, and located
on 80 acres on section 34, Newark Township, where
he now resides.
During the late war, he sent four sons into the
army, and twice enlisted himself; but was not ac-
cepted, on account of his personal sacrifice in risking
the lives of his sons. Mr. and Mrs. Richard h.ive
been the parents of ^s^ sons and six daughters. He
is a staunch Republican, and with his wife belongs
to the United Brethren Church. They have been
Christians 40 years.
■^^^^'ohn H. Jessup, farmer, section 25, Newark
Township, is the son of Isaac M. and
7^^^ Eleanor (Schermerhorn) Jessup. The for-
mer was born in Tompkins Co., N. Y., April 5,
810; the latter Nov. 20, 1815, in Rensselae
County, in the same State. Their marriager
took place in New York, and in 1839 they emigrated
to Michigan, and at first settled in Eaton County,
going afterward to Wayne County. They maintained
their residence there for 15 years, and in the spring
of 1853 removed to Ionia County, wher^they are at
present located. Four daughters and five sons were
born to them : Jane M., Abram M., John H., Alida
A., Jacob S., Andrew S., Mary E., Edward T. and
Eleanor E. The last named child died when nearly
three years old. .
Mr. Jessup, of this sketch, was bom Dec. 24, 1837
in Rensselaer Co., N. Y. He was 17 years old when
his father located in Michigan, and he obtained his
education in the common schools of the Peninsular
State. On reaching the period of his legal freedom,
he found himself with the world before him, to wrest
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success from opportunity, or to wait in listless apathy
for the fortune that comes soonest to manly, well-
directed endeavor. In December, i860, he came to
Gratiot County, and became the owner of 63 acres of
unimproved land in Newark Township, of which he
is still proprietor. He built the customary log house,
and continued its occupancy until 1880. In that
year, he completed and took possession of a fine
brick residence. To his original farm he has added
85 acres, and is now carrying on successful agricul-
ture on 148 acres, of which 123 acres are finely im-
proved land. Mr. Jessup belongs to the Republican
element in politics, and has officiated three years as
School Director in his district.
In October, 1864, he was drafted, and assigned to
service in the 23d Mich. Vol. Inf., and was in the
army nine months. He participated in the actions
at Franklin and Nashville, Tenn., and at Port Ander-
son, N. C. Was honorably discharged from the ser-
vice of the United States in June, 1865, at Washing-
ton, D. C.
Mr. Jessup was married Dec. 29, 1859, at Lyons,
Ionia County, to Margaret R., daughter of Amos and
Betsey (Grant) Dean, natives of the State of New
York, where they were married, and whence they re-
moved their family to Ionia Co., Mich., in 1854, and
in 1 86 1 again removed to Gratiot County, and located
in North Shade Township. The father died June
29, 1857. The mother resides in Sumner Township.
Mrs. Jessup is the second daughter of her parents,
and is one of nine children born to them, viz. : Amos
W., Nancy B., Darius E., Ezra J., Thomas H., Emma
A., Rosa M. and Emery V. She was born in Yates
Co., N. Y., Aug. 28, 1840. The sons and daughters
of Mr. and Mrs. Jessup are named: Charles H.,
Nettie E., Arthur H., George L., Frank A., William
T., Glen O^ and Bertha M.
^Ibert Pierson, farmer, section 32, Washing-
ton Township, is a son of Silas and Phoebe
(Davis) Pierson, natives of Essex Co., N. J.
Silas Pierson was a carpenter and joiner, and
in 1839 moved to Morrow Co., Ohio, where he
and his wife both died. The subject of this
sketch was lx)rn in Essex Co., N. J., Oct. 13, 181 7.
When 18 years old, he wasCapprenticed for three
years to the trade of harness-maker, at the expiration
of which time he engaged in farming in Morrow Co.,
Ohio. In 1853, he removed to Gratiot County, pur-
chasing of the Government 80 acres on section 32,
Washington Township. There are now 60 acres
nicely improved. In the spring of 1867, he built a
large bam, and in 1873 he erected a neat dwelling, at
a cost of (1,000.
March 10, 1844, he was married to Lucy J.,
daughter of Samuel and Maria (Gould) Linscott,
natives respectively of the State of Maine and New
York city. Mr. Linscott was by occupation a mason.
Mr. Pierson has been Highway Commissioner of
his township for three years, and has served occa-
sionally on juries. He built the second house in
Washington Township. There was at that time no
to his place the men to whom he went five miles to
was Dewitt, Clinton County. He and wife are mem-
bers of the Christian Church. In politics he is a
supporter of the Republican party.
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^homas M. Granger, farmer, section 8, Pine
River Township, was born March 3, 1841,
in Hartsville, Steuben Co., N. Y., and is the
third son of Allen and Margaret (Bover)
Granger. His father was bom in Vermont,
and his mother was a native of New York.
They settled soon after their marriage in Canisteo,
Steuben Co., N. Y., and they still reside in that
county.
Mr. Granger is the third son of his parents and one
of ten children born to them. He received a common-
school education, and at the age of 20 made his
entry into the world in an independent capacity, and
paid his father $75 for the year's service yet re- maining of his minority. He was empty-handed, but preserved a spirit of determination second to that of no man, the results of which, coupled with persist- ent labor, good sense and judgment, are plainly manifest in his surroundings. He came to Gratiot County in September, 1867, and settled at Ithaca. He remained in that place and vicinity nearly eight years. In 187-. he Jx)ught 80 acres of land in Sum- ner Township, which he continued to improve three v- -^<-C[!; •■■nov)-^— > Digitized by Google Digitized by Google !f »-*< K ^M^ jT ^^cf- Digitized by Google "^ A. '^.juX Digitized by Google ■f I I Digitized by Google -r i ^ V GRATIOT COUNTY, 313 •^^ years, when he sold out and went to Alma. There he built a house and barn and resided about 18 months, when he exchanged the property for 80 acres of land belonging to P. Richardson, located in Pine River Township, where he has since followed the vocation of farming. He has purchased 17 acres ad- ditional, and has 75 acres under improvement. Mr. Granger is an adherent to the tenets of the National Greenback party. He was married May 11, 1859, in Steuben Co., N. Y., to Mary B., daughter of Burnett and Margaret (Gibling) McDermott, natives of Ireland, where Mrs. Granger was born, Jan. 5, 1839. Three children — George W., Ella L. and Carrie L. — have been born to Mr. and Mrs. Granger. The only son and eldest child met his death at Fremont, Newaygo County, Dec. 21, 1 88 T, by a terrible accident. He was en- gaged in making what is called a ** fly switch " at the railroad station where he was employed, and was killed while in the performance of his duty. The father and mother are members of the Methodist Episcopal Church. olla A. Feet, farmer, section 31, Lafayette Township, is a son of John and Betsy (Clark) Peet, natives of Connecticut and New York, respectively. The former was by occupation a farmer, but alsa worked at the trade of a shoemaker. Rolla A. was bom Aug. 18, 1830, in the State of New York, and worked on his father's farm Until he was nearly 2 1 years old. Early in 1851 he went to Ohio, and worked on a farm until he was fully of age. He then married Mary Odell, daughter of Nathan and Betsy (Wright) Odell, and resided for a time in Lorain Co., Ohio. Mr. Peet enlisted in Co. B, First Ohio Light Artillery, in 1864, and was mustered out at Camp Dennison, Ohio, July 24, 1865. Returning home, he engaged in the dairy business one year, then sold his farm and came to Michigan in the spring of 1867. He first settled on 300 acres in Kent County. In 1875 he again re- moved, this time to Lafayette Township, Gratiot Co., settling on the south half of section 31. Of his 320 acres, 100 are cleared and 100 more chopped. Mr. Peet s first marriage was blessed with six children, as follows : Frank M., bom Nov. 22, 1852 ; Odell, July 9, 1855 ; Gertrude, June 2, 1859; Louis M., Feb. 27, 1862 ; Benj. J., Nov. 21, 1867 ; Anna, Sept. 17, 1874. He is liberal in his religious views, and politically he votes with the National party. In 1881, the first Mrs. Peet died, and he was again married to Miss Ida M. Fuller, a daughter of James and Polly (Schance) Fuller, She was born in Eaton Co., Mich., Sept. 17, 1865, and at the age of five came with her parents to Gratiot County. As one of the leading and representative agricul- turists and citizens of Gratiot County, we take pleasure in presenting Mr. Peet s portrait in this volume. eorge G. Nichols, jeweler at St. Louis, was born March 10, 1845, at Plattsburg, N. Y. He is the son of Gardner and Sabra (Martin) Nichols. His father was a son of Levi Nich- ols, proprietor of the Nichols House, at Platts- burg, and was also born in that place. Levi Nichols died at the advanced age of 94. The management of the hotel devolved upon Gardner Nichols before the death of his father, and he conducted it several years. In the spring of 1863 he removed his family to Medina, Lenawee Co., Mich., where he bought a farm of 160 acres of land. Mr. Nichols was then 18 years old, and he attended the academy at Oak Grove several terms. In Jan- uary, 1864, he determined to risk the fate of war, and enrolled as a soldier. He enlisted in Co. G, 30th Mich. Vol. Inf., and was in the service of the United States six months. He returned to Medina, and after attenjiing school two terms went to Adrian and en- tered^e employ of Japhet Cross to learn the de- tails of the jeweler s trade. He remained nearly four years, and Jan. 10, 1870, came to St. Louis in impaired health, to obtain the benefit of the mineral water. After three months he became so much im- proved that he determined to engage in business and opened an establishment at the stand now occupied by Mclntyre s drug store. He conducted the repair business, and as he succeeded in working up a con- siderable degree of trade he added jewelry, and by his good management has firmly established nimself I A C J- i ^i^« U^h^ ;j. Digitized by Google II (^ <, • ^ '.^-X 3M \. • M U > •/ \ GRATIOT COUNTY. in his business. He removed to his present quar- ters in May, 1882. In May, 1879, he was burned out on the old site, but with a very slight loss above his insurance. His business is prosperous and he employs his brother, John M. Nichols, as assistant in repairing and engraving. He is also agent for the New American Sewing Machine, No. 7. Mr. Nichols was married Sept. 27, 1876, at Has- tings, Barry Co., Mich., to Blanche, daughter of A. J. Newton. She was bom in Ohio. Mr. and Mrs. N. are the parents of one child, Carrie E.,born Nov. 11, 1878, at St. Louis. Mr. Nichols is a member of the Knights of Honor. ^ euben D. Maxwell, farmer, section 7, North Star Township, was bom in Monroe ^ Co., N. Y., June 3, 1834, and is a son of ■* Cyrus Maxwell, who brought his family from Troy to Geauga Co., Ohio, in 1836, and to Monroe Co., Mich., in 1844, where the subject of this sketch resided until after the war. He served one year in that great struggle, in Co. H, Ninth Mich. Vol. Inf. ; resided in Ingham Co., Mich., from 1866 to 1879, where he followed farming five years and ran a dray eight years ; then came to this county, where he has since been engaged in agriculture, and now owns 124J4 acres of good land. Oct. 29, 1861, Mr. Maxwell married Miss Jane, daughter of Daniel Hillman, now deceased. She was born in Upper Canada, and was brought by her parents to Jackson Co., Mich., when only four years of age (1844). Mr. and Mrs. M. have three chil- dren, namely : Grace, Newton and Ira. I^^M^A*^^^'* Boop, farmer, section 5, North Shade fi^-^;^! Township, is a son of John and Mary W" of John and (Mills) Roop, the former a native 01 New York, and the latter of Canada. Farming ^ was their occupation. Mr. John Roop came \ when a young man to Toledo, Ohio, near which place he owned a fann. After a period, he moved 25 miles west of that city, and in 185610 Montcalm County, this State, wherein 1882 his wife died. He is yet living with his daughter, Mrs. Ev£ line Thompson, in Montcalm County. The subject of this sketch was bom March i( 1832, iif Lucas Co., Ohio, near Toledo, remainin with his parents until 22 years of age as a farme Spending one year in Indiana, he came to Montcali Co., Mich., where he remained two years engaged i various occupations. He cleared the land whei Carson City now stands. In 1857, he located on tract of 40 acres on section 5, North Shade Towi ship, to which he subsequently added 40 acres. E now has 78 acres well improved, with house, ban etc. Mr. Roop has been Justice of the Peace sevc years, and School Director a number of terms. E is a Republican, and a member of Ithaca Chapte No. 70, R. A. M. In the year 1856, Mr. Roop married Miss Eliz; beth, daughter of William F. and Eliza (Earls) Big low, natives of the State of New York. Her mothi died a number of years ago, and her father is yet li ing, in Carson City, Mich. The two children of M and Mrs. Roop are: Charles, born Aug. 24, 1858, ar Alpheus, May 7, 1867. % -H V. |?ornelius K. Samson, physician and dm ?^ gist at St. Louis, was bom in Dov< I -^ Dutchess Co., N. Y., March 21, 1825, and V ? a son of John and Sarah (Upson) Samso / The father was born in Dover, in 1776; tl mother was a native of Waterbury, Conn., where si was born in 17.80, In June, 1836, they came Michigan and settled in Woodstock, Lenawee Count John Samson died Oct. 20, 1837. The demise of \ wife occurred in i860, at White Church, Kan. Dr. Samson was a resident of Woodstock until was 27 years of age, and was engaged in famiir In 1852 he went to Adrian and opened a store I the sale of books and stationery, and also enter upon the study of medicine. He continued the ma agement of his book trade about a year, and af devoting some time to his medical studies, he coi menced his career as a practitioner. In Novemb 1872, he came to St. Louis and purchased a stock drugs and continued to operate at the stand wh< he first established himself, on the comer of Mill a Center Streets, four years. In 1876 he purchased t ' ■' / ; N j:— r ■ - - :: , Digitized by Google r-> v^ r J ^'s Cratiot county. 315 building where he has since conducted his business. His stock includes drugs, patent medicines, oils and paints, books, stationery, groceries, etc. His trade is popular and prosperous, and he has a good office practice. He compounds the following proprietary medicines : Alterative Tonic, Ague and Chill-Fever Pills, Compound Cough Elixir, Carminative, Cough Syrup, Dysentery Pills, Constipation Pills, Dyspeptic Elixir, Canker Lotion, Expectorant, Hair Dye, Horse and Cattle Powders, Hoof and Healing Ointment, Heave Powders, Nerve and Bone Liniment, Com- pound Carthartic Pills, Family Panacea, Syrup Sarsa- parilla Compound, Soothing Drops, Vegetable Liver Pills, Peptonic Vermifuge, Fluid Extract of Witch- Hazel and Healing Salve. Dr. Samson was married Dec. 2, 1852, in Brook- lyn, Jackson Co.,* Mich., to Wealtha L. Youngs. Two children have been born of their marriage : Ellie M. and Mary L. The former is the wife of I. C. Kendall. tndrew S. Jolly, farmer, section 20, Wash- ington Township, is a son of Charles N- and Tryphena (Pulfrey) Jolly, natives of New York State. They followed farming in that State, where the former died in 1842. The latter died in Gratiot County, in 1880. An- drew S. was born Nov. 20, 1835, in Fayette Town- ship, Seneca Co., N, Y. At the age of 10, he com- menced peddling, which he followed for eight years. Coming to Monroe Co., Mich., he worked in the woods and on a farm for a year and a half; and then came to Gratiot County, in 1854. In 1863, he enlisted in Co. L, First Michigan En- gineers, and was assigned to the \rmy of the Cum- berland. He fought at Murfreesboro, Tenn., but was generally on detached duty; and was finally mustered out in September, 1865, at Nashville, Tenn., and discharged the following month, at Jackson, Mich. In 1854, he married Mary J., daughter of Daniel Brown, a farmer, and a native of New York. She was born in Pennsylvania. Mr. and Mrs. Jolly first located on 40 acres in Fulton Township. In March, 1 866, they removed to section 17, Washington Town- ship, and in 1869 they removed to section 7, same township. In 1 87 3, they settled at their present home on section 20, consisting of 240 acres, 100 of which are improved. They have a family of nine children, are members of the United Brethren Church, and Mr. Jolly is a member of Moses Wisner Post, No. loi, G. A. R., at Ithaca, and votes the Republican ticket. ohn Jackson, farmer, section 4, North Shade { ^1^ Township, is a son of John and Hannah 1^ (Mathers) Jackson, farmers of Yorkshire, M£ England, who came to America in 1827, and jl^ resided in the State of New York the remainder \ of their lives. Mr. John Jackson was bom Nov. 20, 181 7, in Yorkshire, England, came to this country with his parents and when he was a lad nearly grown they died, and he left the old homestead and en- gaged in a distillery two years, then in farming in New York State until 1869, when he came to this county, locating on section 4, North Shade Township, on a tract of 77 acres of partially improved land, which he now has in fine cultivation. He owns altogether 400 acres. In religious belief Mr. Jack- son is a Universalist, and in politics a Republican. In 1850, Mr. Jackson was married to Miss Sarah A., daughter of Isaac and Jemima (White) Leonard, the former an agriculturist and a native of New York, and the latter of Connecticut; both died in New York State. Mr. and Mrs. Jackson have the follow- ing children: Martha, bom in 1852; Edwin, 1854; and John, 1865. The parents are members of the Grange, and Mrs. J. is also a Universalist. ^ -VW^—J- ^ (■-■' n •^1 I eorge Bichardson, druggist, grocer and jeweler, Ithaca, was bom in Monroe Co., 1^iv:n N. Y., May 13, 1836, and is the son of ^#^ George S. and Laura L. (Tyler) Richardson natives of Connecticut and Vermont, and of English-German and New England ancestry. They reside in Oakland County, aged respectively 75 and 74. The subject of this biography went when two years old with his parents to Genesee County, this State. r Digitized by Google 7-<^DI];>:01]r>T- -^'^^^^r GRATIOT COUNTY, \ I A {\ ^ His father being a drover, George had his full time for school until 20 years of age. He then engaged on the New York Central railroad as brakeman, afterwards changing to the Chicago, Rock Island & Pacific, on which road he was for a time a conductor. After four years of railroad life, he became a foreman in the Holland saw-mill in Saginaw County, where he remained two years. On the breaking out of the great civil war, he re- sponded to the first call of President Lincoln for troops, and enlisted in the first company of volunteers raised in Oakland County, of which he was made a Sergeant. This company was never mustered into the service, as many more companies offered than were needed under the call for three-months men. After the disbanding of the company, he enlisted in Co. A, I St Mich. Lancers. That kind of troops Was discontinued after seven months, but being deter- mined to fight for his country he enrolled himself in Co. I, 2 2d Mich. Vol. Inf., and served under Gen. Thomas. Shortly after his enlistment, he was se- lected as special messenger for Gen. Thomas at headquarters. Here he remained until July, 1865, and after his discharge he returned to Gratiot County. He then settled on a farm of 320 acres, 160 of which he had purchased in 1861, in Lafayette Town- ship. Only 10 acres were then improved, but after six years' residence he has improved 100 acres. He still retains 280 acres of that farm. In the spring of 1872, he came to Ithaca and purchased 44 feet front- age on Center Street, on which he established a grocery store. In 1875, he and Mr. Weatherwax erected the first brick building in the village. It was built 80 feet deep, with a front of 22^ feet, but is now 1 10 feet deep. The firm was Richardson & Weatherwax for two and a half years, when Mr. R. became sole proprietor. When he started in busi- ness, his stock was worth but$1,200; but when, in
1 88 1, he sold out to D. G. Hall, his stock was valued
at $7,000, and he did an annual business of$18,000.
Jan. 12, 1884, he resumed the business, now carry-
ing a stock worth $6,000. The period from 1 88 1 to 1884 was spent at Petoskey, this State, two years of the time in the drug business. July 3, 1862, in North ville, Wayne Co., Mich., he was married to Miss Jennie A. Watson, daughter of J. T. and Harriet (Wilcox) Watson, natives of Gene- see Co., N. Y., and of Scotch and English descent. She was born in Livingston Co., Mich., May 13, 1842, and when 16 years old went with her parents to Oakland County, where she lived until her mar- riage, teaching school for some time previous to that event. Mr. and Mrs. R. have been the parents of seven children, four of whom survive : Flora H., bom April 22, 1863; Rena L., July 3, 1867; Hattie H., Oct. 28, 187 1 ; and George E., May i, 1878. The deceased are : Iva, Laura L. and Jennie. The par- ents attend the Congregational Church. Mr. R. is politically a Republican, and has held the offices of Justice of the Peace apd Township Treasurer in La- fayette Township. He was also Postmaster at La- fayette for ^st years. He belongs to the Masonic fraternity. yron A. Hioks, merchant, Bridge ville, Washington Township, is a son of Andrus and Betsy (Tilton) Hicks, natives of New York State. Mr. Hicks has been most of his life a tanner and furrier in New York State, where he and wife yet live. Byron was born May 27, 1844, in St. Lawrence Co., N. Y., and lived with his parents, working summers and attending school winters, until 15 years old. In October, i860, he came to St. John's, this State, where he was engaged in the store of John Hicks, in buying wheat, and at other employment. In 1864 he came to Gratiot County and engaged in buying staves, making his headquarters at J. B. Smith s ho- tel at Pompei. In the spring of 1865, he bought the grocery of Wilbur Coon, of Pompei, and carried on business there until the spring of 1867, when he removed to Bridgeville. He now keeps a full line ot groceries, dry goods, boots and shoes, and has a pros- perous trade. While at Pompei, he was married to Mary Aver>% the daughter of John R. and Lovina (Saunders) Avery, natives of Rhode Island and Connecticut, respectively. Mr. Avery was a farmer. Mary Avery was born in the State of Wisconsin, in 1845, and died at Bridgeville in 1868, leaving one child, which died shortly after its mother. Mr. Hicks was again married, to Sarah M. Avery, a sister of his first wife, in April, 1870. This union has been blessed with '.V^^-^ Digitized by Google ». '■■• i V r GRA TIO T CO UNTY. X-A 317 <( three children, viz. Bessie L., Clyde B. and Leo M. ^ Mr. Hicks has held the office of Supervisor from :*„ Washington Township, being elected in 1882. He * has also been Township Treasurer for four years, and Township Clerk. He is a member of the Masonic Order, belonging to a lodge at St. John s. In politics, he is a supporter of the Democratic party. P^g- J ''\ ^ enretoh Moench, fanner, section 4, North Shade Township, was born Feb. 2, 181 7, in Germany, of German parents, namely: John D. and Barbara Hoffman, who died in Schwartzburg-Rudolstadt, Germany. The sub- ject of this sketch emigrated to America in 1853, landing at New York, and settling in Waterloo, Jackson Co., Mich. In 18 or 19 months, that is, in 1^55) he moved to this county, locating on sections 3 and 4, North Shade Township, the tract containing 320 acres, all wild land. Of this he has since sold ooe-half, and he now has about 70 acres in good cul- tivation. Mr. Moench was married in 1855 to Wilhelmina, daughter of Conrad and Jacobenia Walter, natives of \'/ Wurtemburg, Germany, the former by occupation a butcher, and both long since deceased. The chil- dren of Mr. and Mrs. Moench are : Lewis W., Polly L., Henry R. and Wilhelmina. Their Church rela- tions are Evangelical and Lutheran. Politically, Mr. M. was formerly Republican, but is now Democratic. [eter Hofitaian, farmer, section 32, North Star Township, was bom in France, Feb. 19, 181 6, a son of Frederick Hoffman, who was a native of Germany, and died in Havre de Grace, on his way to America. Peter was educated in his native country, and when he was 1 4 years of age the family emigrated to America, landing at Charleston, S. C. ; two months later they came to Canton, Ohio, and in 1833 to Sandusky Co., Ohio, where Mrs. H. entered 80 acres of land, and finally died. Peter Hoffman came to Hillsdale Co., Mich., in Februar>', 1849, and to Gratiot County in April, 1854, settling upon his present place May 13 following, — ^in the wild woods, with only savage beasts for neighbors. He had wild meat for a con- stant article of food for years. He built the first house in North Star Township, a double log house, on section 29, on a part of the land he had entered. By industry and economy patiently exercised for many years, Mr. H. succeeded in developing and furnishing a fine farm. He has been engaged in ag- riculture all his life, except six months when he was in the boot and shoe trade in Alma, this county, and 18 months in Pompei. Dec. 2^, 1840, is the date of Mr. Hoffman's mar- riage to Miss Elizabeth Kay, daughter of Moses Kay, now deceased: she is a native of Crawford Co., Ohio. Mr. and Mrs. H. have had seven children, six of whom are living, namely: Eliza A., now the wife of Mr. Trask; Charles N.; Adolphus P.; Ann M., now Mrs. Johnson ; Mary E , now Mrs. Hous- man ; and Phocion P. The deceased was James, who died at the age of 1 1 years. Mr. H. owns 40 acres of land, and his wife 80 acres : total, 1 20 acres. He has been Highway Commissioner many years. r ""^^^AA^gg jlS cpB 'vw^^^^ rank B. Lathrop, farmer, section 29, Bethany Township, is a son of George C. and Mary E. (Hall) Lathrop, and was ^^ born in Washtenaw Co., Mich., Dec. 24, 1840. ^v^ His father, a farmer, was a native of New York Stale, and is still living at Meadville, Ingham County, this State. His mother, also a native of New York, is still living. When he was but a year old, the family moved to Waterloo Township, Jack- son Co., Mich., locating upon a half section of land, and remaining there 20 years, and then moved to Ingham County. Mr. Lathrop was brought up to agricultural pur- suits, attending winter terms of school. He was married in Ingham County, May 29, 187 1, to Miss Frances, daughter of William C. and Artemisia Mun- son, who was born in New London, Huron Co., Ohio, Feb. 26, 1845. Mr. L. followed farming in Ingham County until 1875. January 7 of that year, he bought his present farm of 80 acres, then all timber land. He has cleared 31 acres, and is under full headway toward permanent prosperity. He has been School Insi)ector and Drain Commissioner one year each in his township, and is a member of the Order , of Knights of Labor, V^ s /N r y ^^:^ ^dmyJM^-^ 'J- Digitized by Google ^^v.-: 3i« -r<:aii.-.ULs:>T- GRATIOT COUI^TY. \ /S ">.'•, A 1 ^ The children in this family are: Miles, born in Ingham County, June 19, 1872; Carleton, Sept 20, 1875; Charles, born m Bethany Township, June 4, 1878; Fidelia, July 4, 1880; and Asher, March 31, 1882. [homas W. B. Greaser, farmer on section 17, Fulton Township, is a son of William and Elizabeth (McCombs) Creaser (see sketch of William Creaser) ; and was bom in the Prov- ince of Quebec, Oct. 19, 185 1. He was quite young when his parents removed to Upper Canada. He received a common-school education when in the Dominion, and was aboul 20 years old when his parents came to Gratiot Co., Mich. He continued to live with his father until 25 years of age. In 1880 he settled on 50 acres of partly im- proved land on section 17, Fulton, to which he has added 40 acres. He has 35 acres improved. Feb. 18, 1879, in Newark Township, he married Miss Ida M., eldest daughter of George L. and Car- oline (Jones) Naldrett. To this marriage two sons ha>e been bom, Albert N. and Charles C. Politically, Mr. C. is a Democrat. ^i-Q^Viny^ -iMjafi;©i© Tohn Harrison, farmer^ section 17, Bethany Township, is a son of Thomas and Eliza (Hunter) Harrison, and was born in Kitley Township, Leeds Co., Canada, Jan. 19, 1833, His parents followed the occupation of farm- ing, and Mr. Harrison was a constant resident under the parental roof-tree and followed the same vocation until 16 years old. Mr. Harrison was united in marriage, April 17, 1853, with Miss Margaret, daughter of Andrew and Mary (Thompson) Lawson. She was born in Ensley Township, Leeds Co., Canada, June 30, 1 839. They have had five children, namely : Thomas, born June 10, 1857; Walter, bom Aug. 31, 1850; Eliza J., bom Sept. 9, 1861 ; James H., born Dec. 26, 1863, died April 2, 1864; and John A., born Feb. 10, 1865, died April 3, 1866. In March, 1866, Mr. H. and family came to this State and located at St. Louis, this county, and was there variously engaged for some time. In t spring of 1869, he purchased 80 acres of land on t section on which he now resides, lived on it for V or three years, and then moved to St. Louis, t] county, and afterward retumed to the farm. When he first purchased the land, it was oovei with timber, and through his own energetic labors acres have been cleared and 50 acres placed un( good cultivation. He has a good bam and comn dious residence and good orchard. Their son Thomas is a farmer by occupation, sides in the same township as the parents, and v united in marriage to Miss Angeline Quidort. W ter was married to Miss Isabel Broadhead, h farmer, and resides with the parents. Eliza J., th only daughter, is the wife of V. B. Ludwig, at pres( living in Ludington, this State, and engaged in ** li saving service." Mr. and Mrs. Harrison are members of the O gregational Church and honored and respec citizens of their township. Mr. H. has held the position of Township Dr Commissioner for two years. H- ^^^ -H .dward N. DuBois, farmer section North Star Township, was bom June 1820, in Cayuga Co., N. Y.; his pare were Abraham and Elizabeth (Graves) I Bois, the former a native of Dutchess Co., Y., and the latter of Connecticut. They ei grated to Plymouth Township, Richland Co., 01 in 1822, where Edward was brought up and lean the shoemaker s trade. After following this vocat for about six years, he went, in Januaiy, 1853, Califomia, for his health, which he fortunately rec ered. He retumed in January, 1854, and soon afl ward commenced farming. In 1857 he settled Fulton Township, this county, and in 1867 upon present farm, where he has since lived with the ception of six years when lie resided in Ithaca. July I, 1841, Mr. DuBois married Miss Adel A., daughter of Samuel and Lydia (Weeden) Boa man. Of their nine children only three are n living, namely, George M,, Ida B. (wife of 1 Jeffrey) and Edward. One daughter, Ella, died her 17th year. The others deceased were, Theodc Mary E., Harry and Frank. Mr. DuBois and his s< -^<-^D!]::'Cils>-^ Digitized by Google r- -x^:^ { I I I I V ^/ GRATIOT COUNTY. Vv>^ 319 *> own altogether 2 1 o acres of land, where they are car- rying on a prosperous business in agriculture. Mr. DuBois was Deputy Sheriff of this county 13 years. Justice of the Peace four years in Fulton Township, and Highway Commissioner in North Star Township one year. He was the first Village Mar- shal of Ithaca, and held that position three years. :yTon H. Sawyer, attorney, at Ithaca, is a son of Robert and Caroline W. (Webb) Sawyer, natives of New York and Con- necticut. The former has followed the occu- pation of farmer, and, with his wife, resides in Hillsdale County, this State. Byron H. was bom Nov. 29, 1846, near Lima, Steuben Co., Ind., and lived with his parents until 22 years old. He attended the common schools, and at 17 com- menced a course at the Medina Academy, where he studied two years. Entering the office of Sawyer & Bean, he read law for one year, after which he took a two years' course in the Law Department of the University of Michigan, graduating with the class of 187 2. Forming a partnership with Thomas J. Hiller, he practiced law at Hudson, Lenawee County, until 1879, when he came to Ithaca. Here he has since resided and practiced law. He also deals in real estate, and he owns 120 acres on section 5, North Star Township, 65 of which are improved. He has been Village Attorney of Ithaca for two years, and is now Trustee of the village and Circuit Court Com- missioner. He is a member of the I. O. O. F., and is politically a Republican. rohn McCuaig, farmer, section 17, North Shade Township, is a brother of Alexander McCuaig, whose sketch is given, with f parentage, on anoth^ page. The subject of this sketch was bom June 15, 1835, in Newton Township, Canada. He remained with his parents on the farm, and attending school until 21 years of age ; lived five years in Wayne Co., Mich. ; then from November, 1861, he lived a year in the town of New Haven ; and finally located on 80 acres of wild land, where he now resides and has 60 acres finely improved. His large and commodious bam he built in 1 88 1. He has been an industrious and judicious manager, and has accordingly enjoyed a good degree of prosperity. In 1861 Mr. McCuaig married Miss Jane, daugh- ter of William and Mary Clements, who was bom Dec. 10, 1 84 1, in Canada. Their eight children are : Mary A., John D., William H., Annie E., Samuel S., Myron, Alexander and Ernest S. In 1864, Mr. McC. enlisted in Co. A, 23d Mich. Inf., which was assigned to the Army of the Cum- berland, 2d Brigade, 2d Division, 23d Army Corps. He was in the battles of Franklin and Nashville, Tenn., and in all the engagements in which his regi- ment participated. On the mustering out of his regiment, he was transferred to the 28th Mich. Inf., and was finally mustered out at Raleigh, N. C, in October, 1865. Mr. McCuaig has been Town Treas- urer 1 1 terms, and has held several school offices. In all these capacities he has served the community well, being able, judicious, and a man of unimpeach- able integrity. — ^ — >^ h \^ (- ^ -^<^m J, Miller, farmer and teacher, sec- tion 24, Bethany Township, is a son of John U. and Esther, nee Cronce, Miller, ^^ and was bom in Erie Co., Ohio, March i, j) ' 1 841 , in which county his father and mother i_ both died, the former June 18, 1853, and the latter Dec. 8, 1863. The father of our subject was a farmer by occupation, and on his farm, under the ennobling influences of kind and loving parents, our subject was reared. He attended the common schools of his native county, and assisted on the farm until he attained the age of 18 years, when he entered on the " morning " of his . vocation, and taught school winters and assisted on the farm sum- mers. At this period in his life, although thoroughly competent to pursue his chosen profession, he de- voted a portion of two years to the pursuit of his studies in Oberlin College, the more thoroughly to prepare himself for the work of educating others. In December, 1865, Mr. M. came to Ingham County, this State, and purchased 50 acres of land in that county. He then returned to his native county and was united in marriage, March 6, 1866, to y^.m>^ -4>^^^ '.'^"^^J^' r >>-. Digitized by Google i^ 320 -^<•:l][l:v:^o^.>T■ \- GRATIOT COUNTY. ^ V ^ Miss Abbie E., daughter of Gilbert B. and Sarah (Roc) Hasbrook. She was bom in Dutchess Co., N. Y., Feb. 3, 1846, and to their union two children have been born, namely, Alva R., May 4. 1869, and Fred J.. March 26, 1871. After their marriage they came to the land pur- chased by Mr. M. in Ingham County, and resided on the same until the following December, when they sold it and removed to this county. They located on 40 acres of land on section 24, Bethany Township, where they now reside. Mr. M. has cleared and brought under cultivation about 30 acres of this land, built himself a good barn, and has under contempla- tion the erection of a new and commodious building as a residence. Mr. M. has taught 12 terms of school in this county, and has given universal satisfaction as to competency. He has held the office of Justice of the Peace for ten years, and is recognized as one of the representative men of his township. The husband and wife are both members of the Methodist Episcopal Church and respected and es- teemed citizens of Bethany Township. a£ oreDBo W. Kyes, farmer, section 19, Pine f River Township, was born in Jackson Co., Mich., Sept. 20, 1832, and is the son of James and Cassandra Kyes, both of whom were I^, bom in the State of New York. Mr. Kyes has has been a farmer since the days of his boy- hood. Previous to engaging in farm labor, he passed his time in obtaining his education at the common school. In January, 1859, he came to Gratiot County and purchased the farm on which he has since lived, comprising 80 acres of wild land. He has placed 60 acres under improvement and cultiva- tion, and thus added his quota to the progress and agricultural advancement of Gratiot County. Politi- cally, Mr. Kyes is a Democrat. He was married in Calhoun Co., Mich., Jan. 26, 1855, to Sarah S., daughter of Frederick and Sarepta (Fox) Wright. Her parents were among the earliest settlers in Graliot County, and the family name is one of the leading ones in its pioneer records. Mrs. Kyes was bom Sept. 18, 1837, in Jackson Co., Mich. Of eight children born to Mr. and Mrs. Kyes five ^^■^^:y ~:^:^^ — -^<m':. survive — Emmet M., Frederick M., Albert C, Charles R. and Hattie M. Those deceased were named Gertrude, Frank and Melissa. Mrs. Kyes died Dec. 8, 1883. ^^^! SS^ ^- — ^^ nman N. Cowdrey, farmer, section 25, Newark Township, is a son of William P. and Mary (Bmce) Cowdrey. The parents were of Scotch descent, and after their mar- riage settled in Southern Ohio, where the wife and mother died in 1847. The senior Cowdrey removed his family, eight years after the loss of his wife, to Michigan, and located in Newark Township, Gratiot County, where he resided until his death, which occurred March 16, 1883. Mr. Cowdrey was bom March 8, 1848, in Ohio. He was in his first year of life when his mother died, and was a lad of nine when his father settled in Gratiot County, where he spent the intervening years until he reached the period of his legal freedom. When he was 15 years old (in 1863), he enlisted in the I St Mich. Regiment Engineers and Mechanics as a musician, and served until November, 1865. His command was with Sherman in the historic march to Atlanta and the sea. On the morning of the day when he awoke and found himself the legal inheritor of man's estate, he started for Ohio with the purpose of fitting himself to pursue the calling of a carf)enter and joiner. He found plenty of employ at that business summers, and engaged in teaching winters, thus altemating for a period of ten years, and at the end of that time (in 1879) abandoned his trade. In 1872, he purchased 40 acres of improved land in the township of which his father was a citizen, and in 1876 erected thereon the necessary farm buildings. In 1879 he became a resident in Newark Township, and has since been closely identified with all its in- terests. In politics, he is a Republican of decided type. He has officiated one year as Constable, sev- eral years as Superintendent of Schools, one term as Supervisor, and is a member of the Board of County School Examiners, of which body he has been Secre- tary two years, and is present Chairman. He was elected to a term of four years as Justice of the Peace, . but resigned at the end of the first year. He now owns, in addition to his first purchase, 66 acres of - :[:!]^>^ b Digitized by Google Digitized by Google r Digitized by Google 'M r-y^Q -T-rdm'Mh^T r \V :j GRATIOT COUNTY. y-\ * A.' i r-'- ^ .^f. /v • V 323 "^ land in North Star Township, and has 85 acres im- proved. Among the reminiscences of the life of Mr. Cow- drey is one unique and startling incident, which oc- curred while his father was ^n route to Gratiot County. They traveled in the manner common to emigrants of that primitive period — family and effects in a wagon drawn by an ox team. The road was shaded on one side by the uncut forest, and the boy and his father occupied the front scat together. The day was windy, and suddenly a hollow bass-wood tree, about 30 inches in diameter, fell across the wagon. The top was forked, and, as the tree fell, the spreading limbs enclosed the occupants of the seat, and they were preserved unharmed. The wagon was almost entirely demolished. Mr. Cowdrey was married Nov. 5, 1874, in Ohio, to Alwilda, daughter of James and Sarah Hibbins. Her parents were natives of Ohio, and the children bom to them numbered seven, six of whom are liv- ing. Their names are : Mary E., Martha E , Al- wilda, Laura B., Edwin T. (deceased), Nettie M. and Roberta. Mrs. Cowdrey is the third daughter, and was born Jan. 27, 1854. Frank C, born July 20, 1877, and James R., May 19, 1882, are the two children bom to Mr. and Mrs. Cowdrey. The latter is a member of the United Brethren Church. ohn Jeffrey (deceased), a pioneer settler of Gratiot County, to whom the township and village of Ithaca are largely indebted, and with whose name their growth and progress are indissolubly connected, was a native of Mon- mouth Co., N. J., where he was bom Aug. 26, 1812. The record of his early life is incomplete, but suf- ficient is known to warrant the inference that the years of his later youth and earlier manhood were passed in the exercise of the traits of character which secured the prosperity of his prime and later life, and rendered him a valuable acquisition to the citizenship of a new country. His earliest known occupation was in freighting on the Erie Canal, where he was engaged some years, but met only moderate success. He went to Niagara Co., N. Y., in 1836, which section was then in its early days. He bought 'V a considerable tract of land, and for a number of years devoted his energies to the improvement and cultivation of his farm. He achieved a success in proportion to his efforts, and accumulated what was then considered a fair competency. In 1853 he vis- ited several of the Western States for the purpose of fixing on a suitable field for the development of his plans and projects in life, and finally located a tract of land at the geographical center of Gratiot County, which included the site of the present village of Ithaca. He took possession of his property in 1855, at which date his permanent residence and the im- provements on his estate began. In 1856 he platted the village of Ithaca, and on the third day of March of the same year the Board of Supervisors estab- lished there the county seat. In i860 the action was re-affirmed . Mr. Jeffrey's location of land in 1853 included 1,120 acres, and he was continually buying additional tracts up to the date of his death.' It was his policy to make no sale? of land save to actual settlers, to which principle he strictly adhered. At the time he died he was the proprietor of about 5,000 acres, in- cluding chpice farming and pine lands, and also a considerable portion of the original plat of the village. At the time Mr. Jeffrey became a resident of Gratiot County, the country in every direction was for miles an unbroken wilderness, and the position in which he found himself was one that required the exercise of untiring energy and exertion. But he possessed an iron constitution, perseverance and judgment, which made him equal to the emergency, and in the aggre- gate he probably underwent as much hardship and suffered as many privations as any of the early pio- neers of Gratiot County ; and to no one of them is the county more indebted for its present remarkable status of advancement and improvement. Pmdence, economy, temperance and industry were marked traits of his character, and all the acts of his life were tempered by good judgment, sound sense and consideration for the permanent prosperity and wel- fare of the community to which he belonged, and of which he was for so many years a useful and hon- ored member. He died March 5, 1874. The portrait of Mr. Jeffrey appears on another page. It is a valuable addition to the collated his- tory and biography of Gratiot County, and without it no book of the character claimed for the present volume would be in any sense complete. ^ t S./ .^ Digitized by Google ^r-'X V 324 — 7<'ia[l:v;DD^>-r- (9i?^ T/07' CO UNTY, .^.v^V's^ ' J -»- . • •. f r J Mr. Jeffrey was married Dec. 10, 1868, in St. Louis, to Mrs. Louisa (Smith) Baney. She was born March 6, 1835, in Newfane, Niagara Co., N. Y., and is the daughter of George and Arvilla (Bromley) Smith. Her first husband -was David Baney, to whom she was married June 30, 1864, and by whom she had two children : Glenn E.,bom June 12, 1865, in Pompei, Gratiot County ; and May P., born March 25, 1867. Mr. Jeffrey left two children : John, born Oct. 21, 1869, and Ira, Dec. 24, 187 1. His widow f became the wife of Joseph H. Seaver, June 18, 1879. O \q\lvl Broadhead, farmer, section 18, Beth- any Township, is a son of Cornelius and Elizabeth (Jersey) Broadhead, and was born in Maryland, July 20, 1829. When he was a small boy the family moved to the State of New York, locating in Ulster County. As he grew up he followed mill sawing for*i4 years. In 1856 he came to Michigan and was married, in New- ark Township, this county, to Miss Emily Rooks, daughter of David and Sophia (Thompson) Rooks, who was born in Erwin, Steuben Co., N. Y., May 3, 1837. Their children are: Charles W., born July 24, 1862; Cora I., Jan. 10, 1865 ; Hattie E., Nov. 3, 1867; Ray, March 6, 1870. Cora I. is the wife of Walter Harrison, a farmer of Bethany Township. Mr. B. is a member of the Masonic fraternity, and has served as Constable several years. 'i A<ajec;0|@- •'M'^S^^^TTVKk I [illiam F. Brown, farmer, section 21, North Star Township, was born April 5, 18 18, in Massachusetts. His parents were Will- iam and Clarissa [nee Flowers) Brown, natives also of Massachusetts. The latter died when William F. was but three years old. Mr. Brown is a descendant of one of three brothers who came from England among the first settlers of America. His parents located in Genesee Co., N. Y.,in 1819, where his mother died. His father mar- ried again, and in 1827 moved to Chautauqua Co., N. Y , and in 1833 to Warren Co., Penn. The subject of this sketch left home at the age 18 years, worked by the month several years, and in 1863 came to this county, where now, in North Star Township, he owns 70 acres of land. He was mar- ried March 20, 1841, to Miss Mary, daughter of Francis Ploof. Of the four children bom to Mr. and Mrs. Brown two are living, namely, Eli W. and Charles W. One son, George F., was killed in thd late war while fighting in defense of his country, in a skirmish near Louisa Court-House, soon after the battle of Spottsylvania Court-House. He was but 2 1 years of age. The other deceased son, James L., died when three years old. Eli W. is in Billings, Montana Territory, and Charles W. resides on a part of the homestead. Mrs. B. died Nov. 30, 1840, and Mr. B. married again Aug. 20, 1857, Miss Louisa M. Miner, daughter of Warren and Sophinia Miner, and by her had one child. Jay A. They have an adopted son, James W., now 28 years of age. Mr. Brown is a member of the Masonic fraternity and Mrs. B. of the Methodist Episcopal Church. elcome F. Fartello, farmer, section 10, Bethany Township, is a son of Welcome J. and Rhoda (Phinney) Partello, and was born in Cazenovia, N. Y, Oct. 22, 1818. When eight years old his parents came to Washtenaw County, this State, settling in Salem Township, the second family in that township. There the father bought 80 acres of timber land, built a good log house, dug a well, and cleared 12 acres when he discovered that he had located on the wrong piece of land. Accordingly he moved. When the subject of this sketch was 1 9 years old the family moved to Clinton Co., Mich., ^s^ miles east of DeWitt. At the last mentioned place, July 31, 1845, he married Amelia J. Hoople, who was borH in Canada, Nov. 28, 182 1. By this marriage seven children have been born, viz.: Livonia, Julia, Welcome, Persis, Elson, Dwight and Olivia. In Clinton County Mr. P. was most of the time engaged in agricultural pursuits, and had some real estate in the village of DeWitt. In March, 1856, he came to Bethany and took possession of a quarter- section of timber land where he now resides, having 60 acres in a profitable state of cultivation and Digitized by Google r-.K --tC^hq^dii^^t^ Gl^A no T CO UNTY. J ^^ the value of the place enhanced by a number of improvements. When he first arrived on this tract it was all a wild forest. He moved with a yoke of oxen led by a horse. His father had settled on an adjoining place the year previous, and died eight years afterward: was the first Supervisor of the township. His mother died two years later. He has been Justice of the Peace three years. The children are now scattered as follows : Livo- nia is the widow of Stephen R. Goodwin, and resides in Bethany Township ; Julia is the wife pf William Denman, a farmer in Huron Co., Ohio; Welcome is engaged in connection with a railroad at San Anto- nio, Texas; Persis is the wife of Harvey Atwell, a farmer in Bethany Township; Elson is living at home ; Dwight is also at home , and Olivia is the wife of Ira Bentley, a farmer in Huron Co., Ohio. illiam SeiMed, farmer, section 8, New Ha- ven Township, was born in Salt Creek Township, Wayne Co., Ohio, March 25, 1833. His parents, Henry and Mary A. (Steele) Seifried, were natives of Pennsylva- nia and of German descent. His father was a farmer by occupation, and after the year 1854 he lived until his death in the vicinity of Des Moines, Iowa. Mr. William Seifried, the subject of this notice, lived with his parents (after 15 years of age in Wy- andot Co., Ohio,) until his marriage, April 27, 1854, to Miss Martha, daughter of Isaac and Eva (Bor- ders) George, natives of Pennsylvania and of " Penn- sylvania Dutch " ancestry. Both died in their na- tive State. Mrs. S. was born in Westmoreland Co., Pa., Oct. 9, 1832, and when five years of age her residence was changed to Wayne Co., Ohio. Six months after marriage Mr. and Mrs. S. moved to Hancock Co., Ohio. When the first call for 600,000 more troops was made to aid in suppressing the great insurrection, Mr. S. enlisted, Aug. 11, 1862, in Co. G, ii8th Ohio Vol. Inf., commanded by Capt. Samuel Howard, of the Army of the Cumberland. He participated in all the engagements of his regiment until the battle of Perryville, and for the nine months following that event his regiment was detailed for special duty on ' ' Vr >^;^. ^^fL i^<^Il [] the Kentucky Central railroad ; then they were in ac- tive service again, being in the engagements at Cov- ington Heights, Perryville, Knoxville, London, Mossy Creek, Resaca, Chattanooga, Buzzard Roost, Kene- saw Mountain, etc. He was then sick for more than two years in the hospitals at Chattanooga, Lookout Mountain, Nashville and Camp Dennison, Ohio, where he was honorably discharged. May 22, 1865. After residing then at his home in Hancock Co., Ohio, until fall, he came to Maple Grove, Barry Co., Mich. A little more than two years afterward he moved to Kent County, where he preached eight months as a minister of the " Church of God," then one year in the same capacity in Saginaw County. In 1870 he came to this county and homestead ed 80 acres where he now resides, and has improved 50 acres. He was the third settler on this section. Mr. S. is now a minister in the Free- Will Baptist Church, serving acceptably. He is a strong Prohi- bitionist Republican, and has held some of the of- fices of public trust in his district. His wife is also a member of the Free-Will Baptist Church. The children in this family are: Isaac G., born May 31, 1855; Henry F., March i, 1857; John W., Feb. 21, 1859; George M., Aug. i, i86r ; David M., Nov. 1 1, 1865 ; and Ella E., Oct. 9, 1867. I A ^ reeman H. Bice, farmer, section 1 1, Fulton Township, is a son of Freeman and Sally (Hobart) Rice, natives of the State of New York. They settled after marriage in their na- v tive State, and afterward removed to Delaware (J Co., Ohio., where they lived until the fall of They afterwards removed to Mecosta County, this State, where the father died, in September, 1871. The mother afterwards removed to Eaton County, where she died, in June, 1873. Their family comprised six sons and one daughter. Freeman H., the fourth son, was born in Genesee Co., N. Y., Feb. 19, 1830, and was seven years old when his parents removed to Ohio. He lived at home until about 34 years of age, and in the fall of 1864 came to Gratiot Co., Mich., and settled on 120 acres in Fulton Township, which he had bought during the administration of President Pierce. He has now 80 acres improved. r Digitized by LnOOQ IC A 326 — <^Ii;u'^ui]^>-r v^/ >(-^> /^ i GRATIOT COUNTY, ^ Oct. 14, 1863, in Eaton Co., Mich., he was married ) to Mrs. Mary E., daughter of Martin and Abigail ' Williams, and widow of Chester B. Rice (a brother of Freeman H,, who died Aug. 10, 1861). Mrs. ' J Rice had by her first marriage one daughter, Sarah * A., and by her second a daughter and a son, — Viola and Herbert F. Mr. Rice is politically a Republi- can. 'ohn M. Walker, farmer, section 34, New- ark Township, is the son of Stephen and 'Lydia (White) Walker. They were natives respectively of New York and New Hampshire, and after their marriage settled in the former State. They came to Lenawee Co., Mich., in its pioneer days and there passed the ultimate years of their lives. Five children were born to them, — Martha, David, John M., Nathaniel and Ransom. Mr. Walker is the second son of his parents and was bom March 15, 1 831, in Niagara Co., N. Y. He was two years old when his parents removed to Michigan, and he continued under the parental authority until he reached his majority. He then apprenticed himself to learn the business of wagon- making and served two years. He was engaged in labor at his trade and as farm assistant five years, when he bought a farm in Lenawee County contain- ing 75 acres, which he continued to manage until the spring of 1880, when he sold out and came to Gratiot County. He bought 100 acres of land in a State of partial improvement in Newark Township, on which he has since continued to reside and of which he has now 75 acres under cultivation. Mr. WaH:er held the position of School Director in Len- awee County six years consecutively, and in the fall of 1 88 1 was elected School Assessor of District No. 4, Newark Township, of which position he is present incumbent. In political affiliation he is a Republican. Mr. Walker was married in Fairfield, Lenawee Co., Mich., Oct. 12, 1856, to Elsie E., daughter of Job T. and Lydia (Laycock) Reynolds. Her parents were settlers in Jackson County, where the father died in 1840, and the mother seven years later. Mr. and Mrs. Walker are the parents of five living children : Milton D. died when he was nine years old ; Ran som D., Cynthia L, Elveretta E., Lydia A. and Jessie S. are the names of those surviving. _5QSL- (■■ \ cr "oS5" aoob W. Snyder, general farmer, section ML^ 21, New Haven Township, was bom in "^ Montgomery Co., N. Y., Feb. 27, 1819. When 13 years of age he commenced to work out for neighbors, at farm labor, as his par- :nts were poor; and his education was conse- quently limited. He was a laboring man in this capacity till he was about 30 years of age. In the meantime,'Sept. 27, 1838, he married Miss Mehita- ble, daughter of David and Amy (Chapman) Hopkins, who was born in Stafford, Genesee Co., N. Y., Aug. 27, 182 1. When six years of age she moved with the family to Allegany County, same State. Mr. Snyder came to Michigan in the fall of 1853, locating first in Ionia County, and two years later in this county, pre-empting 80 acres on the section where he now resides, and undergoing the experi- ences common to frontier life, more fully described elsewhere in this volume. He and his noble wife bravely persevered and surmounted all obstacles. During the noted famine of 1856, they received but$3 donation. Mr. Snyder has improved 60 acres of
the old homestead, and he has never changed his
residence since his first settlement. In national af-
fairs he is a Republican, and he has held various of-
fices in his township and district.
The children of Mr. and Mrs. Snyder are : Ame-
lia, Edwin F., Laura and Amy M., living ; and Har-
^rison, who died in the army, and Mary J., who died
in infancy.
homas A. Porter, farmer, section 18, Beth-
M any Township, is a son of John and Jane
(Atchison) Porter, and was bom in Indiana,
Nov. 5, 1827. When six months old the fam-
ily moved to Canada. When he was 16 years
of age he left home and learned the millwright
trade, which he followed in various parts of the
United States until 1861, and he has worked at it
some since that date. He was for a time in Califor-
nia, where he was a member of a vigilance com-
mittee. His re»idence for six years was above
Sacramento, near Auburn, Placer County, and he
followed lumbering.
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He first came to Michigan in 1845, stopping on
the Saginaw Bay. In 1 861, he returned to St. Clair
Co., Mich., and shortly afterward he went to Saginaw
County, where he "located" 960 acres of land for
himself and brothers, his share being a third: at one
time he owned 2,200 acres. He cleared 75 acres.
As he was interested in lumbering in Missaukee
County, he operated there two years. He then took
an 18-months trip through the South, visiting the
old battle-grounds. He entered the navy and was
assigned to the U. S. gunboat " Pittsburg," of the
Mississippi Squadron, being in the service ten
months, and engaged in several skirmishes.
After the close of the war he returned to Saginaw ;
came to his present location in May, 1882, purchas-
ing 45 acres. It is all in cultivation, and Mr. P. has
shown himself to be a judicious and prosperous
farmer.
Since 1854 he has belonged to the Masonic frater-
nity. He was married in St. Clair Co., Mich., Nov.
28, 1861, to Miss Julia P. Beech, daughter of Lucius
and Julia A. Beech, who was born in that county,
April 4, 1835.
Stanley L. Nichols, farmer, section 14, Pine
River Township, was bom in Monroe Co.,
N. Y., June 16, 1837, and is the son of
Ezra and Hannah (Hipp) Nichols, both of
whom were natives of New York. At the age
of 18, Mr. Nichols began for himself in the
world, and, for three years, worked out by the month
as a farm laborer. He has devoted most of his life
to the sanae noble calling, with the exception of about
eight years, three of which were spent in the army
and the remaining five years he labored as a teacher.
He enlisted Aug. 14, 1862, in the 4th Mich. Cav.,
and received honorable discharge at Nashville, Tenn.
The regiment was attached to the Army of the Cum-
berland, and Mr. Nichols took an active part in the
various engagements in which it was involved, and
upon him, as well as all others belonging to the same
command, reflected the luster of the 4th Mich. Cav.
in the capture of Jefferson Davis.
In April, 1879, he came to Gratiot County and
bought 40 acres of land in section 14, Pine River
Township. The entire tract was unimproved, and he
has since placed 20 acres under cultivation. He is a
Republican in political sentiment, and a member of
the Masonic Order. He was married in BerkshiireCo.,
Mass., Dec. li, 1866, to Ellen E. Harrison, daughter
of John and Chloe Harrison. Her mother was a
narive of New York, her father of Massachusetts.
Mrs. Nichols was born Oct. 18, 1843, in Lenawee
Co., Mich. Three children have been added to the
family circle — Maud C, Stanley E. and Ida L. The
parents are members of the Methodist Episcopal
Church.
ephthah Earl, farmer, section 23, Newark
Township, was born June 20, 1830, in Sen-
eca Co., N. Y., and is the son of Stephen
and Ann E. (Evans) Earl. Both parents were
born in the State of New York, where they
lived until the spring of 1841, when they re-
moved to Michigan and settled in Kalamazoo County,
where they continued to reside during the remainder
of their lives. The mother died in January, 1863 ; the
father's demise occurred in the following April.
At the age of 19, Mr. Earl became his own man,
pursuing the vocation of agriculture, to which he had
been trained. He passed six years as a farm laborer
and two years was engaged in butchering, associated
with his father. In the spring of 1861 he came to
Gratiot County and bought the place where he has
since resided, and labored until he has placed 60
acres under first-class cultivation. He has sold ^st
acres. The family remained in occupancy of the
pioneer log house unril the summer of 1881, when
a fine frame house was erected on the farm in which
they have since resided.
Mr. Earl was married Dec. 7, 1854, in Ionia Co.,
Mich., to Mary J., third daughter of Nathan and
Chloe (Tyler) Benjamin. Mrs. Earls parents were
natives of the State of New York, and on leaving
there first settled in Ohio, afterward removing to
Oakland Co., Mich, and from thence to Ionia County.
They passed the last years of their lives with their
children, the mother dying Jan. 18, 1866. The
father breathed his last nine days later.
Mrs. E. was bom in Oakland County, Aug. 8, 1833.
She and her husband assumed the care of Viola M.
Benjamin, a niece, when she was five years old, who
remained with them until her marriage. They have
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^ also a foster-child, Leonard E. Smith, born Jan. 26,
(^ 1874, who has been in their charge since his birth.
3* Mr. Earl is a Republican in political sentiment. He
I has held the various offices of his school district and
^6; is a member of the Odd Fellows fraternity.
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illiam Isenhath, farmer, Pine River, is a
son of John C. and Catherine Isenhath,
natives of Germany, where they lived and
died. William was born in Germany, Feb. 6,
1837, and resided in his native country until
20 years of age. Coming to the United States, he
located in Erie Co., Pa., and was employed in farm-
ing for two and a half years. He then went to Ohio,
and, lived in Ashtabula County until the breaking out
of the war, when he enlisted in the nth New York
Battery. He was in the service somewhat over one
year, and was then discharged on account of disa-
bility.
In December, 1862, he came to Gratiot County,
and with his brother-in-law, purchased 40 acres of
land. He afterwards traded his share of the land for
40 acres on section 30, Pine River Township, where
he now resides. He has since added 20 acres, and
has 30 acres nicely improved and under the plow.
Nov. 20, 1863, in Gratiot County, he was married
to Catherine Mulen, a native of Pennsylvania. This
union has been blessed with nine children, seven of
whom survive : Henry A., Mary A., Alvin, Willie E.,
Annie B., Wilda M. and Frankie D. Adeline and
Elmer L. died in .infancy. Mr. and Mrs. Isenhath
are consistent members of the Lutheran Church. In
politics, Mr. I. votes the Republican ticket.
alvin C. Kryder, farmer, section 36, New-
ark Township, was born Oct. 6, 1839, in
Ohio. His parents, Jonas and Mary (Ever-
hard) Kryder, were born respectively in Penn-
sylvania and Ohio. He was engaged in farm-
ing in his native State until the age of 24 years.
He went to Illinois in 1863 and there remained 15
years, and engaged in farming in Christian County.
In the spring of 1878 he sold his farm in the Sucker
State and removed to Michigan, settling where he
now resides in Newark Township, where he became
proprietor of 40 acres of improved land by purchase.
Mr. Kryder is a Republican in political affiliation.
He was married Jan. 25, 1866, in Medina Co.,
Ohio, to Charity, fourth daughter of Joseph and
Sarah (Lance) Coolman. Following are the records
of the five children born of this marriage, three of
whom survive: Leslie A., bom July 3, 1867, died
July 31, 1868; Frankie F., born Jan. 17, 1869, died
May 24, 1877; J. S. Shirley, Sept. 11, 1870; Orie
D. F., Dec. 18, 1872, and Cordie M. U., Nov. 26,
1874.
Mr. Kryder enlisted Jan. 25, 1865, in the 41st Reg.
111. Vol. Inf., and was in the service six months, re-
ceiving honorable discharge July 27, 1865, at Chi-
cago. He was never in active service, as before the
regiment could be duly equipped, mustered in and
reach the front the rebellion was in a state of collapse
and military necessities virtually at an end.
eely Amsbury, farmer, section 36, Seville
Township, was born Jan. 14^ 1853, in Jack-
son Co., Mich., and is a son of Ira and Sarah
(Patch) Amsbury. His father was bom in
Wayne Co., N. Y., and came when a child to
Michigan with his parents. He was a farmer
by occupation, and came to Gratiot County. On the
breaking out of the war of the Rebellion he became
a soldier, enlisring Oct. 8, 1864, in Co. C, 8th Mich.
Vol. Inf. Among the noted incidents of the war in
which he took part was the surrender of Gen. Lee
to Gen. Grant at Appomattox Court-House. He re-
ceived his discharge July 30, 1865. At the rime of
his enlistment he was Supervisor of Seville Town-
ship, which office he filled seven years. He was also
Township Clerk two years. He died Feb. 5, 1873.
The mother is still residing in Seville Township.
Mr. Amsbury was brought up to the calling of
life. In 186 1 he came to Gratiot County with his
parents, where his father located 80 acres of land in
Seville Township, chiefly in an unimproved condi-
Uon. The family encountered all the variety and
incidents common to pioneer life. Mr. Amsbury
owns 25 acres of improved land on which he is en-
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gaged in prosperous farming. Politically he is a
member of the National Greenback party, and in the
years 1882 and '83 was elected Township Treasurer.
He was married in 1878 to Izora, daughter of Ira
and Jane Phelps. The parents and daughter were
natives of Wayne Co., N. Y.; the latter was bom in
i860. She died April 30, 1 881, in Seville.
rs. Mindwell L. (Spencer) Crispel, re-
siding on section 9, New Haven "Town-
ship, was born in Ontario Co., N. Y., Jan.
26, 182 1. Her parents were also natives of
'^ that State, of English descent. Her father^
\ Aaron Spencer, of Puritanical stock, died in
California in 1874; and her mother, Martha, nee
Moore, was of New England ancestry, and died in
When 13 years old the subject of this sketch came
with her parents to Hillsdale Co., Mich,, where she
attended the common school and was married,
March 14, 1838, to John A. Crispel, a native of
Ulster Co., N. Y., born June 20, 181 2. He came to
this State in 1836,-where he lived until his death, in
Jackson County, Oct. 7, 1880, aged nearly 70. He
was a farmer, a prominent and exemplary citizen of
the community, and satisfactorily filled several public
offices, as Supervisor, etc. In religion he was a
Spiritualist, and in politics a Republican. As a
farmer he owned at one time two whole sections, less
only 40 acres.
Mrs. C. is now in her 64th year, enjoying good
health and her mental activity unimpaired. She has
ever been an active, intelligent and philanthropic
member of society. She attends the Methodist
Episcopal Church.
— K^/
;rigg8 B. Ellison, farmer on secrion3i, Pine
River^ Township, is a son of George and
Julia (Drake) Ellison, natives of Orange Co.,
N. Y. The father died in that county in 18 14;
the mother afterwards came to Michigan, and
and died in Jackson County. The subject of this
biographical sketch was born in Orange Co., N. Y.,
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June 29, 181 2. He being quite young at his fathers
death, the first 15 years of his life were mostly passed
with friends of the family in Orange County. He
was then apprenticed to the baker s trade, at which
he worked until 19 years of age. In 1 831, he went
on a whaler, and made two voyages, lasting six years.
In 1838, he came to Michigan and bought 120 acres
of land in Jackson County, on which he settled and
lived nearly 14 years. Selling out, he bought a farm
in an adjoining township, where he Kved for seven
years. He then sold again, and in November, 1854,
came to Gratiot County and bought 160 acres of
partly improved land on section 3 r, Pine River Town-
ship, where he now resides. He has disposed of 120
acres, and of the remaining 40, 35 acres are under
good cultivation. He has a good residence and a
comfortable barn.
March 17, 1842, in Jackson Co., Mich., he was
married to Miss Ardelia D., daughter of Francis and
Henrietta (Carpenter) Bargarow. He was of Eng-
lish and French ancestry, and she was a native of
Connecticut. Their daughter Ardelia was bom in
Saratoga Co., N. Y., June 2, 1825. Mr. and Mrs.
Ellison have had a family of three, two living: Mary
J., Carrie A. (died Jan. 5, 1867, aged 23) and Joseph
A. Mr. Ellison has held for several years the office
of Constable in his township. Politically, he is an
ardent Republican.
orman H. Wells, general farmer and
stock-raiser, section 15, New Haven Town-
"^ ship, was born in Westphalia, Clinton Co.,
Mich., April 13, 1843. His parents, David
and Melinda (Gould) Wells, were natives of
^ Connecticut and of English descent, and emi-
grated to Michigan about 1836, settling first in Oak-
land County, as pioneers; later, in Westphalia
Township, Clinton County, where Mr. David Wells
resided until his death, Aug. 28, 1883, having lived
in that county 41 years! His wife had died Sept. 3,
1859, in that county.
Norman H., the subject of this sketch, remained
at Yiome until 19 years of age, working on the farm
and in his father's brick-yards and attending school
in his district, and at Wacousta, three miles away.
He received a good education and taught public
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school a short time. At the age above mentioned he
set out as a common laborer, lumbering and farming,
and attending school, in Portland, Ionia County,
preparing to take a course at the State Agricultural
College at Lansing, but lack of funds prevented him
from carrying out the much desired project. In
1864 he came to this county and bought 80 acres, on
section 13, New Haven Township. This was then
principally covered with timber. He has since
added by purchase 40 acres, and of the total 120
acres he has improved 1 00 acres, putting it in fine
condition. He also owns 80 acres on section 23, of
which he has 40 acres improved. Both of these
farms are well equipped with the necessary buildings,
orchards, etc. In 1874 he purchased 40 acres on
section 15, to which he has recently added 40 acres,
and has made some improvements upon the place.
In an early day Mr. Wells established a general
store in Newark Township for country patronage.
His was the first successful store in the country in
this county, and he is considered the father of that
branch of mercantile life in Gratiot County. He af-
terward sold out to George E. Blain, and returned to
farming, in which vocation he has been successful.
He owns an aggregate of 320 acres, divided into four
different farms, having a total of 180 acres of good
arable land. He has also been a real-estate dealer
and loan agent for Eastern parties for some time, ex-
hibiting a high order of business qualifications. He
is a thoroughgoing, energetic and common-sense
farmer. In political matters he is a Republican;
was the first Township Superintendent of Schools
after the abolition of the county-superintendency sys-
tem, and has also been Township Inspector, Justice
of the Peace and Highway Commissioner, holding
each office two years. In all these capacities he has
faithfully served the public.
Mr. Wells was married Nov. 6, 1870, in North
Shade Township, this county, to Miss Martha, daugh-
ter of John and Sarah A. (Leonard) Jackson, natives
respectively of England and New York, who came to
the above mentioned township in 1869. Mrs. W. was
born in Brownville, Jefferson Co., N. Y., Oct. 6, 185 1,
and came to this county when 17 years old. She
has taught school several terms, successfully. Both
she and Mr. W. are members of the Methfxiist Epis-
copal Chnrch. Their four children are: Herbert J.,
Laura A., John Floyd and Sarah J.
V-
This family have in their possession an English
sugar-bowl which was owned by great-grandparents,
and is more than 150 years old; and another, of the
American order, that is nearly 100 years old. They
also have a hymn-book, 65 years old.
0868 8teyen8, mechanic, carpenter and
joiner, section 31, Ithaca Township, was
born in Gloucestershire, Eng., Oct. 30
18 19, and was the son of Emanuel and Eliz-
abeth (Gasser) Stevens, natives of England
and of English descent. In his native coun-
try the father was a tinsmith, and he came to Amer-
ica in 1 83 1, settling in the State of New York. He
there engaged in farming, and died in 1842. The
mother died in Tuscola Co., Mich., in 1881, at the
age of 86 years.
When 1 2 years old Moses came with his parents
to this country, and he lived in New York State un-
til he was 2 1 years old. He was then married to
Susan M. Hulett. They came afterwards to Tus-
cola County, this State, where she died, in Septem-
ber, 187 1. April I, 1874, he was married to Sabra
Blair, who died in the same county a year later.
Oct. 3, 1876, he was a third time married, at East
Saginaw, Mich.; and he took for his life partner this
time Mrs. Elmira M. Potter {^e Lake), daughter of
Nicholas and Alzina (Cross) Lake, natives of St. Law-
rence Co., N. Y., and of English descent They
followed farming, and removed at an early day to
Ontario, Canada. After 20 years* residence there,
they came to Forestville, Sanilac County, where the
father died, in September, 1S54. His wife afterwards
removed to Gratiot County, and then went on a visit
to Iosco County, where she died, in December. 1874.
Elmira M. was bom at Smith Falls, Can., Jan 24,
1833. At the age of 19, she came to this State ; and
she was married at Grand Ledge, Eaton Co , Oct
12, 1856, to William Potter, a native of New York.
Three months later, they came to this county, and
located a half a mile from Ithaca. Mr. Potter im-
proved 120 acres of land, and died Sept 7, 1863,
aged nearly 33, leaving to the care of his widow
three children, Ida B., George W. and Cora M.
Mr, Stevens had by his first marriage three sons ■
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335
and seven daughters, all of whom are living except
one son and two daughters. Mr. and Mrs. Stevens
now live on the Potter homestead. They belong to
the society known as Seventh-Day Adventists. In
politics Mr. Stevens is an adherent of the Republican
party.
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rohn Fool, general farmer and stock-raiser,
section 12, New Haven Township, is a na-
tive of Jefferson Co., N. Y., where he was
born Oct, 22, 1823. His father, Isaac Pool,
was also a native of the Empire State, of Eng-
lish and Welsh descent, was a carpenter and
joiner by trade, as well as farmer at times, and emi-
grated to Wisconsin in 1854, settling in Waushara
County, where he was a prominent and respected
citizen, and finally died. John's mother. Diadem,
fuc Buck, was also a native of New York State, of
English ancestry, and died in Wisconsin.
The subject of this sketch was only five years
old when his parents moved with him from his
native place to St. Lawrence Co., N. Y., where he
worked on a farm and at the carpenter's trade, and
attended school, until he was of age. He then
worked as a common laborer a few years near home.
When 22 years of age, he bought 50 acres of land in
St. Lawrence County, partly improved, and set to
work upon it. Three years later he returned to his
native county, where, June 13, 1849, he married Miss
Lucy, daughter of John and Lydia (Jones) Kanautz,
natives of the Empire State. Mr. K. was of pure
German descent, and Mrs. K. of New England par-
entage and of English extraction. The former, an
agriculturist, died in St. Lawrence County, May 30,
1880, and the latter in Jefferson County, July 31,
1850. Mrs. P. was born in Pamela Township, Jef-
ferson County, Oct. 27, 1820, and was the third
daughter and fourth child of her parents. Mr. and
Mrs. P. have had three children, only one of whom
survives, namely: Anna E., born Aug. i, 1854, and
married May 26, 1874, to Alex. McLaren, now resid-
ing in New Haven Township on a farm; Amanda J.,
tx)rn April 10, 1852, and died Feb. 4, 1853; and
John W., bom April 2, 1862, died June 2, 1880.
After marriage, Mr. P. followed farming on his
place for three years, sold out, and one year later he
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purchased property in the village of Herman, St.
Lawrence Co., N. Y., where he was engaged as a
general laborer and farmer. He sold out there, and
in the fall of 1854 came to Gratiot County, and pur-
chased, under the Graduation Act, the southwest
quarter of section 12, New Haven Township, where
he now lives. Before settling here, however, he
spent a short time in Iowa, then in Ionia County,
this State, where he purchased 80 acres in the town-
ship of Fair Plains. While there, he and his family
suffered a great deal from chills and fever. He sold
out there in November, 1855, and the following Feb-
ruary returned to this county and settled on his land.
It was then a wilderness. Here, in a log shanty,
13 X 17 feet, he and his little family started out again
to make a permanent home. The scenes of frontier
life here, and the kindness and sociability of their
early neighbors, are remembered with an ever-in-
creasing fascination and delight.
His little cabin, afterward enlarged to 14 x 22,
stood till the spring of 1 861, when it was supplanted
by a good-sized house, which still stands in striking
contrast with his present mansion, built in 1874.
His barn, 30 x 40 feet in dimensions, was erected in
1858, the first frame barn in the township. By addi-
tions to this structure, he has made it one of the
largest barns in this part of the county. He has 200
acres of the best land in the township, with 100 acres
well improved, watered and stocked, with a thrifty
orchard of three acres, etc.
Mr. Pool has always been a strong Republican,
and as a citizen of his township he has been honored
with various offices, as Highway Commissioner for
several years. Township Treasurer six years, etc.
He and his wife are members of the Baptist Church.
Portraits of Mr. and Mrs. Pool are given in prox-
imity to this sketch, as they are representative of a
worthy and exemplary class of citizens.
'ohn Hamilton, M. D., physician and sur-
geon at Pompei, was born in Paisley, Ren-
frewshire, Scotland, Oct. 31, 1830. He is
a son of Thomas Hamilton, deceased, a native
of Scotland, and who emigrated to America
and settled in Carlton Place, near Ottawa,
Canada, in 1842, and where two years later, in
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1844, his family, including our subject, joined h.m.
Dr. Hamilton in early life manifested a desire to
become a medical practitioner, and devoted his time
and energies to the accomplishment of that purpose.
schools, and then attended the High School at Al-
monte, Canada. He then turned his attention to
teaching, and followed the same for some 12 years,
devoting all his leisure tinie to research after medical
knowledge, and afterward, before coming to tlie
United States, was engaged in practice for some
time. He then came to Michigan and entered the
Detroit Medical College, from which he graduated
with honors in 1876. In April of that year the
Doctor came to Pompei, this county, entered upon
the practice of his profession, and has built up a
lucrative and successful one.
The Doctor was united in marriage to Miss Jessie
Lang, daughter of Arthur Lang, deceased, and was
born in Almonte, Canada. Ten children have been
bom to their union : Amelia, Helen, Thomas, Arthur,
Marion, Jessie, John D., William R. and Harry H.
Amelia is the wife of Hiram White, and lives in
Cranbrook, Huron Co., Canada. Helen is also mar-
ried, and is the wife of John Taylor, who resides near
Dr. Hamilton is a member of the L O. O. F. and
Masonic Order.
obert P. Fleming, farmer, section 30, Pine
River Township, was born at Ann Arbor,
Mich., Feb. i, 1834, and is a son of Charles
M. and Peninah J. Fleming. His parents
were both natives of the State of New York.
During the years of his minority, the life
of Mr. Fleming was passed in the manner common
to the farmers' sons of the place and period. The
succeeding five years he spent in working by the
month, and expended his earnings in the purchase of
40 acres of land in Jackson County, on which he
settled at the age of 26 years. Between five and
six years later he sold the place, and in October, 1865,
came to Gratiot County, and bought 50 acres of
land in Pine River Township, most of which was in
an unimproved condition. Of this he has placed 40
acres under cultivation. Mr. Fleming is a Republi-
can in political affinity.
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He was married March i, i860, at Eaton Rapids,
to Eliza A., daughter of Gardner Rice, a native of
the State of New York. Mrs. Fleming was bom
July 30, 1835, in Cayuga Co., N. Y. Six of seven
children born of this marriage yet survive, — Edward
E., James H., Willie F., Carrie E., Cora E. and El-
vira P. Calvin A. died when nearly two years old.
The parents belong to the Presbyterian Church.
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Fi|nilliam J. Naldrett, farmer, section 36,
.l^^W New Haven Township, is a native of Eng-
land, where he was bom April 10, 1828.
His parents, Clement and Hannah (His-
cock) Naldrett, were also natives of the same
county. (See sketch of George S. Naldrett.)
Mr. Naldrett was trained to the occupation of
gardener in his native land, and at the age of 21
came to the United States. He first found employ-
ment in a nursery near the city of Rochester, N. Y.,
where he remained about three months. He prac-
ticed all the economy possible and saved suflficient
money to enable him to proceed to Michigan. He
came directly to Ann Arbor, where he remained six
years, chiefly occupied in gardening. In the fall of
1854 he went to Lansing, Mich., and during the ses-
sion of the Legislature in the winter following he
was employed at the State House as fireman. He
was engaged in gardening through the next summer,
and in August, 1855, bought 58 acres of unimproved
land on section 30, Newark Township, Gratiot County,
built a small house and entered at Once upon the
labor of improving and cultivating his farm. In the
fall of 1853 he had purchased 80 acres of land on
section 29 in the same township, which he has since
sold. He has increased his homestead farm to 112
acres and has put 70 acres under good cultivation.
Mr. Naldrett is connected with the Order of Masonr}'
and is an adherent to the Democratic party in politi-
cal views.
He was married Sept. 28, 1854, in Detroit, to
Mary, third daughter of Christian and Barbara Leon-
ard. Her parents were narives of Germany, and she
was born Sept. 29, 1831, in Baden, in the same coun-
try. When she was 21 years old her parents came
with their family [to America, settling at Ann Arbor,
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Mich., where they both died. Of six children born
to Mr. and Mrs. Naldrett, three died in infancy —
George, Cornelia and Clara. Those surviving are
William C, Rose B. and Ernest H.
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illet Beynolds, farmer, owning 40 acres on
section 17, North Star Township, was
born in Chenango Co., N. Y., Feb. 7, 1834.
His father, Abel Reynolds, deceased, was a
native of Rhode Island. Mr. R., the sub-
ject of this sketch, was reared as a farmer, and
received his education in the common school in his
native county. He came to Clinton County, Mich.,
in 1854, and to this county in 1856, where he has
since lived, except three years temporarily in Oak-
land Co., Mich. He served three years in the great
war, as a Corporal of Co. G, Fifth Mich. Cav., par-
ticipating in the battles of Gettysburg, Williamsport,
Hagerstown, Boonsboro, Snicker s Gap, and in oppos-
ing Early's raid on Washington.
Mr. Reynolds was married in 1856 to Miss Lydia
J., daughter of Nathaniel Neal (deceased), who was
born Dec. 25, 1833, in Oswego Co., N. Y. Their
four children are : Elizabeth, who married B. B.
Tuttle; Jennette; Emma J., who married Marion
Miner; and Helen L.
Mr. R. and wife are members of the Seventh-Day
I homas J. Clark, farmer, section 21, Pine
River Township, was bom July 5, 1855, in
the city of Norfolk, and is the son of
Thomas and Rosa Clark. His parents lived in
New York and had but two children, Thomas
and William. The father was a naval officer
and lost his life in the engagement at Hampton
Roa.ds when the Congress and the Cumberland were
sunk by the Merrimac, an iron-clad Confederate ves-
sel, now called the Virginia.
Wli^in Mr. Clark was ten years old he came to
\f loliigan under the guidance and management of
the CThildren's Aid Society, which at that time sent
out 4^^ children to find home and friends in the shel-
tering homes of the Peninsular State. He spent the
intervening years until 1868, in Lenawee County, with
different individuals arid variously employed. In
the year named he went to live with Thomas J. King,
of Hillsdale County, and, for three years, he worked
for his board and clothes, after which he received
wages, continuing to make his home with Mr. King
until 1880, when he came to Gratiot County, where
he owned 80 acres of land on section 22, Pine River
Township, which he had bought seven years previ-
ous and had been partly improved. This he ex-
changed for 80 acres on section 21, on which he now
resides. He has placed 40 acres under good cul-
tivation and, in 1881, erected a fine bam of modern
architecture.
Mr. Clark was married Dec. 9, 1880, to Myrtie H.,
daughter of Reuben and Rebecca (Smith) King.
She was born April 2, 1856, in Jackson County, Mich.,
and her parents were natives respectively of New
York and England. Mr. and Mrs. Clark have two
children, Lloyd L. and Hiel C.
Mr. Claik is actively interested in local politics and
is a Republican of decided type. He is a valuable
cirizen from his active, public spirit and warm inter-
est in the progress and well-being of the community.
He is rapidly placing his farm in the best possible
shai)e for future profit, and deservedly is awarded the
respect and confidence of his fellow-townsmen.
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ohn Franklin Henry, farmer, section 31,
North Star, was born in the village of
|IS^ Dummerston, Windham Co., Vt,, April 29,
liJ^ 1829. His parents, John and Sandona (Daven-
port) Henry, were also natives of the Green
Mountain State; they moved to Bellows Falls,
in the same county, when the subject of this sketch
was very young. Here the latter attended the village
school during the winter seasons, and after he was
1 3 years old he worked upon the farm. In the win-
ter of 185 1-2 he went to California, where he en-
gaged in packing supplies by mule express to the
miners in the mountains. About the ist of October,
1854, he started on his return, on the' steamer
" Yankee Blade," which, just after leaving the coast,
was purposely wrecked by the Captain, who ran her
on the breakers, expecting to* secure the money on
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board; but he was caught and placed in custody.
A picture of this wreck is still in the possession of Mr.
Henry. Remaining in California until the following
July, he returned to his home in Vermont. During
the month of August, 1862, he and family came to
Gratiot County on a visit, and concluded to remain.
He owns 67 acres of good farming land, where he is
prosperously engaged as an agriculturist and cheese
manufacturer.
Jan. 30, 1856, Mr. Henry married Miss Mary P.,
daughter of Thomas Mills, now deceased. She was
born in Colchester, Chittenden Co., Vt., on the shore
of Lake Champlain. The children of Mr. and Mrs.
Henry are the following named : Edgar L., Inez L.
(deceased), Charlotte M., Georgia B., Charles B. and
George Hugh. Mr. and Mrs. H. are members of the
Baptist Church, and he is also a member of the
Orders of Masonry and Knights of Honor.
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i ownsend A. Ely, Postinaster at Alma, was
born Aug. 27, 1843, at Wabash, Ind., and is
the only son of Gen. Ralph and Mary E.
(Halstead) Ely. (See sketch.) The parents
were married at Brookville, Ind., and after
marriage settled at Wabash, where they re-
sided two years. They returned to New York, their
native State, and after a year s residence there they
came to Ionia Co., Mich., where Gen. Ely purchased
200 acres of unimproved land, and he entered into
the merits of pioneer life. He vigorously prosecuted
the improvement and cultivation of his farm. In
April. 1856, he sold the place, and purchased 160
acres of land in Arcada Township, Gratiot County.
The family constituted the first settlers on the north
side of Pine River. Gen. Ely again commenced life
as a pioneer, built a log house, platted the village of
Alma, and embarked in various pursuits for the pur-
pose of furthering the advancement of the place, and
establishing, so far as lay in his power, substantial
business interests at that point. He was engaged
chiefly in farming, trade and milling interests until
1 86 1, when he enlisted. On leaving the army in the
fall of 1866, he went to Florida and purchased 130
acres of land, a part of which was located in the vi-
cinity of Jacksonville. The remainder was situated
120 miles south of that city, and there he set out an
orange orchard, which included 40 acres of land.
He spent a year in planting, and the second year
lost the entire result of his labor, the frost killing all
the young trees. He became disheartened, and re-
turned to Alma, where he resumed farming, and pur-
sued that vocation until 1874, when he was elected
Auditor General of Michigan, and was re-elected to
the office in 1876. While engaged in the discharge
of the duties of the position, his business relations at
Alma and in Gratiot County practically terminated •
and when his connection with the office of Auditor
General ceased, he interested himself in lumbering
in Emmett County, where he remained until his
death, which occurred April 14, 1883. His family
included one son and six daughters.
At the age of 17, Mr. Ely, of this sketch, succeeded
to the charge of the farm and other business interests
of his father, who had entered the service of the
United States, and he continued the management of
his business and domestic affairs until the close of
the war. Mr. Ely became roused, by the course and
exigencies of the struggle with the South, to an inter-
est in its issues, and enlisted Feb. 25, 1865, in the
8th Mich. Inf. He became Sergeant of Co. C, and
was promoted to Second Lieutenant April 25, 1865.
He was in the service until Aug. 14, 1865, and was
under fire at Fort Stedman, and at the siege at
Petersburg. He received honorable discharge at
Detroit, Mich.
When he was 23 years old, he embarked in busi-
ness for himself, and purchased 240 acres of land in
He continued the management and improvement of
his property three years, when he sold out. He was
appointed Mail Messenger between St. Louis and
Saginaw, a position which he filled two years and
nine months. He resigned the situation to accept
one as conductor on the Saginaw Valley and St.
Louis railroad. He operated in that capacity three
years and three months, and resigned to establisli
himself in the hardware business at Alma. A year
later he sold out, and was appointed to his present
position of Postmaster at Alma. He succeeded to
the place Aug. 6, 1881, by appointment under Post-
master-General James, and has discharged the obli-
gations of the office with credit and honor, and to the
entire satisfaction of the public. In political princi-
ple, he is an adherent to the tenets of the Repul
can party.
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Mr. Ely was married at Alma, Sept. 25, 1866, to
Maggie C, daughter of Dewitt C. and Edna F.
(Utley) Chapin. Mrs. Ely was born at Chicago,
111., June 27, 1845. Ralph C, born March 5, 1870,
is the only child of Mr. and Mrs. Ely.
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eorge Johnson, farmer, section 36, North
Shade Township, is a son of Robert and
Ann (Bell) Johnson, the latter a native of
England; the former, a native of Ireland, set-
tled in Canada in 1842 ; in 1866 he came to
this county and settled on 40 acres of wild
land, on section 26, North Shade Township, where
he yet resides.
The subject of this sketch was born Aug. 17, 1857,
in Peterboro, Can., and was brought by his parents
10 this county; at 20 years of age he commenced
working by the month on a farm, and by this means
he accumulated a sufficient amount of means to buy
a farm of 80 acres, on section 36, North Shade Town-
ship, where he now has about 50 acres in a high
state of cultivation.
Oct. 18, 1881, Mr. Johnson was married to Miss
Sarah, daughter of George and Lovina (Belden) Ed-
monds. The latter were natives of New York Slate,
Mr. E. a farmer. He located on section 26, North
Shade Township, in 1873, where the family yet re-
side. Mr. and Mrs. J. are the parents of two chil-
dren, namely : Glenn, born Aug. 6, 1882; and Ora,
Sept. T I, 1883.
On political issues Mr. Johnson is a Republican.
>rneliu8 A. Deline, farmer, section 35,
Newark Township, was born Aug. 20, 183 1,
in Ridge way, Orleans Co., N. Y. His parents,
Peter and Charity (Snell) Deline, were natives
of Montgomery County in the same State.
They passed the years of their marrit^d life there
until 1862, when they settled in Newark Township,
and there the father still resides. The mother died
May 15, 1869. Their family included seven daugh-
ters and one son. The sisters of Mr. Deline were
named Miranda E., Mary J., Catherine E., Hannah
L., Francis E., Martha A. and Julia J.
Mr. Deline is the eldest child. He obtained a fair
education in the common schools and engaged in
farming with his father until he was 23 years of a|e.
In October, 1862, he came to Gratiot County and
bought no acres of unimproved land, located on
section 35 of Newark Township, and section 2 of
Fulton Township. He has since added by purchase
40 acres to his original tract of land, and now has
120 acres in advanced cultivation and most promis-
ing condition. The log cabin, which was his home
in his early days of labor and struggle, has been sup-
planted by a fine residence, of which he look posses-
sion in May, i^8o. He is a Democrat.
He was married July 4, 1854, in Ia)ckport, Niag-
ara Co., N. Y., to Mary S., daughter of Peter and Su-
sannah (Ziglar) Jones. Her parents Were natives of
Pennsylvania, and their family comprised 12 children,
viz. : John F., Evan, Rebecca A., Sarah, Lany E.,
Amanda, Rhoda A., Siglar, Lovisa, Lovina, Mary S. and
Lotilla, Mrs. Deline was the eighth daughter and was
born Oct. 15, 1836, in Genesee Co., N. Y. All the
children of Mr. and Mrs. Deline, seven in number,
died in infancy
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laron Stanton, deceased, a pioneer on sec-
tion 18, North Star Township, was a native
of the State of New York, where he was born
May 28, 1827. His father, Hiram Stanton,
brought his family to Lenawee Co., Mich.,
when Aaron was a small boy, and where the latter
was reared on the farm and educated in the common
school. When he was 18 years of age the family re-
moved to Clinton Co., Mich., where he resided until
December, 1854, when he came to North Star Town-
ship, this county, settling on section 18, the present
home of the family.
Although Mr. Stanton s occupation was principally
that of farming, his natural genius and practical
ability early led him to the skillful use of tools. He
therefore worked much in wood, and some in a saw-
mill. He was married Dec. 11, 1854, to Miss Han-
nah Hawkins, daughter of Benjamin Hawkins. She
also was a native of New York State. Mr. and Mrs.
S. had four children, namely: Philena J. (Pritchard),
George L., Annie F. and William A. Mr. Stanton
died Feb. 21, 1863, in Alexandria, Va., of measles,
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about six months after he was enrolled into the
United States service, as a member of Co. D, 26th
Mich. Vol. Inf. He was then a member of the Free-
Will Baptist Church, but formerly of the Christian
Church in this county, there being no Church of his
choice in his* neighborhood. Mrs. Stanton after-
ward (1867) married M. M. Heath, and by him has
had six children, two of whom are now living,
namely, Emma M. and George E.
oren M. Butphin, dealer \xi wines and
liquors at Alma, was born April 5, 1852, in
Niagara Co., N. Y. He is a son of Ralph
^j^ and Margaret (Crego) Sutphin, both of whom
/^ were natives of New York. They first located
, ;^ in Niagara County and afterwards removed to
Michigan, where they settled in Jackson, and after a
residence there of more than three years they moved
to Clinton County, where the father died, March 14,
1864. The mother is still a resident of that county.
Mr. Sutphin was in the first year of his life when
his parents came to Michigan. He passed his early
years in obtaining an education, and at t6 was em-
ployed as a sawyer in a mill, where he worked nearly
three years. Ten years succeeding he was employed
as a clerk. In August, 1883, he came to Gratiot
County and located at Alma, where he established
himself in the business in which he still continues.
In political faith he is a Republican.
He was married in Ensley Township, Newaygo
County, March 27, 1872, to Adelia M., daughter of
Calvin and Ellen Cook. Parents and daughter are
natives of Ohio. Mr. and Mrs. Sutphin have two
children : Claude L. and Maud M.
tv'lte^lHv rederick Boyer, farmer, section 20, New
]<^j^Silii9 ark Township, was born May 18, 1834, in
\()S^^ "'^ Herkimer Co., N. Y. His parents, Joseph
^J^ and Nancy (Shell) Boyer, were also natives of
^K^ the Empire State. He was 14 years old wlien
i he came to Michigan and settled in Eaton
County, where he remained until 1858. In 1854
he came to Gratiot County and bought 80 acres of
land, and of this he took possession in August, i860.
The place was in a wholly unimproved state and he
built a log house and proceeded, with all his energie
to clear and put his farm in a suitable condition f(
the successful pursuit of agriculture.
In 1862 he enlisted in the 26th Reg. Mich. Vo
Inf., and. served until July 14, 1865, when he wa
honorably discharged at Detroit. Among other ei
gagements in which he participated were those <
Cold Harbor and the siege of Petersburg. In one <
the numerous skirmishes in which he took part, I:
received a slight wound in the right hip. On retun
ing to Gratiot County he resumed his farm labors an
has put 57 acres under a fair state of improvement
A {^ood frame house has replaced the log cabin of h
pioneer days, and he is in circumstances which wa
rant him in expecting a future of comfort. He is i
sympathy with the beliefs and issues of the Dem(
cratic party, and has held the various offices in h
school district.
Mr. Boyer was married March 17, 1858, in Eatc
County, to Mary H. Boyer, a native of Herkimer Cc
N. Y., and of their marriage five children have be<
born : Catharine M., Imelda L., John P. and Hem
H. Another daughter, Ellen L., died when she w;
18 years old.
eorge W. Jennings, lumberman and fa
mer, residing at Alma, was bom Aug. \
1828, in Erie Co., N. Y., and is the son <
Hiram and Mary (Rhodabaugh) Jenning
The parents were natives respectively of Vi
i;inia and Pennsylvania. After marriage th<
settled in Erie Co., N. Y., where they passed the r
mainder of their lives, the mother dying in 1829, tl
fatlierin the fall of 1873. He was a blacksmith I
trade. Their family included four children.
Mr. Jennings obtained his education in the cor
nion and high schools of the section where he Wi
reared. He was nine months old when his moth
died. At the age of 15 years, he engaged with
blacksmith to learn the trade, and worked as an a;
prentice about two years. Just before he was i
years old his health failed, and he accordingly abai
doned the trade of blacksmith, and embarked as
sailor on a whaling vessel. He continued in th
vocation nearly five years. He suffered shipwTe<
once off the coast of Japan. After leaving the s<
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he returned to Erie County, and spent three years in
lumbering. In 1854 he came to Clinton Co., Mich^
where he pursued the same vocation six years. In
1858 he came to Gratiot County, and settled in Ar-
cada Township, where he bought 320 acres of unim-
proved land. On this he built a " block " house,,
claimed to be the best in Gratiot County erected
after that method. He operated on this farm until
1862, when he removed to Alma, and has since been
engaged as stated. Politically, Mr. Jennings is a
Republican. In i860 he was elected Justice of the
Peace, and held the office successively until 1875.
He was Supervisor of Arcada one term, and held
various minor offices. He is a member of the Ma-
sonic fraternity.
Mr. Jennings was first married at Maple Rapids,
Clinton County, in July, 1854, to Zilpha A., daughter
of Harvey P. and Lydia Lansing, natives of New
York. Mrs. Jennings was born in 1839, in New York,
and of her marriage three children were born : Frank
E., Ida M. and George. The latter died when three
years old. Mr. Jennings was a second time married
at St. John's, Qinton County, April 29, 1 866, to Sibyl,
daughter of Alexander and Jane (Sprague) Fraker.
Mrs. Jennings was born Jan. 29, 1845, in St. Law-
rence Co., N. Y., and her parents were also natives
of that State. Three children have been born to
them : Harry A., Jennie M. and Morton F. The
eldest of these died when nine months old. Both
parents are members of the Congregational Church.
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iram W. Havens, farmer, section 27, North
Shade Township, is a son of Samuel and
Sarah A. (Tubbs) Havens, the former a
native of New Jersey and the latter of New
York. Mr. Samuel Havens was a farmer. His
first wife's maiden name was Amy Bennett: she
died at an early day, and he subsequently married
Miss Tubbs. He moved from New York to Michi-
gan in 1837, settling in Lenawee County, where he
died, in 1861 ; his widow is yet living, in Seneca
Township, Lenawee Co., Mich.
The subject of this sketch was born March 28,
1837, in Niagara Co., N. Y.; remaining at home with
his parents until he was 24 years of age, he came, in
1862, to Michigan and located 80 acres of wild land.
on the section where he now resides. He resided
in Lenawee County five, years longer, and then came
to Gratiot County ; but not until he was 35 years of
age did he settle here to make it his permanent
home. He has been Highway Commissioner three
terms and School Inspector one term; has always
been a Republican.
In 1872 Mr. Havens was married to Miss Ellen,
daughter of Samuel and Rebecca (Burras) Huyck,
natives of Huron Co., Ohio, who first moved to Will-
iams County, that Slate, then returned to Huron
County, thence to Lenawee Co., Mich., Fulton Co.,
Ohio, and finally Bloomer Township, Montcalm Co.,
Mich., where they now reside. Mr. and Mrs. Ha-
vens' two children are, Alta M., born June 13, 1875,
and Hiram W., April 18, 1883, both in this county.
amuel Lepley, farmer, section 34. Newark
Township, was born in Union Co., Pa., Oct.
25, 1816, and is the son of John and Mary
Lepley, both natives of the same State, where
they married and reared their family. Mr.
Lepley is a born and bred farmer, having spent
the years of his early life in the practice of the details
of that business, preparatory to making it the calling
of his life. At 15 years of age he found himself at
liberty to make a decided encounter with the world
on his own behalf, and from that age until the year
1849 he was engaged in agriculture at various places.
In the year named he came to Hillsdale Co., Mich.,
and in 1855 came to Gratiot County. He bought
120 acres of unimproved land in the township of
Newark, settled on it and operated in true pioneer
style. He reduced his estate by the sale of 40 acres
and has, in the brief time included within the date
named and the current year (1884), placed 70 acres
of the remainder in satisfactory farming condition.
Mr. Lepley is a Democrat in political proclivity,
and has always been keenly alive to everything that
seemed to bear any reasonable promise of benefit to
the community in which he has lived. He was in-
strumental in establishing the first school in the dis-
trict in which he resides. Having been elected Di-
rector, he conducted a subscription and raised a small
sum of money, with which he hired a teacher, paying
her one dollar a week. For the first month she had
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one pupil, but the school has been sustained ever
since, and now numbers about 50 students. Mr. Lep-
ley has held the office of Township Collector seven
years in succession.
He was first married in Seneca Co., Ohio, to Eliz-
abeth, daughter of Charles Caty, who was a German
by birth. Mrs. Lepley was born in Maryland. Of
her marriage to Mr. Lepley, eight children werelx)rn,
whose names are : John W., Maria H., William F.,
James C, Cyrus, Mary J., Sarah L. and Andrew J.
The mother died in March, 1872. Mr. Lepley was
again married April 16, 1873, in Clinton Co., Mich.,
to Mrs. Mary (Boardman) Leary, daughter of Watson
and Elizabeth Boardnian,and widow of Walter Leary.
rank £. Jennings, with the firm of Brad-
ley & Jennings, resident at Alma, was born
July 4, 1857, at Maple Rapids, Clinton
Co., Mich. He is a son of George W. Jen-
nings, who was a native of the State of New
York. His mother, Zilpha (Lansing) Jennings,
was born in Michigan. After their marriage they
settled in Gratiot County. Their family included
two children : F. E. and Ida M. The mother died
in Alma, in 1865. The father is still a resident there.
He was formerly proprietor of the planing mill at
Alma, where the son was trained to the same busi-
ness.
Mr. Jennings was educated at the common and
graded schools, and at the age of 20 years he went
to Ithaca, where he was apprenticed for two years to
learn the trade of making sash, doors and blinds.
At the expiration of his indenture he went into part-
nership with his father. This relation continued two
years, when it was dissolved by the withdrawal of
Mr. Jennings, senior. Mr. Jennings, of this sketch,
formed a partnership with A. Bradley in the fall of
1883, under the firm style of Bradley & Jennings,
which relation continued until early in 1884, when
Mr. Jennings sold his interest. He is at present
contemplating erecting a store and entering mercan-
tile life.
He was married at Saginaw, May 13, 1882, to Dora,
daughter of A. J. and Louisa Brooke. Mrs. Jen-
nings and her parents were natives of Wood Co.,
Ohio. One child has been born to Mr. and Mrs.
Jennings : Nina, Oct. 13, 1883.
Mr. Jennings is an active temperance worker and
belongs to Blue Ribbon Society and Order of Good
Templars. He is a Republican in [xjlitical senti-
ment.
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ra B. Ellsworth, merchant at Riverdale,
Seville Township, was born May 26, 1826,
in Erie Co., N. Y., and is a son of William
^j^ and Lydia (Bentley) Ellsworth, natives respect-
ively of Vermont and Canada. The father
was a farmer in New York, and removed to
Canada, where he lived some eight years ; thence to
Lexington, Sanilac Co., Mich., in 1837. He and
wife both died in Sanilac County.
Their son, Ira, lived at home until 18 years old,
when he lived a year with a Mr. Hurd in Marshall,
this State. He returned to Lexington and for five
years following was engaged in farming. He was
then for six seasons on the waters of Lakes Huron
and Erie, sailing to Cleveland and Sandusky. Coming
to Montcalm County in 1861, he followed fanning
seven or eight years.
During the civil war he enlisted, Oct. 16, 1864, in
Co. A, ist Mich. Eng. and Mech., and served under
Gen. Sherman. The regiment participated in the
battles around Knoxville, but was principally occu-
pied in such work as repairing bridges. He was
discharged at Washington in 1865 and returned to
his family in Montcalm County. They removed to
Millbrook in 187 1, and to Stanton three yea^ later.
They then lived a short time at Belltown, and for a
year kept a hotel at Ithaca. His last move was to
Riverdale, where he also engaged in the hotel busi-
ness, following that a little over four years, before
entering mercantile life.
He was married in 1847 to Almira Vancamp,
daughter of John Vancamp. She was bom in 1829,
and died in 1850, leaving five children: Jefferson,
Dewitt, Henry, Emeline and Ira. He subsequently
married Louisa Pherris, a widow, the daughter of
Rufus and Elizabeth Colbum, natives of New York
State. Mr. C. was a manufacturer, and died when
the daughter was quite young.
Mr. Ellsworth is a member of Ithaca Lodge, No.
123, F. & A. M., of Riverdale Lodge, No. 343, 1. O.
O. F. and of Pine River Lodge, No. 343, 1. O. G. T,
Politically he is an ardent Prohibitionist.
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German F. F. Schneider, of the firm of
Wright, Schneider & Stuttz, merchants and
dealers in grain at Alma, was bom June 29,
1849, in Pomerania, Germany. William C. and
Louise (Penzel) Schneider, his parents, were
natives of the same country and emigrated to the
United States in the month of June, 1864. They at
once located in Detroit, whence they removed in Oc-
tober, 1882, to Alma, and are still living there.
Mr. Schneider had reached the age of 15 years
when his family came to the New World ; and, owing
to his father having become incapacitated from effort
by illness, he has been their sole dependence and
support. His first piece of labor was in the capacity
of a wood-sawyer. He sawed and split a cord of
" iron- wood," and has still a clear remembrance of
profoundly wishing that he had never seen America.
During the first year of his residence in Detroit he
was variously employed, meanwhile suffering much
from fever and ague. He found so little satisfaction
and comfort in the disorder that, while operating as a
laborer in Elm wood Cemetery, he could not help en-
vying the freedom from hardship and disease of the
silent sleepers in the city of the dead. The year fol-
lowing he became an employe' at the Russell House,
where he was engaged nearly three years. In 1868
he entered the dry-goods establishment of Sebastian
Kirchner, of Detroit, and a year and a half later en-
gaged with Campbell & Linn as a clerk. After four
months he was employed by Freedman Bros., enter-
ing their service when they opened their new store on
Woodward Avenue. In July, 1870, he engaged with
James Lowrie & Sons, where he remained until July,
1878, when he again became connected with the
house of Freedman Bros. Two years later he was
employed by Taylor, Wolfenden & Co. He remained
with them 11 months, and in August, 1881, came to
Alma. He formed an association with A. W. Wright
and George D. Barton for the sale of general mer-
chandise, under the firm style of Barton, Schneider
& Co. This relation continued five months, when
Mr. Barton withdrew and was succeeded by James
A. Stuttz, the style becoming Wright, Schneider &
Stuttz. The firm is established on a substantial
basis, and its yearly transactions amount to $100,- 000 in merchandise only. Mr. Schneider belongs to the German Lutheran Church, of which his parents are also members. In political principle and action he is a Republican, and holds tolerant views. He is a member of the A. O. U. W., Peninsular Lodge, No. 12, at Detroit. The portrait of Mr. Schneider, on another page, is a valuable addition to the coUecrion of pictures of young and rising men of the present generation pre- sented in this volume. ff^l ill illiam A. Bradley, farmer on section 3 1 Seville Township, is a son of William and j^p Harriet J. (Fisk) Bradley. The father was jJV^ born in 1808, in Litchfield Co., Conn., and the mother in 182 1, in Brattleboro, Vt. He was first a tin peddler, then a tanner, and later a real-estate dealer. He and wife now reside at 182, Duffield Street, Brooklyn, N. Y. They have four sons, four daughters, all younger than the sons, and 18 grandchildren, and the fortunate family has not as yet had a single visit from death. The subject of this notice was born Aug. 27, 1845, in Sullivan Co., N. Y., and remained at home with his parents until he was 22 years old. He was first engaged in lumbering, and later in farming. He came from the Empire State to Grand Rapids, Mich., in the year 1870 and remained there one year look- ing after his father s affairs. He then came with his brother to Gratiot County and lo'-.ated on 320 acres of wild land on section 30, Seville. They built a fine house and a large barn, and cleared a portion of the land, and Dec. 31, 1873, Mr. B. was united in the bonds of matrimony to Miss Mary E. Whitney, daughter of Chauncey B. and Mary (Birmingham) Whitney, natives of Cayuga Co., N. Y. They came from that State to Ingham Co., Mich., in 1854, and in 1867 came to Sumner Township, Gratiot County. Mr. and Mrs. Bradley have a family of three : Wel- lington, Chandler and Forrest. Mr. B. enlisted in September, 1 861, in Co. F, 56th N. Y. Vol. Inf. The regiment was on detached duty with the Eastern army much of the time at Washing- ton, and participated in two engagements, which nearly annihilated it. The remnant were finally discharged in New York State, with due honors. Mr. B. is polit- ically a Republican. He is a member of Col. Ely Post, No. 158, G. A. R. v. -/ f r 1 ,1 1 V -^<:D!];-CI]!1>;>-^— Digitized by LnOOQ IC ^^ 348 ;.1 irrr *> • • "' % nzn • #- ♦ I GRA TIO T CO UNTY, -^si^^^isr --®i> '•t ^i^^ Mr. Franklin, the subject of this sketch, was born Sept. 29, 1829, and remained with his parents at home until he was 26 years of age. At that age he came to the New World, landing in New York. He then came to Detroit, Mich., and remained in Wayne County for six years, when he came to Gratiot County, and located upon 40 acres of land on section 20, North Shade Township. To his original claim he has since added 140 acres, and he now has about 70 acres under cultivation. He has been largely en- gaged in stock-raising, and has one of the best equipped farms in the county. In 1876 he built a large bam, and in 1883 he erected a residence, at a cost of about$2,000.
In 1856 Mr. Franklin was united in marriage with
Miss Ellen, the eldest daughter of James and Honor
(Dean) Watts, natives of England. Mr. Watts was a
farmer by occupation. He died Nov. 12, 1883, in his
native country. Mrs. Franklin was born in England,
March 14, 1 831, and came to America Dec. 19, 1857.
Mr. and Mrs. Franklin are the parents of six children,
as follows: Ellen, Mary, John, Anna, Addie and
William.
Mr. Franklin and his wife are members of the
Baptist Church, at Carson City.
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fames Knowles, farmer on the east half of
the southeast quarter of section 17, Beth-
any Township, is a son of Willard and
Minim (Nearpass) Knowles, and was born in
Jackson Co., Mich., April 25, 1836 : was brought
up on a farm. When he was 1 7 years old, the
family moved to Sauk Co., Wis., where they resided
a number of years, and where his father bought 40
acres of land.
In the last mentioned place. May 4, 1850, he was
married to Miss Elizabeth, daughter of Henry and
Mary (Staples) Oler, and a native of Ohio. By this
marriage six children have been born, four of whom
are living, namely : Charles, Mary E., Albert and
Almeda. The deceased are William and Lewis. Mrs.
K. died Aug. 4, 1874, in Wisconsin, and Mr. Knowles
again married, June 7, 1877, Mary Thomas, a native
of Wisconsin, who was bom in 1850. By this mar-
riage there have been three children, — Leonard,
Rosa and Ernest.
Mr. Knowles returned to Jackson County, this
State, in the fall of 1878, for one year, and then came
to Bethany Township, this county, and purchased his
present farm of 80 acres, 30 acres of which are well
improved.
While a resident of Wisconsin, during the war, Mr.
K. was drafted for the army, attached to Co. H, 6th
Wis. Inf., and served bravely, engaging in the battles
at Hatchers Run, South Side, Yellow House, Lee s
surrender, etc., besides a number of skirmishes. He
was discharged at Jefferson ville, Ind. During the
service he was slightly wounded in the right shoulder,
by a minie ball.
He and his wife are members of the Baptist
Church.
P. Covert, of the firm of Retan & Covert,
proprietors of the Retan House at Ithaca,
was born Feb. 4, 1846, in Seneca Co., N.
Y. He is a son of Joshua and Rebecca
(White) Covert. The father was bom in 1817
in Seneca Co., N. Y., is one of the descendants
of three brothers who came to America from Holland
in the latter part of the 17 th century. They settled
respectively in Pennsylvania, New Jersey and New
York. From the latter Mr. Covert is descended.
His mother was born in 1 819, in New Jersey ; both
parents ate yet living, in Ovid, Clinton Co., Mich.
Mr. Covert was educated in his native county,
where he resided with his parents until he was 16
years old, when they moved to Munday, Genesee
Co., Mich. There his father bought 160 acres of
land, in an unimproved condition and covered with
oak timber. The place was sold 13 years later and
was justly considered the finest in the township, hav-
ing been the field of the unremitted labors and cares
of the father and his five sons. The family removed
to Ovid Center, where Mr. Covert, senior, engaged
in the drug business one year and then retired.
At the age of 22 years Mr. Covert engaged in the
sale and shipment of cattle, in company with James
Fires. This enterprise was conducted two years with
success, when the same parties opened a meat market
at Ovid. This relation and busine.ss existed seven
years. On its discontinuance, Mr. Covert established
himself singly, and continued to operate until April
25 > 1883. At that date, associated with his father-
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in-law, H. K. Retan, he bought the Fox House at
Ithaca, which they remodeled and converted into the
Retan House. It is the leading hotel at Ithaca, and
has a capacity for 60 guests, and is doing a fine busi-
ness. The popular and gentlemanly proprietors have
secured an excellent reputation for the home and its
management. Mr. Covert is the owner also of a fine
home and three lots at Ovid. He is a member of the
Masonic Order, and also belongs to the Order of A.
O. U. W., an insurance organization. He was a mem-
ber of the Village Council of Ovid two years.
Mr. Covert was married at Ovid, Oct. 14, 1872, to
Harriet, daughter of H. K. Retan. One son — Leroy
J., was bom at Ovid, Sept. 19, 1874.
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Tehu E. Parkinson, farmer, section 9, Pine
River Township, was born Nov. 16, 18 16,
in Greene Co., Pa. He is a son of Jona-
than and Elizabeth (Whitlock) Parkinson, both
natives and life-long residents of the Keystone
State.
Mr. Parkinson is the youngest of the children be-
longing to his fathers household, and he received
such education as was afforded by the common
schools of the section where he was bom and reared.
He was an industrious and ambitious boy, and at 19
years of age he took a farm to work on shares, which
he continued to mahage four years. For some years
subsequent he rented different farms, and also be-
came proprietor of several by alternate purchase and
sale. In June, 1866, he came to Gratiot County,
and bought 80 acres of land in Pine River Township,
all in an entirely original condition. He afterwards
bought 80 acres additional on section 4, and has no
acres under most creditable cultivation. His fertile
fields and premises arranged and kept in fine order,
together with his elegant brick house, which he erect-
ed in 1880 on section 9, all attest his prudence, judg-
ment and good management. Politically, Mr. Par-
kinson is in affiliation with the National Greenback
party.
While a resident of Pennsylvania, he lived in
close proximity to the Virginia border, and being
a Politirer he suffered many indignities and much
persecution, which in nowise tended to diminish his
loyalty to his political faith. On the organization of
the Republican party he adopted its principles, and
furthered its issues with all the zeal of his nature.
On the outbreak of the rebellion, his sympathies were
strongly with the North, and in September, 1861, he
enlisted in the 6th W. Va. Vol. Inf. He remained
in the service over three years. The regiment was
principally occupied in keeping open the communi-
cations between Grafton and Parkersburg, and also
with Wheeling, besides doing special duty in giving
all possible attention to the guerrillas that infested
the mountains of West Virginia, a species of warfare
involving the regiment in many petty engagements,
which were fraught with more danger than impor-
tance. Mr. Parkinson was the first who safely con-
ducted a party of contrabands, 13 in number, from
bondage to freedom, piloting them through the mili-
tary lines at the peril of his life, as the act was an
infringement of military orders, and if detected the
perpetrator was liable to be shot for disobedience.
He received honorable discharge at Grafton. Mr.
Parkinson is a gentleman of well-known philanthropy
and generosity, and enjoys in an unusual degree the
confidence and esteem of his fellow townsmen and
neighbors.
He was married Feb. 27, 1837, in Greene Co., Pa.,
to Sarah Bradford, a native of that county, where she
was born Oct. 8, 18 15. Of this marriage, 12 children
have been born, of whom six are living : Mary J.,
Henr}' J., Minerva, Nancy, Sarah A. and Clarinda.
The deceased were as follows : Robert, Eli, a child
that died in infancy, Rebecca, Elizabeth and Pau-
lina. The family attend the M. E. Church.
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ohn A. Bias, farmer, on the southwest quar-
r ter of the northwest quarter of section 15,
Bethany Township, is a native of the Em-
pire State. He was born in Cattaraugus Co.,
N. Y., March 14, 1849, ^"^ *s a son of Solomon
and Emily Sias. In 1859 his parents came to
Pine River Township, this county, coming up Pine
River from Saginaw in a canoe, with a family of
seven children. His father purchased 20 acres on
section 2, Pine River Township, and resided there
some years. He died at the residence of his daugh-
ter, Ann Woodmansee, Feb. 4, 1884. His first wife
died in New York, and his second wife is yet living.
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He was a manufacturer of saleratus, potash, pearl-
ash, etc.
Mr.. John A. Sias, the subject of this sketch,
bought 40 acres north of St. Louis, in the fall of
1877, resided there about six months, and then came
to his present place, where he owns 40 acres and has
30 acres in cultivation.
He was married in Ithaca, this county, July 5,
1875, to Miss Nancy E., daughter of John G., and
Esther Thompson. She was bom in Ohio, Jan. 8,
1848. Their two children are Bessie, bom May 9,
1876, in Pine River Township; and Katie, born in
Bethany Township, July 10, 1877.
omer Burns, farmer, section 23, Arcada
Township, was born in Rutland Co., Vt.,
Sept. II, 1 81 7, and is a son of Stephen and
Rhoda (Record) Burns. Stephen Burns was a
native of Scotland, and by occupation a farmer.
Coming to this country early in life, he settled in
Vermont, where he died when Homer was but two
years old. Rhoda Record was a native of Vermont,
of New England parentage, and of English and Ger-
man descent. After Mr. Burns' death she married
again, and she died in the State of Wisconsin, about
1873.
When he was six years old Homer s mother and
step-father removed to Chenango Co., N. Y., and five
years later they went to Cheshire Co., N. H. Homer's
step-father, a blacksmith, not treating him kindly, at
the age of 1 1 he set out to care for himself. He was
employed at^ various things until 22 years old, in
Cheshire County, and then went to Oneida Co.,
N. Y., where for nine years he worked in a pail fac-
tory. June 27, 1843, at North Bay, Vienna Town-
ship, that county, he was married to Caroline M.,
daughter of Benjamin B. and Caroline (Hosmer)
Murray, natives of New York and of Scotch descent.
They followed farming, and moved to Hillsdale Co.,
Mich., where Mr. Murray died, July 2, 1873, at the
age of 78, and Mrs. Murray, March 29, 1883, aged
72. Caroline was born in Oneida, Vienna Township,
Oneida Co., N. Y., March 2, 1826, and died in Ar-
cada Township, this county, April 2, 1881, aged 57
years and one month, leaving a family of four chil-
dren. For 16 years previous to her death she had
been an invalid, but she bore her sufferings with true
Christian fortitude, and complained, not even to her
family, of her lot. She was a professing ChrisUan,
and died as she had lived, a kind-hearted mother
and an affectionate wife. To her husband and sons
and daughters, her loss is irreparable, and Gratiot
County has lost one of its noblest pioneer women.
In 1847, Mr. Bums and family settled in Fayette
Township, Hillsdale County, and seven years later
they came to Gratiot County, locating on 180 acres
on section 25, Arcada. Their land was then covered
with the primitive forest, and not a stick had been
cut from it. They built the second log hut in the
township. During the first 18 months after his
arrival the immigrants were so numerous that Mr.
Bums spent 100 days of that time in helping new
comers to build their dwellings. He has , retained
140 acres of his original purchase and has 100 acres
in a high state of cultivation. Though advanced in
years he is active and energetic and one of the en-
terprising citizens of the county.
Mr. and Mrs. Bums have had five children, three
of whom survive: Caroline A., born April 19, 1847;
Benjamin H., March 24, 1854; Charles E., Sept. 2,
1856. Charles A. was born March 23, 1845, and
died when four months old ; Adella R. was bora Oct
26, i860, and died Feb. 9, 1883. Mr. Bums has
held all the various school offices at different times
and is now Assessor. He has been in office ever
since his coming to the county. In political senti-
ment he is a Democrat.
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Ider William 8. Everest, minister and
farmer, section 11, New Haven Township,
was bom in Sweden, Monroe Co., N. Y.,
1^ Oct. 23, 1820. His father, Silas Everest, was
a native of Vermont and a soldier in the war
j of 1 8 1 2, and his grandfather was a soldier in the
Revolutionary war. Mr. E. is of the fourth genera
tion in America from the old French Huguenot fami-
lies of Normandy. His father was a mechanic, and
died in 1858, aged 71; and his mother, Dora, ^^
Surgis, was a native of Connecticut, of Welsh
descent, and died in 1854, in Oakland Co., Mich.
The subject of this sketch was taken with the
family to Orleans Co., N. Y., when two years old.
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where, in a village, he was reared and educated
until 13 years of age, when the family removed upon
a farm ; one year later (1834) they settled in Wayne
Co., Mich., in a comparatively new section of the
country.
July 2, 1843, Mr. E. married Miss Eliza, daughter
of Henry and Maria (Worden) Balwin, natives of
Dutchess Co., N. Y., of New England parentage and
of Holland Dutch descent. Mrs. E. was born in
the towhship of Rose, Wayne Co., N. Y., March 15,
1827, and was brought to Michigan when only nine
years old, the family settling in Wayne County. A
year later they removed to Royal Oak Township^
Oakland County. In this place Mr. E. remained,
taking care of his parents until the death of his
mother, when the remainder of the family moved to
Montcalm County, this State, in 1854. Three years
later his father died, and he resided there until Oc-
tober, 1872, except the years 1864-5, when ^^ ^^s
engaged in the ministry at Ithaca. At the date
above mentioned he sold out his farming interests in
Montcalm County and settled on the quarter-section
where he now resides, and where he has made im-
provements and established a comfortable home.
The cultivated area comprises 90 acres.
Elder Everest began the public Christian ministry,
in the Regular Baptist Church, in 1850, and has un-
interruptedly continued in the ministry since that
time. His wife has been an active member of the
same Church for 34 years. The Elder is a staunch
Republican, has been Township Supervisor, School
Superintendent, Highway Commissioner, etc., and is
a charter member of the blue lodge, F. & A. M., at
Carson City.
The children of Mr. and Mrs. E. are : William
H., Edward E., Anna E,. Worden J. and Ada E.,
besides one deceased, Maria.'
Dlamore B. Moulton, farmer, section 31,
Pine River Township, was born July 8,
1838, in Jackson Co., Mich. His parents,
Warren C. and Caroline (Woodward) Moulton,
were natives of the State of New York, and
after their marriage settled in Jackson County, where
they still reside.
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Mr. Moulton remained a resident of his native
county until he was 22 years old, and in the fall of
1863 came to Gratiot County and bought the fanri
where he now resides, consisting of 40 acres, chiefly
in a state of nature. He has increased his property
by an additional purchase of 20 acres, and has 30
acres under improvement and fine cultivation. Mr.
Moulton is an outspoken adherent of the Republican
party.
He was married in Jackson Co., Mich., Dec. 24,
1862, to Mary J., daughter of B. B. and Ardelia Elli-
son, residents of Pine River Township. Mrs. Moul-
ton was born in Jackson Co., Mich., April 11, 1845.
Of this union, one child has been born, Carra B. She
died Nov. 12, 1880, when nearly 17 years old. The
parents attend the M. E, Church.
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ames Qreeley, farmer, section 20, Bethany
iii^yiSf Township, occupying the west half of the' /S
northwest quarter of the section, is a son
of Philip and Polly (Garland) Greeley, and
was bom Dec. 31, 18 14; was reared on a farm.
His father was a Deputy Sheriff of Penobscot
County, and was thrown from his horse and killed,
leaving a wife and six children, in good circumstan-
ces.
The subject of this sketch was the third in the
family of children. When 18 years of age he left
home and began in the world for himself. He went
to Boston and for three years did odd jobs with a
team. He then went to Maine and bought a farm
of 50 acres in Garland, where he resided until 1853.
He was married in Hampden, Penobscot County,
May 23, 1836, to Miss Sophronia Dow, a daughter of
Amos and Hannah Dow, who was born in Hampden,
Aug. 14, 181 2. Of the seven children born of this
marriage, four are living, viz.: Henry C, bom in
Garland, June 14, 1837, and died June 1, 1863;
Mary, born July 18, 1829, is now the wife of Martin
R. Weeks, a carpenter in St Louis, Mich.; David,
born Nov. 4, 1841, now in the lumber business in
Foxcraft, Maine, and manufacturing spools ; Sophro-
nia G., Oct. 23, 1844, died March 27, 1857; Lucy
W., July 19, 1847, and died April 10, 187 1; Amos
D., Sept. 16, 1849, '^ow at home; and Charles F.,
' Ju^yr7>jS5S> !^ow in the employment of Wright &
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Ketchum, a lumber firm of Saginaw. The first two
were bom in Garland, David in Hampden, and the
last two in Kenduskeag.
Mr. Greeley followed farming in Maine until April,
1876, when he came to Midland City, Mich., remained
nearly a year, then pursued farming two years in that
county, and finally, in 1879, came to his present
place, purchasing 80 acres, where he has 30 acres
cultivated and made a number of improvements
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^(|Wriexander JohDSton, farmer, section ^6y
Pine River Township, was born Sept. 27,
^^^™ 1 83 1, in Scotland, of which country his
parents, Joseph and Jane (Morrison) Johnston,
were also natives. Mr. Johnston was 19 years
of age when he came to America. He went
first to the State of Pennsylvania, and three years
later to Canada. He resided 12 years in the Domin-
ion, and in the spring of 1866 he came to Gratiot
County. He bought 60 acres of land in an unim-
proved condition, on which he built a small frame
house, and at once proceeded to the work of clearing
and improving. He has placed 50 acres in a fine
state of cultivation. Mr. Johnston is independent in
political views.
He was married July 12, 1856, to Maria, daughter
of Samuel and Elizabeth (Black) Thompson, natives
of the North of Ireland, where Mrs. Johnston was
born, Dec. 25, 183.^. Of this union seven children
have been born, five surviving : Mary J., Margaret
E., Sarah E., Annie M. and George A. William and
Joseph are deceased. The parents coincide with the
Presbyterians in religious belief.
^diiey H. Dobson, farmer on section 32,
Township, Hillsdale Co., Mich., Sept. 25, 1847,
and is a son of John and Julia A. (McCurdy)
^ Dobson, natives of New York. They now re-
side on a farm in North Shade Township, this county.
Adney came to that township with his parents when
seven years old and was there reared. Being on a
new farm and in a new country, more hard work
than schooling fell to his share, and he worked with
his father almost constantly until 187 1.
Oct. 17, 1 87 1, he was united in marriage to Susan,
daughter of Manford and Susan (Riggs) Felton, na-
tives of New York and Massachusetts. Mr. Felton
is still living, in Ingham County, at the age of 68.
Mrs. Felton died when Susan was two weeks old.
Mr. and Mrs. Dobson resided for two and a half
years in North Shade Township, and then moved to
their present place of 80 acres on section 32, Arcada
Township, which he had purchased in 1872. When
he moved there in May, 1874, he found a dense for-
est ; but he has now 60 acres nicely improved. He
has done all the work of clearing and fencing him-
self, assisted only by one yoke of cattle. Mr. and
Mrs. Dobson have two children : Ada, born July 21,
1872, and Inez Maud, born Aug. 23, 1881. Politic-
ally he is a staunch Republican.
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.eymour S. Teed, farmer and stock-raiser, '^
section 31, New Haven Township, was born f^
in North Star Township, this county, Sept. Q.
24, 1856. His parents, Joseph B. and Louisa ^
J. (Stone) Teed, were natives of Pennsylvania "^^
and descendants of the early Dutch settlers of
that State. In the fall of 1854 they came and
located a quarter of section 17, North Star Township,
there being but three families before them. In 1868
they moved to New Haven Township, where Mr. T.
died, Nov. 27, 1878, at the age of 60 >^ years. His
widow, now aged 48 years, is living with her son, and
enjoys good health and a high degree of activity.
She has been the mother of seven children, six of
whom are yet living.
The family were pioneers in this county, and Sey-
mour S., the subject of this sketch, among the first
born in North Star Township, was therefore com-
pelled to commence hard work at a comparatively
early age. He was 1 2 years of age when the family
moved to New Haven, and here, in the first school- ^
house erected in the township, he began to receive
his first book knowledge. He was extraordinarily
studious, and, " pursuing knowledge under difficul-
ties" at night, he injured his sight for life. He at-
tended a college at Ionia for a time, and at the age i
of 2 1 began teaching in Ionia, Clinton and Gratiot ^
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Counties. Since the death of his father, in 1878, he
of his mother. There are 55 acres in cultivation,
and Mr. T. proves himself to be a practical and pro-
gressive agriculturist. He has been School Inspector
three years ; is an active and intelligent Republican,
a public-spirited citizen, and in every public capacity
has shown himself to be a man of the strictest
integrity.
Mr. Teed was married June 30, 1878, in North
Shade Township, to Miss Melissa, daughter of John
W. and Catharine (Slepp) Force: the latter are
natives of Pennsylvania and of Dutch descent. Mrs.
T. was bom July 27, 1 861, in Lorain Co., Ohio, and
was 1 1 J^ years old when brought by her parents to
this county. Mr. and Mrs. Teed have one child,
Bertha, born May 21, 1879. They are active mem-
bers of the " Church of God " at Carson City.
rohn B. Adams, merchant at Riverdale, Se-
ville Township, is a son of Bradley and
of Vermont and Massachusetts. The father
was a carpenter and millwright and a man of
energetic character, well adapted to the build-
ing of material interests and with the natural capac-
ity to enjoy and make useful the future which he
merited. But disasters by fire and losses in other
avenues prevented such a consummation. He came
from New York to Michigan and located at Ypsilanti,
Mich. A year later he purchased a tract of land in
Shiawassee County, but after a twelvemonth of labor
he discovered that his title was worthless. The loss
entailed was $4,800, which rendered him compara- tively destitute. After spending a year with his son in Saginaw County, he once morb bought a farm and engaged in its management. His wife died in 1863 in Brant, Saginaw County ; his own demise, at St. Charles, in the same county, followed a year later. Mr. Adams was born Nov. 11, 1836, in Brattleboro, Vt. He was reared under his parents' care until he reached his majority. He was reared as a farmer's son and acquired a liberal degree of tact, which with his natural talents and practical experience has en- abled him to carve out for himself a successful career. His first venture in business life was in lumber inter- i \ /S v. ■■6-'>^" \f%^ ^^^m^yM^^ ests at first, and later in mercantile aflfairs, in which ^^t! he is still engaged. He has operated singly since ' 1883. During the 28 years previous to that date he .7 . was associated in business relations with a man named Freeman. At one period of his life he was engaged in navigation, and acted as engineer, mate, master and owner of a vessel, plying between St. Charles and Bay City. After this he was engaged as a lumberman in Montcalm County one year. In 1876 he came to Gratiot County and located on sec- tions 21, 28 and 29, Seville Township, where he was heavily interested in lumbering. He brought his family to Gratiot County in February, 1878, and after- ward purchased 320 acres of land on section 30, Seville Township, where he at present resides. His wife, formerly Miss Ett Maxfield, was born in December, 1836, and is a daughter of Varius and Persis Maxfield, natives respectively of New Hamp- shire and New York. They are now residents of Genesee Co., Mich., and are aged 76 and 68 years. Mr. Adams is a member of Riverdale Lodge, No. 343, 1. O. O. F., and Pine River Lodge, No. 343, 1. O. G. T. In political sentiment he is an ardent Prohibitionist. His portrait is given on page 354. alter Qraham, farmer on the east half of the northwest quarter of section 20, Beth- any Township, is a son of William K. and Margaret E. Graham*; the father died in the spring of 1883, in Lowell, Kent Co., Mich.: mother is also deceased. The subject of this sketch was bom in the north part of England, June 17, 1843. When he was nine years of age the family emigrated to Canada, and five years afterward to Lowell, Kent Co., Mich., where the parents both died. He came to this county in the fiall of 1864 and purchased 40 acres, being the northwest quarter of the northeast quarter of secdon 20, which he still owns. The following spring, March 30, 1865, Mr. Gra- ham married Mary E. Adams, a native of Ohio. By this marriage there have been ten children, as fol- lows : George W., John W., Ida M., Jay W., Frank I., Fred, Edna M., Henry, Mary D. and Margaret D. (twins). After a residence of eight years on his farm he c J. ^ ■.V . Digitized by Google ,/: >■ f •:iia>;>-r GRATIOT COUNTY. J formed a partnership with George }. Acker and Charles B. Graham in St. Louis, in the manufacturing of sash, doors and blinds, in which relation he con- tinued seven years, with marked success. He was in the furniture business six years, sold out and formed a partnership with his brother, C. B. Graham, in the grocery trade in St. Louis. The latter died one year later and Mr. Graham sold his interest and returned to the farm. He now has 1 30 acres of land, with 45 acres under'good cultivation. Mr. and Mrs. Graham are members of the Presby- terian Church. ;• 1 o larleB L. Fleming, senior member of the firm of Fleming & Church, dealers in fan- cy and staple groceries at St. Louis, was born Feb. 8, 1842, in Concord, Jackson Co., Mich. He is a son of Charles M. and Elvira (Hum- phrey) Fleming. His father in early life followed the business of a blacksmith and afterward engaged in agriculture, and later as a merchant ; he was born Oct. 31, 1809, in Seneca Co., N. Y., and is now liv- ing in retirement at St. Louis, whither he removed about 1864, and where he has since resided. The mother was born Sept. 10, 18 18, at Clyde, N. Y. Mr. Fleming was brought up on a farm and com- pleted his education by a course of study at May- hew s Commercial College at Albion, Mich. He was engaged 16 years as a traveling salesman and passed the last five years of that period in the employ of Johnson & Co., of Detroit, handling specialties in the drug line. In 1878 he came to St. Louis, and in June, 1879, purchased an interest in his father's bus- iness, with whom he continued about a year and a half. At the expiration of that time his present asso- ciate, John M. Church, purchased his fathers inter- est, and this connection has existed ever since, with gratifying success. Mr. Fleming was married Dec. 11, 1866, in Leroy, Ingham Co., Mich., to Abigail, daughter of Joshua and Elthina (Wilkinson) Barnes. She was bom Sept. 29, 1846, at Bakersfield, Vt. Following is the record of the children of Mr. and Mrs. Fleming: LinaA. was born Oct. 30, 1867, in Pine River Township; Lewis A. was also born in that township, Sept. 30, 187 1, and died Jan. 26, 1873. Duane I. was bom June 6, 1875, in Howell, Livingston Co., Mich. Ida May was born in Pine River Township, May 25, 1879. The parents and eldest daughter are members of the Presbyterian Church. vriflfred ^ %m - Oct. >ta Caroline (Barker) ScattergQod. B. Soattergood, resident at Ithaca, 1^ was bom in Plymouth, Wayne Co., Mich., 25, 1853, and is a son of Joshua and His parents moved to St. Johns when he was 12 years old, and, three years later, went to Mankato, Minn., where he resided eight years. He attended school until he was 16 years old and was then placed in a jeweler s shop at Mankato to learn the details of the business. He served three years and con- tinued to follow the business until 1876, when he came to Ithaca and bought out the jewelry stock of A. A. Wood. He transacted business at the stand occupied by his predecessor three years and then transferred his stock to the store with C. E. Fink, where he operated two years. Mr. Scattergood sold his interest to Dixi G. Hall, who removed the same to the Richardson Block, where the management of the business in all its details is in the hands of the former proprietor. Mr. Scattergood was married Oct. 25, 1883, in Hillsdale Co., Mich., to Nellie, daughter of Dr. James W. Niblack. She is a native of Ohio. ^^^^ -H Y ^iram B. Qiddings, groceryman and provis- ion merchant at St. Louis, was born July i, 1 850, at Palmyra, Portage Co., Ohio. He is a son of Jonathan C. and Mary E. Giddings 1 who settled at St Louis in 1866. He was then 16 years old, and he attended school until he was 18, when he entered the employ of his brother Charles W. Giddings (see sketch), as clerk in his furniture store. He operated in that capacity three years, when he engaged as assistant in the grocery of Thom- as McDowell, with whom he remained two years. He then went to Saginaw City and was there appoint- ed Deputy Sheriff under R. W. Andrus. He oflficia- (\- •A I r.\i^ Digitized by Google r- ^' /<v ■7<:tlIl?ADI]r>v ^^."^^ r;-:i^: .N GRATIOT COUNTY. 357 *S ted one year and then entered the employ of his chief in his grocery, where he remained two years. In 1879 he returned to St. Louis, and, after a short pe- riod spent as a clerk, he opened his present business^ in which he established himself in August, 1880. He is a member of the Royal Arcanun. Mr. Giddings was married June 23, 1880, at Sagi- naw City, to Gertrude B., daughter of Orrin J. and Jennie E. (Jeffreys) Showers. She died at St. Louis, July 18, 1883, leaving one child — Orrin C, born June 29, 1881. — H— HQJ^i ^ tofctn I . — ddney Thompson, farmer, section 8, North Star Township, is the son of Jeremiah D. and Elizabeth (Hoag) Thompson, and was born in the county of Schoharie, State of New York, Jan 17, 18 13. His father was a native of Dutchess County apd his mother of Albany County, N. Y., both of English extraction. Our subject is enabled to trace the genealogy of his family on his father's side as far back as the year 16 10, viz. : His father was a son of Silas Thompson who was bom in Dutchess Co., N. Y., and who was a son of Caleb Thompson, born in New Haven, Conn., in 1732, a son of Samuel Thompson, bom in the same State in 1 696, a son of Samuel Thompson, born in Connecticut in 1669, a son of John Thomp- son, bom in England in 1632, and he a son of Anthony Thompson, who was born in the same country in 1610. Mr. Thompson remained with his parents in the Empire State, attending the common schools, assist- ing on the farm and developing into manhood, when he accompanied them to Lenawee County, this State, in which place they arrived and settled in 1834. The family at this time consisted of the father, mother and 14 children, and earnestly and energeti- cally did they, with one united effort, enter on the task of clearing and improving the parental home- steads Their trials and struggles were numerous, yet their souls were animated with that spirit of de- tenninadon which so often, in the lives of Michigan's pioneers, has surmounted the " hill of difficulty " and conquered adversity that they successfully battled against and overcame them. Mr. T. having acquired a fair education in his native State, devoted consider- \ :>/-;= : able of his time to teaching, especially during the winters, and thus was enabled to replenish the family coffer with the proceeds of his mental labor. March 8, 1838, Mr. Thompson was married to Miss Sarah Abbott, who died Jan. 22, r839, leaving one child to the care of the father. Mr. T. was mar- ried a second time, Nov. 11, 1840, to Miss Catharine Baragar; by her he had three children, two of whom — Jerry D. and Mary E. — are living. Mrs. T. died April 24, 1876, leaving her husband a widower for the second time. Oct. 6, 1878, Mr. T. was mar- ried to Mrs. Eleanor Hill, daughter of John English, with whom he is now living and by whom he has had two children, namely : Sidney, Jr., and Walter. Mrs. T. had four children by her first husband, named as follows: Minnie, Marian, Mary and Elsie Hill. Mr. Thompson owns a farm of 40 acres in North Star Township, and was Supervisor of the township for four years. While living in Lenawee County he was Postmaster at Dover about four years. Notary Public six years. School Inspector 21 years, and Township Clerk for 18 years. ohn Bums, manufacturer of and dealer in \ saddlery and horse furnishing goods at St. Louis, was bom Jan. 18, i860, at Toronto, Can., and is the son of Hugh and Betsey (Mc- Cormick) Bums. His father was a Canadian by birth and a marine captain by vocation, which line of business he is still pursuing. The mother was a native of Toronto and died when her son was but two years old. Mr. Burns has been the maker of his own fortunes and career since he was nine years old. In his boy- hood he went to school and labored altemately as he found opportunity, and at the age of 14 years he set about to learn his trade, and four years after he went to Detroit, where he worked in a hamess shop six months. He proceeded thence to Bay City, where he remained three years. After spending six months at Saginaw, he went into business for himself at Port- land, Ionia County, and was engaged in business about two years, with reasonable success. In Febm- ary, 1883, he came to St. Louis and opened a shop for the prosecution of his business, opposite the Wes- sell House. Five months later he removed to the ^ r -: V/ f ^^^?^ -^<^D[|:^{Dai> ju ^••.w ^ Digitized by Google i >7S '1 ^ 358 ^■■:;.,„i^^i.^ <:^DD:->:(iD>.>r ,3>V ^A GRATIOT COUNTY. stand he now occupies, where he has a well-assorted and valuable stock. He employs several assistants and contemplates the enlargement and extension of his manufacturing and retail business. -J- roshua Scattergood, flour, feed and provis- ion dealer at Ithaca, was bom April 7,1814, in Bucks Co., Pa. He is a lineal descend- ant from the early Quaker element of New Jersey, his ancestors on both sides being mem- bers of the Society of Friends, and of English extraction. His father, Thomas Scattergood, was, in his early manhood, extensively engaged in the shad- fishing in the Delaware River; was an officer in the war of 181 2 and stationed at Havre de Grace; (his military accouterments were preserved a long time by his descendants;) he died in 1834, at Lambert ville, N. J., where he was keeping hotel, and was 46 years old. His mother, Elizabeth (English) Scattergood, Burlington Co., N. J., in 1784, and died in the city of Burlington at the age of 66 years. Mr. Scattergood obtained a fair education at the public schools and at 16 engaged as a clerk, in which employment he continued until he was 22 years old. In 1836 he went to Plymouth, Wayne Co., Mich., and there secured a position in the same capacity, where he was occupied three years. In 1839 he en- tered into partnership with Benj. G. Barker for the purpose of prosecuting mercantile interests. The connection was discontinued at the end of three years, Mr. Barker retiring. Mr. Scattergood con- ducted the business singly until 1866, when he dis- posed of his stock and interests by sale and removed to St. John's,. Clinton Co., Mich. He opened there a grocery establishment, which he conducted between two and three years. He made another remove to Mankato, Blue Earth Co., Minn., where, associated with his son Theodore, he engaged in the manufac- ture of fanning-mills and steel-toothed horse-rakes. Five years later, his health became so much impaired ■that he retired from business for the time being. He came to Ithaca in the fall of 1883, and has since been engaged in selling the celebrated patent flour of Minnesota. In November of that year, he erected a building for business purposes, where he is engaged in trade, as stated. Besides his property here he owns real estate at Mankato. He is a charter member of Tonquish Lodge, No. 32, I. O. O. F., of which fra- ternity he has been a long time a member. While in Plymouth he held the offices of Justice of the Peace and Township Clerk, occupying the incumben- cy of each four years. Mr. Scattergood was married at Plymouth, June 4, 1839, to Caroline E., daughter of B. G. and Deborah Barker. The parents moved from the city of New York to Detroit in 1835. Mrs. Scattergood was bom in New York and died in Plymouth, in October, 1854, and left fis^ children— Theodore, Edward B., Will- iam B., Helen C. and Alfred B. Mr. Scattergood was again married Sept. 10, 1857, at Plymouth, to Harriet B. Barker, sister of his former wife. Of this union one child — Bessie— has been born. .lijah H. Trayifl, farmer, section 19, Pine River Township, was born Oct 28, 1835, in Cayuga Co., N. Y. His parents, Lewis and Minerva (Roberts) Travis, were natives of the State of New York. They removed to Oak- land Co., Mich., in i860, and later came to Clinton County, where the mother died. The father died in Montcalm County. Mr. Travis was educated in the common schools and was bred to the pursuit of agriculture. In 1859 he came to Michigan, and after a stay of six months he returned to his native State. The next year, i860, he became a settler in this State, and in February, 1863, he bought the farm on which he has since re- sided, in Pine River Township. It included 80 acres of wild land, of which he retains 40 acres, with 30 under cultivation. Mr. Travis is a Republican in his political views. He was married the first time Jan. 2, 1862, in Oak- land Co., Mich., to Nancy S., daughter of Ralph and Hannah Quick. She died July 22, 1866, and left one child, Bert S. On the 21st of September, 1879, Mr. Travis was again married, at Alma, to Mrs. Hes- ter A. (Hart) Baker, daughter of Philo and Dorothy Hart, and widow of Lewis K. Baker, who was one of the pioneers of Arcada Township, and who died Oct. 19, 1876. Her parents were natives of New York, and her mother died in Chautauqua County in that State. About the year 1868 her father came to Vr r V A V r J o ^^ -^<-^tia:<[ltl^>-^ Digitized by Google r '^ xV v/ ^r ^:[10>:(in>.>r r GRATIOT COUNTY, 359 Michigan, and now resides at Alma. Mrs. Travis was born May 25, 1838, in Chautauqua Co., N. Y., and was 18 years old when she came to Michigan. She is the mother of two children by her first mar- riage : Forest W. and Mary H. Mr. and Mrs. Travis are members of the Presbyterian Chur<?h. Acggc ^i® *^- "I I I -»»$|^)^99V*i»
^rank £. Miirdock, of the firm of Murdock
Bros., dealers in granite and marble ceme-
tery work, building work, cemetery fencing
and stone goods at St. Louis, was born Feb. 24,
1849, in Dexter, Washtenaw Co., Mich. He
began learning his trade in Dexter, and when he
was 15 years old he went to Ypsilanti, where he spent
a year perfecting himself in its details. He has
worked at the same in various places, and came to
St. Louis, Jan. i, 1883. He purchased the interest
of a former partner of his brother, who had estab-
lished the business in which the firm of Murdock
Bros, are engaged. They have supplied the mate-
rials for a number of prominent buildings in Gratiot
County, among which are the opera house at St.
Louis, the dwelling of Mr. Turck, at Alma, and the
union school house at Ithaca. They deal in the
New England granite and marble and all other pop-
ular stones for use or ornament.
Mr. Murdock was married Dec. 27, 1878, in Plym-
outh, Wayne Co., Mich., to Lillie, daughter of Hon.
Bethuel and Annis Noyes. She was bom April 24,
1854, at Plymouth,- and of this marriage, one child —
Agnes — was bom Jan. 31, 1 881, in Norwalk, Ohio.
ev. G^eorge Older, residing on section 20,
North Star Township, was born in New
Pound Co., England, Dec. 15, 1824. He
is a son of Samuel Older (deceased), who was
a native of the same country in which our
subject was born, and who emigrated to the
United States in 1832 and settled in Athens Co.,
Ohio. Here our subject lived, assisting his father on
the farm, which was situated on Minker Run, near
Nelsonville, and attending the common schools of
the county and developing into manhood.
Mr. Older was married in April, 1846, to Alletha,
daughter of Robert Calliss, deceased, and moved to
Wood Co., Ohio. They remained there for several
years, and then removed to this State, arriving here
in 1865 and locating in Sumner Township, this
county.
Rev. Older began his studies for the ministry after
coming to this State, and traveled as a minister of
the United Brethren Church for 13 years, and visited
some 19 or 20 of the counties and organized many
Churches. He is still engaged in the cause of Chris-
tianity, and preaches regulariy every two weeks.
Mrs. Older died Aug. 5, 1858, leaving four chiU
dren— Perry C, Randolph M., Emily A. and Martha
E. — and many friends and relatives to mourn her
loss.
Rev. Older was again married Aug. 23, i860, to
Miss Frances Kimberlin, and to this union one child,
John, was born. Rev. Older owns 40 acres of land
on which he and his family reside.
V.
ohn T. Noble, barber at St. Louis, the
oldest resident of the tonsorial profession
at this point, was bom Oct. 4, 1849, in
France. He is the son of John and Anna (Su-
[)ine) Noble, who were natives of France, bom
respecdvely in 1824 and 1831. They came to
the United States in 1854, and, nine months after
their arrival in the new world, they went to Gallic
polis, Gallia Co., Ohio, where they resided 13 years,
the father following the vocation of a stone-cutter.
In the spring of 1866, they came to Chesaning, Sag-
inaw County, and two years later to Bath, Clinton
Co., Mich., where they still live. His father owns 40
acres of land.
Mr. Noble learned the'trade of his father, but, find-
ing it distasteful, resolved to devote himself to some-
thing more to his liking. He worked in a barber's
shop in Chesaning, and one 'in St. John's, where he
acquired the skill necessary to the manipulation of
the razor and shears. In the fall of 1869, he came
to St. Louis, and opened the business in which he
has been continuously engaged ever since. He has
three chairs, and is assisted by his wife.
Mr. Noble is one of the oldest members of the Fire
Department at St. Louis, being one of the first com-
pany. He organized the first Hose Company in the
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place and was foreman seven years. In 1883, he
was Chief of the Department, which, during the same
year, he represented at the National Convention held
at Cincinnati. While occupying the position of chief
officer, he was presented with, a fine silver trumpet by
the Rubber and Gutta Percha MY g Co. of New
York, valued at \$45. He is the iiventor and pat-
entee of Noble's Durable Reel Hose Cart, which was
patented June 26, 1883, and is considered a first-
class machine.
In the fall of 1876, he went into training as a foot-
runner, and, running his first race the following spring,
traveled as a professional athlete for two years. He
ran at one time 10 1 yards in ten seconds.
Mr. Noble was married Aug. 5, 187 1, at St. Louis,
to Emma A. Gifford. She was born Nov. 26, 1853.
Her parents dame to Gratiot County in its very earli-
est days, she being but five months old when they
became pioneers. They built at first, for purposes
of shelter, a bough house, on the Alma road. Her
father owned a large farm, now known as the Good-
rich place. Mr. and Mrs. Noble have two children —
John E., born May 7, 1871, and Sarah S., bom March
10, 1877.
^dward B. White, farmer, section 5, Pine
River Township, was bom Nov. 24, 1832,
in Lake Co., Ohio. He is the son of Nor-
man and Albina (Gloyd) White, natives of
Massachusetts. Some years after their mar-
riage they went to Lake Co., Ohio, and later in
life to Medina County, in that State. They were the
parents of 1 2 children.
Mr. White is the fifth son, and was about three
years old when his parents went to Medina County.
His father was a famier, and he lived at home until
he was nearly 24 years of age. In May, i860, he
came to Gratiot County, and became the possessor
by purchase of 40 acres of unimproved land, and not
40 acres. He has expended his time and energies
with judicious management, and has a snug farm
with 35 acres in fine improvement and under good
cultivation. Mr. White is a citizen in excellent
standing in his township, and has been Postmaster
of Forest Hill (Pine River Township) two years.
He was married Sept. 11, 1856, in Medina Co.,
Ohio, to Almeda, fourth daughter of Daniel and
Susannah (Whitcomb) Ross. She was bom March
12, 1840, in Medina County, and her parents were
natives respectively of Vermont and Canada. Mr.
and Mrs. White have fiSt, children living : Cora A.,
Myrtie A., Orrin E., Ardie L. and Lettie E. They
are the foster parents of a boy whom they took in
charge when he was two weeks old, and have reared
him as their own child. He is called Ernest White.
Mr. and Mrs. White belong to the Disciples' Church.
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-^ f ohn L. Sinclair, Register of Deeds of Gra-
_ ^ tiot County, residing at Ithaca, was bom
S^^ March 26, 1848, at Invemess, Scotland.
His father, John Sinclair, was a native of the
same place, born Aug. 26, 18 18, and died
near London, Ontario, Dec. 4, 1855, whither he
emigrated and worked at his trade of contractor and ^
builder until his death. The mother, Catherine
(McKay) Sinclair, is a native of Scotland and is still
living, near London, Ont.
Mr. Sinclair was still young when his father died,
and at 12 years pf age was left to face the vrorld
alone. He went at 14 years of age to Ailsa Craig,
Ont., where he engaged as a clerk in the store of A.
G. Mcintosh, general merchant. He remained there
until the fall of 1866, when he came to St Louis, and
engaged a short time in lumbering. His next em-
ploy was with Luther Smith as clerk in his mercan-
tile establishment, and he passed the next two years
in his service and that of J. W. Wesels. He returned
at the expiration of that time to London, Ont., where
he became a clerk for R. McKenzie, grocery and
provision merchant. He came to Ithaca in the fall
of 1873 and entered the employ of John W. Howd,
with whom he remained three years. He next en-
gaged with Nelson & Barber, with whom he remained
until the fall of 1882, when he was placed in nomi-
nation for the office of County Register, on the Dem-
ocratic ticket, and made a successful mn against
George S. Van Buskirk, scoring a considerable num-
a number of years as Village Clerk of Ithaca. Mr.
Sinclair has taken 12 degrees in Masonry, of which
Order he has been a member nearly 15 years. He
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years.
He was married June 10, 1870, at St. Louis, to
Mary J. Finch. She was born in Waterloo, Jackson
^ Co., Mich., in August, 1847, and is the daughter of
r Reuben and Jane Finch. She died in Ithaca in
1877, leaving two children — Anna S. and Ernest L.
I Mr. Sinclair was again married in May, 1880, to Juli-
i ette L., daughter of Lathrop M. Lyon, and was born
j in Clyde, N. Y.
larles B. Wright, farmer, section 19, Pine
River Township, was born Oct. 28, 1846,
in Parma, Jackson Co., Mich. He is the son
of Frederick and Sarepta (Fox) Wright, and
his father was a prominent pioneer of Gratiot
County, with whose progress and comparative rank
among the counties of the Peninsula State his name
is inseparably connected.
Mr. Wright was nearly 13 years of age when his
parents came to Gratiot County, and he has resided
chiefly in Pine River Township from that period of
his boyhood. He has pursued farming all his life
and now owns 80 acres of land, with 65 acres under
first class cultivation. Politically he is identified
with the Democraric party.
Mr. Wright was married Oct. 28, 1866, in Pine
River Township, to Sarah, daughter of Henry and
Susannah (Bigley) Wolf. She was born in Ravenna,
Ohio, Jan. 17, 1845, and her parents were natives of
Pennsylvania. Mr. and Mrs. Wright have lost two
children by death : Charles R. and Jessie M., who
died in infancy. There are now living: Mary E.,
Susannah and James KL*
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Ijgah Beard, formerly clergyman and
farmer, section 5, North Star Township,
was bom in Erie Co., N. Y., Jan 12, 1807.
li SL He is a son of Victory Beard, deceased, a
' » native of Connecticut and a soldier under Gen.
j Wadsworth in the war 181 2, and who moved
bis family to Delaware Co., Ohio, in 18 16. Here our
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father s farm and developed into manhood.
Elder Beard was married Aug. 16, 1829, to Miss
Emeline, daughter of Peter Sunderland, a narive of
Pennsylvania, and was bom in Miami Co., Ohio, in
1 810, and to their union six children, all girls, have
been born, namely: Mary E. (Martin), Louisa
(Vance), Elmira (Vance), Catharine (Herrington),
Christina (Herrington) and Annie E. (Morris).
In early manhood Elder Beard turned his attention
to the gospel, and in addition to his farm labors was
engaged in preaching in the Christian Church until
1855, when he moved with his family to this county.
His labors as a minister have been quite extensive.
He organized the first Christian Church in Green-
bush, Clinton Co., this State; and the first one in
Gratiot County, in Bams' settlement. North Star
Township, and preached throughout this and Ginton
Counties. He has recently sold his farm to his son-
in-law, who has taken possession of it, and has also
retired from the ministry, satisfied with his labors.
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I^ilas Moody, farmer, resident on section 9,
Pine River Township, was born in Chat-
ham, Medina Co., Ohio, May 30, 1839.
His parents, William and Maria (Ross) Moody,
were natives respectively of Massachusetts and
Vermont. The father is a minister of the Dis-
ciples* Church, and has been an active laborer in its
interests for more than 50 years. He was born Aug.
29, i8io,and was married Aug. 29, 1838, in Granger,
Medina Co., Ohio. Ebenezer Moody, his father, was
descended from one of three brothers who emigrated
from England to Newburyport, Mass., about the year
1632. He married Lucy Wood about the year 1776,
and of their family of nine children, two yet survive.
He was a soldier of 181 2.
Mr. Moody was a pupil in the common schools
until he was 17 years of age, after which he spent
four years in teaching and study, and attended a
select school at Chatham summers. He spent seven
winters in teaching school. In 1861, he came to
Gratiot County and bought 80 acres of wild land.
Subsequent purchases have increased the aggregate
of his estate to 400 acres, and of this 200 acres are
under cultivation. He taught two winter terms of
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school in Gratiot County, and spent the winter sea-
sons of the following 20 years in traffic in hay. in
which he has been extensively engaged, as well as in
the purchase and sale of oats, pork and other agri-
cultural products. His stock includes eight horses,
17 head of cattle, 180 Sheep and 10 hogs.
In political connections, Mr. Moody is a Republi-
can of decided type, and has been for many years an
important factor in local affairs. He has been Town-
ship Clerk, School Inspector, Highway and Drain
Commissioner, and has held several other positions
of trust. He is President of the Gratiot County Ag-
ricultural Society, and has been connected with the
County Board eight years.
Mr. Moody was married in Chatham, Medina Co.,
Ohio, April 6, 1861, to Ellen M., second daughter of
Luther and Hannah (Jackson) Clapp. She was born
in Chatham Jan. 8, 1842, and her parents were na-
rives of Hampshire Co., Mass. The household in-
cludes two children, George A. and Ira C. Two
others, Arthur N. and Edith C, have passed to the
land of voiceless mystery.
Mr. and Mrs. Moody are both zealous members of
the Disciples' Church, and during the past 14 years
Mr. Moody has officiated as Superintendent of a
Sunday-school. He is also President of the county
Sunday-school organization.
fohn Lanshaw, farmer, section 17, Pine
River Township, was born Jan. 25, 1830.
He is the son of Hans and Anna Lanshaw,
'^jx? who passed their entire lives in the Father-
iT land. Mr. Lanshaw passed the first 25 years
of his life in his native country in the vocation
of a farmer. He came to the United States in July,
1854, and went at once to New Jersey, where he re-
mained four years, coming thence to Detroit. He
spent three years in that city, and after a subsequent
stay in Oakland County for a short period, he came
in January, 1866, lo Gratiot County, for the purpose
of engaging in farming in accordance with early plans
and purposes. He bought 100 acres of land in Pine
River Township, to which he has added by subse-
quent purchase, and now is proprietor of 1 80 acres,
with no in a state of advanced cultivation.
Mr. Lanshaw took a deep interest in. the events of
the civil war, and finally became a soldier. He en-
listed in March, 1865, in the 2 2d Reg. Midi. Vol.
Inf. Three months after going to the field, 500
members of the regiment were transferred to the 29th
Mich. Vol. Inf. He was among the number, and
served in that command until his discharge at De-
troit on the last day of August, 1865.
In the summer of 1883, he replaced his pioneer
house with a substantial residence, where he now re-
sides in the comfort and content which is sure to
follow persistent and well-directed effort. He be- | {"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": 0.39335182309150696, "perplexity": 12793.100301050814}, "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-2017-22/segments/1495463609613.73/warc/CC-MAIN-20170528101305-20170528121305-00355.warc.gz"} |
http://math.stackexchange.com/questions/80802/is-a-discrete-set-inside-a-compact-space-necessarily-finite | # Is a discrete set inside a compact space necessarily finite?
Is it true that if $A$ is discrete as a subspace of $X$, and $X \;$ is compact, then $A$ is finite?
If this doesn't hold, then does it hold for $X\;$ manifold?
-
It is not true in general. Let $X = \{0\}\cup\{2^{-n}:n\in\mathbb{N}\}$ with the topology inherited from $\mathbb{R}$; then $X$ is compact, and $X\setminus \{0\}$ is an infinite discrete subset of $X$. Of course every closed discrete subset of a compact space is finite, so infinite discrete subsets won’t be closed, but in general they will exist. For instance, the space $X$ just described can be embedded in any infinite compact metric space.
-
Thank you very much! For my purpose the fact that "every closed discrete subset of a compact space is finite" is just what I need – Abramo Nov 10 '11 at 10:37
Take the subspace $\{0\}\cup\{\frac1n; n\in\mathbb N\}$ of the real line. It is compact and contains an infinite discrete subspace $\{\frac1n; n\in\mathbb N\}$.
You can construct a similar example as a subspace of unit circle, so this fails for manifolds too. (It suffices to make a quotient of $[0,1]$ by identifying zero and one, which leaves the above subspace unchanged.)
More generally, for arbitrary discrete space you can construct a compactification
-
Loved the part about compactification!! – André Caldas Nov 10 '11 at 14:37
Abramodj: I just want to point out that closed discrete subset of a compact space is finite is consequence of a more general fact that a discrete space is compact iff it is finite. Now since closed subset of a compact space is compact, so closed discrete subset of compact space are compact and hence finite.
-
Thanks! This is a very important remark – Abramo Nov 10 '11 at 18:00 | {"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": 0.943756639957428, "perplexity": 140.6851046165451}, "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-2015-32/segments/1438042985647.51/warc/CC-MAIN-20150728002305-00158-ip-10-236-191-2.ec2.internal.warc.gz"} |
https://stacks.math.columbia.edu/tag/066N | Lemma 15.65.16. Let $R$ be a ring. Let $f_1, \ldots , f_ r \in R$ be elements which generate the unit ideal. Let $a, b \in \mathbf{Z}$. Let $K^\bullet$ be a complex of $R$-modules. If for each $i$ the complex $K^\bullet \otimes _ R R_{f_ i}$ has tor amplitude in $[a, b]$, then $K^\bullet$ has tor amplitude in $[a, b]$.
Proof. This follows immediately from Lemma 15.65.15 but can also be seen directly as follows. Note that $- \otimes _ R R_{f_ i}$ is an exact functor and that therefore
$H^ i(K^\bullet )_{f_ i} = H^ i(K^\bullet ) \otimes _ R R_{f_ i} = H^ i(K^\bullet \otimes _ R R_{f_ i}).$
and similarly for every $R$-module $M$ we have
$H^ i(K^\bullet \otimes _ R^{\mathbf{L}} M)_{f_ i} = H^ i(K^\bullet \otimes _ R^{\mathbf{L}} M) \otimes _ R R_{f_ i} = H^ i(K^\bullet \otimes _ R R_{f_ i} \otimes _{R_{f_ i}}^{\mathbf{L}} M_{f_ i}).$
Hence the result follows from the fact that an $R$-module $N$ is zero if and only if $N_{f_ i}$ is zero for each $i$, see Algebra, Lemma 10.23.2. $\square$
There are also:
• 2 comment(s) on Section 15.65: Tor dimension
In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar). | {"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": 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": 2, "x-ck12": 0, "texerror": 0, "math_score": 0.9992074370384216, "perplexity": 173.19715474313088}, "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/1634323587608.86/warc/CC-MAIN-20211024235512-20211025025512-00389.warc.gz"} |
http://www.chegg.com/homework-help/questions-and-answers/proton-travels-uniform-magnetic-electric-fields-magnetic-field-negative-x-direction-magnit-q2406631 | ## Motion in Magnetic Field
A proton travels through uniform magnetic and electric fields. The magnetic field is in the negative x direction and has a magnitude of 1.93 mT. At one instant the velocity of the proton is in the positive y direction and has a magnitude of 2150 m/s. At that instant, what is the magnitude of the net force acting on the proton if the electric field is (a) in the positive z direction and has a magnitude of 5.66 V/m, (b) in the negative z direction and has a magnitude of 5.66 V/m, and (c) in the positive x direction and has a magnitude of 5.66 V/m? | {"extraction_info": {"found_math": false, "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": 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": 0.9352247714996338, "perplexity": 169.22031887880567}, "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-2013-20/segments/1368706890813/warc/CC-MAIN-20130516122130-00065-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://www.manhattanprep.co.uk/college/toefl/ | ### Does it really weigh 5 lbs?
The 5 lb. Book of TOEFL Practice Problems is an essential resource for any student taking the TOEFL. Packed with over 1,500 test-like practice problems in organized sets with easy-to-follow explanations, this book will help you build fundamental skills through targeted practice. (And yes, it really does weigh 5 lbs.) | {"extraction_info": {"found_math": false, "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": 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": 0.8534511923789978, "perplexity": 6690.948417651393}, "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-2019-47/segments/1573496670448.67/warc/CC-MAIN-20191120033221-20191120061221-00054.warc.gz"} |
https://www.physicsforums.com/threads/what-is-the-entropy-change-of-aluminum.152777/ | # What is the entropy change of aluminum?
1. Jan 23, 2007
### KrazyX24
1. The problem statement, all variables and given/known data
In an experiment, 240 g of aluminum (with a specific heat of 900 J/kgK) at 100°C is mixed with 40.0 g of water (4186 J/kgK) at 20°C, with the mixture thermally isolated.
a: What is the equilibrium temp in C?
b: What is the entropy change of aluminum?
c: What is the entropy change of the water?
d: What is the entropy change of the aluminum-water system?
2. Relevant equations
Q=mC(Tf - Ti)
MwCw(Tf - 20c) + MaCa(Tf - 100c)= 0
S(entropy)= Q/T
3. The attempt at a solution
Basically I'm kinda stuff trying to solve for the final temp, I get 11.9C but that cannot be right since that means the water-Al system lost heat. :grumpy:
any help is very welcome
2. Jan 23, 2007
### KrazyX24
Nevermind, solved it just now. T(Final) = CaMa + CwMwTi/CwMw + CaMa
Final temp came out to be 65.1*C.
B: S = (MaCa)ln(Tf/Ti) = -21.2 J/K
C: S = (MwCw)ln(Tf/Ti) = 24 J/K
D: 24-21.2= 2.8 J/K | {"extraction_info": {"found_math": false, "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": 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": 0.8088658452033997, "perplexity": 5056.2181265244}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "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-2017-04/segments/1484560280801.0/warc/CC-MAIN-20170116095120-00091-ip-10-171-10-70.ec2.internal.warc.gz"} |
http://scitation.aip.org/content/aip/journal/jcp/133/1/10.1063/1.3455712 | • journal/journal.article
• aip/jcp
• /content/aip/journal/jcp/133/1/10.1063/1.3455712
• jcp.aip.org
1887
No data available.
No metrics data to plot.
The attempt to plot a graph for these metrics has failed.
Phase space structure and dynamics for the Hamiltonian isokinetic thermostat
USD
10.1063/1.3455712
/content/aip/journal/jcp/133/1/10.1063/1.3455712
http://aip.metastore.ingenta.com/content/aip/journal/jcp/133/1/10.1063/1.3455712
## Figures
FIG. 1.
(a) Section through the physical potential , Eq. (19), , , . (b) Section through the exponentiated potential, , .
FIG. 2.
Lifetime distributions for the three DOF Hamiltonian isokinetic thermostat. The lifetime distribution is derived from the distribution of gap times obtained by initiating trajectories on the incoming DS and propagating them until they cross the outgoing DS. (a) H121, . (b) H321, . (c) H521, .
FIG. 3.
Coordinate distributions for three DOF Hamiltonian isokinetic thermostat obtained by averaging over a single trajectory. Numerical distributions for the coordinate (histograms) are compared with the Boltzmann distribution (solid line). (a) H121, . (b) H321, . (c) H521, .
FIG. 4.
Coordinate distributions for three DOF Hamiltonian isokinetic thermostat obtained by averaging over a single trajectory. Numerical distributions for the coordinate (histograms) are compared with the Boltzmann distribution (solid line). (a) H121, . (b) H321, . (c) H521, .
FIG. 5.
Coordinate distributions for three DOF Hamiltonian isokinetic thermostat obtained by averaging over a single trajectory. Numerical distributions for the coordinate (histograms) are compared with the Boltzmann distribution (solid line). (a) H121, . (b) H321, . (c) H521, .
FIG. 6.
Moments of the distribution of the coordinate obtained using the three DOF Hamiltonian isokinetic thermostat (squares) are compared with those for the Boltzmann distribution (circles). Odd moments for the Boltzmann distribution are identically zero. (a) H121, . (b) H321, . (c) H521, .
FIG. 7.
Lifetime distributions for the four DOF Hamiltonian isokinetic thermostat. The lifetime distribution is derived from the distribution of gap times obtained by initiating trajectories on the incoming DS and propagating them until they cross the outgoing DS. (a) J121, . (b) J321, . (c) J521, .
FIG. 8.
Coordinate distributions for four DOF Hamiltonian isokinetic thermostat obtained by averaging over a single trajectory. Numerical distributions for the coordinate (histograms) are compared with the Boltzmann distribution (solid line). (a) J121, . (b) J321, . (c) J521, .
FIG. 9.
Coordinate distributions for four DOF Hamiltonian isokinetic thermostat obtained by averaging over a single trajectory. Numerical distributions for the coordinate (histograms) are compared with the Boltzmann distribution (solid line). (a) J121, . (b) J321, . (c) J521, .
FIG. 10.
Moments of the distribution of the coordinate obtained using the four DOF Hamiltonian isokinetic thermostat (squares) are compared with those for the Boltzmann distribution (circles). Odd moments for the Boltzmann distribution are identically zero. (a) J121, . (b) J321, . (c) J521, .
FIG. 11.
Comparison of the numerically determined for the four DOF harmonic potential with the theoretical expression (A14) over the energy range . The phase space volume was determined by random sampling of a phase space hypercube using points. All are divided by [cf. Eq. (A15)].
FIG. 12.
Number of points per energy bin vs energy (width , ) for the J321 four DOF Hamiltonian. The red curve is a fit to the numerical data using a fifth-order polynomial. The fit to the data yields a value .
## Tables
Table I.
Computed mean gap times, fluxes, reactive phase space volumes, energy surface volumes, and entropy deficits for lifetime distributions for three DOF and four DOF model Hamiltonians. Details of the computations are discussed in Appendix B.
/content/aip/journal/jcp/133/1/10.1063/1.3455712
2010-07-07
2014-04-18
Article
content/aip/journal/jcp
Journal
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This is a required field | {"extraction_info": {"found_math": false, "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": 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": 0.8684430718421936, "perplexity": 4732.0275978821755}, "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-2014-15/segments/1397609533957.14/warc/CC-MAIN-20140416005213-00375-ip-10-147-4-33.ec2.internal.warc.gz"} |
https://stats.stackexchange.com/questions/363532/why-use-parametric-test-at-all-if-non-parametric-tests-are-less-strict | # Why use parametric test at all if non parametric tests are 'less strict'
I have read from several sources, even in my undergrad courses, that parametric tests require the data to have a certain distribution, for instance normal, whilst non-parametric don't.
I have analyzed several real-life data consisting of thousands of rows. After analyzing them, I have found none of them have any normal distributions, therefore ANOVA, t-tests, chi-Square and other parametric tests that require normal distributions are out of the picture.
I have also shared this normal distribution rarity issue here. It seems it is also generally agreed that normal distribution is rare.
My question is if data with a normal distribution are rare in real life, then won't it mean that parametric tests that require normal distributions, such as ANOVA, t-test, and Chi-Square, are pretty much not used often, i.e. useless?
I am not a statistics student, so please don't use too much mathematics or heavy statistical terms.
• As a small detail, chi-square tests to do with frequencies of categories have nothing to do with normal distributions. More importantly, the "for instance" in your first paragraph is really important and needs to be expanded. For example, generalized linear models allowing non-identity links and non-normal families work well for many problems. I'd say most data I work with are positively skewed and sometimes more awkward still, but that does not mean jumping to nonparametric tests. But such models don't usually feature in introductory texts or courses. – Nick Cox Aug 23 '18 at 12:49
It is true that precisely normal populations are rare in the real world.
However, some very useful procedures are 'robust' against mild non-normality. Perhaps the most important of them is the t test, which performs remarkably well with samples of moderate or large size that are not exactly normal.
Also, some tests that were derived for use with normal data have better power than nonparametric alternatives (that is, they are more likely to reject the null hypothesis when it is false), and this advantage persists to an extent when these tests are used with slightly non-normal data.
Nonparametric tests such as sign tests and the rank-based Wilcoxon, Kruskal-Wallis, and Friedman tests lose information when data are reduced to ranks (or to +'s and -'s), and the result can be failure to find a real effect when it is present in experimental data.
You are correct that some ANOVA tests behave badly when data are not normal, but many tests using the chi-squared distribution are for categorical data and normality is not an issue.
Recently, new nonparametric methods of data analysis have been invented and come into common use because computation is cheaper and more convenient now than it was several years ago. Some examples are bootstrapping and permutation tests. Sometimes they require hundreds of thousands or millions of computations compared with dozens for traditional tests. But the extra computation may take only seconds or a few minutes with modern computers.
Admittedly, some statisticians are not familiar with these new methods and fail to take appropriate advantage of them. Also, part of the reluctance to change is that consumers of or clients for statistical analyses may not trust results from procedures they have never heard of. But that is changing over time.
Fortunately, modern software and computers also make it possible to visualize data in ways that were previously tedious to show. As a very simple example (not using very fancy graphics), here are two plots of some data that I know cannot possibly be normal (even though they do manage to pass a couple of tests of normality because of the small sample size.)
These data are also pretty obviously not centered at $0.$ The optimum statistical procedure to confirm that would not be a t test or even a nonparametric Wilcoxon test. But both of these tests reject the null hypothesis that the data are centered at $0$: the t test with a P-value 0.013, the Wilcoxon test with P-value 0.0099. Both P-values are less than 0.05, so both confirm the obvious at the 5% level.
It is hardly a loss to science if I don't get around to using the optimal test. And some of the people reading my findings might be a lot more comfortable having the results of a t test. Maybe the next generation of clients will be more demanding.
• (+1) Helpful overview. But it's a bit of a slur that there are statisticians who don't know about bootstrapping or permutation tests. If there are, then their job titles are indeed inappropriate. – Nick Cox Aug 23 '18 at 12:55
Tests such as t-tests don't actually require the data to be normal. What they require is that the distribution of the sample mean of the data (under the null hypothesis) follows a normal distribution (or very close to it). This will cause the t-statistic to follow a t-distribution, as it should. This happens when the data is normal, but also frequently when the data is not normal, as long as the sample size is moderately large. This is a consequence of the central limit theorem. Try this: make some fake non-normal data. This will represent your population. Repeatedly draw a sample of a large size from this data, and calculate its sample mean. Plot all of these sample means and you will see that they look normal. You can also plot all of the t-statistics and you will see that they look like they follow a t-distribution.
• For the t-statistic to have a t-distribution you need more than normality of the numerator. The behavior of the denominator and the dependence of the numerator and denominator also matter. – Glen_b Aug 23 '18 at 23:09
I think I can summarise the other answers as follows: in many non-normal cases (if the breach of normality is not too big), parametric tests still have good power, while (important!) the actual type I-error rate is close to the nominal $\alpha$-level, so why not use them?
I would like to add that parametric tests offer the huge advantage of providing an estimate of the effect size, while Wilcoxon etc. only offer p-values.
• I'd agree strongly that estimates of effect size are highly desirable, but your statement about Wilcoxon etc. is an exaggeration. It can be thought of as estimating $P(X > Y)$, where $X, Y$ are the outcomes being compared for two groups, That can be an interesting and useful measure. In my view it's a major indictment of most nonparametric statistics texts (and most chapters on nonparametrics within general texts) that give little or no emphasis to what is being estimated. – Nick Cox Aug 23 '18 at 12:41
All computation is based on model building. When you count two apples you imply, that there are either two identical things or a precise definition of what an apple exactly is and on what an apple exactly not is. The truth is: There is no sharp and precise definition of what an apple is, but our usual feeling, whether something is an apple, is "precise" enough.
An ANOVA or a t-test needs the distribution to be perfectly normal in order to produce a perfectly true p-value. However, nobody is in need of a p-value to be exact to the 10th digit. Never!
So the question boils down to the question, when is a distribution "close enough to normal" and fact is, many distributions are "close enough" to make parametric tests worthwile learning and using.
Parametric tests perform very well when you need an easy to understand effect measure like Cohen's d or when you are in need of a power calculation.
That being said, there will probably be a trend away from classical tests to computationally involving tests. However, for the foreseeable future, linear regression will always come with a t-test for each predictor and when you compute Bravais-Pearson correlation, standard computer programs will test that using the t-distribution. Right now, parametric tests are dominant.
• Now that you have mentioned linear regression, yes, it does give out a t-test for each predictor/feature to determine its contribution's significance, and many people actually use linear regression and still look at the t-test results even though the data is far from normal distribution. And your apple analogy makes sense in this case. So, are you saying that we could just use the parametric tests for data that "looks" normal enough (histogram/Q-Q plot)? What about in linear regression? Many people use it and look at the t-test without even bothered to check if it fits the assumptions. – user2552108 Aug 23 '18 at 8:07
• The t-test is a test of means. Even if data are not normally distributed, the mean of data often is. May I ask you to read my answer to a different question on this topic? I think, you may learn something of interest about the "Central Limit Theorem": stats.stackexchange.com/questions/307574/… . Based on that, there is a rule of thumb, that you can use the t-test, if the number of observations is larger then 50, some say larger then 30. – Bernhard Aug 23 '18 at 11:45
• Also: > What about in linear regression? Linear regression is just a model as well. Whatever you find in linear regression is only true as far as things have a linear relationship. You will find linear regression all over medicine, even if nothing in the human body is ever linear. You'll find it in psychology, even if nothing in the psyche is ever linear etcpp. That is why you have to understand the limitations of your models - so that you can use models, where appropriate. As the famous saying goes: All modells are wrong, some models are useful. – Bernhard Aug 23 '18 at 12:51
• 3rd: > Many people use it and look at the t-test without even bothered to check if it fits the assumptions Those people were taught to look at the residuals and check, whether those are somewhat normally distributed. Not looking at the residuals of linear regression is dangerous. Learn, when to be relaxed about normality and linearity assumptions, but do check your residuals after regression! – Bernhard Aug 23 '18 at 12:54 | {"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": 0.6172940731048584, "perplexity": 585.0254026440091}, "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-2020-45/segments/1603107891624.95/warc/CC-MAIN-20201026175019-20201026205019-00519.warc.gz"} |
https://math.stackexchange.com/questions/12250/eulers-formula-for-connected-planar-graphs | Euler's formula for connected planar graphs
Euler's formula for connected planar graphs (i.e. a single connected component) states that $v-e+f=2$. State the generalization of Euler's formula for planar graphs with $k$ connected components (where $k\geq1$).
The correct answer is $v-e+f=1+k$, but I'm not understanding the reasoning behind it. Anyone care to share some insight?
• Write down Euler's formula for each connected component and combine them. – Qiaochu Yuan Nov 28 '10 at 21:15
• Can you elaborate some more please :) – Snowman Nov 28 '10 at 21:27
• What do you have trouble understanding? – Qiaochu Yuan Nov 28 '10 at 21:27
• Well it's the first time I've really come across this formula. I tried doing what you said: $v-e+f=2$, and I wrote that down several times to see if I could do anything with it, but I couldnt. – Snowman Nov 28 '10 at 21:29
• Then you should try to understand Euler's formula better first. (For one thing, there is a slight subtlety in the definition of f that you should be aware of.) Try playing around with examples and/or going through a proof. – Qiaochu Yuan Nov 28 '10 at 21:42
For many approaches to Euler's formula look at:
http://www.ics.uci.edu/~eppstein/junkyard/euler/
The usual proof of Euler's formula works by first triangulating the graphs, then removing triangles one by one until you reach a single triangle; all these respect the Euler characteristic $v-e+f$. The proof is completed by calculating $v-e+f$ for a triangle.
You can do the same here - the first phase is the same, and in the end you will be left with $k$ triangles. Then all you have to do is calculate $v-e+f$ for $k$ unconnected triangles. Since $v=e$ for any collection of triangles, the result is the same as the number of faces, which is $1+k$: one face per triangle, and an extra outer face.
Consider 2 components...
Both are similar components now for first excluding face f4 three faces for each component is considered so for both components V - E + (F-1) = 1 since, V = 10, E = 12 So, for adding both we get 2V - 2E + 2F-2 = 2
Now we will consider face F4 which will be unbounded face for whole graph and will we counted once so,adding 1 on both sides 2V - 2E + 2F-1 = 3 Where, total number of vertices = 2V total number of edges = 2E total number of faces = 2F-1 total number of components = k = 2
so, Vtotal - Etotal + Ftotal = k+1 can be proved. hope this helps ....
Given k many components you can "connect" it by adding k-1 many edges, say e'=e+(k-1). Then v-e'+f=2 just says v-e-k+1+f=2 or that v-e+f=1+k.
Note that this agrees with the regular connected version where k just equals 1. | {"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": 0.4969097971916199, "perplexity": 464.7612567815124}, "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-2019-43/segments/1570987750110.78/warc/CC-MAIN-20191020233245-20191021020745-00514.warc.gz"} |
https://chemistry.stackexchange.com/questions/32423/synthesis-challenge | # Synthesis Challenge
I have been trying to make a monomer reached a dead end in the middle. A B C are the products I have made so far respective order. After reaching C I wanted to prepare 2 but could not find a way to do so. haloform had a high chance of brominating Hydroxyl group at other end I speculate. Acid catalysed Haloform on A did not result in 1 but ended up with B again [with suprisingly 2 % more yield than I got with simple base hydrolysis. Now at this point I have no option but to produce 1 and then go for 2. I need references or suggestion to make 2 from C cause that will greatly reduce my work load. I am running short of time for my summer project.
• Protect terminal OH, reduce ketone, eliminate to styrene, ozonolysis with oxidative work-up?
– Jan
Jun 5, 2015 at 22:17
• @Jan You could probably write this up as an answer
– bon
Jun 6, 2015 at 17:38
• @punarbasu-roy I'm not sure which compounds you need help synthesizing. Correct me if I'm wrong, but you need help with making compound 1 and 2? Jun 7, 2017 at 13:44
The route I would try to prepare 1 would be to purchase 4-Bromo-4'-hydroxybiphenyl which is commercially available (Alfa Aesar sells it - see http://www.alfa.com/en/catalog/A10819)
First Step: 1) Protect phenol moeity with benzyl group via refluxing a solution of 4-Bromo-4'-hydroxybiphenyl (1.0 eq, 1.00 g), milled potassium carbonate (4.0 eq), benzyl bromide (1.1-1.25 eq), and acetone (25-30 mL). Reaction will most likely take 10-20 hours to be complete. Once reaction is complete, cool to ambient temperature and filter reaction mixture. Concentrate the filtrate to dryness.
• If you dont have Benzyl bromide, you can use benzyl chloride (1.1-1.25 eq) and potassium iodide (0.1-0.5 eq).
**Alternatively, instead of filtering the reaction mixture, you could add water (50-75 mL) to the mixture to cause the product to crystallize out (this will only work if the product is a solid at room temperature). If you dont see any solids after adding water, you can try adding an ice-water bath under the mixture to encourage crystallization.
Once isolated the material, allow the protected product (benzyl ether) to be dried in a desiccator or vacuum oven to remove traces of water.
Second Step: 2) Perform a Grignard reaction with protected product (above). The Grignard reaction can be prepared either in THF or diethyl ether using Mg metal/iodine as catalyst, or using isopropylmagnesium chloride solution in THF).
Once the Grignard reaction has been prepared, pour the reaction onto dry ice. This will form the Protected Compound 1 as the magnesium salt. Add water to solubilize the salt, then wash the mixture with diethyl ether (1-2 times to remove impurities) and then add concentrated $\ce{HCl}$ (37%) until pH 1-2 is acheived which will precipitate out the protected Compound 1.
Third Step: 3) Dissolve protected Compound 1 in ethyl acetate, add small amount of Palladium on carbon, and hydrogenate the mixture under hydrogen pressure (balloon pressure will work just fine too) at room temperature overnight.
Once reaction is complete, degas the mixture with nitrogen or argon, filter, and concentrate to provide the desired Compound 1.
• I am not sure how feasable is your reaction scheme. It is just too big. Lately I have found a better way, You can have a look. journal of material chemistry 1991, 1(4), 611-619 Jun 6, 2015 at 13:54
If you have the capability, convert the ketone to an enol ether and ozonolyse / oxidative cleave the alkene portion. You might want to cleave your acetate first, make your ether and then silylate , but you'd be silylating to make the enol ether anyway. | {"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": 0.37492766976356506, "perplexity": 4617.530533893743}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "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/1656104585887.84/warc/CC-MAIN-20220705144321-20220705174321-00612.warc.gz"} |
https://www.physicsforums.com/threads/geometric-formulas-of-linear-perspective.57527/ | # Geometric formulas of linear perspective
1. Dec 22, 2004
### theophoretos
10 years ago i tried (as an artist) to solve the problem of how to translate the 3 dimensional cartesian coordinate onto the 2 dimensional surface with the precise foreshortening. i've only ever figured out 3 formulas for 3 different standpoints... then i gave up. now i recollected my notes, and put them on line.
http://www.geocities.com/easternhistory/perspective.html
the linear perspective developed since the renaissance has never been complete. these 3 formulas are the only completed one i know of. can any math persons figure out the algebraic situation behind this geometric formulation of the translation of 3 d onto the 2 d?
2. Dec 22, 2004 | {"extraction_info": {"found_math": false, "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": 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": 0.979954183101654, "perplexity": 1208.6625988556602}, "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-2016-50/segments/1480698544358.59/warc/CC-MAIN-20161202170904-00031-ip-10-31-129-80.ec2.internal.warc.gz"} |
https://www.top3d.app/tutorials/compliant-mechanisms-synthesis-top3d | Compliant Mechanisms Synthesis – Top3d
In mechanical engineering, compliant mechanisms are flexible mechanisms that transfer an input force or displacement to another point through elastic body deformation. These are usually monolithic (single-piece) or jointless structures with certain advantages over the rigid-body, or jointed, mechanisms. In this tutorial, you will learn how to change the top3d program to solve compliant mechanism synthesis.
A compliant mechanism problem involves loading cases: input loading case and dummy loading case. The code also needs to implement a new objective function and its corresponding sensitivity analysis. To demonstrate this implementation, let us consider a three-dimensional force inverter problem as shown in figure below. With an input load defined in the positive direction, the design goal is to maximize the negative horizontal output displacement. Both the top face and the side force are imposed with symmetric constraints; i.e., nodes can only move within the plane.
The new loading conditions as well as input and output points are defined as follows:
% USER-DEFINED LOAD DOFs
% [Input Dummy]
il = [0 nelx]; jl = [nely nely]; kl = [0 0];
F = sparse(loaddof,[1 2],[1 -1],ndof,2);
Step.2: Define Boundary Conditions
The boundary conditions are defined as below:
% USER-DEFINED SUPPORT FIXED DOFs
% Top face
[iif,kf] = meshgrid(0:nelx,0:nelz);
fixednid = kf*(nelx+1)*(nely+1)+iif*(nely+1)+1;
fixeddof_t = 3*fixednid(:)-1;
% Side face
[iif,jf] = meshgrid(0:nelx,0:nely);
fixednid = iif*(nely+1)+(nely+1-jf);
fixeddof_s = 3*fixednid(:);
% Two pins
iif = [0 0]; jf = [0 1]; kf = [nelz nelz];
fixednid = kf*(nelx+1)*(nely+1)+iif*(nely+1)+(nely+1-jf);
fixeddof_p = [3*fixednid(:); 3*fixednid(:)-1; 3*fixednid(:)-2];
% Fixed DOFs
fixeddof = union(fixeddof_t,fixeddof_s);
fixeddof = union(fixeddof, fixeddof_p);
fixeddof = sort(fixeddof);
% Displacement vector
U = zeros(ndof,2);
freedofs = setdiff(1:ndof,fixeddof);
The external springs with stiffness $0.1$ are added at input and output points after line 71.
K(din,din) = K(din,din) + 0.1;
K(dout,dout) = K(dout,dout) + 0.1;</pre>
Step.4: Changing objective function and sensitivity analysis
The expressions of the objective function and sensitivity are modified in lines 74-76.
U1 = U(:,1); U2 = U(:,2);
ce = reshape(sum((U1(edofMat)*KE).*U2(edofMat),2),[nely,nelx,nelz]);
c = U(dout,1);
dc = penal*(E0-Emin)*xPhys.^(penal-1).*ce;
Step.5: Changing OC subroutine
The convergence criteria for the bi-sectioning algorithm (lines 82-83) is improved by the following lines:
l1 = 0; l2 = 1e9; move = 0.1;
while (l2-l1)/(l1+l2) > 1e-4 && l2 > 1e-40
To improve the convergence stability, the damping factor of OC-method changes from 0.5 to 0.3 and also takes the positive sensitivities into account, then line 85 is changed to:
xnew = max(0,max(x-move,min(1,min(x+move,x.*(max(1e-10,-dc./dv/lmid)).^0.3))));
Step.6: Running the program
The final design shown above is promoted by the line in the Matlab:
top3d(40,20,5,0.30,3.0,1.5) | {"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": 0.5018267035484314, "perplexity": 6131.626188820892}, "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-2022-05/segments/1642320300997.67/warc/CC-MAIN-20220118182855-20220118212855-00451.warc.gz"} |
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Topic: when a linear closed operator presearves measurability
Replies: 5 Last Post: Jul 20, 2004 4:00 PM
Messages: [ Previous | Next ]
Robert E. Beaudoin Posts: 52 Registered: 12/8/04
Re: when a linear closed operator presearves measurability
Posted: Jul 20, 2004 4:00 PM
Robert E. Beaudoin wrote:
> Thomas Mautsch wrote:
>
>>In ne:<cd9teu$an7$1@dizzy.math.ohio-state.edu> schrieb Robert E. Beaudoin:
>>
>>
>>>G. A. Edgar wrote:
>>>) In article <cd92ek$a0e$1@dizzy.math.ohio-state.edu>, cervinia wrote:
>>>)>
>>>)>Problem:
>>>)>
>>>)>Let $X$ be a separable Banach space and $A:D(A)\subset X\rightarrow X$
>>>)>a closed, linear operator.
>>>)>
>>>)>Suppose that $u$ is some (Lebesgue) measurable function from, say,
>>>)>$R$ -the set of reals to $X$, such that $u(t)\in D(A)$ for almost all
>>>)>$t\in R$.
>>>)>
>>>)>Question: which are the (most general) sufficient conditions on $A$ to
>>>)>ensure the measurability of the map $t\rightarrow Au(t)$ ?
>>>)
>>>) We need: inverse image (under Au) of an open set U in X is
>>>) measurable in R. Well, U is open in X, so $X \times U$ is open
>>>) in $X \times X$. The graph G of A is closed in $X \times X$,
>>>) so the intersection $(X \times U) \cap G$ is a Borel set in
>>>) $X \times X$. Its projection onto the first coordinate is
>>>) therefore an analytic set in $X$. ($X$ and $X \times X$ are both
>>>) Polish spaces.) That projection is $A^{-1}(U)$.
>>>)
>>>) So: what we need for $u$ is that the inverse image of an analytic
>>>) set is Lebesgue measurable. Someone who knows more descriptive set
>>>) theory will have to say if this follows from inverse image
>>>) of Borel set is Lebesgue measurable. Is the collection of Lebesgue
>>>) measurable sets closed under operation A?
>>>)
>>>This seems easy enough: Let M_t be Lebesgue measurable for each
>>>(finite sequence) t, and let M be the result of applying operation
>>>A to the M_t's. For each t one can choose a Borel set B_t and
>>>a Borel measure-zero set N_t so that B_t - N_t is a subset of M_t
>>>which in turn is a subset of the union of B_t and N_t. Let S be the
>>>result of applying operation A to the sets B_t - N_t and let N be
>>>the union of the N_t's. As there are only countably many t's, N has
>>>measure zero, and as S is analytic it is Lebesgue measurable. But
>>
>> ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>>
>>
>>>M is sandwiched between S and the union of S with N, so M is
>>>measurable. So I think the answer to your question is yes, and
>>>beyond measurability of u and closedness of A are needed.
>>
>>
>>S is a subset of X, an *arbitrary* seperable Banach space.
>>What does "S is Lebesgue measurable" mean?
>>
>
>
> No, the sets M_t, B_t, and N_t are subsets of the reals, and
> so S is a subset of the reals. What is being proved is that
> the collection of Lebesgue measurable subsets of the reals is
> closed under operation A. From that it follows that the
> preimage of an analytic subset of X via a measurable function
> from the reals to X is a Lebesgue measurable subset of the reals.
> (The analytic subset of X can be obtained by applying operation
> A to a family of closed subsets of X, and so its preimage is
> the result of applying operation A to the preimages of the closed
> sets.)
>
> Hope that helps.
>
> Bob Beaudoin
>
It occurred to me this morning that there is an unfortunate
collision of terminology here that may be a source of confusion.
Namely, the term "operation A" in my replies (and G. A. Edgar's
question) refers not to the closed linear operator A of the
original post but to Suslin's operation A: If M_t is a family
of sets indexed by finite sequences of natural numbers then
operation A applied to this family is the union, over all
infinite sequences s of natural numbers, of the intersection
of M_<>, M_<s_0>, M_<s_0, s_1>, .... (So if each M_t is a
set of reals then so is S.) This is standard terminology in
descriptive set theory, as this operation is commonplace in that
subject. For example, every analytic set in a Polish
space is the result of applying operation A to a family of
closed sets.
even sorrier about any confusion this terminology may have
caused. Hope this clears things up.
Bob Beaudoin
Date Subject Author
7/16/04 cervinia
7/16/04 G. A. Edgar
7/16/04 Robert E. Beaudoin
7/19/04 Thomas Mautsch
7/19/04 Robert E. Beaudoin
7/20/04 Robert E. Beaudoin | {"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": 0.9682255983352661, "perplexity": 1865.307864125206}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "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-2015-22/segments/1432207928715.47/warc/CC-MAIN-20150521113208-00230-ip-10-180-206-219.ec2.internal.warc.gz"} |
http://blog.gmane.org/gmane.editors.winedt/month=20090501 | 1 May 06:00 2009
### Re: replace include with file?
this is just what i needed, thank you very much!! It's just that, i can't seem to find that in the winedt directory!!
On Fri, May 1, 2009 at 12:04 AM, WinEdt Team wrote:
hello everyone!is there a way in winedt i can replace every
\include{file.tex} in my latex project with the respective file's contents?
thanks very much
Yes. The macro %B\Macros\Samles\Expand.edt does that. You can
take a look and possibly change things around (if needed) and
then execute the command:
Exe('%B\Macros\Samles\Expand.edt');
This one will create and open a new file
%P\%N-Expanded%T
rather than overwriting the original main file.
Also, this one will expand \input and \include directives and
it will also expand any included files inside included files.
This can all be changed but it will take some modifications to
the macro. It is best that you build the tree before executing
the macro so that included filenames can be properly qualified
(especially if the files are in different folders).
Best regards,
alex
1 May 18:31 2009
### Re: replace include with file?
```> this is just what i needed, thank you very much!! It's just
> that, i can't seem to find that in the winedt directory!!
The macro was included in WinEdt 5.5 Build 20071003 (or later).
It may not run with older versions of WinEdt...
%B\Macros\Samles\Expand.edt
should (of course) be
%B\Macros\Samples\Expand.edt
If you really don't have this macro I can send it as an
attachment privately but as mentioned above it may not run
properly with older versions of WinEdt.
best regards,
alex
```
1 May 19:11 2009
### Re: replace include with file?
i have a current version of winedt, it should be included..thatt's weird.. if it's not difficult, please send me the file!
thanks again
sotiris
On Fri, May 1, 2009 at 7:31 PM, WinEdt Team wrote:
this is just what i needed, thank you very much!! It's just
that, i can't seem to find that in the winedt directory!!
The macro was included in WinEdt 5.5 Build 20071003 (or later).
It may not run with older versions of WinEdt...
%B\Macros\Samles\Expand.edt
should (of course) be
%B\Macros\Samples\Expand.edt
If you really don't have this macro I can send it as an
attachment privately but as mentioned above it may not run
properly with older versions of WinEdt.
best regards,
alex
1 May 19:20 2009
### Re: replace include with file?
```WinEdt Team a écrit :
>> this is just what i needed, thank you very much!! It's just
>> that, i can't seem to find that in the winedt directory!!
>
> The macro was included in WinEdt 5.5 Build 20071003 (or later).
> It may not run with older versions of WinEdt...
Sorry, but I have WinEdt 5.5 Build 20071003 and there is no file
Expand.edt in %B\Macros\Samples
F. Pétiard
```
1 May 19:55 2009
### Re: replace include with file?
```> >> this is just what i needed, thank you very much!! It's just
> >> that, i can't seem to find that in the winedt directory!!
> >
> > The macro was included in WinEdt 5.5 Build 20071003 (or later).
> > It may not run with older versions of WinEdt...
>
> Sorry, but I have WinEdt 5.5 Build 20071003 and there is no
> file Expand.edt in %B\Macros\Samples
It is possible that the macro was written and published on the
list after WinEdt 5.5 has been released in response to a
similar request/ question. The file is dated November 2007 so
it is newer than the above build.
Anyway, for those interested:
http://www.winedt.com/work/Expand.zip
Have fun (it works recursively
Best regards,
alex
```
1 May 20:07 2009
### Re: replace include with file?
```WinEdt Team a écrit :
>> >> this is just what i needed, thank you very much!! It's just
>> >> that, i can't seem to find that in the winedt directory!!
>> >
>> > The macro was included in WinEdt 5.5 Build 20071003 (or later).
>> > It may not run with older versions of WinEdt...
>>
>> Sorry, but I have WinEdt 5.5 Build 20071003 and there is no
>> file Expand.edt in %B\Macros\Samples
>
> It is possible that the macro was written and published on the
> list after WinEdt 5.5 has been released in response to a
> similar request/ question. The file is dated November 2007 so
> it is newer than the above build.
>
> Anyway, for those interested:
>
> http://www.winedt.com/work/Expand.zip
>
> Have fun (it works recursively
>
> Best regards,
>
> alex
>
>
OK, thank you.
François
```
10 May 13:57 2009
### The Chinese characters will be messy code when I copy from winedt and then paste into other programs.
```Dear Winedters,
Today, I meet a very strange thing: The Chinese characters will be messy code when I copy from winedt and then
paste into other programs.
For instance, I type the 中国 into my winedt's document window, then I copy & paste these two chinese
characters into emeditor/ultraedit/notpad/Microsoft Office word, etc., I'll obtain something like this:
Öйú
Why does this happen? Any hints will be highly appreciated.
PS. My WinEdt's version is: Build: 20071003 (v. 5.5) and I've met this sort of problem for several times till
now.
--
--
Hongsheng Zhao <zhaohscas <at> yahoo.com.cn>
Xinjiang Technical Institute of Physics and Chemistry
GnuPG DSA: 0xD108493
2009-5-10
```
11 May 20:30 2009
### Re: The Chinese characters will be messy code when I copy from winedt and then paste into other programs.
```> Today, I meet a very strange thing: The Chinese characters will
> be messy code when I copy from winedt and then paste into other
> programs.
>
> For instance, I type the ?? into my winedt's document window,
> then I copy & paste these two chinese characters into
> emeditor/ultraedit/notpad/Microsoft Office word, etc., I'll
> obtain something like this:
>
> Öйú
>
> Why does this happen? Any hints will be highly appreciated.
>
> PS. My WinEdt's version is: Build: 20071003 (v. 5.5) and I've
> met this sort of problem for several times till now. --
This happens because WinEdt is not a Unicode editor. However,
you can instruct it to use unicode format for clipboard
exchanges: Options -> Preferences -> Advanced. Help in the
dialog will explain what to do. Try a few code pages (such as
950) and you should get it right...
Best regards,
alex
```
18 May 09:32 2009
### font problem in WinEdt editor
```Hello,
For a year now I've had installed the JErik's Toolkit Installator
(JErik's WinEdt optional settings and appearance > Erik's preferences,
settings and appearance) available from www.winedt.org. I really like
the modified font scheme in the text editor in WinEdt. The font is a
delight to work with on a laptop.
Since a few days, I've installed a new font (Deja-vu) on my machine for
programming tasks. To my surprise, my font in the WinEdt text editor has
changed to some default font. In winedt, Options > Preferences > font
says it's Courier New. I try to change the font or its size, but it
stays to Courier New and to the same size. No matter which font or font
size I choose, the font still remains Courier New at size 12.
The font in the log panel (at the bottom) has however been changed to
the "Deja-vu" font!!!
Can anyone plz explain what has gone wrong here and how to be able to
change the font again?
If anyone out there is using the JErik's Toolkit Installator and is
using the font scheme from this macro, do you happen to know how to get
it back? The toolkit installator tells me that its font scheme is
installed. I don't want to uninstall the Toolkit Installator as then I
would be losing other changes I made in WinEdt also (This is according
to JErik's Toolkit Installator website).
Best Regards,
Y.Calleecharan
```
21 May 17:42 2009
### WinEdt and Sweave
```Hello!
I've been using WinEdt with Latex. I like being able to compile and view the
results within WinEdt.
And I also use R-WinEdt with R. I program in WinEdt and submit my code to R
from there.
My question is about Sweave. I added the Sweave macro to my installation of
WinEdt. The added menu does not appear in the instance of R-WinEdt. When I
attempt to use "Sweave and show", I just get a _err.log and a _run.log file
called up into WinEdt with nothing in them. How do I make this work?
What does work for me is writing my sweave code in WinEdt, calling the file
with the Sweave command in R. And then compiling the resulting .tex file in
WinEdt. I want to do everything from WinEdt (i.e. have WinEdt call R and then
give me the pdf of dvi file in a viewer).
thanks,
James
```
Gmane | {"extraction_info": {"found_math": false, "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": 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": 0.8775065541267395, "perplexity": 8079.8517072418235}, "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-2015-40/segments/1443737940789.96/warc/CC-MAIN-20151001221900-00214-ip-10-137-6-227.ec2.internal.warc.gz"} |
http://dev.goldbook.iupac.org/terms/view/F02565 | ## FWHM (Full Width at Half Maximum)
https://doi.org/10.1351/goldbook.F02565
See:
half-width
,
line width
Sources:
Green Book, 2nd ed., p. 31 [Terms] [Book]
PAC, 1996, 68, 2223. (Glossary of terms used in photochemistry (IUPAC Recommendations 1996)) on page 2244 [Terms] [Paper] | {"extraction_info": {"found_math": false, "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": 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": 0.8566476106643677, "perplexity": 20991.98137953577}, "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-2019-09/segments/1550247479729.27/warc/CC-MAIN-20190216004609-20190216030609-00544.warc.gz"} |
https://www.physicsforums.com/threads/no-2d-momentum-average-for-a-particle-in-a-box.725499/ | # No 2D momentum average for a particle in a box?
1. Nov 28, 2013
### Duave
Hello Everyone, Happy Thanksgiving. I have physics issues. I went around the entire boundless universe in the last two days, and found out the Schrodinger forgot to develop the math for the momentum expectation value for a 2-D particle in a box. It's nowhere to be found. I am a chemistry major, and so I need help from the physics department to engineer the math to complete quantum mechanics. Can anyone help me with my marvelous discovery below? It's series of equations used as an attempt to solve the problem that I posted. Everyone's help would be greatly appreciated. Thank you.
1. The problem statement, all variables and given/known data
Suppose that a particle of mass m is confined to a rectangular region between 0<x<L and 0<y<L/2 by an infinitely high potential energy function.
Calculate the expectation value p$^{2}$, the square of the magnitude of the momentum
2. Relevant equations
3. The attempt at a solution
p^2(x)=∫(2/L) sin(n*pi*x/L)(ih[d/dx](2/L) sin(n*pi*x/L)dx
p^2(y)=∫(4/L) sin(2n*pi*y/L)(ih[d/dx](4/L) sin(2n*pi*y/L)dy
<p^2> =p^2(x) +p^2(y)
<p^2> =1/2 +1
<p^2> =3/2
Last edited: Nov 28, 2013
2. Nov 28, 2013
### bp_psy
The basic idea is good but the results of your integrals are wrong.
On the other hand this problem is usually done without doing the integrals.
Think about the relation between <p^2> and <E> is, considering that the Hamiltonian is H=p^2/2m inside the box. Try doing it for the 1D case then go for the 2D case.
3. Nov 28, 2013
### Duave
@bp_psy,
Thank you for your response. The image that I posted is of the one-dimensional case.
https://scontent-a.xx.fbcdn.net/hphotos-ash3/541843_10151745284505919_675157014_n.jpg
It's all over the internet, and I still had to ask about the 2D case. I don't understand "how to take it to the next level".
1. The problem statement (with respect to your response)
I'm not sure if I can just solve P^2 by simply:
P^2(x)/2m = E
3. The attempt at a solution (with respect to your response)
P^2(x)= 2m*E
E=$\frac{h^2}{8mL^2}$*[n^2(i) +4*n^2(ii)]
hence,
P^2(x)= 2m*$\frac{h^2}{8mL^2}$*[n^2(i) +n^2(ii)]
hence,
P^2(y)= 2m*$\frac{h^2}{8mL^2}$*[n^2(i) +4*n^2(ii)]
P^2= P^2(x) + P^2(y)
P^2= {2m*$\frac{h^2}{8mL^2}$*[n^2(i) +n^2(ii)]} + {2m*$\frac{h^2}{8mL^2}$*[n^2(i) +4*n^2(ii)]}
P^2= 2m*E
{2m*$\frac{h^2}{8mL^2}$*[n^2(i) +n^2(ii)]} + {2m*$\frac{h^2}{8mL^2}$*[n^2(i) +4*n^2(ii)]} = $\frac{h^2}{8mL^2}$*[n^2(i) +4*n^2(ii)]
I'M LOST..........
4. Nov 28, 2013
### bp_psy
You seem to get the basic idea but you should always mark when you are talking about expectations <p(x)>^2 is not the same as p(x)^2 and E is not the same as <E>.
No each direction is associated with some of the energy not the whole energy.So just one of the ns, n_x for p_x and n_y for p_y
In this case <p>^2/2m=(1/2m)(<p(x)>^2+<p(y)>^2)=<E>=<E_x>+<E_y>. Each component of the momentum is associated with some of the energy. The energy associated with each direction is the same as for the the 1D case You are also missing some ∏ factors and you forget to simplify some m factors.
5. Nov 29, 2013
### B-80
This is how to proceed with calculating any expectation value (this has nothing to do with physics by the way, it's elementary probability theory). And you're basically right, except you're trying to calculate the average of p^2, yet you're only applying p once in the integral. Make sure you apply p two times to get the average of p^2.
I'm not sure what you're doing in line 3, but just compute the integral you have there in line 2 with the momentum operator applied twice over the region where the wave function is not zero.
Draft saved Draft deleted
Similar Discussions: No 2D momentum average for a particle in a box? | {"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": 0.9292202591896057, "perplexity": 954.0768346067935}, "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-2017-43/segments/1508187823282.42/warc/CC-MAIN-20171019103222-20171019123222-00811.warc.gz"} |
https://hectorpefo.github.io/2017-04-07-minimize-product/ | Consider the following game. In front of you is a stack of 10 cards printed with the numbers 0 through 9, one per card. The stack is shuffled and, sight unseen, you draw a number from the top. You look at the number and place it somewhere in the multiplication equation below. You then draw another number, look at it, and place it somewhere else in the equation. You do that two more times, until all four slots are filled. Once a digit is placed, it can’t be moved, and it can’t be drawn again because it’s no longer in the stack.
Your goal is to build a multiplication equation with the lowest possible product. What is the optimal strategy? And how much of this game is luck and how much is skill? In other words, how much does the expected product under the optimal strategy differ from simply placing the cards randomly?
## Solution:
First we’ll consider how to proceed with only pencil and paper, and then we’ll bring out the computer to determine how our strategy would play out for all possible sequences of four cards.
Here is the expectation for a randomly chosen $AB \times CD$ (relying on the linearity of expectation):
$E = E(100A\cdot C + 10A \cdot D + 10 B \cdot C + B \cdot D)$ $= 121 E(A\cdot C)$ $= 121 \times \frac{1}{90}\left(\sum_{m=0}^9 \sum_{n=0}^9 mn - \sum_{n=0}^9 n^2\right) = 121 \times \frac{58}{3} = 2339\frac{1}{3}$
Where should we put the first card—on the right or on the left (we’ll assume it goes in the top row, though of course it doesn’t matter)? Here’s a (non-airtight) argument that cards showing $4$ and below should go on the left, and the others on the right.
The expectation for starting with the number $m$, placing it top-left, and then placing the others randomly:
$E(m\mbox{ top-left}) = E(100m \cdot C + 10m \cdot D + 10B \cdot C + B \cdot D)$ $= 110 E(m \cdot C) + 11E(B \cdot C)$ $E(m \cdot C) = \left(\sum_{n=0}^9 \frac{1}{9} mn\right) - \frac{1}{9}m^2 = \frac{45m-m^2}{9}$ $E(B \cdot C) = \frac{1}{72}\left(\left(\sum_{n=0}^9\sum_{k=0}^9 nk\right) - \left(\sum_{n=0}^9 n^2\right) - \left( 2\times \sum_{n=0}^9 mn\right) + 2m^2 \right)$ $= \frac{1740-90m+2m^2}{72}$ $E(m\mbox{ top-left}) = 110 \times \frac{45m-m^2}{9} + 11 \times \frac{1740-90m+2m^2}{72}$ $= \frac{1595}{6} + \frac{2145}{4}m - \frac{143}{12}m^2$
Similarly, the expectation for placing $m$ top-right and then proceeding randomly:
$E = E(100A \cdot C + 10A \cdot D + 10C \cdot m + D \cdot m)$ $= 110\times \frac{1740-90m+2m^2}{72} + 11 \times \frac{45m-m^2}{9}$ $= \frac{7975}{3} - \frac{165}{2}m + \frac{11}{6}m^2$
Comparing these values allows us to see that placing a first number less than or equal to $4$ on the top-left is the best bet, while placing one greater than or equal to $5$ on the right is the best bet. This gives us a good, though admittedly not decisive, reason to think that whatever the optimal strategy is, it involves the same decision for the first move. That is important, because it greatly simplifies the problem.
There are $5040$ possible sequences of four cards, and $24$ possible ways to place the cards in any given sequence, and so it might seem that the space of possibilities you have to consider is unsurveyably vast. However, when you have placed the first card and have received your second, there are three places to choose from, and only $56$ sequences of third and fourth cards to consider. So you compute an expectation for each place, by assuming you’ve placed the second card there, and for each of the eight possible third cards, noting the lower of the expectations of placing it in the two remaining open places (computed by averaging the products produced by placing each of the seven remaining cards in the last open place). Average those lower expectations to get the expectation of placing the second card in that place (and then playing optimally). Choose the place with the least expectation, and you will already have done the figuring needed to place the third card when you receive it.
You’re done!
The code below quickly finds the optimal strategy for every possible four-card sequence. It confirms our educated guess that we should put first-cards showing $4$ and under on the left and $5$ and above on the right, and it yields an overall expectation of about $1056.84$, which is about $45.18\%$ of the expectation of playing randomly.
Here’s a chart detailing the crux of the strategy, which is the placement of the second card (in the chart, “UL” means upper-left, etc.).
As you can see, the strategy resists easy summary—there’s no simple intuition behind it. However, a few observations can make sense of it.
In general we want low numbers to end up on the left and high ones on the right. An interesting exception is a first-card value of $0$, where the upper-right card will have an out-sized effect on the product. So we profit by taking the opportunity to put a second low card there right away. With a second card of $4$, $5$, or $6$, we should hold out for a smaller number in the crucial upper right (of which there’s at least a $9/14$ chance in the final two cards), while not risking having to put an even higher number in the lower left (of which there’d be at least a $9/14$ chance).
And we profit from matching very low numbers with not-so-high numbers, and not-so-low numbers with very high ones. For example, $19\times 35$ is $665$, whereas $15\times 39$ is $585$. This explains why when the first card is $1$ a second-card $9$ goes in the lower right, whereas when the first card is $3$ a second-card $5$ goes in the upper right.
And if you get a $5$ (which goes upper-right) followed by a $6$, you have a $9/14$ chance of getting at least one of $7$, $8$, and $9$ in the remaining two cards; so it pays to take the hit and place the $6$ on the left, treating it as a very high “low card,” and leaving open the lower right for the expected higher card. Similar reasoning explains why it pays to treat $4$ as a not-so-high high second card with a low first card (apart from $0$), and to treat $5$ as a not-so-low low second card given a high first card.
### Code:
# fivethirtyeight.com Riddler https://fivethirtyeight.com/features/can-you-outsmart-our-elementary-school-math-problems/
# A situation is a tuple (A,B,C,D), representing AB*CD, where each element
# is a digit or -1 to represent an unfilled position.
# Strategy is a "dictionary" that contains optimal moves for pairs of
# a situation and a number (the number on the new card):
# E.g., Strategy[((2,-1,-1,9),4)] = 2 means that 4 should go in the third
# (python tuple index 2) spot.
Strategy = {}
# Expectation is a dictionary from situations to the expectation of them
# given optimal strategy.
Expectation = {}
def Process(situation):
# Determine the optimal strategies for playing with this situation
# and any next card, and generate the expectation of playing
# optimally starting from this situation.
global Strategy, Expectation
accum = 0
num_newcards = 0
for newcard in range(10):
if newcard in situation:
continue
least_expected_product = [-1,10000]
for i in range(4):
if situation[i] == -1:
sitlist = list(situation)
sitlist[i] = newcard
newsit = tuple(sitlist)
if not -1 in newsit:
Expectation[newsit] = \
(10*newsit[0]+newsit[1])*(10*newsit[2]+newsit[3])
elif not newsit in Expectation:
Process(newsit)
E = Expectation[newsit]
if E < least_expected_product[1]:
least_expected_product = [i,E]
Strategy[(situation,newcard)] = least_expected_product[0]
accum += least_expected_product[1]
num_newcards += 1
Expectation[situation] = accum/num_newcards
Process((-1,-1,-1,-1))
print("Optimal strategy expects",Expectation[(-1,-1,-1,-1)]) | {"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": 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": 0.8218282461166382, "perplexity": 600.9705796625498}, "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-2023-14/segments/1679296944452.74/warc/CC-MAIN-20230322180852-20230322210852-00790.warc.gz"} |
https://hapax.github.io/mathematics/boring/ | Indescribably boring numbers
March 23, 2021. I turn the old joke about interesting numbers into a proof that most real numbers are indescribably boring. In turn, this implies that there is no explicit well-ordering of the reals. The axiom of choice, however, implies all are relatively interesting.
Introduction
It’s a running joke among mathematicians that there are no boring numbers. Here’s the proof. Let $B$ be the set of boring numbers, and suppose for a contradiction it is non-empty. Define $b = \min B$ as the smallest boring number. Since this is a highly unusual property, $b$ is interesting after all! Joke it may be, but there is a sting in the tail. By thinking about how the joke works, we will be led to some rather deep (and perhaps disturbing) insights into set theory and what it can and cannot tell us about the mathematical world.
Integers and rationals are interesting
The joke implicitly uses the fact that “numbers” refers to “whole numbers”
$\mathbb{N} = \{0, 1, 2, 3, \ldots\}.$
If it didn’t, then the minimum we used to get our contradiction wouldn’t always work! For instance, say we work with the integers
$\mathbb{Z} = \{\ldots, -2, -1, 0, 1, 2, \ldots\}.$
The set of boring integers $B_\mathbb{Z}$ may be unbounded below. Does this cause a problem? Not really. We can just define the smallest boring number as the smallest element minimising the absolute value, i.e.
$b = \min \text{argmin}_{k\in B_\mathbb{Z}} |k|.$
(The $\text{argmin}$ might actually give us two numbers, $\pm b$, so the negative one is the smallest.) Thus, there are no boring integers. What about boring rational numbers? This is somewhat more elaborate, but if $B_\mathbb{Q}$ is the set of boring rationals, we can define the “smallest” boring number as
$b = \min \text{argmin}_{a/b\in B_\mathbb{Q}} (|a| + |b|),$
where $a/b$ is a fraction in lowest terms. Once again, there may be multiple minimisers of $|a| + |b|$, but only a finite number, so we can choose the smallest. We conclude there are no boring rationals. This pattern suggests there are no boring real numbers. We should be able to find some function with a finite number of minima, and then choose the smallest, right? I’m going to argue that no such function can ever be described. Then I’m going to explain why it might exist anyway, depending on which axioms of set theory we use!
Most real numbers are boring
“Boring” and “interesting” are subjective. We’ll use something a tad more well-defined, and replace “interesting” with describable. A number is describable if it has some finite description, using words, mathematical symbols, even a computer program, which uniquely singles out that number. For instance, $\sqrt{2}$ is the positive solution of $x^2 = 2$, $\pi$ is the ratio of a circle’s circumference to its diameter, and $e$ is the limit
$e = \lim_{n\to\infty} \left(1 + \frac{1}{n}\right)^n.$
It turns out that almost every real number is indescribable, or “boring”, in our official translation of that term. The argument is very simple, and proceeds by simply counting the number of finite descriptions. Each such description consists of a finite sequence of symbols (letters, mathematical squiggles, algorithmic instructions), each of which could be elements of some very large alphabet of symbols. For instance, the text
$\sqrt{2} \text{ is the positive solution of x^2 = 2.}$
can be converted into (decimal) unicode as
8730 50 32 105 115 32 116 104 101 32 112 111 115 105 116 105 118 101
32 115 111 108 117 116 105 111 110 32 111 102 32 120 94 50 61 50 46
Imagine some “super unicode” which lets us converts any symbol into a number. The super unicode alphabet may be arbitrarily large, so we will take it to consist of every natural number $\mathbb{N}$. Then a finite description using any symbols can be written as a sequence of the corresponding natural numbers, a trick I will call “unicoding”. To find the number of finite descriptions, we just count the sequences! There is a nice scheme for showing that these are in one-to-one correspondence with the natural numbers themselves, and hence countably infinite. We take a sequence, say
$(6, 2, 0, 5)$
and convert the first bracket and all commas into $1$s, and each number into the corresponding number of $0$s:
$10000001001100000_2.$
In turn, this can be converted to decimal, $66144$. Going in the other direction, any whole number can be written in binary and then converted into sequence:
$14265092 = 110110011010101100000100_2$
becomes $(0,1,0,2,0,1,1,1,0,5,2)$. Thus, we have a simple, explicit correspondence between finite sequences of natural numbers and the natural numbers themselves. This basically completes the proof, for the simple reason that there are infinitely more real numbers than there are natural numbers. This is established by Cantor’s beautiful diagonal argument, which I won’t repeat here. The upshot is that, via unicoding and then the binary correspondence, finite descriptions can only capture an infinitesimally small fragment of the real numbers. Most literally cannot be talked about.
The set $B_\mathbb{R}$ includes almost every real number, though quite definitely not every real number you can think of. But, armed with our previous jokes, it’s tempting to think that we can waltz in and make the same joke about $\mathbb{R}$, simply plucking out the smallest element of $B_\mathbb{R}$. Of course, that won’t quite work, because the set need not be bounded below. So instead, suppose there is some explicit function $f$ such that $b \in B_\mathbb{R}$ is the smallest minimizer of $f$, i.e.
$b = \min \text{argmin}_{x \in B_\mathbb{R}} f(x).$
If I knew $f$ explicitly, we’d have a description of $b$ after all. Contradiction! But the contradiction here does not imply $B_\mathbb{R}$ is non-empty. After all, most of $\mathbb{R}$ is indescribable for simple set-theoretic reasons. Instead, it means that there cannot be any explicit function $f$. More generally, there cannot be any explicit rule which, given a subset of $\mathbb{R}$, gives some unique number. If there was, we could apply it to $B_\mathbb{R}$ and get the same contradiction. (See Appendix A for discussion of the related Berry paradox.)
An existential aside
There’s a loophole here. Our argument doesn’t establish that $f$ doesn’t exist, just that it has no finite description. And although it might seem weird to trust in the existence of something that we can’t really talk about, we do just this with the real numbers! I believe in all the real numbers, even the ones I can never describe. Is this reasonable? It depends who you ask. There is a philosophy of mathematics called intuitionism which tells us that mathematics is a human invention, and therefore enjoins us to only reason about the things we can construct ourselves. No indescribable real numbers if you please!
I’m not sure about this “mathematical creationism”, and think there are more things in the mathematical heavens than are dreamt of in our finite human philosophy. Why should human limitations be mathematical ones? That said, it’s not the case that anything goes. We should have some firm basis for believing in the existence of those things we can’t discuss, and for the real numbers, the firm basis is drawing a continuous line on a piece of paper, or thinking about infinite decimal expansions. These are models of the real numbers, concrete-ish objects which capture the essence of the abstract entity $\mathbb{R}$. They convince us (or at least me) that there is nothing magical stopping someone from drawing certain points on the line, or continuing certain expansions forever.
Similarly, the indescribable things we would like to exist and reason about in set theory might depend on our models of set theory! I won’t get into the specifics, but an important point is there are many different models of set theory, with different properties, and it seeks unlikely that any one model is right. These properties are abstracted into axioms, formal rules about what exists and what you can or can’t do with sets. Because models of set theory are deep, highly technical constructions, most of the time we go the other way round, and play around with axioms instead. Only later do we go away and find models which support certain sorts of behaviour. The point of all this is to make it a bit less counterintuitive when I say that the existence and properties of boring numbers depend on which axioms we decide to use.
All real numbers are relatively interesting
So, let’s return to our problem of boring real numbers. We argued there was no explicit, finitely describable rule for picking an element out of $B_\mathbb{R}$. But we can always make the existence of such a rule — describable or not — an axiom of our theory! There are two ways to go about doing this. Note that in the first example of boring natural numbers, we use the minimum of the set. We had to be a bit more clever with the integers and rationals, but it essentially boiled down to creating a special sort of ordering on the set, so that any subset (including the boring numbers) has a smallest element. We wrote this is in a complicated way as
$b = \min \text{argmin}_{x \in B} f(x)$
for some function $f$, but we could just as well write
$b = \min_{\mathcal{W}} B,$
where $\mathcal{W}$ denote this ordering on the big set. To be clear, for the integers it is
$0, -1, 1, -2, 2, -3, 3, \ldots$
and for the rationals it is
$0, -\frac{1}{1}, \frac{1}{1}, -\frac{2}{1}, -\frac{1}{2}, \frac{1}{2}, \frac{2}{1}, \ldots.$
This is called a well-ordering. Although it may not be describable, we could simply require, as an axiom of set theory, that any set can be well-ordered! More explicitly,
Any set $A$ has a well-ordering $\mathcal{W}_A$ such that any subset of $A$ has a unique minimum element with respect to $\mathcal{W}_A$.
Although it doesn’t spoil our conclusion that most real numbers are boring, such an axiom would allow us to turn the old joke into an argument that all real numbers are relatively interesting, where “relatively interesting” means that there is a finite description where we are allowed to use the well-ordering $\mathcal{W}$. The proof goes as you might expect: let $B^{\mathcal{W}}_\mathbb{R}$ be the set of relatively boring numbers, i.e. numbers with no finite explicit description, even when allowed to use the well-ordering $\mathcal{W}$. Since $\mathcal{W}$ is a well-ordering, we can define
$b = \min_{\mathcal{W}} B^{\mathcal{W}}_\mathbb{R}.$
End of proof! So, although most real numbers are strictly boring, with a well-ordering all of them are relatively interesting.
Choosing an order
Well-ordering is not usually treated as an axiom. Historically, set theorists prefer to use a simpler rule called the axiom of choice, which is logically equivalent, as we will argue informally in a moment, but somehow less suspect. As Jerry Bona joked,
The axiom of choice is obviously true and the well-ordering principle obviously false.
(Actually, Bona’s joke mentions a third equivalent form called Zorn’s lemma, but it would confuse matters too much to explain.) Loosely, the axiom of choice just says we can pick an element from a non-empty set. Pretty reasonable huh? If a set is nonempty, it has an element, so we can pluck one out. In fact, it’s usually stated in terms of a family of sets $A_i$, where the subscript $i$ ranges over some indexing set $I$:
Given a family of nonempty sets $A_i$, $i \in I$, we can collect a representative from each set, labelled $f_i \in A_i$.
The well-ordering principle implies the axiom of choice, since I can just take the union of all the sets $A_i$, well-order it with $\mathcal{W}$, and then define $f_i = \min_{\mathcal{W}} A_i$. That’s my set of representatives! The other way round is conceptually straightforward. To well-order a set $A = A_0$, start by choosing an element $f_0 \in A_0$ by the axiom of choice. Then remove it to define a new set $A_1 = A_0 - \{f_0\}$, and select another element $f_1 \in A_1$. Continue in this way, at each stage simply deleting the element from the previous stage and choosing a new one, using
$A_{n+1} = A_n - \{f_n\} = A_{n-1} - \{f_n, f_{n-1}\} = \cdots = A_0 - \{f_i : i < n\}$
as long as the set is nonempty. The well-ordering is simply the elements in the order we made the choice:
$\mathcal{W}_A = \{f_0, f_1, f_2, \ldots \} = \{f_n \in A_n : A_n \neq \varnothing\}.$
There are two issues with this construction. The first is that it might feel sketchy to use the axiom of choice “as we go” to build the sets, rather than starting with a pre-defined family. But no one said this wasn’t allowed! Second, our method only seems to work for sets as most as large as the natural numbers, since we indexed elements with $n \in \mathbb{N}$. But we can extend it to an arbitrary set using a generalisation of natural numbers called ordinals. We loosely sketch how this is done in Appendix B. Once the dust settles, we find that the axiom of choice is equivalent to well-ordering.
Conclusion
The overarching theme of this post is how much mileage we can get from a bad joke. The answer: quite a lot! We learned not only that there are no boring integers and rational numbers, but via a simple counting argument, that the vast majority of real numbers are indescribably boring. This is equivalent to having no explicit way to well-order the reals. On the other hand, by giving ourselves the ability (via the axiom of choice) to pluck elements at will from non-empty sets, we are able to supply the reals with a well-ordering. So, all reals are relatively interesting, even if we can’t talk about them.
Acknowledgments
As usual, thanks to J.A. for the discussion which led to this post, and also for proposing an elegant mapping analogous to unicoding.
Consider the phrase
The smallest real number with no finite, explicit description.
If “smallest” refers to an explicitly definable well-ordering of the reals, then this would seem to pick out a unique number with a finite, explicit description. Contradiction! We used this to argue no explicit well-ordering exists. But let’s compare this to the Berry paradox, which asks us to consider the phrase
The smallest positive integer not definable in under sixty letters.
This phrase clocks in at under sixty letters, and would seem to define a number. Contradiction! Since “smallest” here makes perfect sense (we are dealing with positive integers), to resolve the Berry paradox, we must assume either (a) there is no set $B$ of numbers not definable in under sixty letters, analogous to the original boring number joke, or (b) Berry’s phrase somehow fails to define a number. The most popular solution seems to be (b), on the grounds that referring to the set makes it some kind of “meta-definition”, rather than a definition per se.
Of course, this seems be committed to a very specific notion of “definition”, but the problem persists if we replace “definable” with “meta-definable”, since the smallest non-meta-definable number is really a meta-meta-definition. Let $B^{(0)}$ be the set of numbers not definable in under sixty letters, $B^{(1)}$ the numbers not meta-definable in under $70$ letters, and in general, $B^{(n)}$ the numbers not meta${}^{(n)}$-definable in under $60+10n$ letters. We call any number in the union of all these sets $\mathcal{B} = \cup_{n\geq0} B^{(n)}$ “lim-definable”. This is closed under the operation of going meta. Now consider the phrase
The smallest positive integer not finitely lim-definable.
Since lim-definability is closed under going meta, as is “finite”, this is now a definition at the same level. Option (b) is no longer available to us, so only option (a) remains, and it follows that, like the joke that began it all, all positive integers are finitely lim-definable. This is of course obviously true.
Our argument against an explicit well-ordering is very closely related to the Berry paradox. The point of considering lim-definability is that we can build the same descriptive hierarchy for the real numbers, take the union, and rule out option (b). This leaves two ways to avoid a contradiction: no lim-definable ordering exists (involving some finite but unbounded number of references to sets in the hierarchy), or like the Berry paradox, every real is lim-definable. But unlike the positive integers, we know from set theory that the second option can’t be true! We still have a countable number of lim-definitions, as we can argue from unicoding. So there must be no lim-definable ordering of the reals, and no explicit well-ordering in particular.
Appendix B: ordinals and the axiom of choice
Ordinals are sets which we use to stand in for numbers. The smallest ordinal is $0$, which is defined as the empty set $\varnothing = \{\}$. Each ordinal $\alpha$ has a unique successor $\alpha + 1$, defined by simply appending a copy of $\alpha$ to itself:
$\alpha + 1 = \{\alpha, \{\alpha\}\},$
To illustrate, we apply the successor operation to $0 = \varnothing$ a few times:
$1 = 1 + 0 = \{0\}, \quad 2 = 1 + 1 = \{0, 1\}, \quad 3 = 2 + 1 = \{0, 1, 2\}.$
Going on in this way gives us all the finite ordinals, but there are also infinite ordinals. The smallest infinite ordinal, conventionally denoted $\omega$, can be identified with the natural numbers:
$\omega = \{0, 1, 2, 3, 4, \ldots\}.$
It is called a limit ordinal since it is not the successor of any finite ordinal. It is bigger than all the finite ones, $n < \omega$. The successor is defined as before,
$\omega + 1 = \{\omega, \{\omega\}\},$
thereby giving a precise meaning to “infinity plus one”! We won’t say more about the structure of these ordinals. The main point is that we can always “count” the elements in a set $A$ using ordinals, no matter how big it is. Let’s now return to the problem of proving the axiom of choice implies that any set $A$ can be well-ordered. The basic idea is to start with $0$, but keep on counting up “past infinity”, defining
$A_{\alpha+1} = A_0 - \{f_\beta : \beta < \alpha\}$
for any ordinal $\alpha$. The resulting set of representatives, labelled by ordinals, is
$\mathcal{W}_A = \{f_\alpha \in A_\alpha: A_\alpha \neq \varnothing\},$
with $f_\alpha < f_\beta$ just in case the ordinals $\alpha < \beta$. This is a well-ordering since the cardinals are themselves well-ordered. Now, we’ve skipped many important technical details, but the main point was that the argument looks pretty similar to the previous one!
Written on March 23, 2021 | {"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": 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": 0.8777060508728027, "perplexity": 309.1546387099114}, "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-2021-21/segments/1620243991514.63/warc/CC-MAIN-20210518191530-20210518221530-00619.warc.gz"} |
http://blog.fkraiem.org/2013/10/06/pseudo-random-sequences-and-finite-fields/ | # Pseudo-random sequences and finite fields
One way to symmetrically encrypt a message is to generate a sequence of bits of the same length as the message, and perform a bitwise exclusive-or between the message and the sequence. Then the recipent performs the same operation, and recovers the original message. (This is one way to construct a stream cipher.)
Clearly, the security level provided by such an encryption scheme depends entirely on the way in which the sequence was generated. If it is truly random, then we obtain a so-called one time-pad, which, as long as it is used only once, guarantees perfect secrecy. At the other extreme, if the sequence consists of only 0-bits, then the encryption process does nothing at all and an adversary can directly read the message.
So why do we not just use one-time pads and call it a day? This is because one-time pads are not practical: they require us to first generate a bunch of truly random data of the same size as the message, and then transmit it between the sender and the recipient. This transmission must be secure, since we don’t want an adversary to obtain the key, but then if we can transmit the key securely, we might as well transmit the message we want to send in the first place, since they have the same size.
So we must find some kind of compromise: we generate a small amount of truly random data (called the seed), and then starting from the seed we generate a pseudo-random sequence. A pseudo-random sequence is deterministic, but in such a way that it is still difficult for an attacker to predict its behavior. A common construction is to iterate a function $f : E \to E$, where $E$ is some finite set with $n$ elements. Then we choose an element $x_0 \in E$ truly randomly, and the sequence is $x_0$, $x_1 = f(x_0)$, $x_2 = f(x_1)$, etc. Of course since our set is finite, after a while we will obtain a value $x_j = x_i$ for some $i < j$, and the sequence will repeat the cycle $x_i, x_{i+1}, \dots, x_{j-1}$. Thus our sequence will be periodic, and surely it is desirable to have as long a period as possible (ideally, equal to $n$). How should we choose our function $f$ to achieve this? One is tempted to make up a function which does seemingly random things. Von Neumann proposed using $E = \{0,\dots,10^m\}$ for some $m$ and $f$ defined as follows: to compute $f(x)$, first square $x$, and then take the $m$ middle digits of $x^2$ as the result. Unfortunately, as Von Neumann realized when he tried to implement it, this doesn't really work too well. If we implement it in Sage like this:
def f(x, m):
x2 = str(x^2)
while len(x2) < 2*m:
x2 = "0" + x2
start = (m/2)+1
res = x2[start:start+m]
return int(res)
def vonneumann(x0, m, n):
x = x0
for i in range(n):
print(x)
x = f(x, m)
we see that if the value of $x_0$ is chosen at random, the generator will very often have a short period. Somewhat paradoxically, a pseudo-random generator chosen at random will be bad. In order to ensure good pseudo-randomness, we must design our generator carefully. Enter the theory of finite fields.
## Construction
We construct a bit sequence $(a_i)$ (i.e., a sequence with values in the finite field $\mathbf{F}_2$) as follows: the first $m$ bits $a_0, \dots, a_{m-1}$ are chosen truly randomly, not all zero, and after that each bit is computed from the $m$ preceeding bits with a relation of the form
$a_i = h_{m-1}a_{i-1} + h_{m-2}a_{i-2} + \dots + h_0a_{i-m},$
where the $h_i$ are coefficients in $\mathbf{F}_2$. Another way to look at this construction, in the framework of the previous paragraph, is to take $E = \mathbf{F}_2^m \setminus \{0\}$ and to consider the function $f:E \to E$ which gives
$f(a_{i-m}, \dots, a_{i-1}) = (a_{i-m+1},\dots,a_{i}).$
So the function computes the next bit, appends it to the input, and discards the oldest bit. In terms of linear algebra, we have
$\begin{pmatrix} a_{k} \\ a_{k+1} \\ \vdots \\ a_{k+m-1} \end{pmatrix} = U \begin{pmatrix} a_{k-1} \\ a_{k} \\ \vdots \\ a_{k+m-2} \end{pmatrix} = U^k \begin{pmatrix} a_0 \\ a_1 \\ \vdots \\ a_{m-1} \end{pmatrix},$
where $U$ is the $m\times m$ matrix
$U = \begin{pmatrix} 0 & 1 & 0 & \cdots & 0 \\ 0 & 0 & 1 & \cdots & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & 0 & \cdots & 1 \\ h_0 & h_1 & h_2 & \cdots & h_{m-1} \end{pmatrix}.$
Now, our set $E = \mathbf{F}_2^m\setminus \{0\}$ has cardinality $2^m-1$, and we know that this is the maximal possible period for our sequence, so our goal is to determine the coefficients $h_i$ of the recurrence relation so as to obtain a sequence of period $2^m-1$. We note that they do not depend on the initial values $(a_0, \dots, a_{m-1})$. Indeed, if our sequence has period $2^m-1$, every possible non-zero $m$-uple will occur, and so we can choose any one of them as our starting point without changing the overall behavior of the sequence.
## Obtaining a sequence of maximal period
Taking $\mathbf{a} = (a_0, \dots, a_{m-1})$ as our starting values, the period of the sequence is the smallest positive integer $k$ such that $U^k\mathbf{a} = \mathbf{a}$. In other words, such that $\mathbf{a}$ is an eigenvector of $U^k$ associated to the eigenvalue $1$. We start by searching for the values of $k$ for which $U^k$ has $1$ as an eigenvalue. It is easily seen that the characteristic polynomial of $U$ (often called the feedback polynomial of the sequence) is
$h(x) = x^m + h_{m-1}x^{m-1} + \dots + h_0.$
Since it depends only on the coefficients $h_i$ in the recurrence relation of our sequence, we can choose the $h_i$ so that $h(x)$ is irreducible (over $\mathbf{F}_2$). (The theory of finite fields tells us that over a finite field, there always exist irreducible polynomials of any degree.) Thus we will assume that $h(x)$ is irreducible.
Now, $h(x)$ determines in the usual way a field extension $K = \mathbf{F}_2(\alpha)$ of degree $m$, where $\alpha$ is a root of $h(x)$. We know also that $h(x)$ splits completely in $K$, and that its roots are given by $\alpha^{2^i}$, for $i = 0,\dots,m-1$ (obtained by repeated application of the Frobenius automorphism $x \mapsto x^2$ on $\alpha$). Being the roots of the characteristic polynomial of $U$ in $K$, they are its eigenvalues, and so finally the eigenvalues of $U^k$ are of the form $\alpha^{2^ik}$, for $i = 0,\dots,m-1$. We claim that if one of them is $1$, then all of them are, which implies that $U^k = I$. Indeed,
$(\alpha^{2^ik})^{2^{m-i}} = \alpha^{2^ik2^{m-i}} = \alpha^{2^mk} = \alpha^k,$
since $\alpha^{2^m} = \alpha$, and so if $\alpha^{2^ik} = 1$, then $\alpha^k = 1$ and all the eigenvalues are $1$. It is clear that in this case, all vectors are eigenvectors associated with $1$, so we obtain finally that the period of the sequence is the smallest positive integer $k$ such that $U^k = I$. In other words, the order of $U$ in the group $\mathrm{GL}_m(\mathbf{F}_2)$.
The last thing we want to show is that the order of $U$ in the group $\mathrm{GL}_m(\mathbf{F}_2)$ is equal to the order of $\alpha$ in the group $K^\times$. (We remark that this is independent of our choice of $\alpha$ as a root of $h(x)$: since $h(x)$ is irreducible, all its roots are images of each other under conjugation automorphisms, and thus have the same order.)
Recall that $U$ diagonalises (in $K$) to
$\begin{pmatrix} \alpha & 0 & 0 & \cdots & 0 \\ 0 & \alpha^2 & 0 & \cdots & 0 \\ 0 & 0 & \alpha^4 & \cdots & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & 0 & \cdots & \alpha^{2^{m-1}} \end{pmatrix},$
and so $U^k$ diagonalises to
$\begin{pmatrix} \alpha^k & 0 & 0 & \cdots & 0 \\ 0 & \alpha^{2k} & 0 & \cdots & 0 \\ 0 & 0 & \alpha^{4k} & \cdots & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & 0 & \cdots & \alpha^{2^{m-1}k} \end{pmatrix},$
and it is clear that if $k$ is the order of $\alpha$ in $K^\times$ (or in general if $\alpha^k = 1$), then $U^k$ diagonalises to the unit matrix, meaning we have $U^k = I$. Conversely, if $U^k$ is the unit matrix, then all its eigenvalues are $1$ and in particular we have $\alpha^k = 1$. Thus $U^k = I$ if and only if $\alpha^k = 1$, meaning the order $U$ in $\mathrm{GL}_m(\mathbf{F}_2)$ is equal to the order of $\alpha$ in $K^\times$. Since the multiplicative group of a finite field is cyclic, it is always possible to find an element $\alpha$ of order $2^m-1$ (actually, there are $\varphi(2^m-1)$ of them), and letting $h(x)$ be its minimal polynomial we obtain what we want: a sequence of maximal period. Such a polynomial, whose roots are generators of the multiplicative group of the field extension it induces, is called a primitive polynomial in finite field theory. (This is different from primitive polynomials in ring theory.) Thus, if the feedback poynomial is irreducible and primitive, the sequence will be of maximal length.
## But…
This is not the end of the story, however. First, we have the natural question of whether the converse of the previous statement holds. The answer is yes, although we need to develop some more theory and use different mathematical machinery (namely, representations of our sequence as a formal power series) in order to prove it.
Next we have the question of cryptographic strength: our sequence has maximal period all right, but how random does it really look? From a statistical point of view, it is excellent. For example, one can prove that our sequence contains an equal number of zeroes and ones, and in general that all $k$-uples, for some $k \le m$, have the same number of occurences. From a non-predictability point of view, however, it is horrendous. If an attacker knows as little as $2m$ consecutive bits of the sequence, then he can recover the coefficients $h_i$ of the recurrence relation, and thus reconstruct the whole sequence, just by solving a system of linear equations.
So, a challenge is to find ways to make the sequence less predictable, without hurting its good statistical properties… | {"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": 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": 0.9395588040351868, "perplexity": 120.18701675533708}, "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-2017-13/segments/1490218188891.62/warc/CC-MAIN-20170322212948-00586-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://planetmath.org/infinitedimensionalhamiltoniansystem1 | # infinite dimensional hamiltonian system
infinite dimensional hamiltonian system
An infinite dimensional Hamiltonian system takes the form
$(IHS)\;\;\left\{\begin{array}[]{rll}\partial_{t}u-\Delta_{x}u&=H_{v}(t,x,u,v)&% \\ -\partial_{t}v-\Delta_{x}v&=H_{u}(t,x,u,v)&\forall(t,x)\in\mathbb{R}\times% \Omega\end{array}\right.$
where $\Omega\subset{\mathbb{R}}^{N}$ is a smoothly bounded domain, $H\in\mathcal{C}^{1}(\mathbb{R}\times\overline{\Omega}\times\mathbb{R}^{2},% \mathbb{R})$.
Title infinite dimensional hamiltonian system InfiniteDimensionalHamiltonianSystem1 2013-03-11 19:28:50 2013-03-11 19:28:50 linor (11198) (0) 1 linor (0) Definition | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 3, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "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": 0.998083233833313, "perplexity": 7336.707554467551}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "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/1568514571506.61/warc/CC-MAIN-20190915134729-20190915160729-00172.warc.gz"} |
https://docs.vespa.ai/en/reads-and-writes.html | This guide covers the aspects of accessing documents in Vespa. Documents are stored in content clusters. Writes (PUT, UPDATE, DELETE) and reads (GET) pass through a container cluster. Find a more detailed flow at the end of this article.
Vespa's indexing structures are built for high-rate, memory-only operations for field updates. Refer to the feed sizing guide for write performance, in particular partial updates for in-memory-only writes.
Vespa supports parent/child for de-normalized data. This can be used to simplify the code to update application data, as one write will update all children documents.
Applications can add custom feed document processors and multiple container clusters - see indexing for details.
Vespa is eventually consistent - find details on dynamic behavior in elastic Vespa. Also see the Vespa consistency model. It is recommended to use the same client instance for updating a given document - both for data consistency but also performance (see concurrent mutations). Read more on write operation ordering. For performance, group field updates to the same document into one update operation.
Applications can auto-expire documents. This feature also blocks PUTs to documents that are already expired - see indexing and document selection. This is a common problem when feeding test data with timestamps, and the writes a silently dropped.
Also see troubleshooting.
Get
Get a document by ID.
Put
Write a document by ID - a document is overwritten if a document with the same document ID exists.
Remove
Remove a document by ID. If the document to be removed is not found, it is not considered a failure. Read more about data-retention. Also see batch deletes.
Update
Also referred to as partial updates, as it updates some/all fields of a document by ID. If the document to update is not found, it is not considered a failure.
Update supports create if nonexistent.
Updates can have conditions for test-and-set use cases.
All data structures (attribute, index and summary) are updatable. Note that only assign and remove are idempotent - message re-sending can apply updates more than once. Use conditional writes for stronger consistency.
All field types assign (may also be used to clear fields) Numeric field types increment. Also see auto-generate weightedset keys decrement multiply divide Composite types add For array and weighted set. To put into a map, see the assign section remove match Pick element from collection, then apply given operation to matched element accessing elements within a composite field using fieldpaths Tensor types modify Modify individual cells in a tensor - can replace, add or multiply cell values add Add cells to mapped or mixed tensors remove Remove cells from mapped or mixed tensors
## API and utilities
Documents are created using JSON or in Java:
/document/v1/ API for get, put, remove, update, visit. vespa-feed-client Java library and command line client for feeding document operations using /document/v1/ over HTTP/2 Asynchronous, high-performance Java implementation, with retries and dynamic throttling Simpler alternative to the Vespa HTTP client (below) Supports a JSON array of feed operations, as well as JSONL: one operation JSON per line Vespa HTTP client Note: This will be replaced by the vespa-feed-client. Jar writing to Vespa either by method calls in Java or from the command line. It provides a simple API with high performance using multiplexing and multiple parallel async connections. It is recommended in all cases when feeding from a node outside the Vespa cluster. Java Document API Provides direct read-and write access to Vespa documents using Vespa's internal communication layer. Use this when accessing documents from Java components in Vespa such as searchers and document processors. vespa-feeder Utility to feed data with high performance. vespa-get gets single documents, vespa-visit gets multiple.
## Components
Use the vespa-feed-client or /document/v1/ API directly to read and write documents. (Note that the vespa-http-client will be discontinued, use the vespa-feed-client as a drop-in replacement). Alternatively, use vespa-feeder to feed files or the Java Document API.
Next is indexing and/or document processing where documents are prepared for indexing (and optionally processed using custom code), before being sent to the content node. The distributor maps the document to bucket, and sends it to proton nodes:
Document processing The document processing chain is a chain of processors that manipulate documents before they are stored. Document processors can be user defined. When using indexed search, the final step in the chain prepares documents for indexing. The Document API forwards requests to distributors. It calculates the correct content node using the distribution algorithm and the cluster state. With no known cluster state, the client library will send requests to a random node, which replies with the updated cluster state if the node was incorrect. Cluster states are versioned, such that clients hitting outdated distributors do not override updated states with old states. The distributor keeps track of which content nodes that stores replicas of each bucket (maximum one replica each), based on redundancy and information from the cluster controller. A bucket maps to one distributor only. A distributor keeps a bucket database with bucket metadata. The metadata holds which content nodes store replicas of the buckets, the checksum of the bucket content and the number of documents and meta entries within the bucket. Each document is algorithmically mapped to a bucket and forwarded to the correct content nodes. The distributors detect whether there are enough bucket replicas on the content nodes and add/remove as needed. Write operations wait for replies from every replica and fail if less than redundancy are persisted within timeout. The cluster controller manages the state of the distributor and content nodes. This cluster state is used by the document processing chains to know which distributor to send documents to, as well as by the distributor to know which content nodes should have which bucket. Proton node has a bucket management system, which sends requests to a set of document databases, which each consists of three sub-databases. In short, this node activates and deactivates buckets for queries. | {"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": 0.18401925265789032, "perplexity": 5181.670855021447}, "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-2021-43/segments/1634323587908.20/warc/CC-MAIN-20211026134839-20211026164839-00340.warc.gz"} |
http://crypto.stackexchange.com/tags/protocol-design/hot?filter=year | # Tag Info
13
$Encrypt(m|H(m))$ is not an operating mode providing authentication; forgeries are possible in some very real scenarios. Depending on the encryption used, that can be assuming only known plaintext. Here is a simple example with $Encrypt$ a stream cipher, including any block cipher in CTR or OFB mode. Mallory wants to sign some message $m$ of his choice. ...
11
I'll comment only the statement referring to an AES-256 replacement with 4096-bit key: According to our engineers, this will take 23840 times longer to crack than aes256 Bob writing that is not able to correctly transcribe even the numbers that engineer Alice allegedly spelled: most likely, $23840$ is intended to be $2^{3840}$, which is the ratio ...
9
What happens if the sender is at another point in the sequence? ... the key is pressed while out of range to the car. In a rolling code (code hopping) system, the keyfob transmitter maintains a synchronization counter C, incremented every time a button is pushed. The car receiver stores the most recent validated synchronization counter it has received ...
7
ElGamal appears to be used instead of Diffie-Hellman (or IES) in OpenPGP mostly because when that format was put together, there were some unresolved intellectual property issues surrounding both RSA and Diffie-Hellman, while ElGamal was unproblematic. This trend for ElGamal seems to stick around, mostly by force of habit, e.g. when switching to ...
7
As @D.W. guessed, the branching program for a circuit essentially reveals the original circuit. It's not clear what you mean by "apply the whole obfuscation process to the circuit-revealing branching program," but the prospects for that do not seem good: evaluating the branching program is highly sequential (polynomial depth), and you would need to ...
6
We simply have to trust this party because this scheme requires a trusted dealer (a party that distributes the shares to the secret to the participants - this can be you or some other party - but if its you you should trust yourself). We can use verifiable secret sharing, that allows the parties to check whether the shares they have obtained are consistent, ...
6
Some brief thoughts: Shared secret Generation: $$s=E_a(B)=E_b(A)$$ The shared secret is generated by encrypting the other users public key with your private key. This is effectively an ECDH step, which is very reasonable, and one of the key aims of C25519$^{[1]}$. Key Generation: $$s_0=\mathrm{SHA256}(s); s_i=\mathrm{SHA256}(s_{i-1})$$ First, using the ...
5
This is a classical example. Here is the proof system… Bob gives two gloves to Alice so that she is holding one in each hand. Bob can see the gloves at this point, but Bob doesn't tell Alice which is which. Alice then puts both hands behind her back. Next, she either switches the gloves between her hands, or leaves them be, with probability $1/2$ each. ...
5
QKD aims at exchanging key material to be used with encryption based on OTPs between two parties and thus to achieve perfect secrecy for transmitted messages. There are, however, several drawbacks for practical use in a wired setting of QKD (required hardware and their vulnerability to hacks, limited distance which does not support end-to-end ...
5
When they write “well-typed”, they’re simply stating that the process $P$ is well-typed in context, or type environment. (Where the type environment contains a set of type assumptions occurring in $P$.) Keeping it simple: you can think of the term as a kind of classification. The term origins in Type Theory and is (more-or-less frequently) used in relation ...
5
For the moment assume $g$ is a secret (uniformly random) generator, but that $p$ may be known to the adversary. Then given only $g^a, g^b$, the Diffie-Hellman key $g^{ab}$ is information-theoretically uniform (up to small statistical error), i.e., it cannot even be found by brute force because the adversary does not have enough information to determine it. ...
5
You should encrypt the data using a well-vetted standard, like TLS (for data in motion) or GPG (for data at rest). Designing your own is more likely to lead to sadness. The format of the data that you protect in this way is up to you and can be broken down into structs and chunks and headers etc. to your heart's delight.
5
This is pretty much the schoolbook implementation of a shared random number generation (generate, commit, publish). So yeah, it's secure. But this only works for large random numbers, here's a small adaption that allows for arbitrary size integers: If you need an $n$-bit random number everyone should generate $n$-bit random numbers - this is independent of ...
5
Given: The attacker can call PRP() and the inverse function prp() on any message of his choosing. PRP is a pseudorandom permutation indistinguishable to the attacker from a random permutation. Assuming R and K are "sufficiently large", perfectly random, and never leaked to the attacker -- in particular, during a chosen-ciphertext attack, the decryptor only ...
5
RFC 6176 lists four reasons why SSL 2.0 must not be used, in its section 2: Message authentication uses MD5 [MD5]. Most security-aware users have already moved away from any use of MD5 [RFC6151]. Handshake messages are not protected. This permits a man-in-the- middle to trick the client into picking a weaker cipher suite than it would ...
5
The current specification says that tracker GET requests specify the following variables: uploaded=... (bytes) downloaded=... (bytes) left=... (bytes) This is great for public trackers but is poorly designed for private trackers. The problem is that the numbers don't always add up as they should and this can be for several reasons. For example, you might ...
5
Assumption: the normal user can read the message, which is displayed on his screen. Generic attack: the user uses a camera to take a snapshot of the screen when the message is displayed. And voila! What you seek is demonstrated to be impossible.
5
No, this protocol does not provide perfect forward secrecy. Record the initial key transport message (shared via RSA-OAEP). If the attacker later gets access to the corresponding RSA private key, and decrypts the original key transport message, the entire symmetric key evolution sequence for that session will trivially unfold.
4
“Well-typed” relates to a type system. This is a general concept in computer science, the usage here is an example of the general concept and is not specific to cryptography. “Well-typed” does not refer to a cryptographic protocol, but to a theory (model) in which a protocol is described. A type system is a way to assign properties (called types) to ...
4
I am wondering if using Skein or the Keccak hash algorithm in this construction (as a stream cipher) is secure: In the case of Skein and Keccak it should be secure. However, both of those have defined their own cipher modes which you should IMO prefer. (For speed and compatibility, if not security.) The Skein one is defined in section 4.10 of the ...
4
I am assuming that the vault shall store arbitrary-length messages and associate with each message a token consisting of six decimal digits. Otherwise, as has been noted (see below), the problem is probably either impossible or trivial. I interpret your requirements to mean that the detokenization algorithm is also available to an attacker that has gotten ...
4
The claims made are pretty much all nonsense or do not represent an accurate understanding of the state of the art. I'm not going to go into a point-by-point response; suffice it to say that I would not trust any advice or representations they may make about what is or isn't secure. Their system might be fine, or it might not be, but their public ...
4
Use the exponential variant of ElGamal, where the plaintext is encoded in the exponent. Elliptic curve ElGamal is fine. In fact, any public key cryptosystem which allows raising ciphertexts to a power such that this operation corresponds homomorphically to multiplication for the plaintext. Your commitments are $c_x = \mathsf{E}(x)$; $c_y = \mathsf{E}(y)$; ...
4
Two things going on that together may make plain-hash-then-encrypt insecure. First, the distinction between secure MACs and hashes, which is that a hash function may allow you to derive $H(m')$ from $H(m)$ even if you only know how $m'$ and $m$ differ. Length extension attacks on SHA-1 and SHA-2 are a practical way that can happen, but there could be others ...
4
I would say there are three general areas of necessary expertise for most crypto-related jobs: Knowledge of primitives and their use cases. Knowledge of protocols and understanding how to reason about their security. Deep and abiding understanding of how incredibly stupid people are, including oneself. The most that knowing the math is going to do for ...
4
Canetti ("Towards realizing random oracles," Crypto 1997) gave a reasonably efficient (very efficient, by the standards of most obfuscation work) "virtual black-box" obfuscator for "point functions," i.e., functions of the form $I_x(y) = 1$ if $x=y$, $0$ otherwise. Such functions can be used, e.g., for password checking. Virtual black-box obfuscation ...
4
I would generate this key, then encrypt it in such a way that it would take years (but not decades!) to crack, then release it publicly. Yes, you are in effect putting the master key in a time capsule. The problems of time capsules in general apply: the release time will not be exact and a breakthrough in e.g. CPU design could hasten it. If no one's ...
3
In here, it is 1-2 oblivious transfer meaning that for each $i$, the receiver gets $A'_{i1}$ or $A'_{i2}$ but the sender does not know which. The length of the elements $A'_{ij}$ is not important as long as you choose a correct oblivious transfer protocol.
3
The answer depends on how you would layer the encryption on top of the existing protocol. If you implemented your own Skype client, you could deal with compression issues yourself. That might allow you to use format preserving encryption, perhaps on the compressed data stream and not the audio itself. However, you would need to be careful – speech ...
3
If you want $N$ serial numbers, your serial numbers will have to use $n$ bits for uniqueness, where $n = \log_2 N$. So if you have 100 bits to use for the serial, you could use 20 to get about a million serials and have 80 bits to use for a cryptographic MAC or signature. Now there are two approaches, the symmetric and the asymmetric. In the symmetric ...
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[1] Mingzhong Cai, Hristo A. Ganchev, Steffen Lempp, Joseph S. Miller and Mariya I. Soskova. Defining totality in the enumeration degrees. J. Amer. Math. Soc. Abstract, references, and article information View Article: PDF [2] Hristo A. Ganchev and Mariya I. Soskova. Definability via Kalimullin pairs in the structure of the enumeration degrees. Trans. Amer. Math. Soc. 367 (2015) 4873-4893. Abstract, references, and article information View Article: PDF [3] Adam R. Day and Joseph S. Miller. Cupping with random sets. Proc. Amer. Math. Soc. 142 (2014) 2871-2879. Abstract, references, and article information View Article: PDF [4] Adam R. Day and Joseph S. Miller. Randomness for non-computable measures. Trans. Amer. Math. Soc. 365 (2013) 3575-3591. Abstract, references, and article information View Article: PDF [5] Sebastiaan A. Terwijn. The finite intervals of the Muchnik lattice. Trans. Amer. Math. Soc. 364 (2012) 2521-2538. Abstract, references, and article information View Article: PDF [6] Joseph S. Miller. Two notes on subshifts. Proc. Amer. Math. Soc. 140 (2012) 1617-1622. MR 2869146. Abstract, references, and article information View Article: PDF [7] George Barmpalias, Rod Downey and Noam Greenberg. Working with strong reducibilities above totally $\omega$-c.e. and array computable degrees. Trans. Amer. Math. Soc. 362 (2010) 777-813. MR 2551506. Abstract, references, and article information View Article: PDF [8] Joseph S. Miller and Liang Yu. On initial segment complexity and degrees of randomness. Trans. Amer. Math. Soc. 360 (2008) 3193-3210. MR 2379793. Abstract, references, and article information View Article: PDF This article is available free of charge [9] Noam Greenberg. The role of true finiteness in the admissible recursively enumerable degrees. Memoirs of the AMS 181 (2006) MR 2213065. Book volume table of contents [10] Barbara F. Csima and Antonio Montalbán. A minimal pair of $K$-degrees. Proc. Amer. Math. Soc. 134 (2006) 1499-1502. MR 2199198. Abstract, references, and article information View Article: PDF This article is available free of charge [11] Carl G. Jockusch Jr., Angsheng Li and Yue Yang. A join theorem for the computably enumerable degrees. Trans. Amer. Math. Soc. 356 (2004) 2557-2568. MR 2052189. Abstract, references, and article information View Article: PDF This article is available free of charge [12] Peter Cholak, Richard Coles, Rod Downey and Eberhard Herrmann. Automorphisms of the lattice of $\Pi_1^0$ classes; perfect thin classes and anc degrees. Trans. Amer. Math. Soc. 353 (2001) 4899-4924. MR 1852086. Abstract, references, and article information View Article: PDF This article is available free of charge [13] Richard A. Shore and Theodore A. Slaman. A splitting theorem for $n-REA$ degrees. Proc. Amer. Math. Soc. 129 (2001) 3721-3728. MR 1860508. Abstract, references, and article information View Article: PDF This article is available free of charge [14] Rodney G. Downey and Richard A. Shore. There is no degree invariant half-jump. Proc. Amer. Math. Soc. 125 (1997) 3033-3037. MR 1401736. Abstract, references, and article information View Article: PDF This article is available free of charge [15] Oleg V. Belegradek. Degrees of unsolvability of first order decision problems for finitely presented groups . Proc. Amer. Math. Soc. 124 (1996) 623-625. MR 1307493. Abstract, references, and article information View Article: PDF This article is available free of charge [16] John J. Thurber. Every ${\rm low}\sb 2$ Boolean algebra has a recursive copy . Proc. Amer. Math. Soc. 123 (1995) 3859-3866. MR 1283564. Abstract, references, and article information View Article: PDF This article is available free of charge [17] Rod Downey and Carl G. Jockusch. Every low Boolean algebra is isomorphic to a recursive one . Proc. Amer. Math. Soc. 122 (1994) 871-880. MR 1203984. Abstract, references, and article information View Article: PDF This article is available free of charge [18] Rodney Downey and Julia F. Knight. Orderings with $\alpha$th jump degree ${\bf 0}\sp {(\alpha)}$ . Proc. Amer. Math. Soc. 114 (1992) 545-552. MR 1065942. Abstract, references, and article information View Article: PDF This article is available free of charge [19] S. Barry Cooper. The jump is definable in the structure of the degrees of unsolvability. Bull. Amer. Math. Soc. 23 (1990) 151-158. MR 1027898. Abstract, references, and article information View Article: PDF [20] C. J. Ash, C. G. Jockusch and J. F. Knight. Jumps of orderings . Trans. Amer. Math. Soc. 319 (1990) 573-599. MR 955487. Abstract, references, and article information View Article: PDF This article is available free of charge [21] Richard A. Shore. Defining jump classes in the degrees below ${\bf 0}'$ . Proc. Amer. Math. Soc. 104 (1988) 287-292. MR 958085. Abstract, references, and article information View Article: PDF This article is available free of charge [22] R. G. Downey. Two theorems on truth table degrees . Proc. Amer. Math. Soc. 103 (1988) 281-287. MR 938684. Abstract, references, and article information View Article: PDF This article is available free of charge [23] Andrea Sorbi. On quasiminimal e-degrees and total e-degrees . Proc. Amer. Math. Soc. 102 (1988) 1005-1008. MR 934883. Abstract, references, and article information View Article: PDF This article is available free of charge [24] Manuel Lerman and Richard A. Shore. Decidability and invariant classes for degree structures . Trans. Amer. Math. Soc. 310 (1988) 669-692. MR 973174. Abstract, references, and article information View Article: PDF This article is available free of charge [25] C. J. Ash. Errata to: Recursive labelling systems and stability of recursive structures in hyperarithmetical degrees'' [Trans.\ Amer.\ Math.\ Soc.\ {\bf 298} (1986), no.\ 2, 497--514; MR0860377 (87j:03060)] . Trans. Amer. Math. Soc. 310 (1988) 851. MR 949898. Abstract, references, and article information View Article: PDF This article is available free of charge [26] R. G. Downey, J. B. Remmel and L. V. Welch. Degrees of splittings and bases of recursively enumerable subspaces . Trans. Amer. Math. Soc. 302 (1987) 683-714. MR 891641. Abstract, references, and article information View Article: PDF This article is available free of charge [27] Christine Ann Haught. Lattice embeddings in the recursively enumerable truth table degrees . Trans. Amer. Math. Soc. 301 (1987) 515-535. MR 882702. Abstract, references, and article information View Article: PDF This article is available free of charge [28] R. G. Downey and C. G. Jockusch. T-degrees, jump classes, and strong reducibilities . Trans. Amer. Math. Soc. 301 (1987) 103-136. MR 879565. Abstract, references, and article information View Article: PDF This article is available free of charge [29] C. J. Ash. Recursive labelling systems and stability of recursive structures in hyperarithmetical degrees . Trans. Amer. Math. Soc. 298 (1986) 497-514. MR 860377. Abstract, references, and article information View Article: PDF This article is available free of charge [30] Peter Clote. On recursive trees with a unique infinite branch . Proc. Amer. Math. Soc. 93 (1985) 335-342. MR 770549. Abstract, references, and article information View Article: PDF This article is available free of charge
Results: 1 to 30 of 44 found Go to page: 1 2 | {"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": 0.9163221716880798, "perplexity": 2770.1271355764584}, "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/1448398466178.24/warc/CC-MAIN-20151124205426-00168-ip-10-71-132-137.ec2.internal.warc.gz"} |
https://manualzz.com/doc/23600519/stk-installation-guide | # STK Installation Guide
STK Installation Guide
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Contents
Section 1: Installing STK
System and Hardware Requirements ........................................................................................1-1
Installing STK.............................................................................................................................1-2
Requesting and Installing an STK License...............................................................................1-3
Resetting Your Current User Area ............................................................................................1-3
Installation Notes for Systems using Windows XP Service Pack 2 and Windows Vista......1-3
Appendix A: Configuring Dongles
Installing Dongle Drivers ..........................................................................................................A-1
Troubleshooting Dongle Installation........................................................................................A-2
Appendix B: Configuring a UNIX or Windows Network License Server
Installing a Windows Network License Server .......................................................................B-1
Installing a UNIX Network License Server.............................................................................B-3
Appendix C: Performing Remote Installations
Using a Software Distribution System to Install STK and STK Modules.............................C-1
Installing STK and STK Modules Unattended (or Silently)...................................................C-2
Appendix D: AGI Desktop Product Architecture
Section 1: Installing STK
Instructions for installing the Satellite Tool Kit (STK) follow. If you have questions that are not
support.
System and Hardware Requirements
Notes:
In order to install STK, you must be an administrator or have elevated install
permission for the machine on which STK is being installed.
You must also have read permissions for the HKEY_CLASSES_ROOT setting in
the system registry. To check the registry setting:
1. Run regedit from StartÆRun… or the command line to access the system
registry.
2. Right-click HKEY_CLASSES_ROOT and select Permissions….
3. Select Users and ensure that Allow for Read permissions is checked.
Component
Minimum Requirements
Recommended
Requirements
System and Hardware Requirements
CPU
1 GHz
2+ GHz
Note: Not supported on CPUs that do
not support Streaming SIMD Extensions
2 (SSE2). Some older AMD CPUs do
not support SSE2. Check the CPU
specifications.
RAM
1 GB
2 GB
Operating System
Windows XP/ XP Professional
x64/Vista/7
Windows XP/
XP Professional
x64/Vista/7
Web Browser
Internet Explorer 5.5
Internet Explorer 7.0
3D Visualization Requirements
Video Card
OpenGL-compatible card (128 MB
memory)
High-end
OpenGL-compatible card
(512+ MB memory)
OpenGL Version
1.2
2.0+
Disk Space
1.5 GB
1.5 GB
1-2
STK Installation Guide
Notes: Windows x64 Operating Systems
STK will run as a 32-bit application in a 64-bit Windows environment.
Video Cards
Video cards based on chipsets from ATI and nVIDIA have shown excellent
performance and compatibility with STK when using recent drivers in desktop or
laptop computers.
Graphics integrated on the motherboard in value desktop or laptop computers may
have insufficient levels of 3D performance and will compete with STK and other
applications for CPU resources which can create an unacceptable STK user
experience.
Matrox Gxxx and 3Dlabs cards should be avoided due to various incompatibilities
with STK and/or OpenGL.
OpenGL
STK will automatically use OpenGL 1.1 with remote access applications (such as
Microsoft Remote Desktop) and virtual PC applications (such as VMWare and
Microsoft Virtual PC) that do not support OpenGL 1.2 extensions.
Using OpenGL 1.1 with these applications will display the central body surface in
the STK 3D Graphics window, with the following limitations:
•
•
You can add only the base texture to the globe. Additional textures will be
rejected.
PDTT files will not work.
Installing STK
To install STK:
1. Insert the STK DVD into your DVD drive. If AutoRun is enabled, the installation
automatically starts.
Note:
If AutoRun is not enabled, run install.exe on the STK DVD.
2. Select the software you want to install and click Start Installation. (It is recommended that
you accept the default selections.) The Welcome screen for your first selection is displayed.
3. The install program will step you through installing the software applications you selected.
Symbol Server will be installed, if they do not already exist on your system.
4. When all the applications are installed, click Next.
STK Installation Guide
1-3
5. If you selected Run License Manager, the License Manager Wizard dialog box appears.
Requesting and Installing an STK License
Note:
Do not remove your old licenses if you want to continue to use a version of STK
older than STK 8. STK 9 licenses will not work with releases of STK older than
STK 8. You can remove the old licenses after you have removed the old STK
version.
If you close the License Manager without choosing one of the options, you can re-open it at any time by
clicking Start, Programs, AGI Support Tools, License Manager. You cannot run STK without
licensing it through the License Manager first.
When you run STK for the first time, STK prompts you for the following:
•
Define a user area for your scenario files. By default your user area is C:\Documents and
Settings\<user id>\My Documents\STK <version number>, which you can change by clicking the
Browse button
•
Select the default source for the SGP4 and GPS Propagators.
•
Select the types of files in the STK 8 user directory that you want to copy to the STK 9 user
directory.
If at any time you want to set your user area to another folder location or your folder was inadvertently
removed or corrupted, you can recreate the folder by using the Start menu option Reset Current User
Settings and running STK. When you run STK, you will see the same prompts that were presented to you
when you ran STK for the first time.
Installation Notes for Systems using Windows XP Service Pack 2 and
Windows Vista
If the Windows Firewall application is enabled, you may need to adjust the settings to allow the newly
installed STK Application to run properly with your network configuration.
Upon starting an AGI Application, the Windows Firewall may display a Windows Security Alert dialog
box prompting you to choose one of the following regarding the new application you started:
Keep Blocking. If you choose to "Keep Blocking" the application, you will not be able to access the
features on the associated ports via unsolicited incoming network traffic.
Unblock. If you choose to "Unblock" the application, you will be able to access the features on the
associated ports, including unsolicited incoming network traffic.
1-4
STK Installation Guide
Ask Me Later. If you choose to "Ask Me Later", the Windows Security Alert dialog box will prompt you
later if you want to "Block" or "Unblock" the application.
For more information on the Windows Firewall, go to Deploying Windows Firewall Settings for
Microsoft Windows XP with Service Pack 2 Website.
The following tables list the ports each AGI Application uses. You may need to make some adjustments
while using the Windows Service Pack 2 Firewall Utility.
AgUiApplication.exe (STK)
Feature
Port
Protocol
Description
MPI
Random
TCP
Message Passing Interface for parallel application processing
DIS
3000
UDP
Default port( BroadCast, Multicast ) used for Distributed
processing, it is configurable
Connect
5001
TCP
Default port used for STK/Connect commands, it is
configurable
AgUiApplication.exe (STK with Node Lock License)
Feature
Port
Protocol
Description
Messaging
2342
TCP
Only with Node Lock Licenses, Multiple instantiations of the
Feature
Port
Protocol
Description
Client
Connections
Random
TCP
Listens for client communications
Messaging
Random
UDP
lmgrd.exe
27000
TCP
AGIViewer.exe (AGIViewer)
Feature
Port
Protocol
Description
MPI
Random
TCP
Message Passing Interface for parallel application processing
Appendix A: Configuring Dongles
A dongle is a physical device that allows you to utilize flex licensing with STK and its modules. These
instructions will take you through the process of installing a dongle for use with STK.
Note: Dongle drivers for I-Button dongles are not supported on Vista because
I-Button dongles are being discontinued by the manufacturer.
Before installing a dongle, you must first have the following:
1. A license file supplied by AGI.
2. The dongle itself, a device that attaches to a computer’s parallel or USB port.
Attaching the Dongle
Note the Flex-ID number of your dongle, which will appear on parallel port dongles as a twelve digit
number preceded by either an “8-“, in the case of AGI dongles or a “7-“, in the case of third-party
produced dongles. The Flex-ID number of a USB dongle is an eight character string preceded by a “9-“.
Warnings: Contact AGI technical support before making any attempt to install a third-party
dongle.
Do not tamper with the dongle’s construction. If you damage the device by
handling it inappropriately, you will be charged for a replacement.
Installing Dongle Drivers
1. Insert the STK Installation DVD.
2. Open Windows Explorer, to the x:/DongleDriver Folder directory, where x is the letter of the
drive containing the STK installation DVD.
3. Select one of the following to install the Dongle Drivers:
o
For a standard Windows operating system, click flexid.exe.
o
For a 64-bit Windows operating system, open the HASP4_driver_cmdline folder in the
DongleDriver\HASP_FLEXID9 folder and click haspdinst.exe.
4. Restart your computer, if instructed.
5. Install STK licenses as you normally would.
Troubleshooting Dongle Installation
If you have followed the installation instructions carefully and still cannot utilize the dongle, take the
following steps:
1. Browse to <STK install directory>\AGI\LicenseManager\Bin and launch LmTools.exe.
A-2
STK Installation Guide
2. On the System Settings page, in the Flex-ID field, the dongle ID should be displayed. If the
dongle ID is not present, then either the dongle is not connected properly, or the dongle
driver is not functioning.
•
Verify the physical seating of the dongle and reinstall the driver.
•
If the problem persists, contact technical support.
3. If the FLEXID field is properly populated, then the problem is likely related to the license
file. Verify that:
•
The license file HostID matches the dongle ID.
•
The license file is in the correct directory.
•
The license file version is equal to or higher than the version of STK installed on the
computer.
•
If after verifying the settings, the problem persists, contact technical support.
Appendix B: Configuring a UNIX or Windows Network
Note:
strategies, refer to the FLEXlm End Users Guide.
A network license server is an area on a network where you can house and manage STK licenses for
multiple users. You can configure any machine on your network to act as the network license server,
provided the directory path to licenses on the server machine is shared, and that all of the clients that will
be accessing licenses from the server can see it.
It is recommended that you to have just one network license server, and that each instance of STK be
configured to request all licenses from the same server. You may not be able to access some licenses if
one client is attempting to get licenses from multiple network license servers. For example, if you are
pointing to one server for your STK license, and you try to point to a different server for your
Note:
A network fileserver is a good choice for a network license server installation,
although any machine usually available on the network is acceptable.
1. Install the network license server software on the server.
Procedures for performing these tasks for Windows and UNIX license servers follow.
Installing a Windows Network License Server
To install the network license server software:
1. Insert the DVD into the DVD drive.
2. Browse to <DVD drive>:\\AGI_License_Server\<version>\Windows\ and click setup.exe.
3. Continue to the License Agreement window, where you will need to read the AGI Desktop
Software Licensing Agreement. Accept the license agreement and click Next.
4. At the AGI License Server Destination Folder window, specify the location where your
license server files will be stored on the server. Click Next.
Note:
The installation process results in creation of a license folder to store your network
license files. By default, the license folder is created in C:\Documents and
Settings\All Users\Application Data\AGI\LicenseData on Windows XP and
5. At the Ready to Install the Program window, select Install.
B-2
STK Installation Guide
6. After the installation has finished, identify the AGI License Server Host ID and IP address
for the machine. Do this by running LMTools.exe in the AGI License Server folder,
selecting the System Settings tab. The value for Ethernet Address is the Host ID.
7. When you finish, e-mail or telephone AGI with the Host ID and IP address of network
license server machine to request server licenses. A Technical Support Engineer will
step 4). The client license will be used to direct individual workstations to the network license server to
After you have installed licenses on the network license server machine, you will need to start the License
You can configure the license server machine so that the license daemon starts automatically at boot by
changing the services settings for the AGI License Server on the machine that is acting as the network
1. Log on to the network license server machine.
2. Open the Services window.
Notes:
Windows XP users will find Services inside of their Administrative Tools in the
Control Panel.
If you are running Windows XP, and working in Category View, Administrative
Tools will be in the Performance & Maintenance category of your Control Panel.
3. When the Services window appears, double-click AGI License Server in the services list.
This will open the Properties page for the AGI License Server Service.
4. On the General tab, change the Startup Type to Automatic, if it is not already.
5. Click the Start button in the Services Status area.
6. Click OK to dismiss the Properties page.
Warnings:
If you are using network licenses and you are prompted to register when you
run STK after a client workstation install, either all of your network licenses
If STK starts up and cannot find the network license server it will attempt to
connect to the network license server multiple times. This process will be
repeated for each STK license. This process may take a significant amount of
time, and STK may appear to stop responding when actually it is searching for
STK Installation Guide
B-3
Installing a UNIX Network License Server
To install a Network License Server on UNIX:
2. Insert the DVD into your DVD drive.
3. Mount the DVD drive.
4. Change directories so that you are in the AGI_License_Server/unix directory on the DVD (e.g.,
5. At the user prompt, type ./install.Flexlm and press RETURN.
6. Choose whether to also view these installation instructions on the UNIX machine by pressing Y
or N.
Note:
The install instructions are in HTML format, and can be displayed on any platform
on which an AGI application runs. To properly view them you'll need a Browser
that is Java-capable and can support frames. Although this requires a HTML
Browser such as Netscape Navigator 4.x or Internet Explorer 4.x, it does not
require that the computer have access to the Internet. The Browser is used in this
case to display HTML files and not to connect to the internet.
7. At the prompt, enter the directory path of the machine that will act as the License Server.
Warning: If you are installing the License Server on a machine other than the one that will
actually act as the server, you will need to copy the License Server files from the
<InstallDir>/NetworkDaemon directory onto the hard drive of the machine that
will act as the License Server.
8. At the prompt, choose the operating system for the machine on which you are performing the
installation.
Note:
This is not necessarily the same operating system on which your AGI Application
will be running.
9. Allow the installation to continue. The on-screen instructions will guide you through the rest of
the installation process.
1. After the installation has finished, identify the Host ID and IP address for the machine that will
act as the Network License Server. From the UNIX directory on the DVD, enter hostid.sh to
return the host ID of the machine from which this command was entered.
2. E-mail, FAX or telephone AGI support with the Host ID and IP address of the machine that will
B-4
STK Installation Guide
Server installation: <install directory>/NetworkDaemon/Flexllm/V9.2/<operating
The client license will be used to direct individual workstations (clients) to the Network License
If you do not want the license daemon to run automatically, use the following steps to start it manually.
1. Log onto the License Server machine.
2. Change directories to the directory where you installed the Network Daemon files and type:
End Users Manual.
To configure the system so that the license daemon starts automatically at boot, place the following
command in the appropriate file:
Check the table following for instructions on automating this process on various platforms.
Platform
Instructions
Digital
UNIX
CD to the init.d directory and type ls to list the files contained in this directory. Create a file
beginning with Sxxxlmgrd (scripts are run in numerical order, so xxx should be one of the
last files run). Place the command in that file. You may need to enter additional commands
or structure the file accordingly (check other S files to see the format used on your system).
Now create a symbolic link to the newly created file in /sbin/rc2.directory.
HP-UX
Place the command in the localrc() function of the /etc/rc file.
AIX
Place the command at the bottom of the /etc/rc file (before the exit command).
SGI IRIX/ CD to the init.d directory and type ls to list the files contained in this directory. Create a file
Sun Solaris beginning with Sxxx (scripts are run in numerical order, so xxx should be one of the last
STK Installation Guide
Platform
B-5
Instructions
files run). Place the command in that file. You may need to enter additional commands or
structure the file accordingly (check other S files to see the format used on your system).
Now create a symbolic link to the newly created file in the /sbin/rc2.d directory.
Linux
Create a file called /etc/rc.d/init.d/lmgrd. The contents of the file should read:
#!/bin/sh
./etc/rc.d/init.d/functions
case "\$1" in
start)
echo -n "Starting lmgrd license daemon: "
stop)
echo -n "Stopping lmgrd license daemon"
<PathToExecutable>/lmdown -c
*)
echo "Usage: lmgrd {start|stop}"
exit 1
esac
exit 0
Be sure lmgrd, lmdown and the full path of your license file is in this script. Make this script
world executable using the following command:
chmod 0755 /etc/rc.d/init.d/lmgrd
CD to the /etc/rc.d/rc3.d directory and type ls -al to see the files in that directory.
Create a link to ../init.d/lmgrd by typing the following:
ln -s ../init.d/lmgrd Sxxxlmgrd
where xxx is the number you have chosen. You may need to enter additional commands or
structure the file accordingly (check other S files to see the format used on your system).
If you use your RHLinux workstation in X mode all of the time (i.e., your login screen is
graphical) be sure to make the previous symlink in /etc/rc.d/rc5.d as well. Change runlevels,
or reboot to have the license daemon start at boot.
Appendix C: Performing Remote Installations
This section describes how to remotely install STK and STK modules, either using a software distribution
system or the Windows command line.
Using a Software Distribution System to Install STK and STK Modules
Install packages for STK and associated STK Modules are fully compatible with most commercially
available software distribution systems. All AGI install packages are Windows Installer-based.
Consult the documentation of your specific distribution system on how to prepare the installs for
distribution with site-specific options. Most systems handle both .msi files and setup.exe files.
Product-specific information on the STK install package follows.
Install prerequisites:
Package
.net 2.0
Location on Install Media
\Prerequirements\Microsoft\Framework.net\v2.0.5072
7.42\<.exe per operating system – 32-bit or 64-bit>
Msiexec 3.1
\Prerequirements\Microsoft\Msiexec\v3.1.0.0\instmsi
30.exe
\Prerequirements\Microsoft\Msiexec\v3.1.0.0\Window
sInstaller-KB893803-v2-x86.exe
Redistributable from
Microsoft. Install when
.net is less than 2.0.
Select appropriate one for
Redistributables from
Microsoft. Install when
msiexec is less than 3.0.
MS Visual
C++ 2008
Support
Files
MS Visual
C++ 2005
SP1
Support
Files
Microsoft
XML 6.0
Parser
Manager
MathPlayer
\Prerequirements\Microsoft\VCRedist\v2008\vcredist
_x86.exe
Redistributables from
Microsoft.
\Prerequirements\Microsoft\VCRedist\v2005\vcredist
_x86.exe
Redistributables from
Microsoft.
\Prerequirements\Microsoft\msxml6\v6.0.0.0\msxml6.
msi
Run msxml6.msi.
2525B
Symbol
Server
\Prerequirements\ObjectRaku\2525B_Symbol_Serve
Run setup.exe. This is not
a single executable install.
Used to display equations
in the Help file. Single
executable install.
Optional. Install if you
plan to use 2525B
symbols. Single
executable install.
\Prerequirements\DesignScience\MathPlayer\v2.11.1
5.0\MathPlayerSetup.exe
C-2
STK Installation Guide
STK install:
Package
STK
Location on Install Media
\STK\Setup.exe or \STK\STK 9.msi
Planetary Data
\AGI_Planetary_Data_Supplement\v9.0.0\setu
p.exe
\STK_Engine_Resources\v9.0.0\setup.exe
STK Engine
Resources
Not a single executable install.
Location.
Optional. Install for extended
planetary data. Run setup.exe
Optional. Run setup.exe. For
application development.
Package
STK/Analyzer
Location on Install Media
\STKAnalyzer\setup.exe
STK/Scheduler
\STKScheduler\setup.exe
Environment
\STKRAE\setup.exe
Optional. Separate CD. Install if
you plan to use STK/Analyzer.
Single executable install.
Optional. Separate CD. Install if
you plan to use STK/Scheduler.
Single executable install. Inputs:
user folder.
Optional. Separate CD. Inputs:
database location
GIS Analyst Extension CD:
Package
Msiexec 3.1
Location on Install Media
\Prerequirements\Microsoft\Msiexec\v3.1.0.0\in
stmsi30.exe
\Prerequirements\Microsoft\Msiexec\v3.1.0.0\
WindowsInstaller-KB893803-v2-x86.exe
ArcGIS 9.0.0
\ArcgisInstall\arcgis\setup.exe
\ArcgisInstall\arcgis\ ArcGISEngine93sp1.msp
Redistributables from Microsoft.
Install when msiexec is less than
3.0.
Installs ArcGIS Run-time 9.3.
Installs ArcGIS Run-time 9.3
service pack 1.
Installing STK and STK Modules Unattended (or Silently)
An unattended installation is one that does not require user interaction, and a silent (or quiet) installation
is one that does not display any indication of its progress. However, most people use these terms
interchangeably.
Information on how to perform unattended installations for STK follows. You will need to perform this for
each desired install described in the tables above.
Basic MSI Silent Installations
To run a Basic MSI setup silently, the end user needs to type the following at the command line:
msiexec /i Product.msi /qn
STK Installation Guide
Note:
/q [n|b|r|f]
The /q option is used to set the user interface level in conjunction with the following flags:
•
q or qn creates no user interface
•
qb creates a basic user interface
These user interface settings display a modal dialog box at the end of installation:
•
qr displays a reduced user interface
•
qf displays a full user interface
•
qn+ displays no user interface
•
qb+ displays a basic user interface
Basic MSI projects do not create or read response files. To set installation properties for a Basic MSI
project, run a command line such as:
msiexec /i Product.msi /qn INSTALLDIR=D:\ProductFolder USERNAME="Valued Customer"
To run a setup.exe, users can run the command:
Setup.exe /s /v"/qn". | {"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": 0.3265712559223175, "perplexity": 12777.613382384185}, "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-2020-16/segments/1585370496669.0/warc/CC-MAIN-20200330054217-20200330084217-00358.warc.gz"} |
https://www.studypug.com/ie/multivariable-calculus/directional-derivatives | Directional derivatives
Directional derivatives
Lessons
Notes:
Suppose we have a vector $\vec{v} =\lt v_1, v_2\gt$. The unit vector will be:
$\vec{v} = \frac{1}{\sqrt{v^2_1 + v^2_2}} \lt v_1,v_2\gt$
Suppose we have a vector $\vec{v} =\lt v_1, v_2,v_3\gt$. The unit vector will be:
$\vec{v} = \frac{1}{ \sqrt{v_1^2 + v_2^2 + v_3^2} } $
When given an angle of a direction ($\theta$ ), we say that the unit vector (that points to the direction) is:
$\vec{u} = \lt \cos \theta, \sin \theta \gt$
Directional Derivatives of 2 Variable Functions
A Directional Derivative is the rate of change (of $x$ and $y$) of a function at a point $P=(x_0,y_0,z_0)$, at the direction of the unit vector
Suppose there is a 2-variable function $z=f(x,y)$. Then the directional derivative is:
$D_{\vec{u}}f(x,y) = f_x(x,y)a + f_y(x,y)b$
where the $\vec{u} = $ is the unit vector that points in the direction of change. Directional Derivatives of 3 Variable Functions
Suppose there is a 3-variable function $w=f(x,y,z)$. Then the directional derivative is:
$D_{\vec{u}}f(x,y,z) = f_x(x,y,z)a + f_y(x,y,z)b + f_z(x,y,z)c$
where the $\vec{u} = $ is the unit vector that points in the direction of change.
• Introduction
Directional Derivatives Overview:
a)
Things to Know Before Knowing Directional Derivatives
• Calculating unit vectors
• An example
• Angle to a unit vector
• An example
b)
Directional Derivatives of 2 Variable Functions
• The rate of change of $x$ and $y$
• $D_{\vec{u}}f(x,y) = f_x(x,y)a + f_y(x,y)b$
• An example
c)
Directional Derivatives of 3 Variable Functions
• The rate of change of $x$ and $y$
• $D_{\vec{u}}f(x,y,z) = f_x(x,y,z)a + f_y(x,y,z)b + f_z(x,y,z)c$
• An example
• 1.
Finding the Unit Vector & Angle of Direction
Find the unit vector of $\vec{v} =\lt 5, -2\gt.$
• 2.
Find the unit vector of $\vec{v} =\lt -1, 3, 5\gt.$
• 3.
Find the unit vector, given that the unit vector is in the direction of $\theta=\frac{\pi}{3}$.
• 4.
Finding the Directional Derivative of 2 Variable Functions
Find the direction derivative of $z=\sqrt{x^2+2y}$ at any given point, in the direction of $\vec{v} = \lt 1, 3\gt$
• 5.
Find the direction derivative of $z=xy \ln (\frac{x}{y})$ at any given point, where the direction of the unit vector is at $\theta=\frac{\pi}{6}$.
• 6.
Finding the Directional Derivative of 3 Variable Functions
Find the direction derivative of $f(x,y,z)=xy^3+yz^2$ in the direction of $\vec{v} =\lt 1, 2, 4\gt$.
• 7.
Find the direction derivative of $f(x,y,z)=\ln (x)e^{yz}$ in the direction of $\vec{v} =\lt -3, 1, 2\gt$ . | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 32, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "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": 0.9814695119857788, "perplexity": 489.7724271007682}, "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-2020-40/segments/1600400213006.47/warc/CC-MAIN-20200924002749-20200924032749-00019.warc.gz"} |
https://math.stackexchange.com/help/badges/78?page=3 | # Help Center > Badges > Quorum
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Awarded Nov 6 '18 at 14:02 to | {"extraction_info": {"found_math": false, "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": 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": 0.8017102479934692, "perplexity": 1719.9394062164472}, "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/1568514574588.96/warc/CC-MAIN-20190921170434-20190921192434-00171.warc.gz"} |
http://mathhelpforum.com/geometry/67734-first-time-user-here-looking-help-find-angle.html | # Thread: First Time User here looking help to find angle
1. Hi. It's my first time and hoping someone can help me solve for the angle (see attached picture). I've been at it for hours and have just turned my brain to
mush.
The sketch may be unclear so the dimensions on top are 0.882, right is 0.705 and Radii are 0.380.
Thanks!.
ohh yeah, and i'd really like to know how it was solved
THanks.
Attached Thumbnails
2. using trig, I get $\phi \approx 44^{\circ}$ | {"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": 0, "img_math": 0, "codecogs_latex": 1, "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": 0.631135106086731, "perplexity": 749.9889970898383}, "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-2016-36/segments/1471982293468.35/warc/CC-MAIN-20160823195813-00110-ip-10-153-172-175.ec2.internal.warc.gz"} |
https://mathoverflow.net/questions/315505/if-goldbachs-conjecture-is-eventually-true-is-it-necessarily-true/315510 | # If Goldbach's Conjecture is eventually true, is it necessarily true?
We have all heard that if Goldbach's conjecture is independent, then it is true. This is because if GC is false then there is an even number which is not the sum of two primes, and hence a finite proof. What if this number is very large? Maybe beyond our reach?
If one proves that it is independent that eventually every even number is the sum of two primes, can we conclude that eventually every even number is the sum of two primes? Even if we may never know the $$e$$ from which it is Goldbach's conjecture, all the way, into infinity?
If we know that there is an $$e$$ from which every even number after and including $$e$$ is the sum of two primes, is independent, can we conclude that $$e$$ and every even number beyond, is the sum of two primes?
Even if we may never know what $$e$$ is?
Let $$e$$ be the least even integer such that $$e$$ is the sum of two primes and for every $$k=2n$$ where $$n \in \mathbb{N}$$ where $$k$$ is greater than $$e$$, then $$k$$ is also the sum of two primes. Suppose it is independent of ZFC that $$e$$ exists. Does it follow that $$e$$ exists?
• When you say "independent", shouldn't the next words be "of XYZ", where XYZ is the name of some axiomatic theory? – S. Carnahan Nov 17 '18 at 6:35
• What other axioms would it be? Aka math – user131478 Nov 17 '18 at 6:40
• @Erin ZFC is not the same as "math", I don't understand that comment (and it feels somewhat rude, unfortunately). As shown in the answers, this is already something that PA and much weaker theories address. – Andrés E. Caicedo Nov 17 '18 at 21:18
• @Erin No, sorry; if the question requires editing, it should be edited. If you post on your own blog, you have control of the content. – Andrés E. Caicedo Nov 17 '18 at 21:30
• please don't delete a question which has been answered, the whole point of MO is to have a permanent record of questions and answers. – Carlo Beenakker Nov 17 '18 at 21:34
We can't readily conclude that. Each $$\Sigma_1$$ statement of arithmetic is provable in PA and hence in ZFC, but not every $$\Pi_2$$ statement (which is what you would seem to need here) is.
Indeed the $$\Pi_1$$ statement Con(ZFC) is already not provable (under the assumption that your Eventual Twin Prime Conjecture is independent).
• Thank you Bjorn. Are you saying that it is not necessarily true that if the existence of $e$ is independent then it exists? – user131478 Nov 17 '18 at 8:49
• Yes, "$e$ doesn't exist " is the $\Pi_2$ statement – Bjørn Kjos-Hanssen Nov 17 '18 at 12:27
• Cool, thanks! I am trying to accept and upvote the answer. – user131478 Nov 17 '18 at 15:16
Let $$S$$ be the set of even integers which are not a sum of two primes. Goldbach’s conjecture is that $$S$$ has no members larger than $$2.$$.
And, as you say, if we somehow know that it is consistent (with some system) both that it is true and that it is false, then it is true. This since, if it is false, there is a specific counter-example which can be certified by a proof. Perhaps a proof which would take more pages than there are molecules in the known universe , but still a finite proof.
Similarly a statement such as "$$S$$ has no members greater than $$10^{2000000}!$$" is true, if independent, for the same reason.
Your hypothetical conjecture is that $$S$$ is finite. If that is true, that does not force existence of a finite proof. | {"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": 23, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8555825352668762, "perplexity": 303.7417228513962}, "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-2021-10/segments/1614178361808.18/warc/CC-MAIN-20210228235852-20210301025852-00159.warc.gz"} |
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## UnkleRhaukus one year ago 3 | (x^3-6x^2+11x-6) Delete Cancel Submit
• This Question is Closed
1. whpalmer4
• one year ago
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3
Surely you aren't asking for help doing synthetic division, are you?
2. UnkleRhaukus
• one year ago
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prove the above 3 divides that polynomial (i know the answer already )
3. UnkleRhaukus
• one year ago
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(or disprove)
4. ganeshie8
• one year ago
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$$(x^3-6x^2+11x-6) \equiv ( x^3+ 11x) \equiv (x^3-x) \mod 3$$
5. ganeshie8
• one year ago
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$$(x)(x^2-1) \equiv x(x+1)(x-1) \equiv 0 \mod 3$$ assuming x is an integer, product of 3 consecutive integers are divisible by 3
6. whpalmer4
• one year ago
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and it factors to $$(x-1)(x-2)(x-3)$$...
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Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy. | {"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": 1, "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": 0.9985608458518982, "perplexity": 13759.165174302203}, "config": {"markdown_headings": true, "markdown_code": false, "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-2015-18/segments/1429246636650.1/warc/CC-MAIN-20150417045716-00000-ip-10-235-10-82.ec2.internal.warc.gz"} |
https://mathtuition88.com/tag/ip/ | ## Key Topics for IP Additional Mathematics
The following are some of the most important topics for Integrated Programme (IP) Additional Mathematics. Also applicable for the usual ‘O’ level Additional Mathematics.
Notice that Secondary 3 topics are very important as well, for the final Promo or ‘O’ levels. This can be a major problem for students who only start to study seriously in Secondary 4 — it can be a tough job to catch up with the important Secondary 3 topics.
## Secondary 3 topics
• Binomial Theorem
• Indices and Logarithms
• Coordinate Geometry of Circles
• Linear Law
## Secondary 4 topics
• Trigonometry: R formula and Graphs
• Differentiation and its Applications
• Integration and its applications (including area under the curve)
## IP Math Syllabus (Integrated Programme Mathematics)
Students and parents new to IP (Integrated Programme) may be confused on what is the Mathematics syllabus of IP Math. Indeed, it is very confusing as every school has its own syllabus. In general, the syllabus as a whole is not that different from ‘O’ level Mathematics, but the order in which the school teaches is unique to each school.
In general, the topics can be divided as follows, following the famous assessment book “Mathematics (Integrated Programme)” by Wong-Ng Siew Hiong who is a teacher at RI. This is one of the very few IP Math books available in local bookstores.
## Secondary 3 IP Math Syllabus
1. Geometrical Properties of Circles
3. Matrices & Simultaneous Equations
4. Quadratic Functions, Inequalities & Roots of Equations
5. Sets
6. Relations & Functions
7. Indices & Surds
8. Exponential, Logarithmic & Modulus Functions
9. Polynomials & Partial Fractions
10. Graphical Solutions & Transformations
11. Circular Measure
12. Plane Geometry
13. Coordinate Geometry & Equations of Circles
14. Linear Law
15. Trigonometry
16. Further Trigonometry
## Secondary 4 IP Math Syllabus
1. Binomial Theorem
2. Probability
3. Statistics
4. Vectors
5. Differentiation Techniques
6. Differentiation and its Applications
7. Integrated Techniques
8. Applications of Integration
9. Integration Applications — Area and Kinematics
## Hwa Chong IP dropout shares his story: Student hacked and sabotaged Project Work of rival group
This is the dark side of the Integrated Programme, parents and students should read this (and definitely watch the video).
Something in the video is quite shocking: According to the interviewee Edwin, someone in his HCI batch “hacked into the files of another Project Work (PW) group to sabotage them so that they wouldn’t do well”. This is certainly “absurd”, as Edwin put it. (Note that PW is widely considered the least important of all subjects.) Such is the level of competitiveness in the top tier IP schools? Such unethical students are really the black sheep of IP program and society in general, it reflects the “black heart” of the student.
Good luck to Edwin, he seems like a nice guy. Perhaps this may be a blessing in disguise for him, his path less travelled may lead him to a better life in the Land Down Under (Australia).
Source (Text and Video): https://www.straitstimes.com/singapore/education/i-flunked-the-ip
Excerpt:
“With his top honours in finance and economics, Singaporean Edwin Chaw, who recently graduated from the University of Melbourne, should enjoy good job prospects when he returns home.
But the 26-year-old is applying for jobs in Melbourne, Australia, instead, as he believes that his past as a “dropout” from the elite Integrated Programme at Hwa Chong Institution still haunts him.”
## Promotion Criteria for IP Schools
Entering IP is not all smooth sailing, there is still much work to be done. Most IP schools will set a minimum criteria to proceed in the Integrated Program (i.e. skip ‘O’ levels). Those students who don’t make the criteria may be streamed into the ‘O’ level track.
A recent post from Kiasuparents summarized nicely the situation for the top 4 IP schools:
At the end of the day, it’s each sch’s perogative to set the IP promotion bar at a level it deems fit. For HCI/NYGH case, that bar was set at 65%, while RI set it at 60% and RGS at 50%. The R sch students also have the flexibility to choose the best subjects for GPA calculation (and not have to include all subjects).
Source: Kiasuparents
Hence, basically for HCI/NYGH an average grade of B3 and above is needed to proceed in the IP track, while for RI it is B4, and RGS is just pass (50%). Note that IP exam papers tend to be tougher than usual, hence it is not as easy as it sounds to get B3 in an IP school, or even to pass.
While the ‘O’ level track is not bad in the sense that it provides an ‘O’ level certificate as a backup, the problem is that IP schools are so entrenched in the IP system, and so used to teaching IP syllabus, their teachers may or may not be proficient in teaching ‘O’ level material. See this news: RI’s O Level Scores: Only 1 student out of 10 made it to JC. Hence, there is always an inherent risk in being streamed to the ‘O’ level track.
## A Maths Tuition: Trigonometry Formulas
Many students find Trigonometry in A Maths challenging.
This is a list of Trigonometry Formulas that I compiled for A Maths. Students in my A Maths tuition class will get a copy of this, neatly formatted into one A4 size page for easy viewing.
A Maths: Trigonometry Formulas
$\mathit{cosec}x=\frac{1}{\sin x}$$\mathit{sec}x=\frac{1}{\cos x}$
$\cot x=\frac{1}{\tan x}$$\tan x=\frac{\sin x}{\cos x}$
(All Science Teachers Crazy)
$y=\sin x$
$y=\cos x$
$y=\tan x$
$\frac{d}{\mathit{dx}}(\sin x)=\cos x$
$\frac{d}{\mathit{dx}}(\cos x)=-\sin x$
$\frac{d}{\mathit{dx}}(\tan x)=\mathit{sec}^{2}x$
$\int {\sin x\mathit{dx}}=-\cos x+c$
$\int \cos x\mathit{dx}=\sin x+c$
$\int \mathit{sec}^{2}x\mathit{dx}=\tan x+c$
Special Angles:
$\cos 45^\circ=\frac{1}{\sqrt{2}}$
$\cos 60^\circ=\frac{1}{2}$
$\cos 30^\circ=\frac{\sqrt{3}}{2}$
$\sin 45^\circ=\frac{1}{\sqrt{2}}$
$\sin 60^\circ=\frac{\sqrt{3}}{2}$
$\sin 30^\circ=\frac{1}{2}$
$\tan 45^\circ=1$
$\tan 60^\circ=\sqrt{3}$
$\tan 30^\circ=\frac{1}{\sqrt{3}}$
$y=a\sin (\mathit{bx})+c$ Amplitude: $a$; Period: $\frac{2\pi }{b}$
$y=a\cos (\mathit{bx})+c$ Amplitude: $a$; Period: $\frac{2\pi }{b}$
$y=a\tan (\mathit{bx})+c$ Period: $\frac{\pi }{b}$
$\pi \mathit{rad}=180^\circ$
Area of $\triangle \mathit{ABC}=\frac{1}{2}\mathit{ab}\sin C$
Sine Rule: $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$
Cosine Rule: $c^{2}=a^{2}+b^{2}-2\mathit{ab}\cos C$
## O Level Logarithm Question (Challenging)
Question:
Given $\displaystyle\log_9{a} = \log_{12}{b} =\log_{16}{(a+b)}$, find the value of $\displaystyle\frac{a}{b}$.
Solution:
Working with logarithm is tricky, we try to transform the question to an exponential question.
Let $\displaystyle y=\log_9{a} = \log_{12}{b} =\log_{16}{(a+b)}$
Then, we have $a=9^y=3^{2y}$
$b=12^y=3^y\cdot 2^{2y}$
$a+b=16^y=2^{4y}$.
Here comes the critical observation:
Observe that $\boxed{a(a+b)=b^2}$.
Divide throughout by $b^2$, we get $\displaystyle (\frac{a}{b})^2+\frac{a}{b}=1$.
Hence, $\displaystyle (\frac{a}{b})^2+\frac{a}{b}-1=0$.
Solving using quadratic formula (and reject the negative value since $a$ and $b$ has to be positive for their logarithm to exist),
We get $\displaystyle\frac{a}{b}=\frac{-1+\sqrt{5}}{2}$.
If you have any questions, please feel free to ask me by posting a comment, or emailing me.
(I will usually explain in much more detail if I teach in person, than when I type the solution)
## Hwa Chong IP Sec 2 Maths Question – Equation of Parabola
Question:
Given that a parabola intersects the x-axis at x=-4 and x=2, and intersects the y-axis at y=-16, find the equation of the parabola.
Solution:
Sketch of graph:
Now, there is a fast and slow method to this question. The slower method is to let $y=ax^2+bx+c$, and solve 3 simultaneous equations.
The faster method is to let $y=k(x+4)(x-2)$.
Why? We know that x=4 is a root of the polynomial, so it has a factor of (x-4). Similarly, the polynomial has a factor of (x-2). The constant k (to be determined) is added to scale the graph, so that the graph will satisfy y=-16 when x=0.
So, we just substitute in y=-16, x=0 into our new equation.
$-16=k(4)(-2)$.
$-16=-8k$.
So $k=2$.
In conclusion, the equation of the parabola is $y=2(x+4)(x-2)$.
## Sec 2 IP (HCI) Revision 1: Expansion and Factorisation
This is a nice worksheet on Expansion and Factorisation by Hwa Chong Institution (HCI).
There are no solutions, but if you have any questions you are welcome to ask me, by leaving a comment, or by email.
Hope you enjoy practising Expansion and Factorisation. | {"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": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 54, "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": 0.676173985004425, "perplexity": 3157.4903312540637}, "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-2022-40/segments/1664030335365.63/warc/CC-MAIN-20220929194230-20220929224230-00091.warc.gz"} |
https://docs.nvidia.com/cuda/libdevice-users-guide/__nv_fast_sincosf.html | ## 3.108. __nv_fast_sincosf
Prototype:
void @__nv_fast_sincosf(float %x, float* %sptr, float* %cptr)
Description:
Calculate the fast approximate of sine and cosine of the first input argument x (measured in radians). The results for sine and cosine are written into the second argument, sptr, and, respectively, third argument, zptr.
Returns:
• none
Note:
For accuracy information for this function see the CUDA C++ Programming Guide, Appendix E.2, Table 9.
Denorm input/output is flushed to sign preserving 0.0.
Library Availability:
Compute 2.0: Yes
Compute 3.0: Yes
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# If xyz ≠ 0, is x(y + z) >= 0?
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If xyz ≠ 0, is x(y + z) >= 0? [#permalink]
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28 Oct 2010, 22:37
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If xyz ≠ 0, is x(y + z) >= 0?
(1) |y + z| = |y| + |z|
(2) |x + y| = |x| + |y|
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Re: If xyz ≠ 0, is x(y + z) >= 0? [#permalink]
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08 Jan 2011, 15:39
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ajit257 wrote:
If xyz ≠ 0, is x (y + z) = 0?
(1) ¦y + z¦ = ¦y¦ + ¦z¦
(2) ¦x + y¦ =¦x¦ + ¦y¦
Can some explain the concept of absolute values
I think the question should be:
If xyz ≠ 0, is x (y + z) >= 0?
xyz ≠ 0 means that neither of unknowns is 0.
(1) |y + z| = |y| + |z| --> either both $$y$$ and $$z$$ are positive or both are negative, because if they have opposite signs then $$|y+z|$$ will be less than $$|y|+|z|$$ (|-3+1|<|-3|+1). Not sufficient, as no info about $$x$$.
(2) |x + y| = |x| + |y| --> the same here: either both $$x$$ and $$y$$ are positive or both are negative. Not sufficient, as no info about $$z$$.
(1)+(2) Either all three are positive or all three are negative --> but in both cases the product will be positive: $$x(y+z)=positive*(positive+positive)=positive>0$$ and $$x(y+z)=negative*(negative+negative)=negative*negative=positive>0$$. Sufficient.
For theory on absolute values check: math-absolute-value-modulus-86462.html
For practice check: search.php?search_id=tag&tag_id=37 (DS), search.php?search_id=tag&tag_id=58 (PS), inequality-and-absolute-value-questions-from-my-collection-86939.html (700+ DS).
Hope it helps.
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Re: If xyz ≠ 0, is x(y + z) >= 0? [#permalink]
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29 Oct 2010, 00:15
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1
Note that |a+b|=|a|+|b| means that the sign of a & b is the same ... either they are both positive or both negative.
In this question, we are given xyz is not 0, hence none of those numbers can be 0.
(1) sign(y)=sign(z) ... Insufficient ... the given product can still be positive of negative (take y=z=4, x=1 and x=-1)
(2) sign(x)=sign(y) ... Insufficient ... again the product may have eithe sign (take x=1, y=1 ... then take z=1 or z=-2)
(1+2) sign(x)=sign(y)=sign(z) ... whether they are all positive or all negative, the given product will always be positive ... Sufficient
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Re: If xyz ≠ 0, is x(y + z) >= 0? [#permalink]
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Updated on: 29 Apr 2013, 05:03
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If xyz ≠ 0, is x(y + z) >= 0?
(1) |y + z| = |y| + |z|
(2) |x + y| = |x| + |y|
Originally posted by ajit257 on 08 Jan 2011, 14:42.
Last edited by Bunuel on 29 Apr 2013, 05:03, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If xyz ≠ 0, is x(y + z) >= 0? [#permalink]
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09 Jan 2011, 10:59
2
Thanks Brunuel but as written, wouldnt the answer be A?
If X(Y+Z)=0? and X does not equal 0, this is true only if Y= -Z and this is true only if either:
Y is negative and Z is possitive or Z is positive and Y is negative
If |Y+Z| = |y| + |Z|, if either of the two cases is true, |Y+Z| < |Y| + |Z| so B would be sufficient.
If |X+Y| = |X| + |Y|, this is true only if X and Y are both positive. This does not supply information about Z so insufficient. For instance, X and Y and Z can all be possiive which makes the question true or X and Y can be possitive and Z negative which makes it false.
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Re: If xyz ≠ 0, is x(y + z) >= 0? [#permalink]
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09 Jan 2011, 11:09
2
abmyers wrote:
Thanks Brunuel but as written, wouldnt the answer be A?
If X(Y+Z)=0? and X does not equal 0, this is true only if Y= -Z and this is true only if either:
Y is negative and Z is possitive or Z is positive and Y is negative
If |Y+Z| = |y| + |Z|, if either of the two cases is true, |Y+Z| < |Y| + |Z| so B would be sufficient.
If |X+Y| = |X| + |Y|, this is true only if X and Y are both positive. This does not supply information about Z so insufficient. For instance, X and Y and Z can all be possiive which makes the question true or X and Y can be possitive and Z negative which makes it false.
Yes, in it's current form the answer is A:
If xyz ≠ 0, is x (y + z)=0?
xyz ≠ 0 means that neither of unknowns is 0, so as $$x\neq{0}$$ then $$x(y + z)=0$$ is true only if $$y+z=0$$. So the question is whether $$y+z=0$$ is true.
(1) |y + z| = |y| + |z| --> if $$y+z=0$$ is true then $$LHS=|y+z|=0$$ and in order RHS to equal to zero both $$y$$ and $$z$$ must be zero, but we are given that neither of unknowns is 0, so $$y+z\neq{0}$$. Sufficient.
(2) |x + y| = |x| + |y| --> insufficient, as no info about $$z$$.
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Re: If xyz ≠ 0, is x(y + z) >= 0? [#permalink]
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11 Dec 2013, 07:32
I am bit confused here with x(y + z) >= 0? Greater equal to 0.
I know x(y + z) will always be greater than Zero, combining both options, but mind is saying as x(y + z) can not be equal to zero, in that case should I say x(y + z) is not >= 0 and answer is C as we concluded bcz it will always be greater than zero, but not >= to 0.
Thanks
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Re: If xyz ≠ 0, is x(y + z) >= 0? [#permalink]
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11 Dec 2013, 07:56
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PiyushK wrote:
I am bit confused here with x(y + z) >= 0? Greater equal to 0.
I know x(y + z) will always be greater than Zero, combining both options, but mind is saying as x(y + z) can not be equal to zero, in that case should I say x(y + z) is not >= 0 and answer is C as we concluded bcz it will always be greater than zero, but not >= to 0.
Thanks
$$\geq{0}$$ translates to: more than or equal to 0. How can a number simultaneously be more than 0 AND equal to it?
The question asks is x(y + z) more than or equal to 0. We get that it's more than 0, thus we have an answer to our question.
Hope it's clear.
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Re: If xyz ≠ 0, is x(y + z) >= 0? [#permalink]
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11 Dec 2013, 08:21
Got it Bunuel, actually I was thinking too much about the range of solution.
(super set)
{0,1,2,3,10000 infinity } solutions hold true for >=0
(subset)
{1,2,3,1000 infinity } each element also hold true for >=0, even if we don't have 0 in solution set, e.g 1>=0 (yes)
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Re: If xyz ≠ 0, is x(y + z) >= 0? [#permalink]
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11 Feb 2014, 06:18
Bunuel wrote:
abmyers wrote:
Thanks Brunuel but as written, wouldnt the answer be A?
If X(Y+Z)=0? and X does not equal 0, this is true only if Y= -Z and this is true only if either:
Y is negative and Z is possitive or Z is positive and Y is negative
If |Y+Z| = |y| + |Z|, if either of the two cases is true, |Y+Z| < |Y| + |Z| so B would be sufficient.
If |X+Y| = |X| + |Y|, this is true only if X and Y are both positive. This does not supply information about Z so insufficient. For instance, X and Y and Z can all be possiive which makes the question true or X and Y can be possitive and Z negative which makes it false.
Yes, in it's current form the answer is A:
If xyz ≠ 0, is x (y + z)=0?
xyz ≠ 0 means that neither of unknowns is 0, so as $$x\neq{0}$$ then $$x(y + z)=0$$ is true only if $$y+z=0$$. So the question is whether $$y+z=0$$ is true.
(1) |y + z| = |y| + |z| --> if $$y+z=0$$ is true then $$LHS=|y+z|=0$$ and in order RHS to equal to zero both $$y$$ and $$z$$ must be zero, but we are given that neither of unknowns is 0, so $$y+z\neq{0}$$. Sufficient.
(2) |x + y| = |x| + |y| --> insufficient, as no info about $$z$$.
Hi Bunuel is this approach valid?
By property Is |x - y| >= |x| - |y|, and they are only equal when both x and y have the same signs.
In statement 1, we only know that z and y have the same signs but no info on x. Insuff. In Statement 2, we have that 'x' and 'y' have the same sign but no info on 'z'. Both together we know that all of them have the same sign. Thus the answer will always be >0. Sufficient. C
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Re: If xyz ≠ 0, is x(y + z) >= 0? [#permalink]
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26 Feb 2014, 20:03
hi, is it possible to get to final answer using the following approach?
xy + xz >= 0
if x>0, then y >= -z
if x<0, then y <= -z
is this hypothesis of any use or is it too detailed for this problem? just wondering b/c I usually solve these type of problems using this approach but I was stuck on this one even after 4 mins.
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Re: If xyz ≠ 0, is x(y + z) >= 0? [#permalink]
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26 Jun 2014, 04:50
What did I miss here? This was my first question I attempted to answer on this forum - looks like a great practice forum - but where / how do you see what the ABCDE multiple choice options are? I didn't see a drop down anywhere.... I think I missed something.....I tried to click on a letter to see the offered answer, but it selected it for me! Where do I view the possible answers assigned to the letters? Thanks in advance!
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Re: If xyz ≠ 0, is x(y + z) >= 0? [#permalink]
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26 Jun 2014, 07:21
jamielinderart wrote:
What did I miss here? This was my first question I attempted to answer on this forum - looks like a great practice forum - but where / how do you see what the ABCDE multiple choice options are? I didn't see a drop down anywhere.... I think I missed something.....I tried to click on a letter to see the offered answer, but it selected it for me! Where do I view the possible answers assigned to the letters? Thanks in advance!
This is a data sufficiency question. Options for DS questions are always the same.
The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
I suggest you to go through the following post ALL YOU NEED FOR QUANT.
Hope this helps.
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Re: If xyz ≠ 0, is x(y + z) >= 0? [#permalink]
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27 Apr 2015, 06:20
Easiest to attack this question without writing anything down.
Stem: if xyz does not equal 0 then you know neither of the variables can equal zero.
Solve: is x(y+z) >= 0?
St (1) tells us y and z have the same signs. Whether they are both negative or both positive. NS.
St(2) tells up x and y have the same signs. Whether they are both negative or both positive. NS.
St(1) & St(2) provide sufficient information to answer the question. pos *pos*pos >= 0. neg*neg*neg>=0. Suff
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Re: If xyz ≠ 0, x (y + z) ≥ 0? [#permalink]
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20 May 2015, 18:26
If xyz ≠ 0, x (y + z) ≥ 0?
(1) | y + z | = |y| + |z| insufficient as we do not know about x.
(2) | x + y | = |x| + |y|
insufficient as we do not know z.
Together We know x,y,z all will have same sign (- or +) .
So
x (y + z) ≥ 0
anyone knows why we need xyz ≠ 0?
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Re: If xyz ≠ 0, is x(y + z) >= 0? [#permalink]
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24 Jun 2019, 17:07
monirjewel wrote:
If xyz ≠ 0, is x(y + z) >= 0?
(1) |y + z| = |y| + |z|
(2) |x + y| = |x| + |y|
Are x & (y+z) same sign?
1) y & z are same sign (Using Property 1). No info about x. Not sufficient.
2) x & y are same sign (Using Property 1). No info about y. Not sufficient.
1+2) x & y & z are all same sign.
+ (+ + +) => +
- (- + -) => +
Sufficient
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Re: If xyz ≠ 0, is x(y + z) >= 0? [#permalink] 24 Jun 2019, 17:07
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https://stats.stackexchange.com/questions/285690/how-to-make-predictions-with-the-posterior-predictive-distribution | # How to make predictions with the posterior predictive distribution?
In the paper Deep Survival Analysis (Ranganath, 2016), the author specifies a generative model for deep survival analysis.
Say $\mathbf{x}$ denotes the set of covariates, $\mathbf{\beta}$ the parameters for the data with some prior $p(\mathbf{\beta})$, $k$ a fixed scalar, and $n$ be the index of an observation. The generative model is defined as
\begin{gather*} b \sim \mathcal{N}(0, \sigma_b)\\ a \sim \mathcal{N}(0, \sigma_W)\\ z_n \sim \text{DEF}(\mathbf{W})\\ \mathbf{x}_n \sim p(\cdot | \mathbf{\beta}, z_n)\\ t_n \sim Weibull(log(1+\exp(z_n^Ta+b)),k) \end{gather*}
The latent variable $z_i$ comes from a DEF which generates the observed covariates and the time to failure. Given covariates $\mathbf{x}$, the model makes predictions via the posterior predictive distribution:
\begin{gather*} p(t|\mathbf{x}) = \displaystyle\int_zp(t|z)p(z|\mathbf{x})dz. \end{gather*}
My question now is the following:
1. How can this specific posterior predictive distribution make these predictions computationally? Do you first generate your most probable latent variables $z_n$ given your data $\mathbf{x}$ and do you then try to find the most probable $t$, given your most probable latent variables $z_n$?
"Makes predictions" can mean a lot of things.
• You can make a point prediction, i.e., a single number summary.
• Or a point prediction plus some indication of uncertainty or variability.
• Or one or multiple quantile forecasts, e.g., to create a fan plot
• Or finally a full predictive density.
Of course, from each of these you can extract the ones mentioned before.
In your present case, I'd be surprised if there was some analytic way of calculating (any kind of) predictions. So I assume that the author simulated the entire model many times, which would give him a simulated posterior predictive density. This can then be used to extract quantiles, or the posterior mean forecast by taking the expectation.
Incidentally, I doubt one will be interested in the most probable posterior value, i.e. a maximum a posteriori (MAP) prediction, or the mode of the posterior predictive density. The mean of the density is a much more common point prediction. Of course, it all depends on what loss function you are trying to minimize with a one-number summary: the posterior mean will minimize squared loss (in expectation), whereas the posterior median will minimize expected absolute loss.
• So assuming that I want to make point predictions, I would do the following: 1) Select a number of rows, where I set the target variable $t$ to be missing, for these missing variables, the model will make an estimation. These observations are our so called test set. 2) Run the generative model via variational inference to estimate latent parameters $z_n$, regression parameters for $a$ and $b$ in the Weibull distribution. 3) Calculate the mean of the density for the observations where $t$ is missing, and take them as my point predictions. Would this procedure make any sense? – hendiadys Jun 20 '17 at 9:21
• That's the way I would go about it. (Assuming that the mean or expectation is the one-number summary you are interested in.) – Stephan Kolassa Jun 20 '17 at 14:27 | {"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": 0.9202262163162231, "perplexity": 649.2858870685341}, "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-2019-26/segments/1560627999003.64/warc/CC-MAIN-20190619163847-20190619185847-00307.warc.gz"} |
http://www.maa.org/programs/faculty-and-departments/course-communities/iterative-methods-for-solving-amathbfx-b | # Iterative Methods for Solving $$A\mathbf{x} = b$$
Module with 2 tutorials, with exercises and a Java applet, for iterative solution methods
Identifier:
http://faculty.pepperdine.edu/dstrong/Java/IterativeMethods/
Rating:
Creator(s):
David M. Strong
Cataloger:
David Strong
Publisher:
Pepperdine University
Rights:
David M. Strong
Format Other:
Java may need to be enabled in the Java Console
An applet for iterative solution methods (Jacobi, Gauss-Seidel, and SOR) is a rare find. The graphics can help one learn about the geometric features of these methods. It is unfortunate that the applet is limited to $$2\times2$$ systems. A version for higher systems (without the graphics) would be a nice addition. | {"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": 1, "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": 0.3291720151901245, "perplexity": 3033.9590042854616}, "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-2014-42/segments/1413507450767.7/warc/CC-MAIN-20141017005730-00080-ip-10-16-133-185.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/2735152/does-partition-of-unity-implies-second-countable/2735168 | # Does partition of unity implies second countable?
Reading the definition of partition of unity:
Let $A\subset \Bbb R^n$ and let $\mathcal{O}$ be an open cover of $A$. Then there is a collection $\Phi$ of $C^\infty$ functions $\varphi$ defined in an open set containing $A$, with the following properties:
1. For each $x \in A$ we have $0 \leq \varphi(x) \leq 1$.
2. For each $x \in A$ there is an open set $V$ containing $x$ such that all but finitely many $\varphi \in \Phi$ are $0$ on $V$.
3. For each $x \in A$ we have $\sum_{\varphi \in \Phi}\varphi(x)=1$ (by 2 for each $x$ their sum is finite in some open set containing $x$).
4. For each $\varphi \in \Phi$ there is an open set $U$ in $\mathcal{O}$ such that $\varphi = 0$ outside of some closed set contained in $U$.
Make me feel that implies second countable because of condition (2), but I am no quite sure if this hold.
There is a property called paracompactness stating that every open cover has an open locally finite refinement. So to a given open cover $\mathcal{U}$ there is a refining open cover $\mathcal{V}$ such that every point $x$ has a neighborhood $W$ that intersects only finitely many members of $\mathcal{V}$.
The existence of partition of unity is equivalent to paracompactness. And paracompactness does not imply second countability. Also, every metrizable space is paracompact. Note that second countability is a global property, but paracompactness and metrizability is not. Any topological sum of paracompact or metrizable spaces is paracompact or metrizable, but if you have uncountably many nontrivial summands, then the sum won't be second countable.
• As a specific example, the Sorgenfrey line (the real line under the lower limit topology, where open sets are $[a,b)$, $[a, \infty)$, or $(-\infty, b)$) is paracompact Hausdorff, but not second countable. – Fargle Apr 13 '18 at 9:03
Remark: If a topological space $$X$$ is connected and has a $$C^\infty$$ atlas, then:
$$X \text{ admits partitions of unity}\Leftrightarrow X \text{ is Hausdorff and second-countable}$$
The proof of $$(\Leftarrow)$$ can be found in any book about smooth manifolds (for example, in Lee's Introduction to Smooth Manifolds, theorem 2.23).
Here are an outline for $$(\Rightarrow)$$:
(a) Hausdorff: Let $$p,q\in X$$ be distinct. Take a partition of unity $$\{\varphi_U,\varphi_V\}$$ subordinate to the open cover $$\{U:=M-\{p\},V:=M-\{q\}\}$$. In that case, $$\varphi_U(p)=\varphi_V(q)=0$$ and $$\varphi_U(q)=\varphi_V(p)=1$$. The idea is to take small neighbourhood $$W_p$$ such that $$\varphi_U(x)$$ is close to $$0$$ and $$\varphi_V(x)$$ is close to $$1$$ for $$x\in W_p$$. Similarly, take a small $$W_q$$ at which $$\varphi_U(y)$$ is close to $$1$$ and $$\varphi_V(y)$$ is close to $$0$$ for $$y\in W_q$$. Then $$W_p,W_q$$ separate $$p,q$$.
(b) Second-countable: Discussed here.
• Your claim is not true, unless you also assume $X$ has at most countably many connected components. For example, a disjoint union of uncountably many copies of $\mathbb R$ admits partitions of unity, but is not second-countable. – Jack Lee Jan 20 at 16:30
• Thanks for that, @JackLee. I was implicitly assuming $X$ to be connected, but forgot to mention it. I'll correct it. – rmdmc89 Jan 20 at 23:32 | {"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": 24, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9376689195632935, "perplexity": 83.53463539124256}, "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-2019-43/segments/1570986692723.54/warc/CC-MAIN-20191019090937-20191019114437-00427.warc.gz"} |
https://cran.rstudio.com/web/packages/IDSpatialStats/vignettes/transdist.html | ## Introduction
When analysing the spatial dynamics of an epidemic, transmission from one individual to another is often characterized by the spatial distance separating two linked cases. Describing this fundamental aspect of the transmission process requires the a reconstruction of transmission pathways which link individual cases. However, this information is often unavailable or incomplete due to poor case detection and the high cost of contact-tracing. Therefore, we developed an approach that uses information on case location, onset time, pathogen generation time to estimate the mean spatial distance of transmission events. The method does not require data on individual transmission pathways and is robust in settings where data are partially observed.
This vignette describes how to use functions in the transdist family of the IDSpatialStats package. These functions allow the user to simulate spatial epidemic data and estimate the mean of the transmission kernel and its change over the duration of an epidemic. Derivation of the statistical methods employed by these functions are described in detail by Salje et al. [-@salje_estimating_2016]. The functions used in this vignette are implemented in IDSpatialStats versions 0.3.4 and above.
## Simulating epidemics
We use a stochastic spatial branching process to simulate epidemiological data in the sim.epidemic function. Simulations begin with an index case at $$(x,y,t) = (0,0,0)$$ and transmission events that link two cases follow according to a random Markov process in $$(x,y)$$ space (i.e. Brownian motion). The spatial distance traversed by each transmission event is given by a user specified probability distribution which serves as the kernel function. The number of branching events (i.e. when one individual transmits to $$>2$$ individuals) occurs according to a Poisson distribution, with its mean and variance set to the basic reproduction number $$R_0$$ of the infectining pathogen.
When specifying the spatial kernel, the trans.kern.func argument expects a list object containing a probability distribution function and its named arguments. For example, to simulate an epidemic where transmission typically occurs at the local level, but long distance transmissions events sometimes occur, an exponential transmission kernel might be used because of its long tail. Alternatively, if transmission is expected to consistently occur within a given range, then a normal kernel may be more appropriate.
set.seed(123)
# Exponential transmission kernel with mean = sd = 100
dist.func <- alist(n=1, a=1/100, rexp(n, a))
# Simulate epidemic with constant R value
a <- sim.epidemic(R=1.5,
gen.t.mean=7,
gen.t.sd=2,
min.cases=100,
tot.generations=10,
trans.kern.func=dist.func)
sim.plot(a)
In simulations with a constant $$R$$ value, the number of cases will continue to increase with each time step. This effect may not be appropriate when simulating settings where intervention efforts or depletion of susceptibles causes heterogeneity in $$R$$ over the course of the epidemic. Thus, the sim.epidemic function accepts either a scalar value for a constant $$R$$ value or a vector of $$R$$ values with a length equal to tot.generations, allowing simulations with a variable $$R$$ value.
# Simulate epidemic with variable R value
R1 <- 2
R2 <- 0.5
tg <- 12
R.vec <- seq(R1, R2, (R2 - R1)/(tg - 1))
a <- sim.epidemic(R=R.vec,
gen.t.mean=7,
gen.t.sd=2,
min.cases=100,
tot.generations=tg,
trans.kern.func=dist.func)
sim.plot(a)
## Estimation of mean transmission distance $$\mu_t$$
Our approach estimates the mean spatial distance traversed during a transmission event using information on the location $$(x, y)$$ and onset time $$t$$ of each case, and the infecting pathogen's generation time $$g(x)$$. Pathogen generation time is used to probabalistically estimate the number of transmission events required to link two cases, denoted as $$\theta$$. In settings where genetic data or contact tracing provide evidence for $$\theta$$, the mean transmission distance can be directly calculated as the mean observed distance between all linked case pairs occurring within two time points $$t_1$$ and $$t_2$$ to give $$\mu^{obs}_t(t_1, t_2)$$. However, this assumes the number of transmission events separating all case pairs is homogeneous ($$\theta = 1$$). When data that indicate case linkage is lacking, this assumption is limiting because the distance between two cases depends on the number of transmission events separating them. Therefore, the mean transmission distance at each time interval $$\mu_t$$ must be estimated as a weighted mean: $\mu_t(t_1,t_2,\mu_k,\sigma_k) = \sum_i w(\theta=i,t_1,t_2) \cdot \mu_a(\theta=i,\mu_k,\sigma_k).$ Where, $$w(\theta=i,t_1,t_2)$$ gives the weight for each of the $$i$$ elements of $$\theta$$ and the second term $$\mu_a(\theta=i,\mu_k,\sigma_k)$$ gives the mean distance separating case pairs that are linked by the $i$th value of $$\theta$$.
We have implemented four nested functions that are used to estimate $$w(\theta=i,t_1,t_2)$$. Listed in order, they are comprised of est.wt.matrix.weights, est.wt.matrix, get.transdist.theta, and est.transdist.theta.weights. Although, these functions are documented separately, they are all driven by the est.transdist family of functions and do not need to be run manually unless desired.
### Calculate Wallinga-Teunis matrices
The est.wt.matrix.weights function buids upon code from the R0 package [@R0_package_2015] to calculate the basic Wallinga-Teunis matrix [@wallinga_different_2004]. This matrix gives the probability that a case at time $$t_i$$ (rows) infects a case at time $$t_j$$ (columns), i.e. ($$\theta = 1$$), based on the generation time distribution of the pathogen $$g(x)$$. For an epidemic of with $$t$$ unique case times, est.wt.matrix.weights gives a $$t \times t$$ matrix.
case.times <- c(1,2,2,3,3)
g.x <- c(0, 2/3, 1/3, 0, 0) # must sum to 1
a <- est.wt.matrix.weights(case.times=case.times, gen.t.dist=g.x); a
The est.wt.matrix function produces a Wallinga-Teunis type matrix for all infector-infectee case pairs. Given the Wallinga-Teunis matrix produced by est.wt.matrix.weights and total case count $$n$$, this function calculates an $$n \times n$$ matrix giving the probability that case $$i$$ (rows) infected case $$j$$ (columns). The Wallinga-Teunis matrix in object a can be handed directly to est.wt.matrix via the basic.wt.weights argument, or if this argument is NULL, the est.wt.matrix.weights function is called automatically.
b <- est.wt.matrix(case.times=case.times, gen.t.dist=g.x, basic.wt.weights=a)
b <- est.wt.matrix(case.times=case.times, gen.t.dist=g.x); b # both are equivalent
### Estimation of weights of $$\theta$$
The get.transdist.theta estimates the number of transmission events $$\theta$$ separating pairs of cases using the probabilities in the infector-infectee Wallinga-Teunis matrix produced by the est.wt.matrix function. Sampling all possible transmission trees is impractical for most datasets, so this function constructs a transmisison tree by randomly selecting the infector of each case in the epidemic and then $$\theta$$ is determined by finding the product of all probabilites in the chain of transmission that link the randomly sampled case pairs.
gen.time <- 1
n.gen <- round((max(case.times) - min(case.times)) / gen.time) + 1 # Number of generations
c <- get.transdist.theta(wal.teun.mat=b,
cases=case.times,
gen.t.mean=gen.time,
max.sep=n.gen*2)
The object c here contains a three-dimensional array [$$i$$,$$j$$,$$\theta$$], where the rows $$i$$ and columns $$j$$ represent unique case times and the third dimension $$k$$ is the number of transmission events $$\theta$$. Each cell gives the probability that two cases occurring at times $$i$$ and $$j$$ are connected by $$\theta$$ transmission events in the randomly sampled transmission tree. Probabilities in each [$$i$$,$$j$$, ] row are normalized across all $$\theta$$ values. The get.transdist.theta function samples a single randomized transmission tree from the epidemic data, therefore we want to simulate many interations of this random sampling to get a better estimate of the true distribution of $$\theta$$.
The est.transdist.theta.weights function estimates the distribution of $$\theta$$ across all $$t_i$$ and $$t_j$$ combinations by simulating many iterations of transmission trees using the get.transdist.theta function. Its output is the same the get.transdist.theta function, however, it represnts the normalized probabilites after n.rep number of simulations.
d <- est.transdist.theta.weights(case.times=case.times,
n.rep=5,
gen.t.mean=gen.time,
t1=0,
t.density=g.x)
### Estimating mean of transmission kernel $$\mu_k$$
To estimate the overall mean of the transmission kernel over the duration of the epidemic we must combine all measures of $$\mu_t$$ into an overall measure $$\mu_k$$. The workhorse function est.trandsdist estimates the overall mean $$\mu_k$$ and standard deviation $$\sigma_k$$. This function first calls the est.wt.matrix.weights, est.wt.matrix, get.transdist.theta, and est.transdist.theta.weights functions described above to estimate the distribution of $$\theta$$ across all case pairs and then calculates each of the weights $$w(\theta=i,t_1,t_2)$$. The weights are calculated as the proportion of all case pairs occuring at $$t_i$$ and $$t_j$$ that are separated by each estimated $$\theta$$ over all simulations: $\hat{w}(\theta = i, t_1, t_2) = \frac{\sum^{N_{sim}}_{k=1} \sum^n_{i=1} \sum^n_{j=1} \boldsymbol{I}_1(t_i=t_1, t_j=t_2, \Theta_{ij} = \theta)} {N_{sim} \sum^n_{i=1} \sum^n_{j=1} \boldsymbol{I}_2(t_i=t_1, t_j=t_2)}.$ Here, the functions $$\boldsymbol{I}_1$$ and $$\boldsymbol{I}_2$$ indicate if two cases occurred at time $$t_i$$ and $$t_j$$ and were linked by $$\theta$$ transmission events, or if they just occurred at $$t_i$$ and $$t_j$$ respectively. In words this can be written as: $\hat{w}(\theta = i, t_1, t_2) = \frac{\text{Number of cases at} \,t_1\, \text{and} \,t_2\, \text{across all simulations separated by} \,\theta\, \text{transmission events}} {\text{Number of cases at} \,t_1\, \text{and} \,t_2\, \text{across all simulations}}.$
Once the weights of the $$\theta$$ values are estimated, the est.transdist function calculates the mean $$\mu_k$$ and standard deviation $$\sigma_k$$ as the average weighted estimate over all combinations of $$t_i$$ and $$t_j$$. If we now let $$k$$ index the vector of $$\theta$$ values, then: $\hat \mu_k = \hat \sigma_k = \frac{1}{\sum_i \sum_j n_{ij}} \sum_i \sum_j \frac{2 \cdot \mu^{obs}_t (t_i,t_j) \cdot n_{ij}}{\sum_k \hat w (\theta = k, t_i,t_j) \cdot \sqrt{2 \pi k}}.$ For a derivation of this equation from the mean squared dispersal distance, see section 2.3 of Salje et al. [-@salje_estimating_2016].
The est.trandist function requires the epidemiological data to be a matrix with three columns [$$x$$,$$y$$,$$t$$] and estimates of the mean and standard deviation of the infecting pathogen's generation time (for calculating Wallinga-Teunis matrices). Additional constraints on the estimation of $$\mu_k$$ and $$\sigma_k$$ can be defined in the remaining arguments, such as the time step in which the analysis should begin (t1), the maximum number of time steps (max.sep) and spatial distance (max.dist) to consider when estimating $$\theta$$, the number of randomized transmission tree simulations to run (n.transtree.reps).
set.seed(123)
dist.func <- alist(n=1, a=1/100, rexp(n, a))
# Simulate epidemic
a <- sim.epidemic(R=2,
gen.t.mean=7,
gen.t.sd=2,
min.cases=100,
tot.generations=8,
trans.kern.func=dist.func)
# Estimate mean and standara deviation of transmission kernel
b <- est.transdist(epi.data=a,
gen.t.mean=7,
gen.t.sd=2,
t1=0,
max.sep=1e10,
max.dist=1e10,
n.transtree.reps=10)
The output of the est.transdist function contains estimates of $$\mu_k$$ and $$\sigma_k$$ under the assumption that mean and standard deviation of the dispersal kernel are equal. If this expectation is not met, i.e. $$\mu_k \gg \sigma_k$$ or $$\mu_k \ll \sigma_k$$, the upper bounds for $$\mu_k$$ and $$\sigma_k$$ can be found by taking $$\sqrt 2$$ times the values estimated under the assumption of equality (see section 2.5 of Salje et al. [-@salje_estimating_2016]).
### Uncertainty around mean estimate
To estimate the uncertainty around $$\hat{\mu}_k$$ due to observation error, we have implemented a wrapper function called est.transdist.bootstrap.ci that performs bootstrap iterations using the est.transdist function. Upon each iteration, the epidemiological data are resampled with replacement and $$\mu_k$$ is re-estimated. The est.transdist.bootstrap.ci function contains all the same arguments as the est.transdist function, with additional arguments defining the number of bootsrapped iterations to perform, the high and low boundaries of the desired confidence interval, and options for running the bootstrap analysis in parallel.
b <- est.transdist.bootstrap.ci(epi.data=a,
gen.t.mean=7,
gen.t.sd=2,
t1=0,
max.sep=1e10,
max.dist=1e10,
n.transtree.reps=10,
boot.iter=10,
ci.low=0.025,
ci.high=0.975)
When parallel computation is enabled (the default is parallel = FALSE), the function uses the makeCluster() function of the parallel package to make the appropriate cluster type for the operating system of the local machine (SOCK cluster for Windows or a Fork cluster for Unix-like machines). The cluster is then registered as the parallel backend for the foreach package, which is used to run the bootstraps in parallel. If the the n.cores argument is NULL the function will automatically use half of the clusters available on the local machine. The user can also manually define the number of cores in the n.cores argument.
b <- est.transdist.bootstrap.ci(epi.data=a,
gen.t.mean=7,
gen.t.sd=2,
t1=0,
max.sep=1e10,
max.dist=1e10,
n.transtree.reps=10,
boot.iter=10,
ci.low=0.025,
ci.high=0.975,
parallel=TRUE,
n.cores=2)
### Change in mean transmission distance over time
An estimate of $$\mu_k$$ over the duration of an epidemic is indicative of the overall spatial dependence in the transmission process. However, conditions may change over the course of an epidemic that alter the spaital scale upon which transmission operates. The est.transdist.temporal function estimates the change in $$\mu_k$$ over time to quantify temporal heterogeneity in the spatial dependence of transmission. This function re-estimates $$\mu_k$$ for all cases leading up to each unique time step. Some time steps at the beginning of an epidemic may be returned as NA if there are not enough unique cases to estimate $$\mu_k$$ and/or its bootstrapped confidence intervals for a given time step. Note that this method uses the cumulative number of cases up to each unique time step to calculate the change in $$\mu_k$$ over time. So, estimates made for time steps early in the epidemic may be affected by sampling error due to low sample size.
# Estimate mean transmission kernel over time
b <- est.transdist.temporal(epi.data=a,
gen.t.mean=7,
gen.t.sd=2,
t1=0,
max.sep=1e10,
max.dist=1e10,
n.transtree.reps=5,
mean.equals.sd=TRUE,
parallel=FALSE)
plot(b[,1], pch=19, col='grey', ylim=c(min(b[,1], na.rm=TRUE), max(b[,1], na.rm=TRUE)),
xlab='Time step', ylab='Estimated mean of transmission kernel')
abline(h=100, col='red', lty=2)
axis(3, 1:nrow(b), b[,2])
low <- loess(b[,1] ~ as.vector(1:length(b[,1])))
low <- predict(low, newdata=data.frame(as.vector(1:length(b[,1]))))
lines(low, lwd=3, col='blue')
Bootstrapped confidence intervals for the change in $$\mu_k$$ over time can also be estimated using the est.transdist.temporal.bootstrap.ci function.
nc <- parallel::detectCores() # use all available cores
b <- est.transdist.temporal.bootstrap.ci(epi.data=a,
gen.t.mean=7,
gen.t.sd=2,
t1=0,
max.sep=1e10,
max.dist=1e10,
n.transtree.reps=10,
mean.equals.sd=TRUE,
boot.iter=10,
ci.low=0.025,
ci.high=0.975,
parallel=TRUE,
n.cores=nc)
plot(b[,1], pch=19, col='grey', ylim=c(min(b[,1:3], na.rm=TRUE), max(b[,1:3], na.rm=TRUE)),
xlab='Time step', ylab='Estimated mean of transmission kernel')
abline(h=100, col='red', lty=2)
axis(3, 1:nrow(b), b[,4])
low <- loess(b[,1] ~ as.vector(1:nrow(b)), span=1)
low <- predict(low, newdata=data.frame(as.vector(1:nrow(b))))
lines(low, lwd=3, col='blue')
for(i in 2:3) {
low <- loess(b[,i] ~ as.vector(1:nrow(b)), span=1)
low <- predict(low, newdata=data.frame(as.vector(1:nrow(b))))
lines(low, lty=2, lwd=3, col='blue')
}
### Caveats
The above examples are performed with toy simulations and function arguments chosen to expedite anaylses. In cases where the transmission kernel used in simulations has a long tail (i.e. exponential, gamma, log normal) and it is combined with a low R value, $$\mu_k$$ may be under- or over-estimated due to sampling error caused by low sample size. Increasing the number of times to repeat transmission tree simulations n.transtree.reps, or the number of bootstraps to perform boot.iter may provide better estimates of $$\mu_k$$ and its uncertainty, but this will also increase computation time, especially for large datasets.
## Application to foot-and-mouth disease
To provide an example of how the functions shown above can be applied to real data, we estimate the mean transmission distance for the 2001 foot-and-mouth epidemic among farms in Cumbria and Dumbfriesshire, UK. These data can be found in the fmd data object included in the sparr package [@sparr_package_2018]. It contains transformed ($$x$$,$$y$$) coordinates of the infected farms and the time step $$t$$ in which it was infected, which is given in days since the index farm was infected. The generation time for foot-and-mouth disease is estimated to have a mean of 6.1 days and a standard deviation of 4.6 days [@haydon_construction_2003], so we use these in the gen.t.mean and gen.t.sd arguments.
library(sparr)
data(fmd)
fmd <- cbind(fmd$cases$x, fmd$cases$y, fmd$cases$marks)
nc <- parallel::detectCores()
# Estimate transmission distance with bootstrapped confidence intervals
ci <- est.transdist.bootstrap.ci(epi.data=fmd,
gen.t.mean=6.1,
gen.t.sd=4.6,
t1=0,
max.sep=1e10,
max.dist=1e10,
n.transtree.reps=10,
boot.iter=10,
ci.low=0.025,
ci.high=0.975,
parallel=TRUE,
n.cores=nc)
# Change in transmission distance and its bootstrapped confidence intervals over time
tci <- est.transdist.temporal.bootstrap.ci(epi.data=fmd,
gen.t.mean=6.1,
gen.t.sd=4.6,
t1=0,
max.sep=1e10,
max.dist=1e10,
n.transtree.reps=10,
mean.equals.sd=FALSE,
boot.iter=10,
ci.low=0.025,
ci.high=0.975,
parallel=TRUE,
n.cores=nc) | {"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": 1, "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": 0.8016907572746277, "perplexity": 1330.1645504666785}, "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/1568514573465.18/warc/CC-MAIN-20190919081032-20190919103032-00057.warc.gz"} |
https://xaviergeerinck.com/2018/05/24/bellman-equations/ | # Bellman Equations
## Summary
So what did we learn up until now in our Introduction and Markov Property, Chain, Reward Process and Decision Process posts?
Initially we defined our basic concepts:
• State: What does our current environment look like?
• Action: What action are we taking?
• Policy: When taking action $a$ in state $s$, where do we go to?
Whereafter we introduced a concept of reward in our MRP
• Immediate Reward $Rt$: We want to steer our agent towards the action with the highest reward. Example: We want it to go forward on a cliff, and not fall off. This is given through the sum of our future rewards: $Rt = r{t + 1} + r{t + 2} + … + r_T$
• Discounted Reward $Gt$ To prevent us from constantly following the same path and reward, we add a discount factor that will reduce the reward over time. Written as: $Gt = R{t + 1} + γ R{t + 2} + γ^2R{t + 3} + … = \sum^{\infty}{k=0}γ^k R_{t+k+1}$
To this we also added probabilities due to the fact of it being described as an MDP and that nothing is certain.
• Transition Probability: What is the expected state to end up in after taking a certain action? $P{ss'}^a = P[S{t+1} = s' \mid St = s, At = a]$
• Reward Probability: What is the expected reward of ending up in a certain state after taking an action? $Rs^a = E[r{t+1} \mid St = s, At = a]$
So that we were finally able to write 2 new functions that allow us to interpret our expected value of a certain state.
• State-Value Function: Value when we follow policy $\pi$ forever starting from our state $s$ given by $V^{\pi}(s) = \mathbb{E}_{\pi}[G_t \mid s_t = s] = \mathbb{E}_{\pi}[\sum^{\infty}_{k=0}γ^kr_{t+k+1} \mid s_t=s]$
• Action-Value Function: Value when we follow policy $\pi$ after taking action $a$ on our state $s$ given by $Q{\pi}(s, a) = \mathbb{E}_{\pi}[Gt \mid s_t = s, a_t = a] = \mathbb{E}_{\pi}[\sum^{\infty}_{k=0}γ^kr_{t+k+1} \mid s_t=s,a_t=a]$
Now we know that, how are we able to create some kind of algorithm that allows us to find a path through our states, taking specific actions, that will eventually lead to the highest return. Knowing that our states do not depend on each other? (See MDP). Or in math terms, how can we find our optimal policy $\pi^*$ which maximizes the return in every state?.
For this, let us introduce something called Bellman Equations.
## Bellman Equations
### Introduction
As written in the book by Sutton and Barto, the Bellman equation is an approach towards solving the term of "optimal control". Which is done through the creation of a functional equation that describes the problem of designing a controller to minimize a measure of a dynamical system's behavior over time.. This approach of Bellman utilizes the concepts of a state and a value function as we saw before.
Note: A value function we could also write as the "optimal return function"
Afterwards, this class of methods for solving these optimal control problems came to be known as dynamic programming.
Dynamic Programming: is a method for solving a complex problem by breaking it down into a collection of simpler subproblems, solving each of those subproblems just once, and storing their solutions.
To know if we can solve a problem through the use of Dynamic Programming, we can take a look at the Principle of Optimality which was also created by Richard E. Bellman.
Principle of Optimality: An optimal policy has the property that whatever the initial state and initial decision are, the remaining decision must constitute an optimal policy with regard to the state resulting from the fist decision.
### Bellman Equation - State-Value Function $V^\pi(s)$
So what the Bellman function will actually does, is that it will allow us to write an equation that will represent our State-Value Function $V^\pi(s)$ as a recursive relationship between the value of a state and the value of its successor states.
\begin{aligned} V^\pi(s) =& \mathbb{E}{\pi}[Gt | St = s] \ =& \mathbb{E}{\pi}[r{t+1} + \gamma G{T+1} | St = s] \ =& \sum{a} \pi(a | s) \sum{s', r} P(s' , r | s, a)[ r + \gamma \mathbb{E}{\pi}[G{t + 1} | S{t + 1} = s] ] \ =& \sum{a} \pi(a | s) \sum{s', r} P(s' , r | s, a)[ r + \gamma v_{\pi}(s') ], \forall s \in S \end{aligned}
Note: We do not go into detail here on how it works or to derive it, for more details about that, feel free to read the paper.
If we now want to find the best value function $V^$, then that means that we need to find: $V^(s) = max{\pi}V^{\pi}(s)$ or in terms of our last equation: $V^(s) = max{a} \sum_{s', r} P(s' , r | s, a)[ r + \gamma V^{}(s') ]$ which is our Bellman Optimality Equation
### Bellman Equation - Action-Value Function $Q^\pi(s,a)$
For the Action-Value Function we follow the same intuition as in the State-Value one, but here including the action. Eventually leading us to this equation:
\begin{aligned} Q^\pi(s, a) =& \mathbb{E}{\pi}[Gt | St = s, At = a] \ =& \sum{a} \pi(a | s) \sum{s', r} P(s' , r | s, a)[ r + \gamma v_{\pi}(s') ] \end{aligned}
Which leads to our Bellman Optimality Equation: $Q^(s, a) =\sum{s', r} P(s' , r | s, a)[ r + \gamma max{a'} Q^(s', a') ]$
## Solving
In the next article, we will talk about some algorithms that will allow us to solve something called a "GridWorld" later on. | {"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": 1, "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": 0.7459810376167297, "perplexity": 658.2551972713391}, "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/1674764499801.40/warc/CC-MAIN-20230130034805-20230130064805-00848.warc.gz"} |
https://www.usna.edu/Users/cs/roche/courses/f12si413/u05/index.html | Unit 5: Semantic Analysis
This is the archived website of SI 413 from the Fall 2012 semester. Feel free to browse around; you may also find more recent offerings at my teaching page.
• Programming Language Pragmatics (PLP), Chapter 4 intro, 4.1, 4.3 (especially the paragraph on "Building a Syntax Tree"), and 4.6.
• PLP, All of chapter 4
• Code from these notes:
• Slides: note-taking version
• Homework for this unit: HW 7
# 1 The problems with parse trees
The starter code for today's class is a "beefed-up" calculator language that includes things like assignment and comparison. Here's the grammar (bison style):
run: stmt run
| stmt
stmt: ares STOP
ares: VAR ASN bres
| bres
bres: res
| bres BOP res
res: exp
| res COMP exp
exp: exp OPA term
| term
term: term OPM factor
| factor
factor: NUM
| LP bres RP
| VAR
And here's a simple program in this language:
x := (5 + 3) * 2;
x > 3 - 7;
Now check out the parse tree for that "simple" program:
That's pretty messy. We saw in lab how the grammar can be simplified somewhat to help shrink down the waste, but that only goes so far. As you know from implementing some simple interpreters in your lab, all this complication in the grammar directly affects the speed of interpreting (or compiling) programs in the language. When programs get really big, and we want to compile them really quickly, this becomes an issue.
An even more critical issue can arise when the syntax of our grammar doesn't match the desired semantics of the language. For example, the natural way to make an operator be left-associative is to write the grammar using left recursion. But, as you know, left recursion doesn't work with top-down parsers. So we rewrite the grammar to be right-recursive (using all those tail rules). This makes the parsing go faster, and is fine if you are writing the parser and interpreter together (like in your lab from last week). But if the program gets more complicated, we will notice quickly that the parse tree that results from this top-down grammar with tail rules is essentially right-associative rather than left. In other words, the parse tree (syntax) doesn't match the semantic meaning of the program. What can we do about this?
# 2 Abstract Syntax Trees (ASTs)
Abstract Syntax Trees (ASTs) provide a way of representing the semantic meaning of our program in a simple way that is independent of the actual syntax. This is a little confusing, so I'll emphasize again that the AST has nothing to do with the syntax - it's an abstraction away from the syntax of the language! Here's an example of the AST for the same example from before:
x := (5 + 3) * 2;
x > 3 - 7;
The first thing you should notice is that this is a lot simpler than the previous parse tree. This AST represents the actual meaning of our small program - what that program is actually supposed to do.
Notice how the arithmetic operations like times and greater-than are represented. The operation goes up top (or any function call, for that matter), and the arguments go below it, in order.
The top three nodes (assign, print, and null) are a bit different - they are statements rather than expressions. Remember from way back when that an expression is a code fragment that returns or computes some value, whereas a statement doesn't return any value; rather, a statement does something. These statements are ordered, and we represent that ordering by a child relationship: the last child of a statement is the next statement in sequence. Of course the special "null" statement indicates that this sequence ends.
You should also observe that this AST is simpler in most respects than the preceding parse tree, but it also has some new things that the parse tree didn't. For example, in the program above, it's implicit that an expression should be printed out if it's not part of an assignment. The AST makes this explicit.
One more thing to make sure you notice: the AST does not depend on a single programming language. For example, I bet you could write the Scheme program or the C++ program corresponding to the AST above pretty easily. Moreover, a Scheme program that does exactly the same thing could generate exactly the same AST as a program in another language! Of course, the specific components of some language will affect what's in the AST (for example, no lambdas in our calculator language), but the point is that the AST doesn't depend on any syntactical choices of the language - only on the meaning of the program.
# 3 Static type checking
Assume booleans are a "real" type in your language (i.e., they're not just integers like in C), and you have a program like (7 > 2) + 3. This is an error because 7 > 2 is a boolean, and you can't add a boolean to a number. Specifically, it's a type error, because the problem is that the types of the two operands for the plus operator are "incompatible", meaning basically that they can't be added together.
When we talk about compilation, a lot of things are divided between "static" or "dynamic". This sometimes means different things in different context, but usually it's:
• Static means something is computed or known at compile-time, before actually executing the program.
• Dynamic means something is computed or known only at run-time, as the program executes.
Generally speaking, the more we can do statically (at compile-time), the faster everything is. Here we're specifically talking about catching type errors, and this is always a nice thing to do at compile-time if we can. Why? Well, maybe this type error is buried somewhere deep in the user's code. Maybe the program does some big, long, difficult computation, and then at the very end, just as it's about to display the brilliant result, it gets a type error and crashes. What a tragedy! If we had compile-time (static) type checking, that wouldn't happen, because that error would have been noticed by the compiler before the program ever started running.
The AST is created at compile-time, just after the parsing phase. So any type-checking we do with the AST will be static-time checking. For a simple expression like (7 > 2) + 3, the process is pretty simple: starting at the leaves, we label every node in the AST with its type. Whenever there's an operation like > or +, we check that the types of the arguments are compatible, and then label the node with the type of whatever results. In this case, the > node gets labeled as a boolean, and of course 3 is a number, so when we go to label the + node, we see that these are incompatible and give an error. (By the way, the statement nodes like "assign" and "print" just have type void.)
Hooray! Errors are a good thing - they save the programmer time and help assure that the actual program (with no errors) works as intended. But static type checking gets a lot more complicated when we have variables. Look back up at the AST for this program above:
x := (5 + 3) * 2;
x > 3 - 7;
To do the type-checking here, we would need to know the type of x in the second statement, in order to check that it's actually a number and therefore compatible with 3 - 7 in the > operation. Of course you can wee that, yes, x is going to be a number here. But how would the compiler know? In order to do this kind of type checking, we would need static typing, which means that the types of every variable are known at compile-time. For example, Java has static typing; that's why you have to declare the types of all your variables! Scheme, on the other hand, is not statically typed.
But before we can really talk about static typing, we have to answer the more fundamental question of what does a variable refer to, at any given point in the program. This means we need to know about things like scope. Which is what the next unit's all about! | {"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": 0.32464170455932617, "perplexity": 951.0454877863124}, "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-2018-09/segments/1518891815318.53/warc/CC-MAIN-20180224033332-20180224053332-00486.warc.gz"} |
http://eprint.iacr.org/2012/382 | ## Cryptology ePrint Archive: Report 2012/382
On the Joint Security of Signature and Encryption Schemes under Randomness Reuse: Efficiency and Security Amplification
Afonso Arriaga and Manuel Barbosa and Pooya Farshim
Abstract: We extend the work of Bellare, Boldyreva and Staddon on the systematic analysis of randomness reuse to construct multi-recipient encryption schemes to the case where randomness is reused across different cryptographic primitives. We find that through the additional binding introduced through randomness reuse, one can actually obtain a security amplification with respect to the standard black-box compositions, and achieve a stronger level of security. We introduce stronger notions of security for encryption and signatures, where challenge messages can depend in a restricted way on the random coins used in encryption, and show that two variants of the KEM/DEM paradigm give rise to encryption schemes that meet this enhanced notion of security. We obtain a very efficient signcryption scheme that is secure against insider attackers without random oracles.
Category / Keywords: public-key cryptography / Randomness reuse, Signcryption, Insider Security.
Publication Info: Full version of the paper published at ACNS 2012.
Date: received 8 Jul 2012, last revised 8 Jul 2012
Contact author: mbb at di uminho pt
Available format(s): PDF | BibTeX Citation
Short URL: ia.cr/2012/382
[ Cryptology ePrint archive ] | {"extraction_info": {"found_math": false, "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": 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": 0.8110095858573914, "perplexity": 7211.4082144952645}, "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-2016-07/segments/1454701146600.56/warc/CC-MAIN-20160205193906-00221-ip-10-236-182-209.ec2.internal.warc.gz"} |
http://clay6.com/qa/15529/the-condition-for-the-coaxial-system-x-2-y-2-2-lambda-x-c-0-where-lambda-is | Browse Questions
# The condition for the coaxial system $x^2+y^2+2 \lambda x +c=0,$ where $\lambda$ is a parameter and c is a constant to have distinct limiting points, is
$\begin {array} {1 1} (a)\;c=0 & \quad (b)\;c < 0 \\ (c)\;c=-1 & \quad (d)\; c > 0 \end {array}$
(d) c > 0 is the correct answer.
edited Jan 20, 2014 by meena.p | {"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": 0.8632944226264954, "perplexity": 1164.019456887806}, "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-2017-04/segments/1484560281202.94/warc/CC-MAIN-20170116095121-00058-ip-10-171-10-70.ec2.internal.warc.gz"} |
http://mathematica.stackexchange.com/questions/36861/suspend-spacing-between-repeated-and-number | # Suspend spacing between Repeated and number
The spacing of the first expression includes extra space before the 5. I would like to have the same spacing as the second line.
HoldForm[4 .. 5]
HoldForm[a .. b]
Is there a way to suspend Mathematica's spacing, perhaps with a StyleBox?
-
## 1 Answer
the extra space you see is due to multiplication
SetOptions[EvaluationNotebook[],
NumberMultiplier -> "\[NegativeThinSpace]"]
- | {"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": 0.9858299493789673, "perplexity": 3225.3077214088557}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "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-2015-11/segments/1424936468536.58/warc/CC-MAIN-20150226074108-00065-ip-10-28-5-156.ec2.internal.warc.gz"} |
https://electronics.stackexchange.com/questions/146520/digitally-controlled-audio-fader-circuit/266555 | # Digitally controlled audio fader circuit?
I have two audio signals and I want to fade in one signal in just as the other signal fades out and repeat the process backwards and so on... I want to control the circuit using some digital means or voltage control, however the actual circuit should be analog. Any suggestion for an affordable solution?
Or you can use digital pot chips like AD5242 series dual I2C digital pots, coupled with some op amps.
Here is a reference design for you:
simulate this circuit – Schematic created using CircuitLab
The two pots there is the digital pot chip AD5242BRUZ10 commanded by the Arduino. You can program the Arduino to handle MIDI interface and plug this into your professional audio system rack.
OPA4134 is a proper audio grade op amp but it is expensive. You can experiment with orders of magnitude cheaper but pin compatible LM324, or get rid of the two voltage followers and use the cheaper OPA134 audio op amp that is pin compatible with 741.
TL431 is a 2.5V reference chip used as a virtual ground here.
• There's no zero crossover detection in this circuit so isn't there a click in the audio whenever you change the volume? – PkP Jan 4 '15 at 23:39
• @PkP I have a virtual ground voltage at 2.5V so if you reference the signal to that point you have no zero crossing issue at all. – Maxthon Chan Jan 5 '15 at 1:43
Using light to control the 'fades'/volume of each channel by using a LED and photoresistor(s). You can simply control the LED with an Arduino. Because of the LED is driven by PWM, you need to change the PWM frequency. See also example at my answer (and the reason why).
I made some drafts/examples at my question, my question is about if there is component that combines the two. There is, called vectrols but they are very expensive. You can make your own, it's cheap! More info and pictures at my question and answer.
Changed and simplified schematic:
More info at my question: Digital Optical Volume Control with LED and photoresistor (light to seperate circuits, optical pot)
Use a digital signal processor (DSP). Convert both inputs from analog to digital, multiply them with values ranging from 0 to 1, sum them together and feed to the DAC.
You can also use digital volume control ICs, such as CS3310 (http://www.cirrus.com/en/products/cs3310.html) but a DSP might even be cheaper in the end. Depends on the number of channels and what kind of ICs you can find.
• I was looking for an analog approach here - analog circuit with digital control. I have a very basic 8bit MCU in the system and I would like to keep it that way. – user34920 Jan 4 '15 at 13:24
• @user: The point is a small DSP will be smaller, simpler, and quite possibly cheaper if you have it do all the digital stuff, compared to adding analog fading to a smaller processor. – Olin Lathrop Jan 4 '15 at 14:15
• @OlinLathrop - Can you direct me to a solution that would be under $3 and won't require investing in development tools or software? – user34920 Jan 4 '15 at 14:24 • @user: Low end DSPs for uder$3 are certainly available. You already have a processor in there, so you gain a little more budget by replacing it with the DSP and having the DSP perform the existing processor's function too. As far as firmware development, that's part of engineering just about any meaningful electronic product. You are already doing it anyway. Doing it in a upgraded processor instead doesn't change that much. – Olin Lathrop Jan 4 '15 at 14:28
• @OlinLathrop - Can you give me just a single example? – user34920 Jan 4 '15 at 14:41 | {"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": 0.23980078101158142, "perplexity": 1785.9389100013275}, "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-2019-26/segments/1560627999948.3/warc/CC-MAIN-20190625213113-20190625235113-00089.warc.gz"} |
https://www.physicsforums.com/threads/complex-polynomial-theorem.24209/ | # Complex Polynomial Theorem
1. May 5, 2004
### Ed Quanta
Can someone help me prove this?
Where f(z) is a complex polynomial of degree n, and g(z) is a complex polynomial of degree n-1, and f(q)=0, I can't seem to prove
f(z)=(z-q)g(z)
I have substitituted for each of the polynomials and distributed out the z and q terms, but I am unsure how to manipulate this equation. Help anyone?
I am at the point so far where I have
anz^n + an-1z^n-1 +...+a1z+a0= bn-1z^n +bn-2z^n-1+...b1z^2+b0z-q(bn-1z^n-1+bn-2z^n-2+...b0)
But unable to manipulate this further.
2. May 5, 2004
### fourier jr
I think this is a standard theorem (or a variation of one) that you can find in any textbook on abstract algebra or polynomials. It isn't really a complex analysis problem.
3. May 5, 2004
### HallsofIvy
Staff Emeritus
The first thing you should do is state the theorem clearly. The way you put it, it could be interpreted as saying that "If f(z) is any nth order polynomial such that f(q)= 0 and g(z) is any n-1 order polynomial then f(z)= (z-q)g(z)" and that, of course, is not true.
The theorem you want says that "If f(z) is any nth order polynomial such that f(q)= 0 then THERE EXIST an n-1 order polynomial g such that f(z)= (z-a)g(z)". To do that, first use the "Euclidean Algorithm" to prove that, for any function f(z), over the complex numbers and any complex number q, There exist a function g(z) and a constant a such that f(z)= (z-a)q(z)+ a.
4. May 5, 2004
### Ed Quanta
Thanks for your reply. I am just not sure how to apply the Euclidan algorithm to something other than numbers. Since f(q) or f(a) as you call it equals zero, can we say that a divides f(z)?
5. May 6, 2004
### HallsofIvy
Staff Emeritus
The Euclidean algorithm, in it's simplest form, says that if a and b are any two numbers, then there exist two number Q and r such that
b= aQ+ r where (absolute value of) r is less than (absolute value of) a.
That is essentially "division". Q is the quotient of b divided by a and r is the remainder.
However, it is also true for polynomials: If a and b are any polynomials, then there exist polynomials Q and r such that b= aQ+ r and the degree of r is less than the degree of a.
In particular, if a= x-q so that it has degree 1, then r must have degree 0 and so is a constant (a number).
Also, in this example, b= f(z), a= (z-q) so f(z)= (z-q)Q(z)+ r and f(q)= 0*Q(z)+ r= 0 so r must equal 0.
6. Jul 23, 2004
### mathwonk
I am delighted that you are studying this question. This is an old high school algebra theorem formerly called the "root - factor" theorem. I.e. if f(x) is a polynomial (could be with real or rational or even integral coefficients) then q is a root of f (i.e. f(q) = 0), if and only if x-q is a factor of f(x).
This is very basic to all algebraic manipulations used throughout mathematics, but I have essentially never had a single student in 25 years of teaching college who knew this principle, although it was taught in all high school algebra courses in the 1950's.
As Halls of Ivy explained it follows just by dividing f(x) by x-q and noticing that you can keep dividing until the remainder is a constant r. Then you have f(x) = (x-q)g(x) +r, for some polynomial g(x), whose degree must be one less than deg(f). Then if you plug in x=q you will see that f(q) = r. Hence f(q) = 0 if and only if the remainder r after division by x-q was zero, if and only if x-q divided f(x) evenly.
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https://www.itwissen.info/en/speed-of-light-c-114890.html | # speed of light (c)
The speed of light (c) is a primary physical constant for the propagation speed of light and electromagnetic waves.
The speed of light (c0) is exactly 299,792.458 km/s in a vacuum. In calculations, 300,000 km/s is used. In denser media such as metals or glass, this speed is reduced to the signal propagation time "c". This is calculated from the shortening factor, the Nominal Velocity of Propagation( NVP), which is multiplied by the speed of light.
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Englisch: speed of light - c Updated at: 24.03.2019 #Words: 76 Links: light, constant, indium (In), media, signal Translations: DE Sharing: | {"extraction_info": {"found_math": false, "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": 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": 0.8830475807189941, "perplexity": 2333.1786732551286}, "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-2022-21/segments/1652662525507.54/warc/CC-MAIN-20220519042059-20220519072059-00371.warc.gz"} |