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Becker muscular dystrophy (BMD) is a disease that causes the muscles to deteriorate. It is one of several muscular dystrophies, which are genetic (or inherited) diseases of the voluntary muscles or the muscles used to move parts of the body. Although BMD may affect all of the voluntary muscles, patients tend to maintain the function of the smooth, or involuntary muscles, such as those of the bladder and bowel. BMD is caused by a mutation, or defect, in the DMD gene. This gene provides instructions for making the protein known as dystrophin. This protein helps to keep muscle cells intact, and proper levels of dystrophin are critical for muscle function. People with BMD are deficient in dystrophin; the dystrophin may be produced in low quantities or produced in a form that does not function properly. BMD may affect all races and ethnicities. However, it primarily affects males and occurs in about one in 30,000 male births. BMD is similar to a more common disease called Duchenne muscular dystrophy (DMD), which affects about one in 3,500 male births. Both conditions are caused by mutations in the DMD gene and both tend to affect more males than females. However, the mutations in the DMD gene are slightly different in each disease. Furthermore, the symptoms of BMD tend to be milder, more variable, typically occur later in life, and they progress more slowly than DMD. Onset of BMD is generally in adolescence or adulthood. Symptoms usually appear around 10 years of age, but can occur between the ages of two and 21. The disease progresses slowly and may vary from patient to patient but all voluntary muscles may be affected, especially those of the hips, pelvis, thighs, and shoulders. Muscle shrinking tends to be more severe in the lower body. By the age of 30, the muscle degeneration in BMD becomes so severe that most patients cannot walk. As the muscles of the heart are affected by the disease, heart problems occur between age 20 and 40. Patients with BMD usually die of heart failure. In BMD, the average age of death is 42 years. Although there is no known cure for BMD, many treatments are available to improve symptoms and maximize quality of life. With proper treatment, many individuals with BMD survive well into mid or late adulthood and have normal life expectancies. Because Becker muscular dystrophy (BMD) is an inherited disorder, risk factors include having a family history of the disease. BMD is a recessive inherited genetic condition. Normal individuals have two copies of most genes (one inherited from the father and one from the mother). In a recessive genetic disorder, both copies of a certain gene need to be defective for the condition to manifest itself. It has been shown that mutations in the dystrophin gene, which is located on the X chromosome, may cause BMD. Females have two copies of the X chromosome, but males have one X chromosome and one Y chromosome. Males inherit an X chromosome from the mother and a Y chromosome from the father, so a male can only inherit the dystrophin gene from the mother. Daughters inheriting the defective gene will be carriers while sons inheriting the gene will have BMD. General: Becker muscular dystrophy (BMD) is caused by a defect, or mutation, in the DMD gene, which provides the instructions for making a protein called dystrophin. The mutation prevents the full-length protein from being produced. This protein normally helps maintain the structure and function of muscle cells. Individuals with BMD have lower than normal levels of this protein, so it cannot function fully. Although the reasons are not clearly understood, muscle cells lacking dystrophin eventually die. Inheritance: Because Becker muscular dystrophy (BMD) is an inherited disorder, risk factors include having a family history of the disease. BMD is a recessive inherited genetic condition. Normal individuals have two copies of most genes (one inherited from the father and one from the mother). In a recessive inherited disorder, both copies of a certain gene need to be defective for the condition to occur. Mutations in the dystrophin gene DMD may cause BMD. This gene is located on the X chromosome, which is one of the sex chromosomes. Females have two X chromosomes, while males have an X and a Y chromosome. If a female has one copy of the defective gene, the second X chromosome with a working copy of the gene can compensate. This is why women with the condition tend to experience milder symptoms. If a male has one copy of the defective gene, there is no other copy to compensate, which is why males experience more severe symptoms. Interestingly, males cannot pass on a defective X chromosome in X-linked recessive conditions. A female who has a mutant DMD gene on one X chromosome has a 50% risk of passing the mutant gene to a son. Therefore, if the mother has one mutated gene, each son will have a 50% chance of being affected with BMD. Males who have a mutant DMD gene on their X chromosome are affected by BMD. However, they are not at risk for passing the mutation to their sons. Therefore, BMD is a condition that is genetically inherited by individuals from their mother. On the other hand, a male with BMD may pass the defective clotting factor gene to his daughters. Because males only pass X chromosomes to their daughters, each daughter of a male with BMD will carry one defective DMD gene. Random occurrence: About 30% of known cases of males with BMD do not have the genetic mutation or defect associated with the disease. This may occur because of a mutation in the egg or developing embryo. SIGNS AND SYMPTOMS General: Becker muscular dystrophy (BMD) is a disease that causes the muscles to deteriorate. It is a disease of the voluntary muscles, which are the muscles used to move parts of the body. Although BMD may affect all of the voluntary muscles, patients tend to maintain the function of the smooth or involuntary muscles, such as those of the bladder and bowel. The most common symptoms of the muscle breakdown that BMD patients experience are weakness and fatigue. By the age of 30, the muscle degeneration in BMD becomes so severe that most patients cannot walk. Cognitive dysfunction: Some but not all patients with BMD have some degree of cognitive dysfunction. Researchers believe that cognitive dysfunction seen in BMD is caused by the defective dystrophin gene. Studies have found that the frequencies of learning disabilities, behavioral problems, and autism are higher among individuals with BMD than among the general population. These conditions do not appear to worsen with time. Although little is known about the incidence of intellectual disabilities in BMD, it is estimated that about one-third of patients with Duchenne muscular dystrophy have some cognitive disabilities. Lack of coordination: BMD may affect the development of motor skills during childhood. Children with BMD may take longer than other children to learn to crawl or walk. Children with BMD also tend to be clumsy and may walk unsteadily, fall often, and have difficulty getting up from the floor. Heart disorders: While muscular weakness is typically the first sign of BMD, some cases of the disease are not diagnosed until the patient develops a heart condition known as dilated cardiomyopathy. In dilated cardiomyopathy, the heart is not able to pump blood efficiently. Symptoms may include irregular heart beat, fatigue, and shortness of breath. Muscular disorders: Muscle weakness in BMD progresses slowly. Over time, this leads to difficulty walking and frequent falls among those with BMD. Most patients with BMD are unable to walk unassisted by age 30. Muscle damage tends to be more severe in the lower body. Among the muscles that are most affected by the disease are those of the hips, pelvis, thighs, and shoulders. Muscles in the arms, neck, and other areas are also affected in BMD. Early in the progression of the disease, the muscles in the calves may grow larger. This is a form of compensation known as pseudohypertrophy that is temporary as the muscle is eventually replaced with cartilage and fatty tissue. To compensate for weakening muscles, a person in the early stages of BMD may walk with a "waddling" gait, walk in his or her toes, or stick out the abdomen while walking. The Gower sign, in which a person needs to "walk up" his or her body with the hands in order to assume a standing position, is commonly seen in BMD. While this sign is not specific to BMD, it does indicate weakness in the hip muscles. Contracture, which is shortening of the muscles in a way that restricts mobility and movement, is another common muscular symptom of BMD. Contractures may be seen in the elbows, heels, and legs. Respiratory problems: People with BMD may develop breathing problems as a result of wasting of the muscles that control inhaling and exhaling. In the early stages of breathing problems, symptoms may include headaches, difficulty concentrating, difficulty staying awake, and nightmares. Skeletal disorders: People with BMD may have skeletal conditions in the chest and back. Scoliosis, or curvature of the spine, is often seen in patients with BMD. This is generally due to the weakening of the muscles that support the spine. TYPES OF THE DISEASE Becker muscular dystrophy (BMD) is one of several muscular dystrophies, which are genetic (or inherited) diseases of the voluntary muscles, or the muscles used to move parts of the body. While much variation among individuals with Becker muscular dystrophy has been observed, there are no specified different types of the disease. General: Symptoms of Becker muscular dystrophy (BMD) are typically apparent by 11 years of age but may appear between the ages of two and 21. BMD is generally suspected when a patient experiences muscle weakness and continues to become weaker. Because BMD is an inherited disorder, a family history of the disease may indicate performing a complete physical exam. The clinician will ask about muscle weakness, fatigue, clumsiness, and falls. He or she will perform tests to determine whether the source of muscular weakness is from the muscles themselves or from the nerves that control them. Because BMD is less severe than Duchenne muscular dystrophy, neck muscle strength is often maintained for a longer period of time. This may help a clinician to distinguish between the two diseases. Biopsy: A biopsy is the surgical removal of a small piece of tissue for examination. For BMD, the sample is generally taken from the thigh muscle. A laboratory technician can determine whether dystrophin is present in the muscle cells and in what amount. Blood tests: Tests that measure an enzyme called creatine kinase (CK, also known as creatine phosphokinase or CPK) in the blood can be used to identify muscle defects. CK is an enzyme that helps carry out a chemical reaction on creatine, a substance used by muscle for energy. Because CK may leak out of damaged muscle cells, the CK levels rise in the blood in patients with BMD. CK levels may also rise due to other factors, such as a heart attack or normal exercise. Therefore, the serum CK test may not be able to diagnose a patient specifically with BMD because other diseases that affect the muscles, as well as normal exercise, also result in increased levels of serum CK. A blood test may also measure the level of transaminases in the blood. Transaminases are enzymes that allow amino acids to be broken down. High levels of transaminases are usually associated with liver disease. However, a high level of transaminases may also be due to the breakdown of muscle tissue, such as in BMD. Electrocardiogram: An electrocardiogram (ECG or EKG) observes and records the electrical waves that cause the heart muscles to pump. When performing this test, the clinician will be looking especially for cardiomyopathy, a type of heart disease in which the heart doesn't work effectively. Electromyogram: An electromyogram measures electrical impulses in muscle tissue. These tend to be diminished in BMD. Genetic testing: Genetic testing looks specifically for mutations in the dystrophin gene. There are advanced methods of genetic testing available, including direct genomic sequence analysis. Imaging: X-rays may be done on the spine to diagnose the severity and follow the progress of scoliosis. This is particularly important during adolescence when the development of scoliosis typically occurs. However, scoliosis is not specific to BMD. Pulmonary function: Pulmonary function tests may be done to determine how effectively the individual is breathing and whether the muscles that control breathing are being affected. Poor results from pulmonary functions tests may indicate that the muscles that cause an individual to inhale and exhale are being affected by BMD. General: General complications of Becker muscular dystrophy (BMD) are largely due to muscle degeneration. Complications may include progressive disability, decreased mobility, decreased ability to care for one's self, and deformities. Cognitive: People with BMD may have some cognitive impairment, including learning disabilities. These tend to fall into three categories: attention focusing, verbal learning and memory, and emotional interaction. Researchers believe that cognitive dysfunction seen in BMD is caused by the defective dystrophin gene. Developmental: BMD may affect the development of motor skills during childhood. Gastrointestinal: As people with BMD lose muscle mass and tone, the digestive system may be affected. Complications that may arise include dysphagia, which includes swallowing problems and the risk for entry of foods or liquids into the lungs (pulmonary aspiration), and constipation. Heart: Dilated cardiomyopathy is a common complication of BMD in which the heart cannot pump blood effectively. In this condition, the muscles of the heart become weakened or the heart may become enlarged. If left untreated, cardiomyopathy may become serious or even fatal. Muscles: Muscular complications of BMD may include joint contractures in which joints lose mobility and flexibility because the muscles, tendons, and ligaments become shortened and/or stiffened. Contractures most often affect the knees, hands, feet, elbows, wrists, and fingers. If not treated, contractures may become severe. Other complications may include muscle cramps. Respiratory: The degeneration of muscle mass in BMD affects the diaphragm and other muscles that control breathing. This can lead to several breathing problems, including pneumonia and respiratory failure. In the early stages of breathing problems, symptoms may include headaches, difficulty concentrating, difficulty staying awake, and nightmares. Decreased respiratory function also increases the risk of infection. Skeletal: People with BMD may develop skeletal abnormalities such as scoliosis, in which the spine curves to the side, or lordosis, in which the spine curves forward creating a swayback. This is generally due to the weakening of the muscles that support the spine. Other: Individuals with BMD are at an increased risk of malignant hyperthermia with the use of certain anesthetics. In this condition, an anesthetic, which is given to dull pain and to partially paralyze a person during surgery, causes muscles to become rigid and to break down. Additional symptoms include high fever, increased heart rate, and increased levels of acid in the body's tissues. There is no known cure for Becker muscular dystrophy (BMD). The goal of treatment is to improve symptoms and maximize quality of life. Assistive devices: As BMD progresses and the individual loses mobility, assistive devices such as braces, standing frames, walkers, and wheelchairs may be needed. Braces on the lower legs may also help to lengthen the muscles and prevent contractures, which are shortenings of the muscle fibers that limit range of motion and prevent mobility. A brace may be prescribed for wear at night to keep the foot from pointing downward and to keep the Achilles tendon stretched while the individual is sleeping. Other devices that may be helpful include a transfer board for helping the individual move in and out of the wheelchair, mechanical lifts, shower chairs, and adjustable beds. Diet: While there are no known specific dietary prescriptions or restrictions for people with BMD, dietary approaches to manage constipation may be needed. The diet should therefore be high in fluid and fiber as well as fruits, vegetables, and whole grains. When mobility is limited, calorie needs decrease. Being overweight or obese may worsen the complications of BMD. Therefore, it is important that an individual eat a diet that helps to maintain a healthy weight. Occupational therapy: Occupational therapy aims to improve function in specific activities and functions, such as aspects of self care, driving, and using a computer. Pain relief: In most cases, BMD symptoms and complications do not cause pain. However, in some cases, patients may find muscle cramps painful and can find relief with over-the-counter pain relievers. Physical activity: Swimming and water exercises may help individuals with BMD to keep muscles strong and toned without causing stress. Exercise should not be to the point of exhaustion. Physical therapy: Because inactivity may worsen the condition of the muscles in BMD, activity is encouraged. The goals of physical therapy are to allow greater motion in the joints and to maintain muscle strength and tone. Physical therapy may also help to prevent, delay, or improve shortening of the muscle fibers known as contractures, and curvature of the spine known as scoliosis. Range-of-motion exercises, performed regularly, may also help to delay contracture. Exercises can be done to help correct spinal curvature or scoliosis. Psychological support: Because the stress of a degenerative disease can be difficult, psychotherapy or a support group may be helpful for patients and families with BMD. Muscular dystrophy support groups, for example, provide a forum in which members can share experiences and problems. Individuals with learning disabilities can also be evaluated by a mental health professional. Special exercises and educational therapies may be prescribed. Respiratory support: If breathing problems become severe, respiratory assistance may be needed. A special mask worn while sleeping can deliver positive airway pressure. As breathing deteriorates, a cough assistance device can help the patient to cough and to keep the lungs clear. Speech therapy: If speech and swallowing are affected by muscle wasting of BMD, a speech therapist may be helpful. Recommendations may include avoiding certain food textures and eating or drinking positions. Surgery: Once contractures have set in, surgery may be the only option available to relieve them. A tendon release procedure, also known as a heel cord surgery, is often done to treat ankle and other contractures while the individual is still walking. After this surgery, a patient will often need lower leg braces. In severe scoliosis, surgery may be necessary. In this procedure, a metal rod with hooks is placed into the spine. Transplantation: In cases of severe cardiomyopathy, a type of heart disease in which the heart is not able to pump blood efficiently, a heart transplant may be considered. Note: Currently, there is insufficient evidence available on the safety and effectiveness of integrative therapies for the prevention or treatment of Becker muscular dystrophy (BMD). The integrative therapies listed below should be used only under the supervision of a qualified healthcare provider and should not be used in replacement of other proven therapies or preventive measures. Good scientific evidence: Vitamin D: Vitamin D deficiency has been associated with muscle weakness and pain in both adults and children. Limited research has reported vitamin D deficiency in patients with low back pain, and supplementation may lead to pain reduction in many patients. Avoid if allergic or hypersensitive to vitamin D or any of its components. Vitamin D is generally well-tolerated in recommended doses. Doses higher than recommended may cause toxic effects. Individuals with hyperparathyroidism (overactive thyroid), kidney disease, sarcoidosis, tuberculosis, or histoplasmosis are at a higher risk of experiencing toxic effects. Vitamin D is generally considered safe for pregnant women. It may be necessary to give infants vitamin D supplements along with breast milk. The recommended intake of vitamin D for normal infants, children, and adolescents is 200 International Units (IU) daily. Unclear or conflicting scientific evidence: Coenzyme Q10: Coenzyme Q10 (CoQ10) is produced by the human body and is necessary for the basic functioning of cells. CoQ10 levels are reported to decrease with age and to be low in patients with some chronic diseases such as muscular dystrophies. Early studies in patients with muscular dystrophy taking CoQ10 supplements describe improvements in exercise capacity, heart function, and overall quality of life. Additional research is needed in this area. Avoid in patients with allergy or hypersensitivity to CoQ10. Although few side effects have been associated with CoQ10, there have been reports of nausea, stomach upset, or rash. Caution is advised in people who have bleeding disorders or who are taking drugs that increase the risk of bleeding. Caution is advised in patients with diabetes or hypoglycemia and in those taking drugs, herbs, or supplements that affect blood sugar. Use cautiously in patients with liver disease, as large doses of CoQ10 (greater than 300mg per day) may elevate aminotransferase levels. Use cautiously in patients with biliary obstruction or liver disease as these conditions may increase CoQ10 concentrations. CoQ10 may decrease blood pressure and caution is advised in patients with low blood pressure or taking blood pressure medications. Elevations of liver enzymes have been reported rarely, and caution is advised in people with liver disease or taking medications that may harm the liver. CoQ10 may lower blood levels of cholesterol or triglycerides. Based on limited human evidence, thyroid hormone levels may be altered. There is not enough scientific evidence to support the use of CoQ10 during pregnancy or breastfeeding. Creatine: Creatine is naturally synthesized in the human body from amino acids primarily in the kidney and liver and transported in the blood for use by muscles. Creatine loss is suspected to cause muscle weakness and breakdown in Duchenne muscular dystrophy, a condition that is related to BMD. Further research of creatine supplementation for muscular dystrophy is needed before a recommendation can be made. Avoid in patients with allergy or hypersensitivity to creatine. Use of creatine supplements has been associated with symptoms of asthma. There have been rare reports of loss of appetite, stomach upset, diarrhea, or nausea with creatine use. Avoid in patients with liver or kidney disease. Use cautiously in patients with diabetes or low blood sugar. Creatine may cause muscle cramps or muscle breakdown, leading to muscle tears or discomfort. Weight gain and increased body mass may occur. Heat intolerance, fever, dehydration, reduced blood volume, or electrolyte imbalances (and resulting seizures) may occur. Chronic administration of a large quantity of creatine is reported to increase the production of formaldehyde, which may potentially cause serious unwanted side effects. Creatine may increase the risk of compartment syndrome of the lower leg, a condition characterized by pain in the lower leg associated with inflammation and ischemia (diminished blood flow), which is a potential surgical emergency. Creatine cannot be recommended during pregnancy or breastfeeding due to a lack of safety information. Fair negative scientific evidence: Selenium: Early studies suggest that selenium supplementation is not helpful in muscular dystrophy. Avoid if allergic or sensitive to products containing selenium. Avoid with a history of nonmelanoma skin cancer. Selenium is generally regarded as safe for pregnant or breastfeeding women. However, animal research reports that large doses of selenium may lead to birth defects. There are currently no known methods of preventing Becker muscular dystrophy (BMD). If there is a family history of BMD, genetic counseling may help the family understand the risks of having a child with BMD. Genetic testing can determine whether an individual is a carrier of BMD. Because men with BMD may become fathers, it is important to know what inherited disease an individual has (Duchenne muscular dystrophy or BMD). Sisters of people with BMD may also be tested for carrier status. Because fathers only pass X chromosomes to their daughters, all daughters of a father with BMD will have at least one mutated X chromosome. This information has been edited and peer-reviewed by contributors to the Natural Standard Research Collaboration (www.naturalstandard.com). - American Academy of Pediatrics Section on Cardiology and Cardiac Surgery. Cardiovascular health supervision for individuals affected by Duchenne or Becker muscular dystrophy. Pediatrics. 2006;116(6):1569-73. View abstract - Hoogerwaard EM, Ginjaar IB, Bakker E, et al. Dystrophin analysis in carriers of Duchenne and Becker muscular dystrophy. Neurology. 2005;65(12):1984-6. View abstract - Duan D. Myodys, a full-length dystrophin plasmid vector for Duchenne and Becker muscular dystrophy gene therapy. Curr Opin Mol Ther. 2008;10(1):86-94. View abstract - Holloway SM, Wilcox DE, Wilcox A, et al. Life expectancy and death from cardiomyopathy amongst carriers of Duchenne and Becker muscular dystrophy in Scotland. Heart. 2007; View abstract - Hoogerwaard EM, Ginjaar IB, Bakker E, et al. Dystrophin analysis in carriers of Duchenne and Becker muscular dystrophy. Neurology. 2005;65(12):1984-6. View abstract - Kesari A, Pirra LN, Bremadesam L, et al. Integrated DNA, cDNA, and protein studies in Becker muscular dystrophy show high exception to the reading frame rule. Hum Mutat. 2008; View abstract - Li Q, Li SY, Hu DG, et al. Prenatal molecular diagnosis of Duchenne and Becker muscular dystrophy. Beijing Da Xue Bao. 2006;38(1):53-6. View abstract - MDA. Muscular Dystrophy Association. www.mda.org. Accessed March 27, 2008. - Miura P, Jasmin BJ. Utrophin upregulation for treating Duchenne or Becker muscular dystrophy: how close are we? Trands Mol Med. 2006;12(3):122-9. View abstract - Natural Standard: The Authority on Integrative Medicine. www.naturalstandard.com. Copyright © 2008. - Petrie CJ, Mark PB, Dargie HJ. Cardiomyopathy in Becker muscular dystrophy: does regional fibrosis mimic infarction? J Cardiovasc Magn Reson. 2005;7(5):82305. View abstract - Skura CL, Fowler EG, Wetzel GT, et al. Albuterol increases lean body mass in ambulatory boys with Duchenne or Becker muscular dystrophy. Neurology. 2008;70(2):137-43. View abstract - Stockley TL, Akber S, Bulgin N, et al. Strategy for comprehensive molecular testing for Duchenne and Becker muscular dystrophies. Genet Test. 2006;10(4):229-43. View abstract - Takagi A, Nakase H. Malignant hyperthermia-like reactions in Duchenne or Becker muscular dystrophy: review and hypothesis. Rinsho Shinkeigaku. 2008;48(2):101-5. View abstract - Young HK, Barton BA, Waisbren S, et al. Cognitive and psychological profile of males with Becker muscular dystrophy. J Child Neurol. 2008;23(2):155-62. View abstract Copyright © 2011 Natural Standard (www.naturalstandard.com)
Quantitative research methods are designed to collect numerical data that help measure variables. It is structured and statistical with objective and conclusive results. It uses a grounded theory method that relies on data collection that is systematically analyzed. Quantitative research is a methodology to use when you need to draw concise conclusions from your research and make predictions of the results. Qualitative research is a methodology designed to collect non-numerical data to gain insights. It is non-statistical and semi or completely unstructured. Qualitative data collects information that seeks to seek in-depth information on the topic rather than just measuring its worth numerically. This type of research measures opinions, views, and attributes versus hard numbers that would be presented in a graph or a chart. Qualitative researchers seek to delve deeper into the topic of the study to gain information on general perceptions and attitudes. Data analysis is broad, exploratory, and downright complex, and when you simplify it, it boils down to two methodologies: Qualitative and quantitative data. The differences between qualitative and quantitative research are: Qualitative research is a method of inquiry that study the way society and people think and feel. Quantitative research is a method of scientific and empirical approach that uses more statistical and objective techniques. Qualitative research follows a subjective approach whereas the approach of quantitative research is objective, as the researcher is uninvolved and attempts to precise the observations and analysis on the topic to answer the inquiry. Qualitative research is exploratory while quantitative research is conclusive. The reasoning used to synthesize data in qualitative is inductive but the reasoning in quantitative research is deductive. Elements in the analysis of qualitative research are words, pictures, and objects while those in quantitative research are numerical and statistical data. Qualitative research is holistic in nature while quantitative research is particularistic. In essence, qualitative research develops the initial understanding, and quantitative research schedules a final course of action. Qualitative research is conducted with the aim of exploring and discovering ideas in the ensuing process, while the purpose of quantitative research is to examine the cause and effect relationship between variables. The methods used in qualitative research are in-depth interviews, focus groups, etc whereas the methods of quantitative research consist of structured interviews and observations. Formulating hypotheses: Qualitative research helps you gather intricacies and details of a particular study, which you can to initially being your research with. Those ideas can become hypotheses to be proven through quantitative research. Validating hypotheses: Quantitative research will give numbers that can statistically be analyzed to validate the hypotheses. Was there a mass opinion or was it a subjective perception or attitude? The hard facts obtained will help objectively make decisions for the target audience as a whole. Objectives In Market Research B2C market research While B2C market research usually uses quantitative methods, the use of a fresh product or service facilitates the use of a qualitative methodology. A quantitative approach requires that the respondent has the knowledge or experience to answer the questions asked in the questionnaire. In the case of a new product or concept, however, it is hard to quantify sophisticated consumption perceptions without a proper glimpse of understanding of its structure. With qualitative methodology, it observes new and untainted responses and reactions, collects both verbal and socially cued impressions. This helps understand the responses in-depth, enough to hopefully quantify it later on. B2B market research In B2B research, professionals are harder to catch hold off for quantitative research methodologies like surveys, one-on-one interviews, etc. For this reason, it is often more efficacious to conduct qualitative interviews for in-depth insight and reduce wastage of resources and time on comparatively superficial data. There are many versatile approaches to both quantitative and qualitative data. A market research method that employs researchers to study how consumers behave in market conditions under different sets of variables and non-variables. Guided or semi-structured techniques that investigate the consumer’s response to a product or brand. 3. Focus groups A group of 6 – 12 consumers gathered in an online or offline space based on their predetermined criteria to identify their perceptions and behavior about market demand and supply. A series of semi-structured questions that investigated customer inclinations, reviews, requirements, characteristics, or expectations. Secondary research employs information that has already been compiled by other entities. Qualitative methods: Qualitative research may be carried out in a number of ways based on the nature and context of the study. These options give researchers the opportunity to remain flexible while collecting and interpreting data. Some common approaches are ethnography, action research, phenomenological research narrative inquiry, and grounded theory. Quantitative Methods: Multiple techniques of statistical research are vital in conducting quantitative market research. Some of the most common and widely used forms are descriptive research, correlational research, and quasi-experimental research. Data Analysis And Interpretation Qualitative Data Interpretation Qualitative data analysis is mainly categorical. Data here is not described through numerical values or patterns, but through instead with descriptive context. Traditionally, narrative data is gathered by conducting a variety of techniques like: Observations: These are mainly behavioral patterns that occur within observational groups. Documents: Different types of documentation resources can be coded and divided based on the material contained. Interviews: One of the most popular forms of narrative methodologies, the interview approach allows for high-focused data segregation. Quantitative Data Interpretation If quantitative data interpretation could be described in one word, it would be numerical. There is rarely anything guaranteed in data analysis due to the subjectivism on how to go about versatile methodologies, but one thing guaranteed is that quantitative research is all about numbers and statistics. Quantitative analysis refers to a set of processes by which numerical data is analyzed. More often than not, it involves the use of statistical modeling such as standard deviation, mean and median. The most common statistical terms are: It represents a numerical average for a set of responses. When dealing with singular or multiple data sets, the mean represents a central value of a specific segment of numbers. It is the sum of the values divided by the number of values within the data set. Other similar terms used are average and arithmetic mean. Another statistical term commonly appearing in quantitative analysis is the standard deviation. It reveals the distribution of the responses around the mean and describes the degree of consistency within the responses. This is a measurement gauging the rate of a response in a data set. When using a survey, for example, frequency distribution has the capability of determining the number of times a specific ordinal scale response appears. Typically, quantitative data is measured by visually presenting correlation tests between two or more variables of significance. Different processes can be used interchangeably and comparisons can be made to ultimately arrive at a consensus. Other signature interpretation processes of quantitative data include Regression analysis, cohort analysis, and predictive and prescriptive analysis. The term “mixed methods” refers to an emergent methodology of research that advances the systematic integration of quantitative and qualitative data within a single investigation or sustained program of inquiry. The basic premise of this methodology is that such integration permits a more complete and synergistic utilization of data than do separate quantitative and qualitative data collection and analysis. Thus for better optimization, we should take the best of both worlds of qualitative and quantitative research.
Interpreting algebraic expressions write algebraic expressions for each of the following: a nmultiply by 5 then add 4 b add 4 to n then multiply by 5. An algebraic expression is a mathematical expression that consists of variables, numbers and operations the value of this expression can change the value of this expression can change exercises. • algebraic expression is formed from variables and constants using different operations expressions are used to write word problems in math terms. Write the words for and read aloud the math expressions in the bingo game again, this time read each using a variety of words which indicate the appropriate operation for example the second expression could be read. Example 2 writing algebraic expressions exercises 3-18 section 12 writing expressions 13 write the phrase as an expression then evaluate when x = 5 and y = 20. Writing algebraic expressions objective: be able to write an algebraic expression for a word phrase or write a word phrase for an expression notes in order to translate a word phrase into an algebraic expression, we must first know some key word phrases for the basic operations. Get your first taste of algebraic expressions with this introduction page your student will practice translating written phrases into algebraic equations. Write the algebraic expressions from the sentences these pre algebra worksheets have the answers on the 2nd page of the pdf read the sentences and determine how to write the algebraic expression or equations. Section 11 evaluating algebraic expressions 3 use what you learned about evaluating expressions to complete exercises 4 -7 on page 6 work with a partner use the strategy shown in example 1 to write an. Writing algebraic expressions - chapter summary once 3rd grade students have been exposed to the basics of algebra, including variables and combining like terms, in addition to the commutative. Name and evaluate algebraic expressions learn with flashcards, games, and more — for free. Students will practice writing algebraic expressions this engaging math game will help students grasp basic algebra skills in this interactive math lesson, students will accomplish the following tasks. Introduction: write the following expression: five plus two chances are you were able to turn this phrase into [math]5 + 2[/math] in algebra, you will be asked to do the same however, one or more of the terms will have an unknown quantity to write the unknown, you will need to use a variable a. Variable and verbal expressions date_____ period____ write each as an algebraic expression 1) the difference of 10 and 5 2) the quotient of 14 and 7. Evaluating expressions using algebra calculator learn how to use the algebra calculator to evaluate expressions example problem evaluate the expression 2x for x=3. Write an algebraic expression to represent each verbal expression the product of 12 and the sum of a number and negative 3 $16:(5 write a verbal sentence to represent each. Algebra 1 - basics worksheets writing variables expressions worksheets this algebra 1 - basics worksheet will create word problems for the students to translate into an algebraic statement. Learn how to write expressions with variables to describe situations described in word problems practice this lesson yourself on khanacademyorg right now:. Learning how to simplify algebraic expressions is a key part of mastering basic algebra and an extremely valuable tool for all mathematicians to have under their belt simplification allows a mathematician to change a complex, long, and/or awkward expression into a simpler or more convenient one that's equivalent. Write an algebraic expression to represent this phrase: 3 times a number, t the phrase is 3 times a number, t use a number, an operation sign, or a variable to represent each part of that phrase. Practice writing variable addition, subtraction, multiplication and division sentences to represent a word problem. Section p3 algebraic expressions 25 algebraic expressions a basic characteristic of algebra is the use of letters (or combinations of letters) to represent numbers. - write simple algebraic expressions by interpreting math phrases - recognize the concept of variables and use them in a math expression - understand easy word problems and write math expressions (or equations) to represent them. Algebra is a language that uses letters, symbols, and numbers to express relationships in order to write algebraic expressions it helps to know the key words and their algebraic definition. Write each of the following words on the board and ask students to read them and tell you what they think they are: variable, constant, coefficient, term, algebraic expression write the students' definition or example on the board. Shmoop's free basic algebra guide has all the explanations, examples, and exercises you've been craving algebraic expressions we usually don't write 1 as a. Simplifying algebraic expressions is the same idea, except you have variables (or letters) in your expression basically, you're turning a long expression into something you can easily make sense of basically, you're turning a long expression into something you can easily make sense of. The worksheets in this page provide practice to students on translating phrases into algebraic expressions like linear expressions, single & multiple variable expressions, equations and inequalities this will help the students to translate real-life problems into algebraic expressions and find a solution in an easier way. Writing algebraic expressions often requires more than typing the simple numbers and letters found on your keyboard what about exponents, radicals, mathematical characters or. Learn how to write simple algebraic expressions practice: writing expressions with variables writing expressions with variables & parentheses next tutorial.
3 class periods of 45 minutes each Students will determine the relationship between the angle of the sun and the length of shadow it projects. Students will understand how the tilt of Earth causes this angle change, and affects temperatures in certain regions and thus causes seasons. Background for Teachers Notes to Teacher: Each data collection should be recorded at the same time of day. The longer you collect data, the clearer the pattern will be to your students. Plan to avoid a daylight savings change but if you can chart the sun over a solstice (Dec. 22 most likely) this would be very instructive. Student Prior Knowledge Students should understand the angle of isolation and solar radiation. It would be helpful to complete the "Angle of Insolation" lab before you begin this lab. - Assemble needed supplies. - Run off enough copies of the student sheets for all participating students. - Hook: When students arrive in class have them all follow you outside. Have students stand in a single file line so each person can see his or her shadow. (Do this without telling them why they are facing the direction they are.) Direct students attention to their shadows. Ask for several volunteers to explain what they think will happen to their shadow as the day progresses. Take as many responses as you get. Come to a class consensus. Hopefully students should realize that their shadow will get shorter as noon approaches and longer past noon. Bring students back to the classroom. - Ask if anyone knows how your shadow might change throughout the year. Take any responses. Tell the students they will be collecting data on shadow length for the next few weeks to answer this question. - Pass out the student sheets. Allow students to read through the background information in their labs. - Review with students what the angle of insolation means. - Have students read through the lab procedures and make their predictions. - Allow students to 10 minutes once a week to collect data. - Provide time for students to answer questions when data collection is complete. - Discuss questions. Answers to Analysis Questions: - The angle of sunlight gets larger as summer approaches. - Warmer because the solar radiation is more direct, it is not scattered as it would be at a smaller angle. - This marks a turning of the seasons, the days become shorter because the sun is not as high in the sky. The smaller the angle the cooler the temperatures will become as the radiation begins to scatter more and more as the winter solstice approaches. - The suns angle changes because the earth is tilted on its axis. As it rotates around the sun sometimes the northern hemisphere is tilted towards the sun and at other times the southern hemisphere is tilted towards the sun. - When a hemisphere is tilted towards the sun the angle of insolation is greater because the sun is higher in the sky. The will cause a warm season. When the hemisphere is tilted away the opposite occurs. This is the cause of the seasons, seasons are a part of the climate of an area because they affect long term weather patterns. - The earths distance from the sun at various points in its rotation is irrelevant. The seasons are caused by the tilt of the earth affecting the angle of insolation. The earth is actually closer to the sun in the winter. - Not significantly. This means there are no significant seasonal changes. The climate remains the same throughout the year. - Rate of change should be consistent between all students (within reason). The rate of change would be greater the further you are from the equator, with the greatest change at the poles. Answers will vary but should be detailed and relevant. Students should also use complete sentences. Sample Grading Rubric: Lesson Design by Jordan School District Teachers and Staff.
In the molecular dance that gave birth to life on Earth, RNA appears to be a central player. But the origins of the molecule, which can store genetic information as DNA does and speed chemical reactions as proteins do, remain a mystery. Now, a team of researchers has shown for the first time that a set of simple starting materials, which were likely present on early Earth, can produce all four of RNAâs chemical building blocks. Those building blocksâcytosine, uracil, adenine, and guanineâhave previously been re-created in the lab from other starting materials. In 2009, chemists led by John Sutherland at the University of Cambridge in the United Kingdom devised a set of five compounds likely present on early Earth that could give rise to cytosine and uracil, collectively known as pyrimidines. Then, 2 years ago, researchers led by Thomas Carell, a chemist at Ludwig Maximilian University in Munich, Germany, reported that his team had an equally easy way to form adenine and guanine, the building blocks known as purines. But the two sets of chemical reactions were different. No one knew how the conditions for making both pairs of building blocks could have occurred in the same place at the same time. Now, Carell says he may have the answer. On Tuesday, at the Origins of Life Workshop here, he reported that he and his colleagues have come up with a simple set of reactions that could have given rise to all four RNA bases. Dividing Droplets Could Explain Origin of Life Researchers have discovered that simple “chemically active” droplets grow to the size of cells and spontaneously divide, suggesting they might have evolved into the first living cells. Ingredients regarded as crucial for the origin of life on Earth have been discovered at the comet that ESA’s Rosetta spacecraft has been probing for almost two years. They include the amino acid glycine, which is commonly found in proteins, and phosphorus, a key component of DNA and cell membranes. Scientists have long debated the important possibility that water and organic molecules were brought by asteroids and comets to the young Earth after it cooled following its formation, providing some of the key building blocks for the emergence of life. While some comets and asteroids are already known to have water with a composition like that of Earth’s oceans, Rosetta found a significant difference at its comet – fuelling the debate on their role in the origin of Earth’s water. But new results reveal that comets nevertheless had the potential to deliver ingredients critical to establish life as we know it. Rosetta’s comet contains ingredients for life Amino acids are biologically important organic compounds containing carbon, oxygen, hydrogen and nitrogen, and form the basis of proteins. Hints of the simplest amino acid, glycine, were found in samples returned to Earth in 2006 from Comet Wild-2 by NASA’s Stardust mission. However, possible terrestrial contamination of the dust samples made the analysis extremely difficult. Now, Rosetta has made direct, repeated detections of glycine in the fuzzy atmosphere or ‘coma’ of its comet. (...) How can life originate from a lifeless chemical soup? This question has puzzled scientists since Darwin's 'Origin of species'. University of Groningen chemistry professor Sijbren Otto studies 'chemical evolution' to see if self-organization and autocatalysis will provide the answer. His research group previously developed self-replicating molecules—molecules that can make copies of themselves—and have now observed diversification in replicator mutants. They found that if you start with one ancestral set of replicator mutants, a second set will branch off spontaneously. This means that ecological diversity as encountered in biology may well have its roots at the molecular level. The results were published on Jan. 4, 2016, in Nature Chemistry. Life must have started at some point, but how remains a mystery. Charles Darwin himself speculated in a letter to Joseph Hooker in 1871: 'But if (and oh what a big if) we could conceive in some warm little pond with all sorts of ammonia and phosphoric salts,—light, heat, electricity & c. present, that a protein compound was chemically formed, ready to undergo still more complex changes, at the present day such matter wd be instantly devoured, or absorbed, which would not have been the case before living creatures were formed.' It is impossible to know how life on Earth really started, but that doesn't stop scientists from trying to find out how it could have started. This is not just a matter of curiosity. The processes involved include autocatalysis (where molecules promote the formation of copies of themselves) and self-organization (where molecules spontaneously organize themselves into higher-order structures) which are important concepts in such fields as materials science. Otto has been working on chemical evolution for several years now. 'It started with a chance discovery', he explains. 'We found some small peptides that could arrange themselves into rings, which could then form stacks.' Once a stack began to form, it would continue to grow and would then multiply by breaking into two smaller stacks. These would both grow and break again, and so on. The stacks also stimulated the formation of the rings from which they are composed. The stacks and rings are called 'replicators', as they are able to make copies of themselves. Jan Sadownik, a postdoc in the Otto group, discovered that if you offer the replicators two different types (A and B) of building blocks ('food') they will make copies of themselves. He observed the emergence of a set of replicator mutants that specialized in food A, but also incorporated some B. The rings mainly comprised the A building blocks, with just a few B's. Some days later Sadownik saw a second set of mutants emerge that specialized in food B, but also tolerated some A. This second set proved to be a descendant of the first set, which meant there was an ancestral relationship between the sets. This is very similar to how new species form from existing ones during biological evolution, except that this process of species formation does not involve full-fledged biological organisms, but occurs instead at the molecular level. (...) (...) After the first touchdown at Agilkia, the gas-sniffing instruments Ptolemy and COSAC analyzed samples entering the lander and determined the chemical composition of the comet’s gas and dust, important tracers of the raw materials present in the early solar system. COSAC analyzed samples entering tubes at the bottom of the lander kicked up during the first touchdown, dominated by the volatile ingredients of ice-poor dust grains. This revealed a suite of 16 organic compounds comprising numerous carbon and nitrogen-rich compounds, including four compounds — methyl isocyanate, acetone, propionaldehyde and acetamide — that have never before been detected in comets. Meanwhile, Ptolemy sampled ambient gas entering tubes at the top of the lander and detected the main components of coma gases — water vapour, carbon monoxide, and carbon dioxide, along with smaller amounts of carbon-bearing organic compounds, including formaldehyde. Importantly, some of these compounds detected by Ptolemy and COSAC play a key role in the prebiotic synthesis of amino acids, sugars, and nucleobases — the ingredients for life. For example, formaldehyde is implicated in the formation of ribose, which ultimately features in molecules like DNA. The existence of such complex molecules in a comet, a relic of the early solar system, imply that chemical processes at work during that time could have played a key role in fostering the formation of prebiotic material. (...) How Structure Arose in the Primordial Soup Life’s first epoch saw incredible advances — cells, metabolism and DNA, to name a few. Researchers are resurrecting ancient proteins to illuminate the biological dark ages. Mimicking natural evolution in a test tube, scientists at The Scripps Research Institute (TSRI) have devised an enzyme with a unique property that might have been crucial to the origin of life on Earth. Aside from illuminating one possible path for life's beginnings, the achievement is likely to yield a powerful tool for evolving new and useful molecules. "When I start to tell people about this, they sometimes wonder if we're merely suggesting the possibility of such an enzyme—but no, we actually made it," said Gerald F. Joyce, professor in TSRI's Departments of Chemistry and Cell and Molecular Biology and director of the Genomics Institute of the Novartis Research Foundation. Joyce was the senior author of the new report, which was published online ahead of print by the journal Nature on October 29, 2014. The Challenge of Making Copies The new enzyme is called a ribozyme because it is made from ribonucleic acid (RNA). Modern DNA-based life forms appear to have evolved from a simpler "RNA world," and many scientists suspect that RNA molecules with enzymatic properties were Earth's first self-replicators. The new ribozyme works essentially in that way. It helps knit together a "copy" strand of RNA, using an original RNA strand as a reference or "template." However, it doesn't make a copy of a molecule completely identical to itself. Instead it makes a copy of a mirror image of itself—like the left hand to its right—and, in turn, that "left-hand" ribozyme can help make copies of the original. No one has ever made such "cross-chiral" enzymes before. The emergence of such enzymes in a primordial RNA world—which the new study shows was plausible—could have overcome a key obstacle to the origin of life. Biology on Earth evolved in such a way that in each class of molecules, one chirality, or handedness, came to predominate. Virtually all RNA, for example, are right-handed and called D-RNA. That structural sameness makes interactions within that class more efficient—just as a handshake is more efficient when it joins two right or two left hands, rather than a left and a right. "Scientists generally are taught to think that there has to be a common chirality among interacting molecules for biology to work," said Joyce. It seems likely, however, that simple RNA molecules on the primordial Earth would have consisted of mixes of both right- and left-handed forms. Despite this reasoning, 30 years ago Joyce, then a graduate student, published a paper in Nature showing that self-replicators would have had a tough time evolving in such a mix. Any strand of RNA that gathered stray nucleotides onto itself would eventually have incorporated an RNA nucleotide of the opposite handedness—which would have blocked further assembly of that copy. "Since then we've all been wondering how RNA replication could have started on the primitive Earth," Joyce said. (...) Stanley Miller, the chemist whose landmark experiment published in 1953 showed how some of the molecules of life could have formed on a young Earth, left behind boxes of experimental samples that he never analyzed. The first-ever analysis of some of Miller's old samples has revealed another way that important molecules could have formed on early Earth. The study discovered a path from simple to complex compounds amid Earth's prebiotic soup. More than 4 billion years ago, amino acids could have been attached together, forming peptides. These peptides ultimately may have led to the proteins and enzymes necessary for life's biochemistry, as we know it. In the new study, scientists analyzed samples from an experiment Miller performed in 1958. To the reaction flask, Miller added a chemical that at the time wasn't widely thought to have been available on early Earth. The reaction had successfully formed peptides, the new study found. The new study also successfully replicated the experiment and explained why the reaction works. (...) Imagination is perhaps the most powerful tool we have for creating the future. The same might be said when it comes to creating the past, especially as it pertains to origin of life. Under what conditions did the energetic processes of life first evolve? That question is the subject of a remarkable perspective piece just published in Science. Authors William Martin, Filipa Sousa, and Nick Lane come to the startling conclusion that the energy-harvesting system in ancient microbes can best be understood if it is viewed a microcosm of the larger-scale geochemical processes of the day. In particular, they imagine a process by which natural ion gradients in alkaline hydrothermal vents, much like the "Lost City" ecosystem still active in the mid-Atlantic today, ignited the ongoing chemical reaction of life. When it comes to origin of life discussions the so-called "RNA World" often comes to mind. While fascinating, that set of ideas is not what is under discussion here. According to the authors, it's all about the acetogens, the methanogens, and the chemical transformations that were key to their evolution. These microorganisms synthesize ATP using electrons from H+ to reduce CO2. In the process they generate either acetate or methane. The shared backbone in the energy metabolism of these microorganisms is the most primitive CO2-fixing pathway we know of—the acetyl-coenzyme A pathway. This pathway is generally referred to as the hub of metabolism as is links glycolytic energy production in the cell with oxidative energy production in its endosymbionts, the mitochondria. (...) A reconstruction of Earth's earliest ocean in the laboratory revealed the spontaneous occurrence of the chemical reactions used by modern cells to synthesize many of the crucial organic molecules of metabolism (bottom pathway). Whether and how the first enzymes adopted the metal-catalyzed reactions described by the scientists remain to be established. Credit: Molecular Systems Biology The chemical reactions behind the formation of common metabolites in modern organisms could have formed spontaneously in the earth's early oceans, questioning the events thought to have led to the origin of life. In new research funded by the Wellcome Trust, researchers at the University of Cambridge reconstructed the chemical make-up of the earth's earliest ocean in the laboratory. The team found the spontaneous occurrence of reaction sequences which in modern organisms enable the formation of molecules essential for the synthesis of metabolites such as amino acids, nucleic acids and lipids. These organic molecules are critical for the cellular metabolism seen in all living organisms. The detection of one of the metabolites, ribose 5-phosphate, in the reaction mixtures is particularly noteworthy, as RNA precursors like this could in theory give rise to RNA molecules that encode information, catalyze chemical reactions and replicate. It was previously assumed that the complex metabolic reaction sequences, known as metabolic pathways, occurring in modern cells were only possible due to the presence of enzymes. Enzymes are highly complex molecular machines that are thought to have come into existence during the evolution of modern organisms. However, the team's reconstruction reveals that metabolism-like reactions could have occurred naturally in our early oceans, before the first organisms evolved. Almost 4 billion years ago life on Earth began in iron-rich oceans that dominated the surface of the planet. This was an oxygen-free world, pre-dating photosynthesis, when the redox state of iron was different and much more soluble to act as potential catalysts. In the Archean sea, iron, other metals and phosphate, facilitated a series of reactions which resemble the core of cellular metabolism occurring in the absence of enzymes. The findings suggests that metabolism predates the origin of life and evolved through the chemical conditions that prevailed in the worlds earliest oceans. "Our results show that reaction sequences that resemble two essential reaction cascades of metabolism, glycolysis and the pentose-phosphate pathways, could have occurred spontaneously in the earth's ancient oceans," says Dr. Markus Ralser at the Department of Biochemistry at the University of Cambridge and the National Institute for Medical Research, who led the study. "In our reconstructed version of the ancient Archean ocean, these metabolic reactions were particularly sensitive to the presence of ferrous iron which was abundant in the early oceans, and accelerated many of the chemical reactions that we observe. We were surprised by how specific these reactions were" he added. (...)
Quantitative Methods - Common Probability Distribution Calculations Cumulative Distribution Functions A cumulative distribution function or CDF, expresses a probability's function in terms of lowest to highest value, by giving the probability that a random variable X is less than or equal to a particular value x. Expressed in shorthand, the cumulative distribution function is P(X < x). A cumulative distribution function is constructed by summing up, or cumulating all values in the probability function that are less than or equal to x. The concept is similar to the cumulative relative frequency covered earlier in this study guide, which computed values below a certain point in a frequency distribution. Example: Cumulative Distribution Function For example, the following probability distribution includes the cumulative function. \|X = x\|\|P(X = x)\|\|P(X < x) or cdf\| \|-12 to -3\|\|0.15\|\|0.30\| \|-3 to 4\|\|0.25\|\|0.55\| \|4 to 10\|\|0.25\|\|0.80\| From the table, we find that the probability that x is less than or equal to 4 is 0.55, the summed probabilities of the first three P(X) terms, or the number found in the cdf column for the third row, where x < 4. Sometimes a question might ask for the probability of x being greater than 4, for which this problem is 1 - P(x < 4) = 1 - 0.55 = 0.45. This is a question most people should get - but one that will still have too many people answering 0.55 because they weren't paying attention to the "greater than". Discrete Uniform Random Variable A discrete uniform random variable is one that fulfills the definition of "discrete", where there are a finite and countable number of terms, along with the definition of "uniform", where there is an equally likely probability that the random variable X will take any of its possible values x. If there are n possible values for a discrete uniform random variable, the probability of a specific outcome is 1/n. Example: Discrete Uniform Random Variable Earlier we provided an example of a discrete uniform random variable: a random day is one-seventh likely to fall on a Sunday. To illustrate some examples on how probabilities are calculated, take the following discrete uniform distribution with n = 5. \|X = x\|\|P(X = x)\|\|P(X < x)\| According to the distribution above, we have the probability of x = 8 as 0.2. The probability of x = 2 is the same, 0.2. Suppose that the question called for P(4 < X < 8). The answer would be the sum of P(4) + P(6) + P(8) = 0.2 + 0.2 + 0.2 = 0.6. Suppose the question called for P(4 < X < 8). In this case, the answer would omit P(4) and P(8) since it's less than, NOT less than or equal to, and the correct answer would be P(6) = 0.2. The CFA exam writers love to test whether you are paying attention to details and will try to trick you - the probability of such tactics is pretty much a 1.0! Binomial Random Variable Binomial probability distributions are used when the context calls for assessing two outcomes, such as "success/failure", or "price moved up/price moved down". In such situations where the possible outcomes are binary, we can develop an estimate of a binomial random variable by holding a number of repeating trials (also known as "Bernoulli trials"). In a Bernoulli trial, p is the probability of success, (1 - p) is the probability of failure. Suppose that a number of Bernoulli trails are held, with the number denoted by n. A binomial random variable X is defined as the numberof successes in n Bernoulli trials, given two simplifying assumptions: (1) the probabilityp of success is the same for all trials and (2) the trials are independent of each other. Thus, a binomial random variable is described by two parameters: p (the probability of success of one trial) and n (the number of trials). A binomial probability distribution with p = 0.50 (equal chance of success or failure) and n = 4 would appear as: \|x (# of successes)\|\|p(x)\|\|cdf, P(X < x)\| The reference text demonstrates how to construct a binomial probability distribution by using the formula p(x) = (n!/(n - x)!x!)(px)(1 - p)n-x. We used this formula to assemble the above data, though the exam would probably not expect you to create each p(x); it would probably provide you with the table, and ask for an interpretation. For this table, the probability of exactly one success is 0.25; the probability of three or fewer successes is 0.9325 (the cdf value in the row where x = 3); the probability of at least one is 0.9325 (1 - P(0)) = (1 - 0.0625) = 0.9325. The expected value of a binomial random variable is given by the formula np. In the example above, with n = 4 and p = 0.5, the expected value would be 40.5, or 2. The variance of a binomial random variable is calculated by the formula np(1 - p). Using the same example, we have variance of 40.50.5 = 1. If our binomial random variable still had n = 4 but with a greater predictability in the trial, say p = 9, our variance would reduce to 40.90.1 = 0.36. For successive trials (i.e. for higher n), both mean and variance increase but variance increases at a lower rate - thus the higher the n, the better the model works at predicting probability. Creating a Binomial Tree The binomial tree is essentially a diagram showing that the future value of a stock is the product of a series of up or down movements leading to a growing number of possible outcomes. Each possible value is called a node. \|Figure 2.9: Binomial Tree\| Continuous Uniform Distribution A continuous uniform distribution describes a range of outcomes, usually bound with an upper and lower limit, where any point in the range is a possibility. Since it is a range, there are infinite possibilities within the range. In addition, all outcomes are all equally likely (i.e. they are spread uniformly throughout the range). To calculate probabilities, find the area under a pdf curve such as the one graphed here. In this example, what is the probability that the random variable will be between 1 and 3? The area would be a rectangle with a width of 2 (the distance between 1 and 3), and height of 0.2, 20.2 = 0.4. What is the probability that x is less than 3? The rectangle would have a width of 3 and the same height: 0.2. 30.2 = 0.6 Career Education & ResourcesLearn about the difficulty of the CFA exams with a description of the tests, some statistics on pass rates and suggestions that can help you pass the exams. ProfessionalsA financial analyst researches companies and economic conditions to make business, sector and industry recommendations. Career Education & ResourcesRead about what it takes to become a financial analyst in a corporation or securities firm, and learn how far you can rise in the profession. Career Education & ResourcesLearn what education and certifications you need to become a financial planner, as well as the future prospects and earnings potential for financial planners. Career Education & ResourcesThe non-profit sector offers a stable selection of jobs for those who seek other types of fulfillment from their jobs than just purely financial. Career Education & ResourcesLearn about the basic requirements for getting hired as a portfolio manager, and discover how most professionals in the field rise into the position. Your PracticeThese four professional organizations are among the most respected and well known in the industry. ProfessionalsFind out what equity research analysts do on a day-to-day basis, and learn more about the typical career progression for these securities professionals. ProfessionalsThe Chartered Financial Analyst Level II exam is the second of three tests that CFA candidates must pass. ProfessionalsLearn more about the career options available to financial data analysts, and determine whether the profession is a good match for you. Professionals who help individuals manage their finances by providing ... Formerly known as the Association for Investment Management and ... A professional designation given by the CFA Institute (formerly ... A financial professional who studies various industries and companies, ... The differences between a Chartered Financial Analyst (CFA) and a Certified Financial Planner (CFP) are many, but comes down ... Read Full Answer >> According to the CFA Institute, a person who holds a CFA charter is not a chartered financial analyst. The CFA Institute ... Read Full Answer >> The types of positions that a Chartered Financial Analyst (CFA) is likely to hold include any position that deals with large ... Read Full Answer >> Prepaid expenses benefit both businesses and individuals. Prepaid expenses are the types of expenses that are bought or paid ... Read Full Answer >> If you are looking specifically for an investment banking position, an MBA may be marginally preferable over the CFA. The ... Read Full Answer >> You may still pass the Chartered Financial Analysis (CFA) Level I even if you fare poorly in the ethics section, but don't ... Read Full Answer >>
Economics Basics: Production Possibility Frontier, Growth, Opportunity Cost and Trade A. Production Possibility Frontier (PPF) Under the field of macroeconomics, the production possibility frontier (PPF) represents the point at which an economy is most efficiently producing its goods and services and, therefore, allocating its resources in the best way possible. If the economy is not producing the quantities indicated by the PPF, resources are being managed inefficiently and the production of society will dwindle. The production possibility frontier shows there are limits to production, so an economy, to achieve efficiency, must decide what combination of goods and services can be produced. Let's turn to the chart below. Imagine an economy that can produce only wine and cotton. According to the PPF, points A, B and C - all appearing on the curve - represent the most efficient use of resources by the economy. Point X represents an inefficient use of resources, while point Y represents the goals that the economy cannot attain with its present levels of resources. As we can see, in order for this economy to produce more wine, it must give up some of the resources it uses to produce cotton (point A). If the economy starts producing more cotton (represented by points B and C), it would have to divert resources from making wine and, consequently, it will produce less wine than it is producing at point A. As the chart shows, by moving production from point A to B, the economy must decrease wine production by a small amount in comparison to the increase in cotton output. However, if the economy moves from point B to C, wine output will be significantly reduced while the increase in cotton will be quite small. Keep in mind that A, B, and C all represent the most efficient allocation of resources for the economy; the nation must decide how to achieve the PPF and which combination to use. If more wine is in demand, the cost of increasing its output is proportional to the cost of decreasing cotton production. Point X means that the country's resources are not being used efficiently or, more specifically, that the country is not producing enough cotton or wine given the potential of its resources. Point Y, as we mentioned above, represents an output level that is currently unreachable by this economy. However, if there was a change in technology while the level of land, labor and capital remained the same, the time required to pick cotton and grapes would be reduced. Output would increase, and the PPF would be pushed outwards. A new curve, on which Y would appear, would represent the new efficient allocation of resources. When the PPF shifts outwards, we know there is growth in an economy. Alternatively, when the PPF shifts inwards it indicates that the economy is shrinking as a result of a decline in its most efficient allocation of resources and optimal production capability. A shrinking economy could be a result of a decrease in supplies or a deficiency in technology. An economy can be producing on the PPF curve only in theory. In reality, economies constantly struggle to reach an optimal production capacity. And because scarcity forces an economy to forgo one choice for another, the slope of the PPF will always be negative; if production of product A increases then production of product B will have to decrease accordingly. B. Opportunity Cost Opportunity cost is the value of what is foregone in order to have something else. This value is unique for each individual. You may, for instance, forgo ice cream in order to have an extra helping of mashed potatoes. For you, the mashed potatoes have a greater value than dessert. But you can always change your mind in the future because there may be some instances when the mashed potatoes are just not as attractive as the ice cream. The opportunity cost of an individual's decisions, therefore, is determined by his or her needs, wants, time and resources (income). This is important to the PPF because a country will decide how to best allocate its resources according to its opportunity cost. Therefore, the previous wine/cotton example shows that if the country chooses to produce more wine than cotton, the opportunity cost is equivalent to the cost of giving up the required cotton production. Let's look at another example to demonstrate how opportunity cost ensures that an individual will buy the least expensive of two similar goods when given the choice. For example, assume that an individual has a choice between two telephone services. If he or she were to buy the most expensive service, that individual may have to reduce the number of times he or she goes to the movies each month. Giving up these opportunities to go to the movies may be a cost that is too high for this person, leading him or her to choose the less expensive service. Remember that opportunity cost is different for each individual and nation. Thus, what is valued more than something else will vary among people and countries when decisions are made about how to allocate resources. C. Trade, Comparative Advantage and Absolute Advantage Specialization and Comparative Advantage An economy can focus on producing all of the goods and services it needs to function, but this may lead to an inefficient allocation of resources and hinder future growth. By using specialization, a country can concentrate on the production of one thing that it can do best, rather than dividing up its resources. For example, let's look at a hypothetical world that has only two countries (Country A and Country B) and two products (cars and cotton). Each country can make cars and/or cotton. Now suppose that Country A has very little fertile land and an abundance of steel for car production. Country B, on the other hand, has an abundance of fertile land but very little steel. If Country A were to try to produce both cars and cotton, it would need to divide up its resources. Because it requires a lot of effort to produce cotton by irrigating the land, Country A would have to sacrifice producing cars. The opportunity cost of producing both cars and cotton is high for Country A, which will have to give up a lot of capital in order to produce both. Similarly, for Country B, the opportunity cost of producing both products is high because the effort required to produce cars is greater than that of producing cotton. Each country can produce one of the products more efficiently (at a lower cost) than the other. Country A, which has an abundance of steel, would need to give up more cars than Country B would to produce the same amount of cotton. Country B would need to give up more cotton than Country A to produce the same amount of cars. Therefore, County A has a comparative advantage over Country B in the production of cars, and Country B has a comparative advantage over Country A in the production of cotton. Now let's say that both countries (A and B) specialize in producing the goods with which they have a comparative advantage. If they trade the goods that they produce for other goods in which they don't have a comparative advantage, both countries will be able to enjoy both products at a lower opportunity cost. Furthermore, each country will be exchanging the best product it can make for another good or service that is the best that the other country can produce. Specialization and trade also works when several different countries are involved. For example, if Country C specializes in the production of corn, it can trade its corn for cars from Country A and cotton from Country B. Determining how countries exchange goods produced by a comparative advantage ("the best for the best") is the backbone of international trade theory. This method of exchange is considered an optimal allocation of resources, whereby economies, in theory, will no longer be lacking anything that they need. Like opportunity cost, specialization and comparative advantage also apply to the way in which individuals interact within an economy. Sometimes a country or an individual can produce more than another country, even though countries both have the same amount of inputs. For example, Country A may have a technological advantage that, with the same amount of inputs (arable land, steel, labor), enables the country to manufacture more of both cars and cotton than Country B. A country that can produce more of both goods is said to have an absolute advantage. Better quality resources can give a country an absolute advantage as can a higher level of education and overall technological advancement. It is not possible, however, for a country to have a comparative advantage in everything that it produces, so it will always be able to benefit from trade. A transaction in international trade where the seller is responsible ... The geographic area in which a single currency would create the ... A 1979 arrangement between several European countries which links ... A period of time in which several European countries faced the ... The successor to the European Monetary System (EMS), the combination ... A merger occurring between companies in the same industry. Horizontal ... Find out how ceteris paribus arguments are applied in economics, including examples about the money supply, rent control ... Find out why economics can be considered a deductive social science, like sociology, and how human action and behavior informs ... Discover the difference between accounting and economics by comparing and contrasting the financial discipline of accounting ... Learn in what year the United States ran its largest negative balance of trade as a result of imports greatly exceeding the ...
Simply put, the standard deviation is a measure that you use to see how your data is spread out around the average or mean. By using the standard deviation, you can easily see if the data is mostly near the average, more spread out, if it concentrates above or below the average, among others. Representing Standard Deviation On A Graph While when you have small data it may be easier for you to determine how the data is dispersed, this can’t be said when you are looking at bigger data. So, one of the tools that researchers and statisticians use is graphs, more specifically the Bell curve or the normal distribution as it is also known. Looking to know more about the z score? A Real-Life Example One of the difficulties that may students experience when they are starting with statistics is that they have a hard time understanding how they are going to put all this knowledge into practice. So, there is nothing like seeing a real-life example so that you fully understand it and, hopefully, be able to identify others on your own. There is a common statement that is made that says that most students get Cs while only a few get Fs and As. But is this true? While you could collect data from your school and put this exercise into practice, we can state that this statement is true. But how can you display it in an effective way? Discover how to easily calculate the z score. As we mentioned above, the best way is to use the Bell curve. In fact, besides grades, you can also use this graph to represent nutrition habits, people’s heights, people’s weighs, and even exercise routines that you want to examine deeply. While these representations may not look very useful for you, you need to know that businesses, governments, and even schools use this type of data and graphs not only to know where they stand at the time as well as to make predictions for the future. For example, let’s say that a college offers 4 different degrees but most students only apply for two of them. So, these schools are looking at their students’ numbers falling but they now understand what is happening. So, they can decide on either increasing the features and improving the publicity for the two degrees that have fewer students applying to, or they can decide to increase the vacancy numbers for the two degrees that have more students. Calculating The Standard Deviation By Hand Notice that while you may have already used a software to calculate standard deviations, we believe that it is important that you know how to make them by hand. This way, you will understand the ropes of how it is determined and it will be easier for you to conclude something about the results that you get. So, to determine the standard deviation by hand, just follow the next steps: Step #1: Discover The Variance: The variance represents how close or how far the data in your sample is from the mean. One of the things to retain is that the lower the variance the more the data is concentrated near the mean. On the other hand, the higher the variance, the more the data is spread far from the mean. Let’s say that you are measuring trees and that their heights are as follow: 7, 8, 8, 7.5, and 9 feet. With this data, it is easy to see that the mean is 7.9. Learn how to calculate the z score using Excel. So, to determine the variance, you will need to subtract the tree height by the mean: 7 – 7.9 = -0.9 8 – 7.9 = 0.1 8 – 7.9 = 0.1 7.5 – 7.9 = -0.4 9 – 7.9 = 1.1 Step #2: Take The Square Root Of The Variance: In our simple example of the tree heights, you would have to make the following calculations: (-0.9)^2 = 0.81 (0.1)^2 = 0.01 (0.1)^2 = 0.01 (-0.4)^2 = 0.16 (1.1)^2 = 1.21 Step #3: Sum The Squared Numbers: 0.81 + 0.01 + 0.01 + 0.16 + 1.21 = 2.2 And now, you ill need to divide the sum of squares by (n-1). Considering that we were looking at 5 trees, n-1 = 4. So: 2.2 / 4 = 0.55 0.55 is the variance for this sample of tree heights. Learn more about the standard deviation here. Step #4: Take The Square Root Of The Variance: Now, to determine the standard deviation, you will need to: √0.55 = 0.741619848709566 In this case, you should always round your number to the second or third decimal. So, the standard deviation in our sample of tree heights is 0.74.
Number Sense, Properties and Operations items focus on the understanding of numbers (whole numbers, fractions, decimals, integers) and their application in real life situations, as well as on computation estimates. Emphasis is placed on understanding numerical relationships as expressed in ratios, proportions and percents and on students' abilities in estimation, mental computations and generalization of numerical patterns. Measurement items focus on the ability of students to describe real world objects using numbers. Students are asked to identify attributes, select appropriate units and apply measures to communicate ideas so that they are understandable to others. Students may be required to read instruments with emphasis on precision and accuracy using metric and customary units. Items also include estimates, measurements, and applications of measurements of length, time, money, temperature, mass/weight, area, perimeter, distance, rates, volume, capacity and angles. Geometry items focus on geometric relationships and skills that are important in school, as well as in the real world. Important concepts include projection, transformation, congruence, similarity, coordinate geometry, spatial relations and trigonometric ratios. Students need to be able to model and visualize geometric figures in one, two and three dimensions, as well as communicate geometric ideas. Data Analysis, Statistics and Probability items focus on the importance of data analysis and the representation of data across all disciplines, and they reflect the prevalence of these activities in our society. Knowledge of probability, sampling and statistics, and the ability to make inferences from tables and graphs are necessary in today's world. Algebra and Functions items emphasize a conceptual understanding of algebra as a means of representing situations that involve variable qualities with expressions, equations, inequalities, patterns and systems of equations or inequalities. Some emphasize algebraic processing as a problem-solving tool. Functions are viewed not only in terms of algebraic formulas, but also in terms of verbal descriptions, tables of values and graphs. July 14 - 19 August 11 - 13
\|dB\|\|Power ratio\|\|Amplitude ratio\| \|6\|\|3\|\|.981\|\|1\|\|.995 ≈ 2\| \|3\|\|1\|\|.995 ≈ 2\|\|1\|\|.413\| \|−3\|\|0\|\|.501 ≈ 1⁄2\|\|0\|\|.708\| \|−6\|\|0\|\|.251\|\|0\|\|.501 ≈ 1⁄2\| \|An example scale showing power ratios x and amplitude ratios √ and dB equivalents 10 log10 x.\| The decibel (dB) is a logarithmic unit used to express the ratio of two values of a physical quantity. One of these values is often a standard reference value, in which case the decibel is used to express the level[a] of the other value relative to this reference. The number of decibels is ten times the logarithm to base 10 of the ratio of two power quantities. A change in power by a factor of 10 corresponds to a 10 dB change in level. At the half power point an audio circuit or an antenna exhibits an attenuation of approximately 3 dB. A change in amplitude by a factor of 10 results in a change in power by a factor of 100, which corresponds to a 20 dB change in level. A change in amplitude ratio by a factor of 2 (equivalently factor of 4 in power change) approximately corresponds to a 6 dB change in level. The definition of the decibel is based on the measurement of power in telephony of the early 20th century in the Bell System in the United States. One decibel is one tenth of one bel, named in honor of Alexander Graham Bell; however, the bel is seldom used. Today, the decibel is used for a wide variety of measurements in science and engineering, most prominently in acoustics, electronics, and control theory. In electronics, the gains of amplifiers, attenuation of signals, and signal-to-noise ratios are often expressed in decibels. In the International System of Quantities, the decibel is defined as a unit of measurement for quantities of type level or level difference, which are defined as the logarithm of the ratio of power- or field-type quantities. The decibel symbol is often qualified with a suffix that indicates the reference quantity that has been used or some other property of the quantity being measured. For example, dBm indicates a reference power of one milliwatt, while dBV is referenced to 1 volt RMS. - 1 History - 2 Definition - 3 Properties - 4 Advantages and disadvantages - 5 Uses - 6 Suffixes and reference values - 7 Related units - 8 Fractions - 9 See also - 10 Notes - 11 References - 12 External links The decibel originates from methods used to quantify signal loss in telegraph and telephone circuits. The unit for loss was originally Miles of Standard Cable (MSC). 1 MSC corresponded to the loss of power over a 1 mile (approximately 1.6 km) length of standard telephone cable at a frequency of 5000 radians per second (795.8 Hz), and matched closely the smallest attenuation detectable to the average listener. The standard telephone cable implied was "a cable having uniformly distributed resistance of 88 ohms per loop mile and uniformly distributed shunt capacitance of 0.054 microfarad per mile" (approximately 19 gauge). In 1924, Bell Telephone Laboratories received favorable response to a new unit definition among members of the International Advisory Committee on Long Distance Telephony in Europe and replaced the MSC with the Transmission Unit (TU). 1 TU was defined such that the number of TUs was ten times the base-10 logarithm of the ratio of measured power to a reference power level. The definition was conveniently chosen such that 1 TU approximated 1 MSC; specifically, 1 MSC was 1.056 TU. In 1928, the Bell system renamed the TU into the decibel, being one tenth of a newly defined unit for the base-10 logarithm of the power ratio. It was named the bel, in honor of the telecommunications pioneer Alexander Graham Bell. The bel is seldom used, as the decibel was the proposed working unit. Since the earliest days of the telephone, the need for a unit in which to measure the transmission efficiency of telephone facilities has been recognized. The introduction of cable in 1896 afforded a stable basis for a convenient unit and the "mile of standard" cable came into general use shortly thereafter. This unit was employed up to 1923 when a new unit was adopted as being more suitable for modern telephone work. The new transmission unit is widely used among the foreign telephone organizations and recently it was termed the "decibel" at the suggestion of the International Advisory Committee on Long Distance Telephony. The decibel may be defined by the statement that two amounts of power differ by 1 decibel when they are in the ratio of 100.1 and any two amounts of power differ by N decibels when they are in the ratio of 10'N(0.1). The number of transmission units expressing the ratio of any two powers is therefore ten times the common logarithm of that ratio. This method of designating the gain or loss of power in telephone circuits permits direct addition or subtraction of the units expressing the efficiency of different parts of the circuit... In April 2003, the International Committee for Weights and Measures (CIPM) considered a recommendation for the inclusion of the decibel in the International System of Units (SI), but decided against the proposal. However, the decibel is recognized by other international bodies such as the International Electrotechnical Commission (IEC) and International Organization for Standardization (ISO). The IEC permits the use of the decibel with field quantities as well as power and this recommendation is followed by many national standards bodies, such as NIST, which justifies the use of the decibel for voltage ratios. The term field quantity is deprecated by ISO 80000-1, which favors root-power. In spite of their widespread use, suffixes (such as in dBA or dBV) are not recognized by the IEC or ISO. The ISO Standard 80000-3:2006 defines the following quantities. The decibel (dB) is one-tenth of a bel: 1 dB = 0.1 B. The bel (B) is 1⁄2 ln(10) nepers: 1 B = 1⁄2 ln(10) Np. The neper is the change in the level of a field quantity when the field quantity changes by a factor of e, that is 1 Np = ln(e) = 1, thereby relating all of the units as nondimensional natural log of field-quantity ratios, 1 dB = 0.11513… Np = 0.11513…. Finally, the level of a quantity is the logarithm of the ratio of the value of that quantity to a reference value of the same kind of quantity. Therefore, the bel represents the logarithm of a ratio between two power quantities of 10:1, or the logarithm of a ratio between two field quantities of √10:1. The bel is rarely used either without a prefix or with SI unit prefixes other than deci; it is preferred, for example, to use hundredths of a decibel rather than millibels. Thus, five one-thousandths of a bel would normally be written '0.05 dB', and not '5 mB'. The method of expressing a ratio as a level in decibels depends on whether the measured property is a power quantity or a field quantity; see Field, power, and root-power quantities for details. When referring to measurements of power quantities, a ratio can be expressed as a level in decibels by evaluating ten times the base-10 logarithm of the ratio of the measured quantity to reference value. Thus, the ratio of P (measured power) to P0 (reference power) is represented by LP, that ratio expressed in decibels, which is calculated using the formula: The base-10 logarithm of the ratio of the two power levels is the number of bels. The number of decibels is ten times the number of bels (equivalently, a decibel is one-tenth of a bel). P and P0 must measure the same type of quantity, and have the same units before calculating the ratio. If P = P0 in the above equation, then LP = 0. If P is greater than P0 then LP is positive; if P is less than P0 then LP is negative. Rearranging the above equation gives the following formula for P in terms of P0 and LP: Field quantities and root-power quantities When referring to measurements of field quantities, it is usual to consider the ratio of the squares of F (measured field) and F0 (reference field). This is because in most applications power is proportional to the square of field, and it is desirable for the two decibel formulations to give the same result in such typical cases. Thus, the following definition is used: The formula may be rearranged to give Similarly, in electrical circuits, dissipated power is typically proportional to the square of voltage or current when the impedance is held constant. Taking voltage as an example, this leads to the equation: where V is the voltage being measured, V0 is a specified reference voltage, and GdB is the power gain expressed in decibels. A similar formula holds for current. The term root-power quantity is introduced by ISO Standard 80000-1:2009 as a substitute of field quantity. The term field quantity is deprecated by that standard. Since logarithm differences measured in these units are used to represent power ratios and field ratios, the values of the ratios represented by each unit are also included in the table. \|Unit\|\|In decibels\|\|In bels\|\|In nepers\|\|Corresponding power ratio\|\|Corresponding field ratio\| \|1 dB\|\|1 dB\|\|0.1 B\|\|0.11513 Np\|\|10 1⁄10 ≈ 1.25893\|\|10 1⁄20 ≈ 1.12202\| \|1 B\|\|10 dB\|\|1 B\|\|1.1513 Np\|\|10\|\|10 1⁄2 ≈ 3.16228\| \|1 Np\|\|8.68589 dB\|\|0.868589 B\|\|1 Np\|\|e2 ≈ 7.38906\|\|e ≈ 2.71828\| All of these examples yield dimensionless answers in dB because they are relative ratios expressed in decibels. The unit dBW is often used to denote a ratio for which the reference is 1 W, and similarly dBm for a 1 mW reference point. - Calculating the ratio of 1 kW (one kilowatt, or 1000 watts) to 1 W in decibels yields: - The ratio of √1000 V ≈ 31.62 V to 1 V in decibels is (31.62 V/1 V)2 ≈ 1 kW/1 W, illustrating the consequence from the definitions above that GdB has the same value, 30, regardless of whether it is obtained from powers or from amplitudes, provided that in the specific system being considered power ratios are equal to amplitude ratios squared. - The ratio of 1 mW (one milliwatt) to 10 W in decibels is obtained with the formula - The power ratio corresponding to a 3 dB change in level is given by A change in power ratio by a factor of 10 corresponds to a change in level of 10 dB. A change in power ratio by a factor of 2 is approximately a change of 3 dB. More precisely, the factor is 10 3⁄10, or 1.9953, about 0.24% different from exactly 2. Similarly, an increase of 3 dB implies an increase in voltage by a factor of approximately √, or about 1.41, an increase of 6 dB corresponds to approximately four times the power and twice the voltage, and so on. In exact terms the power ratio is 10 6⁄10, or about 3.9811, a relative error of about 0.5%. In order to add or subtract levels the values that are expressed in decibel first must be divided by 10 (or 20). The definition of the decibel in ISO 80000-3 assigns a value to the decibel (approximately 0.11513) thus the division by 10 in formulas for the addition or subtraction of levels should be a division by 10 dB. Ignoring that can cause a mistake of a factor of 8.686 in the number of decibels. None of the formulas published in ISO standards regarding noise and acoustics take this into account and they shall be used as if the decibel has no value (or is unity). The decibel has the following properties: - The logarithmic scale nature of the decibel means that a very large range of ratios can be represented by a convenient number, in a similar manner to scientific notation. This allows one to clearly visualize huge changes of some quantity. See Bode plot and semi-log plot. For example, 120 dB SPL may be clearer than "a trillion times more intense than the threshold of hearing". - Level values in decibels can be added instead of multiplying the underlying power values, which means that the overall gain of a multi-component system, such as a series of amplifier stages, can be calculated by summing the gains in decibels of the individual components, rather than multiply the amplification factors; that is, log(A × B × C) = log(A) + log(B) + log(C). Practically, this means that, armed only with the knowledge that 1 dB is approximately 26% power gain, 3 dB is approximately 2× power gain, and 10 dB is 10× power gain, it is possible to determine the power ratio of a system from the gain in dB with only simple addition and multiplication. For example: - A system consists of 3 amplifiers in series, with gains (ratio of power out to in) of 10 dB, 8 dB, and 7 dB respectively, for a total gain of 25 dB. Broken into combinations of 10, 3, and 1 dB, this is: - 25 dB = 10 dB + 10 dB + 3 dB + 1 dB + 1 dB - With an input of 1 watt, the output is approximately - 1 W x 10 x 10 x 2 x 1.26 x 1.26 ≈ 317.5 W - Calculated exactly, the output is 1 W x 10 25⁄10 = 316.2 W. The approximate value has an error of only +0.4% with respect to the actual value which is negligible given the precision of the values supplied and the accuracy of most measurement instrumentation. - A system consists of 3 amplifiers in series, with gains (ratio of power out to in) of 10 dB, 8 dB, and 7 dB respectively, for a total gain of 25 dB. Broken into combinations of 10, 3, and 1 dB, this is: Advantages and disadvantages \|\|This article contains a pro and con list, which is sometimes inappropriate. (April 2015)\| According to Mitschke, "The advantage of using a logarithmic measure is that in a transmission chain, there are many elements concatenated, and each has its own gain or attenuation. To obtain the total, addition of decibel values is much more convenient than multiplication of the individual factors." The human perception of the intensity of sound and light approximates the logarithm of intensity rather than a linear relationship (Weber–Fechner law), making the dB scale a useful measure. Decibels are still the commonly used units to express ratios in a number of fields, even when the original meaning of the term is obscured. Decibels are the traditional way of expressing gain or margin in such diverse disciplines as control theory, antenna and radio frequency transmission theory, and even assessment of nuclear hardness.[dubious ] Various published articles have criticized the unit decibel as having shortcomings that hinder its understanding and use: According to its critics, the decibel creates confusion, obscures reasoning, is more related to the era of slide rules than to modern digital processing, are cumbersome and difficult to interpret. Representing the equivalent of zero watts is not possible, causing problems in conversions. Hickling concludes "Decibels are a useless affectation, which is impeding the development of noise control as an engineering discipline". A common source of confusion in using the decibel occurs when deciding about the use of 10 × log or 20 × log. In the original definition, it was a power measurement, and as employed in that context, the formulation 10 × log should be used, as deci means one tenth. The user must be clear whether the quantity expressed is power or amplitude. It is useful to consider how power or energy is expressed, e.g., current × current × resistance, 1⁄2 × velocity × velocity × mass. Where the power is a square function of a field variable (such as voltage, current, or pressure), then 10 × log is the correct expression for the square, or 20 × log for the field variable itself. For the same reason that humans excel at additive operation over multiplication, decibels are awkward in inherently additive operations: "if two machines each individually produce a [sound pressure] level of, say, 90 dB at a certain point, then when both are operating together we should expect the combined sound pressure level to increase to 93 dB, but certainly not to 180 dB!" "suppose that the noise from a machine is measured (including the contribution of background noise) and found to be 87 dBA but when the machine is switched off the background noise alone is measured as 83 dBA. ... the machine noise [level (alone)] may be obtained by 'subtracting' the 83 dBA background noise from the combined level of 87 dBA; i.e., 84.8 dBA." "in order to find a representative value of the sound level in a room a number of measurements are taken at different positions within the room, and an average value is calculated. (...) Compare the logarithmic and arithmetic averages of ... 70 dB and 90 dB: logarithmic average = 87 dB; arithmetic average = 80 dB." The decibel is commonly used in acoustics as a unit of sound pressure level. The reference pressure for sound in air is set at the typical threshold of perception of an average human and there are common comparisons used to illustrate different levels of sound pressure. Sound pressure is a field quantity, therefore the field version of the unit definition is used: The human ear has a large dynamic range in sound reception. The ratio of the sound intensity that causes permanent damage during short exposure to that of the quietest sound that the ear can hear is greater than or equal to 1 trillion (1012). Such large measurement ranges are conveniently expressed in logarithmic scale: the base-10 logarithm of 1012 is 12, which is expressed as a sound pressure level of 120 dB re 20 μPa. Since the human ear is not equally sensitive to all sound frequencies, noise levels at maximum human sensitivity, somewhere between 2 and 4 kHz, are factored more heavily into some measurements using frequency weighting. (See also Stevens' power law.) In electronics, the decibel is often used to express power or amplitude ratios (gains), in preference to arithmetic ratios or percentages. One advantage is that the total decibel gain of a series of components (such as amplifiers and attenuators) can be calculated simply by summing the decibel gains of the individual components. Similarly, in telecommunications, decibels denote signal gain or loss from a transmitter to a receiver through some medium (free space, waveguide, coaxial cable, fiber optics, etc.) using a link budget. The decibel unit can also be combined with a suffix to create an absolute unit of electric power. For example, it can be combined with "m" for "milliwatt" to produce the "dBm". Zero dBm is the level corresponding to one milliwatt, and 1 dBm is one decibel greater (about 1.259 mW). In professional audio specifications, a popular unit is the dBu. The dBu is a root mean square (RMS) measurement of voltage that uses as its reference approximately 0.775 VRMS. Chosen for historical reasons, the reference value is the voltage level which delivers 1 mW of power in a 600-ohm resistor, which used to be the standard reference impedance in telephone circuits. In an optical link, if a known amount of optical power, in dBm (referenced to 1 mW), is launched into a fiber, and the losses, in dB (decibels), of each component (e.g., connectors, splices, and lengths of fiber) are known, the overall link loss may be quickly calculated by addition and subtraction of decibel quantities. Video and digital imaging In connection with video and digital image sensors, decibels generally represent ratios of video voltages or digitized light levels, using 20 log of the ratio, even when the represented optical power is directly proportional to the voltage or level, not to its square, as in a CCD imager where response voltage is linear in intensity. Thus, a camera signal-to-noise ratio or dynamic range of 40 dB represents a power ratio of 100:1 between signal power and noise power, not 10,000:1. Sometimes the 20 log ratio definition is applied to electron counts or photon counts directly, which are proportional to intensity without the need to consider whether the voltage response is linear. However, as mentioned above, the 10 log intensity convention prevails more generally in physical optics, including fiber optics, so the terminology can become murky between the conventions of digital photographic technology and physics. Most commonly, quantities called "dynamic range" or "signal-to-noise" (of the camera) would be specified in 20 log dB, but in related contexts (e.g. attenuation, gain, intensifier SNR, or rejection ratio) the term should be interpreted cautiously, as confusion of the two units can result in very large misunderstandings of the value. Photographers typically use an alternative base-2 log unit, the stop, to describe light intensity ratios or dynamic range. Suffixes and reference values Suffixes are commonly attached to the basic dB unit in order to indicate the reference value by which the ratio is calculated. For example, dBm indicates power measurement relative to 1 milliwatt. In cases where the unit value of the reference is stated, the decibel value is known as "absolute". If the unit value of the reference is not explicitly stated, as in the dB gain of an amplifier, then the decibel value is considered relative. The SI does not permit attaching qualifiers to units, whether as suffix or prefix, other than standard SI prefixes. Therefore, even though the decibel is accepted for use alongside SI units, the practice of attaching a suffix to the basic dB unit, forming compound units such as dBm, dBu, dBA, etc., is not. The proper way, according to the IEC 60027-3, is either as Lx (re xref) or as Lx/xref, where x is the quantity symbol and xref is the value of the reference quantity, e.g., LE (re 1 μV/m) = LE/(1 μV/m) for the electric field strength E relative to 1 μV/m reference value. Outside of documents adhering to SI units, the practice is very common as illustrated by the following examples. There is no general rule, with various discipline-specific practices. Sometimes the suffix is a unit symbol ("W","K","m"), sometimes it is a transliteration of a unit symbol ("uV" instead of μV for microvolt), sometimes it is an acronym for the unit's name ("sm" for square meter, "m" for milliwatt), other times it is a mnemonic for the type of quantity being calculated ("i" for antenna gain with respect to an isotropic antenna, "λ" for anything normalized by the EM wavelength), or otherwise a general attribute or identifier about the nature of the quantity ("A" for A-weighted sound pressure level). The suffix is often connected with a dash (dB-Hz), with a space (dB HL), with no intervening character (dBm), or enclosed in parentheses, dB(sm). Since the decibel is defined with respect to power, not amplitude, conversions of voltage ratios to decibels must square the amplitude, or use the factor of 20 instead of 10, as discussed above. - dBu or dBv - RMS voltage relative to . Originally dBv, it was changed to dBu to avoid confusion with dBV. The "v" comes from "volt", while "u" comes from the volume unit used in the VU meter. dBu can be used regardless of impedance, but is derived from a 600 Ω load dissipating 0 dBm (1 mW). The reference voltage comes from the computation . In professional audio, equipment may be calibrated to indicate a "0" on the VU meters some finite time after a signal has been applied at an amplitude of +4 dBu. Consumer equipment typically uses a lower "nominal" signal level of -10 dBV. Therefore, many devices offer dual voltage operation (with different gain or "trim" settings) for interoperability reasons. A switch or adjustment that covers at least the range between +4 dBu and -10 dBV is common in professional equipment. - dB(mVRMS) – voltage relative to 1 millivolt across 75 Ω. Widely used in cable television networks, where the nominal strength of a single TV signal at the receiver terminals is about 0 dBmV. Cable TV uses 75 Ω coaxial cable, so 0 dBmV corresponds to −78.75 dBW (−48.75 dBm) or approx. 13 nW. - dBμV or dBuV - dB(μVRMS) – voltage relative to 1 microvolt. Widely used in television and aerial amplifier specifications. 60 dBμV = 0 dBmV. Probably the most common usage of "decibels" in reference to sound level is dB SPL, sound pressure level referenced to the nominal threshold of human hearing: The measures of pressure (a field quantity) use the factor of 20, and the measures of power (e.g. dB SIL and dB SWL) use the factor of 10. - dB SPL - dB SPL (sound pressure level) – for sound in air and other gases, relative to 20 micropascals (μPa) = 2×10−5 Pa, approximately the quietest sound a human can hear. For sound in water and other liquids, a reference pressure of 1 μPa is used. An RMS sound pressure of one pascal corresponds to a level of 94 dB SPL. - dB SIL - dB sound intensity level – relative to 10−12 W/m2, which is roughly the threshold of human hearing in air. - dB SWL - dB sound power level – relative to 10−12 W. - dB(A), dB(B), and dB(C) - These symbols are often used to denote the use of different weighting filters, used to approximate the human ear's response to sound, although the measurement is still in dB (SPL). These measurements usually refer to noise and its effects on humans and other animals, and they are widely used in industry while discussing noise control issues, regulations and environmental standards. Other variations that may be seen are dBA or dBA. According to ANSI standards, the preferred usage is to write LA = x dB. Nevertheless, the units dBA and dB(A) are still commonly used as a shorthand for A-weighted measurements. Compare dBc, used in telecommunications. - dB HL - dB hearing level is used in audiograms as a measure of hearing loss. The reference level varies with frequency according to a minimum audibility curve as defined in ANSI and other standards, such that the resulting audiogram shows deviation from what is regarded as 'normal' hearing. - dB Q - sometimes used to denote weighted noise level, commonly using the ITU-R 468 noise weighting See also dBV and dBu above. - dB(mW) – power relative to 1 milliwatt. In audio and telephony, dBm is typically referenced relative to a 600 ohm impedance, which corresponds to a voltage level of 0.775 volts or 775 millivolts. - dB(full scale) – the amplitude of a signal compared with the maximum which a device can handle before clipping occurs. Full-scale may be defined as the power level of a full-scale sinusoid or alternatively a full-scale square wave. A signal measured with reference to a full-scale sine-wave will appear 3 dB weaker when referenced to a full-scale square wave, thus: 0 dBFS(fullscale sine wave) = −3 dBFS(fullscale square wave). - dB(true peak) - peak amplitude of a signal compared with the maximum which a device can handle before clipping occurs. In digital systems, 0 dBTP would equal the highest level (number) the processor is capable of representing. Measured values are always negative or zero, since they are less than or equal to full-scale. - Power in dBm measured at a zero transmission level point. - dB(Z) – decibel relative to Z = 1 mm6·m−3: energy of reflectivity (weather radar), related to the amount of transmitted power returned to the radar receiver. Values above 15–20 dBZ usually indicate falling precipitation. - dB(m2) – decibel relative to one square meter: measure of the radar cross section (RCS) of a target. The power reflected by the target is proportional to its RCS. "Stealth" aircraft and insects have negative RCS measured in dBsm, large flat plates or non-stealthy aircraft have positive values. Radio power, energy, and field strength - relative to carrier—in telecommunications, this indicates the relative levels of noise or sideband power, compared with the carrier power. Compare dBC, used in acoustics. - energy relative to 1 joule. 1 joule = 1 watt second = 1 watt per hertz, so power spectral density can be expressed in dBJ. - dB(mW) – power relative to 1 milliwatt. In the radio field, dBm is usually referenced to a 50 ohm load, with the resultant voltage being 0.224 volts. - dBμV/m, dBuV/m, or dBμ - dB(μV/m) – electric field strength relative to 1 microvolt per meter. Often used to specify the signal strength from a television broadcast at a receiving site (the signal measured at the antenna output will be in dBμV). - dB(fW) – power relative to 1 femtowatt. - dB(W) – power relative to 1 watt. - dB(kW) – power relative to 1 kilowatt. - dB(isotropic) – the forward gain of an antenna compared with the hypothetical isotropic antenna, which uniformly distributes energy in all directions. Linear polarization of the EM field is assumed unless noted otherwise. - dB(dipole) – the forward gain of an antenna compared with a half-wave dipole antenna. 0 dBd = 2.15 dBi - dB(isotropic circular) – the forward gain of an antenna compared to a circularly polarized isotropic antenna. There is no fixed conversion rule between dBiC and dBi, as it depends on the receiving antenna and the field polarization. - dB(quarterwave) – the forward gain of an antenna compared to a quarter wavelength whip. Rarely used, except in some marketing material. 0 dBq = −0.85 dBi - dB(m2) – decibel relative to one square meter: measure of the antenna effective area. - dB(m−1) – decibel relative to reciprocal of meter: measure of the antenna factor. - dB(Hz) – bandwidth relative to one hertz. E.g., 20 dB-Hz corresponds to a bandwidth of 100 Hz. Commonly used in link budget calculations. Also used in carrier-to-noise-density ratio (not to be confused with carrier-to-noise ratio, in dB). - dBov or dBO - dB(overload) – the amplitude of a signal (usually audio) compared with the maximum which a device can handle before clipping occurs. Similar to dBFS, but also applicable to analog systems. According to ITU-T Rec. G.100.1 the Level in dBov of a digital system is defined as:: , with the maximum signal power , for a rectangular signal with the maximum amplitude . The level of a tone with a digital amplitude (peak value) of is therefore . - dB(relative) – simply a relative difference from something else, which is made apparent in context. The difference of a filter's response to nominal levels, for instance. - dB above reference noise. See also dBrnC - dBrnC represents an audio level measurement, typically in a telephone circuit, relative to the circuit noise level, with the measurement of this level frequency-weighted by a standard C-message weighting filter. The C-message weighting filter was chiefly used in North America. The Psophometric filter is used for this purpose on international circuits. See Psophometric weighting to see a comparison of frequency response curves for the C-message weighting and Psophometric weighting filters. - dB(K) – decibels relative to kelvin: Used to express noise temperature. - dB(K−1) – decibels relative to reciprocal of kelvin—not decibels per kelvin: Used for the G/T factor, a figure of merit utilized in satellite communications, relating the antenna gain G to the receiver system noise equivalent temperature T. - mB(mW) – power relative to 1 milliwatt, in millibels (one hundredth of a decibel). 100 mBm = 1dBm. This unit is in the Wi-Fi drivers of the Linux kernel and the regulatory domain sections. Np or cNp - Another closely related unit is the neper (Np) or centineper (cNp). Like the decibel, the neper is a unit of level. The linear approximation 1cNp =~ 1% for small percentage differences is widely used finance. Attenuation constants, in fields such as optical fiber communication and radio propagation path loss, are often expressed as a fraction or ratio to distance of transmission. dB/m means decibels per meter, dB/mi is decibels per mile, for example. These quantities are to be manipulated obeying the rules of dimensional analysis, e.g., a 100-meter run with a 3.5 dB/km fiber yields a loss of 0.35 dB = 3.5 dB/km × 0.1 km. - Apparent magnitude - Cent (music) - dB drag racing - Decade (log scale) - Equal-loudness contour - Noise (environmental) - Richter magnitude scale - Signal noise - IEEE Standard 100 Dictionary of IEEE Standards Terms, Seventh Edition, The Institute of Electrical and Electronics Engineering, New York, 2000; ISBN 0-7381-2601-2; page 288 - "ISO 80000-3:2006". International Organization for Standardization. Retrieved 20 July 2013. - Utilities : VRMS / dBm / dBu / dBV calculator, Analog Devices, retrieved 2016-09-16 - Johnson, Kenneth Simonds (1944). Transmission Circuits for Telephonic Communication: Methods of Analysis and Design. New York: D. Van Nostrand Co. p. 10. - Don Davis and Carolyn Davis (1997). Sound system engineering (2nd ed.). Focal Press. p. 35. ISBN 978-0-240-80305-0. - R. V. L. Hartley (Dec 1928). "'TU' becomes 'Decibel'". Bell Laboratories Record. AT&T. 7 (4): 137–139. - Martin, W. H. (January 1929). "DeciBel—The New Name for the Transmission Unit". Bell System Technical Journal. 8 (1). - 100 Years of Telephone Switching, p. 276, at Google Books, Robert J. Chapuis, Amos E. Joel, 2003 - William H. Harrison (1931). "Standards for Transmission of Speech". Standards Yearbook. National Bureau of Standards, U. S. Govt. Printing Office. 119 - Consultative Committee for Units, Meeting minutes, Section 3 - "Letter symbols to be used in electrical technology – Part 3: Logarithmic and related quantities, and their units", IEC 60027-3 Ed. 3.0, International Electrotechnical Commission, 19 July 2002. - Thompson, A. and Taylor, B. N. sec 8.7, "Logarithmic quantities and units: level, neper, bel", Guide for the Use of the International System of Units (SI) 2008 Edition, NIST Special Publication 811, 2nd printing (November 2008), SP811 PDF - "International Standard CEI-IEC 27-3 Letter symbols to be used in electrical technology Part 3: Logarithmic quantities and units". International Electrotechnical Commission. - Mark, James E. (2007). Physical Properties of Polymers Handbook. Springer. p. 1025. … the decibel represents a reduction in power of 1.258 times. - Yost, William (1985). Fundamentals of Hearing: An Introduction (Second ed.). Holt, Rinehart and Winston. p. 206. ISBN 0-12-772690-X. … a pressure ratio of 1.122 equals + 1.0 dB - Fedor Mitschke, Fiber Optics: Physics and Technology, Springer, 2010 ISBN 3642037038. - David M. Pozar (2005). Microwave Engineering (3rd ed.). Wiley. p. 63. ISBN 978-0-471-44878-5. - Fiber Optics. Springer. 2010. - Sensation and Perception, p. 268, at Google Books - Introduction to Understandable Physics, Volume 2, p. SA19-PA9, at Google Books - Visual Perception: Physiology, Psychology, and Ecology, p. 356, at Google Books - Exercise Psychology, p. 407, at Google Books - Foundations of Perception, p. 83, at Google Books - Fitting The Task To The Human, p. 304, at Google Books - C W Horton, "The bewildering decibel" Elec. Eng., 73, 550-555 (1954) - C S Clay (1999), Underwater sound transmission and SI units, J Acoust Soc Am 106, 3047 - R Hickling (1999), Noise Control and SI Units, J Acoust Soc Am 106, 3048 - Nicholas P. Cheremisinoff (1996) Noise Control in Industry: A Practical Guide, Elsevier, 203 pp, p. 7 - Andrew Clennel Palmer (2008), Dimensional Analysis and Intelligent Experimentation, World Scientific, 154 pp, p.13 - J.C. Gibbings, Dimensional Analysis, p.37, Springer, 2011 ISBN 1849963177. - R J Peters, Acoustics and Noise Control, Routledge, Nov 12, 2013, 400 pages, p.13 - "Electronic Engineer's Handbook" by Donald G. Fink, Editor-in-Chief ISBN 0-07-020980-4 Published by McGraw Hill, page 19-3 - National Institute on Deafness and Other Communications Disorders, Noise-Induced Hearing Loss (National Institutes of Health, 2008). - Bob Chomycz (2000). Fiber optic installer's field manual. McGraw-Hill Professional. pp. 123–126. ISBN 978-0-07-135604-6. - Stephen J. Sangwine and Robin E. N. Horne (1998). The Colour Image Processing Handbook. Springer. pp. 127–130. ISBN 978-0-412-80620-9. - Francis T. S. Yu and Xiangyang Yang (1997). Introduction to optical engineering. Cambridge University Press. pp. 102–103. ISBN 978-0-521-57493-8. - Junichi Nakamura (2006). "Basics of Image Sensors". In Junichi Nakamura. Image sensors and signal processing for digital still cameras. CRC Press. pp. 79–83. ISBN 978-0-8493-3545-7. - What is the difference between dBv, dBu, dBV, dBm, dB SPL, and plain old dB? Why not just use regular voltage and power measurements? – rec.audio.pro Audio Professional FAQ - Rupert Neve, Creation of the dBu standard level reference - deltamedia.com. "DB or Not DB". Deltamedia.com. Retrieved 2013-09-16. - The IEEE Standard Dictionary of Electrical and Electronics terms (6th ed.). IEEE. 1996 . ISBN 1-55937-833-6. - Jay Rose (2002). Audio postproduction for digital video. Focal Press,. p. 25. ISBN 978-1-57820-116-7. - Morfey, C. L. (2001). Dictionary of Acoustics. Academic Press, San Diego. - ANSI, S1.4-19823 Specification for Sound Level Meters, 2.3 Sound Level, p. 2-3. - Bigelow, Stephen. Understanding Telephone Electronics. Newnes. p. 16. ISBN 978-0750671750. - ITU-R BS.1770 - "Glossary: D's". National Weather Service. Retrieved 2013-04-25. - "Radar FAQ from WSI". Archived from the original on 18 May 2008. Retrieved 2008-03-18. - "Definition at Everything2". Retrieved 2008-08-06. - Carr, Joseph (2002). RF Components and Circuits. Newnes. pp. 45–46. ISBN 978-0750648448. - "The dBµ vs. dBu Mystery: Signal Strength vs. Field Strength?". radio-timetraveller.blogspot.com. Retrieved 13 October 2016. - David Adamy. EW 102: A Second Course in Electronic Warfare. Retrieved 2013-09-16. - ITU-T Rec. G.100.1 The use of the decibel and of relative levels in speechband telecommunications https://www.itu.int/rec/dologin_pub.asp?lang=e&id=T-REC-G.100.1-201506-I!!PDF-E&type=items - dBrnC is defined on page 230 in "Engineering and Operations in the Bell System," (2ed), R.F. Rey (technical editor), copyright 1983, AT&T Bell Laboratories, Murray Hill, NJ, ISBN 0-932764-04-5 - K. N. Raja Rao (2013-01-31). Satellite Communication: Concepts And Applications. Retrieved 2013-09-16. - Ali Akbar Arabi. Comprehensive Glossary of Telecom Abbreviations and Acronyms. Retrieved 2013-09-16. - Mark E. Long. The Digital Satellite TV Handbook. Retrieved 2013-09-16. - Mac E. Van Valkenburg (2001-10-19). Reference Data for Engineers: Radio, Electronics, Computers and Communications. Retrieved 2013-09-16. - setting the TX power for a Wi-Fi device in Linux showing units in mBm - kernel notification of change in regulatory domain showing units in mBm
What is VBA SIN Function The VBA SIN function is listed under the math category of VBA functions. When you use it in a VBA code, it returns the sine of a supplied angle. You can learn more about sine from here. how to use it To use VBA's SIN function you need to understand its syntax and arguments: - Number: An integer to specify the angle (in radians) that you want to calculate the sine of. Example to use SIN Function in VBA To practically understand how to use VBA SIN function, you need to go through the below example where we have written a vba code by using it: Sub example_SIN() Range("B1").Value = Sin(Range("A1")) End Sub In the above code, we have used SIN to get the sine of the angle which we have in the cell in A1 and returned the result in the cell B1. Below are some important points which you need to take care while using SIN function in VBA. - If the value specified is a value other than a number or a number that can’t be recognized as a number, VBA will return the run-time 13 error. - You can multiply the result returned by the SIN with pi/180 to convert it into a radian and 180/pi to convert it into degrees. About the Author Puneet is using Excel since his college days. He helped thousands of people to understand the power of the spreadsheets and learn Microsoft Excel. You can ﬁnd him online, tweeting about Excel, on a running track, or sometimes hiking up a mountain.
About This Chapter 1. How to Convert Grams to Amu This lesson explains the concept of the Atomic Mass Unit (AMU). The definition and significance of the unit is explained. The lesson also uses examples to describe how to convert from grams to AMU. 2. Malleability in Chemistry: Definition & Examples This lesson defines malleability and the origin of this physical property. The lesson provides examples of how malleability of metals can be observed in everyday life. 3. Mixture in Chemistry: Definition & Examples Very few of the chemicals and substances we encounter on a daily basis are in their pure form. Many of them are mixtures. In this lesson, you will learn about the types of mixtures recognized by scientists. 4. Primary Structure of Protein: Definition & Overview The primary structure of a protein is what is encoded in the DNA. All other protein structures involve folding of the protein, chemical interactions within the protein, and protein-protein interactions. This lesson describes primary protein structure. 5. Reactant in Chemistry: Definition & Examples This lesson defines reactants within chemical reactions and how reactants are written in chemical reactions. The role of chemical reactions in reactions is explained, and several examples are provided to provide important context. 6. Reduction in Chemistry: Definition & Overview When atoms are greedy for electrons, they steal them from other atoms. This reduces their charge. You can see the effects of reduction in the world around you. Learn more about reduction in chemistry and see some examples of it. 7. Significant Figure: Definition, Examples & Practice Problems In this lesson, you'll learn about the concept of significant figures and apply it to addition, subtraction, multiplication, and division. You'll learn what numbers are significant, why they are significant, and how to deal with zeroes in a number. 8. Solubility in Chemistry: Definition & Properties This lesson defines solubility and discusses this property in the context of chemistry. The lesson also includes a discussion of the impact that temperature and intermolecular interactions can have on solubility. 9. Strong Acid: Definition & Examples Acids are very common in nature and in chemical reactions. In this lesson, you will learn what makes a substance an acid and how to recognize strong acids from others. 10. Strong Base: Definition & Examples Next time you open your medicine cupboard or pick up some cleaning supplies, beware you might be handling some strong bases! In this lesson, learn the definition of a strong base and where you can find them, then test your new knowledge with a quiz. 11. Tertiary Structure of Protein: Definition & Overview Tertiary protein structure turns a simple polypeptide with pretty little ribbons and twists into a big, globular mass. Amino acid side chains are the culprit. Read this lesson to find out why. 12. The Law of Definite Proportions: Definition & Examples Have you ever had to double a baking recipe? The trick is to always keep the ingredient proportions the same as in the original recipe. This cooking principle follows the Law of Definite Proportions in chemistry, which is the focus of this lesson. 13. What are Calories? - Definition & Explanation In this lesson, the concept of the calorie is defined as a measurement unit for energy. A brief history of the development of the calorie is included in the lesson as well as examples of unit conversions and basic calculations with this unit. 14. What Are Chemical Properties? - Definition & Examples Characterizing substances by their properties is essential in identifying them. In this lesson, you'll learn how chemical properties give us clues about the nature of a substance by looking at some common examples. 15. What Is a Chemical Change? - Properties, Types & Examples Chemical changes are fundamental changes that produce new combinations of matter. A distinction is made between chemical and physical changes. The signs of chemical changes are discussed, and several types of chemical changes are explored in this lesson. 16. What Is a Chemical Compound? - Definition & Examples Very few single chemical elements are encountered in everyday life. In this lesson, you will learn about chemical compounds through some examples to gain a better understanding of what they are and how they form. 17. What is a Chemical Formula? - Definition, Types & Examples Chemical formulas provide a lot of information about chemical substances, such as how many and what atoms they are made of, as well as the way the atoms are arranged. In this lesson, we'll discuss the different types of chemical formulas. 18. What Is a Chemical Property of Matter? - Definition & Examples All matter is characterized based on its properties. In this lesson, you will learn about the different chemical properties of matter and ways to identify them. 19. What is Chemistry? - Definition, History & Topics Chemistry is the science of matter. This may sound simple, but chemistry is a complex and broad topic that broaches a wide variety of fields. From the core of the earth to the farthest reaches of the universe, chemistry is everything and everywhere. 20. What is Inorganic Chemistry? - Definition, Impact Factor & Examples With this lesson, you will learn the definition of inorganic chemistry. You will also learn the types of inorganic compounds, how they react and their applications in several industry sectors. 21. What Is Scientific Notation? - Definition, Rules & Examples Scientific notation is part of the language of math and science and allows us to deal with a vast array of numbers, large and small. Learn more about what it is, why it's important, and how to use it. Earning College Credit Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level. To learn more, visit our Earning Credit Page Transferring credit to the school of your choice Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you. Other chapters within the General Studies Science: Help & Review course - Chemical Compounds & Bonds Overview - Drawing Conclusions from a Scientific Investigation - Electricity Fundamentals & Overview - Energy & Heat Overview - Essential Biology Concepts - Essential Concepts in Physics - Evolutionary Principles - Genetics & Evolution Overview - Food Webs Overview - Components of Living Things - Intro to Biodiversity, Adaptation & Classification - Human Body Systems: Functions & Processes - Foundations of Chemical Compounds & Bonds - Foundations of Chemical Reactions, Acids, and Bases - Foundations of Energy & Heat - Foundations of Magnetism - Fundamentals of Mechanics - Lab Equipment for Scientific Study - Measurement & the Metric System Fundamentals - Nuclear Energy Fundamentals - Planning a Scientific Investigation Or Experiment - Plant & Soil Ecology - Populations & Relationships in Ecology - Sound & Light Waves - Studying Biological Communities - The Periodic Table, Atoms & Elements - Using Data for Investigation & Experimentation - Scientific Data: Organization, Analysis & Drawing Conclusions - Types of Living Things - Plant Structure & Processes - Fundamentals of Matter - Mechanics of Physics - Introduction to Relativity - Fundamentals of Electricity - Introduction to Magnetism - Fundamentals of Waves, Sound and Light - Space, The Solar System and the Universe - Introduction to Atmospheric Science - Geology Basics - Fundamentals of Genetics - Foundations of Science - Scientific Research & Experiments
Cassini Reveals Saturn's Eerie-Sounding Radio Emissions July 25, 2005 (Source: Jet Propulsion Laboratory / University of Iowa) Saturn's radio emissions could be mistaken for a Halloween sound track. That's how two researchers describe their recent findings, published in the July 23 issue of the Geophysical Research Letters. Their paper is based on data from the Cassini spacecraft radio and plasma wave science instrument. The study investigates sounds that are not just eerie, but also descriptive of a phenomenon similar to Earth's northern lights. "All of the structures we observe in Saturn's radio spectrum are giving us clues about what might be going on in the source of the radio emissions above Saturn's auroras," said Dr. Bill Kurth, deputy principal investigator for the instrument. He is with the University of Iowa, Iowa City. Kurth made the discovery along with Principal Investigator Don Gurnett, a professor at the University. "We believe that the changing frequencies are related to tiny radio sources moving up and down along Saturn's magnetic field lines." Samples of the resulting sounds can be heard at www.nasa.gov/cassini , http://saturn.jpl.nasa.gov and http://www-pw.physics.uiowa.edu/cassini/ . The radio emissions, called Saturn kilometric radiation, are generated along with Saturn's auroras, or northern and southern lights. Because the Cassini instrument has higher resolution compared to a similar instrument on NASA's Voyager spacecraft, it has provided more detailed information on the spectrum and the variability of radio emissions. The high-resolution measurements allow scientists to convert the radio waves into audio recordings by shifting the frequencies down into the audio frequency range. The terrestrial cousins of Saturn's radio emissions were first reported in 1979 by Gurnett, who used an instrument on the International Sun-Earth Explorer spacecraft in Earth orbit. Kurth said that despite their best efforts, scientists still haven't agreed on a theory to fully explain the phenomenon. They will get another chance to solve the radio emission puzzle beginning in mid-2008 when Cassini will fly close to, or possibly even through, the source region at Saturn. Gurnett said, "It is amazing that the radio emissions from Earth and Saturn sound so similar." Other contributors to the paper include University of Iowa scientists George Hospodarsky and Baptiste Cecconi; Mike Kaiser (currently at Goddard Space Flight Center, Greenbelt, Md.); French scientists Philippe Louarn, Philippe Zarka and Alain Lecacheux; and Austrian scientists Helmut Rucker and Mohammed Boudjada. Cassini, carrying 12 scientific instruments, on June 30, 2004, became the first spacecraft to orbit Saturn. It is conducting a four-year study of the planet, its rings and many moons. The spacecraft carried the Huygens probe, a six-instrument European Space Agency probe that landed on Titan, Saturn's largest moon, in January 2005. The Cassini-Huygens mission is a cooperative project of NASA, the European Space Agency and the Italian Space Agency. The Jet Propulsion Laboratory, a division of the California Institute of Technology in Pasadena, manages the Cassini-Huygens mission for NASA's Science Mission Directorate, Washington. JPL designed, developed and assembled the Cassini orbiter. The radio and plasma wave science team is based at the University of Iowa, Iowa City. For information on the Cassini mission visit http://saturn.jpl.nasa.gov and http://www.nasa.gov/cassini. Carolina Martinez (818) 354-9382 Jet Propulsion Laboratory, Pasadena, Calif. Gary Galluzzo (319) 384-0009 University of Iowa, Iowa City NEWS RELEASE: 2005-119
In geography, latitude is a geographic coordinate that specifies the north-south position of a point on the Earth's surface. Latitude is an angle (defined below) which ranges from 0° at the Equator to 90° (North or South) at the poles. Lines of constant latitude, or parallels, run east-west as circles parallel to the equator. Latitude is used together with longitude to specify the precise location of features on the surface of the Earth. On its own, the term latitude should be taken to be the geodetic latitude as defined below. Briefly, geodetic latitude at a point is the angle formed by the vector perpendicular (or normal) to the ellipsoidal surface from that point, and the equatorial plane. Also defined are six auxiliary latitudes which are used in special applications. Two levels of abstraction are employed in the definition of latitude and longitude. In the first step the physical surface is modeled by the geoid, a surface which approximates the mean sea level over the oceans and its continuation under the land masses. The second step is to approximate the geoid by a mathematically simpler reference surface. The simplest choice for the reference surface is a sphere, but the geoid is more accurately modeled by an ellipsoid. The definitions of latitude and longitude on such reference surfaces are detailed in the following sections. Lines of constant latitude and longitude together constitute a graticule on the reference surface. The latitude of a point on the actual surface is that of the corresponding point on the reference surface, the correspondence being along the normal to the reference surface which passes through the point on the physical surface. Latitude and longitude together with some specification of height constitute a geographic coordinate system as defined in the specification of the ISO 19111 standard.[a] Since there are many different reference ellipsoids, the precise latitude of a feature on the surface is not unique: this is stressed in the ISO standard which states that "without the full specification of the coordinate reference system, coordinates (that is latitude and longitude) are ambiguous at best and meaningless at worst". This is of great importance in accurate applications, such as a Global Positioning System (GPS), but in common usage, where high accuracy is not required, the reference ellipsoid is not usually stated. In English texts the latitude angle, defined below, is usually denoted by the Greek lower-case letter phi (? or ?). It is measured in degrees, minutes and seconds or decimal degrees, north or south of the equator. The precise measurement of latitude requires an understanding of the gravitational field of the Earth, either to set up theodolites or to determine GPS satellite orbits. The study of the figure of the Earth together with its gravitational field is the science of geodesy. This article relates to coordinate systems for the Earth: it may be extended to cover the Moon, planets and other celestial objects by a simple change of nomenclature. The graticule is formed by the lines of constant latitude and constant longitude, which are constructed with reference to the rotation axis of the Earth. The primary reference points are the poles where the axis of rotation of the Earth intersects the reference surface. Planes which contain the rotation axis intersect the surface at the meridians; and the angle between any one meridian plane and that through Greenwich (the Prime Meridian) defines the longitude: meridians are lines of constant longitude. The plane through the centre of the Earth and perpendicular to the rotation axis intersects the surface at a great circle called the Equator. Planes parallel to the equatorial plane intersect the surface in circles of constant latitude; these are the parallels. The Equator has a latitude of 0°, the North Pole has a latitude of 90° North (written 90° N or +90°), and the South Pole has a latitude of 90° South (written 90° S or -90°). The latitude of an arbitrary point is the angle between the equatorial plane and the normal to the surface at that point: the normal to the surface of the sphere is along the radius vector. The latitude, as defined in this way for the sphere, is often termed the spherical latitude, to avoid ambiguity with the geodetic latitude and the auxiliary latitudes defined in subsequent sections of this article. Besides the equator, four other parallels are of significance: The plane of the Earth's orbit about the Sun is called the ecliptic, and the plane perpendicular to the rotation axis of the Earth is the equatorial plane. The angle between the ecliptic and the equatorial plane is called variously the axial tilt, the obliquity, or the inclination of the ecliptic, and it is conventionally denoted by i. The latitude of the tropical circles is equal to i and the latitude of the polar circles is its complement (90° - i). The axis of rotation varies slowly over time and the values given here are those for the current epoch. The time variation is discussed more fully in the article on axial tilt.[b] The figure shows the geometry of a cross-section of the plane perpendicular to the ecliptic and through the centres of the Earth and the Sun at the December solstice when the Sun is overhead at some point of the Tropic of Capricorn. The south polar latitudes below the Antarctic Circle are in daylight, whilst the north polar latitudes above the Arctic Circle are in night. The situation is reversed at the June solstice, when the Sun is overhead at the Tropic of Cancer. Only at latitudes in between the two tropics is it possible for the Sun to be directly overhead (at the zenith). On map projections there is no universal rule as to how meridians and parallels should appear. The examples below show the named parallels (as red lines) on the commonly used Mercator projection and the Transverse Mercator projection. On the former the parallels are horizontal and the meridians are vertical, whereas on the latter there is no exact relationship of parallels and meridians with horizontal and vertical: both are complicated curves. On the sphere the normal passes through the centre and the latitude (?) is therefore equal to the angle subtended at the centre by the meridian arc from the equator to the point concerned. If the meridian distance is denoted by m(?) then where R denotes the mean radius of the Earth. R is equal to 6,371 km or 3,959 miles. No higher accuracy is appropriate for R since higher-precision results necessitate an ellipsoid model. With this value for R the meridian length of 1 degree of latitude on the sphere is 111.2 km (69.1 statute miles) (60.0 nautical miles). The length of 1 minute of latitude is 1.853 km (1.151 statute miles) (1.00 nautical miles), while the length of 1 second of latitude is 30.8 m or 101 feet (see nautical mile). In 1687 Isaac Newton published the Philosophiæ Naturalis Principia Mathematica, in which he proved that a rotating self-gravitating fluid body in equilibrium takes the form of an oblate ellipsoid. (This article uses the term ellipsoid in preference to the older term spheroid.) Newton's result was confirmed by geodetic measurements in the 18th century. (See Meridian arc.) An oblate ellipsoid is the three-dimensional surface generated by the rotation of an ellipse about its shorter axis (minor axis). "Oblate ellipsoid of revolution" is abbreviated to 'ellipsoid' in the remainder of this article. (Ellipsoids which do not have an axis of symmetry are termed triaxial.) Many different reference ellipsoids have been used in the history of geodesy. In pre-satellite days they were devised to give a good fit to the geoid over the limited area of a survey but, with the advent of GPS, it has become natural to use reference ellipsoids (such as WGS84) with centre at the centre of mass of the Earth and minor axis aligned to the rotation axis of the Earth. These geocentric ellipsoids are usually within 100 m (330 ft) of the geoid. Since latitude is defined with respect to an ellipsoid, the position of a given point is different on each ellipsoid: one cannot exactly specify the latitude and longitude of a geographical feature without specifying the ellipsoid used. Many maps maintained by national agencies are based on older ellipsoids, so one must know how the latitude and longitude values are transformed from one ellipsoid to another. GPS handsets include software to carry out datum transformations which link WGS84 to the local reference ellipsoid with its associated grid. The shape of an ellipsoid of revolution is determined by the shape of the ellipse which is rotated about its minor (shorter) axis. Two parameters are required. One is invariably the equatorial radius, which is the semi-major axis, a. The other parameter is usually (1) the polar radius or semi-minor axis, b; or (2) the (first) flattening, f; or (3) the eccentricity, e. These parameters are not independent: they are related by Many other parameters (see ellipse, ellipsoid) appear in the study of geodesy, geophysics and map projections but they can all be expressed in terms of one or two members of the set a, b, f and e. Both f and e are small and often appear in series expansions in calculations; they are of the order and 0.08 respectively. Values for a number of ellipsoids are given in Figure of the Earth. Reference ellipsoids are usually defined by the semi-major axis and the inverse flattening, . For example, the defining values for the WGS84 ellipsoid, used by all GPS devices, are from which are derived The difference between the semi-major and semi-minor axes is about 21 km (13 miles) and as fraction of the semi-major axis it equals the flattening; on a computer monitor the ellipsoid could be sized as 300 by 299 pixels. This would barely be distinguishable from a 300-by-300-pixel sphere, so illustrations usually exaggerate the flattening. The graticule on the ellipsoid is constructed in exactly the same way as on the sphere. The normal at a point on the surface of an ellipsoid does not pass through the centre, except for points on the equator or at the poles, but the definition of latitude remains unchanged as the angle between the normal and the equatorial plane. The terminology for latitude must be made more precise by distinguishing: The importance of specifying the reference datum may be illustrated by a simple example. On the reference ellipsoid for WGS84, the centre of the Eiffel Tower has a geodetic latitude of 48° 51? 29? N, or 48.8583° N and longitude of 2° 17? 40? E or 2.2944°E. The same coordinates on the datum ED50 define a point on the ground which is 140 metres (460 feet) distant from the tower. A web search may produce several different values for the latitude of the tower; the reference ellipsoid is rarely specified. where M(?) is the meridional radius of curvature. The distance from the equator to the pole is For WGS84 this distance is . The evaluation of the meridian distance integral is central to many studies in geodesy and map projection. It can be evaluated by expanding the integral by the binomial series and integrating term by term: see Meridian arc for details. The length of the meridian arc between two given latitudes is given by replacing the limits of the integral by the latitudes concerned. The length of a small meridian arc is given by \|0°\|\|110.574 km\|\|111.320 km\| \|15°\|\|110.649 km\|\|107.550 km\| \|30°\|\|110.852 km\|\|96.486 km\| \|45°\|\|111.132 km\|\|78.847 km\| \|60°\|\|111.412 km\|\|55.800 km\| \|75°\|\|111.618 km\|\|28.902 km\| \|90°\|\|111.694 km\|\|0.000 km\| When the latitude difference is 1 degree, corresponding to radians, the arc distance is about The distance in metres (correct to 0.01 metre) between latitudes - 0.5 degrees and + 0.5 degrees on the WGS84 spheroid is The following graph illustrates the variation of both a degree of latitude and a degree of longitude with latitude. Historically a nautical mile was defined as the length of one minute of arc along a meridian of a spherical earth. An ellipsoid model leads to a variation of the nautical mile with latitude. This was resolved by defining the nautical mile to be exactly 1,852 metres. However for all practical purposes distances are measured from the latitude scale of charts. As the Royal Yachting Association says in its manual for day skippers: "1 (minute) of Latitude = 1 sea mile", followed by "For most practical purposes distance is measured from the latitude scale, assuming that one minute of latitude equals one nautical mile". There are six auxiliary latitudes that have applications to special problems in geodesy, geophysics and the theory of map projections: The definitions given in this section all relate to locations on the reference ellipsoid but the first two auxiliary latitudes, like the geodetic latitude, can be extended to define a three-dimensional geographic coordinate system as discussed below. The remaining latitudes are not used in this way; they are used only as intermediate constructs in map projections of the reference ellipsoid to the plane or in calculations of geodesics on the ellipsoid. Their numerical values are not of interest. For example, no one would need to calculate the authalic latitude of the Eiffel Tower. The expressions below give the auxiliary latitudes in terms of the geodetic latitude, the semi-major axis, a, and the eccentricity, e. (For inverses see below.) The forms given are, apart from notational variants, those in the standard reference for map projections, namely "Map projections: a working manual" by J. P. Snyder. Derivations of these expressions may be found in Adams and online publications by Osborne and Rapp. The geocentric latitude is the angle between the equatorial plane and the radius from the centre to a point on the surface. The relation between the geocentric latitude (?) and the geodetic latitude (?) is derived in the above references as The geodetic and geocentric latitudes are equal at the equator and at the poles but at other latitudes they differ by a few minutes of arc. Taking the value of the squared eccentricity as 0.0067 (it depends on the choice of ellipsoid) the maximum difference of may be shown to be about 11.5 minutes of arc at a geodetic latitude of approximately 45° 6?.[c] The parametric or reduced latitude, ?, is defined by the radius drawn from the centre of the ellipsoid to that point Q on the surrounding sphere (of radius a) which is the projection parallel to the Earth's axis of a point P on the ellipsoid at latitude ?. It was introduced by Legendre and Bessel who solved problems for geodesics on the ellipsoid by transforming them to an equivalent problem for spherical geodesics by using this smaller latitude. Bessel's notation, u(?), is also used in the current literature. The parametric latitude is related to the geodetic latitude by: The alternative name arises from the parameterization of the equation of the ellipse describing a meridian section. In terms of Cartesian coordinates p, the distance from the minor axis, and z, the distance above the equatorial plane, the equation of the ellipse is: The Cartesian coordinates of the point are parameterized by Cayley suggested the term parametric latitude because of the form of these equations. The rectifying latitude, ?, is the meridian distance scaled so that its value at the poles is equal to 90 degrees or radians: where the meridian distance from the equator to a latitude ? is (see Meridian arc) and the length of the meridian quadrant from the equator to the pole (the polar distance) is Using the rectifying latitude to define a latitude on a sphere of radius defines a projection from the ellipsoid to the sphere such that all meridians have true length and uniform scale. The sphere may then be projected to the plane with an equirectangular projection to give a double projection from the ellipsoid to the plane such that all meridians have true length and uniform meridian scale. An example of the use of the rectifying latitude is the Equidistant conic projection. (Snyder, Section 16). The rectifying latitude is also of great importance in the construction of the Transverse Mercator projection. The authalic (Greek for same area) latitude, ?, gives an area-preserving transformation to a sphere. and the radius of the sphere is taken as The conformal latitude, ?, gives an angle-preserving (conformal) transformation to the sphere. where gd(x) is the Gudermannian function. (See also Mercator projection.) The conformal latitude defines a transformation from the ellipsoid to a sphere of arbitrary radius such that the angle of intersection between any two lines on the ellipsoid is the same as the corresponding angle on the sphere (so that the shape of small elements is well preserved). A further conformal transformation from the sphere to the plane gives a conformal double projection from the ellipsoid to the plane. This is not the only way of generating such a conformal projection. For example, the 'exact' version of the Transverse Mercator projection on the ellipsoid is not a double projection. (It does, however, involve a generalisation of the conformal latitude to the complex plane). The isometric latitude, ?, is used in the development of the ellipsoidal versions of the normal Mercator projection and the Transverse Mercator projection. The name "isometric" arises from the fact that at any point on the ellipsoid equal increments of ? and longitude ? give rise to equal distance displacements along the meridians and parallels respectively. The graticule defined by the lines of constant ? and constant ?, divides the surface of the ellipsoid into a mesh of squares (of varying size). The isometric latitude is zero at the equator but rapidly diverges from the geodetic latitude, tending to infinity at the poles. The conventional notation is given in Snyder (page 15): For the normal Mercator projection (on the ellipsoid) this function defines the spacing of the parallels: if the length of the equator on the projection is E (units of length or pixels) then the distance, y, of a parallel of latitude ? from the equator is The isometric latitude ? is closely related to the conformal latitude ?: The formulae in the previous sections give the auxiliary latitude in terms of the geodetic latitude. The expressions for the geocentric and parametric latitudes may be inverted directly but this is impossible in the four remaining cases: the rectifying, authalic, conformal, and isometric latitudes. There are two methods of proceeding. The first is a numerical inversion of the defining equation for each and every particular value of the auxiliary latitude. The methods available are fixed-point iteration and Newton-Raphson root finding. The other, more useful, approach is to express the auxiliary latitude as a series in terms of the geodetic latitude and then invert the series by the method of Lagrange reversion. Such series are presented by Adams who uses Taylor series expansions and gives coefficients in terms of the eccentricity. Osborne derives series to arbitrary order by using the computer algebra package Maxima and expresses the coefficients in terms of both eccentricity and flattening. The series method is not applicable to the isometric latitude and one must use the conformal latitude in an intermediate step. The following plot shows the difference between the geodetic latitude and the auxiliary latitudes other than the isometric latitude (which diverges to infinity at the poles) for the case of the WGS84 ellipsoid. In every case the auxiliary latitude is the less (in magnitude) than the geodetic latitude. The differences shown on the plot are in arc minutes. The horizontal resolution of the plot fails to make clear that the maxima of the curves are not at 45° but calculation shows that they are within a few arc minutes of 45°. Some representative data points are given in the table following the plot. Note the closeness of the conformal and geocentric latitudes. This was exploited in the days of hand calculators to expedite the construction of map projections.:108 To first order in the flattening f, the auxiliary latitudes can be expressed as ? = ? - Cf sin 2? where the constant C takes on the values [, , , 1, 1] for ? = [?, ?, ?, ?, ?]. ? - ? ? - ? ? - ? ? - ? ? - ? The geodetic latitude, or any of the auxiliary latitudes defined on the reference ellipsoid, constitutes with longitude a two-dimensional coordinate system on that ellipsoid. To define the position of an arbitrary point it is necessary to extend such a coordinate system into three dimensions. Three latitudes are used in this way: the geodetic, geocentric and parametric latitudes are used in geodetic coordinates, spherical polar coordinates and ellipsoidal coordinates respectively. At an arbitrary point P consider the line PN which is normal to the reference ellipsoid. The geodetic coordinates P(?,?,h) are the latitude and longitude of the point N on the ellipsoid and the distance PN. This height differs from the height above the geoid or a reference height such as that above mean sea level at a specified location. The direction of PN will also differ from the direction of a vertical plumb line. The relation of these different heights requires knowledge of the shape of the geoid and also the gravity field of the Earth. The geocentric latitude ? is the complement of the polar angle in conventional spherical polar coordinates in which the coordinates of a point are P(r,??,?) where r is the distance of P from the centre O, is the angle between the radius vector and the polar axis and ? is longitude. Since the normal at a general point on the ellipsoid does not pass through the centre it is clear that points P' on the normal, which all have the same geodetic latitude, will have differing geocentric latitudes. Spherical polar coordinate systems are used in the analysis of the gravity field. The parametric latitude can also be extended to a three-dimensional coordinate system. For a point P not on the reference ellipsoid (semi-axes OA and OB) construct an auxiliary ellipsoid which is confocal (same foci F, F?) with the reference ellipsoid: the necessary condition is that the product ae of semi-major axis and eccentricity is the same for both ellipsoids. Let u be the semi-minor axis (OD) of the auxiliary ellipsoid. Further let ? be the parametric latitude of P on the auxiliary ellipsoid. The set (u,?,?) define the ellipsoid coordinates.:§4.2.2 These coordinates are the natural choice in models of the gravity field for a rotating ellipsoidal body. The relations between the above coordinate systems, and also Cartesian coordinates are not presented here. The transformation between geodetic and Cartesian coordinates may be found in Geographic coordinate conversion. The relation of Cartesian and spherical polars is given in Spherical coordinate system. The relation of Cartesian and ellipsoidal coordinates is discussed in Torge. Astronomical latitude (?) is the angle between the equatorial plane and the true vertical at a point on the surface. The true vertical, the direction of a plumb line, is also the direction of the gravity acceleration, the resultant of the gravitational acceleration (mass-based) and the centrifugal acceleration at that latitude. Astronomic latitude is calculated from angles measured between the zenith and stars whose declination is accurately known. In general the true vertical at a point on the surface does not exactly coincide with either the normal to the reference ellipsoid or the normal to the geoid. The angle between the astronomic and geodetic normals is usually a few seconds of arc but it is important in geodesy. The reason why it differs from the normal to the geoid is, because the geoid is an idealized, theoretical shape "at mean sea level". Points on the real surface of the earth are usually above or below this idealized geoid surface and here the true vertical can vary slightly. Also, the true vertical at a point at a specific time is influenced by tidal forces, which the theoretical geoid averages out. Astronomical latitude is not to be confused with declination, the coordinate astronomers use in a similar way to specify the angular position of stars north/south of the celestial equator (see equatorial coordinates), nor with ecliptic latitude, the coordinate that astronomers use to specify the angular position of stars north/south of the ecliptic (see ecliptic coordinates).
As provided by the National Science Teachers Association (NSTA): The National Science Education Standards (NSES p. 23) defines scientific inquiry as: Scientific Inquiry - the diverse ways in which scientists study the natural world and propose explanations based on the evidence derived from their work. Scientific inquiry also refers to the activities through which students develop knowledge and understanding of scientific ideas, as well as an understanding of how scientists study the natural world." The Science as Inquiry Standard in NSES includes the abilities necessary to do scientific inquiry and understanding about scientific inquiry. Scientific inquiry reflects how scientists come to understand the natural world, and it is at the heart of how students learn. From a very early age, children interact with their environment, ask questions, and seek ways to answer those questions. Understanding science content is significantly enhanced when ideas are anchored to inquiry experiences. Scientific inquiry is a powerful way of understanding science content. Students learn how to ask questions and use evidence to answer them. In the process of learning the strategies of scientific inquiry, students learn to conduct an investigation and collect evidence from a variety of sources, develop an explanation from the data, and communicate and defend their conclusions. The National Science Teachers Association (NSTA) recommends that all K–16 teachers embrace scientific inquiry and is committed to helping educators make it the centerpiece of the science classroom. The use of scientific inquiry will help ensure that students develop a deep understanding of science and scientific inquiry. Regarding the use of scientific inquiry as a teaching approach, NSTA recommends that science teachers: Regarding students’ abilities to do scientific inquiry, NSTA recommends that teachers help students: A) Learn how to identify and ask appropriate questions that can be answered through scientific investigations. B) Design and conduct investigations to collect the evidence needed to answer a variety of questions. C) Use appropriate equipment and tools to interpret and analyze data. D) Learn how to draw conclusions and think critically and logically to create explanations based on their evidence. E) Communicate and defend their results to their peers and others. Regarding students’ understanding about scientific inquiry, NSTA recommends that teachers help students understand: a. That science involves asking questions about the world and then developing scientific investigations to answer their questions. b. That there is no fixed sequence of steps that all scientific investigations follow. Different kinds of questions suggest different kinds of scientific investigations. c. That scientific inquiry is central to the learning of science and reflects how science is done. d. The importance of gathering empirical data using appropriate tools and instruments. e. That the evidence they collect can change their perceptions about the world and increase their scientific knowledge. f. The importance of being skeptical when they assess their own work and the work of others. g. That the scientific community, in the end, seeks explanations that are empirically based and logically consistent. —Adopted by the NSTA Board of Directors, October 2004 Science Inquiry by the : The 5 features of science inquiry, students: Goals of the NIH Module: Doing Science: The Process of Scientific Inquiry helps students achieve four major goals associated with scientific literacy: The Process of Scientific Inquiry Students explore the basics of scientific inquiry, refine their critical-thinking skills, and appreciate the purpose of scientific research. l. The first is to help students understand the basic aspects of scientific inquiry. Science proceeds by a continuous, incremental process that involves generating hypotheses, collecting evidence, testing hypotheses, and reaching evidence-based conclusions. Rather than involving one particular method, scientific inquiry is flexible. Different types of questions require different types of investigations. Moreover, there is more than one way to answer a question. Although students may associate science with experimentation, science also uses observations, surveys, and other non-experimental approaches. ll. The second objective is to provide students with an opportunity to practice and refine their critical-thinking skills. Such abilities are important, not just for scientific pursuits, but for making decisions in everyday life. Our fast-changing world requires today’s youth to be life-long learners. They must be able to evaluate information from a variety of sources and assess its usefulness. They need to discriminate between objective science and pseudoscience. Students must be able to establish causal relationships and distinguish them from mere associations. lll. The third objective is to convey to students the purpose of scientific research. Ongoing research affects how we understand the world around us and provides a foundation for improving our choices about personal health and the health of our community. In this module, students participate in a virtual investigation that gives them experience with the major aspects of scientific inquiry. The lessons encourage students to think about the relationships among knowledge, choice, behavior, and human health in this way: Knowledge (what is known and not known) + Choice = Power Power + Behavior = Enhanced Human Health lV. The final objective of this module is to encourage students to think in terms of these relationships now and as they grow older. Use this to plan an inquiry-based science program by providing short-term objectives for students: 1: Inquiring Minds - Engage: Students become engaged in the process of scientific inquiry. Scientists learn about the natural world through scientific inquiry. • Scientists ask questions that can be answered through investigations. • Scientists design and carry out investigations. • Scientists think logically to make relationships between evidence and explanations. • Scientists communicate procedures and explanations. 2: Working with Questions - Explore: Students consider what makes questions scientifically testable. Students gain a common set of experiences upon which to begin building their understanding. Scientists ask questions that can be answered through investigations. • Testable questions are not answered by personal opinions or belief in the supernatural. • Testable questions are answered by collecting evidence and developing explanations based on that evidence. 3: Conducting a Scientific Investigation - Explain/Elaborate: Students conduct an investigation in the context of a community health department. They propose possible sources of the health problem and describe how they might confirm or refute these possibilities. Scientific explanations emphasize evidence. • Scientists think critically about the types of evidence that should be collected. Scientists analyze the results of their investigations to produce scientifically acceptable explanations. 4: Pulling It All Together - Evaluate: Students deepen their understanding of scientific inquiry by performing their own investigation and evaluating one performed by another student. Scientific inquiry is a process of discovery. • It begins with a testable question. • Scientific investigations involve collecting evidence. • Explanations are evidence based. • Scientists communicate their results to their peers. Use this for ongoing assessment of your instruction and student learning: Abilities necessary to do scientific inquiry • Identify questions that can be answered through scientific investigations. • Use appropriate tools and techniques to gather, analyze, and interpret data. • Develop descriptions, explanations, predictions, and models using evidence. • Think critically and logically to make the relationships between evidence and explanations. • Recognize and analyze alternative explanations and predictions. • Communicate scientific procedures and explanations. • Use mathematics in all aspects of scientific inquiry. Understandings about scientific inquiry • Different kinds of questions suggest different kinds of scientific investigations. Some investigations involve observing and describing objects, organisms, or events; some involve collecting specimens; some involve experiments; some involve seeking more information; some involve discovery of new objects; and some involve making models. • Mathematics is important in all aspects of scientific inquiry. Structure and function in living systems • Some diseases are the result of intrinsic failures of the system. Others are the result of damage by infection by other organisms. Populations and ecosystems • Food webs identify the relationships among producers, consumers, and decomposers in an ecosystem. Understandings about science and technology • Science and technology are reciprocal. Science helps drive technology. Technology is essential to science, because it provides instruments and techniques that enable observations of objects and phenomena that are otherwise unobservable. • The potential for accidents and the existence of hazards imposes the need for injury prevention. Safe living involves the development and use of safety precautions and the recognition of risk in personal decisions. Risks and benefits • Risk analysis considers the type of hazard and estimates the number of people who might be exposed and the number likely to suffer consequences. The results are used to determine the options for reducing or eliminating risks. • Important personal and social decisions are made based on perceptions of benefits and risks. Science and technology in society • Technology influences society through its products and processes. Technology influences the quality of life and the ways people act and interact. Science as a human endeavor • Science requires different abilities, depending on such factors as the field of study and type of inquiry. Science is very much a human endeavor, and the work of science relies on basic human qualities, such as reasoning, insight, energy, skills, and creativity. Nature of science • Scientists formulate and test their explanations of nature using observation, experiments, and theoretical and mathematical models. Instead of passive absorption of materials, students are developing skills, analyzing and evaluating evidence, experiencing and discussing, and talking to their peers about their own understanding - Engage, Explore, Explain, Elaborate, Evaluate. 1. Understanding science is more than knowing facts. 2. Students build new knowledge and understanding based on what they already know and believe. 3. Students formulate new knowledge by modifying and refining their current concepts and by adding new concepts to what they already know. 4. Learning is mediated by the social environment in which learners interact with others. 5. Effective learning requires that students take control of their own learning. 6. The ability to apply knowledge to novel situations (that is, to transfer learning) is affected by the degree to which students learn with understanding. It should be a goal of the instructor to foster the development of science process skills. The application of these skills allows students to investigate important issues in the world around them. Inquiry-based units will include many or most of the following process skills. These process skills should be incorporated into students? instruction as developmentally appropriate. Classifying - arranging or distributing objects, events, or information representing objects or events in classes according to some method or system Communicating - giving oral and written explanations or graphic representations of observations Comparing and contrasting - identifying similarities and differences between or among objects, events, data, systems, etc. Creating models - displaying information, using multisensory representations Gathering and organizing data - collecting information about objects and events which illustrate a specific situation Generalizing - drawing general conclusions from particulars Identifying variables - recognizing the characteristics of objects or factors in events that are constant or change under different conditions Inferring - drawing a conclusion based on prior experiences Interpreting data - analyzing data that have been obtained and organized by determining apparent patterns or relationships in the data Making decisions - identifying alternatives and choosing a course of action from among the alternatives after basing the judgment for the selection on justifiable reasons Manipulating materials - handling or treating materials and equipment safely, skillfully, and effectively Measuring - making quantitative observations by comparing to a conventional or nonconventional standard Observing - becoming aware of an object or event by using any of the senses (or extensions of the senses) to identify properties Predicting - making a forecast of future events or conditions expected to exist Note: As an example, these processes are applied in the three key ideas in Standard 1, which outline scientific inquiry. Inquiry may proceed in a cyclical pattern, with students moving from Key Idea 1 to Key Idea 3 and back to 1 again. *As presented by the State University of New York at: http://www.emsc.nysed.gov/ciai/ When you research information you must cite the reference. Citing for websites is different from citing from books, magazines and periodicals. The style of citing shown here is from the MLA Style Citations (Modern Language Association). When citing a WEBSITE the general format is as follows. Author Last Name, First Name(s). "Title: Subtitle of Part of Web Page, if appropriate." Title: Subtitle: Section of Page if appropriate. Sponsoring/Publishing Agency, If Given. Additional significant descriptive information. Date of Electronic Publication or other Date, such as Last Updated. Day Month Year of access < URL >. Amsel, Sheri. "Inquiry – Understand What it is from Different Sources" Exploring Nature Educational Resource ©2005-2019. July 22, 2019 < http://www.exploringnature.org/db/view/Inquiry-ndash-Understand-What-it-is-from-Different-Sources >
Listening is a hugely important skill as it helps children interpret instructions. Given that early schooling is highly verbal, it is essential to master listening early on. Here are some games to help improve listening skills with your children:- Colour Story: Give each child a different coloured building brick. Tell a story and weave the colours into the story. Each time a child hears there colour, have them wave their brick in the air. Name that Sound: Make sounds and have your children name them. For example, make a siren sound, the noise of an aeroplane, horses hooves, birdsong and so on. Shopping Game: Take up to 20 store cupboard food items or play food and lay them out on the floor. Tell each child a list of three items that you want from the shop and have them walk over to the food, pick out their three items and bring them to you. Play rounds increasing the length of the list each time. Simon Says: You must know this old classic? Instruct children to perform an action prefixed with 'Simon Says...'. 'Simon Says "Touch your nose"', 'Simon says "Twist around"'. Any command without 'Simon Says' must be ignored. Happy Endings: Tell the first part of a story and have your children each make up a different ending to the story. Either read from a book, or make up your own short stories. Vegetables are REALLY interesting...no, really! Babies will eat anything that is fed to them, and aren't discerning about vegetables. Most toddlers will eat most vegetables too and not question them, but as they grow older, and perhaps helped by peer pressure as their social networks grow, children might decide that they don't like certain, or even any, vegetables. Is it the colour? ...the texture? ...the taste? There are a multitude of reasons why children may begin to turn their noses up at vegetables, but do what you can to fight their reluctance and try to keep vegetables firmly on the agenda. One way to make vegetables interesting is to have children think about them properly. Make a vegetable chart and depending on how old your children are, order them in different ways. The youngest children will be able to order by size or to sort them by colour. Older children might be able to start with the sweetest through to the most bitter. You may even be able to teach them about seasonality. Although most vegetables are now available from the supermarkets all year round, there is a pattern of seasonality at which point differet vegetables are available. Perhaps you don't know yourself? In which case, spend time with your older children looking at the seasons of vegetables. Work out which are traditionally available in spring, summer, autumn and winter! Theme days offer a great way to spice up the lives of your little ones a bit, and help them to learn new concepts along the way. If you hold a theme day once a week or once a month, it will also help to mark time for preschoolers who will begin to understand the concept of a week or a month respectively. Choose a theme, dress up for it, play themed games and undertake themed craft. There are lots of colourful themes to choose from, here are a few ideas:- - Emergency services - Doctors and nurses - Princes and princesses - Fairy Tales - Literary characters (from adult or children's books) - Animals (farm, zoo or wild animals) The only limit is your imagination, you can even choose really abstract themes - your little ones don't mind, they will simply love the involvement. Have fun with apples - here are some activity ideas for you to try with your little ones... Apple prints - Start by covering the table and putting out different coloured paints in shallow dishes. Cut two apples in half; one vertically so you get the core and seed shape. The other horizontally so you get the seeds in a star shape. Dip each paint brush into the paint and cover the apple. Carefully press each print onto card. Paint on a stalk or some more seeds, when its dry, to finish it. Think of someone you appreciate or care about to send the card to them as a surprise. Talk about how nice it is to send other people notes of thanks. This is a great way to show the little ones how to appreciate others. Hand-print apple tree - Take some brown paint and cover hands with it to make a great tree trunk! Press onto some card or paper. Take an apple and cut it in half then paint on green paint. Do lots of apple prints to make leaves for the tree! Use a finger dipped in red paint to add apples to the tree. Talk about apple seeds growing into little saplings, then growing into big trees and producing apples on them. Apples and counting - Take an apple and cut it into slices. How many slices can you count together. Then pick out all the seeds. How many are there to start with? What about if you take one away or add a few more? Eat some of the slices and how many are left? Do lots of counting activities and see how good even the smallest toddler can be at counting with a bit of help. Number recognition - Draw some apples - about ten of them - and colour them in in red, yellow and green. Write the numbers 1 to 10 on some paper and cut them out. Place a number in front of a couple of plates and ask your little one to count out the right number of apples into each place. So, if the number 2 is written they must count out 2 apples. Colour sorting - Take 3 envelopes and draw an apple on the front of each one. Colour one red, one yellow and one green. See if your child can sort all the apples you coloured in the above activity and put them in the right envelope. Help them to start with, and then see if they can do it alone without you looking. Try it with some other things too. Healthy eating - Show your little ones how lovely apples can be to eat too! They are great for printing, and counting and craft but best of all they taste great! Go on an apple tree hunt round your area and see how many you can find... or other trees with fruit on them. Have fun! Using technology to teach and inspire children is vital in this day where computers are commonplace, digital gadgets are all over the place and technology is so much more accessible. Many children have their own toy cameras now, which is great to see the world through the eyes of the children. However, you can try to give the camera usage a little more direction by setting the children photography projects such as:- - Things that make me happy (ice cream, friends) - Things that are brightly coloured (coat, bike) - Things that don't belong here (litter dropped on the pavement etc.) - Things that are beautiful (nature, trees) - Things featuring numbers (shop phone number, house number) - Things featuring letters (road names, signs) - Things we need (post boxes, front doors) - People I love... etc. You could set the challenge of photographing things that begin with the alphabet letters. - Find an Apple, Bed, Cup, Desk, Egg, Fence etc. - Find various colours: find find 5 red items. - Find a certain number of things: find 3 socks, 2 teddies etc. When the pictures are taken, show the children how to load the images onto the computer. Describe what happens as you flick through the pictures and sort them. Show them how you print them and trim to size etc. You could then create a booklet displaying the images in order and writing the appropriate letter on each page. Colouring has to be the number one activity, entertaining children around the world on a daily basis, but what does it teach? As with so many baby and toddler activities, colouring assists learning across a broad spectrum of skills:- - Fine motor skills: this is all about coordination, young children will learn to hold crayons and to control their hand movements. Such control is essential before your children can start writing so colouring is a precursor to being able to write. - Knowledge and understanding of the world: exposure to different pictures to colour in will help to teach children about the world around them; talk about the scenes that they are colouring, and make sure that they know what each object in the scene is, this will broaden vocabulary as well as nurture a wider contextual understanding. - Colours: colouring helps your little ones learn their colours. Children will also begin to learn the effect of mixing different colours. - Concentration: colouring will help your children to concentrate on a project and to see it through to its conclusion. There are so many lessons that colouring a simple picture can teach. Make sure you always have a small pack of crayons in your handbag, and a sheet or two to colour in (you can quickly find pictures to colour on the Internet, we have lots at ToucanLearn!). The next time you find yourself having to wait somewhere with your little ones, or stuck in traffic, you'll be grateful that you can just whip out some colouring, and your little ones will be improving themselves along the way. Here's a quick and easy activity to introduce colours... Find some cardboard boxes and if you can, paint each one a primary colour, or simply colour in one side of paper and stick it onto each side of the boxes. Get your little ones to help choose which colours to opt for and get them to help the colouring. Head off round the house with your little, one hunting for small items that match the colours to put in each coloured box. Encourage them to choose what to put in, which items to reject for being the wrong colour and ask them to hold the boxes. Some ideas of things to go in: - Play plates/cutlery - Play fruit - Small balls - Coloured blocks When you have collected a good selection, mix them all up and see if your little ones can place them in the right boxes, naming the coloures each time. Ask where each ones goes, and give lots of praise if they get it right. Getting young toddlers to sit still on the London Underground can be slightly tricky because it's such an exciting place to be, and lots of other tube passengers are standing, so why shouldn't your little one?! Luckily there is so much distinct iconography inside tube trains that can inspire even the youngest traveller to play fun games. Look for different colours, shapes and letters. Look around a tube carriage and you'll see yellow warning triangles, red circles for London Underground's logo and no entry signs on doors between carriages, blue rectangles and squares with notices inside. You'll see the tube maps with lots of coloured lines on - ask your little one what colours they see. Look for letters in the signs and adverts stuck all over the carriage, look for the letters that your children's names begin with. Look for numbers - especially the number of how old they are. Play I-Spy looking for items of different colours ('I-Spy, with my little eye, something that is red'). Older children can look around and spot all the different warning signs and instructions littered around the carriage - have you ever noticed just how many rules there are when you embark on an Underground journey?! Of course most of these games will adapt to any train ride, and even journeys on buses or planes too. You'll be amazed at just how quickly your journey goes, no matter how long it is. Just take care that you don't have so much fun that you miss your stop! So often activities that the children enjoy doing can be beneficial in different ways besides them having fun. They may think they are just having some painting time but in fact they are learning about other things too. In the activity below, they are practicing their painting and printing skills, but learn all about shapes and numbers too with a little guidance. Prepare an area for painting. Find some cookie cutters that are simple shapes (square, circle etc.) or some plastic shapes from a shape sorter. You could use household recycling such as kitchen roll tubes, the ends of small boxes or plastic pots. Put some different coloured paint into 6 different shallow dishes and place a shape into each one ready to go. Ask your child to do some printing with the shapes Encourage them to do it neatly, in rows, so the shapes can be easily identified. When they have done a few, then suggest they do an abstract piece of art and drag the shapes, mix the colours and over print the shapes to make something of their choice. Ask them what the picture is? Is is a sunset over hills; is it a dinosaur on the beach? Keep a note of their explanation on the back of the picture. When all the pictures are dry, have a chat about the shapes and ask some questions. - Which is the square? - What is the yellow shape called? - How many circles are there? - Which is the biggest shape? - Which has most sides? - How many blue shapes are there? Count and answer the questions together first and then see if your child can do it alone. Display the picture and practice each time you pass by. Learning can be so much fun and so easy! For lots more ideas for activities, and explanations about learning for parents and childminders, go to ToucanLearn! Walking to pre-school or nursery in the bad, autumnal weather can be a real bore for little ones, especially those who are only just out of the buggy. Here are a few ideas to perk up your walk together and do a bit of fun learning on the way! Weathery Walk - walk the way you might in different types of weather. - Trudge through snow - Battle against raging rain - Fan yourself in the heat of the hot sun - Keep upright in the blowy wind Colour-Spy - spot things that are certain colours. Find 3 red things (traffic light, post box, car) etc. Letter Think - think of things that begin with certain letters. Name 4 things beginning with "d". Even little ones can do this with come help. Give a clue to help them get to a "d" word. Wonkey Walks - Walk in different ways between the trees you pass. So, walk like a frog to the next tree. Then walk like a monkey to the next tree. Tree Races - If you live on a quiet road you could race to the next tree. See who gets there first. Count the Steps - estimate how may steps you need to get to the next landmark (tree/traffic lights) and simply count how many steps you actually take. How close were you? Car Count - name a colour and count how many cars you see on the way of that colour. Walking to school or nursery is a great, healthy way to start the day; these ideas will make it fun too! Have a good day! Here is the famous rainbow song; teach it to your child and sing it often as a reminder of all the colours around you! Red, And Yellow, And Pink, And Green, Orange, And Purple and Blue, I can sing a rainbow, Sing a Rainbow, Sing a Rainbow too! Have some fun learning colours with rainbows, the most colourful things in the world! - Rainbow picture: Cut out all sorts of colourful things from magazines and catalogues. Place all the red things in one pile, all the green in another etc. Then draw a big rainbow on a page and stick on all the coloured pieces of paper in each appropriate arc. - Floor rainbow: Go round the house collecting things that are colours of the rainbow. Find red bricks, blue cars, yellow socks. Then make a huge rainbow on the floor placing all the red things in one arc, all the blue in the next etc. - Rainbow puzzle: Draw a rainbow shape on a page using a thick black pen. Use paint, glitter, coloured pens to fill in the colours When dry, cut out each arc to make a rainbow puzzle, and go round the house finding things that match each of the colours. Re-make the rainbow like a puzzle. - Rainbow of clothes: Children often have such colourful clothes. Head off to the wardrobe and find items for the colours of the rainbow. Make them into a big clothing rainbow on the bed. - Sing the song: and as you say the colours, point to something int he room that is that colour. See how you get on! - Colour Eye Spy: Take a look round the room and play I Spy with my little eye, something that is.... and add your chosen colour. It's very easy for little ones to get the hang of this game and they will quickly be good at spotting colours! Have lots of colourful fun! Why not make some fun 'stained glass' effect pictures to hang in your little one's windows and see them light up in the bright sunshine? For this activity you'll need:- - some black card - assorted coloured tissue papers - a craft knife (for you to use in preparation) - some child safe scissors Prepare some templates one evening whilst the children safely tucked up in bed! Take the sheets of card and cut them into shapes and then, using the craft knife, cut holes in them. Make sure you have thick borders around your holes because these will become 'frames' for the tissue paper to be stuck to. Here are some ideas of pictures you can make- - Parrot: cut out a parrot shape then cut out holes inside the tail, holes for the body and wings, the head and perhaps a crest on top - Rainbow: cut rainbow arcs into a whole piece of card, making one arc hole for each colour of your rainbow - Fish: cut the card into a fish shape then score out stripy markings using the craft knife - Peacock: If you're feeling really artictic, cut out the shape of a peacock making a fan tail with long holes with small round holes at the top If you aren't overly artistic, just cut shapes into the card because once the tissue effect has been created, they'll still make wonderful patterns. Once you have prepared your templates, have your children cut out coloured pieces of tissue to stick over the holes. Use this as an exercise to practice your colours by talking about the colours you need and what colours you are cutting out. Glue the tissue shapes into place and then hang your pictures in the window. As the light shines through, you'll have some lovely bright art! Often when we take the children out in the fresh air to teach them about the outside world, we head for the local park or nature reserve. Our towns and cities are often overlooked as places to take children when in fact there is a wealth of opportunity for them to learn in built up areas. So, how does an excursion around the town provide opportunities for learning? Excursions in and around towns can help in the following ways: - It builds on children's everyday experiences - It helps create a sense of community - It helps teach about the different cultures that might exist around where you live - It promotes the idea of being out in the open air taking walks, keeping healthy and staying active - It can help children gain confidence about being out and learning about road safety - It helps children learn about how seasons can effect the environment in which they live Things to look out for: - Different styles of buildings (cottages, old office block, modern houses, old shops) - 'Street furniture': street lamps, phone boxes, ride-on toys, post boxes, benches, display signs etc. - Road signs - Letters and numbers on shop fronts - Road and rail networks - Different vehicles (colours, styles, types) - Building materials: concrete, bricks, wood, glass, metal - Sounds and smells - The people around and what they do (bus drivers, road sweepers, children, adults doing gardening etc.) How can you enhance the experience? Here are a few ideas: - Talk about what you see as you go along your walk. If you see a bus, look at it's wheels, the colour of the paintwork, how many people are on it, adverts on the side etc. - Listen to noises and discuss smells. Try and name all the noises (pedestrian crossing 'beeps', diggers, car horns, sirens, shops blaring music) - Ask questions: where is the red car?, what's in the tree?, who can see a bus? - Spot different materials used in towns and talk about how strong they are: iron railings, wooden fence, plastic door, brick houses etc - Look at signs and talk about them. What might they all mean? - Stop to watch a building site or a dustbin lorry collecting bins. Chat about what they are doing and what happens. - Look at road signs and the symbols used eg speed limit numbers, construction signs, house numbers; discuss different colours used - blue/white for information, red/white and yellow/black for warnings, green/white for environmental information, bright colours for shop fronts etc. - Look for shapes: square garage door, rectangle front door, round letter box etc. - Take some photos of your trip and turn them out as a map. - For older children and pre-schoolers, you can couple the outing with other activities when you get back home - Ask them where they want to walk to? Involve them in the planning of the trip and supplies they will need (eg. snack, drink) - Make a map of the trip and follow it, draw in any landmarks you pass - Ask them to remember things they saw on the trip and draw them when they get home Have fun and enjoy your environment! Shapes and colours are amongst the first concepts that babies learn and learning them helps to stimulate connections in the brain that will continue to serve your baby as they learn throughout their childhood. Learning both shapes and colours with your baby can be fun for both of you. Here's a fun idea on how to familiarise your baby with both. Take two potatoes and cut them in half so that at least one of the cross sections makes a circle. Now carve the other faces into a rectangle, square and triangle. You now have four large stampers! Dip the face of the potatoes in finger paint and stamp different coloured shapes onto a large sheet of paper. Practice the stamping and discuss each shape with your baby - count the sides on the shape and point your finger around each shape as you show them. Start with a single colour and state the colour with each stamp: 'red circle', 'red square', 'red triangle', 'red rectangle'. Wipe the paint off the face each time and then start on another colour. When you have played with these for a bit, show the effect of mixing colours; demonstrate how two colours mixed together create a different colour. Try mixing various combinations of colours to create a varied array. Playing with shapes and colours will help to cement these concepts in your child's mind and start them on a learning path that will set them up well for school in a few years! It's never too early to introduce your toddlers to science - you don't call it science, of course, but there are plenty of fun activities that you can do to help build an understanding of the world around them. Here are a few ideas:- Weather: Create a series of card pictures for different types of weather, and a picture for each of the seasons. Each morning look at the weather and put the appropriate weather and season pictures up on the wall. Faces: Create a large picture of a head and then create a series of different eyes, noses, mouths, ears, eyebrows, hair and pairs of glasses. Have your toddler create faces, placing features in the right place. Discuss different coloured eyes, different shaped features and talk about what glasses are for. Planting: Buy some cress or mung beans, plant them in a plastic pot, water them and watch them grow. Have your child chart the progress each day as they germinate and shoot up. Discuss the ways that they change each day, draw how they look and at the end, make a sandwich and enjoy them! Talk about how healthy they are and that good food makes you grow. Colours: Show how mixing finger paints creates different colours. Create swirling patterns on paper by pouring on generous amounts of paint and swirling with your finger. Growing: Use a wall to mark the height of your children. Have them stand against the wall, make a pencil mark at the height they stand and measure how tall they are. Add a date, and repeat on the first day of each month. Sometimes you'll see almost no difference, other months you might notice change. Over a prolonged time you will see how they grow. Discuss what makes you grow and the concept that your little ones are growing into big children. These are just a few ideas, there are hundreds more activities that you can undertake with your toddlers to get them used to the concepts of science, and to spark an interest in the world around them.
Which of the following pairs is incompatible? RNA polymerase – makes an RNA molecule from an RNA template DNA ligase – connects segments of DNA DNA gyrase – relaxes the supercoil in DNA before the transposase fork replicates – cuts the backbone of DNA, leaving “sticky ends” DNA polymerase – makes a DNA molecule from a template DNA RNA polymerase – makes an RNA molecule from an RNA template Clarification: RNA polymerase is an enzyme that catalyzes the copying of a DNA sequence into an RNA sequence during transcription. RNA polymerase uses a DNA template to synthesize a strand of RNA. RNA polymerase can be called DNA-dependent RNA polymerase. During transcription, DNA helicase unwinds the DNA double helix, while RNA polymerase catalyzes the synthesis of an RNA strand from DNA. 1. The answer is; C When the mRNA joins the subunits of the ribosome, the tRNA begins to announce amino acids equivalent to the linear sequence of codons on the mRNA. The tRNA enters the ribosome at the A site of the ribosome, the amino acid separates and forms a polypeptide hyperlink with the opposite amino acid at the P site, and the tRNA moves empty from the E site. The answer is; VS During DNA replication, DNA will not be reduced to elements. DNA helicases unwind and unwind double-stranded DNA, and DNA polymerase begins to copy each support. This occurs through the inclusion of complementary base pairs to the leading and lagging strands. The answer is; VS In eukaryotes, where the nucleus is compartmentalized by a nuclear membrane of the cytoplasm, mRNA reaches the nucleus through the nuclear pores and travels to the cytoplasm. In the cytoplasm are ribosomes which can be protein translation factories. mRNA binds to ribosome subunits and translation begins in proteins. The answer is; B The base pairing rule ensures that gene integrity is maintained throughout replication and transcription. Cytosine can only pair with guanine, while adenine only pairs with thiinums or uracil (in RNA). This reduces the mismatch mismatch error price. The answer is this; 1) mRNA – a) carries the instructions for protein synthesis from the nucleus to the ribosome 2) tRNA – b) transports amino acids to the ribosome to build protein 3) rRNA – c) relates to the functioning of ribosomal subunits b half is true Clarification: please do my best C. The few errors made by DNA polymerase are normally corrected by restorative enzymes. Clarification: DNA replication is a vital process because daughter cells will want identical DNA as a guardian. DNA replication causes this. During DNA replication, certain errors can occur. Although these errors are few and many among them, they do happen. If multiple errors occur, it can lead to DNA damage. Restoration enzymes, resembling DNA ligase, help restore errors in DNA so that any pieces break easily. Restoration enzymes repair DNA so that no genetic information is lost. copies of the DNA clarification: DNA polymerase makes an RNA molecule from a DNA template Clarification: DNA polymerase is an enzyme involved in the technique of DNA replication. DNA replication replicates or synthesizes new DNA replication from parental DNA. The enzymes mentioned in the consultation perform specific work consistent with their description, in addition to DNA polymerase, since this enzyme is responsible for the inclusion of nucleotides in the synthesis strand of the DNA template strand. Thus, the chosen option is correct. DNA polymerase attacks along the previous strand on the 3′-5′ path, creating a new strand with the identical 5′-3′ path. The solutions can be: c) DNA is minimized in elements… c) enters the cytoplasm to the ribosome b) is placed collectively using basic pairing guidelines rRNA – related to the functioning of ribosomal subunits. tRNA – transports amino acids to the ribosome to build protein. mRNA – takes the instructions for protein synthesis from the nucleus to the ribosome If you want to know more about the problem, read: Translation is the basic level of the protein synthesis process. This is where RNA (tRNA) carries in amino acids that pair up with messenger RNA (mRNA) code created from DNA in the nucleus. It happens inside the ribosome. DNA is reduced to elements in the technique of DNA cloning, not replication. During replication, DNA uncoils and uncompresses first with the help of an enzyme called helicase. This creates a fork between the double-stranded DNA, exposing each strand. Each of these strands serves as a template for the new code-specific molecule. DNA polymerase helps by adding complementary bases to create mRNA, which is the process of transcription. mRNA is normalized primarily based on the DNA template from which it was created. It is placed collectively using basic pairing guidelines. There are only 4 bases and this one contains guanine, cytosine, adenine and thymine. Similarly, mRNA also has 4 bases, but instead of thymine it has uracil. Guanine simply pairs with cytosine and vice versa. Thymine pairs with adenine and adenine pairs with uracil (in RNA). There are several types of RNA. mRNA is called messenger RNA. Due to its title, it passes the code to the ribosomes, which are able to tell the cell which amino acids to make for the DNA template it copied from the nucleus. tRNA is called switch RNA. Its function is to advertise amino acids to the ribosome. tRNA comprises 3 particular bases which code for a particular amino acid. It corresponds to mRNA from the nucleus. Before tRNA is available, mRNA first interacts with rRNA or ribosomal RNA. This particular RNA is discovered inside the ribosome. When mRNA enters the ribosome and binds to rRNA, their interaction triggers the tRNA method. The correct answer is C) RNA polymerase makes an RNA molecule from an RNA template. Clarification: RNA polymerase works when transcription is in progress. Transcription is the production of a strand of RNA from a strand of DNA that has been separated but will return to its helical shape. Subsequently, RNA polymerase makes an RNA molecule from a DNA template. Also, the model contains thymine as an alternative to uracil (only present in RNA), so it is DNA. The correct answer might be the option that RNA is created from DNA using base pairing guidelines. Clarification: The method of synthesizing RNA from one strand of DNA is called transcription. During transcription, several enzymes act to aid in RNA synthesis, one of which is RNA polymerase. RNA polymerase catalyzes the addition of a nucleotide to the ascending RNA strand using the base pairing rule. The bottom pairing rule means that A will bind to U as an alternative to thymine in RNA and G will bind to C in the complementary strand. So the option RNA is created from DNA using base pairing guidelines is the correct answer.
Circuits for teaching physics - 1 Rationale - 2 Learning physics with circuits - 3 Sensors - 4 Outputs - 5 Example circuits - 6 Micro-controllers - 7 Data-handling - 8 Supporting apparatus - 9 Sample lessons - 10 Teachers using circuits - 11 More resources - 12 References I've taught my students to build electronic circuits, and, separately, I've taught my students to devise their own experimental apparatus. While these two movements in my teaching have been two of the most successful, I've yet to successfully combine them, yet to ask them to build their own circuits as lab apparatus for studying something else. It's so promising that I've decided to ask others to join me in the trial. Having our physics students build their own apparatus might have multiple benefits: - Save schools that would otherwise buy commercial apparatus a large fraction of the cost. - Allow schools that would otherwise miss out because they couldn't afford the commercial apparatus. - Allow more students of more schools to borrow lab equipment for homework, or even have more students own their lab equipment outright. - Pedagogical benefits - We hope to increase student ownership of the process of learning in the laboratory. Students may be more interested in the measurement of a physical variable when they have created the apparatus. - Allow students to learn a skill to be used in other environments, including students who would not elect to learn circuits or programming, but would elect physics. - Attract students interested in circuits and programming to physics. - Learning about identifying resistors and what makes appropriate substitutions helps students understand why orders of magnitude are an important way of making comparisons. After they've started to learn the resistor color code, I ask my students which color-band is the most important, i.e. getting which one wrong would most likely affect the operation of the circuit. - Specifying or substituting components, for example choosing among diodes or transistors, should help a student learn about the physical characteristics of those components. - Students should be less iffy about the nature of electrical connections than students who study physics without building circuits. Learning physics with circuits What will students learn about physics with circuits they build? Traditionally, physics students learn about circuits as a topic of physics after learning about electricity and magnetism. Instead, here I am suggesting we teach students about circuits as tools for learning in a wider range of fields of physics, from mechanics to astronomy, with rich opportunities to learn the traditional things about circuits scattered along the way. So, for starters, students should be expected to learn about the traditional topics in circuits, such as resistance, capacitance, induction, EMF, parallel and series combinations, amplification, and various more advanced topics. But using circuits they can investigate waves, interference, optics, kinematics, dynamics, electric and magnetic fields, energy transfers, thermodynamics, the spectrum, and more. In February, 2014, I took a poll of teachers in the Syracuse area, asking which circuits, from a list I thought might be easy yet useful, they'd most like to make in a workshop to take to their schools. The following table of results shows how important photo-gates are to physics teachers. One could argue that volt-meters are so popular that they're universally already-owned. Or, one could argue that they are not popular because they are used for studying electricity, not as canonical a topic as the kinematics studied with the photo-gates. Some circuits use only discrete components, many use integrated circuits like the 555 timer or the 741 op amp, and some use micro-controllers to gather data or run a complex algorithm or interface. The micro-controller requires special consideration, because each unit, be it a chip or a board, can cost anywhere between $1 and $40. With the right programming-circuit and software, a $2 chip can be programmed as easily as a $10 chip, and may be versatile enough to do what some are doing with their $30 boards. There is a multitude of sensors that can be connected to processors or directly to outputs. Sensors can be used to study the physical phenomena sensed, but they also can be used to teach the different ways of processing their signals. - Humidity sensors - Humidity sensors may output relative or absolute humidity values, and are often packaged with a temperature sensor so we can convert to the other value through software. - Light-dependent resistors - LDRs are usually cadmium sulfide, which changes resistance according to how much light is falling on the cell. Cadmium is a toxic metal, so we usually use non-toxic alternatives like photo-transistors or photo-diodes or solar cells, especially for children's use. They react to changes in light more slowly than diodes and transistors, but they are easy to model as predictable, variable resistors. - Potentiometers and rheostats - Variable resistors are usually a knob or a slider that change resistance from zero to some given value. Some, marked α (alpha) or A, are logarithmically tapered so that they can control audio or light over a wide, exponential range of values. Linear variable resistors are marked β (beta) or B. - Temperature-dependent resistors may have a negative or positive temperature coefficient, according to whether their resistance goes down or up when their temperature goes up. See wikipedia for more information, including a discussion of how they can increase temperature because the circuit is adding energy via the current used to sense its resistance. http://en.wikipedia.org/wiki/Thermistor - Thermopiles are semiconductor devices that change resistance or voltage in a circuit depending on their temperature, and they are thermally shielded so that they rise and fall in temperature with remote objects they face through a window in their otherwise heavy insulation. The window is usually made of a material that doesn't allow visible light, so that it is tuned to sensing temperatures corresponding to a peak wavelength in far infrared. These are the sensors used for non-contact thermometers, like those medical personnel use to take a person's temperature via ear or mouth. - Passive infrared motion detectors - PIR devices often output a voltage between their supply and 1.5V when not detecting changing infrared light, then short their output to ground when they do detect changing infrared light. When using such PIR detectors with a micro-controller or similar logic ICs, pull the output up with a resistor, which may be an internal feature in micro-controllers like the Arduino, so that the output is clearly high or low. - Switches can be purchased or hand-made from all sorts of materials, like chewing-gum wrappers. A multitude of types of switches can be salvaged from old electronic equipment, like remote controls, tape players, and phones. They connect one or more conduits to one or more other conduits, and may make the connection when pushed, or disconnect when pushed, or toggle between connected and disconnected when pushed and released. They may spring back to a default position or they may stay in any state. - Tilt switches - These switches consist of a metal ball or mercury that makes contact only when it is tilted a certain amount. This is how mercury thermostats work. - Ultrasonic distance sensors - These sensors send a train of ultrasonic pings when their trigger pin is taken high or low, then set an echo pin high or low for the duration of the flight of the pings to a reflecting object and back. - Vibration switches - These switches consist of a stiff wire surrounded by a metal coil that only contacts the wire when shaken. There are ways to connect sensors from commercial systems, the most well-known companies being Vernier and PASCO, to circuits—Some sensors output analog values on one wire when powered on two others, while some speak a digital code that may be open to the public. For example, Vernier publishes a guide to connecting their sensors to the Arduino. PASCO explains how the wires on various sensors function. See #Display for a discussion of displaying characters. - Circuits can vibrate a speaker to make sound, and the pitch, timbre, and/or volume can indicate criteria. - Piezo buzzers - Piezo buzzers buzz a certain tone with an applied voltage, but can be made to make more interesting sounds. - Piezo elements - Piezo elements click when the voltage applied goes over some threshold, and the clicking can be very fast, so one may make square waves of many frequencies with them. All the following transducers may be arranged in character or graphical displays, including light bars, bar graphs, multi-dimensional arrays, and two-dimensional screens. - Light emitting diodes - LEDs usually convert a specific voltage to a narrow band of light with a frequency correlated to that voltage. i.e., blue LEDs operate at a higher voltage than red LEDs. LEDs can turn on and off extremely quickly, so dimming is usually handled by running them with a square wave of varying duty cycle. When they're not busy emitting, LEDs can also be used as photodiodes to detect light levels. - Incandescent lamps - Incandescent lamps can be had over a wide range of voltages, and their brightness and color depend on the voltage applied. - Plasma lamps - Plasma lamps, for instance neon bulbs, require high voltages to light, but can be visible with very little current. - Liquid crystal display - LCDs typically use minuscule amounts of power compared to other ways of displaying characters or graphics. At around $10 per display, they are an inexpensive and efficient way to display a short line or two of text. While many displays are proprietary, there are also many with common protocols that allow easy control. Relays are switches controlled by current, for instance allowing a 5-volt DC system to control a 110-volt AC system without any electrical connection between the two systems. - Magnetic relay - Magnetic relays are the switches you may hear in the car when you turn on or off a device, for example when a low-current line to a switch on the dashboard switches a high-current line through the headlights. - Solid state relay - SSRs rely on semiconductor properties to allow a small current to light an LED which controls a photo-transistor or light-activated silicon-controlled rectifier (LASCR), thus electrically isolating the two systems through light. They can be ten times the cost of magnetic relays, but can last much longer and act much more quickly. A photo-gate timer uses light emitters and receivers to detect the passage of an object. The simplest timer would be a single light receiver, such as a photodiode or light-dependent resistor, that darkens when the leading edge of an object passes over it and lightens when that object's trailing edge passes over it. A circuit could be made to count beats of a clock between the two events. Then, for example, the known length of the object could be divided by the time between the two events to determine the average velocity of the object through the gate. A more commonly used system in the teaching laboratory is a set of two gates, where the source is not the ambient light but a light-emitting diode (LED) paired with a photodiode designed to be sensitive to the color of the LED, that color usually being infrared. Each gate is triggered when the leading edge of the object first blocks the light. By only paying attention to the leading edge, the timing is independent of the geometry of the object and its shadow. By using infrared instead of visible light, spurious signals from visible light and shadow in the lab are removed, and the receiver does not have to be calibrated for laboratories of varying brightness. The disadvantage of infrared is it is harder to tell whether the emitter is operating—Keep an old cell-phone camera handy; because they lack an infrared filter, they can be used to check IR LEDs. It is possible to time events without micro-controllers or computers—Shading the first detector could lower voltage enough to trip a monostable 555 to reset a bank of counter ICs. The least-significant counter IC could be fed clock signals from an astable 555. The last detector could likewise disable counting. But, the complexity of watching multiple gates, ignoring spurious signals, counting time, and reporting that time to a display or computer, makes a micro-controller the best tool for the job. For an example, see photo-gate timer. See bicycle speedometer. Most speedometers are really rotational frequency-meters, with readings calculated according to the circumference of the spinning object. See frequency meter. Exactly the same circuit as wheel speedometer, or may use a lookup table instead of a calculation if it does not have a linear response to wind speed. Read values from a Hall-effect sensor or an integrated-chip, multi-axis magnetometer. See magnetometer for more discussion. The circuit design depends on whether measuring DC or AC current, and whether in contact or not with the measured circuit. Measure the voltage across a thermocouple, the resistance across a thermistor, or use an integrated-chip that responds with data to serial commands. Measure the resistance of a light-dependent resistor (LDR), the voltage through a photodiode (like a solar cell), the current through a reverse-biased photodiode, or the current through a photodiode. For each of two sensors behind two crossed polarizers, measure the resistance of a light-dependent resistor (LDR), the voltage through a photodiode (like a solar cell), the current through a reverse-biased photodiode, or the current through a photodiode. Have the micro-controller write data from whatever input to a memory-chip, or internal memory if sufficient, for retrieval later. Measure the voltage between a pin and ground, using a divider when appropriate. There are thousands of integrated circuits that serve specific purposes, such as counting voltage drops on one pin and providing the count as binary on a set of other pins. Micro-controllers allow us to program a chip to serve a custom purpose, for comparison to the previous example, say counting voltage drops on one pin, comparing the period between the last two drops to the average of the last ten periods, to determine if something is slowing down or speeding up, then lighting a green or red LED accordingly. Micro-controllers allow us to customize them through programming, and most can be re-programmed many times, making them a versatile investment. To learn your commands, they micro-controller must be told them, and there are very many ways this can happen, depending on the model of micro-controller. Here are some methods I've used, with costs for comparison: - Use PICAXE computer software (free) to write the commands in BASIC, compile it, and send it via serial cable ($10-20) to a PICAXE chip ($3-$10) in a programming circuit ($5), then put the chip in the working circuit. - Use linux program MCU8051 (free) to write and compile a program in 8051 assembly language, and send it via serial cable ($10-$20) to a parallel-eeprom programming board ($100) to an Atmel 89C2051 chip ($1). - Use Arduino software (free) to write and compile a program in C and send it via serial or USB to an Arduino board ($10-$30) or an AVR micro-controller ($3-$5), on a breadboard ($5) with supporting components ($1), that has been loaded with the Arduino bootloader. Many of these scenarios require only very minimal computers by today's standards. In fact, it's best to have an older computer (late 1990s, early 200s) that has built-in serial ports and can easily be outfitted with Linux. Learning to program micro-controllers is not completely unlike learning to program computers, and should be an enriching experience for students. There are many ways to read measurements. Some applications require data to be stored and retrieved later, such as in long-term anemometry or thermodynamic studies. - A single count, such as in a timing application using pulses from a 555 IC, can be stored in a digital counter IC. - Micro-controllers can store data in flash memory to be retrieved via a display or serial communications. - Micro-controllers can write to disk drives, flash memory, or removable flash memory. - A circuit can communicate with a computer via a serial connection. Digital circuits can have a numeric display. - 1-4 digits are best displayed by seven-segment LED displays, which can be directly driven by micro-controllers with at least 8 output pins, or driven by counter or driver ICs. - More digits and/or text can be displayed by LCD displays ($10-$20). - Many circuits can communicate with a computer to display and/or store readings, usually through a serial port. - A voltmeter across two points of a circuit can be used with a lookup table to determine measurements. Many laboratories will need equipment such as computers for programming micro-controllers or oscilloscopes for visualizing outputs of sensing circuits. There are many considerations when choosing power supplies - Batteries are excellent for safety. One thing to watch out for is students putting two 9V batteries together, since their terminals almost beg to be put together. 9V batteries are also dangerous to store, having both terminals so close to each other, leading to inadvertent shorts. - I use rechargeable batteries, which easily last through a school-day or through a unit, then go into a recharger. - Some components, like the rugged 555 timer IC, can take a wide range of voltages from supplies. Micro-controllers usually have much stricter operating ranges, and some are incompatible with others, two popular ranges being 4.5V-5.5V, and 3.0V-3.5V. My students usually use a 2xAA, 3xAA, or 4xAAA battery pack or a 9V battery, all which connect to a breadboard with a standard 9V-style-terminated cable. My students use and re-use versatile solderless breadboards. It takes a lesson for them to understand how it makes connections in circuits, and I've found students of all ages over 9 are capable, after a few times practice, of understanding the difference between an abstract diagram and the actual placement of components on the breadboard. Tools for an electronics lab - Needle-nose pliers. - Fine wire cutters. - Chip pullers and inserters. - Digital multimeters; measuring DCV, ACV, mA, A, Ω, and Hz, preferably. - Transistor/diode tester (called "Component Tester" at Radio Shack). Ask each student per pair to make a circuit that produces a tone that they expect to be harmonious with the other student's, then examine the two as X and Y components on an oscilloscope, enjoying the lissajous-figures associated with the harmonic pairs. Build a spectrometer with a solar cell and a stepper motor, then investigate spectra. Build a circuit to measure an unknown resistance by comparison with known resistances. Teachers using circuits These educators have been kind enough to share their experiences using circuits to teach physics: - Peter Siegel, California State Polytechnic University, Pomona - John Liu, St. Cloud State University, Minnesota - William Baird et al., Armstrong Atlantic State University, Savannah, Georgia - See their article The Light-Emitting Diode as a Light Detector in The Physics Teacher, v. 49, p 171 (2011). http://scitation.aip.org/content/aapt/journal/tpt/49/3/10.1119/1.3555506 - Glen R., Watsonville, California - Andy Cave, Polytechnic Institute of New York University - Jason Harper - Kyle Forinash and Ray Wisman - Kyle and Ray have developed many activities that use mobile devices and electric circuits to measure physical phenomena. http://mobilescience.wikispaces.com EnergyTeachers.org is building a list of where to buy electronics components, tools, and kits: http://energyteachers.org/forum/viewtopic.php?f=26&t=3375 OpenTP is creating lessons for students to study physics in a way to move away from labs merely confirming ancient physics. (in French) https://opentp.fr
THE UNIT CIRCLE ANALYTIC TRIGONOMETRY is an extension of right triangle trigonometry. It takes place on the x-y plane. For, trigonometry as it is actually used in calculus and physics, is not about solving triangles. It becomes the mathematical description of things that rotate or vibrate, such as light, sound, the paths of planets about the sun or satellites about the earth. It is necessary therefore to have angles of any size, and to extend to them the meanings of the trigonometric functions. We do that now. Let a radius of length r sweep out an angle θ in standard position, and let its endpoint have coördinates (x, y). The question is: How shall we now define the six trigonometric functions of θ? We will take our cue from the first quadrant. In that quadrant, a radius r will terminate at a point (x, y). Those coördinates define a right triangle. The right-triangle definitions (Topic 2) of the six trigonometric functions follow. According to the Pythagorean theorem, In this way we extend the meaning of the trigonometric functions to angles that terminate in any quadrant. It is in terms of the coördinates (x, y) of the endpoint of a distance r from the origin. But before we give an example, consider this question: Will a function of θ depend on the length of r? To see the answer, pass your mouse over the colored area. No, it will not. The functions are defined as the ratios of the sides, not their lengths. Say that AB, AC are two different radii. But triangles ABD, ACE are similar. (Theorem 15) Proportionally, DB : BA = EC : CA sin θ -- opposite over hypotenuse -- does not depend on the length of the radius. And similarly for the remaining functions. Therefore, we may choose any radius we please. Typically, we take r = 1. That is called the unit circle, as we shall see. The trigonometric functions in fact depend only on the angle θ -- and it is for that reason we say that they are functions of θ. Example 1. A straight line inserted at the origin terminates at the point (3, 2) as it sweeps out an angle θ in standard position. Evaluate all six functions of θ. Answer. x = 3, y = 2. Therefore, according to the definitions: Problem 1. A straight line from the origin sweeps out an angle θ, and it terminates at the point (3, −4). Evaluate the six functions of θ. x = 3, y = −4. Therefore, Problem 2. The signs in each quadrant. a) The algebraic sign of sin θ will always be the sign of which a) Therefore, in which quadrants will sin θ -- y -- be positive? I and II. a) In which quadrants will sin θ be negative? III and IV. b) The algebraic sign of cos θ will always be the sign of which a) Therefore, in which quadrants will cos θ -- x -- be positive? I and IV. a) In which quadrants will cos θ be negative? II and III. c) In which quadrants will the algebraic sign of tan θ (y/x) be positive? I and III. x and y will have the same signs. d) In which quadrants will the algebraic sign of tan θ be negative? II and IV. x and y will have opposite signs. e) csc θ will have the same sign as which other function? sin θ, because they are reciprocals. f) sec θ will have the same sign as which other function? g) cot θ will have the same sign as which other function? A quadrantal angle is an angle that terminates on the x- or y-axis. a) What are the quadrantal angles in degrees? 0°, 90°, 180°, 270°; and angles coterminal with them. b) What are the quadrantal angles in radians? c) When an angle terminates on the x-axis, what is the value of the d) When an angle terminates on the y-axis, what is the value of the Now, it is a fact of arithmetic that there is no number with denominator 0. Wherever x = 0, tan θ will not exist. Where does x = 0? When the angle terminates on the y-axis. Those values of θ will be singularities of tan θ. (Topic 18 of Precalculus.) Problem 4. For which quadrantal angles do the following functions not exist? the x-axis -- cot θ will not exist. cot θ will not exist at θ = 0 and θ = π. b) sec θ c) sin θ sin θ does not exist. The unit circle The trigonometric functions are functions only of the angle θ. Therefore we may choose any radius we please, and the simplest is a circle of radius 1, the unit circle. On the unit circle the functions take a particularly simple form. For example, The value of sin θ is the y-coördinate of the endpoint of the unit radius The value of cos θ is the x-coördinate If a function exists at a quadrantal angle, Consider sin θ at each quadrantal angle. We just saw that the value of sin θ is the y-coördinate: sin θ = y. Therefore at each quadrantal angle, the value of sin θ -- of y -- is either 0, 1, or −1. To evaluate a function at a quadrantal angle, the student should sketch a unit circle. Problem 5. Evaluate the following. No tables a) cos 0° cos 0° = 1. cos θ is equal to the x-coördinate. b) cos 90° = 0 c) cos 180° = −1 d) cos 270° = 0 e) tan 0° tan 0° = 0. tan θ is equal to y/x = 0/1 = 0. f) tan 90° 1/0 does not exist. g) tan 180° = 0 h) tan 270° does not exist. Problem 6. Evaluate the following -- if it exists. No tables. Problem 7. Explain why we can write the following, where n could be any integer: cos nπ = (−1)n (−1)n = ±1, according as n is even or odd. If n is even (or 0), then cos nπ is coterminal with 0 radians, and (−1)n = 1. See the unit circle. While if n is odd, then cos nπ is coterminal with π radians, and (−1)n = −1. Please make a donation to keep TheMathPage online. Copyright © 2019 Lawrence Spector Questions or comments? Private tutoring available.
Oceanic data collection plays a crucial role in understanding and monitoring our vast oceans. It provides valuable insights into various aspects of the marine environment, including temperature, salinity, currents, and marine life. In this article, we will explore the different types of oceanic data that scientists collect and how it helps in studying and conserving our oceans. One of the essential parameters measured in oceanic data collection is temperature. By using specialized sensors and instruments, scientists can accurately measure the temperature at different depths and locations in the ocean. This information helps in understanding ocean currents, heat distribution, and climate patterns. Salinity refers to the amount of dissolved salts present in seawater. It is another critical factor that oceanographers study to understand various processes within the ocean. Salinity affects the density of seawater, which influences ocean circulation patterns. Oceanic data collection allows scientists to measure salinity levels accurately using conductivity sensors. Ocean currents are like highways that transport water across vast distances. These currents play a vital role in distributing heat around the globe and affecting weather patterns. Oceanic data collection involves measuring both surface and deep-water currents using tools such as buoys, drifters, and satellite observations. This information helps in predicting weather conditions and understanding climate change. Understanding marine life is crucial for maintaining healthy ecosystems and sustainable fisheries. Oceanic data collection includes gathering information about marine organisms such as plankton, fish populations, and their habitats. Scientists use techniques like net trawling, acoustic surveys, and underwater cameras to collect this data. By studying marine life patterns over time, researchers can identify changes in biodiversity and ecosystem health. Data Collection Methods: There are several methods used for collecting oceanic data: - Buoys: Buoys are equipped with various sensors and instruments to measure different parameters such as temperature, salinity, currents, and wave height. - Ship-based Sampling: Research vessels travel across the oceans, collecting data through water sampling, deploying instruments, and conducting surveys. - Satellite Observations: Satellites equipped with remote sensing instruments provide valuable data on sea surface temperature, ocean color, and sea level changes. - Autonomous Instruments: These are instruments deployed in the ocean for extended periods to collect data. Examples include Argo floats, which measure temperature and salinity profiles at different depths. Applications of Oceanic Data: Oceanic data collection has numerous applications: - Climate Studies: By analyzing historical oceanic data, scientists can study long-term climate trends and make predictions about future climate scenarios. - Weather Forecasting: Accurate oceanic data helps improve weather forecasting models by providing inputs on factors such as sea surface temperatures and currents. - Fisheries Management: Understanding fish populations and their habitats aids in sustainable fisheries management practices to prevent overfishing. - Coastal Management: Oceanic data plays a crucial role in managing coastal areas by monitoring factors like erosion, pollution levels, and harmful algal blooms. In conclusion, oceanic data collection provides invaluable insights into the complex dynamics of our oceans. By measuring parameters such as temperature, salinity, currents, and marine life patterns, scientists can gain a better understanding of the marine environment. This knowledge is essential for addressing climate change impacts, conserving marine resources, and ensuring the sustainability of coastal communities.
In this lesson, we learn how to graph a line using the slope-intercept method. The first step is to plot the y-intercept, which is the coordinate where the line crosses the y-axis. The slope, which is the coefficient of x, is then used to plot another point on the line. By connecting these points with a straight line, we can accurately graph the line. To ensure the line is graphed correctly, we can check any point on the line to make sure it satisfies the given equation. Shows how to graph a line using the slope-intercept method. This is part 15 of a series of videos about graphing lines. More free YouTube videos by Julie Harland are organized at http://yourmathgal.com
Presentation on theme: "Chapter 11 “Chemical Reactions”"— Presentation transcript: 1 Chapter 11 “Chemical Reactions” Sodium at High SpeedHow will you write an equation to describe this reaction? See 2.0 min. 2 Section 11.1 Describing Chemical Reactions OBJECTIVES:Describe how to write a word equation. 3 Section 11.1 Describing Chemical Reactions OBJECTIVES:Describe how to write a skeleton equation. 4 Section 11.1 Describing Chemical Reactions Learning Target:You will be able to apply the steps to write a balanced chemical equation. 5 All chemical reactions… have two parts:Reactants = the substances you start withProducts = the substances you end up withThe reactants will turn into the products.Reactant + Reactant ® Product+ Product 7 Describing a chemical reaction Four ways Atoms aren’t created or destroyed (according to the Law of Conservation of Mass)A reaction can be described four ways:#1. In a sentence. Questions and problems are often written like this. Every item is a word. Ex:Copper reacts with chlorine to form copper (II) chloride.#2. In a word equation. Some symbols are usedCopper + chlorine ® copper (II) chloride 8 Describing a Chemical Equation #1. Use a sentence equation with words.#2. Use a word equation with some symbols.#3. Use a skeleton equation, which is an unbalanced chemical equation with symbols. Ex:H2 + O2 ®H2O 9 Describing a Chemical Equation #1. Use a sentence equation with words.#2. Use a word equation with some symbols.#3. Use a skeleton equation, which is an unbalanced chemical equation with symbols.Ex: H2 + O2 ®H2O#4. Use a balanced chemical equation. Balance every chemical formula to obey the Law of conservation of Mass. (Balance on the board).Ex: H2 + O2 ® H2O 11 Symbols in equations? – Text page 323 the arrow (→) separates the reactants from the products (arrow points to products)Read as: “reacts to form” or yieldsThe plus sign = “and”(s) after the formula = solid: Fe(s)(g) after the formula = gas: CO2(g)(l) after the formula = liquid: H2O(l) 12 Symbols used in equations (aq) after the formula = dissolved in water, an aqueous solution: NaCl(aq) is a salt water solution used after a product indicates a gas has been produced: H2↑¯ used after a product indicates a solid has been produced: PbI2↓ 13 Symbols used in equations double arrow indicates a reversible reaction (more later)shows that heat is supplied to the reactionis used to indicate a catalyst is supplied (in this case, platinum is the catalyst) 14 Enzymes are biological or protein catalysts in your body. What is a catalyst?A substance that speeds up a reaction, without being changed or used up by the reaction.Enzymes are biological or protein catalysts in your body. 15 Writing Chemical Equations 11.1Writing Chemical EquationsA catalyst is a substance that speeds up the reaction but is not used up in the reaction.Without Catalyst With CatalystHydrogen peroxide decomposes to form water and oxygen gas. a) Bubbles of oxygen appear slowly as decomposition proceeds. b) With the addition of the catalyst manganese(IV) oxide (MnO2), decomposition speeds up. The white “smoke” is condensed water vapor. 16 #3. The Skeleton Equation Uses formulas and symbols to describe a reactionbut doesn’t indicate how many; this means they are NOT balancedAll chemical equations are a description of the reaction. 17 The Skeleton Equation YOU MUST KNOW How to write Chapter 9 Chemical Names & Formulas, binary, polyatomic, and molecular 7 diatomic elements: H2, O2, F2, N2, Cl2, I2, Br2Diatomic= A molecule formed from two atoms.__”Good afternoon, Mrs. HOFNCl I Br !! “ 18 Write a skeleton equation for: Solid iron (III) sulfide reacts with gaseous hydrogen chloride to form iron (III) chloride and hydrogen sulfide gas.Nitric acid dissolved in water reacts with solid sodium carbonate to form liquid water and carbon dioxide gas and sodium nitrate dissolved in water. 20 #4. Balanced Chemical Equations Law of Conservation of Mass: Atoms can’t be created or destroyed in an ordinary reaction:All the atoms we start with we must end up with (meaning: balanced!)A balanced equation has the same number of each element on both sides of the equation. 21 Rules for balancing:Assemble the correct formulas for all the reactants and products, using “+” and “→”Count the number of atoms of each type appearing on both sidesBalance the elements one at a time by adding coefficients (the numbers in front) where you need more - save balancing the H and O until LAST!(hint: I prefer to save O until the very last)Double-Check to make sure it is balanced. 22 NeverNever change a subscript to balance an equation (You can only change coefficients)If you change the subscript (formula) you are describing a different chemical.H2O is a different compound than H2O2Never put a coefficient in the middle of a formula; they must go only in the front2NaCl is okay, but Na2Cl is not. 23 If you cannot balance your equation: Check the chemical formulas you have written for all reactants and products to see if they are correct. 25 Section 11.2 Types of Chemical Reactions OBJECTIVES:Describe the five general types of reactions. 26 Section 11.2 Types of Chemical Reactions OBJECTIVES:Predict the products of the five general types of reactions. 27 Types of Reactions How? We recognize them by their reactants There are probably millions of reactions.We can’t remember them all, but luckily they will fall into several categories.We will learn: a) the 5 major types. (Combination, Decomposition, Single Replacement, Double Replacement, Combustion)We will be able to: b) predict the products.For some, we will be able to: c) predict whether or not they will happen at all.How? We recognize them by their reactants 28 #1 - Combination Reactions Combine = put together2 substances combine to make one compound (also called “synthesis”)Ca + O2 ® CaOSO3 + H2O ® H2SO4We can predict the products, especially if the reactants are two elements.Mg + N2 ® _______Mg3N2 (symbols, charges, cross) 29 Complete and balance:Ca + Cl2 ®Fe + O2 ® (assume iron (II) oxide is the product)Al + O2 ®Remember that the first step is to write the correct formulas – you can still change the subscripts at this point, but not later while balancing!Then balance by changing just the coefficients only 30 #1 – Combination Reactions Additional Important Notes:a) Some nonmetal oxides react with water to produce an acid:SO2 + H2O H2SO3b) Some metallic oxides react with water to produce a base:CaO + H2O Ca(OH)2(This is what happens to make “acid rain”) 31 #2 - Decomposition Reactions decompose = fall apartone reactant breaks apart into two or more elements or compounds.NaCl Na + Cl2CaCO CaO + CO2Note that energy (heat, sunlight, electricity, etc.) is usually required 32 #2 - Decomposition Reactions We can predict the products if it is a binary compound (which means it is made up of only two elements)It breaks apart into the elements:H2OHgO 33 #2 - Decomposition Reactions If the compound has more than two elements you must be given one of the productsThe other product will be from the missing piecesNiCO CO2 + ___H2CO3(aq) ® CO2 + ___heat 34 #3 - Single Replacement Reactions One element replaces anotherReactants must be an element and a compound.Products will be a different element and a different compound.Na + KCl ® K + NaClF2 + LiCl ® LiF + Cl2(Cations switched)(Anions switched) 35 #3 Single Replacement Reactions Metals will replace other metals (and they can also replace hydrogen)K + AlN ®Zn + HCl ®Think of water as: HOHMetals replace the first H, and then combines with the hydroxide (OH).Na + HOH ® 36 #3 Single Replacement Reactions We can even tell whether or not a single replacement reaction will happen:Because some chemicals are more “active” than othersMore active replaces less activeThere is a list on page called the Activity Series of MetalsHigher on the list replaces those lower. 37 The “Activity Series” of Metals LithiumPotassiumCalciumSodiumMagnesiumAluminumZincChromiumIronNickelLeadHydrogenBismuthCopperMercurySilverPlatinumGoldHigher activityMetals can replace other metals, provided they are above the metal they are trying to replace (for example, zinc will replace lead)Metals above hydrogen can replace hydrogen in acids.Metals from sodium upward can replace hydrogen in water.Lower activity 38 The “Activity Series” of Halogens Higher ActivityHalogens can replace otherhalogens in compounds, provided they are above the halogen they are trying to replace.FluorineChlorineBromineIodineLower Activity2NaCl(s) + F2(g) 2NaF(s) + Cl2(g)???MgCl2(s) + Br2(g) No Reaction!??? 39 #3 Single Replacement Reactions Practice: Fe + CuSO4 ®Pb + KCl ®Al + HCl ® 40 #4 - Double Replacement Reactions Two things replace each other.Reactants must be two ionic compounds, in aqueous solutionNaOH + FeCl3 ®The positive ions change place.NaOH + FeCl3 ® Fe+3 OH- + Na+1 Cl-1= NaOH + FeCl3 ® Fe(OH)3 + NaCl 41 #4 - Double Replacement Reactions Have certain “driving forces”, or reasonsWill only happen if one of the products:a) doesn’t dissolve in water and forms a solid (a “precipitate”), orb) is a gas that bubbles out, orc) is a molecular compound (which will usually be water). 42 Complete and balance:assume all of the following reactions actually take place:CaCl2 + NaOH ®CuCl2 + K2S ®KOH + Fe(NO3)3 ®(NH4)2SO4 + BaF2 ® 43 How to recognize which type? Look at the reactants:E + E = CombinationC = DecompositionE + C = Single replacementC + C = Double replacement 45 #5 – Combustion Reactions Combustion means “add oxygen”Normally, a compound composed of only C, H, (and maybe O) is reacted with oxygen – usually called “burning”If the combustion is complete, the products will be CO2 and H2O.If the combustion is incomplete, the products will be CO (or possibly just C) and H2O. 47 SUMMARY: An equation... Describes a reaction Must be balanced in order to follow the Law of Conservation of MassCan only be balanced by changing the coefficients.Has special symbols to indicate the physical state, if a catalyst or energy is required, etc. 48 Reactions Come in 5 major types. We can tell what type they are by looking at the reactants.Single Replacement happens based on the Activity SeriesDouble Replacement happens if one product is: 1) a precipitate (an insoluble solid), 2) water (a molecular compound), or 3) a gas. 49 There are some more practice problems of balancing equations located from: my websiteInteresting LinksBalancing Equations 50 Section 11.3 Reactions in Aqueous Solution OBJECTIVES:Describe the information found in a net ionic equation. 51 Section 11.3 Reactions in Aqueous Solution OBJECTIVES:Predict the formation of a precipitate in a double replacement reaction. 52 Net Ionic EquationsMany reactions occur in water- that is, in aqueous solutionWhen dissolved in water, many ionic compounds “dissociate”, or separate, into cations and anionsNow we are ready to write an ionic equation 53 Net Ionic EquationsExample (needs to be a double replacement reaction)AgNO3 + NaCl AgCl + NaNO31. this is the full balanced equation2. next, write it as an ionic equation by splitting the compounds into their ions:Ag1+ + NO31- + Na1+ + Cl1- AgCl + Na1+ + NO31-Note that the AgCl did not ionize, because it is a “precipitate” 54 Net Ionic Equations3. simplify by crossing out ions not directly involved (called spectator ions)Ag1+ + Cl1- AgClThis is called the net ionic equationLet’s talk about precipitates before we do some other examples 55 Predicting the Precipitate Insoluble salt = a precipitate [note Figure 11.11, p.342 (AgCl)]General solubility rules are found:Table 11.3, p. 344 in textbookReference section - page R54 (back of textbook)Lab manual Table A.3, page 332Your periodic table handout 56 Let’s do some examples together of net ionic equations, starting with these reactants: BaCl2 + AgNO3 →NaCl + Ba(NO3)2 →End of Chapter 11
Presentation on theme: "Circular Motion and Gravitation"— Presentation transcript: 1 Circular Motion and Gravitation HoltChapter 7Honors Physics 2 Chapter 7 Table of Contents Section 1 Circular Motion Circular Motion and GravitationTable of ContentsSection 1 Circular MotionSection 2 Newton’s Law of Universal GravitationSection 3 Motion in Space 3 7.1 Circular MotionAny object that revolves about a single axis undergoes circular motion. 4 7.1 Circular Motion Tangential speed (vt): speed of an object along an imaginary line drawn tangent to the object’s circular pathdepends on an object’s distance from the center of the circular pathis constant in uniform circular motion 5 7.1 Circular Motion Centripetal Acceleration (ac): Tangential acceleration is due to a change in speed.due to a change in directionis directed toward the center of the circleac =vtr2 6 Centripetal Acceleration Section 1 Circular MotionChapter 7Centripetal AccelerationAcceleration is a change in velocity.(a) As the particle moves from A to B, the direction of the particle’s velocity vector changes.(b) For short time intervals, ∆v is directed toward the center of the circle.Centripetal acceleration is always directed toward the center of a circle. 8 Centripetal Acceleration REPEAT Section 1 Circular MotionChapter 7Centripetal Acceleration REPEATCentripetal acceleration results from a change in direction.In circular motion, an acceleration due to a change in speed is called tangential acceleration.A car traveling in a circular track can have both centripetal and tangential acceleration.Because the car is moving in a circle, the car has a centripetal component of acceleration.If the car’s speed changes, the car also has a tangential component of acceleration. 9 7.1 Circular MotionCentripetal Force (Fc): the net force directed toward the center of an object’s pathCentripetal means center seeking.Fc = macFc and ac are in the same direction. The centripetal force is in the plane of the object and perpendicular to the tangential speed of the object.Fc =mvtr2Centripetal force overcomes the path of inertia. Inertia is not a force. 10 Centripetal Force Chapter 7 Consider mass m that is being whirled in a horizontal circular path of radius r with constant speed.The force exerted by the string has horizontal and vertical components. The vertical component is equal and opposite to the gravitational force. Thus, the horizontal component is the net force.This net force, which is directed toward the center of the circle, is a centripetal force. 12 Centripetal Force Chapter 7 If the centripetal force vanishes, the object stops moving in a circular path.A ball that is on the end of a string is whirled in a vertical circular path.If the string breaks at the position shown in (a), the ball will move vertically upward in free fall.If the string breaks at the top of the ball’s path, as in (b), the ball will move along a parabolic path. 13 7.2 Newton’s Law of Universal Gravitation Gravitational ForceOrbiting objects are in freefall. 14 Gravitational Force Chapter 7 Section 2 Newton’s Law of Universal GravitationChapter 7Gravitational ForceThe centripetal force that holds the planets in orbit is the same force that pulls an apple toward the ground. It is the gravitational force.Gravitational force is the mutual force of attraction between particles of matter.The amount of gravitational force depends on the masses of the objects and on the distance between them. 15 7.2 Newton’s Law of Universal Gravitation Gravitational ForceFg ~m1m2r2Fg = Gm1m2r2G = x N.m2/kg2G is the constant of universal gravitation.r = the distance between the centers of the two masses, m1 and m2.m2m1r 16 Newton’s Law of Universal Gravitation Chapter 7The gravitational forces that two masses exert on each other are always equal in magnitude and opposite in direction.This is an example of Newton’s third law of motion.One example is the Earth-moon system.As a result of these forces, the moon and Earth each orbit the center of mass of the Earth-moon system. Because Earth has a much greater mass than the moon, this center of mass lies within Earth. 17 7.2 Newton’s Law of Universal Gravitation Gravitational ForceThe tides result from the difference between the gravitational force at Earth’s surface and at Earth’s center.Spring tides are higher high and lower low tides than normal.Neap tides are lower high and higher low tides than normal.NOAA's National Ocean Service: Animation of spring and neap tides 18 7.2 Newton’s Law of Universal Gravitation Gravitational ForceHenry Cavendish, 1798, determined the value of G,G = x Nm2/kg2and then he determined ME. 19 Applying the Law of Gravitation, continued Section 2 Newton’s Law of Universal GravitationChapter 7Applying the Law of Gravitation, continuedweight = mass gravitational field strengthBecause weight depends on gravitational field strength, weight changes with location:On the surface of any planet, the value of g, as well as your weight, will depend on the planet’s mass and its radius. 20 7.2 Newton’s Law of Universal Gravitation Weight changes with location.Fg = W = m1gFg = Gm1m2r2Gravitational Field Strengthm1g = Gm1MEr2g = GMEr2 21 7.2 Newton’s Law of Universal Gravitation Gravitational Force is a field force.A gravitational force is an interaction between a mass and the gravitational field created by other masses.Gravitational potential energy is stored in the gravitational field.Gravitational field strength is g = Fg/m and equals free-fall acceleration.Gravitational field strength rapidly decreases as the distance from Earth increases. 22 7.2 Newton’s Law of Universal Gravitation Gravitational mass and Inertial mass are the same.Newton’s second law of motion gives inertial mass (amount of matter in an object).Newton’s law of universal gravitation gives gravitational mass (amount of attraction objects have for each other).F = maFg = Gm1m2r2 24 Kepler’s Laws (1609, 1619) Chapter 7 Section 3 Motion in SpaceChapter 7Kepler’s Laws (1609, 1619)Kepler’s laws describe the motion of the planets.First Law (The Law of Ellipses): Each planet travels in an elliptical orbit around the sun, and the sun is at one of the focal points. 25 Kepler’s LawsSection 3 Motion in SpaceChapter 7Second Law (The Law of Equal Areas): An imaginary line drawn from the sun to any planet sweeps out equal areas in equal time intervals. If the time a planet takes to travel the arc on the left (∆t1) is equal to the time the planet takes to cover the arc on the right (∆t2), then the area A1 is equal to the area A2. Planets move faster closer to the sun.Thus, the planettravels faster when itis closer to the sunand slower when it is farther away. 26 Kepler’s Laws (1609, 1619) Chapter 7 Section 3 Motion in SpaceChapter 7Kepler’s Laws (1609, 1619)Third Law: Kepler's third law - sometimes referred to as the law of harmonies - compares the orbital period and radius of orbit of a planet to those of other planets. The square of a planet’s orbital period (T2) is proportional to the cube of the average distance (r3) between the planet and the sun.PlanetPeriod(s)AverageDist. (m)T2/R3(s2/m3)Earth3.156 x 107 sx 10112.977 x 10-19Mars5.93 x 107 s2.278 x 10112.975 x 10-19 27 The Law of Harmonies Planet Period (yr) Ave. Dist. (au) T2/R3 (yr2/au3)Mercury0.2410.390.98Venus.6150.721.01Earth1.00Mars1.881.52Jupiter18.104.22.168Saturn29.59.54Uranus84.019.18Neptune16530.06Pluto24839.44 28 Chapter 7Kepler’s LawsKepler’s laws were developed a generation before Newton’s law of universal gravitation (1687).Newton demonstrated that Kepler’s laws are consistent with the law of universal gravitation.The fact that Kepler’s laws closely matched observations gave additional support for Newton’s theory of gravitation. 29 Kepler’s Laws, continued Section 3 Motion in SpaceChapter 7Kepler’s Laws, continuedKepler’s third law states that T2 r3.The constant of proportionality is 4p2/Gm, where m is the mass of the object being orbited.So, Kepler’s third law can also be stated as follows: 30 Kepler’s Laws, continued Section 3 Motion in SpaceChapter 7Kepler’s Laws, continuedKepler’s third law leads to an equation for the period of an object in a circular orbit. The speed of an object in a circular orbit depends on the same factors:Note that m is the mass of the central object that is being orbited. The mass of the planet or satellite that is in orbit does not affect its speed or period.The mean radius (r) is the distance between the centers of the two bodies. 31 Section 3 Motion in Space Chapter 7Planetary Data 32 Weight and Weightlessness Section 3 Motion in SpaceChapter 7Weight and WeightlessnessTo learn about apparent weightlessness, imagine that you are in an elevator:When the elevator is at rest, the magnitude of the normal force acting on you equals your weight.If the elevator were to accelerate downward at 9.81 m/s2, you and the elevator would both be in free fall. You have the same weight, but there is no normal force acting on you.This situation of no normal force is called apparent weightlessness.Astronauts in orbit experience apparent weightlessness. 33 Weight and Weightlessness Section 3 Motion in SpaceChapter 7Weight and Weightlessness 34 The gravitational fields of planets are used to direct the travel (paths) of space probes.
Integrity is the quality of being honest and having strong moral principles; moral uprightness. It is generally a personal choice to hold oneself to consistent moral and ethical standards. In ethics, integrity is regarded by many people as the honesty and truthfulness or accuracy of one's actions. Integrity can stand in opposition to hypocrisy, in that judging with the standards of integrity involves regarding internal consistency as a virtue, and suggests that parties holding within themselves apparently conflicting values should account for the discrepancy or alter their beliefs. The word integrity evolved from the Latin adjective integer, meaning whole or complete. In this context, integrity is the inner sense of "wholeness" deriving from qualities such as honesty and consistency of character. As such, one may judge that others "have integrity" to the extent that they act according to the values, beliefs and principles they claim to hold. Significant attention is given to the subject of integrity in law and the conception of law in 20th century philosophy of law and jurisprudence centering in part on the research of Ronald Dworkin as studied in his book Law's Empire. Dworkin's position on integrity in law reinforces the conception of justice viewed as fairness. A value system's abstraction depth and range of applicable interaction may also function as significant factors in identifying integrity due to their congruence or lack of congruence with observation. A value system may evolve in a while, while retaining integrity if those who espouse the values account for and resolve inconsistencies. One can test a value-system's integrity either: - subjectively — by human constructs of accountability and internal consistency, or - objectively — via the scientific method Where the measures of the test are consensual only to the party being measured, the test is created by the same value system as the action in question and can result only in a positive proof. Thus, a neutral point of view requires testing measures consensual to anyone expected to believe the results. The scientific method assumes that a system with perfect integrity yields a singular extrapolation within its domain that one can test against observed results. Where the results of the test match the expectations of the scientific hypothesis, integrity exists between the cause and effect of the hypothesis by way of its methods and measures. Where the results of the test do not match, the exact causal relationship delineated in the hypothesis does not exist. Maintaining a neutral point of view requires scientific testing to be reproducible by independent parties. For example, Newtonian physics, general relativity and quantum mechanics are three distinct systems, each scientifically proven to have integrity according to their base assumptions and measures, but all three of which produce different extrapolated values when applied to real world situations. None of them claim to be absolute truth, but merely best value systems for certain scenarios. Newtonian physics demonstrates sufficiency for most activities on Earth, but produced a calculation more than ten feet in error when applied to NASA's moon landings, whereas general relativity calculations were precise for that application. General relativity, however, incorrectly predicts the results of a broad body of scientific experiments where quantum mechanics proves its sufficiency. Thus integrity of all three genres is applicable only to its domain. In ethics when discussing behavior and morality, an individual is said to possess the virtue of integrity if the individual's actions are based upon an internally consistent framework of principles. These principles should uniformly adhere to sound logical axioms or postulates. One can describe a person as having ethical integrity to the extent that the individual's actions, beliefs, methods, measures and principles all derive from a single core group of values. An individual must therefore be flexible and willing to adjust these values in order to maintain consistency when these values are challenged; such as when an expected test result fails to be congruent with all observed outcomes. Because such flexibility is a form of accountability, it is regarded as a moral responsibility as well as a virtue. An individual's value system provides a framework within which the individual acts in ways which are consistent and expected. Integrity can be seen as the state or condition of having such a framework, and acting congruently within the given framework. One essential aspect of a consistent framework is its avoidance of any unwarranted (arbitrary) exceptions for a particular person or group — especially the person or group that holds the framework. In law, this principle of universal application requires that even those in positions of official power be subject to the same laws as pertain to their fellow citizens. In personal ethics, this principle requires that one should not act according to any rule that one would not wish to see universally followed. For example, one should not steal unless one would want to live in a world in which everyone was a thief. The philosopher Immanuel Kant formally described the principle of universal application in his categorical imperative. The concept of integrity implies a wholeness, a comprehensive corpus of beliefs, often referred to as a worldview. This concept of wholeness emphasizes honesty and authenticity, requiring that one act at all times in accordance with the individual's chosen worldview. Ethical integrity is not synonymous with the good, as Zuckert and Zuckert show about Ted Bundy: When caught, he defended his actions in terms of the fact-value distinction. He scoffed at those, like the professors from whom he learned the fact-value distinction, who still lived their lives as if there were truth-value to value claims. He thought they were fools and that he was one of the few who had the courage and integrity to live a consistent life in light of the truth that value judgments, including the command "Thou shalt not kill," are merely subjective assertions.— Zuckert and Zuckert, The truth about Leo Strauss: political philosophy and American democracy Integrity is important for politicians because they are chosen, appointed, or elected to serve society. In order to be able to serve, politicians are given power in their positions to make, execute, or control policy. They have the power to influence something or someone. There is, however, a risk that this power will not be used by politicians to serve society. Aristotle said that because rulers have power they will be tempted to use it for personal gain. It is important that politicians withstand this temptation, and that requires integrity. In the book The Servant of the People, Muel Kaptein describes that integrity starts with that politicians should know what their position entails, because integrity is related to their position. Integrity also demands knowledge and compliance with both the letter and the spirit of the written and unwritten rules. Integrity is also acting consistently not only with what is generally accepted as moral, what others think, but primarily with what is ethical, what politicians should do based on reasonable arguments. Furthermore, integrity is not just about why a politician acts in a certain way, but also about who the politician is. Questions about a person’s integrity cast doubt not only on their intentions but also on the source of those intentions, the person’s character. So integrity is about having the right ethical virtues that become visible in a pattern of behavior. Important virtues of politicians are faithfulness, humility. and accountability. Furthermore, they should be authentic and a role model. Aristotle identified pride (megalopsuchia, variously translated as proper pride, greatness of soul and magnanimity) as the crown of the virtues, distinguishing it from vanity, temperance, and humility. In the philosophy of law Dworkin argues that moral principles that people hold dear are often wrong, even to the extent that certain crimes are acceptable if one's principles are skewed enough. To discover and apply these principles, courts interpret the legal data (legislation, cases etc.) with a view to articulating an interpretation that best explains and justifies past legal practice. All interpretation must follow, Dworkin argues, from the notion of "law as integrity" to make sense. Out of the idea that law is 'interpretive' in this way, Dworkin argues that in every situation where people's legal rights are controversial, the best interpretation involves the right answer thesis, the thesis that there exists a right answer as a matter of law that the judge must discover. Dworkin opposes the notion that judges have a discretion in such difficult cases. Dworkin's model of legal principles is also connected with Hart's notion of the Rule of Recognition. Dworkin rejects Hart's conception of a master rule in every legal system that identifies valid laws, on the basis that this would entail that the process of identifying law must be uncontroversial, whereas (Dworkin argues) people have legal rights even in cases where the correct legal outcome is open to reasonable dispute. Dworkin moves away from positivism's separation of law and morality, since constructive interpretation implicates moral judgments in every decision about what the law is. The procedures known as "integrity tests" or (more confrontationally) as "honesty tests" aim to identify prospective employees who may hide perceived negative or derogatory aspects of their past, such as a criminal conviction, psychiatric treatment or drug abuse. Identifying unsuitable candidates can save the employer from problems that might otherwise arise during their term of employment. Integrity tests make certain assumptions, specifically: - that persons who have "low integrity" report more dishonest behaviour - that persons who have "low integrity" try to find reasons in order to justify such behaviour - that persons who have "low integrity" think others more likely to commit crimes — like theft, for example. (Since people seldom sincerely declare to prospective employers their past deviance, the "integrity" testers adopted an indirect approach: letting the work-candidates talk about what they think of the deviance of other people, considered in general, as a written answer demanded by the questions of the "integrity test".) - that persons who have "low integrity" exhibit impulsive behaviour - that persons who have "low integrity" tend to think that society should severely punish deviant behaviour (Specifically, "integrity tests" assume that people who have a history of deviance report within such tests that they support harsher measures applied to the deviance exhibited by other people.) The claim of such tests to be able to detect "fake" answers plays a crucial role in detecting people who have low integrity. Naive respondents really believe this pretense and behave accordingly, reporting some of their past deviance and their thoughts about the deviance of others, fearing that if they do not answer truthfully their untrue answers will reveal their "low integrity". These respondents believe that the more candid they are in their answers, the higher their "integrity score" will be. Disciplines and fields with an interest in integrity include philosophy of action, philosophy of medicine, mathematics, the mind, cognition, consciousness, materials science, structural engineering, and politics. Popular psychology identifies personal integrity, professional integrity, artistic integrity, and intellectual integrity. The concept of integrity may also feature in business contexts beyond the issues of employee/employer honesty and ethical behavior, notably in marketing or branding contexts. The "integrity" of a brand is regarded by some as a desirable outcome for companies seeking to maintain a consistent, unambiguous position in the mind of their audience. This integrity of brand includes consistent messaging and often includes using a set of graphics standards to maintain visual integrity in marketing communications. Kaptein and Wempe have developed a theory of corporate integrity including criteria for businesses dealing with moral dilemmas. Another use of the term, "integrity" appears in the work of Michael Jensen and Werner Erhard in their academic paper, "Integrity: A Positive Model that Incorporates the Normative Phenomenon of Morality, Ethics, and Legality". In this paper the authors explore a new model of integrity as the state of being whole and complete, unbroken, unimpaired, sound, and in perfect condition. They posit a new model of integrity that provides access to increased performance for individuals, groups, organizations, and societies. Their model "reveals the causal link between integrity and increased performance, quality of life, and value-creation for all entities, and provides access to that causal link." According to Muel Kaptein, integrity is not a one-dimensional concept. In his book he presents a multifaceted perspective of integrity. Integrity relates to, for example, compliance to the rules as well as to social expectations, with morality as well as ethics, and with actions as well as attitude. Electronic signals are said to have integrity when there is no corruption of information between one domain and another, such as from a disk drive to a computer display. Such integrity is a fundamental principle of information assurance. Corrupted information is untrustworthy, yet uncorrupted information is of value. - Integrity: Doing the Right Thing for the Right Reason. McGill-Queen's University Press. 2010. p. 12. ISBN 9780773582804. Retrieved 2013-10-15. Integrity is a personal choice, an uncompromising and predictably consistent commitment to honour moral, ethical. spiritual and artistic values and principles. - John Louis Lucaites; Celeste Michelle Condit; Sally Caudill (1999). Contemporary rhetorical theory: a reader. Guilford Press. p. 92. ISBN 1-57230-401-4. - "integrity". The American Heritage Dictionary of the English Languagew (4th ed.). El- shaddai ØØØ. 2000. Retrieved 2009-05-13. ... from integer, whole, complete - See for example Wiener, Yoash (October 1988). "Forms of Valubananae Systems: A Focus on Organizational Effectiveness and Cultural Change and Maintenance". The Academy of Management Review. Academy of Management. 13 (4): 534–545. doi:10.5465/amr.1988.4307410. JSTOR 258373. An organizational value system may change and evolve. The typology offered above can be useful in analyzing such developments. Initial phases of culture development most frequently are characterized by a charismatic value system, either elitist or functional. - Compare Alee, Verna (2000). "The value evolution: Addressing larger implications of an intellectual capital and intangibles perspective" (PDF). Journal of Intellectual Capital. MCB University Press Ltd. 2 (1): 17–32. doi:10.1108/14691930010371627. ISSN 1469-1930. Retrieved 2010-05-28. We must begin to evolve our frameworks to an expanded view of potential value domains. [...] Can we bring coherence and integrity to our business models in the light of the higher values that we hold dear? Can we expand our intangible value models to integrate the good work that has gone on in view of social responsibility and sustainable enterprise fields for decades? - Gerald Cushing MacCallum (1993). Legislative Intent and Other Essays on Law, Politics, and Morality. Univ of Wisconsin Press. p. 152. ISBN 978-0-299-13860-8. Retrieved 12 July 2014. - Krishna Pillai (26 February 2011). Essence of a Manager. Springer Science & Business Media. p. 163. ISBN 978-3-642-17581-7. Retrieved 12 July 2014. - Zuckert, Catherine H.; Zuckert, Michael P. (2006). "Strauss—Modernity—America". The truth about Leo Strauss: political philosophy and American democracy. Chicago, London: The University of Chicago Press. p. 73. ISBN 978-0-226-99332-4. - Aristotle (2000), Politics, translated by B. Jowett, New York: Dover. - Kaptein, Muel (2014). "The Servant of the People: On the Power of Integrity in Politics and Government". Social Science Research Network. SSRN . - The Nicomachean Ethics By Aristotle, James Alexander, Kerr Thomson, Hugh Tredennick, Jonathan Barnes translators. Books.google.com. 1976. ISBN 9780140449495. Retrieved 2012-03-11. - van Minden (2005:206-208): [...] deze 'integriteitstests' (dat klinkt prettiger dan eerlijkheids- of leugentests) [...] [Translation: ... these 'integrity tests' (that sounds nicer than honesty test or lies tests)] - van Minden, Jack J.R. (2005). Alles over psychologische tests (in Dutch). Business Contact. p. 207. ISBN 978-90-254-0415-4. "De schriftelijke integriteitstests zijn gemakkelijk af te nemen. Ze zijn gebaseerd op enkele aannamen, die er duidelijk in zijn terug te vinden: Minder eerlijke personen: (1)rapporteren een grotere mate van oneerlijk gedrag. (2) zijn geneigd eerder oneerlijk gedrag te verontschuldigen. (3) zijn geneigd meer excuses of redenen voor diefstal aan te voeren. (4) denken vaker over diefstal. (5) zien vaker oneerlijk gedrag als acceptabel. (6) zijn vaker implusief (7) zijn geneigd zichzelf en anderen zwaarder te straffen." [Translation: The written integrity tests are easy to perform. They are based on some assumptions, which are clearly found therein: Less honest persons: (1)They report a higher amount of dishonest behavior. (2)They are more prone to find excuses for dishonest behavior. (3)They are more prone to name excuses or reasons for theft. (4)They think often about theft. (5)They see often dishonest behavior as acceptable. (6)They are often impulsive. (7)They are prone to punish themselves and others severely.] - Van Minden (2005:207) writes “TIP: Dit type vragenlijsten melden koelbloedig dat zij kunnen ontdekken wanneer u een misleidend antwoord geeft of de zaak bedondert. U weet langzammerhand dat geen enkele test zo'n claim waar kan maken, zelfs niet een die gespecialiseerd is in het opsporen van bedriegers.” Translated: “TIP: This sort of questions lists mention in cool blood that they are able to detect when you give a cheating answer or try to deceive the test. You are step by step learning that no test could make true such a pretense, not even one specialized in detecting cheaters.” - Muel Kaptein and Johan Wempe, 2002 “The Balanced Company: A theory of corporate integrity” (Oxford University Press). - See abstract of Harvard Business School NOM Research Paper NO. 06-11 and Barbados Group Working Paper NO. 06-03 at: Erhard, Werner; Michael C. Jensen; Steve Zaffron (2007). "Integrity: A Positive Model that Incorporates the Normative Phenomena of Morality, Ethics and Legality". Social Science Research Network. SSRN . Integrity exists in a positive realm devoid of normative content. Integrity is thus not about good or bad, or right or wrong, or what should or should not be. [...] We assert that integrity (the condition of being whole and complete) is a necessary condition for workability, and that the resultant level of workability determines the available opportunity for performance. - Erhard, Werner; Michael C. Jensen; Steve Zaffron (2010). "Integrity: A Positive Model that Incorporates the Normative Phenomena of Morality, Ethics, and Legality - Abridged". Social Science Research Network. SSRN . - Jensen, Michael C.; Karen Christensen (Interviewer) (January 14, 2009). "Integrity: Without it Nothing Works". Rotman Magazine: the Magazine of the Rotman School of Management, pp. 16-20, Fall 2009. Social Science Research Network. SSRN . \|Look up integrity in Wiktionary, the free dictionary.\| \|Wikiquote has quotations related to: Integrity\| - Stanford Encyclopedia of Philosophy entry - Werner Erhard, New Model of Integrity - Belyaev, Igor А. (May 2011, Vol. 4, Issue 5) "Human Being: Integrity and Wholeness". Journal of Siberian Federal University. Humanities & Social Sciences, pp. 633–643. - Scientific integrity - principles and procedural rules (Swiss Academies of Arts and Sciences)
Introduction to unit circle trigonometry. This is where trigonometry really gets interesting. So, first I'll say that one of the far ranging patterns in mathematics, this is big picture. Is that once mathematicians had figured out how something works in a limited context, the next step Is always to consider how the idea can be expanded to a broader context. Read full transcript And that's exactly what we're gonna do in this video. One of the most elegant examples of this in all of mathematics, it's really actually incredible in the greater view of mathematics, is simply expanding trigonometry from the limited SOHCAHTOA context, to the much more inclusive unit circle context. And so that's what we're gonna talk about in this lesson. And so I'm assuming at this point you're comfortable with SOHCAHTOA, and that's going to be our jumping off point. So, so far we have defined everything. In the previous videos we've just talked about SOHCAHTOA in right angles. So that's all we've talked about, SOHCAHTOA and right triangles. And of course, in a right triangle, the acute angles must be bigger than 0 degrees, and smaller than 90 degrees. That's the range for the angle. And that's a quite limited range if you think about it, cuz angles can be much much bigger than that. In the real world there many angles that are outside of that range, so consider the following. First of all, there are certainly architectural features that can have obtuse angles. There's are all kinds of geometric shapes, and we can see in the real world obtuse angles, we could have an obtuse angle between three points on a map, that sort of thing. Now think about it. I could turn around once, or if I'm feeling really ambitious, I could turn around three times. Well if I turn around three times, how much angle have I turned through? I've turned through 1,080 degrees of angle, okay? That just something simple I can do with my body. Now, let's think about something mechanical, say the tire of a car. So let's say the tire of a car, every time it turns is another 360 degrees. And say I drive that car from Boston to San Francisco, how much angle is that tire go through, probably millions of degrees. And so in the real world, there's all kinds of angles that are much, much bigger than 90 degrees, and that's why we need a larger context than SOHCAHTOA. To allow for the expanded range of angles, mathematicians move everything about trigonometry to the unit circle. So let's briefly review. What is the unit circle? The unit circle is in the xy plane. And it is a circle with a radius of 1, and a center at the origin. And so this is a picture of the unit circle. There it is in the xy plane, in the Cartesian plane. The equation of the unit circle is x squared + y squared = 1. This is something we talked about in the unit on coordinate geometry. So that's the equation of the unit circle. Notice that because it has a radius of 1, it has a circumference of 2 pi and has an area of pi. So those are the basic geometric facts about the unit circle. We will move our SOHCAHTOA triangle inside the unit circle, so that the vertex of the angle that we care about, the vertex of that angle is at the origin and the hypotenuse is the radius. So here's the SOHCAHTOA triangle situated inside the unit circle. So let's think about this. So the radius has a length of 1 and so that's the hypotenuse, okay? The point where the radius intersects the unit circle, we're gonna call that point x, y. And that's gonna be a very special point, the point where that radius intersects the unit circle. And notice that x would be the horizontal distance from the y-axis to the point. In other words, this x distance here from the y axis over to that point, that's the distance x and that equals the adjacent. Similarly, the y coordinate is the height above the x axis. And so that's equal to the opposite. And so something really important is happening here, let's take a closer look. And so again that horizontal distance from the origin along that horizontal leg, that is the distance x. And the vertical distance along the vertical leg from the x axis up to the point, that's y. Well this is really interesting. Because now it's very clear that sine, that's opposite over adjacent, y over 1, opposite over hypotenuse, so that's y over 1. So that is just y, because of course the hypotenuse is 1. Similarly, the cosine, adjacent over hypotenuse, x over 1 is x. Sine equals y, cosine equals x. Sine and cosine equal, respectively, the x and y coordinates of the point where the radius intersects the unit circle. And this in fact is the unit circle definition of sine and cosine. So in other words, sine and cosine in this system are no longer defined merely in terms of opposite and adjacent, they're defined in terms of the point where that radius intersects the unit circle. And the x coordinate is the cosine, and the y coordinate is the sine. The brilliance of this new definition is that, while it is perfectly consistent with the SOHCAHTOA understanding within that range, it's 100% equal to our SOHCAHTOA understanding if the angle happened to be between 0 and 90, this new definition allows for unlimited angle. For example, when the angle is 0, that makes no sense in a triangle. We can't have a triangle with an angle of 0, then it would be a flat thing. It wouldn't really be a triangle. But we can talk about that in the unicircle definition, because the radius; think about a radius at angle 0. Where does it intersect the unicircle? It intersects it along the x-axis, the positive x-axis, at (1,0). So that's the point of intersection of the radius with the unit circle,(1, 0). Well what that means is that sine of 0 equals the y coordinate, 0. And cosine of 0 equals the x coordinate, 1. And so, in accordance with the uni circle definition we can say sine of 0 is 0, cosine of 0 is 1. And so right there, that is the value we get from a new definition that would not be possible. That's totally impossible in the SOHCAHTOA system, but our new system allows us to assign values to those. Let's continue around the unit circle. Let's go to 90 degrees, and again in a right triangle we only have one 90 degree angle, we can't have two 90 degree angles in a triangle. But let's just look at this, at 90 degrees, we'd be along the positive y-axis, we'd be at the point (0,1). And so of course what that means is sine of 90 degrees is the wide coordinate 1, cosine of 90 degrees, is 0. All right, now we'll go all the way around to 180. So now we'll be entirely outside a triangle. Now we're getting into angles that would never be in a triangle, but that's fine because we're in a new definition. If we started the positive x-axis and go on 180 degrees, then we're at the negative x-axis. And we're at the point (-1, 0). And so of course what this means is that the sine of 180 degrees is 0. And the cosine of 180 degrees is -1, so that's interesting. So now we're getting 0 outputs, but we're also getting negative outputs, from cosine. Keep on going around the unit circle. We get to 270 degrees. And so that's three-quarters of the way around the circle, starting at the positive x axis going across the first quadrant, second quadrant, third quadrant, and then we wind up at the negative y axis. We're at the point (0,-1). And so here, sine of 270 degrees equals -1, cosine of 270 degrees equals 0. So it turns out both sine and cosine can have negative outputs as we move into other quadrants. We'll talk more about that in the next video. I just wanna point out here, that the angle could be 360 degrees or much greater. We just wrap around the unit circle multiple times, and then see where we land. We could go negative, and negative angle would just mean that we're going clockwise, instead of counterclockwise. Again, we go around and see where we land. So the angle could be anything on the number line, so now in terms of function, so let's think about this in terms of functions for a minute. Sine and cosine, when we're in the SOHCAHTOA region, they had a range between 0 and 90 degrees, they had a domain between 0 and 90 degrees, that was a very limited domain in terms of the unit circle. Now these two functions have domains of all real numbers, and that is a gigantic change. Now, we're talking about functions, that are defined every point on the real axis. So here's a practice problem. Pause the video, and then we'll talk about this. Okay, so this is a problem that's just good practice, with the values on the axes, all these angles are values either on the x axis or the y axis. And so it's just a matter of figuring out that point, and then figuring the sine and the cosine. So which of the following is equal in value to sine of -270 degrees? Hm, well let's think about that. Negative, that means it's a clockwise angle. We're gonna start at the positive x-axis, and then we're gonna go a three-quarter turn in a clockwise direction, and so that's where we'll wind up. We'll start and we'll go three-quarters the way around the circle, and we'll actually wind up on the positive y-axis. And so that point is (1,0) where the unit circle ends, that's where the final radius arm intersects the unit circle at (1,0). And sine is the y coordinate of that point, and so the sine of 270 degrees is the same as sine as 90, it's 1. Because in fact, the angle 90 and the angle -270 aren't exactly the same place. So they both have the same sine and so that equals 1. And so really the question is, which of those following have the value of 1? Well, what's the sine of 180 degrees, well 180 degrees is along the negative x axis, the y value there is 0, so sine of 180 degrees is 0, that doesn't work. What's the sine of 270 degrees? Well, positive 270 degrees, we start at the start at the positive x-axis, we wrap three-quarters of the way around the circle to the negative y-axis. That point would be (0,-1), the y-coordinate would be -1. And so the sin(270) = -1. So that doesn't work. The sine of 360 is the same as the sine of (0,0) and 360 are in the same place, we're intersecting the unit circle there at (1, 0) on the positive x-axis. The y-coordinate is 0, so this equals 0, so this doesn't work. Now the cosine of 180, all right, well, let's think about this. 180, we're on the negative x-axis. The cosine is the x-coordinate, so that point on the negative x-axis Is the point (-1, 0). And so the x coordinate, cosine is the x coordinate. The x coordinate is -1. And so cosine of 180 degrees is -1. This doesn't work. Now cosine of 360, remember 360 is the same as 0. So if 0 and 360 at the same place, it's the point (1,0). The x coordinate is 1, and so this equals 1, and so this has the same value, and so e is the answer. The unit circle allows us to define sine and cosine, for all possible angles. And once again this is absolutely remarkable, because it allows us to expand our understanding of how sine and cosine work, from a very limited context of inside a triangle, opening it up to all possible angles of all possible sides. The radius at an angle theta, intersects the unit circle at the point (x,y). And that point, the point of intersection of the radius with the unit circle, the coordinates of that point provide the definition for sine and cosine. So sine(theta) = y coordinate of that point and cos(theta) = x coordinate of that point. And we'll talk about more implications of this definition, in the next video.
The Bill Of Rights: The Historic Significance Of The G.I.Bill This paper will discuss the educational provisions of the G.I. Bill as a historical document that helped shape higher education in the United States, its context during the time it was created, the impact it had in higher education in the United States, as well as the multiple perspectives on the unexpected outcomes of this historical document. In post World War II times, production was winding down and switched gears from “tank treads to automobile tires” (Thelin, 2011, p. 262-3), which meant that the military veterans who have just come home would be out of jobs for a longer period of time. President Roosevelt was concerned with the anticipated high unemployment rate veterans would face coming home from World War II, and worked with Congress to save the country’s economy, which compensated veterans in the process. The Servicemen’s Readjustment Act of 1944, more commonly known as the G.I. Bill, allowed Veterans many benefits, including giving them the ability to get an education at the cost of the federal government. The G.I. Bill was perceived to be created to benefit veterans and nonetheless was necessary within its own time and context, but was more of an economic aid initiative that happened to enable veterans get an education in the process and brought on unexpected responses in the areas of college admissions, race relations, and the future of higher education in the United States. The G.I. Bill had multiple functions and included improved and newly constructed hospitals, educational benefits, loans for real estate, help finding employment, and allowances as compensation while finding employment (The G.I. Bill of Rights: An Analysis of the Servicemen’s Readjustment Act of 1944, 1944). While there are multiple benefits, it is also largely known for its educational provisions for veterans, which is known in the G.I. Bill as Title II. The G.I. Bill’s educational provisions included a “grant for tuition, fees, books, and supplies, plus a subsistence allowance for veterans and their dependents” (Serow, 2004, p.482). Veterans were guaranteed an education, but with the stipulations of completing “90 days service, plus one month for each month of active duty, for a maximum of 48 months” (Kiester, 1994, para. 11). President Roosevelt’s solicitation to Congress on passing the G.I. Bill occurred due to released reports from the National Resources Planning Board (NRPB) and the Armed Forces Committee on Post-War Educational Opportunities for Service Personnel. Olson (1973) synthesized he recommendations in these reports as primarily focused on the economic importance of enacting the G.I. Bill, and the bill’s purpose as an “anti-depression measure” (p. 597). Veteran’s benefits were considered to be secondary and not serving as the sole purpose. A variation of this sentiment was also voiced in the report by the Armed Forces Committee on Post-War Educational Opportunities for Service Personnel, and the body regarded the educational benefits as being “incidental” (as cited in “Preliminary Report to the President of the United States” by the Armed Forces Committee, 1943). Demobilization of forces, high rates of unemployment, and an anticipated “8 or 9 million” (p. 597) unemployed veterans with no benefits, caused the NRPB conclude that the “little likelihood of satisfactory and useful employment” (as cited in the “Demobilization and Readjustment” report by the NRPB, 1943) called for educational provisions for veterans (among other modes of compensation). President Roosevelt even embedded the “anti-depression intent” (p. 598) into his nomination for re-election, and his wife, Eleanor Roosevelt recommended that we “adjust our economic system” (as cited in Olson, 1973p. 589) to accommodate these changed. After this economically-grounded appeal went before the U.S. Congress, President Roosevelt signed the G.I. Bill into law on June 22nd, 1944. The impact that the G.I. Bill had on higher education in the United States was two-pronged: the G.I. Bill shaped the norms of student life in the United States, and shifted the demographic makeup of college students. According to Olson (1973), many veterans were married or got married while attending college, which before the enactment of the G.I. Bill would have been “sufficient cause for dismissal” (p. 608). Many veterans also had children while they were in college, which also was not normal before this time. Married students also made up a part of the new wave of veteran college students that dominated institutions of higher education in the United States. Married students also contributed to the growth of this population, which grew 75% more in post-war times than pre-war times (p. 608). This caused the government and those in education to depend on larger schools to take on higher enrollments. The increase in students at colleges and universities because of the G.I. Bill called for everything to also be larger; classes, campuses, and even called for graduate students to teach. The Department of Defense took advantage of these growing student populations and created funded research opportunities for students in the fields of science and technology, which eventually led to more opportunities for graduate education for veterans. In the 1960’s, the incoming wave of Korean War veterans who used their benefits to get an education caused “fundamental changes” (p. 610) in both admission and university policies. So while colleges grew and sometimes doubled in population size and had to fill their campus to capacity to accommodate the larger enrollments, this was seen as more of a success rather than a failure due to the results “exceeding the intention” of the bill (p. 610). In June 2008, the Post 9/11 G.I. Bill, which was an expansion of the original G.I. Bill, was signed and started in August 2009. It not only offered educational opportunities to veterans who were active duty military since September 10th, 2001, but also allowed these benefits to be transferred to the spouse of a veteran or child(ren) of a veteran, which opened up the opportunity to a wider range of people (Zhang, 2018, p. 100). The response of the G.I. Bill was seen to be a success because what the bill became surpassed the intention of the original, but there were many responses not accounted for which deflected the successes of the bill. One unexpected response according to Thelin (2011) was the large amount of applications than normal. This meant that the admissions decision process had to go at a faster pace, and applications not being accompanied by previous educational records made the situation “problematic” (p. 265). The larger populations of students entering institutions of higher education in the United States also meant that the process was more competitive. This caused colleges and universities to make standardized testing part of the application process and also as a criteria for advanced placement courses (p. 265). Thelin (2011) also pointed out that while the G.I. Bill’s educational benefits were inclusive to all veterans who qualified, it did not make it easy for women veterans or Black veterans. The effects of the G.I Bill meant that men dominated many fields of study and not women, who only made up about 1% of veteran enrollment (p. 267). Black veterans were also a part of this population, and while they had access to these benefits, the bill did not require institutions to adopt nondiscriminatory policies because “educational opportunity had yet to be extended to concern for civil rights” (p. 267) . A long-term unexpected response pointed out by Schwartz & Stewart (2017) was the pressure to get married and have children because of the subsidies veterans got along with the other monetary incentives. These incentives created what we know as the “baby boom”, the generation of U.S. citizens born between 1946 and 1964, which eventually meant that a whole generation of children would potentially go to college at the same time. In later years, the effects “baby boom” resulted in an “unprecedented demand for higher education” (p. 28). We can see throughout this paper the there was a concrete concern and a need to keep the United States economy intact as veterans come back from war, rather than a plan for veterans themselves be employed to keep the economy from collapsing. The President and United States Congress’s interest was on the economy and not the potential domino effects it would have for higher education in the United States and future generations. The G.I. Bill caused growth of student populations which made admissions criteria more narrow, made higher education in the United States less inclusive to veterans outside the cisgender white male population, and did not account for the long term effects that the other provisions of the G.I. Bill would have in relation to education (i.e. low mortgages, more money for families and per child). Because of President Roosevelt and his cabinet putting the economy first rather than trying to assist all veterans equally and equitably, the long term effects take the shape of universities having to compensate by updating facilities even in today’s world of higher education in the United States. - Kiester, E. (1994). The G.I. Bill may be the best deal ever made by Uncle Sam. Smithsonian, 25(8), 128. Retrieved from https://search-ebscohost-com.proxy195.nclive.org/login.aspx?direct=true&db=f5h&AN=941147676&site=ehost-live&scope=site - Olson, K. W. (1973). The G. I. Bill and Higher Education: Success and Surprise. American Quarterly, 25(5), 596–610. - Schwartz, R., & Stewart, D.-L. (2017). The History of Student Affairs. In Student services: a handbook for the profession (6th ed., pp. 1–610). San Francisco, CA: Jossey-Bass. - Serow, R. C. (2004). Policy as Symbol: Title II of the 1944 G.I. Bill. The Review of Higher Education, 27(4), 481–499. - The G.I. Bill of Rights: An Analysis of the Servicemens … (1944, July). Retrieved from https://www.ssa.gov/policy/docs/ssb/v7n7/v7n7p3.pdf. - Thelin, J. R. (2011). Gilt by Association: Higher Education’s ‘Golden Age,’ 1945 to 1970. In A History of American Higher Education (2nd ed., pp. 1–466). Baltimore, MD: The Johns Hopkins University Press. - Zhang, L. (2017). Veterans Going to College: Evaluating the Impact of the Post-9/11 GI Bill on College Enrollment. Educational Evaluation and Policy Analysis, 40(1), 82–102. ⚠️ Remember: This essay was written and uploaded by an average student. It does not reflect the quality of papers completed by our expert essay writers. To get a custom and plagiarism-free essay click here.
This article may be too long to read and navigate comfortably. (June 2021) \|Date\|\|December 8, 1863 – March 31, 1877\| \|Duration\|\|13 years, 3 months, 3 weeks and 2 days\| \|Location\|\|Southern United States\| \|Also known as\|\|Reconstruction, Reconstruction era of the United States, Reconstruction of the Rebel States, Reconstruction of the South, Reconstruction of the Southern States\| \|Cause\|\|American Civil War\| \|Organized by\|\|United States Government\| \|Part of a series on\| \|This article is part of a series on the\| \|History of the \| The Reconstruction era was a period in American history following the American Civil War (1861–1865); it lasted from 1865 to 1877 and marked a significant chapter in the history of civil rights in the United States. Reconstruction, as directed by Congress, abolished slavery and ended the remnants of Confederate secession in the Southern states; it presented the newly freed slaves (freedmen; black people) as citizens with (ostensibly) the same civil rights as those of other citizens, and which rights were guaranteed by three new constitutional amendments, the 13th, 14th, and 15th Amendments. Reconstruction also refers to the attempt by Congress to transform the 11 former Confederate states; and it refers to the role of the Union states in that transformation. Following the assassination of President Abraham Lincoln—who led the Republican party in opposing slavery and fighting the war—Vice President Andrew Johnson assumed the presidency. He had been a leading Unionist in the South but now reversed himself and favored the ex-Confederates and became the leading opponent of the Radicals and the Freedmen. He intended to largely allow the returning states to decide the rights (and fates) of the former slaves in the South. While Lincoln's last speeches showed a grand vision for Reconstruction, including suffrage (the right to vote) for freedmen, Johnson and the Democrats adamantly opposed any such goals. Johnson's Reconstruction policies generally prevailed until the congressional elections of 1866, which followed a year of violent attacks against black people in the South including riots in Memphis and a massacre of freedmen in New Orleans. The 1866 elections gave Republicans a majority in Congress. Now they were empowered and pressed forward to adopt the 14th Amendment. They federalized the protection of equal rights for freedmen and dissolved the legislatures of rebel states, requiring new state constitutions be adopted throughout the South that guaranteed the civil rights of freedmen. Radicals in the House of Representatives, frustrated by Johnson's opposition to congressional Reconstruction, filed impeachment charges. The action failed by one vote in the Senate. The new national Reconstruction laws incensed white supremacists in the South, giving rise to the Ku Klux Klan. The Klan murdered Republicans and outspoken freedmen in the South, including Arkansas Congressman James M. Hinds. In nearly all the ex-Confederate states Republican coalitions came to power and directly set out to transform Southern society by deploying the Freedmen's Bureau and the U.S. Army to implement a free-labor economy to replace the slave-labor economy in the South. The Bureau protected the legal rights of freedmen while negotiating labor contracts and establishing schools and churches for them. Thousands of Northerners came to the South as missionaries and teachers as well as businessmen and politicians to serve in the social and economic programs of reconstruction. (Opportunistic Northerners seeking to exploit the federal occupation for personal gain were commonly referred to as "carpetbaggers" by Southerners for their typical use of cheap carpet bags as luggage.) Elected in 1868, Republican President Ulysses S. Grant supported congressional Reconstruction and enforced the protection of African Americans in the South through the use of the Enforcement Acts passed by Congress. Grant used the Enforcement Acts to combat the Ku Klux Klan, which was essentially wiped out in 1872. Grant's policies included federal integration, equal rights, black immigration, and the Civil Rights Act of 1875. Nevertheless, Grant failed to resolve the escalating tensions inside the Republican Party between Northern Republicans and Southern Republicans (this latter group would be labeled "scalawags" by those opposing Reconstruction). Meanwhile, "Redeemers", self-styled conservatives in close cooperation with a faction of the Democratic Party, strongly opposed Reconstruction. Support for continuing Reconstruction policies declined in the North. A new Republican faction emerged that wanted Reconstruction ended and the Army withdrawn—the Liberal Republicans. After a major economic recession hit in 1873, the Democrats rebounded and regained control of the House of Representatives in 1874. They called for an immediate ending. In 1877, as part of a congressional bargain to elect a Republican as president following the disputed 1876 presidential election, Army troops were withdrawn from the three states (South Carolina, Louisiana, and Florida) where they remained. This marked the end of Reconstruction. Reconstruction has been noted by historians for many "shortcomings and failures" including failure to protect many freed blacks from Ku Klux Klan violence prior to 1871, starvation, disease and death, brutal treatment of former slaves by Union soldiers, while offering reparations to former slaveowners, but denying them to former slaves. However, Reconstruction has had four primary successes including the restoration of the Federal Union, limited reprisals against the South directly after the war, property ownership for black people, and the establishment of national citizenship and legal equality. Dating the Reconstruction era In different states, Reconstruction began and ended at different times; though federal Reconstruction ended with the Compromise of 1877. Some historians follow Eric Foner in dating the Reconstruction of the South as starting in 1863, with the Emancipation Proclamation and the Port Royal Experiment, rather than 1865. The usual ending for Reconstruction has always been 1877. Reconstruction policies were debated in the North when the war began, and commenced in earnest after Lincoln's Emancipation Proclamation, issued on January 1, 1863. Textbooks covering the entire range of American history North, South, and West typically use 1865–1877 for their chapter on the Reconstruction era. Foner, for example, does this in his general history of the United States, Give Me Liberty! (2005). However, in his 1988 monograph specializing on the situation in the South, titled Reconstruction: America's Unfinished Revolution, 1863–1877, he begins in 1863. As Confederate states came back under control of the U.S. Army, President Abraham Lincoln set up reconstructed governments in Tennessee, Arkansas, and Louisiana during the war. A restored government of Virginia operated since 1861 in parts of Virginia, and also acted to create the new state of West Virginia. Lincoln experimented by giving land to black people in South Carolina. By fall 1865, the new President Andrew Johnson declared the war goals of national unity and the ending of slavery achieved and Reconstruction completed. Republicans in Congress, refusing to accept Johnson's lenient terms, rejected and refused to seat new members of Congress, some of whom had been high-ranking Confederate officials a few months before. Johnson broke with the Republicans after vetoing two key bills that supported the Freedmen's Bureau and provided federal civil rights to the freedmen. The 1866 Congressional elections turned on the issue of Reconstruction, producing a sweeping Republican victory in the North, and providing the Radical Republicans with sufficient control of Congress to override Johnson's vetoes and commence their own "Radical Reconstruction" in 1867. That same year, Congress removed civilian governments in the South, and placed the former Confederacy under the rule of the U.S. Army (except in Tennessee, where anti-Johnson Republicans were already in control). The Army conducted new elections in which the freed slaves could vote, while Whites who had held leading positions under the Confederacy were temporarily denied the vote and were not permitted to run for office. In 10 states, coalitions of freedmen, recent Black and White arrivals from the North ("carpetbaggers"), and White Southerners who supported Reconstruction ("scalawags") cooperated to form Republican biracial state governments. They introduced various Reconstruction programs including funding public schools, establishing charitable institutions, raising taxes, and funding public improvements such as improved railroad transportation and shipping. In the 1860s and 1870s, the terms "Radical" and "conservative" had distinct meanings. "Conservative" was the name of a faction, often led by the planter class. Conservative opponents called the Republican regimes corrupt and instigated violence toward freedmen and Whites who supported Reconstruction. Most of the violence was carried out by members of the Ku Klux Klan (KKK), a secretive terrorist organization closely allied with the Southern Democratic Party. Klan members attacked and intimidated black people seeking to exercise their new civil rights, as well as Republican politicians in the South favoring those civil rights. One such politician murdered by the Klan on the eve of the 1868 presidential election was Republican Congressman James M. Hinds of Arkansas. Widespread violence in the South led to federal intervention by President Ulysses S. Grant in 1871, which suppressed the Klan. Nevertheless, White Democrats, calling themselves "Redeemers", regained control of the South state by state, sometimes using fraud and violence to control state elections. A deep national economic depression following the Panic of 1873 led to major Democratic gains in the North, the collapse of many railroad schemes in the South, and a growing sense of frustration in the North. The end of Reconstruction was a staggered process, and the period of Republican control ended at different times in different states. With the Compromise of 1877, military intervention in Southern politics ceased and Republican control collapsed in the last three state governments in the South. This was followed by a period which White Southerners labeled "Redemption", during which White-dominated state legislatures enacted Jim Crow laws, disenfranchising most black people and many poor Whites through a combination of constitutional amendments and election laws beginning in 1890. The White Southern Democrats' memory of Reconstruction played a major role in imposing the system of White supremacy and second-class citizenship for black people using laws known as Jim Crow laws. Three visions of Civil War memory appeared during Reconstruction: - The reconciliationist vision was rooted in coping with the death and devastation the war had brought; - the white supremacist vision demanded strict segregation of the races and the preservation of political and cultural domination of Blacks by Whites; any right to vote by Blacks was not to be countenanced; intimidation and violence were acceptable means to enforce the vision; - the emancipationist vision sought full freedom, citizenship, male suffrage, and constitutional equality for African Americans. Reconstruction addressed how the 11 seceding rebel states in the South would regain what the Constitution calls a "republican form of government" and be re-seated in Congress, the civil status of the former leaders of the Confederacy, and the constitutional and legal status of freedmen, especially their civil rights and whether they should be given the right to vote. Intense controversy erupted throughout the South over these issues.[i] Passage of the 13th, 14th, and 15th Amendments is the constitutional legacy of Reconstruction. These Reconstruction Amendments established the rights that led to Supreme Court rulings in the mid-20th century that struck down school segregation. A "Second Reconstruction", sparked by the civil rights movement, led to civil-rights laws in 1964 and 1965 that ended legal segregation and re-opened the polls to Blacks. The laws and constitutional amendments that laid the foundation for the most radical phase of Reconstruction were adopted from 1866 to 1871. By the 1870s, Reconstruction had officially provided freedmen with equal rights under the Constitution, and Blacks were voting and taking political office. Republican legislatures, coalitions of Whites and Blacks, established the first public school systems and numerous charitable institutions in the South. White paramilitary organizations, especially the Ku Klux Klan (KKK) as well as the White League and Red Shirts, formed with the political aim of driving out the Republicans. They also disrupted political organizing and terrorized Blacks to bar them from the polls. President Grant used federal power to effectively shut down the KKK in the early 1870s, though the other, smaller groups continued to operate. From 1873 to 1877, conservative Whites (calling themselves "Redeemers") regained power in the Southern states. They constituted the Bourbon wing of the national Democratic Party. In the 1860s and 1870s, leaders who had been Whigs were committed to economic modernization, built around railroads, factories, banks, and cities. Most of the "Radical" Republicans in the North were men who believed in integrating African Americans by providing them civil rights as citizens, along with free enterprise; most were also modernizers and former Whigs. The "Liberal Republicans" of 1872 shared the same outlook except that they were especially opposed to the corruption they saw around President Grant, and believed that the goals of the Civil War had been achieved, and that the federal military intervention could now end. Material devastation of the South in 1865 Reconstruction played out against an economy in ruins. The Confederacy in 1861 had 297 towns and cities, with a total population of 835,000 people; of these, 162, with 681,000 people, were at some point occupied by Union forces. 11 were destroyed or severely damaged by war action, including Atlanta (with an 1860 population of 9,600), Charleston, Columbia, and Richmond (with prewar populations of 40,500, 8,100, and 37,900, respectively); the 11 contained 115,900 people according to the 1860 Census, or 14% of the urban South. The number of people who lived in the destroyed towns represented just over 1% of the Confederacy's combined urban and rural populations. The rate of damage in smaller towns was much lower—only 45 courthouses were burned out of a total of 830. Farms were in disrepair, and the prewar stock of horses, mules, and cattle was much depleted; 40% of the South's livestock had been killed. The South's farms were not highly mechanized, but the value of farm implements and machinery according to the 1860 Census was $81 million and was reduced by 40% by 1870. The transportation infrastructure lay in ruins, with little railroad or riverboat service available to move crops and animals to market. Railroad mileage was located mostly in rural areas; over two-thirds of the South's rails, bridges, rail yards, repair shops, and rolling stock were in areas reached by Union armies, which systematically destroyed what they could. Even in untouched areas, the lack of maintenance and repair, the absence of new equipment, the heavy over-use, and the deliberate relocation of equipment by the Confederates from remote areas to the war zone ensured the system would be ruined at war's end. Restoring the infrastructure—especially the railroad system—became a high priority for Reconstruction state governments. The enormous cost of the Confederate war effort took a high toll on the South's economic infrastructure. The direct costs to the Confederacy in human capital, government expenditures, and physical destruction from the war totaled $3.3 billion. By early 1865, high inflation made the Confederate dollar worth little. When the war ended, Confederate currency and bank deposits were worth zero, making the banking system a near-total loss. People had to resort to bartering services for goods, or else try to obtain scarce Union dollars. With the emancipation of the Southern slaves, the entire economy of the South had to be rebuilt. Having lost their enormous investment in slaves, White plantation owners had minimal capital to pay freedmen workers to bring in crops. As a result, a system of sharecropping was developed, in which landowners broke up large plantations and rented small lots to the freedmen and their families. The main feature of the Southern economy changed from an elite minority of landed gentry slaveholders into a tenant farming agriculture system. The end of the Civil War was accompanied by a large migration of new freed people to the cities. In the cities, Black people were relegated to the lowest paying jobs such as unskilled and service labor. Men worked as rail workers, rolling and lumber mills workers, and hotel workers. The large population of slave artisans during the antebellum period had not been translated into a large number of freedmen artisans during Reconstruction. Black women were largely confined to domestic work employed as cooks, maids, and child nurses. Others worked in hotels. A large number became laundresses. The dislocations had a severe negative impact on the Black population, with a large amount of sickness and death. Over a quarter of Southern White men of military age—the backbone of the South's White workforce—died during the war, leaving countless families destitute. Per capita income for White Southerners declined from $125 in 1857 to a low of $80 in 1879. By the end of the 19th century and well into the 20th century, the South was locked into a system of poverty. How much of this failure was caused by the war and by previous reliance on agriculture remains the subject of debate among economists and historians. Restoring the South to the Union During the Civil War, the Radical Republican leaders argued that slavery and the Slave Power had to be permanently destroyed. Moderates said this could be easily accomplished as soon as the Confederate States Army surrendered and the Southern states repealed secession and accepted the Thirteenth Amendment–most of which happened by December 1865. President Lincoln was the leader of the moderate Republicans and wanted to speed up Reconstruction and reunite the nation painlessly and quickly. Lincoln formally began Reconstruction on December 8, 1863, with his ten percent plan, which went into operation in several states but which Radical Republicans opposed. 1864: Wade–Davis Bill Lincoln broke with the Radicals in 1864. The Wade–Davis Bill of 1864 passed in Congress by the Radicals was designed to permanently disfranchise the Confederate element in the South. The bill required voters to take the "ironclad oath" swearing that they had never supported the Confederacy or been one of its soldiers. Lincoln blocked it. Pursuing a policy of "malice toward none" announced in his second inaugural address, Lincoln asked voters only to support the Union in the future, regardless of the past. Lincoln pocket vetoed the Wade–Davis Bill, which was much more strict than the ten percent plan. Following Lincoln's veto, the Radicals lost support but regained strength after Lincoln's assassination in April 1865. Upon Lincoln's assassination in April 1865, vice president Andrew Johnson became president. Radicals considered Johnson to be an ally, but upon becoming president, he rejected the Radical program of Reconstruction. He was on good terms with ex-Confederates in the South and ex-Copperheads in the North. He appointed his own governors and tried to close the Reconstruction process by the end of 1865. Thaddeus Stevens vehemently opposed Johnson's plans for an abrupt end to Reconstruction, insisting that Reconstruction must "revolutionize Southern institutions, habits, and manners .... The foundations of their institutions ... must be broken up and relaid, or all our blood and treasure have been spent in vain." Johnson broke decisively with the Republicans in Congress when he vetoed the Civil Rights Act in early 1866. While Democrats celebrated, the Republicans rallied, passed the bill again, and overrode Johnson's repeat veto. Full-scale political warfare now existed between Johnson (now allied with the Democrats) and the Radical Republicans. Since the war had ended, Congress rejected Johnson's argument that he had the war power to decide what to do. Congress decided it had the primary authority to decide how Reconstruction should proceed, because the Constitution stated the United States had to guarantee each state a republican form of government. The Radicals insisted that meant Congress decided how Reconstruction should be achieved. The issues were multiple: Who should decide, Congress or the president? How should republicanism operate in the South? What was the status of the former Confederate states? What was the citizenship status of the leaders of the Confederacy? What was the citizenship and suffrage status of freedmen? By 1866, the faction of Radical Republicans led by Congressman Thaddeus Stevens and Senator Charles Sumner was convinced that Johnson's Southern appointees were disloyal to the Union, hostile to loyal Unionists, and enemies of the Freedmen. Radicals used as evidence outbreaks of mob violence against Black people, such as the Memphis riots of 1866 and the New Orleans massacre of 1866. Radical Republicans demanded a prompt and strong federal response to protect freedmen and curb Southern racism. Stevens and his followers viewed secession as having left the states in a status like new territories. Sumner argued that secession had destroyed statehood but the Constitution still extended its authority and its protection over individuals, as in existing U.S. territories. The Republicans sought to prevent Johnson's Southern politicians from "restoring the historical subordination of Negroes". Since slavery was abolished, the Three-fifths Compromise no longer applied to counting the population of Blacks. After the 1870 Census, the South would gain numerous additional representatives in Congress, based on the full population of freedmen. One Illinois Republican expressed a common fear that if the South were allowed to simply restore its previous established powers, that the "reward of treason will be an increased representation". The election of 1866 decisively changed the balance of power, giving the Republicans two-thirds majorities in both houses of Congress, and enough votes to overcome Johnson's vetoes. They moved to impeach Johnson because of his constant attempts to thwart Radical Reconstruction measures, by using the Tenure of Office Act. Johnson was acquitted by one vote, but he lost the influence to shape Reconstruction policy. The Republican Congress established military districts in the South and used Army personnel to administer the region until new governments loyal to the Union—that accepted the Fourteenth Amendment and the right of freedmen to vote—could be established. Congress temporarily suspended the ability to vote of approximately 10,000 to 15,000 former Confederate officials and senior officers, while constitutional amendments gave full citizenship to all African Americans, and suffrage to the adult men. With the power to vote, freedmen began participating in politics. While many enslaved people were illiterate, educated Blacks (including fugitive slaves) moved down from the North to aid them, and natural leaders also stepped forward. They elected White and Black men to represent them in constitutional conventions. A Republican coalition of freedmen, Southerners supportive of the Union (derisively called "scalawags" by White Democrats), and Northerners who had migrated to the South (derisively called "carpetbaggers")—some of whom were returning natives, but were mostly Union veterans—organized to create constitutional conventions. They created new state constitutions to set new directions for Southern states. Congress had to consider how to restore to full status and representation within the Union those Southern states that had declared their independence from the United States and had withdrawn their representation. Suffrage for former Confederates was one of two main concerns. A decision needed to be made whether to allow just some or all former Confederates to vote (and to hold office). The moderates in Congress wanted virtually all of them to vote, but the Radicals resisted. They repeatedly imposed the ironclad oath, which would effectively have allowed no former Confederates to vote. Historian Harold Hyman says that in 1866 congressmen "described the oath as the last bulwark against the return of ex-rebels to power, the barrier behind which Southern Unionists and Negroes protected themselves". Radical Republican leader Thaddeus Stevens proposed, unsuccessfully, that all former Confederates lose the right to vote for five years. The compromise that was reached disenfranchised many Confederate civil and military leaders. No one knows how many temporarily lost the vote, but one estimate placed the number as high as 10,000 to 15,000. However, Radical politicians took up the task at the state level. In Tennessee alone, over 80,000 former Confederates were disenfranchised. Second, and closely related, was the issue of whether the 4 million freedmen were to be received as citizens: Would they be able to vote? If they were to be fully counted as citizens, some sort of representation for apportionment of seats in Congress had to be determined. Before the war, the population of slaves had been counted as three-fifths of a corresponding number of free Whites. By having 4 million freedmen counted as full citizens, the South would gain additional seats in Congress. If Blacks were denied the vote and the right to hold office, then only Whites would represent them. Many conservatives, including most White Southerners, Northern Democrats, and some Northern Republicans, opposed Black voting. Some Northern states that had referendums on the subject limited the ability of their own small populations of Blacks to vote. Lincoln had supported a middle position: to allow some Black men to vote, especially U.S. Army veterans. Johnson also believed that such service should be rewarded with citizenship. Lincoln proposed giving the vote to "the very intelligent, and especially those who have fought gallantly in our ranks". In 1864, Governor Johnson said: "The better class of them will go to work and sustain themselves, and that class ought to be allowed to vote, on the ground that a loyal Negro is more worthy than a disloyal white man." As president in 1865, Johnson wrote to the man he appointed as governor of Mississippi, recommending: "If you could extend the elective franchise to all persons of color who can read the Constitution in English and write their names, and to all persons of color who own real estate valued at least two hundred and fifty dollars, and pay taxes thereon, you would completely disarm the adversary [Radicals in Congress], and set an example the other states will follow." Charles Sumner and Thaddeus Stevens, leaders of the Radical Republicans, were initially hesitant to enfranchise the largely illiterate freedmen. Sumner preferred at first impartial requirements that would have imposed literacy restrictions on Blacks and Whites. He believed that he would not succeed in passing legislation to disenfranchise illiterate Whites who already had the vote. In the South, many poor Whites were illiterate as there was almost no public education before the war. In 1880, for example, the White illiteracy rate was about 25% in Tennessee, Kentucky, Alabama, South Carolina, and Georgia, and as high as 33% in North Carolina. This compares with the 9% national rate, and a Black rate of illiteracy that was over 70% in the South. By 1900, however, with emphasis within the Black community on education, the majority of Blacks had achieved literacy. Sumner soon concluded that "there was no substantial protection for the freedman except in the franchise". This was necessary, he stated, "(1) For his own protection; (2) For the protection of the white Unionist; and (3) For the peace of the country. We put the musket in his hands because it was necessary; for the same reason we must give him the franchise." The support for voting rights was a compromise between moderate and Radical Republicans. The Republicans believed that the best way for men to get political experience was to be able to vote and to participate in the political system. They passed laws allowing all male freedmen to vote. In 1867, Black men voted for the first time. Over the course of Reconstruction, more than 1,500 African Americans held public office in the South; some of them were men who had escaped to the North and gained educations, and returned to the South. They did not hold office in numbers representative of their proportion in the population, but often elected Whites to represent them. The question of women's suffrage was also debated but was rejected. Women eventually gained the right to vote with the Nineteenth Amendment to the United States Constitution in 1920. From 1890 to 1908, Southern states passed new state constitutions and laws that disenfranchised most Blacks and tens of thousands of poor Whites with new voter registration and electoral rules. When establishing new requirements such as subjectively administered literacy tests, in some states, they used "grandfather clauses" to enable illiterate Whites to vote. Southern Treaty Commission The Five Civilized Tribes that had been relocated to Indian Territory (now part of Oklahoma) held Black slaves and signed treaties supporting the Confederacy. During the war, a war among pro-Union and anti-Union Native Americans had raged. Congress passed a statute that gave the president the authority to suspend the appropriations of any tribe if the tribe is "in a state of actual hostility to the government of the United States ... and, by proclamation, to declare all treaties with such tribe to be abrogated by such tribe". As a component of Reconstruction, the Interior Department ordered a meeting of representatives from all Indian tribes who had affiliated with the Confederacy. The council, the Southern Treaty Commission, was first held in Fort Smith, Arkansas in September 1865, and was attended by hundreds of Native Americans representing dozens of tribes. Over the next several years the commission negotiated treaties with tribes that resulted in additional re-locations to Indian Territory and the de facto creation (initially by treaty) of an unorganized Oklahoma Territory. Lincoln's presidential Reconstruction President Lincoln signed two Confiscation Acts into law, the first on August 6, 1861, and the second on July 17, 1862, safeguarding fugitive slaves who crossed from the Confederacy across Union lines and giving them indirect emancipation if their masters continued insurrection against the United States. The laws allowed the confiscation of lands for colonization from those who aided and supported the rebellion. However, these laws had limited effect as they were poorly funded by Congress and poorly enforced by Attorney General Edward Bates. In August 1861, Maj. Gen. John C. Frémont, Union commander of the Western Department, declared martial law in Missouri, confiscated Confederate property, and emancipated their slaves. President Lincoln immediately ordered Frémont to rescind his emancipation declaration, stating: "I think there is great danger that ... the liberating slaves of traitorous owners, will alarm our Southern Union friends, and turn them against us—perhaps ruin our fair prospect for Kentucky." After Frémont refused to rescind the emancipation order, President Lincoln terminated him from active duty on November 2, 1861. Lincoln was concerned that the border states would secede from the Union if slaves were given their freedom. On May 26, 1862, Union Maj. Gen. David Hunter emancipated slaves in South Carolina, Georgia, and Florida, declaring all "persons ... heretofore held as slaves ... forever free". Lincoln, embarrassed by the order, rescinded Hunter's declaration and canceled the emancipation. On April 16, 1862, Lincoln signed a bill into law outlawing slavery in Washington, D.C., and freeing the estimated 3,500 slaves in the city. On June 19, 1862, he signed legislation outlawing slavery in all U.S. territories. On July 17, 1862, under the authority of the Confiscation Acts and an amended Force Bill of 1795, he authorized the recruitment of freed slaves into the U.S. Army and seizure of any Confederate property for military purposes. Gradual emancipation and compensation In an effort to keep border states in the Union, President Lincoln, as early as 1861, designed gradual compensated emancipation programs paid for by government bonds. Lincoln desired Delaware, Maryland, Kentucky, and Missouri to "adopt a system of gradual emancipation which should work the extinction of slavery in twenty years". On March 26, 1862, Lincoln met with Senator Charles Sumner and recommended that a special joint session of Congress be convened to discuss giving financial aid to any border states who initiated a gradual emancipation plan. In April 1862, the joint session of Congress met; however, the border states were not interested and did not make any response to Lincoln or any congressional emancipation proposal. Lincoln advocated compensated emancipation during the 1865 River Queen steamer conference. In August 1862, President Lincoln met with African-American leaders and urged them to colonize some place in Central America. Lincoln planned to free the Southern slaves in the Emancipation Proclamation and he was concerned that freedmen would not be well treated in the United States by Whites in both the North and South. Although Lincoln gave assurances that the United States government would support and protect any colonies that were established for former slaves, the leaders declined the offer of colonization. Many free Blacks had been opposed to colonization plans in the past because they wanted to remain in the United States. President Lincoln persisted in his colonization plan in the belief that emancipation and colonization were both part of the same program. By April 1863, Lincoln was successful in sending Black colonists to Haiti as well as 453 to Chiriqui in Central America; however, none of the colonies were able to remain self-sufficient. Frederick Douglass, a prominent 19th-century American civil rights activist, criticized Lincoln by stating that he was "showing all his inconsistencies, his pride of race and blood, his contempt for Negroes and his canting hypocrisy". African Americans, according to Douglass, wanted citizenship and civil rights rather than colonies. Historians are unsure if Lincoln gave up on the idea of African American colonization at the end of 1863 or if he actually planned to continue this policy up until 1865. Installation of military governors Starting in March 1862, in an effort to forestall Reconstruction by the Radicals in Congress, President Lincoln installed military governors in certain rebellious states under Union military control. Although the states would not be recognized by the Radicals until an undetermined time, installation of military governors kept the administration of Reconstruction under presidential control, rather than that of the increasingly unsympathetic Radical Congress. On March 3, 1862, Lincoln installed a loyalist Democrat, Senator Andrew Johnson, as military governor with the rank of brigadier general in his home state of Tennessee. In May 1862, Lincoln appointed Edward Stanly military governor of the coastal region of North Carolina with the rank of brigadier general. Stanly resigned almost a year later when he angered Lincoln by closing two schools for Black children in New Bern. After Lincoln installed Brigadier General George Foster Shepley as military governor of Louisiana in May 1862, Shepley sent two anti-slavery representatives, Benjamin Flanders and Michael Hahn, elected in December 1862, to the House, which capitulated and voted to seat them. In July 1862, Lincoln installed Colonel John S. Phelps as military governor of Arkansas, though he resigned soon after due to poor health. In July 1862, President Lincoln became convinced that "a military necessity" was needed to strike at slavery in order to win the Civil War for the Union. The Confiscation Acts were only having a minimal effect to end slavery. On July 22, he wrote a first draft of the Emancipation Proclamation that freed the slaves in states in rebellion. After he showed his Cabinet the document, slight alterations were made in the wording. Lincoln decided that the defeat of the Confederate invasion of the North at Sharpsburg was enough of a battlefield victory to enable him to release the preliminary Emancipation Proclamation that gave the rebels 100 days to return to the Union or the actual proclamation would be issued. On January 1, 1863, the actual Emancipation Proclamation was issued, specifically naming 10 states in which slaves would be "forever free". The proclamation did not name the states of Tennessee, Kentucky, Missouri, Maryland, and Delaware, and specifically excluded numerous counties in some other states. Eventually, as the U.S. Army advanced into the Confederacy, millions of slaves were set free. Many of these freedmen joined the U.S. Army and fought in battles against the Confederate forces. Yet hundreds of thousands of freed slaves died during emancipation from illness that devastated army regiments. Freed slaves suffered from smallpox, yellow fever, and malnutrition. Louisiana 10% electorate plan President Abraham Lincoln was concerned to effect a speedy restoration of the Confederate states to the Union after the Civil War. In 1863, President Lincoln proposed a moderate plan for the Reconstruction of the captured Confederate state of Louisiana. The plan granted amnesty to rebels who took an oath of loyalty to the Union. Black freedmen workers were tied to labor on plantations for one year at a pay rate of $10 a month. Only 10% of the state's electorate had to take the loyalty oath in order for the state to be readmitted into the U.S. Congress. The state was required to abolish slavery in its new state constitution. Identical Reconstruction plans would be adopted in Arkansas and Tennessee. By December 1864, the Lincoln plan of Reconstruction had been enacted in Louisiana and the legislature sent two senators and five representatives to take their seats in Washington. However, Congress refused to count any of the votes from Louisiana, Arkansas, and Tennessee, in essence rejecting Lincoln's moderate Reconstruction plan. Congress, at this time controlled by the Radicals, proposed the Wade–Davis Bill that required a majority of the state electorates to take the oath of loyalty to be admitted to Congress. Lincoln pocket-vetoed the bill and the rift widened between the moderates, who wanted to save the Union and win the war, and the Radicals, who wanted to effect a more complete change within Southern society. Frederick Douglass denounced Lincoln's 10% electorate plan as undemocratic since state admission and loyalty only depended on a minority vote. Legalization of slave marriages Before 1864, slave marriages had not been recognized legally; emancipation did not affect them. When freed, many made official marriages. Before emancipation, slaves could not enter into contracts, including the marriage contract. Not all free people formalized their unions. Some continued to have common-law marriages or community-recognized relationships. The acknowledgement of marriage by the state increased the state's recognition of freed people as legal actors and eventually helped make the case for parental rights for freed people against the practice of apprenticeship of Black children. These children were legally taken away from their families under the guise of "providing them with guardianship and 'good' homes until they reached the age of consent at twenty-one" under acts such as the Georgia 1866 Apprentice Act. Such children were generally used as sources of unpaid labor. On March 3, 1865, the Freedmen's Bureau Bill became law, sponsored by the Republicans to aid freedmen and White refugees. A federal bureau was created to provide food, clothing, fuel, and advice on negotiating labor contracts. It attempted to oversee new relations between freedmen and their former masters in a free labor market. The act, without deference to a person's color, authorized the bureau to lease confiscated land for a period of three years and to sell it in portions of up to 40 acres (16 ha) per buyer. The bureau was to expire one year after the termination of the war. Lincoln was assassinated before he could appoint a commissioner of the bureau. A popular myth was that the act offered 40 acres and a mule, or that slaves had been promised this. With the help of the bureau, the recently freed slaves began voting, forming political parties, and assuming the control of labor in many areas. The bureau helped to start a change of power in the South that drew national attention from the Republicans in the North to the conservative Democrats in the South. This is especially evident in the election between Grant and Seymour (Johnson did not get the Democratic nomination), where almost 700,000 Black voters voted and swayed the election 300,000 votes in Grant's favor. Even with the benefits that it gave to the freedmen, the Freedmen's Bureau was unable to operate effectively in certain areas. Terrorizing freedmen for trying to vote, hold a political office, or own land, the Ku Klux Klan was the nemesis of the Freedmen's Bureau. Bans color discrimination Other legislation was signed that broadened equality and rights for African Americans. Lincoln outlawed discrimination on account of color, in carrying U.S. mail, in riding on public street cars in Washington, D.C., and in pay for soldiers. February 1865 peace conference Lincoln and Secretary of State William H. Seward met with three Southern representatives to discuss the peaceful Reconstruction of the Union and the Confederacy on February 3, 1865, in Hampton Roads, Virginia. The Southern delegation included Confederate Vice President Alexander H. Stephens, John Archibald Campbell, and Robert M. T. Hunter. The Southerners proposed the Union recognition of the Confederacy, a joint Union–Confederate attack on Mexico to oust Emperor Maximilian I, and an alternative subordinate status of servitude for Blacks rather than slavery. Lincoln flatly rejected recognition of the Confederacy, and said that the slaves covered by his Emancipation Proclamation would not be re-enslaved. He said that the Union states were about to pass the Thirteenth Amendment, outlawing slavery. Lincoln urged the governor of Georgia to remove Confederate troops and "ratify this constitutional amendment prospectively, so as to take effect—say in five years.... Slavery is doomed." Lincoln also urged compensated emancipation for the slaves as he thought the North should be willing to share the costs of freedom. Although the meeting was cordial, the parties did not settle on agreements. Historical legacy debated Lincoln continued to advocate his Louisiana Plan as a model for all states up until his assassination on April 15, 1865. The plan successfully started the Reconstruction process of ratifying the Thirteenth Amendment in all states. Lincoln is typically portrayed as taking the moderate position and fighting the Radical positions. There is considerable debate on how well Lincoln, had he lived, would have handled Congress during the Reconstruction process that took place after the Civil War ended. One historical camp argues that Lincoln's flexibility, pragmatism, and superior political skills with Congress would have solved Reconstruction with far less difficulty. The other camp believes that the Radicals would have attempted to impeach Lincoln, just as they did to his successor, Andrew Johnson, in 1868. Johnson's presidential Reconstruction Northern anger over the assassination of Lincoln and the immense human cost of the war led to demands for punitive policies. Vice President Andrew Johnson had taken a hard line and spoke of hanging Confederates, but when he succeeded Lincoln as president, Johnson took a much softer position, pardoning many Confederate leaders and other former Confederates.[full citation needed] Former Confederate President Jefferson Davis was held in prison for two years, but other Confederate leaders were not. There were no trials on charges of treason. Only one person—Captain Henry Wirz, the commandant of the prison camp in Andersonville, Georgia—was executed for war crimes. Andrew Johnson's conservative view of Reconstruction did not include the involvement of Blacks in government, and he refused to heed Northern concerns when Southern state legislatures implemented Black Codes that set the status of the freedmen much lower than that of citizens. Smith argues that "Johnson attempted to carry forward what he considered to be Lincoln's plans for Reconstruction." McKitrick says that in 1865 Johnson had strong support in the Republican Party, saying: "It was naturally from the great moderate sector of Unionist opinion in the North that Johnson could draw his greatest comfort." Billington says: "One faction, the moderate Republicans under the leadership of Presidents Abraham Lincoln and Andrew Johnson, favored a mild policy toward the South." Lincoln biographers Randall and Current argued that: It is likely that had he lived, Lincoln would have followed a policy similar to Johnson's, that he would have clashed with congressional Radicals, that he would have produced a better result for the freedmen than occurred, and that his political skills would have helped him avoid Johnson's mistakes. Historians generally agree that President Johnson was an inept politician who lost all his advantages by unskilled maneuvering. He broke with Congress in early 1866 and then became defiant and tried to block enforcement of Reconstruction laws passed by the U.S. Congress. He was in constant conflict constitutionally with the Radicals in Congress over the status of freedmen and whites in the defeated South. Although resigned to the abolition of slavery, many former Confederates were unwilling to accept both social changes and political domination by former slaves. In the words of Benjamin Franklin Perry, President Johnson's choice as the provisional governor of South Carolina: "First, the Negro is to be invested with all political power, and then the antagonism of interest between capital and labor is to work out the result." However, the fears of the mostly conservative planter elite and other leading white citizens were partly assuaged by the actions of President Johnson, who ensured that a wholesale land redistribution from the planters to the freedmen did not occur. President Johnson ordered that confiscated or abandoned lands administered by the Freedmen's Bureau would not be redistributed to the freedmen but would be returned to pardoned owners. Land was returned that would have been forfeited under the Confiscation Acts passed by Congress in 1861 and 1862. Freedmen and the enactment of Black Codes Southern state governments quickly enacted the restrictive "Black Codes". However, they were abolished in 1866 and seldom had effect, because the Freedmen's Bureau (not the local courts) handled the legal affairs of freedmen. The Black Codes indicated the plans of the Southern whites for the former slaves. The freedmen would have more rights than did free Blacks before the war, but they would still have only second-class civil rights, no voting rights, and no citizenship. They could not own firearms, serve on a jury in a lawsuit involving whites, or move about without employment. The Black Codes outraged Northern opinion. They were overthrown by the Civil Rights Act of 1866 that gave the freedmen more legal equality (although still without the right to vote). The freedmen, with the strong backing of the Freedmen's Bureau, rejected gang-labor work patterns that had been used in slavery. Instead of gang labor, freed people preferred family-based labor groups. They forced planters to bargain for their labor. Such bargaining soon led to the establishment of the system of sharecropping, which gave the freedmen greater economic independence and social autonomy than gang labor. However, because they lacked capital and the planters continued to own the means of production (tools, draft animals, and land), the freedmen were forced into producing cash crops (mainly cotton) for the land-owners and merchants, and they entered into a crop-lien system. Widespread poverty, disruption to an agricultural economy too dependent on cotton, and the falling price of cotton, led within decades to the routine indebtedness of the majority of the freedmen, and the poverty of many planters. Northern officials gave varying reports on conditions for the freedmen in the South. One harsh assessment came from Carl Schurz, who reported on the situation in the states along the Gulf Coast. His report documented dozens of extra-judicial killings and claimed that hundreds or thousands more African Americans were killed: The number of murders and assaults perpetrated upon Negroes is very great; we can form only an approximative estimate of what is going on in those parts of the South which are not closely garrisoned, and from which no regular reports are received, by what occurs under the very eyes of our military authorities. As to my personal experience, I will only mention that during my two days sojourn at Atlanta, one Negro was stabbed with fatal effect on the street, and three were poisoned, one of whom died. While I was at Montgomery, one Negro was cut across the throat evidently with intent to kill, and another was shot, but both escaped with their lives. Several papers attached to this report give an account of the number of capital cases that occurred at certain places during a certain period of time. It is a sad fact that the perpetration of those acts is not confined to that class of people which might be called the rabble. The report included sworn testimony from soldiers and officials of the Freedmen's Bureau. In Selma, Alabama, Major J. P. Houston noted that whites who killed 12 African Americans in his district never came to trial. Many more killings never became official cases. Captain Poillon described white patrols in southwestern Alabama: who board some of the boats; after the boats leave they hang, shoot, or drown the victims they may find on them, and all those found on the roads or coming down the rivers are almost invariably murdered. The bewildered and terrified freedmen know not what to do—to leave is death; to remain is to suffer the increased burden imposed upon them by the cruel taskmaster, whose only interest is their labor, wrung from them by every device an inhuman ingenuity can devise; hence the lash and murder is resorted to intimidate those whom fear of an awful death alone cause to remain, while patrols, Negro dogs and spies, disguised as Yankees, keep constant guard over these unfortunate people. Much of the violence that was perpetrated against African Americans was shaped by gender prejudices regarding African Americans. Black women were in a particularly vulnerable situation. To convict a white man of sexually assaulting Black women in this period was exceedingly difficult. The South's judicial system had been wholly refigured to make one of its primary purposes the coercion of African Americans to comply with the social customs and labor demands of whites.[further explanation needed]Trials were discouraged and attorneys for Black misdemeanor defendants were difficult to find. The goal of county courts was a fast, uncomplicated trial with a resulting conviction. Most Blacks were unable to pay their fines or bail, and "the most common penalty was nine months to a year in a slave mine or lumber camp". The South's judicial system was rigged to generate fees and claim bounties, not to ensure public protection. Black women were socially perceived as sexually avaricious and since they were portrayed as having little virtue, society held that they could not be raped. One report indicates two freed women, Frances Thompson and Lucy Smith, describe their violent sexual assault during the Memphis Riots of 1866. However, Black women were vulnerable even in times of relative normalcy. Sexual assaults on African-American women were so pervasive, particularly on the part of their white employers, that Black men sought to reduce the contact between white males and Black females by having the women in their family avoid doing work that was closely overseen by whites. Black men were construed as being extremely sexually aggressive and their supposed or rumored threats to white women were often used as a pretext for lynching and castrations. During fall 1865, out of response to the Black Codes and worrisome signs of Southern recalcitrance, the Radical Republicans blocked the readmission of the former rebellious states to the Congress. Johnson, however, was content with allowing former Confederate states into the Union as long as their state governments adopted the Thirteenth Amendment abolishing slavery. By December 6, 1865, the amendment was ratified and Johnson considered Reconstruction over. Johnson was following the moderate Lincoln presidential Reconstruction policy to get the states readmitted as soon as possible. Congress, however, controlled by the Radicals, had other plans. The Radicals were led by Charles Sumner in the Senate and Thaddeus Stevens in the House of Representatives. Congress, on December 4, 1865, rejected Johnson's moderate presidential Reconstruction, and organized the Joint Committee on Reconstruction, a 15-member panel to devise Reconstruction requirements for the Southern states to be restored to the Union. In January 1866, Congress renewed the Freedmen's Bureau; however, Johnson vetoed the Freedmen's Bureau Bill in February 1866. Although Johnson had sympathy for the plight of the freedmen, he was against federal assistance. An attempt to override the veto failed on February 20, 1866. This veto shocked the congressional Radicals. In response, both the Senate and House passed a joint resolution not to allow any senator or representative seat admittance until Congress decided when Reconstruction was finished. laws are to be enacted and enforced depriving persons of African descent of privileges which are essential to freemen.... A law that does not allow a colored person to go from one county to another, and one that does not allow him to hold property, to teach, to preach, are certainly laws in violation of the rights of a freeman... The purpose of this bill is to destroy all these discriminations. The key to the bill was the opening section:[This quote needs a citation] All persons born in the United States ... are hereby declared to be citizens of the United States; and such citizens of every race and color, without regard to any previous condition of slavery ... shall have the same right in every State ... to make and enforce contracts, to sue, be parties, and give evidence, to inherit, purchase, lease, sell, hold, and convey real and personal property, and to full and equal benefit of all laws and proceedings for the security of person and property, as is enjoyed by white citizens, and shall be subject to like punishment, pains, and penalties and to none other, any law, statute, ordinance, regulation, or custom to the Contrary notwithstanding. The bill did not give freedmen the right to vote. Congress quickly passed the Civil Rights Bill; the Senate on February 2 voted 33–12; the House on March 13 voted 111–38. Although strongly urged by moderates in Congress to sign the Civil Rights bill, Johnson broke decisively with them by vetoing it on March 27, 1866. His veto message objected to the measure because it conferred citizenship on the freedmen at a time when 11 out of 36 states were unrepresented and attempted to fix by federal law "a perfect equality of the white and black races in every state of the Union". Johnson said it was an invasion by federal authority of the rights of the states; it had no warrant in the Constitution and was contrary to all precedents. It was a "stride toward centralization and the concentration of all legislative power in the national government". The Democratic Party, proclaiming itself the party of white men, North and South, supported Johnson. However, the Republicans in Congress overrode his veto (the Senate by the close vote of 33–15, and the House by 122–41) and the civil rights bill became law. Congress also passed a watered-down Freedmen's Bureau bill; Johnson quickly vetoed as he had done to the previous bill. Once again, however, Congress had enough support and overrode Johnson's veto. The last moderate proposal was the Fourteenth Amendment, whose principal drafter was Representative John Bingham. It was designed to put the key provisions of the Civil Rights Act into the Constitution, but it went much further. It extended citizenship to everyone born in the United States (except Indians on reservations), penalized states that did not give the vote to freedmen, and most important, created new federal civil rights that could be protected by federal courts. It guaranteed the federal war debt would be paid (and promised the Confederate debt would never be paid). Johnson used his influence to block the amendment in the states since three-fourths of the states were required for ratification (the amendment was later ratified). The moderate effort to compromise with Johnson had failed, and a political fight broke out between the Republicans (both Radical and moderate) on one side, and on the other side, Johnson and his allies in the Democratic Party in the North, and the conservative groupings (which used different names) in each Southern state. Concerned that President Johnson viewed Congress as an "illegal body" and wanted to overthrow the government, Republicans in Congress took control of Reconstruction policies after the election of 1866. Johnson ignored the policy mandate, and he openly encouraged Southern states to deny ratification of the Fourteenth Amendment (except for Tennessee, all former Confederate states did refuse to ratify, as did the border states of Delaware, Maryland, and Kentucky). Radical Republicans in Congress, led by Stevens and Sumner, opened the way to suffrage for male freedmen. They were generally in control, although they had to compromise with the moderate Republicans (the Democrats in Congress had almost no power). Historians refer to this period as "Radical Reconstruction" or "congressional Reconstruction". The business spokesmen in the North generally opposed Radical proposals. Analysis of 34 major business newspapers showed that 12 discussed politics, and only one, Iron Age, supported radicalism. The other 11 opposed a "harsh" Reconstruction policy, favored the speedy return of the Southern states to congressional representation, opposed legislation designed to protect the freedmen, and deplored the impeachment of President Andrew Johnson. The South's White leaders, who held power in the immediate post-bellum era before the vote was granted to the freedmen, renounced secession and slavery, but not White supremacy. People who had previously held power were angered in 1867 when new elections were held. New Republican lawmakers were elected by a coalition of White Unionists, freedmen and Northerners who had settled in the South. Some leaders in the South tried to accommodate new conditions. Three constitutional amendments, known as the Reconstruction amendments, were adopted. The Thirteenth Amendment abolishing slavery was ratified in 1865. The Fourteenth Amendment was proposed in 1866 and ratified in 1868, guaranteeing United States citizenship to all persons born or naturalized in the United States and granting them federal civil rights. The Fifteenth Amendment, proposed in late February 1869, and passed in early February 1870, decreed that the right to vote could not be denied because of "race, color, or previous condition of servitude". Left unaffected was that states would still determine voter registration and electoral laws. The amendments were directed at ending slavery and providing full citizenship to freedmen. Northern congressmen believed that providing Black men with the right to vote would be the most rapid means of political education and training. Many Blacks took an active part in voting and political life, and rapidly continued to build churches and community organizations. Following Reconstruction, White Democrats and insurgent groups used force to regain power in the state legislatures, and pass laws that effectively disenfranchised most Blacks and many poor Whites in the South. From 1890 to 1910, Southern states passed new state constitutions that completed the disenfranchisement of Blacks. U.S. Supreme Court rulings on these provisions upheld many of these new Southern state constitutions and laws, and most Blacks were prevented from voting in the South until the 1960s. Full federal enforcement of the Fourteenth and Fifteenth Amendments did not reoccur until after passage of legislation in the mid-1960s as a result of the civil rights movement. For details, see: - Redemption (United States history) - Disenfranchisement after the Reconstruction Era - Jim Crow laws - United States v. Cruikshank (1875), related to the Colfax Massacre - Posse Comitatus Act (1878) - Civil Rights Cases (1883) - Civil rights movement (1896–1954) - Plessy v. Ferguson (1896) - Williams v. Mississippi (1898) - Giles v. Harris (1903) The Reconstruction Acts as originally passed, were initially called "An act to provide for the more efficient Government of the Rebel States" The legislation was enacted by the 39th Congress, on March 2, 1867. It was vetoed by President Johnson, and the veto then overridden by a two-thirds majority, in both the House and the Senate, the same day. Congress also clarified the scope of the federal writ of habeas corpus, to allow federal courts to vacate unlawful state court convictions or sentences, in 1867. With the Radicals in control, Congress passed the Reconstruction Acts on July 19, 1867. The first Reconstruction Act, authored by Oregon Sen. George Henry Williams, a Radical Republican, placed 10 of the former Confederate states—all but Tennessee—under military control, grouping them into five military districts: - First Military District: Virginia, under General John Schofield - Second Military District: North Carolina and South Carolina, under General Daniel Sickles - Third Military District: Georgia, Alabama, and Florida, under Generals John Pope and George Meade - Fourth Military District: Arkansas and Mississippi, under General Edward Ord - Fifth Military District: Texas and Louisiana, under Generals Philip Sheridan and Winfield Scott Hancock 20,000 U.S. troops were deployed to enforce the act. The five border states that had not joined the Confederacy were not subject to military Reconstruction. West Virginia, which had seceded from Virginia in 1863, and Tennessee, which had already been re-admitted in 1866, were not included in the military districts. Federal troops however were kept in West Virginia through 1868 in order to control civil unrest in several areas throughout the state. Federal troops were removed from Kentucky and Missouri in 1866. The 10 Southern state governments were re-constituted under the direct control of the United States Army. One major purpose was to recognize and protect the right of African Americans to vote. There was little to no combat, but rather a state of martial law in which the military closely supervised local government, supervised elections, and tried to protect office holders and freedmen from violence. Blacks were enrolled as voters; former Confederate leaders were excluded for a limited period. No one state was entirely representative. Randolph Campbell describes what happened in Texas: The first critical step ... was the registration of voters according to guidelines established by Congress and interpreted by Generals Sheridan and Charles Griffin. The Reconstruction Acts called for registering all adult males, white and black, except those who had ever sworn an oath to uphold the Constitution of the United States and then engaged in rebellion.... Sheridan interpreted these restrictions stringently, barring from registration not only all pre-1861 officials of state and local governments who had supported the Confederacy but also all city officeholders and even minor functionaries such as sextons of cemeteries. In May Griffin ... appointed a three-man board of registrars for each county, making his choices on the advice of known scalawags and local Freedmen's Bureau agents. In every county where practicable a freedman served as one of the three registrars.... Final registration amounted to approximately 59,633 whites and 49,479 blacks. It is impossible to say how many whites were rejected or refused to register (estimates vary from 7,500 to 12,000), but blacks, who constituted only about 30 percent of the state's population, were significantly over-represented at 45 percent of all voters. State constitutional conventions: 1867–1869 The 11 Southern states held constitutional conventions giving Black men the right to vote, where the factions divided into the Radical, conservative, and in-between delegates. The Radicals were a coalition: 40% were Southern White Republicans ("scalawags"); 25% were White carpetbaggers, and 34% were Black. Scalawags wanted to disenfranchise all of the traditional White leadership class, but moderate Republican leaders in the North warned against that, and Black delegates typically called for universal voting rights. The carpetbaggers inserted provisions designed to promote economic growth, especially financial aid to rebuild the ruined railroad system. The conventions set up systems of free public schools funded by tax dollars, but did not require them to be racially integrated. Until 1872, most former Confederate or prewar Southern office holders were disqualified from voting or holding office; all but 500 top Confederate leaders were pardoned by the Amnesty Act of 1872. "Proscription" was the policy of disqualifying as many ex-Confederates as possible. It appealed to the scalawag element. For example, in 1865 Tennessee had disenfranchised 80,000 ex-Confederates. However, proscription was soundly rejected by the Black element, which insisted on universal suffrage. The issue would come up repeatedly in several states, especially in Texas and Virginia. In Virginia, an effort was made to disqualify for public office every man who had served in the Confederate Army even as a private, and any civilian farmer who sold food to the Confederate States Army. Disenfranchising Southern Whites was also opposed by moderate Republicans in the North, who felt that ending proscription would bring the South closer to a republican form of government based on the consent of the governed, as called for by the Constitution and the Declaration of Independence. Strong measures that were called for in order to forestall a return to the defunct Confederacy increasingly seemed out of place, and the role of the United States Army and controlling politics in the state was troublesome. Historian Mark Summers states that increasingly "the disenfranchisers had to fall back on the contention that denial of the vote was meant as punishment, and a lifelong punishment at that ... Month by month, the un-republican character of the regime looked more glaring." Election of 1868 During the Civil War, many in the North believed that fighting for the Union was a noble cause–for the preservation of the Union and the end of slavery. After the war ended, with the North victorious, the fear among Radicals was that President Johnson too quickly assumed that slavery and Confederate nationalism were dead and that the Southern states could return. The Radicals sought out a candidate for president who represented their viewpoint. In May 1868, the Republicans unanimously chose Ulysses S. Grant as their presidential candidate, and Schuyler Colfax, as their vice-presidential candidate. Grant won favor with the Radicals after he allowed Edwin Stanton, a Radical, to be reinstated as secretary of war. As early as 1862, during the Civil War, Grant had appointed the Ohio military chaplain John Eaton to protect and gradually incorporate refugee slaves in west Tennessee and northern Mississippi into the Union war effort and pay them for their labor. It was the beginning of his vision for the Freedmen's Bureau. Grant opposed President Johnson by supporting the Reconstruction Acts passed by the Radicals. In northern cities Grant contended with a strong immigrant, and particularly in New York City an Irish, anti-Reconstructionist Democratic bloc. Republicans sought to make inroads campaigning for the Irish taken prisoner in the Fenian raids into Canada, and calling on the Johnson administration to recognize a lawful state of war between Ireland and England. In 1867 Grant personally intervened with David Bell and Michael Scanlon to move their paper, the Irish Republic, articulate in its support for black equality, to New York from Chicago. The Democrats, having abandoned Johnson, nominated former governor Horatio Seymour of New York for president and Francis P. Blair of Missouri for vice president. The Democrats advocated the immediate restoration of former Confederate states to the Union and amnesty from "all past political offenses". Grant won the popular vote by 300,000 votes out of 5,716,082 votes cast, receiving an Electoral College landslide of 214 votes to Seymour's 80. Seymour received a majority of white votes, but Grant was aided by 500,000 votes cast by blacks, winning him 52.7 percent of the popular vote. He lost Louisiana and Georgia primarily due to Ku Klux Klan violence against African-American voters. At the age of 46, Grant was the youngest president yet elected, and the first president after the nation had outlawed slavery. Grant's presidential Reconstruction Effective civil rights executive President Ulysses S. Grant was considered an effective civil rights executive, concerned about the plight of African Americans. Grant met with prominent black leaders for consultation and signed a bill into law, on March 18, 1869, that guaranteed equal rights to both blacks and whites, to serve on juries, and hold office, in Washington D.C. In 1870 Grant signed into law a Naturalization Act that gave foreign blacks citizenship. Additionally, Grant's Postmaster General, John Creswell used his patronage powers to integrate the postal system and appointed a record number of African-American men and women as postal workers across the nation, while also expanding many of the mail routes. Grant appointed Republican abolitionist and champion of black education Hugh Lennox Bond as U.S. Circuit Court judge. Final four Reconstruction states admitted Immediately upon inauguration in 1869, Grant bolstered Reconstruction by prodding Congress to readmit Virginia, Mississippi, and Texas into the Union, while ensuring their state constitutions protected every citizen's voting rights. Grant advocated the ratification of the Fifteenth Amendment that said states could not disenfranchise African Americans. Within a year, the three remaining states—Mississippi, Virginia, and Texas—adopted the new amendment—and were admitted to Congress. Grant put military pressure on Georgia to reinstate its black legislators and adopt the new amendment. Georgia complied, and on February 24, 1871, its Senators were seated in Congress, with all the former Confederate states represented. Southern Reconstructed states were controlled by Republican carpetbaggers, scalawags and former slaves. By 1877 the conservative Democrats had full control of the region and Reconstruction was dead. Department of Justice created In 1870, to enforce Reconstruction, Congress and Grant created the Justice Department that allowed the Attorney General Amos Akerman and the first Solicitor General Benjamin Bristow to prosecute the Klan. In Grant's two terms he strengthened Washington's legal capabilities to directly intervene to protect citizenship rights even if the states ignored the problem. Enforcement acts (1870-1871) Congress and Grant passed a series (three) of powerful civil rights Enforcement Acts between 1870 and 1871, designed to protect blacks and Reconstruction governments. These were criminal codes that protected the freedmen's right to vote, to hold office, to serve on juries, and receive equal protection of laws. Most important, they authorized the federal government to intervene when states did not act. Urged by Grant and his Attorney General Amos T. Akerman, the strongest of these laws was the Ku Klux Klan Act, passed on April 20, 1871, that authorized the president to impose martial law and suspend the writ of habeas corpus. Grant was so adamant about the passage of the Ku Klux Klan Act, he earlier had sent a message to Congress, on March 23, 1871, in which he said: "A condition of affairs now exists in some of the States of the Union rendering life and property insecure, and the carrying of the mails and the collection of the revenue dangerous. The proof that such a, condition of affairs exists in some localities is now before the Senate. That the power to correct these evils is beyond the control of State authorities, I do not doubt. That the power of the Executive of the United States, acting within the limits of existing laws, is sufficient for present emergencies, is not clear." Grant also recommended the enforcement of laws in all parts of the United States to protect life, liberty, and property. Prosecuted Ku Klux Klan Grant's Justice Department destroyed the Ku Klux Klan, but during both of his terms, Blacks lost their political strength in the Southern United States. By October, Grant suspended habeas corpus in part of South Carolina and he also sent federal troops to help marshals, who initiated prosecutions of Klan members. Grant's Attorney General, Amos T. Akerman, who replaced Hoar, was zealous in his attempt to destroy the Klan. Akerman and South Carolina's U.S. marshal arrested over 470 Klan members, but hundreds of Klansmen, including the Klan's wealthy leaders, fled the state. Akerman returned over 3,000 indictments of the Klan throughout the South and obtained 600 convictions for the worst offenders. By 1872, Grant had crushed the Klan, and African Americans peacefully voted in record numbers in elections in the South. Attorney General George H. Williams, Akerman's replacement, suspended his prosecutions of the Klan in North Carolina and South Carolina in the Spring of 1873, but prior to the election of 1874, he changed course and prosecuted the Klan. Civil rights prosecutions continued but with fewer yearly cases and convictions. Amnesty act 1872 In addition to fighting for African American civil rights, Grant wanted to reconcile with white southerners, out of a spirit of Appomattox. To placate the South, in May 1872, Grant signed the Amnesty Act, which restored political rights to former Confederates, except for a few hundred former Confederate officers. Grant wanted people to vote and practice free speech despite their "views, color or nativity." Civil Rights Act of 1875 The Civil Rights Act of 1875 was one of the last major acts of Congress and Grant to preserve Reconstruction and equality for African Americans. The initial bill was created by Senator Charles Sumner. Grant endorsed the measure, despite his previous feud with Sumner, signing it into law on March 1, 1875. The law, ahead of its times, outlawed discrimination for blacks in public accommodations, schools, transportation, and selecting juries. Although weakly enforceable, the law spread fear among whites opposed to interracial justice and was overturned by the Supreme Court in 1883. The later enforceable Civil Rights Act of 1964 borrowed many of the earlier 1875's law's provisions. Countered election fraud To counter vote fraud in the Democratic stronghold of New York City, Grant sent in tens of thousands of armed, uniformed federal marshals and other election officials to regulate the 1870 and subsequent elections. Democrats across the North then mobilized to defend their base and attacked Grant's entire set of policies. On October 21, 1876, President Grant deployed troops to protect Black and White Republican voters in Petersburg, Virginia. National support of Reconstruction declines Grant's support from Congress and the nation declined due to scandals within his administration and the political resurgence of the Democrats in the North and South. By 1870, most Republicans felt the war goals had been achieved, and they turned their attention to other issues such as economic policies. African American officeholders Republicans took control of all Southern state governorships and state legislatures, except for Virginia. The Republican coalition elected numerous African Americans to local, state, and national offices; though they did not dominate any electoral offices, Black men as representatives voting in state and federal legislatures marked a drastic social change. At the beginning of 1867, no African American in the South held political office, but within three or four years "about 15 percent of the officeholders in the South were Black—a larger proportion than in 1990". Most of those offices were at the local level. In 1860, Blacks constituted the majority of the population in Mississippi and South Carolina, 47% in Louisiana, 45% in Alabama, and 44% in Georgia and Florida, so their political influence was still far less than their percentage of the population. About 137 Black officeholders had lived outside the South before the Civil War. Some who had escaped from slavery to the North and had become educated returned to help the South advance in the postbellum era. Others were Free people of color before the war, who had achieved education and positions of leadership elsewhere. Other African American men elected to office were already leaders in their communities, including a number of preachers. As happened in White communities, not all leadership depended upon wealth and literacy. \|State\|\|White\|\|Black\|\|% White\|\|Statewide White\| (% in 1870) There were few African Americans elected or appointed to national office. African Americans voted for both White and Black candidates. The Fifteenth Amendment to the United States Constitution guaranteed only that voting could not be restricted on the basis of race, color, or previous condition of servitude. From 1868 on, campaigns and elections were surrounded by violence as White insurgents and paramilitaries tried to suppress the Black vote, and fraud was rampant. Many congressional elections in the South were contested. Even states with majority-African-American populations often elected only one or two African American representatives to Congress. Exceptions included South Carolina; at the end of Reconstruction, four of its five congressmen were African Americans. Social and economic factors Freedmen were very active in forming their own churches, mostly Baptist or Methodist, and giving their ministers both moral and political leadership roles. In a process of self-segregation, practically all Blacks left White churches so that few racially integrated congregations remained (apart from some Catholic churches in Louisiana). They started many new Black Baptist churches and soon, new Black state associations. Four main groups competed with each other across the South to form new Methodist churches composed of freedmen. They were the African Methodist Episcopal Church; the African Methodist Episcopal Zion Church, both independent Black denominations founded in Philadelphia and New York, respectively; the Colored Methodist Episcopal Church (which was sponsored by the White Methodist Episcopal Church, South) and the well-funded Methodist Episcopal Church (predominantly White Methodists of the North). The Methodist Church had split before the war due to disagreements about slavery. By 1871, the Northern Methodists had 88,000 Black members in the South, and had opened numerous schools for them. Blacks in the South made up a core element of the Republican Party. Their ministers had powerful political roles that were distinctive since they did not depend on White support, in contrast to teachers, politicians, businessmen, and tenant farmers. Acting on the principle as stated by Charles H. Pearce, an AME minister in Florida: "A man in this state cannot do his whole duty as a minister except he looks out for the political interests of his people." More than 100 Black ministers were elected to state legislatures during Reconstruction, as well as several to Congress and one, Hiram Rhodes Revels, to the U.S. Senate. In a highly controversial action during the war, the Northern Methodists used the Army to seize control of Methodist churches in large cities, over the vehement protests of the Southern Methodists. Historian Ralph Morrow reports: A War Department order of November 1863, applicable to the Southwestern states of the Confederacy, authorized the Northern Methodists to occupy "all houses of worship belonging to the Methodist Episcopal Church South in which a loyal minister, appointed by a loyal bishop of said church, does not officiate." Across the North, several denominations—especially the Methodists, Congregationalists, and Presbyterians, as well as the Quakers—strongly supported Radical policies. The focus on social problems paved the way for the Social Gospel movement. Matthew Simpson, a Methodist bishop, played a leading role in mobilizing the Northern Methodists for the cause. Biographer Robert D. Clark called him the "High Priest of the Radical Republicans". The Methodist Ministers Association of Boston, meeting two weeks after Lincoln's assassination, called for a hard line against the Confederate leadership: Resolved, that no terms should be made with traitors, no compromise with rebels.... That we hold the national authority bound by the most solemn obligation to God and man to bring all the civil and military leaders of the rebellion to trial by due course of law, and when they are clearly convicted, to execute them. The denominations all sent missionaries, teachers and activists to the South to help the freedmen. Only the Methodists made many converts, however. Activists sponsored by the Northern Methodist Church played a major role in the Freedmen's Bureau, notably in such key educational roles as the bureau's state superintendent or assistant superintendent of education for Virginia, Florida, Alabama, and South Carolina. Many Americans interpreted great events in religious terms. Historian Wilson Fallin Jr. contrasts the interpretation of the Civil War and Reconstruction in White versus Black Baptist sermons in Alabama. White Baptists expressed the view that: God had chastised them and given them a special mission—to maintain orthodoxy, strict biblicism, personal piety, and traditional race relations. Slavery, they insisted, had not been sinful. Rather, emancipation was a historical tragedy and the end of Reconstruction was a clear sign of God's favor. In sharp contrast, Black Baptists interpreted the Civil War, emancipation, and Reconstruction as: God's gift of freedom. They appreciated opportunities to exercise their independence, to worship in their own way, to affirm their worth and dignity, and to proclaim the fatherhood of God and the brotherhood of man. Most of all, they could form their own churches, associations, and conventions. These institutions offered self-help and racial uplift, and provided places where the gospel of liberation could be proclaimed. As a result, black preachers continued to insist that God would protect and help them; God would be their rock in a stormy land. Historian James D. Anderson argues that the freed slaves were the first Southerners "to campaign for universal, state-supported public education". Blacks in the Republican coalition played a critical role in establishing the principle in state constitutions for the first time during congressional Reconstruction. Some slaves had learned to read from White playmates or colleagues before formal education was allowed by law; African Americans started "native schools" before the end of the war; Sabbath schools were another widespread means that freedmen developed to teach literacy. When they gained suffrage, Black politicians took this commitment to public education to state constitutional conventions. The Republicans created a system of public schools, which were segregated by race everywhere except New Orleans. Generally, elementary and a few secondary schools were built in most cities, and occasionally in the countryside, but the South had few cities. The rural areas faced many difficulties opening and maintaining public schools. In the country, the public school was often a one-room affair that attracted about half the younger children. The teachers were poorly paid, and their pay was often in arrears. Conservatives contended the rural schools were too expensive and unnecessary for a region where the vast majority of people were cotton or tobacco farmers. They had no expectation of better education for their residents. One historian found that the schools were less effective than they might have been because "poverty, the inability of the states to collect taxes, and inefficiency and corruption in many places prevented successful operation of the schools". After Reconstruction ended and White elected officials disenfranchised Blacks and imposed Jim Crow laws, they consistently underfunded Black institutions, including the schools. After the war, Northern missionaries founded numerous private academies and colleges for freedmen across the South. In addition, every state founded state colleges for freedmen, such as Alcorn State University in Mississippi. The normal schools and state colleges produced generations of teachers who were integral to the education of African American children under the segregated system. By the end of the century, the majority of African Americans were literate. In the late 19th century, the federal government established land grant legislation to provide funding for higher education across the United States. Learning that Blacks were excluded from land grant colleges in the South, in 1890 the federal government insisted that Southern states establish Black state institutions as land grant colleges to provide for Black higher education, in order to continue to receive funds for their already established White schools. Some states classified their Black state colleges as land grant institutions. Former Congressman John Roy Lynch wrote: "there are very many liberal, fair-minded and influential Democrats in the state [Mississippi] who are strongly in favor of having the state provide for the liberal education of both races". According to a 2020 study by economist Trevon Logan, increases in Black politicians led to greater tax revenue, which was put towards public education spending (and land tenancy reforms). Logan finds that this led to greater literacy among Black men. Railroad subsidies and payoffs Every Southern state subsidized railroads, which modernizers believed could haul the South out of isolation and poverty. Millions of dollars in bonds and subsidies were fraudulently pocketed. One ring in North Carolina spent $200,000 in bribing the legislature and obtained millions of state dollars for its railroads. Instead of building new track, however, it used the funds to speculate in bonds, reward friends with extravagant fees, and enjoy lavish trips to Europe. Taxes were quadrupled across the South to pay off the railroad bonds and the school costs. There were complaints among taxpayers because taxes had historically been low, as the planter elite was not committed to public infrastructure or public education. Taxes historically had been much lower in the South than in the North, reflecting the lack of government investment by the communities. Nevertheless, thousands of miles of lines were built as the Southern system expanded from 11,000 miles (18,000 km) in 1870 to 29,000 miles (47,000 km) in 1890. The lines were owned and directed overwhelmingly by Northerners. Railroads helped create a mechanically skilled group of craftsmen and broke the isolation of much of the region. Passengers were few, however, and apart from hauling the cotton crop when it was harvested, there was little freight traffic. As Franklin explains: "numerous railroads fed at the public trough by bribing legislators ... and through the use and misuse of state funds". According to one businessman, the effect "was to drive capital from the state, paralyze industry, and demoralize labor". Taxation during Reconstruction Reconstruction changed the means of taxation in the South. In the U.S. from the earliest days until today, a major source of state revenue was the property tax. In the South, wealthy landowners were allowed to self-assess the value of their own land. These fraudulent assessments were almost valueless, and pre-war property tax collections were lacking due to property value misrepresentation. State revenues came from fees and from sales taxes on slave auctions. Some states assessed property owners by a combination of land value and a capitation tax, a tax on each worker employed. This tax was often assessed in a way to discourage a free labor market, where a slave was assessed at 75 cents, while a free White was assessed at a dollar or more, and a free African American at $3 or more. Some revenue also came from poll taxes. These taxes were more than poor people could pay, with the designed and inevitable consequence that they did not vote. During Reconstruction, the state legislature mobilized to provide for public need more than had previous governments: establishing public schools and investing in infrastructure, as well as charitable institutions such as hospitals and asylums. They set out to increase taxes which were unusually low. The planters had provided privately for their own needs. There was some fraudulent spending in the postbellum years; a collapse in state credit because of huge deficits, forced the states to increase property tax rates. In places, the rate went up to 10 times higher—despite the poverty of the region. The planters had not invested in infrastructure and much had been destroyed during the war. In part, the new tax system was designed to force owners of large plantations with huge tracts of uncultivated land either to sell or to have it confiscated for failure to pay taxes. The taxes would serve as a market-based system for redistributing the land to the landless freedmen and White poor. Mississippi, for instance, was mostly frontier, with 90% of the bottom lands in the interior undeveloped. The following table shows property tax rates for South Carolina and Mississippi. Note that many local town and county assessments effectively doubled the tax rates reported in the table. These taxes were still levied upon the landowners' own sworn testimony as to the value of their land, which remained the dubious and exploitable system used by wealthy landholders in the South well into the 20th century. \|1869\|\|5 mills (0.5%)\|\|1 mill (0.1%) (lowest rate between 1822 and 1898)\| \|1870\|\|9 mills\|\|5 mills\| \|1871\|\|7 mills\|\|4 mills\| \|1872\|\|12 mills\|\|8.5 mills\| \|1873\|\|12 mills\|\|12.5 mills\| \|1874\|\|10.3–8 mills\|\|14 mills (1.4%) "a rate which virtually amounted to confiscation" (highest rate between 1822 and 1898)\| \|Sources\|\|Reynolds, J. S. Reconstruction in South Carolina, 1865–1877 (Columbia, South Carolina: The State Co., 1905), p. 329.\|\|Hollander, J. H. Studies in State Taxation with Particular Reference to the Southern States (Baltimore: Johns Hopkins Press, 1900), p. 192.\| Called upon to pay taxes on their property, essentially for the first time, angry plantation owners revolted. The conservatives shifted their focus away from race to taxes. Former Congressman John R. Lynch, a Black Republican leader from Mississippi, later wrote: The argument made by the taxpayers, however, was plausible and it may be conceded that, upon the whole, they were about right; for no doubt it would have been much easier upon the taxpayers to have increased at that time the interest-bearing debt of the state than to have increased the tax rate. The latter course, however, had been adopted and could not then be changed unless of course they wanted to change them. National financial issues The Civil War had been financed primarily by issuing short-term and long-term bonds and loans, plus inflation caused by printing paper money, plus new taxes. Wholesale prices had more than doubled, and reduction of inflation was a priority for Secretary McCulloch. A high priority, and by far the most controversial, was the currency question. The old paper currency issued by state banks had been withdrawn, and Confederate currency was worthless. The national banks had issued $207 million in currency, which was backed by gold and silver. The federal treasury had issued $428 million in greenbacks, which was legal tender but not backed by gold or silver. In addition about $275 million of coin was in circulation. The new administration policy announced in October would be to make all the paper convertible into specie, if Congress so voted. The House of Representatives passed the Alley Resolution on December 18, 1865, by a vote of 144 to 6. In the Senate it was a different matter, for the key player was Senator John Sherman, who said that inflation contraction was not nearly as important as refunding the short-term and long-term national debt. The war had been largely financed by national debt, in addition to taxation and inflation. The national debt stood at $2.8 billion. By October 1865, most of it in short-term and temporary loans. Wall Street bankers typified by Jay Cooke believe that the economy was about to grow rapidly, thanks to the development of agriculture through the Homestead Act, the expansion of railroads, especially rebuilding the devastated Southern railroads and opening the transcontinental railroad line to the West Coast, and especially the flourishing of manufacturing during the war. The gold premium over greenbacks was $145 in greenbacks to $100 in gold, and the optimists thought that the heavy demand for currency in an era of prosperity would return the ratio to 100. A compromise was reached in April 1866, that limited the treasury to a currency contraction of only $10 million over six months. Meanwhile, the Senate refunded the entire national debt, but the House failed to act. By early 1867, postbellum prosperity was a reality, and the optimists wanted an end to contraction, which Congress ordered in January 1868. Meanwhile, the Treasury issued new bonds at a lower interest rate to refinance the redemption of short-term debt. While the old state bank notes were disappearing from circulation, new national bank notes, backed by species, were expanding. By 1868 inflation was minimal. Congressional investigation into Reconstruction states 1872 On April 20, 1871, prior to the passage of the Ku Klux Klan Act (Last of three Enforcement Acts), on the same day, the U.S. Congress launched a 21-member investigation committee on the status of the Southern Reconstruction states North Carolina, South Carolina, Georgia, Mississippi, Alabama, and Florida. Congressional members on the committee included Rep. Benjamin Butler, Sen. Zachariah Chandler, and Sen. Francis P. Blair. Subcommittee members traveled into the South to interview the people living in their respective states. Those interviewed included top-ranking officials, such as Wade Hampton III, former South Carolina Gov. James L. Orr, and Nathan Bedford Forrest, a former Confederate general and prominent Ku Klux Klan leader (Forrest denied in his congressional testimony being a member). Other Southerners interviewed included farmers, doctors, merchants, teachers, and clergymen. The committee heard numerous reports of White violence against Blacks, while many Whites denied Klan membership or knowledge of violent activities. The majority report by Republicans concluded that the government would not tolerate any Southern "conspiracy" to resist violently the congressional Reconstruction. The committee completed its 13-volume report in February 1872. While President Ulysses S. Grant had been able to suppress the KKK through the Enforcement Acts, other paramilitary insurgents organized, including the White League in 1874, active in Louisiana; and the Red Shirts, with chapters active in Mississippi and the Carolinas. They used intimidation and outright attacks to run Republicans out of office and repress voting by Blacks, leading to White Democrats regaining power by the elections of the mid-to-late 1870s. While the scalawag element of Republican Whites supported measures for Black civil rights, the conservative Whites typically opposed these measures. Some supported armed attacks to suppress Blacks. They self-consciously defended their own actions within the framework of a White American discourse of resistance against tyrannical government, and they broadly succeeded in convincing many fellow White citizens, says Steedman. The opponents of Reconstruction formed state political parties, affiliated with the national Democratic Party and often named the "Conservative Party". They supported or tolerated violent paramilitary groups, such as the White League in Louisiana and the Red Shirts in Mississippi and the Carolinas, that assassinated and intimidated both Black and White Republican leaders at election time. Historian George C. Rable called such groups the "military arm of the Democratic Party". By the mid-1870s, the conservatives and Democrats had aligned with the national Democratic Party, which enthusiastically supported their cause even as the national Republican Party was losing interest in Southern affairs. The Negro troops, even at their best, were everywhere considered offensive by the native whites.... The Negro soldier, impudent by reason of his new freedom, his new uniform, and his new gun, was more than Southern temper could tranquilly bear, and race conflicts were frequent. Often, these White Southerners identified as the "Conservative Party" or the "Democratic and Conservative Party" in order to distinguish themselves from the national Democratic Party and to obtain support from former Whigs. These parties sent delegates to the 1868 Democratic National Convention and abandoned their separate names by 1873 or 1874. Most White members of both the planter and business class and common farmer class of the South opposed Black civil rights, carpetbaggers, and military rule, and sought white supremacy. Democrats nominated some Blacks for political office and tried to entice other Blacks from the Republican side. When these attempts to combine with the Blacks failed, the planters joined the common farmers in simply trying to displace the Republican governments. The planters and their business allies dominated the self-styled "conservative" coalition that finally took control in the South. They were paternalistic toward the Blacks but feared they would use power to raise taxes and slow business development. Fleming described the first results of the insurgent movement as "good", and the later ones as "both good and bad". According to Fleming (1907), the KKK "quieted the Negroes, made life and property safer, gave protection to women, stopped burnings, forced the Radical leaders to be more moderate, made the Negroes work better, drove the worst of the Radical leaders from the country and started the whites on the way to gain political supremacy". The evil result, Fleming said, was that lawless elements "made use of the organization as a cloak to cover their misdeeds ... The lynching habits of today are largely due to conditions, social and legal, growing out of Reconstruction." Historians have noted that the peak of lynchings took place near the turn of the century, decades after Reconstruction ended, as Whites were imposing Jim Crow laws and passing new state constitutions that disenfranchised the Blacks. The lynchings were used for intimidation and social control, with a frequency associated more with economic stresses and the settlement of sharecropper accounts at the end of the season, than for any other reason. Outrages upon the former slaves in the South there were in plenty. Their sufferings were many. But white men, too, were victims of lawless violence, and in all portions of the North and the late "rebel" states. Not a political campaign passed without the exchange of bullets, the breaking of skulls with sticks and stones, the firing of rival club-houses. Republican clubs marched the streets of Philadelphia, amid revolver shots and brickbats, to save the Negroes from the "rebel" savages in Alabama.... The project to make voters out of black men was not so much for their social elevation as for the further punishment of the Southern white people—for the capture of offices for Radical scamps and the entrenchment of the Radical party in power for a long time to come in the South and in the country at large. As Reconstruction continued, Whites accompanied elections with increased violence in an attempt to run Republicans out of office and suppress Black voting. The victims of this violence were overwhelmingly African American, as in the Colfax Massacre of 1873. After federal suppression of the Klan in the early 1870s, White insurgent groups tried to avoid open conflict with federal forces. In 1874 in the Battle of Liberty Place, the White League entered New Orleans with 5,000 members and defeated the police and militia, to occupy federal offices for three days in an attempt to overturn the disputed government of William Pitt Kellogg, but retreated before federal troops reached the city. None were prosecuted. Their election-time tactics included violent intimidation of African American and Republican voters prior to elections, while avoiding conflict with the U.S. Army or the state militias, and then withdrawing completely on election day. Conservative reaction continued in both the North and South; the White Liners movement to elect candidates dedicated to White supremacy reached as far as Ohio in 1875. The Redeemers were the Southern wing of the Bourbon Democrats, the conservative, pro-business faction of the Democratic Party. They sought to regain political power, reestablish White supremacy, and oust the Radical Republicans. Led by rich former planters, businessmen, and professionals, they dominated Southern politics in most areas from the 1870s to 1910. Republicans split nationally: election of 1872 Congress was right in not limiting, by its Reconstruction acts, the right of suffrage to Whites; but wrong in the exclusion from suffrage of certain classes of citizens and all unable to take its prescribed retrospective oath, and wrong also in the establishment of despotic military governments for the states and in authorizing military commissions for the trial of civilians in time of peace. There should have been as little military government as possible; no military commissions; no classes excluded from suffrage; and no oath except one of faithful obedience and support to the Constitution and laws, and of sincere attachment to the constitutional government of the United States. By 1872, President Ulysses S. Grant had alienated large numbers of leading Republicans, including many Radicals, by the corruption of his administration and his use of federal soldiers to prop up Radical state regimes in the South. The opponents, called "Liberal Republicans", included founders of the party who expressed dismay that the party had succumbed to corruption. They were further wearied by the continued insurgent violence of Whites against Blacks in the South, especially around every election cycle, which demonstrated that the war was not over and changes were fragile. Leaders included editors of some of the nation's most powerful newspapers. Charles Sumner, embittered by the corruption of the Grant administration, joined the new party, which nominated editor Horace Greeley. The loosely-organized Democratic Party also supported Greeley. Grant made up for the defections by new gains among Union veterans and by strong support from the "Stalwart" faction of his party (which depended on his patronage), and the Southern Republican Party. Grant won with 55.6% of the vote to Greeley's 43.8%. The Liberal Republican Party vanished and many former supporters—even former abolitionists—abandoned the cause of Reconstruction. The Republican coalition splinters in the South In the South, political and racial tensions built up inside the Republican Party as they were attacked by the Democrats. In 1868, Georgia Democrats, with support from some Republicans, expelled all 28 Black Republican members from the state house, arguing Blacks were eligible to vote but not to hold office. In most states, the more conservative scalawags fought for control with the more Radical carpetbaggers and their Black allies. Most of the 430 Republican newspapers in the South were edited by scalawags—only 20 percent were edited by carpetbaggers. White businessmen generally boycotted Republican papers, which survived through government patronage. Nevertheless, in the increasingly bitter battles inside the Republican Party, the scalawags usually lost; many of the disgruntled losers switched over to the conservative or Democratic side. In Mississippi, the conservative faction led by scalawag James Lusk Alcorn was decisively defeated by the Radical faction led by carpetbagger Adelbert Ames. The party lost support steadily as many scalawags left it; few recruits were acquired. The most bitter contest took place inside the Republican Party in Arkansas, where the two sides armed their forces and confronted each other in the streets; no actual combat took place in the Brooks–Baxter War. The carpetbagger faction led by Elisha Baxter finally prevailed when the White House intervened, but both sides were badly weakened, and the Democrats soon came to power. Meanwhile, in state after state the freedmen were demanding a bigger share of the offices and patronage, squeezing out carpetbagger allies but never commanding the numbers equivalent to their population proportion. By the mid-1870s: "The hard realities of Southern political life had taught the lesson that black constituents needed to be represented by black officials."[clarification needed] The financial depression increased the pressure on Reconstruction governments, dissolving progress. Finally, some of the more prosperous freedmen were joining the Democrats, as they were angered at the failure of the Republicans to help them acquire land. The South was "sparsely settled"; only 10 percent of Louisiana was cultivated, and 90 percent of Mississippi bottom land was undeveloped in areas away from the river fronts, but freedmen often did not have the stake to get started. They hoped that the government would help them acquire land which they could work. Only South Carolina created any land redistribution, establishing a land commission and resettling about 14,000 freedmen families and some poor Whites on land purchased by the state. Although historians such as W. E. B. Du Bois celebrated a cross-racial coalition of poor Whites and Blacks, such coalitions rarely formed in these years. Writing in 1915, former Congressman Lynch, recalling his experience as a Black leader in Mississippi, explained that: While the colored men did not look with favor upon a political alliance with the poor whites, it must be admitted that, with very few exceptions, that class of whites did not seek, and did not seem to desire such an alliance. Lynch reported that poor Whites resented the job competition from freedmen. Furthermore, the poor Whites: with a few exceptions, were less efficient, less capable, and knew less about matters of state and governmental administration than many of the former slaves.... As a rule, therefore, the Whites that came into the leadership of the Republican Party between 1872 and 1875 were representatives of the most substantial families of the land. Democrats try a "New Departure" By 1870, the Democratic–Conservative leadership across the South decided it had to end its opposition to Reconstruction and Black suffrage to survive and move on to new issues. The Grant administration had proven by its crackdown on the Ku Klux Klan that it would use as much federal power as necessary to suppress open anti-Black violence. Democrats in the North concurred with these Southern Democrats. They wanted to fight the Republican Party on economic grounds rather than race. The New Departure offered the chance for a clean slate without having to re-fight the Civil War every election. Furthermore, many wealthy Southern landowners thought they could control part of the newly enfranchised Black electorate to their own advantage. Not all Democrats agreed; an insurgent element continued to resist Reconstruction no matter what. Eventually, a group called "Redeemers" took control of the party in the Southern states. They formed coalitions with conservative Republicans, including scalawags and carpetbaggers, emphasizing the need for economic modernization. Railroad building was seen as a panacea since Northern capital was needed. The new tactics were a success in Virginia where William Mahone built a winning coalition. In Tennessee, the Redeemers formed a coalition with Republican Governor Dewitt Clinton Senter. Across the South, some Democrats switched from the race issue to taxes and corruption, charging that Republican governments were corrupt and inefficient. With a continuing decrease in cotton prices, taxes squeezed cash-poor farmers who rarely saw $20 in currency a year, but had to pay taxes in currency or lose their farms. But major planters, who had never paid taxes before, often recovered their property even after confiscation. In North Carolina, Republican Governor William Woods Holden used state troops against the Klan, but the prisoners were released by federal judges. Holden became the first governor in American history to be impeached and removed from office. Republican political disputes in Georgia split the party and enabled the Redeemers to take over. In the North, a live-and-let-live attitude made elections more like a sporting contest. But in the Deep South, many White citizens had not reconciled with the defeat of the war or the granting of citizenship to freedmen. As an Alabama scalawag explained: "Our contest here is for life, for the right to earn our bread, ... for a decent and respectful consideration as human beings and members of society." Panic of 1873 The Panic of 1873 (a depression) hit the Southern economy hard and disillusioned many Republicans who had gambled that railroads would pull the South out of its poverty. The price of cotton fell by half; many small landowners, local merchants, and cotton factors (wholesalers) went bankrupt. Sharecropping for Black and White farmers became more common as a way to spread the risk of owning land. The old abolitionist element in the North was aging away, or had lost interest, and was not replenished. Many carpetbaggers returned to the North or joined the Redeemers. Blacks had an increased voice in the Republican Party, but across the South it was divided by internal bickering and was rapidly losing its cohesion. Many local Black leaders started emphasizing individual economic progress in cooperation with White elites, rather than racial political progress in opposition to them, a conservative attitude that foreshadowed Booker T. Washington. Nationally, President Grant was blamed for the depression; the Republican Party lost 96 seats in all parts of the country in the 1874 elections. The Bourbon Democrats took control of the House and were confident of electing Samuel J. Tilden president in 1876. President Grant was not running for re-election and seemed to be losing interest in the South. States fell to the Redeemers, with only four in Republican hands in 1873: Arkansas, Louisiana, Mississippi, and South Carolina. Arkansas then fell after the violent Brooks–Baxter War in 1874 ripped apart the Republican Party there. In the lower South, violence increased as new insurgent groups arose, including the Red Shirts in Mississippi and the Carolinas, and the White League in Louisiana. The disputed election in Louisiana in 1872 found both Republican and Democratic candidates holding inaugural balls while returns were reviewed. Both certified their own slates for local parish offices in many places, causing local tensions to rise. Finally, federal support helped certify the Republican as governor. Slates for local offices were certified by each candidate. In rural Grant Parish in the Red River Valley, freedmen fearing a Democratic attempt to take over the parish government reinforced defenses at the small Colfax courthouse in late March. White militias gathered from the area a few miles outside the settlement. Rumors and fears abounded on both sides. William Ward, an African American Union veteran and militia captain, mustered his company in Colfax and went to the courthouse. On Easter Sunday, April 13, 1873, the Whites attacked the defenders at the courthouse. There was confusion about who shot one of the White leaders after an offer by the defenders to surrender. It was a catalyst to mayhem. In the end, three Whites died and 120–150 Blacks were killed, some 50 that evening while being held as prisoners. The disproportionate numbers of Black to White fatalities and documentation of brutalized bodies are why contemporary historians call it the Colfax Massacre rather than the Colfax Riot, as it was known locally. This marked the beginning of heightened insurgency and attacks on Republican officeholders and freedmen in Louisiana and other Deep South states. In Louisiana, Judge T. S. Crawford and District Attorney P. H. Harris of the 12th Judicial District were shot off their horses and killed by ambush October 8, 1873, while going to court. One widow wrote to the Department of Justice that her husband was killed because he was a Union man, telling "the efforts made to screen those who committed a crime". Political violence was endemic in Louisiana. In 1874, the White militias coalesced into paramilitary organizations such as the White League, first in parishes of the Red River Valley. The new organization operated openly and had political goals: the violent overthrow of Republican rule and suppression of Black voting. White League chapters soon rose in many rural parishes, receiving financing for advanced weaponry from wealthy men. In the Coushatta Massacre in 1874, the White League assassinated six White Republican officeholders and five to 20 Black witnesses outside Coushatta, Red River Parish. Four of the White men were related to the Republican representative of the parish, who was married to a local woman; three were native to the region. Later in 1874 the White League mounted a serious attempt to unseat the Republican governor of Louisiana, in a dispute that had simmered since the 1872 election. It brought 5,000 troops to New Orleans to engage and overwhelm forces of the metropolitan police and state militia to turn Republican Governor William P. Kellogg out of office and seat John McEnery. The White League took over and held the state house and city hall, but they retreated before the arrival of reinforcing federal troops. Kellogg had asked for reinforcements before, and Grant finally responded, sending additional troops to try to quell violence throughout plantation areas of the Red River Valley, although 2,000 troops were already in the state. Similarly, the Red Shirts, another paramilitary group, arose in 1875 in Mississippi and the Carolinas. Like the White League and White Liner rifle clubs, to which 20,000 men belonged in North Carolina alone, these groups operated as a "military arm of the Democratic Party", to restore White supremacy. Democrats and many Northern Republicans agreed that Confederate nationalism and slavery were dead—the war goals were achieved—and further federal military interference was an undemocratic violation of historical Republican values. The victory of Rutherford B. Hayes in the hotly contested Ohio gubernatorial election of 1875 indicated his "let alone" policy toward the South would become Republican policy, as happened when he won the 1876 Republican nomination for president. An explosion of violence accompanied the campaign for Mississippi's 1875 election, in which Red Shirts and Democratic rifle clubs, operating in the open, threatened or shot enough Republicans to decide the election for the Democrats. Hundreds of Black men were killed. Republican Governor Adelbert Ames asked Grant for federal troops to fight back; Grant initially refused, saying public opinion was "tired out" of the perpetual troubles in the South. Ames fled the state as the Democrats took over Mississippi. The campaigns and elections of 1876 were marked by additional murders and attacks on Republicans in Louisiana, North Carolina, South Carolina, and Florida. In South Carolina the campaign season of 1876 was marked by murderous outbreaks and fraud against freedmen. Red Shirts paraded with arms behind Democratic candidates; they killed Blacks in the Hamburg and Ellenton, South Carolina massacres. One historian estimated 150 Blacks were killed in the weeks before the 1876 election across South Carolina. Red Shirts prevented almost all Black voting in two majority-Black counties. The Red Shirts were also active in North Carolina. A 2019 study found that counties that were occupied by the U.S. Army to enforce enfranchisement of emancipated slaves were more likely to elect Black politicians. The study also found that "political murders by White-supremacist groups occurred less frequently" in these counties than in Southern counties that were not occupied. Election of 1876 Reconstruction continued in South Carolina, Louisiana, and Florida until 1877. The elections of 1876 were accompanied by heightened violence across the Deep South. A combination of ballot stuffing and intimidating Blacks suppressed their vote even in majority Black counties. The White League was active in Louisiana. After Republican Rutherford B. Hayes won the disputed 1876 presidential election, the national Compromise of 1877 (a corrupt bargain) was reached. The White Democrats in the South agreed to accept Hayes' victory if he withdrew the last federal troops. By this point, the North was weary of insurgency. White Democrats controlled most of the Southern legislatures and armed militias controlled small towns and rural areas. Blacks considered Reconstruction a failure because the federal government withdrew from enforcing their ability to exercise their rights as citizens. Hayes ends Reconstruction On January 29, 1877, President Grant signed the Electoral Commission Act, which set up a 15-member commission of eight Republicans and seven Democrats to settle the disputed 1876 election. Since the Constitution did not explicitly indicate how Electoral College disputes were to be resolved, Congress was forced to consider other methods to settle the crisis. Many Democrats argued that Congress as a whole should determine which certificates to count. However, the chances that this method would result in a harmonious settlement were slim, as the Democrats controlled the House, while the Republicans controlled the Senate. Several Hayes supporters, on the other hand, argued that the President pro tempore of the Senate had the authority to determine which certificates to count, because he was responsible for chairing the congressional session at which the electoral votes were to be tallied. Since the office of president pro tempore was occupied by a Republican, Senator Thomas W. Ferry of Michigan, this method would have favored Hayes. Still others proposed that the matter should be settled by the Supreme Court. In a stormy session that began on March 1, 1877, the House debated the objection for about twelve hours before overruling it. Immediately, another spurious objection was raised, this time to the electoral votes from Wisconsin. Again, the Senate voted to overrule the objection, while a filibuster was conducted in the House. However, the Speaker of the House, Democrat Samuel J. Randall, refused to entertain dilatory motions. Eventually, the filibusterers gave up, allowing the House to reject the objection in the early hours of March 2. The House and Senate then reassembled to complete the count of the electoral votes. At 4:10 am on March 2, Senator Ferry announced that Hayes and Wheeler had been elected to the presidency and vice presidency, by an electoral margin of 185–184. The Democrats agreed not to block Hayes' inauguration based on a "back room" deal. Key to this deal was the understanding that federal troops would no longer interfere in Southern politics despite substantial election-associated violence against Blacks. The Southern states indicated that they would protect the lives of African Americans; however, such promises were largely not kept. Hayes' friends also let it be known that he would promote federal aid for internal improvements, including help with a railroad in Texas (which never happened) and name a Southerner to his cabinet (this did happen). With the end to the political role of Northern troops, the president had no method to enforce Reconstruction; thus, this "back room" deal signaled the end of American Reconstruction. After assuming office on March 4, 1877, President Hayes removed troops from the capitals of the remaining Reconstruction states, Louisiana and South Carolina, allowing the Redeemers to have full control of these states. President Grant had already removed troops from Florida, before Hayes was inaugurated, and troops from the other Reconstruction states had long since been withdrawn. Hayes appointed David M. Key from Tennessee, a Southern Democrat, to the position of postmaster general. By 1879, thousands of African American "Exodusters" packed up and headed to new opportunities in Kansas. The Democrats gained control of the Senate, and had complete control of Congress, having taken over the House in 1875. Hayes vetoed bills from the Democrats that outlawed the Republican Enforcement Acts; however, with the military underfunded, Hayes could not adequately enforce these laws. African-Americans remained involved in Southern politics, particularly in Virginia, which was run by the biracial Readjuster Party. Numerous African-Americans were elected to local office through the 1880s, and in the 1890s in some states, biracial coalitions of populists and Republicans briefly held control of state legislatures. In the last decade of the 19th century, Southern states elected five Black U.S. congressmen before disenfranchising state constitutions were passed throughout the former Confederacy. Legacy and historiography Besides the election of Southern black people to state governments and the United States Congress other achievements of the Reconstruction era include "the South’s first state-funded public school systems, more equitable taxation legislation, laws against racial discrimination in public transport and accommodations and ambitious economic development programs (including aid to railroads and other enterprises)." Despite these achievements the interpretation of Reconstruction has been a topic of controversy because nearly all historians hold that Reconstruction ended in failure, but for very different reasons. The first generation of Northern historians believed that the former Confederates were traitors and Johnson was their ally who threatened to undo the Union's constitutional achievements. By the 1880s, however, Northern historians argued that Johnson and his allies were not traitors but had blundered badly in rejecting the Fourteenth Amendment and setting the stage for Radical Reconstruction. The Black leader Booker T. Washington, who grew up in West Virginia during Reconstruction, concluded later that: "the Reconstruction experiment in racial democracy failed because it began at the wrong end, emphasizing political means and civil rights acts rather than economic means and self-determination". His solution was to concentrate on building the economic infrastructure of the Black community, in part by his leadership and the Southern Tuskegee Institute. Dunning School: 1900 to 1920s The Dunning School of scholars, who were trained at the history department of Columbia University under Professor William A. Dunning, analyzed Reconstruction as a failure after 1866 for different reasons. They claimed that Congress took freedoms and rights from qualified Whites and gave them to unqualified Blacks who were being duped by corrupt "carpetbaggers and scalawags". As T. Harry Williams (who was a sharp critic of the Dunning School) noted, the Dunning scholars portrayed the era in stark terms: Reconstruction was a battle between two extremes: the Democrats, as the group which included the vast majority of the whites, standing for decent government and racial supremacy, versus the Republicans, the Negroes, alien carpetbaggers, and renegade scalawags, standing for dishonest government and alien ideals. These historians wrote literally in terms of white and black. Revisionists and Beardians, 1930s–1940s In the 1930s, historical revisionism became popular among scholars. As disciples of Charles A. Beard, revisionists focused on economics, downplaying politics and constitutional issues. The central figure was a young scholar at the University of Wisconsin, Howard K. Beale, who in his PhD dissertation, finished in 1924, developed a complex new interpretation of Reconstruction. The Dunning School portrayed freedmen as mere pawns in the hands of the carpetbaggers. Beale argued that the carpetbaggers themselves were pawns in the hands of Northern industrialists, who were the real villains of Reconstruction. These industrialists had taken control of the nation during the Civil War, and set up high tariffs to protect their profits, as well as a lucrative national banking system and a railroad network fueled by government subsidies and secret payoffs. The return to power of the Southern Whites would seriously threaten all their gains, and so the ex-Confederates had to be kept out of power. The tool used by the industrialists was the combination of the Northern Republican Party and sufficient Southern support using carpetbaggers and Black voters. The rhetoric of civil rights for Blacks, and the dream of equality, was rhetoric designed to fool idealistic voters. Beale called it "claptrap", arguing: "Constitutional discussions of the rights of the Negro, the status of Southern states, the legal position of ex-rebels, and the powers of Congress and the president determined nothing. They were pure sham." President Andrew Johnson had tried, and failed, to stop the juggernaut of the industrialists. The Dunning School had praised Johnson for upholding the rights of the White men in the South and endorsing White supremacy. Beale was not a racist, and indeed was one of the most vigorous historians working for Black civil rights in the 1930s and 1940s. In his view, Johnson was not a hero for his racism, but rather for his forlorn battle against the industrialists. Charles A. Beard and Mary Beard had already published The Rise of American Civilization (1927) three years before Beale, and had given very wide publicity to a similar theme. The Beard–Beale interpretation of Reconstruction became known as "revisionism", and replaced the Dunning School for most historians, until the 1950s. The Beardian interpretation of the causes of the Civil War downplayed slavery, abolitionism, and issues of morality. It ignored constitutional issues of states' rights and even ignored American nationalism as the force that finally led to victory in the war. Indeed, the ferocious combat itself was passed over as merely an ephemeral event. Much more important was the calculus of class conflict. As the Beards explained in The Rise of American Civilization (1927), the Civil War was really a: social cataclysm in which the capitalists, laborers, and farmers of the North and West drove from power in the national government the planting aristocracy of the South. The Beards were especially interested in the Reconstruction era, as the industrialists of the Northeast and the farmers of the West cashed in on their great victory over the Southern aristocracy. Historian Richard Hofstadter paraphrases the Beards as arguing that in victory: the Northern capitalists were able to impose their economic program, quickly passing a series of measures on tariffs, banking, homesteads, and immigration that guaranteed the success of their plans for economic development. Solicitude for the freedmen had little to do with Northern policies. The Fourteenth Amendment, which gave the Negro his citizenship, Beard found significant primarily as a result of a conspiracy of a few legislative draftsmen friendly to corporations to use the supposed elevation of the blacks as a cover for a fundamental law giving strong protection to business corporations against regulation by state government. Wisconsin historian William Hesseltine added the point that the Northeastern businessmen wanted to control the Southern economy directly, which they did through ownership of the railroads. The Beard–Beale interpretation of the monolithic Northern industrialists fell apart in the 1950s when it was closely examined by numerous historians, including Robert P. Sharkey, Irwin Unger, and Stanley Coben. The younger scholars conclusively demonstrated that there was no unified economic policy on the part of the dominant Republican Party. Some wanted high tariffs and some low. Some wanted greenbacks and others wanted gold. There was no conspiracy to use Reconstruction to impose any such unified economic policy on the nation. Northern businessmen were widely divergent on monetary or tariff policy, and seldom paid attention to Reconstruction issues. Furthermore, the rhetoric on behalf of the rights of the freedmen was not claptrap but deeply-held and very serious political philosophy. The Black scholar W. E. B. Du Bois, in his Black Reconstruction in America, 1860–1880, published in 1935, compared results across the states to show achievements by the Reconstruction legislatures and to refute claims about wholesale African American control of governments. He showed Black contributions, as in the establishment of universal public education, charitable and social institutions and universal suffrage as important results, and he noted their collaboration with Whites. He also pointed out that Whites benefited most by the financial deals made, and he put excesses in the perspective of the war's aftermath. He noted that despite complaints, several states kept their Reconstruction era state constitutions into the early 20th century. Despite receiving favorable reviews, his work was largely ignored by White historians of his time. In the 1960s, neo-abolitionist historians emerged, led by John Hope Franklin, Kenneth Stampp, Leon Litwack, and Eric Foner. Influenced by the civil rights movement, they rejected the Dunning School and found a great deal to praise in Radical Reconstruction. Foner, the primary advocate of this view, argued that it was never truly completed, and that a "Second Reconstruction" was needed in the late 20th century to complete the goal of full equality for African Americans. The neo-abolitionists followed the revisionists in minimizing the corruption and waste created by Republican state governments, saying it was no worse than Boss Tweed's ring in New York City. Instead, they emphasized that suppression of the rights of African Americans was a worse scandal, and a grave corruption of America's republicanist ideals. They argued that the tragedy of Reconstruction was not that it failed because Blacks were incapable of governing, especially as they did not dominate any state government, but that it failed because Whites raised an insurgent movement to restore White supremacy. White-elite-dominated state legislatures passed disenfranchising state constitutions from 1890 to 1908 that effectively barred most Blacks and many poor Whites from voting. This disenfranchisement affected millions of people for decades into the 20th century, and closed African Americans and poor Whites out of the political process in the South. Re-establishment of White supremacy meant that within a decade African Americans were excluded from virtually all local, state, and federal governance in all states of the South. Lack of representation meant that they were treated as second-class citizens, with schools and services consistently underfunded in segregated societies, no representation on juries or in law enforcement, and bias in other legislation. It was not until the civil rights movement and the passage of the Civil Rights Act of 1964 and the Voting Rights Act of 1965 that segregation was outlawed and suffrage restored, under what is sometimes[when?] referred to as the "Second Reconstruction". In 1990, Eric Foner concluded that from the Black point of view "Reconstruction must be judged a failure." Foner stated Reconstruction was "a noble if flawed experiment, the first attempt to introduce a genuine inter-racial democracy in the United States". According to him, the many factors contributing to the failure included: lack of a permanent federal agency specifically designed for the enforcement of civil rights; the Morrison R. Waite Supreme Court decisions that dismantled previous congressional civil rights legislation; and the economic reestablishment of conservative White planters in the South by 1877. Historian William McFeely explained that although the constitutional amendments and civil rights legislation on their own merit were remarkable achievements, no permanent government agency whose specific purpose was civil rights enforcement had been created. More recent work by Nina Silber, David W. Blight, Cecelia O'Leary, Laura Edwards, LeeAnn Whites, and Edward J. Blum has encouraged greater attention to race, religion, and issues of gender while at the same time pushing the effective end of Reconstruction to the end of the 19th century, while monographs by Charles Reagan Wilson, Gaines Foster, W. Scott Poole, and Bruce Baker have offered new views of the Southern "Lost Cause". Dating the end of the Reconstruction era At the national level, textbooks typically date the era from 1865 to 1877. Eric Foner's textbook of national history Give Me Liberty is an example. His monograph Reconstruction: America's Unfinished Revolution, 1863–1877 (1988) focusing on the situation in the South, covers 1863 to 1865. While 1877 is the usual date given for the end of Reconstruction, some historians such as Orville Vernon Burton extend the era to the 1890s to include the imposition of segregation. Economic role of race Economists and economic historians have different interpretations of the economic impact of race on the postbellum Southern economy. In 1995, Robert Whaples took a random survey of 178 members of the Economic History Association, who studied American history in all time periods. He asked whether they wholly or partly accepted, or rejected, 40 propositions in the scholarly literature about American economic history. The greatest difference between economics PhDs and history PhDs came in questions on competition and race. For example, the proposition originally put forward by Robert Higgs, "in the post-bellum South economic competition among Whites played an important part in protecting blacks from racial coercion", was accepted in whole or part by 66% of the economists, but by only 22% of the historians. Whaples says this highlights: "A recurring difference dividing historians and economists. The economists have more faith in the power of the competitive market. For example, they see the competitive market as protecting disenfranchised blacks and are less likely to accept the idea that there was exploitation by merchant monopolists." The "failure" issue Reconstruction is widely considered a failure, though the reason for this is a matter of controversy. - The Dunning School considered failure inevitable because it felt that taking the right to vote or hold office away from Southern Whites was a violation of republicanism. - A second school sees the reason for failure as Northern Republicans' lack of effectiveness in guaranteeing political rights to Blacks. - A third school blames the failure on not giving land to the freedmen so they could have their own economic base of power. - A fourth school sees the major reason for the failure of Reconstruction as the states' inability to suppress the violence of Southern Whites when they sought reversal for Blacks' gains. Etcheson (2009) points to the "violence that crushed black aspirations and the abandonment by Northern whites of Southern Republicans". Etcheson wrote that it is hard to see Reconstruction "as concluding in anything but failure". Etcheson adds: "W. E. B. DuBois captured that failure well when he wrote in Black Reconstruction in America (1935): 'The slave went free; stood a brief moment in the sun; then moved back again toward slavery.'" - Other historians emphasize the failure to fully incorporate Southern Unionists into the Republican coalition. Derek W. Frisby points to "Reconstruction's failure to appreciate the challenges of Southern Unionism and incorporate these loyal Southerners into a strategy that would positively affect the character of the peace". Historian Donald R. Shaffer maintained that the gains during Reconstruction for African Americans were not entirely extinguished. The legalization of African American marriages and families and the independence of Black churches from White denominations were a source of strength during the Jim Crow era. Reconstruction was never forgotten within the Black community and it remained a source of inspiration. The system of sharecropping granted Blacks a considerable amount of freedom as compared to slavery. What remains certain is that Reconstruction failed, and that for Blacks its failure was a disaster whose magnitude cannot be obscured by the genuine accomplishments that did endure. However, in 2014, historian Mark Summers argued that the "failure" question should be looked at from the viewpoint of the war goals; in that case, he argues: If we see Reconstruction's purpose as making sure that the main goals of the war would be fulfilled, of a Union held together forever, of a North and South able to work together, of slavery extirpated, and sectional rivalries confined, of the permanent banishment of the fear of vaunting appeals to state sovereignty, backed by armed force, then Reconstruction looks like what in that respect it was, a lasting and unappreciated success. In popular culture The journalist Joel Chandler Harris, who wrote under the name "Joe Harris" for the Atlanta Constitution (mostly after Reconstruction), tried to advance racial and sectional reconciliation in the late 19th century. He supported Henry W. Grady's vision of a New South during Grady's time as editor from 1880 to 1889. Harris wrote many editorials in which he encouraged Southerners to accept the changed conditions along with some Northern influences, but he asserted his belief that change should proceed under White supremacy. In popular literature, two early 20th-century novels by Thomas Dixon Jr. – The Leopard's Spots: A Romance of the White Man's Burden – 1865–1900 (1902), and The Clansman: A Historical Romance of the Ku Klux Klan (1905) – idealized White resistance to Northern and Black coercion, hailing vigilante action by the Ku Klux Klan. D. W. Griffith adapted Dixon's The Clansman for the screen in his anti-Republican movie The Birth of a Nation (1915); it stimulated the formation of the 20th-century version of the KKK. Many other authors romanticized the supposed benevolence of slavery and the elite world of the antebellum plantations, in memoirs and histories which were published in the late 19th and early 20th centuries; the United Daughters of the Confederacy promoted influential works which were written in these genres by women. Of much more lasting impact was the story Gone with the Wind, first in the form of the best-selling 1936 novel, which enabled its author Margaret Mitchell to win the Pulitzer Prize, and an award-winning Hollywood blockbuster with the same title in 1939. In each case, the second half of the story focuses on Reconstruction in Atlanta. The book sold millions of copies nationwide; the film is regularly re-broadcast on television. In 2018, it remained at the top of the list of the highest-grossing films, adjusted in order to keep up with inflation. The New Georgia Encyclopedia argues: Politically, the film offers a conservative view of Georgia and the South. In her novel, despite her Southern prejudices, Mitchell showed clear awareness of the shortcomings of her characters and their region. The film is less analytical. It portrays the story from a clearly Old South point of view: the South is presented as a great civilization, the practice of slavery is never questioned, and the plight of the freedmen after the Civil War is implicitly blamed on their emancipation. A series of scenes whose racism rivals that of D. W. Griffith's film The Birth of a Nation (1915) mainly portrays Reconstruction as a time when Southern whites were victimized by freed slaves, who themselves were exploited by Northern carpetbaggers. Reconstruction state-by-state – significant dates Georgia was first readmitted to the U.S. Congress on July 25, 1868, but it was expelled on March 3, 1869. Virginia had been represented in the U.S. Senate until March 3, 1865, by the Restored Government of Virginia. in each state \|South Carolina\|\|December 20, 1860\|\|February 8, 1861\|\|June 25, 1868\|\|April 11, 1877\| \|Mississippi\|\|January 9, 1861\|\|February 8, 1861\|\|February 23, 1870\|\|January 4, 1876\| \|Florida\|\|January 10, 1861\|\|February 8, 1861\|\|June 25, 1868\|\|January 2, 1877\| \|Alabama\|\|January 11, 1861\|\|February 8, 1861\|\|June 25, 1868\|\|November 16, 1874\| \|Georgia\|\|January 19, 1861\|\|February 8, 1861\|\|July 15, 1870\|\|November 1, 1871\| \|Louisiana\|\|January 26, 1861\|\|February 8, 1861\|\|June 25, 1868\|\|January 2, 1877\| \|Texas\|\|February 1, 1861\|\|March 2, 1861\|\|March 30, 1870\|\|January 14, 1873\| \|Virginia\|\|April 17, 1861\|\|May 7, 1861\|\|January 26, 1870\|\|October 5, 1869\| \|Arkansas\|\|May 6, 1861\|\|May 18, 1861\|\|June 22, 1868\|\|November 10, 1874\| \|North Carolina\|\|May 20, 1861\|\|May 20, 1861\|\|June 25, 1868\|\|November 28, 1870\| \|Tennessee\|\|June 8, 1861\|\|July 2, 1861\|\|July 24, 1866\|\|October 4, 1869\| - Reconstruction Era National Monument - Category:African-American politicians during the Reconstruction Era - "The First Vote" by William Waud Harpers Weekly Nov. 16, 1867 - Rodrigue, John C. (2001). Reconstruction in the Cane Fields: From Slavery to Free Labor in Louisiana's Sugar Parishes, 1862–1880. Louisiana State University Press. p. 168. ISBN 978-0-8071-5263-8. - Lynn, Samara; Thorbecke, Catherine (September 27, 2020). "What America owes: How reparations would look and who would pay". ABC News. Retrieved February 24, 2021. - Guelzo 2018, pp. 11–12; Foner 2019, p. 198. - Foner 1988, p. xxv harvnb error: multiple targets (2×): CITEREFFoner1988 (help) - Foner, Eric (2017) . "'What Is Freedom?': Reconstruction, 1865–1877". Give Me Liberty! (5th ed.). W. W. Norton & Company. ISBN 978-0-393-60338-5. - Foner, Eric (Winter 2009). "If Lincoln hadn't died ..." American Heritage Magazine. 58 (6). Retrieved July 26, 2010. - Baker, Bruce E. (2007). What Reconstruction Meant: Historical Memory in the American South. - Blight, David W. (2001). Race and Reunion: The Civil War in American Memory. - Lemann, Nicholas. 2007. Redemption: The Last Battle of the Civil War. pp. 75–77. - Alexander, Thomas B. (1961). "Persistent Whiggery in the Confederate South, 1860–1877". Journal of Southern History 27(3):305–29. JSTOR 2205211. - Trelease, Allen W. 1976. "Republican Reconstruction in North Carolina: A Roll-call Analysis of the State House of Representatives, 1866–1870". Journal of Southern History 42(3):319–44. JSTOR 2207155. - Paskoff, Paul F. 2008. "Measures of War: A Quantitative Examination of the Civil War's Destructiveness in the Confederacy". Civil War History 54(1):35–62. doi:10.1353/cwh.2008.0007. - McPherson, James M. (1992). Abraham Lincoln and the Second American Revolution. Oxford University Press. p. 38. ISBN 978-0-19-507606-6. - Hesseltine, William B. 1936. A History of the South, 1607–1936. pp. 573–74. - Ezell, John Samuel. 1963. The South Since 1865. pp. 27–28. - Lash, Jeffrey N. 1993. "Civil-War Irony-Confederate Commanders And The Destruction Of Southern Railways". Prologue-Quarterly of the National Archives 25(1):35–47. - Goldin, Claudia D., and Frank D. Lewis. 1975. "The economic cost of the American Civil War: Estimates and implications". The Journal of Economic History 35(2):299–326. JSTOR 2119410. - Jones, Jacqueline (2010). Labor of Love, Labor of Sorrow: Black Women, Work, and the Family, from Slavery to the Present. New York: Basic Books. p. 72. - Hunter, Tera W. (1997). To 'Joy My Freedom: Southern Black Women's Lives and Labors after the Civil War. Cambridge, Massachusetts: Harvard University Press. pp. 21–73. - Downs, Jim. 2015. Sick from Freedom: African-American Illness and Suffering during the Civil War and Reconstruction. - Ransom, Roger L. (February 1, 2010). "The Economics of the Civil War". Archived from the original on December 13, 2011. Retrieved March 7, 2010. Direct costs for the Confederacy are based on the value of the dollar in 1860. - Donald, Civil War and Reconstruction (2001), ch. 26. - "The Second Inaugural Address" – via The Atlantic. - Harris, With Charity for All (1999). - Simpson (2009); Harris, William C. 1999. With Charity for All: Lincoln and the Restoration of the Union. - McPherson, James M. (1992). Abraham Lincoln and the Second American Revolution. Oxford University Press. p. 6. ISBN 978-0-19-507606-6. - Alexander, Leslie (2010). Encyclopedia of African American History. ABC-CLIO. p. 699. ISBN 9781851097746. - Donald, Civil War and Reconstruction (2001); Hans L. Trefousse, Andrew Johnson: A Biography (1989). - Donald, Civil War and Reconstruction (2001), ch. 26–27. - Forrest Conklin, "'Wiping Out' Andy" Johnson's Moccasin Tracks: The Canvass of Northern States By Southern Radicals, 1866." Tennessee Historical Quarterly 52.2 (1993): 122–133. - All Blacks would be counted in 1870, whether or not they were citizens. - Valelly, Richard M. (2004). The Two Reconstructions: The Struggle for Black Enfranchisement. University of Chicago Press. p. 29. ISBN 978-0-226-84530-2. - Trefouse, Hans (1975). The Radical Republicans. - Donald, Civil War and Reconstruction (2001), ch. 28–29. - Donald, Civil War and Reconstruction (2001), ch. 29. - Donald, 2001, Civil War and Reconstruction, ch. 30. - Hyman, Harold (1959) To Try Men's Souls: Loyalty Tests in American History, p. 93. - Foner 1988, pp. 273–276 harvnb error: multiple targets (2×): CITEREFFoner1988 (help) - Severance, Ben H., Tennessee's Radical Army: The State Guard and Its Role in Reconstruction, p. 59. - William Gienapp, Abraham Lincoln and Civil War America (2002), p. 155. - Patton, p. 126. - Johnson to Gov. William L. Sharkey, August 1865; quoted in Franklin (1961), p. 42. - Donald, Charles Sumner, p. 201. - Ayers, The Promise of the New South p. 418. - James D. Anderson, The Education of Blacks in the South, 1860–1935, pp. 244–245. - Randall and Donald, p. 581. - Eric Foner, Freedom's lawmakers: a directory of Black officeholders during Reconstruction (1993). - Ellen DuBois, Feminism and suffrage: The emergence of an independent women's movement in America (1978). - Glenn Feldman, The Disfranchisement Myth: Poor Whites and Suffrage Restriction in Alabama (2004), p. 136. - 25 U.S.C. Sec. 72. - "Act of Congress, R.S. Sec. 2080 derived from act July 5, 1862, ch. 135, Sec. 1, 12 Stat. 528". US House of Representatives. Archived from the original on March 17, 2012. Retrieved February 7, 2012 – via USCode.House.gov. - Perry, Dan W. (March 1936). "Oklahoma, A Foreordained Commonwealth". Chronicles of Oklahoma. Oklahoma Historical Society. 14 (1): 30. Retrieved February 8, 2012. - Cimbala, Miller, and Syrette (2002), An uncommon time: the Civil War and the northern home front, pp. 285, 305. - Wagner, Gallagher, and McPherson, The Library of Congress Civil War Desk Reference, pp. 735–736. - Williams (2006), "Doing Less" and "Doing More", pp. 54–59. - Guelzo, Allen C. (1999). Abraham Lincoln: Redeemer President. W.B. Eerdmans. pp. 290, 291. ISBN 9780802838728. - Trefousse (1991), Historical Dictionary of Reconstruction, p. viiii. - "Abraham Lincoln". BlueAndGrayTrail.com. Retrieved July 21, 2010. - Guelzo, Allen C. (1999). Abraham Lincoln: Redeemer President. W.B. Eerdmans. pp. 333–335. ISBN 9780802838728. - Catton (1963), Terrible Swift Sword, pp. 365–367, 461–468. - Guelzo, Allen C. (1999). Abraham Lincoln: Redeemer President. W.B. Eerdmans. p. 390. ISBN 9780802838728. - Hall, Clifton R. (1916). Andrew Johnson: military governor of Tennessee. Princeton University Press. p. 19. Retrieved July 24, 2010. - Guelzo (2004), Lincoln's Emancipation Proclamation: The End of Slavery in America, p. 1. - Sick from Freedom, New York: Oxford University Press, 2012. - Stauffer (2008), Giants, p. 279. - Peterson (1995) Lincoln in American Memory, pp. 38–41. - McCarthy (1901), Lincoln's plan of Reconstruction, p. 76. - Stauffer (2008), Giants, p. 280. - Harris, J. William (2006). The Making of the American South: A Short History 1500–1977. Malden, Massachusetts: Blackwell Publishing. p. 240. - Edwards, Laura F. (1997). Gendered Strife and Confusion: The Political Culture of Reconstruction. Chicago: University of Illinois Press. p. 53. ISBN 978-0-252-02297-5. - Hunter, "To 'Joy My Freedom", p. 34. - Mikkelson, David. "'Black Tax' Credit". Snopes. - Zebley, Kathleen (1998). "Freedmen's Bureau". Retrieved April 29, 2010. - Belz (1998), Abraham Lincoln, Constitutionalism, and Equal Rights in the Civil War Era, pp. 138, 141, 145. - Rawley (2003), Abraham Lincoln and a nation worth fighting for. p. 205. - McFeely (2002), Grant: A Biography, pp. 198–207. - William C. Harris, With Charity for All: Lincoln and the Restoration of the Union (1997). - Trefousse c.1989. - Smith, John David (2013). A Just and Lasting Peace: A Documentary History of Reconstruction. Penguin. p. 17. ISBN 9781101617465. - McKitrick, Eric L. (1988). Andrew Johnson and Reconstruction. Oxford University Press. p. 172. ISBN 9780195057072. - Billington, Ray Allen; Ridge, Martin (1981). American History After 1865. Rowman & Littlefield. p. 3. ISBN 9780822600275. - Lincove, David A. (2000). Reconstruction in the United States: An Annotated Bibliography. Greenwood. p. 80. ISBN 9780313291999. - McFeely-Woodward (1974), p. 125. - Barney, William L., The Passage of the Republic: An Interdisciplinary History of Nineteenth-Century America (1987), p. 245. - Donald, Civil War and Reconstruction (2001), ch. 31. - Oberholtzer 1:128–129. - Donald (2001), p. 527. - Hunter, p. 67. - Barney, The Passage of the Republic, pp. 251, 284–286. - Schurz, Carl (December 1865). Report on the Condition of the South (Report). U.S. Senate Exec. Doc. No. 2, 39th Congress, 1st session. Archived from the original on October 14, 2007. - Blackmon, Douglas A. (2009). Slavery by Another Name: The Re-enslavement of Black Americans from the Civil War to World War II. New York: Anchor Books. p. 16. - Edwards, Laura F. (1997). Gendered Strife and Confusion: The Political Culture of Reconstruction. Chicago: University of Illinois Press. p. 202. ISBN 978-0-252-02297-5. - Farmer-Kaiser, Mary (2010). Freedwomen and the Freedmen's Bureau: Race, Gender, and Public Policy in the Age of Emancipation. New York: Fordham University Press. p. 160. - Jones, "Labor of Love, Labor of Sorrow", p. 70. - Schouler, James (1913). History of the United States of America under the Constitution, Vol. 7: The Reconstruction Period. Kraus Reprints. pp. 43–57. Retrieved July 3, 2010. - Rhodes, History, 6: 65–66. - Foner, Eric; Mahoney, Olivia (2016). "America's Reconstruction: People and Politics After the Civil War". Digital History Project, University of Houston. image 11 of 40. Archived from the original on September 24, 2006. Retrieved October 11, 2006. - Rhodes, History 6: 68. - Trefousse 1989. - Alexander, Leslie M.; Rucker, Walter C. (2010). Encyclopedia of African American History. p. 699. ISBN 978-1-85109-774-6. - Badeau (1887) Grant in Peace, pp. 46, 57. - Teed, Paul E.; Ladd Teed, Melissa (2015). Reconstruction: A Reference Guide. ABC-CLIO. pp. 51, 174 ff. ISBN 978-1-61069-533-6.. Foner (1988) entitles his sixth chapter "The Making of Radical Reconstruction". Benedict argues the Radical Republicans were conservative on many other issues, in: Benedict, Michael Les (1974). "Preserving the Constitution: The Conservative Basis of Radical Reconstruction". Journal of American History. 61 (1): 65–90. doi:10.2307/1918254. JSTOR 1918254. - Kolchin, Peter (1967). "The Business Press and Reconstruction, 1865–1868". Journal of Southern History. 33 (2): 183–196. doi:10.2307/2204965. JSTOR 2204965. - Pope, James Gray (Spring 2014). "Snubbed landmark: Why United States v. Cruikshank (1876) belongs at the heart of the American constitutional canon" (PDF). Harvard Civil Rights–Civil Liberties Law Review. 49 (2): 385–447. - Greene, Jamal (November 2012). "Thirteenth Amendment optimism". Columbia Law Review. 112 (7): 1733–1768. JSTOR 41708163. Archived from the original on January 7, 2015. PDF version. - "1875". A Century of Lawmaking for a New Nation: U.S. Congressional Documents and Debates, 1774. Retrieved October 21, 2020. - 28 U.S.C. § 2254. - Foner 1988, ch. 6 harvnb error: multiple targets (2×): CITEREFFoner1988 (help) - Journal of the Senate of the State of West Virginia for the Sixth Session, Commencing January 21, 1868, John Frew, Wheeling, 1868, p. 10 - Phillips, Christopher, The Rivers Ran Backward: The Civil War and the Remaking of the American Middle Border, Oxford Univ. Press, 2016, p. 296, ISBN 9780199720170 - Chin, Gabriel Jackson (September 14, 2004). "Gabriel J. Chin, "The 'Voting Rights Act of 1867': The Constitutionality of Federal Regulation of Suffrage During Reconstruction", 82 North Carolina Law Review 1581 (2004)". Papers.ssrn.com. SSRN 589301. Cite journal requires - Foner 1988, ch. 6–7 harvnb error: multiple targets (2×): CITEREFFoner1988 (help) - Foner 1988, pp. 274–275 harvnb error: multiple targets (2×): CITEREFFoner1988 (help) - Randolph Campbell (2003), Gone to Texas, p. 276. - Rhodes (1920), Vol. 6, p. 199. - Foner 1988, pp. 316–333 harvnb error: multiple targets (2×): CITEREFFoner1988 (help) - Hume, Richard L.; Gough, Jerry B. (2008). Blacks, Carpetbaggers, and Scalawags: the Constitutional Conventions of Radical Reconstruction. LSU Press. - Jenkins, Jeffery A.; Heersink, Boris (2016). "Republican Party Politics and the American South: From Reconstruction to Redemption, 1865–1880" (PDF): 18. Cite journal requires - Russ, William A., Jr. (1934). "The Negro and White Disfranchisement During Radical Reconstruction". Journal of Negro History. 19 (2): 171–192. doi:10.2307/2714531. JSTOR 2714531. S2CID 149894321. - Mark Wahlgren Summers, The Ordeal of the Reunion: A New History of Reconstruction (2014), pp. 130–131, 159. - Foner 1988, pp. 323–25 harvnb error: multiple targets (2×): CITEREFFoner1988 (help) - Summers, Mark Wahlgren (2014). Railroads, Reconstruction, and the Gospel of Prosperity: Aid Under the Radical Republicans, 1865–1877. Princeton University Press. ISBN 978-0-691-61282-9. - Tyack, David; Lowe, Robert (1986). "The constitutional moment: Reconstruction and Black education in the South". American Journal of Education. 94 (2): 236–256. doi:10.1086/443844. JSTOR 1084950. S2CID 143849662. - Cooper, William J., Jr.; Terrill, Thomas E. (2009). The American South: A History. p. 436. ISBN 978-0-7425-6450-3. - Zuczek, Richard, ed. (2006). Encyclopedia of the Reconstruction Era. 2. p. 635. - Perman, Michael (1985). The Road to Redemption: Southern Politics, 1869–1879. pp. 36–37. Foner 1988, p. 324 harvnb error: multiple targets (2×): CITEREFFoner1988 (help) - Gillette (1982), Retreat from Reconstruction, 1869–1879, p. 99. - Zuczek (2006), Encyclopedia of the Reconstruction Era; 1: 323; 2: 645, 698. - Summers, The Ordeal of the Reunion pp. 160–61. - Smith Grant (2001), pp. 455–457. - Calhoun 2017, pp. 41–42. - Simpson, Brooks D. "Ulysses S. Grant and the Freedmen's Bureau", in The Freedmen's Bureau and Reconstruction: Reconsiderations, edited by Paul A. Cimbala and Randall M. Miller. New York: Fordham University Press, 1999. - Smith (2001). - Grant, pp. 437–453, 458–460. - Montgomery, David (1967). Beyond Equality: Labor and the Radical Republicans, 1862–1872. New York: Alfred Knopf. pp. 130–133. ISBN 9780252008696. Retrieved October 9, 2020. - Gleeson, David (2016) Failing to 'unite with the abolitionists': the Irish Nationalist Press and U.S. emancipation. Slavery & Abolition, 37 (3). pp. 622–637. ISSN 0144-039X - Knight, Matthew (2017). "The Irish Republic: Reconstructing Liberty, Right Principles, and the Fenian Brotherhood". Éire-Ireland (Irish-American Cultural Institute). 52 (3 & 4): 252–271. doi:10.1353/eir.2017.0029. S2CID 159525524. Retrieved October 9, 2020. - Yanoso, Nicole Anderson (2017). The Irish and the American Presidency. New York: Routledge. pp. 75–80. ISBN 9781351480635. - Simon 2002, p. 245. - Peters & Woolley 2018b. - Smith 2001, p. 461. - Calhoun 2017, p. 55. - Foner 2014, pp. 243–44. - McFeely 1981, p. 284; Smith 2001, p. 461; White 2016, p. 471. - Kahan 2018, p. 61. - Simon (1967), Papers of Ulysses S. Grant, Vol. 19, p. xiii. - Osborne & Bombaro 2015, pp. 6, 12, 54 sfnm error: no target: CITEREFOsborneBombaro2015 (help); Chernow 2017, p. 629. - Chernow 2017, p. 628. - Simon 2002. - Brands 2012, pp. 435, 465; Chernow 2017, pp. 686–87; Simon 2002, p. 247. - Brands 2012, p. 465. - Simon 2002, p. 246. - Simon 2002, pp. 247–48. - Smith 2001, pp. 543–45; Brands 2012, p. 474. - Robert J. Kaczorowski, "Federal Enforcement of Civil Rights During the First Reconstruction". Fordham Urban Law Journal 23 (1995): pp. 155 ff. online. - Kahan 2018, pp. 64–65; Calhoun 2017, pp. 317–319. - Smith 2001, pp. 545–546; White 2016, p. 521; Simon 2002, p. 248; Kahan 2018, pp. 64–65; Calhoun 2017, pp. 317–319. - Report of the Joint Select Committee to Inquire into the Condition of Affairs in the Late Insurrectionary States February 19, 1872 Viewed on 1-13-2021 - Simon 2002, p. 248. - Kahan 2018, p. 66. - Smith 2001, p. 547; Calhoun 2017, p. 324. - Smith 2001, p. 547. - Smith 2001, pp. 547–48; Foner 2019, pp. 120–122. - Kahan 2018, p. 122. - Wang 1997, p. 102; Kaczorowski 1995, p. 182. - Chernow 2017, p. 746. - Kahan 2018, pp. 67–68; Chernow 2017, pp. 746. - Chernow 2017, p. 795; Calhoun 2017, p. 479. - Chernow 2017, p. 795. - David Quigley, "Constitutional Revision and the City: The Enforcement Acts and Urban America, 1870–1894", Journal of Policy History, January 2008, Vol. 20, Issue 1, pp. 64–75. - Blair (2005), p. 400. - Smith (2001), Grant, p. 547. - Georgia had a Republican governor and legislature, but the Republican hegemony was tenuous at best, and Democrats continued to win presidential elections there. See 1834 March 28 article in This Day in Georgia History compiled by Ed Jackson and Charles Pou; cf. Rufus Bullock. - McPherson, James M. (1992). Abraham Lincoln and the Second American Revolution. Oxford University Press. p. 19. ISBN 978-0-19-507606-6. - "Date of Secession Compared to 1860 Black Population". America's Civil War. Sewanee: The University of the South. Archived from the original on August 16, 2014. Retrieved April 9, 2014. - Foner 1988, ch. 7 harvnb error: multiple targets (2×): CITEREFFoner1988 (help); Foner, Freedom's Lawmakers, introduction. - Steven Hahn, A Nation under Our Feet - Rhodes (1920) v 6 p. 199; no report on Arkansas. - "Table I. Population of the United States (by States and Territories) in the Aggregate and as White, Colored, Free Colored, Slave, Chinese, and Indian, at Each Census" (PDF). Population by States and Territories – 1790–1870. United States Census Bureau. 1872. Retrieved October 20, 2007. The complete 1870 census documents are available from Census.gov. - Foner, Eric (January 31, 2018). "South Carolina's Forgotten Black Political Revolution". Slate. Retrieved February 3, 2020. - Foner, Eric (1988). Reconstruction: America's Unfinished Revolution, 1863–1877. New York: Harper & Row. pp. 354–355. ISBN 0-06-015851-4. - Stowell, Daniel W. (1998). Rebuilding Zion: The Religious Reconstruction of the South, 1863–1877. Oxford University Press. pp. 83–84. ISBN 978-0-19-802621-1. - Walker, Clarence Earl (1982). A Rock in a Weary Land: The African Methodist Episcopal Church During the Civil War and Reconstruction. - Sweet, William W. (1914). "The Methodist Episcopal Church and Reconstruction". Journal of the Illinois State Historical Society. 7 (3): 157. JSTOR 40194198. - Grant, Donald Lee (1993). The Way It Was in the South: The Black Experience in Georgia. University of Georgia Press. p. 264. ISBN 978-0-8203-2329-9. - Foner, Reconstruction, (1988) p. 93 - Ralph E. Morrow, "Northern Methodism in the South during Reconstruction", Mississippi Valley Historical Review (1954) 41#2 pp. 197–218, quote on p. 202 JSTOR 1895802 - Ralph E. Morrow, Northern Methodism and Reconstruction (1956) - Stowell, Rebuilding Zion: The Religious Reconstruction of the South, 1863–1877, pp. 30–31 - Robert D. Clark, The Life of Matthew Simpson (1956) pp. 245–267 - Norwood, Fredrick A., ed. (1982). Sourcebook of American Methodism. p. 323. - Sweet, William W. (1914). "The Methodist Episcopal Church and Reconstruction". Journal of the Illinois State Historical Society. 7 (3): 161. JSTOR 40194198. - Victor B. Howard, Religion and the Radical Republican Movement, 1860–1870 (1990) pp. 212–13 - Morrow (1954) p. 205 - Fallin, Wilson, Jr. (2007). Uplifting the People: Three Centuries of Black Baptists in Alabama. pp. 52–53. - Anderson, James D. (1988). The Education of Blacks in the South, 1860–1935. University of North Carolina Press. p. 4. - Anderson 1988, pp. 6–15. - Tyack and Lowe. "The constitutional moment: Reconstruction and Black education in the South". (1986): - William Preston Vaughn, Schools for All: The Blacks and Public Education in the South, 1865–1877 (University Press of Kentucky, 2015). - Foner 365–368 - Franklin 139 - Lynch 1913. - B. D. Mayberry, A Century of Agriculture in the 1890 Land Grant Institutions and Tuskegee University, 1890–1990 (1992). - Logan, Trevon D. (2020). "Do Black Politicians Matter? Evidence from Reconstruction". The Journal of Economic History. 80 (1): 1–37. doi:10.1017/S0022050719000755. ISSN 0022-0507. - Foner 387. - Franklin pp. 141–48; Summers 1984 - Stover 1955. - Franklin pp. 147–148. - Foner 375. - Foner 376. - Foner 415–16 - Schell, Herbert S. (1930). "Hugh McCulloch and the Treasury Department, 1865–1869". Mississippi Valley Historical Review. 17 (3): 404–421. doi:10.2307/1893078. JSTOR 1893078. - For an econometric approach, see: Ohanian, Lee E. (2018). The Macroeconomic Effects of War Finance in the United States: Taxes, Inflation, and Deficit Finance. Routledge. - Schell, 1930. - Margaret G. Myers, A financial history of the United States (Columbia UP, 1970), pp 174–196. - Studenski, Paul; Kroos, Herman E. (1963). Financial History of the United States (2nd ed.). - Unger, Irwin (1964). The Greenback Era: A Social and Political History of American Finance 1865–1879. Princeton University Press. - Sharkey, Robert P. (1967). Money, Class, and Party: An Economic Study of Civil War and Reconstruction. Johns Hopkins Press. - Franklin (1961), pp. 168–173. - Steedman, Marek D. (Spring 2009). "Resistance, Rebirth, and Redemption: The Rhetoric of White Supremacy in Post-Civil War Louisiana". Historical Reflections. 35 (1): 97–113. - Fleming, Walter L. (1919). The Sequel of Appomattox: A Chronicle of the Reunion of the States. Chronicles of America series, Vol. 32. New Haven: Yale University Press. p. 21. ISBN 9780554271941. - Perman 1984, p. 6. - T. Harry Williams, "An Analysis of Some Reconstruction Attitudes", Journal of Southern History Vol. 12, No. 4 (November 1946), pp. 469–486 JSTOR 2197687. - Walter L. Fleming, Documentary History of the Reconstruction (1907), II, p. 328. - Fleming, Documentary History of the Reconstruction (1907), II, pp. 328–329. - Oberholtzer, Vol. 1, p. 485. - Trelease, White Terror. - McFeely (2002), Grant: A Biography, pp. 420–422. - J. W. Schuckers, The Life and Public Services of Salmon Portland Chase, (1874), p. 585; letter of May 30, 1868 to August Belmont. - McPherson 1975. - Vaughn, Stephen L., ed. (2007). Encyclopedia of American Journalism. p. 441. - Abbott, Richard H. (2004). For Free Press and Equal Rights: Republican Newspapers in the Reconstruction South. - Earl F. Woodward, "The Brooks and Baxter War in Arkansas, 1872–1874", Arkansas Historical Quarterly (1971) 30#4 pp. 315–336 JSTOR 40038083 - Foner 537–541. - Foner 374–375. - Lynch 1915 - Perman 1984, ch. 3. - Foner, ch. 9. - Foner p. 443. - Foner pp. 545–547. - Nicholas Lemann, Redemption: The Last Battle of the Civil War, New York: Farrar, Straus & Giroux, Pbk. 2007, pp. 15–21. - US Senate Journal, January 13, 1875, pp. 106–107. - Alexander, Danielle (January–February 2004). "Forty Acres and a Mule: The Ruined Hope of Reconstruction". Humanities. 25 (1). Archived from the original on September 16, 2008. Retrieved April 14, 2008. - Foner 555–56. - Rable, George C. (1984). But There Was No Peace: The Role of Violence in the Politics of Reconstruction. Athens: University of Georgia Press. p. 132. - Foner ch. 11. - Nicholas Lemann, Redemption: The Last Battle of the Civil War, New York: Farrar, Straus & Giroux, paperback, 2007, p. 174. - Chacón, Mario L.; Jensen, Jeffrey L. (2020). "Democratization, De Facto Power, and Taxation: Evidence from Military Occupation during Reconstruction". World Politics. 72: 1–46. doi:10.1017/S0043887119000157. ISSN 0043-8871. S2CID 211320983. - Foner 604. - "HarpWeek \| Hayes vs. Tilden: The Electoral College Controversy of 1876–1877". elections.harpweek.com. Retrieved May 14, 2021. - C. Vann Woodward, Reunion and reaction: the compromise of 1877 and the end of reconstruction (1956), pp. 3–15 - Nell Irvin Painter, Exodusters: Black Migration to Kansas After Reconstruction (1976) - James T. Moore, "Black Militancy in Readjuster Virginia, 1879–1883", Journal of Southern History, Vol. 41, No. 2 (May 1975), pp. 167–186 JSTOR 2206012. - "Reconstruction". History.com. Archived from the original on January 24, 2021. Retrieved January 24, 2021. - Fletcher M. Green, "Walter Lynwood Fleming: Historian of Reconstruction", The Journal of Southern History, Vol. 2, No. 4 (November 1936), pp. 497–521. - Louis R. Harlan, Booker T. Washington in Perspective (1988), p. 164; A. A. Taylor, "Historians of the Reconstruction", The Journal of Negro History, Vol. 23, No. 1 (January 1938), pp. 16–34. - Williams, T. Harry (November 1946). "An Analysis of Some Reconstruction Attitudes". Journal of Southern History. 12 (4): 473. JSTOR 2197687. - Beale, The Critical Year, p. 147 - Tulloch, Hugh (1999). The Debate on the American Civil War Era. Manchester University Press. p. 226. ISBN 978-0-7190-4938-5. - Charles, Allan D. (1983). "Howard K Beale". In Wilson, Clyde N. (ed.). Twentieth-century American Historians. Gale Research. pp. 32–38. - Williams, T. Harry (1946). "An Analysis of Some Reconstruction Attitudes". Journal of Southern History. 12 (4): 469–486. doi:10.2307/2197687. JSTOR 2197687. Williams was a Northerner trained in Wisconsin. - Charles A. Beard and Mary R. Beard, The Rise of American Civilization (1927), 2:54 - Hofstadter, Richard (2012) . Progressive Historians. Knopf Doubleday. p. 303. ISBN 978-0-307-80960-5. - Hesseltine, William B. (1935). "Economic Factors in the Abandonment of Reconstruction". Mississippi Valley Historical Review. 22 (2): 191–210. doi:10.2307/1898466. JSTOR 1898466. - Coben, Stanley (1959). "Northeastern Business and Radical Reconstruction: A Re-examination". The Mississippi Valley Historical Review. 46 (1): 67–90. doi:10.2307/1892388. JSTOR 1892388. - Pressly, Thomas J. (1961). "Andrew Johnson and Reconstruction (review)". Civil War History. 7: 91–92. doi:10.1353/cwh.1961.0063. - Montgomery, David (1961). "Radical Republicanism in Pennsylvania, 1866–1873". The Pennsylvania Magazine of History and Biography. 85 (4): 439–457. JSTOR 20089450. - Kenneth M. Stampp and Leon F. Litwack, eds., Reconstruction: An Anthology of Revisionist Writings (1969) pp. 85–106 - Foner 1982; Montgomery, pp. vii–ix. - Du Bois, W. E. B. (1999) . Black Reconstruction in America, 1860–1880. Simon & Schuster. ISBN 9780684856575 – via Google Books. - Williams, 469; Foner p. xxii. - Feldman, Glenn (2004). The Disfranchisement Myth: Poor Whites and Suffrage Restriction in Alabama. Athens: University of Georgia Press. pp. 135–136. - Pildes, Richard H. (2000). "Democracy, Anti-democracy, and the Canon". Constitutional Commentary. 17: 27. Retrieved March 15, 2008. - Foner, A Short History of Reconstruction (1990), p. 255. Foner adds: "What remains certain is that Reconstruction failed, and that for blacks its failure was a disaster whose magnitude cannot be obscured by the accomplishments that endured." p. 256. - Although Grant and Attorney General Amos T. Akerman set up a strong legal system to protect African Americans, the Department of Justice did not set up a permanent Civil Rights Division until the Civil Rights Act of 1957. McFeely (2002), Grant: A Biography, pp. 372–373; 424, 425. - Brown, Thomas J., ed. (2008). Reconstructions: New Perspectives on the Postbellum United States. - See Give Me Liberty - See, e.g., Orville Vernon Burton, The Age of Lincoln (2007), p. 312. - Whaples, Robert (March 1995). "Where Is There Consensus Among American Economic Historians? The Results of a Survey on Forty Propositions". The Journal of Economic History. 55 (1): 139–154. doi:10.1017/S0022050700040602. JSTOR 2123771. - Burton, Vernon (2006). "Civil War and Reconstruction". In Barney, William L. (ed.). A Companion to 19th-century America. pp. 54–56. - Etcheson, Nicole (June 2009). "Reconstruction and the Making of a Free-Labor South". Reviews in American History. 37 (2): 236–242. doi:10.1353/rah.0.0101. S2CID 146573684. - Frisby, Derek W. (2010). "A Victory Spoiled: West Tennessee Unionists During Reconstruction". In Cimballa, Paul (ed.). The Great Task Remaining Before Us: Reconstruction as America's Continuing Civil War. p. 9. - Zuczek (2006), Encyclopedia of the Reconstruction Era, Vol. A–L, pp. 20, 22. - Foner 1988, p. 604 harvnb error: multiple targets (2×): CITEREFFoner1988 (help) reprinted in: Couvares, Francis G.; et al., eds. (2000). Interpretations of American History Vol. I Through Reconstruction (7th ed.). p. 409. ISBN 978-0-684-86773-1. - Summers, Mark Wahlgren (2014). The Ordeal of the Reunion: A New History of Reconstruction. University of North Carolina Press. p. 4. ISBN 978-1-4696-1757-2. - Mixon, Wayne (1977). "Joel Chandler Harris, the Yeoman Tradition, and the New South Movement". The Georgia Historical Quarterly. 61 (4): 308–317. JSTOR 40580412. - Bloomfield, Maxwell (1964). "Dixon's The Leopard's Spots: A Study in Popular Racism". American Quarterly. 16 (3): 387–401. doi:10.2307/2710931. JSTOR 2710931. - Gardner, Sarah E. (2006). Blood and Irony: Southern White Women's Narratives of the Civil War, 1861–1937. University of North Carolina Press. pp. 128–130. ISBN 9780807857670. - Ruppersburg, Hugh; Dobbs, Chris (2017). "Gone With the Wind (Film)". New Georgia Encyclopedia. - Matthews, James M., ed. (1864). The Statutes at Large of the Provisional Government of the Confederate States of America, from the Institution of the Government, February 8, 1861, to its Termination, February 18, 1862, Inclusive; Arranged in Chronological Order. Richmond: R. M. Smith. p. 8 – via Internet Archive. - Matthews (1864), p 104. - Matthews (1864), p 120. - Matthews (1864), p 118. - Journal of the Convention of the People of North Carolina, Held on the 20th Day of May, A. D. 1861. Raleigh: Jno. W. Syme. 1862. p. 18. LCCN 02014915. OCLC 6786362. OL 13488372M – via Internet Archive. - Matthews (1864), p 119. - "Tennessee Admitted as a Member of the Confederacy". Louisville Daily Courier. 33 (6). July 6, 1861. p. 1. Scholarly secondary sources For much more detail see Reconstruction: Bibliography - Barney, William L. Passage of the Republic: An Interdisciplinary History of Nineteenth Century America (1987). D. C. Heath ISBN 0-669-04758-9 - Behrend, Justin. Reconstructing Democracy: Grassroots Black Politics in the Deep South after the Civil War. Athens, Georgia: University of Georgia Press, 2015. - Blair, William (2005). "The use of military force to protect the gains of reconstruction". Civil War History. 51 (4): 388–402. doi:10.1353/cwh.2005.0055. - Blum, Edward J. Reforging the White Republic: Race, Religion, and American Nationalism, 1865–1898 (2005). - Bradley, Mark L. Bluecoats and Tar Heels: Soldiers and Civilians in Reconstruction North Carolina (University Press of Kentucky, 2009), 370 pp. ISBN 978-0-8131-2507-7 - Brands, H. W. (2012). The Man Who Saved the Union: Ulysses S. Grant in War and Peace. New York: Doubleday. ISBN 978-0-385-53241-9. - Brown, Thomas J., ed. Reconstructions: New Perspectives on Postbellum America (2006), essays by 8 scholars excerpt and text search - Calhoun, Charles W. (2017). The Presidency of Ulysses S. Grant. Lawrence: University Press of Kansas. ISBN 978-0-7006-2484-3. scholarly review and response by Calhoun at doi:10.14296/RiH/2014/2270 - Chernow, Ron (2017). Grant. New York: Penguin Press. ISBN 978-1-59420-487-6. - Cimbala, Paul Alan; Miller, Randall M.; Simpson, Brooks D. (2002). An Uncommon Time: The Civil War and the Northern Home Front. Fordham University Press. ISBN 978-0-8232-2195-0. - Cruden, Robert. The Negro in Reconstruction.[full citation needed] - Donald, David H.; et al. Civil War and Reconstruction (2001). - Downs, Gregory P. After Appomattox: Military Occupation and the Ends of War. Cambridge, Massachusetts: Harvard University Press, 2015. - Du Bois, W. E. B. Black Reconstruction in America 1860–1880 (1935), Counterpoint to Dunning School explores the economics and politics of the era from Marxist perspective - Du Bois, W. E. B. "Reconstruction and its Benefits", American Historical Review, 15 (July 1910), 781—799 online edition - Dunning, William Archibald. Reconstruction: Political & Economic, 1865–1877 (1905). Influential summary of Dunning School; blames Carpetbaggers for failure of Reconstruction. online edition - Egerton, Douglas (2014). The Wars of Reconstruction: The Brief, Violent History of America's Most Progressive Era. Bloomsbury Press. ISBN 978-1-60819-566-4. - Etcheson, Nicole. "Reconstruction and the Making of a Free-labor South", Reviews in American History, Volume 37, Number 2, June 2009 in Project MUSE - Fitzgerald, Michael W. Splendid Failure: Postwar Reconstruction in the American South (2007), 224pp; excerpt and text search - Fitzgerald, Michael R. Reconstruction in Alabama: From Civil War to Redemption in the Cotton South (LSU Press, 2017) 464 pages; a standard scholarly history - Fleming, Walter L. The Sequel of Appomattox, A Chronicle of the Reunion of the States (1918). From Dunning School. - Fleming, Walter L. Civil War and Reconstruction in Alabama (1905). the most detailed study; Dunning School full text online from Project Gutenberg - Foner, Eric and Mahoney, Olivia. America's Reconstruction: People and Politics After the Civil War. ISBN 0-8071-2234-3 - Foner, Eric (1988). Reconstruction: America's Unfinished Revolution, 1863–1877. New York: Harper & Row. ISBN 0-06-015851-4. Pulitzer-prize winning history, and most detailed synthesis of original and previous scholarship. - Foner, Eric. Forever Free: The Story of Emancipation and Reconstruction. 2005. - Foner, Eric (2019). The Second Founding How The Civil War And Reconstruction Remade The Constitution. New York: W.W. Norton & Company, Inc. ISBN 978-0-393-35852-0. - Franklin, John Hope. Reconstruction after the Civil War (1961), 280 pages. ISBN 0-226-26079-8. - Guelzo, Allen C. (2004). Lincoln's Emancipation Proclamation: The End of Slavery in America. New York: Simon & Schuster Paperbacks. ISBN 978-1-4165-4795-2. - Guelzo, Allen C. (2018). Reconstruction A Concise History (Hardcover). Oxford University Press. p. 180. ISBN 9780190865696. - Harris, William C. With Charity for All: Lincoln and the Restoration of the Union (1997) portrays Lincoln as opponent of Radicals. - Henry, Robert Selph. The Story of Reconstruction (1938), popular - Holzer, Harold; Medford, Edna Greene; Williams, Frank J. (2006). The Emancipation Proclamation: Three Views (Social, Political, Iconographic). Louisiana State University Press. ISBN 978-0-8071-3144-2. - Hubbs, G. Ward. Searching for Freedom after the Civil War: Klansman, Carpetbagger, Scalawg, and Freedman. Tuscaloosa: University of Alabama Press, 2015. - Jenkins, Wilbert L. Climbing up to Glory: A Short History of African Americans During the Civil War and Reconstruction (2002). - Kaczorowski, Robert J. (1995). "Federal Enforcement of Civil Rights During the First Reconstruction". Fordham Urban Law Journal. 23 (1): 155–86. ISSN 2163-5978. - Kahan, Paul (2018). The Presidency of Ulysses S. Grant: Preserving the Civil War's Legacy. Yardley, PA: Westholme Publishing, LLC. ISBN 978-1-59416-273-2. - Keith, LeeAnna. When It Was Grand: The Radical Republican History of the Civil War (2020) excerpt; also online review - Litwack, Leon. Been in the Storm So Long (1979). Pulitzer Prize; social history of the freedmen - McPherson, James and James Hogue. Ordeal By Fire: The Civil War and Reconstruction (2009) - Milton, George Fort. The Age of Hate: Andrew Johnson and the Radicals. (1930). online edition; from Dunning School - McCarthy, Charles Hallan (1901). Lincoln's Plan of Reconstruction. New York: McClure, Philips, & Company. - McFeely, William S. (1981). Grant: A Biography. Norton. ISBN 0-393-01372-3. - —— (1974). Woodward, C. Vann (ed.). Responses of the Presidents to Charges of Misconduct. New York: Delacorte Press. ISBN 978-0-440-05923-3. - Patrick, Rembert. The Reconstruction of the Nation (1967) online - Perman, Michael. The Road to Redemption: Southern Politics, 1869–1879. Chapel Hill, NC: University of North Carolina Press, 1984 ISBN 978-0807841419 - Perman, Michael. Emancipation and Reconstruction (2003). - Peterson, Merrill D. (1994). Lincoln in American Memory. New York: Oxford University Press. ISBN 978-0-19-802304-3. - Randall, J. G. The Civil War and Reconstruction (1953). - Rhodes, James F. (1920). History of the United States from the Compromise of 1850 to the McKinley–Bryan Campaign of 1896, Volume: 6: 1865–72; Volume: 7: 1877. Highly detailed narrative by Pulitzer Prize winner; argues was a political disaster because it violated the rights of White Southerners. Vol. 6: 1865–1872 (via Questia); Vol. 7 (via Questia); Vol. 6 (via Google Books); Vol. 7 (via Google Books) - Richter, William L. (2009). A to Z of the Civil War and Reconstruction. Scarecrow Press. ISBN 978-0-8108-6336-1. - Roberts, Blain; Kytle, Ethan J. (January 17, 2018). "When the South Was the Most Progressive Region in America". The Atlantic. - Simon, John Y. (2002). "Ulysses S. Grant". In Graff, Henry (ed.). The Presidents: A Reference History (7th ed.). pp. 245–260. ISBN 0-684-80551-0. - Simpson, Brooks D. The Reconstruction Presidents (2009). - Smith, Jean Edward (2001). Grant. New York: Simon & Schuster. ISBN 0-684-84927-5. - Stampp, Kenneth M. The Era of Reconstruction, 1865–1877 (1967); short survey; rejects Dunning School analysis. online - Summers, Mark Wahlgren. The Ordeal of the Reunion: A New History of Reconstruction (2014) text search; online - Summers, Mark Wahlgren. A Dangerous Stir: Fear, Paranoia, and the Making of Reconstruction (2009) excerpt and text search - Thompson, C. Mildred. Reconstruction In Georgia: Economic, Social, Political 1865–1872 (1915; 2010 reprint); full text online free - Trefousse, Hans L. Historical Dictionary of Reconstruction (Greenwood, 1991), 250 entries - Wagner, Margaret E.; Gallagher, Gary W.; McPherson, James M. (2002). The Library of Congress Civil War Desk Reference. New York: Simon & Schuster Paperbacks. ISBN 978-1-4391-4884-6. - Wang, Xi (1997). The Trial of Democracy: Black Suffrage and Northern Republicans, 1860–1910. Athens: The University of Georgia Press. ISBN 978-0-8203-4206-1. - White, Ronald C. (2016). American Ulysses: A Life of Ulysses S. Grant. Random House Publishing Group. ISBN 978-1-58836-992-5. - Woodward, C. Vann (1966). Reunion and Reaction: The Compromise of 1877 and the End of Reconstruction. Oxford University Press. ISBN 978-0-19-506423-0. - Zuczek, Richard. Encyclopedia of the Reconstruction Era (2 vols., 2006). - Foner, Eric (2014). "Introduction to the 2014 Anniversary Edition". Reconstruction: America's Unfinished Revolution, 1863–18 (Updated ed.). ISBN 978-0062383235. - Ford, Lacy K., ed. A Companion to the Civil War and Reconstruction. Blackwell (2005) 518 pp. - Frantz, Edward O., ed. A Companion to the Reconstruction Presidents 1865–1881 (2014). 30 essays by scholars. - Perman, Michael and Amy Murrell Taylor, eds. Major Problems in the Civil War and Reconstruction: Documents and Essays (2010) - Simpson, Brooks D. (2016). "Mission Impossible: Reconstruction Policy Reconsidered". The Journal of the Civil War Era. 6: 85–102. doi:10.1353/cwe.2016.0003. S2CID 155789816. - Smith, Stacey L. (November 3, 2016). "Beyond North and South: Putting the West in the Civil War and Reconstruction". The Journal of the Civil War Era. 6 (4): 566–591. doi:10.1353/cwe.2016.0073. S2CID 164313047. - Stalcup, Brenda, ed. Reconstruction: Opposing Viewpoints (Greenhaven Press: 1995). Uses primary documents to present opposing viewpoints. - Stampp, Kenneth M.; Leon M. Litwack; eds. Reconstruction: An Anthology of Revisionist Writings (1969). Essays by scholars. - Weisberger, Bernard A. "The dark and bloody ground of Reconstruction historiography". Journal of Southern History 25.4 (1959): 427–447. JSTOR 2954450 - Appleton’s American Annual Cyclopedia and Register of Important Events of the Year 1867 (highly detailed compendium of facts and primary sources; details on every U.S. state & the national government) - Appleton’s American Annual Cyclopedia... for 1868 (1873) - Appleton’s American Annual Cyclopedia... for 1869 (1869) - Appleton’s American Annual Cyclopedia... for 1870 (1871) - Appleton’s American Annual Cyclopedia... for 1872 (1873) - Appleton’s American Annual Cyclopedia... for 1873 (1879) - Appleton’s American Annual Cyclopedia... for 1875 (1876) - Appleton’s American Annual Cyclopedia... for 1876 (1877) - Appleton’s American Annual Cyclopedia... for 1877 (1878) - The American year-book and national register for 1869 (1869) online - Barnes, William H., ed., History of the Thirty-ninth Congress of the United States (1868). Summary of Congressional activity. - Berlin, Ira, ed. Freedom: A Documentary History of Emancipation, 1861–1867 (1982), 970 pp. of archival documents; also Free at Last: A Documentary History of Slavery, Freedom, and the Civil War ed by Ira Berlin, Barbara J. Fields, and Steven F. Miller (1993). - Blaine, James G. Twenty Years of Congress: From Lincoln to Garfield. With a review of the events which led to the political revolution of 1860 (1886). By Republican Congressional leader Vol. 2 (via Internet Archive). - Fleming, Walter L. Documentary History of Reconstruction: Political, Military, Social, Religious, Educational, and Industrial 2 vols. (1906). Presents a broad collection of primary sources; Vol. 1:: On National Politics Vol. 2: On States (via Google Books). - Memoirs of W. W. Holden (1911); via Internet Archive. North Carolina "scalawag" governor. - Hyman, Harold M., ed. The Radical Republicans and Reconstruction, 1861–1870 (1967), collection of long political speeches and pamphlets. - Lee, Stephen D. (1899). "The South Since the War". In Evans, Clement A. (ed.). Confederate Military History. XII. Atlanta, Georgia: Confederate Publishing Company. pp. 267–568 – via Internet Archive. - Lynch, John R. The Facts of Reconstruction (New York: 1913). Full text online. One of the first Black congressmen during Reconstruction. - Edward McPherson, The Political History of the United States of America During the Period of Reconstruction (1875), large collection of speeches and primary documents, 1865–1870, complete text online. [The copyright has expired.] - Palmer, Beverly Wilson; Byers Ochoa, Holly; eds. The Selected Papers of Thaddeus Stevens 2 vols. (1998), 900 pp; his speeches plus and letters to and from Stevens. - Palmer, Beverly Wilson, ed. The Selected Letters of Charles Sumner, 2 vols. (1990); Vol. 2 covers 1859–1874. - Peters, Gerhard; Woolley, John T. (2018b). "1868 Democratic Party Platform". The American Presidency Project. - Pike, James Shepherd The prostrate state: South Carolina under negro government (1874) - Reid, Whitelaw After the War: A Southern Tour, May 1, 1865 to May 1, 1866 (1866). By Republican editor. - Smith, John David, ed. We Ask Only for Even-Handed Justice: Black Voices from Reconstruction, 1865–1877 (University of Massachusetts Press, 2014). xviii, 133 pp. - Sumner, Charles 'Our Domestic Relations: or, How to Treat the Rebel States' Atlantic Monthly September 1863, early abolitionist manifesto. Newspapers and magazines - DeBow’s Review major Southern conservative magazine; stress on business, economics and statistics - Harper’s Weekly leading New York news magazine; pro-Radical - Nast, Thomas, magazine cartoons pro-Radical editorial cartoons - Primary sources from Gilder-Lehrman collection - The New York Times daily edition online through ProQuest at academic libraries - Foner, Eric (March 28, 2015). "Why Reconstruction Matters". New York Times. - Simkins, William Stewart (June 1916). "Why the Ku Klux". The Alcalde. 4: 735–748. Archived from the original on September 22, 2006 – via Duke University School of Law / Internet Archive. Also available via WikiSource. - Suryanarayan, P., and White, S. (2020). Slavery, Reconstruction, and Bureaucratic Capacity in the American South. American Political Science Review. \|Wikiquote has quotations related to: Reconstruction era\| - Behn, Richard J., ed. 2020. "Reconstruction". Mr. Lincoln and Freedom. The Lehrman Institute. - Bigelow, Bill. "Reconstructing the South: A Role Play" (teaching activity). Zinn Education Project. - Bragg, William Harris. 2019. "Reconstruction in Georgia". New Georgia Encyclopedia. - Green Jr., Robert P. 1991. "Reconstruction Historiography: A Source of Teaching Ideas". The Social Studies (July/August):153–57. - Jensen, Richard. 2006. "Jensen's Guide to Reconstruction History, 1861–1877". Scholars' Guide to WWW. University of Illinois Chicago. Links to primary and secondary sources. - Mabry, Donald J. 2006. "Reconstruction in Mississippi". The Historical Text Archive. - Smith, Llewellyn M., dir. 2004. "Reconstruction: The Second Civil War", American Experience. PBS. Film connecting the replacement of civil rights with segregation and disenfranchisement at the end of 19th-century during the Jim Crow era. - "Civil Rights During Reconstruction" – Historians Eric Foner, David Blight and Ed Ayers discuss "Civil Rights During Reconstruction" - Seward, William H. 1866. "Proclamation Declaring the Insurrection at an End". American Historical Documents, 1000–1904, (The Harvard Classics 43). - "Reconstruction: Era and Definition". The History Channel. A&E Networks. - "The Civil War: Reconstruction". 2015. – This is part of an extensive assessment of the Civil War and slavery which gives particular attention to children. - "The Civil War and Reconstruction Era, 1845–1877" [HIST 119]. Open Yale Courses. New Haven, Connecticut: Yale University. Full semester course in text/audio/video; materials free under the Creative Commons license. - "The Reconstruction Era and the Fragility of Democracy". Facing History and Ourselves.
Hydrogen chloride or hydrochloric acid(HCl) has the composition of one chlorine and one hydrogen atom. What is the molecular geometry of hydrogen chloride?. Drawing and predicting the HCl molecular geometry is very easy by following the given method. Here in this post, we described step by step to construct HCl molecular geometry. Chlorine and hydrogen come from the 17th and 1st family groups in the periodic table. Chlorine and hydrogen have seven and one valence electrons respectively. Key Points To Consider When drawing The HCl Molecular Geometry A three-step approach for drawing the HCl molecular can be used. The first step is to sketch the molecular geometry of the HCl molecule, to calculate the lone pairs of the electron in the central chlorine atom; the second step is to calculate the HCl hybridization, and the third step is to give perfect notation for the HCl molecular geometry. The HCl molecular geometry is a diagram that illustrates the number of valence electrons and bond electron pairs in the HCl molecule in a specific geometric manner. The geometry of the HCl molecule ion can then be predicted using the Valence Shell Electron Pair Repulsion Theory (VSEPR Theory) and molecular hybridization theory, which states that molecules will choose the HCl geometrical shape in which the electrons have from one another in the specific molecular structure. Finally, you must add their bond polarities characteristics to compute the strength of the one H-Cl single bonds (dipole moment properties of the HCl molecular geometry). One hydrogen-chlorine single bonds in the hydrogen chloride(HCl), for example, are polarised toward the more electronegative value chlorine atom, and because (H-Cl) single bonds have the same size and polarity, their sum is nonzero due to the HCl molecule’s bond dipole moment due to pulling the electron cloud to the two side of linear or tetrahedral geometry, and the HCl molecule is classified as a polar molecule. The molecule of hydrogen chloride(with tetrahedral shape HCl molecular geometry) is tilted at 180 degrees bond angle of H-Cl. It has a difference in electronegativity values between chlorine and hydrogen atoms, with chlorine’s pull the electron cloud being greater than hydrogen’s. But bond polarity of H-Cl is not canceled to each other in the linear or tetrahedral geometry. As a result, it has a nonzero permanent dipole moment in its molecular structure. The HCl molecule has a nonzero dipole moment due to an unequal charge distribution of negative and positive charges in the linear or tetrahedral geometry. Overview: HCl electron and molecular geometry According to the VSEPR theory, the HCl molecule ion possesses linear or tetrahedral molecular geometry. Because the center atom, chlorine, has one H-Cl single bond with the one hydrogen atom surrounding it. The H-Cl bond angle is 180 degrees in the tetrahedral HCl molecular geometry. The HCl molecule has a linear or tetrahedral geometry shape because it contains one hydrogen atom in the tetrahedral and three corners with three lone pairs of electrons. There is one H-Cl single bond at the HCl molecular geometry. After linking the one hydrogen atom and three lone pairs of electrons on the chlorine atom in the tetrahedral form, it maintains the tetrahedral-shaped structure. In the HCl molecular geometry, the H-Cl single bond has stayed in the one terminal and three lone pairs of electrons on the chlorine atom of the tetrahedral molecule. The center chlorine atom of HCl has three lone pairs of electrons, resulting in tetrahedral HCl electron geometry. However, the molecular geometry of HCl looks tetrahedral or linear-shaped and has three lone pairs of electrons on the chlorine of the HCl geometry. It’s the HCl molecule’s slight asymmetrical geometry. As a result, the HCl molecule is polar. How to find HCl hybridization and molecular geometry Calculating lone pairs of electrons on chlorine in the HCl geometry: 1.Determine the number of lone pairs of electrons in the core chlorine atom of the HCl Lewis structure. Because the lone pairs of electrons on the chlorine atom are mostly responsible for the HCl molecule geometry planar, we need to calculate out how many there are on the central chlorine atom of the HCl Lewis structure. Use the formula below to find the lone pair on the chlorine atom of the HCl molecule. L.P(Cl) = V.E(Cl) – N.A(H-Cl) Lone pair on the central chlorine atom in HCl = L.P(Cl) The core central chlorine atom’s valence electron in HCl = V.E(Cl) Number of H-Cl bond = N.A (H-Cl)calculation for chlorine atom lone pair in HCl molecule. For instance of HCl, the central atom, chlorine, has seven electrons in its outermost valence shell, one H-Cl single bond connection. This gives a total of one connection. As a result of this, L.P(Cl) = (7 –1)=6 The lone pair of electrons in the chlorine atom of the HCl molecule is three. Calculating lone pair of electrons on hydrogen in the HCl geometry: Finding lone pair of electrons for the terminal hydrogen atom is similar to the central chlorine atom. We use the following formula as given below Use the formula below to find the lone pair on the hydrogen atom of the HCl molecule. L.P(H) = V.E(H) – N.A(H-Cl) Lone pair on the terminal hydrogen atom in HCl = L.P(H) Terminal hydrogen atom’s valence electron in HCl= V.E(H) Number of H-Cl bonds = N.A ( H-Cl)calculation for hydrogen atom lone pair in HCl molecule. For instance of HCl, their terminal atoms, hydrogen, have one electron in its outermost valence shell, one H-Cl single bond connection. This gives a total of one H-Cl single bond connection. But we are considering only one connection for the calculation. As a result of this, L.P(H) = (1 –1)=0 The lone pair of electrons in the hydrogen atom of the HCl molecule is zero. One hydrogen atom is connected with the central chlorine atom. In the HCl electron geometry structure, the lone pairs on the central chlorine atom are three, lone pairs of electrons in the hydrogen atom have zero. One hydrogen atom has no lone pairs of electrons. It means there are three lone pairs of electrons in the core chlorine atom. Three lone pair of electrons on the central chlorine atom is responsible for the linear or tetrahedral nature of HCl molecular geometry. But in the structure hydrogen atom is polarised sidewise in their linear or tetrahedral geometry. The three lone pairs of electrons are placed at another side of the HCl geometry. Because the hydrogen atom is a lower electronegative value as compared with other atoms in the HCl molecule. One hydrogen atom is polarized towards the sidewise in the HCl structure. But in reality, the HCl has three lone pairs of electrons in its structure. This makes the HCl more asymmetrical in the structure of the molecule. Because there is electric repulsion between bond pairs and lone pairs. But some sort of interaction is there between hydrogen empty hole and lone pairs of electrons of chlorine of another HCl molecule. Here, hydrogen of one molecule acts as an acceptor and chlorine of another molecule as a donor. This is called hydrogen bonding between the two HCl molecules. This is one of the main intermolecular forces in HCl. But in the central, chlorine atom has three lone pairs of electrons and these lone pair electrons are placed in the three corners of the tetrahedral. Calculate the number of molecular hybridizations of the HCl molecule What is HCl hybridization? This is a very fundamental question in the field of molecular chemistry. All the molecules are made of atoms. In chemistry, atoms are the fundamental particles. There are four different types of orbitals in chemistry. They are named s, p, d, and f orbitals. The entire periodic table arrangement is based on these orbital theories. Atoms in the periodic table are classified as follows: s- block elements p- block elements f-block elementsAtoms are classified in the periodic table HCl molecule is made of one chlorine and the hydrogen atom. The hydrogen and chlorine atoms have s and p orbitals. But hydrogen atom has only s orbital in the ground state. Hydrogen comes as the first element in the periodic table. The chlorine atom also belongs to the halogen family group. But it falls as the third element in the periodic table. When these atoms combine to form the HCl molecule, its atomic orbitals are mixed and form unique molecular orbitals due to hybridization. How do you find the HCl molecule’s hybridization? We must now determine the molecular hybridization number of HCl. The formula of HCl molecular hybridization is as follows: No. Hyb of HCl= N.A(H-Cl bond) + L.P(Cl) No. Hy of HCl = the number of hybridizations of HCl Number of H-Cl bonds = N.A (H-Clbonds) Lone pair on the central chlorine atom = L.P(Cl)Calculation for hybridization number for HCl molecule In the HCl molecule, chlorine is a core central atom with one hydrogen atom connected to it. It has three lone pairs of electrons on chlorine. The number of HCl hybridizations (No. Hyb of HCl) can then be estimated using the formula below. No. Hyb of HCl= 3+1=4 The HCl molecule ion hybridization is four. The chlorine and hydrogen atoms have s and p orbitals. The sp3 hybridization of the HCl molecule is formed when one s orbital and three p orbitals join together to form the HCl molecular orbital. Molecular Geometry Notation for HCl Molecule : Determine the form of HCl molecular geometry using VSEPR theory. The AXN technique is commonly used when the VSEPR theory is used to calculate the shape of the HCl molecule. The AXN notation of HCl molecule is as follows: The central chlorine atom in the HCl molecule is denoted by the letter A. The bound pairs (one H-Cl bond) of electrons to the core chlorine atom are represented by X. The lone pairs of electrons on the central chlorine atom are denoted by the letter N.Notation for HCl molecular geometry We know that HCl is the core atom, with one electron pair bound (one H-Cl) and three lone pairs of electrons. The general molecular geometry formula for HCl is AX1N3. According to the VSEPR theory, if the HCl molecule ion has an AX1N3 generic formula, the molecular geometry and electron geometry will both be tetrahedral or linear-shaped forms. \|Name of Molecule\|\|Hydrogen chloride\| \|Chemical molecular formula\|\|HCl\| \|Molecular geometry of HCl\|\|Tetrahedral or linear\| \|Electron geometry of HCl\|\|Tetrahedral or linear\| \|Hybridization of HCl\|\|sp3\| \|Bond angle (H-Cl)\|\|180º degree\| \|Total Valence electron for HCl\|\|8\| \|The formal charge of HCl on chlorine\|\|0\| In this post, we discussed the method to construct HCl molecular geometry, the method to find the lone pairs of electrons in the central HCl atom, HCl hybridization, and HCl molecular notation. Need to remember that, if you follow the above-said method, you can construct the HCl molecular structure very easily. What is HCl Molecular geometry? HCl Molecular geometry is an electronic structural representation of molecules. What is the molecular notation for HCl molecule? HCl molecular notation is AX1N3. The polarity of the molecules The polarity of the molecules are listed as follows - Polarity of BeCl2 - Polarity of SF4 - Polarity of CH2Cl2 - Polarity of NH3 - Polarity of XeF4 - Polarity of BF3 - Polarity of NH4+ - Polarity of CHCl3 - Polarity of BrF3 - Polarity of BrF5 - Polarity of SO3 - Polarity of SCl2 - Polarity of PCl3 - Polarity of H2S - Polarity of NO2+ - Polarity of HBr - Polarity of CS2 - Polarity of HCl - Polarity of CH3F - Polarity of SO2 - Polarity of CH4 Lewis Structure and Molecular Geometry Lewis structure and molecular geometry of molecules are listed below - CH4 Lewis structure and CH4 Molecular geometry - BeCl2 Lewis Structure and BeCl2 Molecular geometry - SF4 Lewis Structure and SF4 Molecular geometry - CH2Cl2 Lewis Structure and CH2Cl2 Molecular geometry - NH3 Lewis Structure and NH3 Molecular geometry - XeF4 Lewis Structure and XeF4 Molecular geometry - BF3 Lewis Structure and BF3 Molecular geometry - NH4+ Lewis Structure and NH4+ Molecular geometry - CHCl3 Lewis Structure and CHCl3 Molecular geometry - BrF3 Lewis Structure and BrF3 Molecular geometry - BrF5 Lewis Structure and BrF5 Molecular geometry - SO3 Lewis Structure and SO3 Molecular geometry - SCl2 Lewis structure and SCl2 Molecular Geometry - PCl3 Lewis structure and PCl3 Molecular Geometry - H2S Lewis structure and H2S Molecular Geometry - NO2+ Lewis structure and NO2+ Molecular Geometry - HBr Lewis structure and HBr Molecular Geometry - CS2 Lewis structure and CS2 Molecular Geometry - CH3F Lewis structure and CH3F Molecular Geometry - SO2 Lewis structure and SO2 Molecular Geometry
SummaryAt this point in the unit, students have learned about Pascal's law, Archimedes' principle, Bernoulli's principle, and why above-ground storage tanks are of major concern in the Houston Ship Channel and other coastal areas. In this culminating activity, student groups act as engineering design teams to derive equations to determine the stability of specific above-ground storage tank scenarios with given tank specifications and liquid contents. With their flotation analyses completed and the stability determined, students analyze the tank stability in specific storm conditions. Then, teams are challenged to come up with improved storage tank designs to make them less vulnerable to uplift, displacement and buckling in storm conditions. Teams present their analyses and design ideas in short class presentations. The 4,200 above-ground storage tanks located along the 50-mile Houston Ship Channel are at high risk for failure during storm events. Because many of these facilities are only protected to 14-15 feet above mean sea level, they are very likely to uplift, displace and buckle during major flood surges. With no existing provisions for shell buckling of uplift due to flooding, it is engineers' responsibility to assess these vulnerabilities and improve the code manual to include these important provisions. Students should have a basic understanding of Pascal's law, Archimedes' principle; the relationship between mass, volume, density and weight; and basic algebra and simple geometry in order to solve and manipulate equations; as well as be familiar with above-ground storage tanks and their associated environmental issues. As prerequisites for this activity, conduct The Physics of Fluid Mechanics and Above-Ground Storage Tanks in the Houston Ship Channel lessons. After this activity, students should be able to: - Explain what above-ground storage tanks are, where and why they are used, and the associated environmental issues. - Explain how Pascal's law and Archimedes' principle relate to the use of above-ground storage tanks and the types of failure associated with these tanks. - Research and apply new scientific knowledge in conjunction with content previously learned in the classroom to answer questions regarding the stability of storage tanks. - Use critical thinking to design a solution to an engineering problem. - Effectively communicate and present unique ideas to an audience. More Curriculum Like This Students are provided with an introduction to above-ground storage tanks, specifically how and why they are used in the Houston Ship Channel. Students learn how the concepts of Archimedes' principle and Pascal's law act out in the form of the uplifting and buckling seen in the damaged and destroyed ... Fluid mechanics, the study of how forces are applied to fluids, is outlined in this unit as a sequence of two lessons and three corresponding activities. Fluid mechanics, the study of how forces are applied to fluids, is outlined in this unit as a sequence of two lessons and three corresponding acti... Students are introduced to Pascal's law, Archimedes' principle and Bernoulli's principle. Fundamental definitions, equations, practice problems and engineering applications are supplied. Students use modeling clay, a material that is denser than water and thus ordinarily sinks in water, to discover the principle of buoyancy. They begin by designing and building boats out of clay that will float in water, and then refine their designs so that their boats will carry as great a load (m... Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards. All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN), a project of D2L (www.achievementstandards.org). In the ASN, standards are hierarchically structured: first by source; e.g., by state; within source by type; e.g., science or mathematics; within type by subtype, then by grade, etc. Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards. All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN), a project of D2L (www.achievementstandards.org). In the ASN, standards are hierarchically structured: first by source; e.g., by state; within source by type; e.g., science or mathematics; within type by subtype, then by grade, etc. - Design a solution to a complex real-world problem by breaking it down into smaller, more manageable problems that can be solved through engineering. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment? Thanks for your feedback! - Evaluate a solution to a complex real-world problem based on prioritized criteria and trade-offs that account for a range of constraints, including cost, safety, reliability, and aesthetics, as well as possible social, cultural, and environmental impacts. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment? Thanks for your feedback! - Analyze complex real-world problems by specifying criteria and constraints for successful solutions. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment? Thanks for your feedback! - Mathematical and computational thinking at the 9–12 level builds on K–8 and progresses to using algebraic thinking and analysis, a range of linear and nonlinear functions including trigonometric functions, exponentials and logarithms, and computational tools for statistical analysis to analyze, represent, and model data. Simple computational simulations are created and used based on mathematical models of basic assumptions. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment? Thanks for your feedback! - Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment? Thanks for your feedback! - Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment? Thanks for your feedback! - Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment? Thanks for your feedback! - Research and development is a specific problem-solving approach that is used intensively in business and industry to prepare devices and systems for the marketplace. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment? Thanks for your feedback! - The design process includes defining a problem, brainstorming, researching and generating ideas, identifying criteria and specifying constraints, exploring possibilities, selecting an approach, developing a design proposal, making a model or prototype, testing and evaluating the design using specifications, refining the design, creating or making it, and communicating processes and results. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment? Thanks for your feedback! - The process of engineering design takes into account a number of factors. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment? Thanks for your feedback! - demonstrate safe practices during laboratory and field investigations; and (Grades 9 - 10) Details... View more aligned curriculum... Do you agree with this alignment? Thanks for your feedback! - communicate valid conclusions supported by the data through various methods such as lab reports, labeled drawings, graphic organizers, journals, summaries, oral reports, and technology-based reports; and (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment? Thanks for your feedback! - express and manipulate relationships among physical variables quantitatively, including the use of graphs, charts, and equations. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment? Thanks for your feedback! - research and describe the connections between physics and future careers; and (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment? Thanks for your feedback! - demonstrate basic principles of fluid dynamics, including hydrostatic pressure, density, salinity, and buoyancy; (Grades 10 - 12) Details... View more aligned curriculum... Do you agree with this alignment? Thanks for your feedback! Each group needs: - computer with access to the Internet, Microsoft PowerPoint® and Excel® (or equivalent programs) - Design Project Worksheet, one per person, a different version for each group; see the Attachment section for five different versions - (optional) any materials students require to construct or draw models or prototypes Professional code manuals contain provisions for external pressure and floatation, anchorage due to seismic activity, and anchorage due to internal pressure for above-ground storage tanks. However, no provisions exist for shell buckling or uplift caused by flooding, despite the fact that these are ongoing issues with extreme consequences. For example, the 4,200 above-ground storage tanks in the Houston Ship Channel contain explosive materials, toxic gases and petrochemicals and are vulnerable to the frequent high-force storms and hurricanes common in the region. The lack of relevant code provisions is the motivation for your engineering design challenge project this week. Now, it is your turn to analyze an above-ground storage tank in given storm conditions to see if your tank will displace. In addition, your team challenge is to come up with an engineering design for a new and/or improved tank, perhaps by an addition or change to an existing tank design that prevents it from buckling or displacing. above-ground storage tank: A storage tank that is unburied (above ground) and used to contain fluids such as petrochemicals and petroleum. These tanks are more susceptible to damage and failure from flooding, displacement and buckling since they do not have much storm protection, if any. buoyancy: The ability of an object to float in a liquid. density: A measurement of the compactness of an object. mass: A measurement of the amount of matter in an object. mass density: Mass per unit volume of a substance. pressure: A measurement of force per unit area. volume: A measurement of the amount of space an object occupies. weight: A measurement of force on an object due to gravity. Schedule this activity to take about five 45-minute class periods spread over a week. The first day of the project includes an introduction and assignment of the design project, and the last day is for student presentations. The three periods between are class time for student groups to work on the project. If the class time for students to work on the project is instead assigned as homework, the class time required for this activity can be significantly reduced to ~1-2 class periods. Archimedes' principle states that the buoyant force is equal to the weight of the water displaced by the above-ground storage tank. If the weight of the water around the storage tank (due to surge) is greater than the weight of the tank, the tank will displace. Pascal's law states that a pressure applied at any point on a confined incompressible fluid is transmitted equally throughout the fluid. The surge creates an increased hydrostatic pressure gradient on the above-ground storage tank that pressurizes the entire tank and can lead to buckling (rupture). The surge height and liquid level inside ASTs vary daily. For this activity, the diameter range for the above-ground storage tanks were assumed to be 20-300 feet and the height range for the tanks were assumed to be 10-30 feet, based on information presented at the SSPEED Center Conference: Hurricane Ike 5 Years Later at Rice University on September 24, 2013. Shell materials were extracted from Section 4.2.2 ASTM Specifications in the API Standard 650: Welded Tanks for Oil Storage, and petrochemicals were chosen randomly. For additional background information about ASTs, refer to the associated lesson. Before the Activity - Assuming a group size of four students, determine how many engineering design groups you will have in each class. Then make copies of the Above-Ground Storage Tank Design Worksheets, one per person; see the Attachments section for five different versions (unique storage tank specifications, tank contents and storm conditions). Each group gets a different worksheet with each person in a group having a copy. If your class has more than five groups, make additional unique worksheet versions, as needed. - Become familiar with the types of failure that above-ground storage tanks experience as well as the equations that students will be asked to derive. With the Students - After having presented to students the Above-Ground Storage Tanks Presentation (a PowerPoint® file) as part of conducting the associated lesson, guide students to engage in conversation about the environmental issues associated with above-ground storage tanks along the Houston Ship Channel. - Divide the class into engineering design groups of four students each and explain that their challenge this week is to design a solution to this real-world problem—the vulnerability of above-ground storage tanks in storm conditions. - Hand out the worksheets to each group and either allot class time to fill out the packet or assign it as a take-home project. The worksheet engages students by asking them to recall definitions learned in class and presenting a few introductory questions about hurricanes, types of failure associated with above-ground storage tanks and how Archimedes' principle and Pascal's law apply to these tanks. - Then, students are asked to derive equations to determine the weight of the above-ground storage tank, the weight of the liquid inside the tank, and the weight of the water displaced by the tank. They use these equations in a floatation analysis to determine whether their groups' given above-ground storage tank will displace in their given storm conditions. - Then students answer some questions about their above-ground storage tanks based on their floatation analysis results. Each engineering team is challenged to come up with at least one design idea to prevent displacement and/or buckling of above-ground storage tanks. - Direct the design teams to follow the instructions in question #8 on the worksheet to create 5-8 minute presentations. In this presentation, expect students to reiterate their given storm conditions, state whether their above-ground storage tanks displace and explain why or why not, present and explain their graphs, and present their design ideas to the class. - Have the engineering design teams make their presentations with the rest of the class as the audience. Encourage the student audience to ask questions about the structural integrity, efficiency, cost, etc., of the presented design ideas. Refer to Figures 1 and 2 and Example Student Designs for examples of student team-generated design ideas for improved above-ground storage tanks to combat displacement and buckling. - Present the Above-Ground Storage Tank Conclusions Presentation. If providing class time to construct models or prototypes, make sure tools and fabrication equipment are being used in a safe manner. If students are struggling to derive the equations, supply helpful hints such as, "begin with the surface area of a cylinder." Once students have derived that equation, tell them to convert that equation to volume, and then convert that equation to mass, etc. Provide hints following the guided derivations supplied in the AST Design Worksheet Answer Key. Definitions and Presentation: Ask questions to review what was learned in the Above-Ground Storage Tanks in the Houston Ship Channel associated lesson. Example questions: What are above-ground storage tanks? Where are they used? Why are they used? Why are they a problem? Who is responsible for cleaning up ruptured above-ground storage tanks after a storm? Also ask students to recap terminology learned in the lesson by discussing the definitions to the vocabulary words. Activity Embedded Assessment Floatation Analysis: Direct students to work in their engineering design teams to derive the necessary equations to determine whether their above-ground storage tanks will displace under the given storm conditions. Observe and review student work to gauge their level of comprehension. Refer to the AST Design Worksheet Answer Key and AST Design Equation Answer Key. Midway Check-In: It is helpful if the instructor holds mid-week "check-point" meetings with each team to check students' work and catch derivation mistakes and floatation analysis errors early. Also use this as a chance to ensure teams are making progress on their design ideas and models as well as preparation of the final presentations. Student Presentations: Direct the teams to prepare and present short class presentations, as described in question #8 on the worksheet. Expect the presentations to reiterate the groups' given storm conditions, state whether their above-ground storage tanks displace and explain why or why not, present and explain their graphs, and present their design ideas to the class. Direct the student audience to ask questions about the structural integrity, efficiency, cost, etc., of the design ideas. Award points for each complete and accurate section of the presentation; deduct points for missing (storm conditions, graph) or incorrect scientific or mathematical information and logic (incorrect derivations or final floatation analysis). To give this activity more of an engineering design project context, have groups divide up responsibilities and assign roles to each group member such as project manager, project engineer, cost engineer, design engineer, etc. Guide them through the engineering design process and have students compose a formal report to turn in for grading. - For lower grades, or for students who struggle with math, provide the equations needed for the floatation analysis so students only need to plug in their unique numbers. - For upper grades, incorporate a wind and/or wave analysis to see if the above-ground storage tank will buckle. Add in extra storm conditions such as wind speed, duration, etc., and wave height, etc., and supply students with the equations needed to determine whether the above-ground storage tank will buckle, or guide students to derive those equations as well. Additional Multimedia Support At some point during the activity, point out to students that in their engineering design teams they are performing many of the steps of the engineering design process, just like engineers do. The basic steps of the engineering design process are: understand the need (including doing research and analysis to define the problem), generate multiple solutions, analyze and select a design solution, make a plan, create a model or prototype, test and improve the design until achieving satisfactory solution to the design challenge. For more information, see https://www.teachengineering.org/engrdesignprocess.php. Material Property Data (searchable database of material properties) MatWeb, LLC. Accessed March 13, 2014. http://www.matweb.com/ Moore, Sarah. Responders Tour Southeast Texas Looking for Oil Spills. Published September 17, 2008. The Beaumont Enterprise. Accessed March 13, 2014. http://www.beaumontenterprise.com/news/article/Responders-tour-Southeast-Texas-looking-for-oil-776445.php#photo-399495 Padgett, Jamie E. Structural Integrity of Storage Tanks. September 24, 2013. SSPEED Center Conference: Hurricane Ike 5 Years Later, Severe Storm Prediction, Education and Evacuation from Disasters, Civil and Environmental Engineering Department, Rice University, Houston, TX. Accessed March 13, 2014. (Inspiration for design project.) http://sspeed.rice.edu/sspeed/downloads/September_2013/Day1/1_5_PADGETT_SSPEED.pdf September 17: Assessing the Damage. Published September 17, 2008. The Beaumont Enterprise. Accessed March 13, 2014. (Pictures of above-ground storage tanks after Hurricane Ike) http://www.beaumontenterprise.com/news/article/Sept-17-Assessing-the-damage-962922.php#photo-525151 Steel Construction Manual. American Institute of Steel Construction. 13th edition. 2005. Fifth printing. 2010. USA. Welded Tanks for Oil Storage. API Standard 650. American Petroleum Institute. 12th edition, March 2013, 514 pages. Washington DC: API Publishing Services, 2013. Accessed March 13, 2014. https://docs.google.com/file/d/0Bw8MfqmgWLS4cC1DSlByaFlLXzQ/edit ContributorsEmily Sappington, Mila Taylor Copyright© 2014 by Regents of the University of Colorado; original © 2013 University of Houston Supporting ProgramNational Science Foundation GK-12 and Research Experience for Teachers (RET) Programs, University of Houston This digital library content was developed by the University of Houston's College of Engineering, based upon work supported by the National Science Foundation under GK-12 grant no. DGE 0840889. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. Last modified: December 5, 2017
A better understanding of the properties of steam may be achieved by understanding the general molecular and atomic structure of matter, and applying this knowledge to ice, water and steam. A molecule is the smallest amount of any element or compound substance still possessing all the chemical properties of that substance which can exist. Molecules themselves are made up of even smaller particles called atoms, which define the basic elements such as hydrogen and oxygen. The specific combinations of these atomic elements provide compound substances. One such compound is represented by the chemical formula H2O, having molecules made up of two atoms of hydrogen and one atom of oxygen. The reason water is so plentiful on the earth is because hydrogen and oxygen are amongst the most abundant elements in the universe. Carbon is another element of significant abundance, and is a key component in all organic matter. Most mineral substances can exist in the three physical states (solid, liquid and vapour) which are referred to as phases. In the case of H2O, the terms ice, water and steam are used to denote the three phases respectively. The molecular arrangement of ice, water, and steam is still not fully understood, but it is convenient to consider the molecules as bonded together by electrical charges (referred to as the hydrogen bond). The degree of excitation of the molecules determines the physical state (or phase) of the substance. All the three phases of a particular substance can only coexist in equilibrium at a certain temperature and pressure, and this is known as its triple point. The triple point of H2O, where the three phases of ice, water and steam are in equilibrium, occurs at a temperature of 273.16 K and an absolute pressure of 0.006 112 bar. This pressure is very close to a perfect vacuum. If the pressure is reduced further at this temperature, the ice, instead of melting, sublimates directly into steam. In ice, the molecules are locked together in an orderly lattice type structure and can only vibrate. In the solid phase, the movement of molecules in the lattice is a vibration about a mean bonded position where the molecules are less than one molecular diameter apart. The continued addition of heat causes the vibration to increase to such an extent that some molecules will eventually break away from their neighbours, and the solid starts to melt to a liquid state. At atmospheric pressure, melting occurs at 0°C. Changes in pressure have very little effect on the melting temperature, and for most practical purposes, 0°C can be taken as the melting point. However, it has been shown that the melting point of ice falls by 0.0072°C for each additional atmosphere of pressure. for example, a pressure of 13.9 bar g would be needed to reduce the melting temperature by 0.1°C. Heat that breaks the lattice bonds to produce the phase change while not increasing the temperature of the ice, is referred to as enthalpy of melting or heat of fusion. This phase change phenomenon is reversible when freezing occurs with the same amount of heat being released back to the surroundings. For most substances, the density decreases as it changes from the solid to the liquid phase. However, H2O is an exception to this rule as its density increases upon melting, which is why ice floats on water. In the liquid phase, the molecules are free to move, but are still less than one molecular diameter apart due to mutual attraction, and collisions occur frequently. More heat increases molecular agitation and collision, raising the temperature of the liquid up to its boiling temperature. Enthalpy of water, liquid enthalpy or sensible heat (hf) of water This is the heat energy required to raise the temperature of water from a datum point of 0°C to its current temperature. At this reference state of 0°C, the enthalpy of water has been arbitrarily set to zero. The enthalpy of all other states can then be identified, relative to this easily accessible reference state. Sensible heat was the term once used, because the heat added to the water produced a change in temperature. However, the accepted terms these days are liquid enthalpy or enthalpy of water. At atmospheric pressure (0 bar g), water boils at 100°C, and 419 kJ of energy are required to heat 1 kg of water from 0°C to its boiling temperature of 100°C. It is from these figures that the value for the specific heat capacity of water (Cp) of 4.19 kJ/kg °C is derived for most calculations between 0°C and 100°C. As the temperature increases and the water approaches its boiling condition, some molecules attain enough kinetic energy to reach velocities that allow them to momentarily escape from the liquid into the space above the surface, before falling back into the liquid. Further heating causes greater excitation and the number of molecules with enough energy to leave the liquid increases. As the water is heated to its boiling point, bubbles of steam form within it and rise to break through the surface. Considering the molecular arrangement of liquids and vapours, it is logical that the density of steam is much less than that of water, because the steam molecules are further apart from one another. The space immediately above the water surface thus becomes filled with less dense steam molecules. When the number of molecules leaving the liquid surface is more than those re-entering, the water freely evaporates. At this point it has reached boiling point or its saturation temperature, as it is saturated with heat energy. If the pressure remains constant, adding more heat does not cause the temperature to rise any further but causes the water to form saturated steam. The temperature of the boiling water and saturated steam within the same system is the same, but the heat energy per unit mass is much greater in the steam. At atmospheric pressure the saturation temperature is 100°C. However, if the pressure is increased, this will allow the addition of more heat and an increase in temperature without a change of phase. Therefore, increasing the pressure effectively increases both the enthalpy of water, and the saturation temperature. The relationship between the saturation temperature and the pressure is known as the steam saturation curve (see image below). Water and steam can coexist at any pressure on this curve, both being at the saturation temperature. Steam at a condition above the saturation curve is known as superheated steam.. If the steam is able to flow from the boiler at the same rate that it is produced, the addition of further heat simply increases the rate of production. If the steam is restrained from leaving the boiler, and the heat input rate is maintained, the energy flowing into the boiler will be greater than the energy flowing out. This excess energy raises the pressure, in turn allowing the saturation temperature to rise, as the temperature of saturated steam correlates to its pressure. Enthalpy of evaporation or latent heat (hfg) This is the amount of heat required to change the state of water at its boiling temperature, into steam. It involves no change in the temperature of the steam/water mixture, and all the energy is used to change the state from liquid (water) to vapour (saturated steam). The old term latent heat is based on the fact that although heat was added, there was no change in temperature. However, the accepted term is now enthalpy of evaporation. Like the phase change from ice to water, the process of evaporation is also reversible. The same amount of heat that produced the steam is released back to its surroundings during condensation, when steam meets any surface at a lower temperature. This may be considered as the useful portion of heat in the steam for heating purposes, as it is that portion of the total heat in the steam that is extracted when the steam condenses back to water. Enthalpy of saturated steam, or total heat of saturated steam This is the total energy in saturated steam, and is simply the sum of the enthalpy of water and the enthalpy of evaporation. hg = hf + hfg Saturated steam table A steam table list the properties of steam at varying pressures. They are the results of actual tests carried out on steam. The table below shows the properties of dry saturated steam at atmospheric pressure - 0 barg until 5 barg. \|Enthalpy (energy) in kJ/kg\|\|Volume of dry saturated steam m3/kg Steam with a temperature equal to the boiling point at that pressure is known as dry saturated steam. However, to produce 100% dry steam in an industrial boiler designed to produce saturated steam is rarely possible, and the steam will usually contain droplets of water. In practice, because of turbulence and splashing, as bubbles of steam break through the water surface, the steam space contains a mixture of water droplets and steam. Steam produced in any shell-type boiler, where the heat is supplied only to the water and where the steam remains in contact with the water surface, may typically contain around 5% water by mass. If the water content of the steam is 5‰ by mass, then the steam is said to be 95% dry and has a dryness fraction of 0.95. The actual enthalpy of evaporation of wet steam is the product of the dryness fraction (X) and the specific enthalpy (hfg) from the steam tables. Wet steam will have lower usable heat energy than dry saturated steam. Actual enthalpy of evaporation = hfgX Actual total enthalpy = hf + hfgX Because the specfic volume of water is several orders of magnitude lower than that of steam, the droplets of water in wet steam will occupy negligible space. Therefore the specific volume of wet steam will be less than dry steam.. Actual specific volume = VgX Where Vg is the specific volume of dry saturated steam. The steam phase diagram The data provided in the steam tables can also be expressed in a graphical form. The image bellow illustrates the relationship between the enthalpy and temperature of the various states of water and steam; this is known as a phase diagram. As water is heated from 0°C to its saturation temperature, its condition follows the saturated water line until it has received all of its liquid enthalpy, hf (A - B). If further heat continues to be added, the water changes phase to a water/vapour mixture and continues to increase in enthalpy while remaining at saturation temperature, hfg (B - C). As the water/vapour mixture increases in dryness, its condition moves from the saturated liquid line to the saturated vapour line. Therefore at a point exactly halfway between these two states, the dryness fraction (X) is 0.5. Similarly, on the saturated steam line the steam is 100% dry. Once it has received all of its enthalpy of evaporation, it reaches the saturated steam line. If it continues to be heated after this point, the pressure remains constant but the temperature of the steam will begin to rise as superheat is imparted (C - D). The saturated water and saturated steam lines enclose a region in which a water/vapour mixture exists - wet steam. In the region to the left of the saturated water line only water exists, and in the region to the right of the saturated steam line only superheated steam exists. The point at which the saturated water and saturated steam lines meet is known as the critical point. As the pressure increases towards the critical point the enthalpy of evaporation decreases, until it becomes zero at the critical point. This suggests that water changes directly into saturated steam at the critical point. Above the critical point the steam may be considered as a gas. The gaseous state is the most diffuse state in which the molecules have an almost unrestricted motion, and the volume increases without limit as the pressure is reduced. The critical point is the highest temperature at which water can exist. Any compression at constant temperature above the critical point will not produce a phase change. Compression at constant temperature below the critical point however, will result in liquefaction of the vapour as it passes from the superheated region into the wet steam region. The critical point occurs at 374.15°C and 221.2 bar a for steam. Above this pressure the steam is termed supercritical and no well-defined boiling point applies. The term "flash steam" is traditionally used to describe steam issuing from condensate receiver vents and open-ended condensate discharge lines from steam traps. How can steam be formed from water without adding heat? Flash steam occurs whenever water at high pressure (and a temperature higher than the saturation temperature of the low-pressure liquid) is allowed to drop to a lower pressure. Conversely, if the temperature of the high-pressure water is lower than the saturation temperature at the lower pressure, flash steam cannot be formed. In the case of condensate passing through a steam trap, it is usually the case that the upstream temperature is high enough to form flash steam. See image below Consider a kilogram of condensate at 5 bar g and a saturation temperature of 159°C passing through a steam trap to a lower pressure of 0 bar g. The amount of energy in one kilogram of condensate at saturation temperature at 5 bar g is 671 kJ. In accordance with the first law of thermodynamics, the amount of energy contained in the fluid on the low-pressure side of the steam trap must equal that on the high-pressure side, and constitutes the principle of conservation of energy. Consequently, the heat contained in one kilogram of low-pressure fluid is also 671 kJ. However, water at 0 bar g is only able to contain 419 kJ of heat, subsequently there appears to be an imbalance of heat on the low-pressure side of 671 - 419 = 252 kJ, which, in terms of the water, could be considered as excess heat. This excess heat boils some of the condensate into what is known as flash steam and the boiling process is called flashing. Therefore, the one kilogram of condensate which existed as one kilogram of liquid water on the high pressure side of the steam trap now partly exists as both water and steam on the low-pressure side. The amount of flash steam produced at the final pressure (P2) can be determined using.. Proportion of flash steam = (hf at P1) - (hf at P2) / hfg at P2 Example.. The case where the high pressure condensate temperature is higher than the low pressure saturation temperature. Consider a quantity of water at a pressure of 5 bar g, containing 671 kJ/kg of heat energy at its saturation temperature of 159°C. If the pressure was then reduced down to atmospheric pressure (0 bar g), the water could only exist at 100°C and contain 419 kJ/kg of heat energy. This difference of 671 - 419 = 252 kJ/kg of heat energy, would then produce flash steam at atmospheric pressure. 670.9 - 419.0 670.9 - 419.0 0.11 kg steam / kg water The proportion of flash steam produced can be thought of as the ratio of the excess energy to the enthalpy of evaporation at the final pressure. Example.. The case where the high pressure condensate temperature is lower than the low pressure saturation temperature. Temperature is at 90°C, that is, sub-cooled below the atmospheric saturation temperature of 100°C. Note.. It is not usually practical for such a large drop in condensate temperature from its saturation temperature (in this case 159°C to 90°C); it is simply being used to illustrate the point about flash steam not being produced under such circumstances. In this case, the sub-saturated water table will show that the liquid enthalpy of one kilogram of condensate at 5 barg and 90°C is 377 kJ. As this enthalpy is less than the enthalpy of one kilogram of saturated water at atmospheric pressure (419 kJ), there is no excess heat available to produce flash steam. The condensate simply passes through the trap and remains in a liquid state at the same temperature but lower pressure, atmospheric pressure in this case. See image below. The vapour pressure of water at 90°C is 0.7 bar absolute. Should the lower condensate pressure have been less than this, flash steam would have been produced. The principles of conservation of energy and mass between two process states. The principles of the conservation of energy and mass allow the flash steam phenomenon to be thought of from a different direction. 1 kg of condensate at 5 bar g and 159°C produces 0.112 kg of flash steam at atmospheric pressure. This can be illustrated schematically in the table below. The total mass of flash and condensate remains at 1 kg. \|5 bar g\|\|Steam trap\|\|0 bar g\| 1 kg condensate 0.112 flash steam The principle of energy conservation states that the total energy in the lower-pressure state must equal the total energy in the higher-pressure state. Therefore, the amount of heat in the flash steam and condensate must equal that in the initial condensate of 671 kJ. Steam tables give the following information.. Therefore, the steam tables, the enthalpy expected in the lower-pressure state is the same as that in the higher-pressure state, thus proving the principle of conservation of energy. Steam is water vapor. At a given temperature there is a certain vapor pressure that exists in equilibrium with liquid water. That is "wet" or saturated steam. If the temperature of the steam exceeds the temperature at which it is in equilibrium with a given pressure of water vapor, the vapor is superheated (heated above the temperature corresponding to the equilibrium vapor pressure) and the steam is referred to as "dry".There is a relationship between pressure and temperature, knowing the temperature, the pressure can be identify. Knowing the pressure, the temperature is also known. If saturated steam is further heated, the moisture will decline. The remaining water droplets are smaller and go over into the vapor phase. At temperatures of 10-20°C above saturated steam temperature overheating has occurred. Due to the poor Heat Transfer superheated steam is better for heat transport (steam flow in long pipelines). Due to the good Heat Transfer saturated steam is better for Heat Transfer (heating of Heat Exchangers saturated steam should be used). Flash steam is released from hot condensate when its pressure is reduced. Even water at an ambient room temperature of 20°C would boil if its pressure were lowered far enough. It may be worth noting that water at 170°C will boil at any pressure below 6.9 bar g. The steam released by the flashing process is as useful as steam released from a steam boiler. As an example, when steam is taken from a boiler and the boiler pressure drops, some of the water content of the boiler will flash off to supplement the "live" steam produced by the heat from the boiler fuel. Because both types of steam are produced in the boiler, it is impossible to differentiate between them. Only when flashing takes place at relatively low pressure, such as at the discharge side of steam traps, is the term flash steam widely used. Unfortunately, this usage has led to the erroneous conclusion that flash steam is in some way less valuable than so-called live steam. In any steam system seeking to maximise efficiency, flash steam will be separated from the condensate, and used to supplement any low pressure heating application. Every kilogram of flash steam used in this way is a kilogram of steam that does not need to be supplied by the boiler. It is also a kilogram of steam not vented to atmosphere, from where it would otherwise be lost. The reasons for the recovery of flash steam are just as compelling, both economically and environmentally, as the reasons for recovering condensate. The condition of steam is determined by three variables.. The vapor pressure and temperature can be measured relatively easily. The volume of steam can look at a similar reference. Rising energy costs In times of rising energy costs, for the operator of an energy-intensive steam and condensate system it is important to understand the sometimes quite sophisticated thermodynamic processes. The same steam and condensate system, which was still treated a few years ago rather trivial, is now due to higher energy prices are suddenly the center of attention. The best way to identify problems, has the operator. He is every day at the facility and should be familiar with each Valve and each pump. Skills are often sufficient to check the energy consumption of a plant and to optimize technical sense. Energy saving measures can be implemented already in small measures. The first energy-saving measure, that the operator should review its system to determine whether the pumps, control Valves, Heat Exchangers, etc. really correspond to the conditions for which they were originally designed. This requires that the operator is know his system and understand basic relationships. Source (partially) for this page.. Spirax Sarco
NO3 is a polyatomic, negatively charged ion. Consequently, it is also known as nitrogen oxoanion. Nitrate is the scientific term for the substance generated when nitric acid loses a proton. Nitrate is an essential nitrogen and oxygen source. It is utilised in agricultural farms as fertilisers (such as ammonium, salt, and potassium) to increase solubility and biodegradability. It also relieves heartache. Nitrogen and oxygen are essential to an ecosystem consisting of vegetation and wildlife. NO3 is readily soluble in water, but excessive concentrations in drinking water are hazardous to human health because they interfere with oxygen transport in the blood. Gilbert N. Lewis, an American chemist, invented the concept of electron dot structure in 1916. Following are rules for constructing the Lewis dot structure of any compound. Follow the octet rule, which states that an atom’s outermost shell should have a total of 8 electrons. (Exceptions include the elements hydrogen and boron) Calculate the total number of valence electrons in a compound based on the number of atoms present. Then, determine the number of bonded and lone pairs. (Bonding pairs involve the quantity of electrons that contribute to bonding between atoms, whereas lone pairs consist of electrons that do not contribute to bonding) After determining the core atom, surround it with the most electronegative atoms. - Form a single bond and count the number of electrons involved. Calculate the electron lone pair using the following formula. Lone pairs electrons = Valence electrons – Bonding electrons Assign the lone pairs to the terminal atoms and ensure that each atom has eight electrons in its last shell. The atom at the centre must complete its octet. Create double or triple bonds based on the number of electrons present on the core atom. Development of NO3 Lewis Dot Structure There is one atom of nitrogen and three atoms of oxygen in the ion NO3. It has one negative charge as well. In the periodic table, nitrogen and oxygen correspond to periods 5A and 6A, respectively. Therefore, oxygen has six valence electrons and nitrogen has five in their outer shells. Observe the quantity of valence electrons. Oxygen containing 3 atoms – 6 * 3 = 18 Due to the presence of a negative charge, an extra valence electron is added: 1 5 + 18 + 1 = 24 are total valence electrons For an atom to occupy the centre position, it must be less electronegative. According to the periodic table, nitrogen is less electronegative than oxygen, hence it is the centre atom of the structure. - Begin the nitrate’s frame dot structure by forming three single bonds between three oxygen and nitrogen atoms. There are 6 valence electrons used. - Based on the above data, the structure has bond pairs – three (6 electrons) lone pairs – 9 pairings (18 electrons) - To begin, finish the octet of the terminal atoms. Arrange the remaining 18 valence electrons such that each oxygen atom receives six valence electrons and three lone pairs are formed. Upon observation, nitrogen has only six valence electrons. Remove two electrons from one of the oxygen atoms and convert a single bond into a double bond to complete its octet. As depicted in the picture below, the structure results in two single bonds and one double bond between nitrogen and oxygen atoms. What is an official fee? Every atom has a formal charge somewhere. Formal charge is a crucial component of Lewis dot structure. It maintains a trace of the electrons assuming that they are distributed equally throughout the atoms of the molecule. It is not concerned with the electronegativity of the atom, but rather represents the electron count. If the atom has acquired an electron, it will have a negative charge, and if it has lost electrons, it will have a positive charge. There are three distinct approaches to calculating the formal charge: a mathematical formula, a graphic, and intuition. The statutory charge of NO3 To mathematically determine the formal charge of a single atom, the formula is The formal charge (F.C) equals (Number of valence electrons) minus (Number of non-bonding pair electrons) minus (Number of bonding pair electrons / 2) The F.C of oxygen forms a double bond with the nitrogen atom. F.C = 6 – 4 – (4/2) = 0; therefore, this atom has no formal charge. F.C. of an atom of nitrogen F.C = 5 – 0 – (8/2) = 1, indicating that nitrogen has a positive formal charge. F.C. of oxygen forming a single bond with an atom of nitrogen F.C = 6 – 6 – (2/2) = -1, which indicates that both oxygen atoms in a single bond with nitrogen have a negative formal charge. To compute the overall charge of the nitrate ion, a pair of positive and negative formal charges on the oxygen atom are cancelled, leaving a single negative formal charge. Therefore, the formal charge of the ion is negative. Combination of FO3 Hybridization is a method for determining the number of atoms linked to an atom’s central and lone pair. It explores the process of how atoms within molecules are positioned in three separate dimensions. The most essential aspect of hybridization is determining the chemical configuration of a molecule formed by a () bond and a pi () bond. The very first bond in a dot structure is always a sigma bond, while the second or third bond is a pi bond. The VSEPR theory states that the number of bond pairs can be determined by calculating the number of sigma () bonds and lone pair of the centre atom, i.e. the steric number, which is the number of electron-dense regions surrounding the atom. Since the steric number is three, there are three single sigma bonds and no lone pairs, which results in sp2 hybridization. The structure itself demonstrates that three sp2 orbitals of nitrogen overlap with one oxygen 1s orbital. Oxygen’s 2p orbitals combine to form a lone pair. The p orbital of nitrogen forms a covalent link with three oxygen atoms. NO3 Molecular Geometry The VSEPR theory leads you to the conclusion that NO3 is sp2-hybridized. The model also asserts that the molecular architecture of the compound is trigonal planar, with each orbital equally spaced at 120 degrees (bond angle) on a plane. A is the centre atom, X is the atom linked to A, (n) is the number of bonded atoms, and N is the number of nonbonding electron pairs, according to the formula AX(n) N. AX is the formula if N is disregarded as there is no lone pair of electrons (3). Therefore, the formula specifies the trigonal planar shape. The trigonal planar form of the NO3 molecule generates symmetry across the NO bonds; as a result, the three dipoles created by the NO bonds cancel each other out, resulting in a dipole of zero for NO3. Consequently, NO3 is a nonpolar molecule. The nitrate ion has only a negative charge, thus high levels of nitrate in any environment source are hazardous. - The nitrate ion is non-polar and has a net dipole moment of zero. The periodic table is of tremendous assistance in determining the Lewis dot structure of NO3, as it provides information on the atomic numbers and electronegativity of the elements.
In physics, an orbit is the gravitationally curved trajectory of an object, such as the trajectory of a planet around a star or a natural satellite around a planet. Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a non-repeating trajectory. To a close approximation, planets and satellites follow elliptic orbits, with the center of mass being orbited at a focal point of the ellipse, as described by Kepler's laws of planetary motion. For most situations, orbital motion is adequately approximated by Newtonian mechanics, which explains gravity as a force obeying an inverse-square law. However, Albert Einstein's general theory of relativity, which accounts for gravity as due to curvature of spacetime, with orbits following geodesics, provides a more accurate calculation and understanding of the exact mechanics of orbital motion. \|Part of a series on\| Historically, the apparent motions of the planets were described by European and Arabic philosophers using the idea of celestial spheres. This model posited the existence of perfect moving spheres or rings to which the stars and planets were attached. It assumed the heavens were fixed apart from the motion of the spheres, and was developed without any understanding of gravity. After the planets' motions were more accurately measured, theoretical mechanisms such as deferent and epicycles were added. Although the model was capable of reasonably accurately predicting the planets' positions in the sky, more and more epicycles were required as the measurements became more accurate, hence the model became increasingly unwieldy. Originally geocentric, it was modified by Copernicus to place the Sun at the centre to help simplify the model. The model was further challenged during the 16th century, as comets were observed traversing the spheres. The basis for the modern understanding of orbits was first formulated by Johannes Kepler whose results are summarised in his three laws of planetary motion. First, he found that the orbits of the planets in our Solar System are elliptical, not circular (or epicyclic), as had previously been believed, and that the Sun is not located at the center of the orbits, but rather at one focus. Second, he found that the orbital speed of each planet is not constant, as had previously been thought, but rather that the speed depends on the planet's distance from the Sun. Third, Kepler found a universal relationship between the orbital properties of all the planets orbiting the Sun. For the planets, the cubes of their distances from the Sun are proportional to the squares of their orbital periods. Jupiter and Venus, for example, are respectively about 5.2 and 0.723 AU distant from the Sun, their orbital periods respectively about 11.86 and 0.615 years. The proportionality is seen by the fact that the ratio for Jupiter, 5.23/11.862, is practically equal to that for Venus, 0.7233/0.6152, in accord with the relationship. Idealised orbits meeting these rules are known as Kepler orbits. Isaac Newton demonstrated that Kepler's laws were derivable from his theory of gravitation and that, in general, the orbits of bodies subject to gravity were conic sections (this assumes that the force of gravity propagates instantaneously). Newton showed that, for a pair of bodies, the orbits' sizes are in inverse proportion to their masses, and that those bodies orbit their common center of mass. Where one body is much more massive than the other (as is the case of an artificial satellite orbiting a planet), it is a convenient approximation to take the center of mass as coinciding with the center of the more massive body. Advances in Newtonian mechanics were then used to explore variations from the simple assumptions behind Kepler orbits, such as the perturbations due to other bodies, or the impact of spheroidal rather than spherical bodies. Lagrange (1736–1813) developed a new approach to Newtonian mechanics emphasizing energy more than force, and made progress on the three body problem, discovering the Lagrangian points. In a dramatic vindication of classical mechanics, in 1846 Urbain Le Verrier was able to predict the position of Neptune based on unexplained perturbations in the orbit of Uranus. Albert Einstein (1879-1955) in his 1916 paper The Foundation of the General Theory of Relativity explained that gravity was due to curvature of space-time and removed Newton's assumption that changes propagate instantaneously. This led astronomers to recognize that Newtonian mechanics did not provide the highest accuracy in understanding orbits. In relativity theory, orbits follow geodesic trajectories which are usually approximated very well by the Newtonian predictions (except where there are very strong gravity fields and very high speeds) but the differences are measurable. Essentially all the experimental evidence that can distinguish between the theories agrees with relativity theory to within experimental measurement accuracy. The original vindication of general relativity is that it was able to account for the remaining unexplained amount in precession of Mercury's perihelion first noted by Le Verrier. However, Newton's solution is still used for most short term purposes since it is significantly easier to use and sufficiently accurate. Within a planetary system, planets, dwarf planets, asteroids and other minor planets, comets, and space debris orbit the system's barycenter in elliptical orbits. A comet in a parabolic or hyperbolic orbit about a barycenter is not gravitationally bound to the star and therefore is not considered part of the star's planetary system. Bodies which are gravitationally bound to one of the planets in a planetary system, either natural or artificial satellites, follow orbits about a barycenter near or within that planet. Owing to mutual gravitational perturbations, the eccentricities of the planetary orbits vary over time. Mercury, the smallest planet in the Solar System, has the most eccentric orbit. At the present epoch, Mars has the next largest eccentricity while the smallest orbital eccentricities are seen with Venus and Neptune. As two objects orbit each other, the periapsis is that point at which the two objects are closest to each other and the apoapsis is that point at which they are the farthest. (More specific terms are used for specific bodies. For example, perigee and apogee are the lowest and highest parts of an orbit around Earth, while perihelion and aphelion are the closest and farthest points of an orbit around the Sun.) In the case of planets orbiting a star, the mass of the star and all its satellites are calculated to be at a single point called the barycenter. The paths of all the star's satellites are elliptical orbits about that barycenter. Each satellite in that system will have its own elliptical orbit with the barycenter at one focal point of that ellipse. At any point along its orbit, any satellite will have a certain value of kinetic and potential energy with respect to the barycenter, and that energy is a constant value at every point along its orbit. As a result, as a planet approaches periapsis, the planet will increase in speed as its potential energy decreases; as a planet approaches apoapsis, its velocity will decrease as its potential energy increases. There are a few common ways of understanding orbits: - A force, such as gravity, pulls an object into a curved path as it attempts to fly off in a straight line. - As the object is pulled toward the massive body, it falls toward that body. However, if it has enough tangential velocity it will not fall into the body but will instead continue to follow the curved trajectory caused by that body indefinitely. The object is then said to be orbiting the body. As an illustration of an orbit around a planet, the Newton's cannonball model may prove useful (see image below). This is a 'thought experiment', in which a cannon on top of a tall mountain is able to fire a cannonball horizontally at any chosen muzzle speed. The effects of air friction on the cannonball are ignored (or perhaps the mountain is high enough that the cannon is above the Earth's atmosphere, which is the same thing). If the cannon fires its ball with a low initial speed, the trajectory of the ball curves downward and hits the ground (A). As the firing speed is increased, the cannonball hits the ground farther (B) away from the cannon, because while the ball is still falling towards the ground, the ground is increasingly curving away from it (see first point, above). All these motions are actually "orbits" in a technical sense – they are describing a portion of an elliptical path around the center of gravity – but the orbits are interrupted by striking the Earth. If the cannonball is fired with sufficient speed, the ground curves away from the ball at least as much as the ball falls – so the ball never strikes the ground. It is now in what could be called a non-interrupted, or circumnavigating, orbit. For any specific combination of height above the center of gravity and mass of the planet, there is one specific firing speed (unaffected by the mass of the ball, which is assumed to be very small relative to the Earth's mass) that produces a circular orbit, as shown in (C). As the firing speed is increased beyond this, non-interrupted elliptic orbits are produced; one is shown in (D). If the initial firing is above the surface of the Earth as shown, there will also be non-interrupted elliptical orbits at slower firing speed; these will come closest to the Earth at the point half an orbit beyond, and directly opposite the firing point, below the circular orbit. At a specific horizontal firing speed called escape velocity, dependent on the mass of the planet, an open orbit (E) is achieved that has a parabolic path. At even greater speeds the object will follow a range of hyperbolic trajectories. In a practical sense, both of these trajectory types mean the object is "breaking free" of the planet's gravity, and "going off into space" never to return. The velocity relationship of two moving objects with mass can thus be considered in four practical classes, with subtypes: - No orbit - Suborbital trajectories - Range of interrupted elliptical paths - Orbital trajectories (or simply "orbits") - Range of elliptical paths with closest point opposite firing point - Circular path - Range of elliptical paths with closest point at firing point - Open (or escape) trajectories - Parabolic paths - Hyperbolic paths It is worth noting that orbital rockets are launched vertically at first to lift the rocket above the atmosphere (which causes frictional drag), and then slowly pitch over and finish firing the rocket engine parallel to the atmosphere to achieve orbit speed. Once in orbit, their speed keeps them in orbit above the atmosphere. If e.g., an elliptical orbit dips into dense air, the object will lose speed and re-enter (i.e. fall). Occasionally a space craft will intentionally intercept the atmosphere, in an act commonly referred to as an aerobraking maneuver. Newton's laws of motionEdit Newton's law of gravitation and laws of motion for two-body problemsEdit In most situations relativistic effects can be neglected, and Newton's laws give a sufficiently accurate description of motion. The acceleration of a body is equal to the sum of the forces acting on it, divided by its mass, and the gravitational force acting on a body is proportional to the product of the masses of the two attracting bodies and decreases inversely with the square of the distance between them. To this Newtonian approximation, for a system of two-point masses or spherical bodies, only influenced by their mutual gravitation (called a two-body problem), their trajectories can be exactly calculated. If the heavier body is much more massive than the smaller, as in the case of a satellite or small moon orbiting a planet or for the Earth orbiting the Sun, it is accurate enough and convenient to describe the motion in terms of a coordinate system that is centered on the heavier body, and we say that the lighter body is in orbit around the heavier. For the case where the masses of two bodies are comparable, an exact Newtonian solution is still sufficient and can be had by placing the coordinate system at the center of mass of the system. Defining gravitational potential energyEdit Energy is associated with gravitational fields. A stationary body far from another can do external work if it is pulled towards it, and therefore has gravitational potential energy. Since work is required to separate two bodies against the pull of gravity, their gravitational potential energy increases as they are separated, and decreases as they approach one another. For point masses the gravitational energy decreases to zero as they approach zero separation. It is convenient and conventional to assign the potential energy as having zero value when they are an infinite distance apart, and hence it has a negative value (since it decreases from zero) for smaller finite distances. Orbital energies and orbit shapesEdit When only two gravitational bodies interact, their orbits follow a conic section. The orbit can be open (implying the object never returns) or closed (returning). Which it is depends on the total energy (kinetic + potential energy) of the system. In the case of an open orbit, the speed at any position of the orbit is at least the escape velocity for that position, in the case of a closed orbit, the speed is always less than the escape velocity. Since the kinetic energy is never negative, if the common convention is adopted of taking the potential energy as zero at infinite separation, the bound orbits will have negative total energy, the parabolic trajectories zero total energy, and hyperbolic orbits positive total energy. An open orbit will have a parabolic shape if it has velocity of exactly the escape velocity at that point in its trajectory, and it will have the shape of a hyperbola when its velocity is greater than the escape velocity. When bodies with escape velocity or greater approach each other, they will briefly curve around each other at the time of their closest approach, and then separate, forever. All closed orbits have the shape of an ellipse. A circular orbit is a special case, wherein the foci of the ellipse coincide. The point where the orbiting body is closest to Earth is called the perigee, and is called the periapsis (less properly, "perifocus" or "pericentron") when the orbit is about a body other than Earth. The point where the satellite is farthest from Earth is called the apogee, apoapsis, or sometimes apifocus or apocentron. A line drawn from periapsis to apoapsis is the line-of-apsides. This is the major axis of the ellipse, the line through its longest part. Bodies following closed orbits repeat their paths with a certain time called the period. This motion is described by the empirical laws of Kepler, which can be mathematically derived from Newton's laws. These can be formulated as follows: - The orbit of a planet around the Sun is an ellipse, with the Sun in one of the focal points of that ellipse. [This focal point is actually the barycenter of the Sun-planet system; for simplicity this explanation assumes the Sun's mass is infinitely larger than that planet's.] The planet's orbit lies in a plane, called the orbital plane. The point on the orbit closest to the attracting body is the periapsis. The point farthest from the attracting body is called the apoapsis. There are also specific terms for orbits about particular bodies; things orbiting the Sun have a perihelion and aphelion, things orbiting the Earth have a perigee and apogee, and things orbiting the Moon have a perilune and apolune (or periselene and aposelene respectively). An orbit around any star, not just the Sun, has a periastron and an apastron. - As the planet moves in its orbit, the line from the Sun to planet sweeps a constant area of the orbital plane for a given period of time, regardless of which part of its orbit the planet traces during that period of time. This means that the planet moves faster near its perihelion than near its aphelion, because at the smaller distance it needs to trace a greater arc to cover the same area. This law is usually stated as "equal areas in equal time." - For a given orbit, the ratio of the cube of its semi-major axis to the square of its period is constant. Limitations of Newton's law of gravitationEdit Note that while bound orbits of a point mass or a spherical body with a Newtonian gravitational field are closed ellipses, which repeat the same path exactly and indefinitely, any non-spherical or non-Newtonian effects (such as caused by the slight oblateness of the Earth, or by relativistic effects, thereby changing the gravitational field's behavior with distance) will cause the orbit's shape to depart from the closed ellipses characteristic of Newtonian two-body motion. The two-body solutions were published by Newton in Principia in 1687. In 1912, Karl Fritiof Sundman developed a converging infinite series that solves the three-body problem; however, it converges too slowly to be of much use. Except for special cases like the Lagrangian points, no method is known to solve the equations of motion for a system with four or more bodies. Approaches to many-body problemsEdit Rather than an exact closed form solution, orbits with many bodies can be approximated with arbitrarily high accuracy. These approximations take two forms: - One form takes the pure elliptic motion as a basis, and adds perturbation terms to account for the gravitational influence of multiple bodies. This is convenient for calculating the positions of astronomical bodies. The equations of motion of the moons, planets and other bodies are known with great accuracy, and are used to generate tables for celestial navigation. Still, there are secular phenomena that have to be dealt with by post-Newtonian methods. - The differential equation form is used for scientific or mission-planning purposes. According to Newton's laws, the sum of all the forces acting on a body will equal the mass of the body times its acceleration (F = ma). Therefore accelerations can be expressed in terms of positions. The perturbation terms are much easier to describe in this form. Predicting subsequent positions and velocities from initial values of position and velocity corresponds to solving an initial value problem. Numerical methods calculate the positions and velocities of the objects a short time in the future, then repeat the calculation ad nauseam. However, tiny arithmetic errors from the limited accuracy of a computer's math are cumulative, which limits the accuracy of this approach. Differential simulations with large numbers of objects perform the calculations in a hierarchical pairwise fashion between centers of mass. Using this scheme, galaxies, star clusters and other large assemblages of objects have been simulated. Newtonian analysis of orbital motionEdit The Earth follows an ellipse round the sun. But unlike the ellipse followed by a pendulum or an object attached to a spring, the sun is at a focal point of the ellipse and not at its centre. The following derivation applies to such an elliptical orbit. We start only with the Newtonian law of gravitation stating that the gravitational acceleration towards the central body is related to the inverse of the square of the distance between them, namely - eq 1. where F2 is the force acting on the mass m2 caused by the gravitational attraction mass m1 has for m2, G is the universal gravitational constant, and r is the distance between the two masses centers. From Newton's Second Law, the summation of the forces acting on m2 related to that bodies acceleration: - eq 2. where A2 is the acceleration of m2 caused by the force of gravitational attraction F2 of m1 acting on m2. Combining Eq 1 and 2: Solving for the acceleration, A2: where is the standard gravitational parameter, in this case . It is understood that the system being described is m2, hence the subscripts can be dropped. We assume that the central body is massive enough that it can be considered to be stationary and we ignore the more subtle effects of general relativity. When a pendulum or an object attached to a spring swings in an ellipse, the inward acceleration/force is proportional to the distance Due to the way vectors add, the component of the force in the or in the directions are also proportionate to the respective components of the distances, . Hence, the entire analysis can be done separately in these dimensions. This results in the harmonic parabolic equations and of the ellipse. In contrast, with the decreasing relationship , the dimensions cannot be separated. The location of the orbiting object at the current time is located in the plane using Vector calculus in polar coordinates both with the standard Euclidean basis and with the polar basis with the origin coinciding with the center of force. Let be the distance between the object and the center and be the angle it has rotated. Let and be the standard Euclidean bases and let and be the radial and transverse polar basis with the first being the unit vector pointing from the central body to the current location of the orbiting object and the second being the orthogonal unit vector pointing in the direction that the orbiting object would travel if orbiting in a counter clockwise circle. Then the vector to the orbiting object is We use and to denote the standard derivatives of how this distance and angle change over time. We take the derivative of a vector to see how it changes over time by subtracting its location at time from that at time and dividing by . The result is also a vector. Because our basis vector moves as the object orbits, we start by differentiating it. From time to , the vector keeps its beginning at the origin and rotates from angle to which moves its head a distance in the perpendicular direction giving a derivative of . We can now find the velocity and acceleration of our orbiting object. The coefficients of and give the accelerations in the radial and transverse directions. As said, Newton gives this first due to gravity is and the second is zero. Equation (2) can be rearranged using integration by parts. We can multiply through by because it is not zero unless the orbiting object crashes. Then having the derivative be zero gives that the function is a constant. which is actually the theoretical proof of Kepler's second law (A line joining a planet and the Sun sweeps out equal areas during equal intervals of time). The constant of integration, h, is the angular momentum per unit mass. In order to get an equation for the orbit from equation (1), we need to eliminate time. (See also Binet equation.) In polar coordinates, this would express the distance of the orbiting object from the center as a function of its angle . However, it is easier to introduce the auxiliary variable and to express as a function of . Derivatives of with respect to time may be rewritten as derivatives of with respect to angle. - (reworking (3)) Plugging these into (1) gives So for the gravitational force – or, more generally, for any inverse square force law – the right hand side of the equation becomes a constant and the equation is seen to be the harmonic equation (up to a shift of origin of the dependent variable). The solution is: where A and θ0 are arbitrary constants. This resulting equation of the orbit of the object is that of an ellipse in Polar form relative to one of the focal points. This is put into a more standard form by letting be the eccentricity, letting be the semi-major axis. Finally, letting so the long axis of the ellipse is along the positive x coordinate. Relativistic orbital motionEdit The above classical (Newtonian) analysis of orbital mechanics assumes that the more subtle effects of general relativity, such as frame dragging and gravitational time dilation are negligible. Relativistic effects cease to be negligible when near very massive bodies (as with the precession of Mercury's orbit about the Sun), or when extreme precision is needed (as with calculations of the orbital elements and time signal references for GPS satellites.). The analysis so far has been two dimensional; it turns out that an unperturbed orbit is two-dimensional in a plane fixed in space, and thus the extension to three dimensions requires simply rotating the two-dimensional plane into the required angle relative to the poles of the planetary body involved. The rotation to do this in three dimensions requires three numbers to uniquely determine; traditionally these are expressed as three angles. The orbital period is simply how long an orbiting body takes to complete one orbit. Six parameters are required to specify a Keplerian orbit about a body. For example, the three numbers that specify the body's initial position, and the three values that specify its velocity will define a unique orbit that can be calculated forwards (or backwards) in time. However, traditionally the parameters used are slightly different. The traditionally used set of orbital elements is called the set of Keplerian elements, after Johannes Kepler and his laws. The Keplerian elements are six: - Inclination (i) - Longitude of the ascending node (Ω) - Argument of periapsis (ω) - Eccentricity (e) - Semimajor axis (a) - Mean anomaly at epoch (M0). In principle once the orbital elements are known for a body, its position can be calculated forward and backwards indefinitely in time. However, in practice, orbits are affected or perturbed, by other forces than simple gravity from an assumed point source (see the next section), and thus the orbital elements change over time. An orbital perturbation is when a force or impulse which is much smaller than the overall force or average impulse of the main gravitating body and which is external to the two orbiting bodies causes an acceleration, which changes the parameters of the orbit over time. Radial, prograde and transverse perturbationsEdit A small radial impulse given to a body in orbit changes the eccentricity, but not the orbital period (to first order). A prograde or retrograde impulse (i.e. an impulse applied along the orbital motion) changes both the eccentricity and the orbital period. Notably, a prograde impulse at periapsis raises the altitude at apoapsis, and vice versa, and a retrograde impulse does the opposite. A transverse impulse (out of the orbital plane) causes rotation of the orbital plane without changing the period or eccentricity. In all instances, a closed orbit will still intersect the perturbation point. If an orbit is about a planetary body with significant atmosphere, its orbit can decay because of drag. Particularly at each periapsis, the object experiences atmospheric drag, losing energy. Each time, the orbit grows less eccentric (more circular) because the object loses kinetic energy precisely when that energy is at its maximum. This is similar to the effect of slowing a pendulum at its lowest point; the highest point of the pendulum's swing becomes lower. With each successive slowing more of the orbit's path is affected by the atmosphere and the effect becomes more pronounced. Eventually, the effect becomes so great that the maximum kinetic energy is not enough to return the orbit above the limits of the atmospheric drag effect. When this happens the body will rapidly spiral down and intersect the central body. The bounds of an atmosphere vary wildly. During a solar maximum, the Earth's atmosphere causes drag up to a hundred kilometres higher than during a solar minimum. Some satellites with long conductive tethers can also experience orbital decay because of electromagnetic drag from the Earth's magnetic field. As the wire cuts the magnetic field it acts as a generator, moving electrons from one end to the other. The orbital energy is converted to heat in the wire. Orbits can be artificially influenced through the use of rocket engines which change the kinetic energy of the body at some point in its path. This is the conversion of chemical or electrical energy to kinetic energy. In this way changes in the orbit shape or orientation can be facilitated. Another method of artificially influencing an orbit is through the use of solar sails or magnetic sails. These forms of propulsion require no propellant or energy input other than that of the Sun, and so can be used indefinitely. See statite for one such proposed use. Orbital decay can occur due to tidal forces for objects below the synchronous orbit for the body they're orbiting. The gravity of the orbiting object raises tidal bulges in the primary, and since below the synchronous orbit the orbiting object is moving faster than the body's surface the bulges lag a short angle behind it. The gravity of the bulges is slightly off of the primary-satellite axis and thus has a component along the satellite's motion. The near bulge slows the object more than the far bulge speeds it up, and as a result the orbit decays. Conversely, the gravity of the satellite on the bulges applies torque on the primary and speeds up its rotation. Artificial satellites are too small to have an appreciable tidal effect on the planets they orbit, but several moons in the Solar System are undergoing orbital decay by this mechanism. Mars' innermost moon Phobos is a prime example, and is expected to either impact Mars' surface or break up into a ring within 50 million years. Orbits can decay via the emission of gravitational waves. This mechanism is extremely weak for most stellar objects, only becoming significant in cases where there is a combination of extreme mass and extreme acceleration, such as with black holes or neutron stars that are orbiting each other closely. The standard analysis of orbiting bodies assumes that all bodies consist of uniform spheres, or more generally, concentric shells each of uniform density. It can be shown that such bodies are gravitationally equivalent to point sources. However, in the real world, many bodies rotate, and this introduces oblateness and distorts the gravity field, and gives a quadrupole moment to the gravitational field which is significant at distances comparable to the radius of the body. In the general case, the gravitational potential of a rotating body such as, e.g., a planet is usually expanded in multipoles accounting for the departures of it from spherical symmetry. From the point of view of satellite dynamics, of particular relevance are the so-called even zonal harmonic coefficients, or even zonals, since they induce secular orbital perturbations which are cumulative over time spans longer than the orbital period. They do depend on the orientation of the body's symmetry axis in the space, affecting, in general, the whole orbit, with the exception of the semimajor axis. Multiple gravitating bodiesEdit The effects of other gravitating bodies can be significant. For example, the orbit of the Moon cannot be accurately described without allowing for the action of the Sun's gravity as well as the Earth's. One approximate result is that bodies will usually have reasonably stable orbits around a heavier planet or moon, in spite of these perturbations, provided they are orbiting well within the heavier body's Hill sphere. Light radiation and stellar windEdit For smaller bodies particularly, light and stellar wind can cause significant perturbations to the attitude and direction of motion of the body, and over time can be significant. Of the planetary bodies, the motion of asteroids is particularly affected over large periods when the asteroids are rotating relative to the Sun. Mathematicians have discovered that it is possible in principle to have multiple bodies in non-elliptical orbits that repeat periodically, although most such orbits are not stable regarding small perturbations in mass, position, or velocity. However, some special stable cases have been identified, including a planar figure-eight orbit occupied by three moving bodies. Further studies have discovered that nonplanar orbits are also possible, including one involving 12 masses moving in 4 roughly circular, interlocking orbits topologically equivalent to the edges of a cuboctahedron. Finding such orbits naturally occurring in the universe is thought to be extremely unlikely, because of the improbability of the required conditions occurring by chance. Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and Newton's law of universal gravitation. It is a core discipline within space mission design and control. Celestial mechanics treats more broadly the orbital dynamics of systems under the influence of gravity, including spacecraft and natural astronomical bodies such as star systems, planets, moons, and comets. Orbital mechanics focuses on spacecraft trajectories, including orbital maneuvers, orbit plane changes, and interplanetary transfers, and is used by mission planners to predict the results of propulsive maneuvers. General relativity is a more exact theory than Newton's laws for calculating orbits, and is sometimes necessary for greater accuracy or in high-gravity situations (such as orbits close to the Sun). - Low Earth orbit (LEO): Geocentric orbits with altitudes up to 2,000 km (0–1,240 miles). - Medium Earth orbit (MEO): Geocentric orbits ranging in altitude from 2,000 km (1,240 miles) to just below geosynchronous orbit at 35,786 kilometers (22,236 mi). Also known as an intermediate circular orbit. These are "most commonly at 20,200 kilometers (12,600 mi), or 20,650 kilometers (12,830 mi), with an orbital period of 12 hours." - Both geosynchronous orbit (GSO) and geostationary orbit (GEO) are orbits around Earth matching Earth's sidereal rotation period. All geosynchronous and geostationary orbits have a semi-major axis of 42,164 km (26,199 mi). All geostationary orbits are also geosynchronous, but not all geosynchronous orbits are geostationary. A geostationary orbit stays exactly above the equator, whereas a geosynchronous orbit may swing north and south to cover more of the Earth's surface. Both complete one full orbit of Earth per sidereal day (relative to the stars, not the Sun). - High Earth orbit: Geocentric orbits above the altitude of geosynchronous orbit 35,786 km (22,240 miles). Scaling in gravityEdit The gravitational constant G has been calculated as: - (6.6742 ± 0.001) × 10−11 (kg/m3)−1s−2. Thus the constant has dimension density−1 time−2. This corresponds to the following properties. Scaling of distances (including sizes of bodies, while keeping the densities the same) gives similar orbits without scaling the time: if for example distances are halved, masses are divided by 8, gravitational forces by 16 and gravitational accelerations by 2. Hence velocities are halved and orbital periods remain the same. Similarly, when an object is dropped from a tower, the time it takes to fall to the ground remains the same with a scale model of the tower on a scale model of the Earth. Scaling of distances while keeping the masses the same (in the case of point masses, or by reducing the densities) gives similar orbits; if distances are multiplied by 4, gravitational forces and accelerations are divided by 16, velocities are halved and orbital periods are multiplied by 8. When all densities are multiplied by 4, orbits are the same; gravitational forces are multiplied by 16 and accelerations by 4, velocities are doubled and orbital periods are halved. When all densities are multiplied by 4, and all sizes are halved, orbits are similar; masses are divided by 2, gravitational forces are the same, gravitational accelerations are doubled. Hence velocities are the same and orbital periods are halved. In all these cases of scaling. if densities are multiplied by 4, times are halved; if velocities are doubled, forces are multiplied by 16. These properties are illustrated in the formula (derived from the formula for the orbital period) The application of certain orbits or orbital maneuvers to specific useful purposes have been the subject of patents. Some bodies are tidally locked with other bodies, meaning that one side of the celestial body is permanently facing its host object. This is the case for Earth-Moon and Pluto-Charon system. - Ephemeris is a compilation of positions of naturally occurring astronomical objects as well as artificial satellites in the sky at a given time or times. - Free drift - Klemperer rosette - List of orbits - Molniya orbit - Orbit determination - Orbital spaceflight - Perifocal coordinate system - Polar Orbits - Radial trajectory - Rosetta (orbit) - VSOP (planets) - Orbital periods and speeds are calculated using the relations 4π2R3 = T2GM and V2R = GM, where R = radius of orbit in metres, T = orbital period in seconds, V = orbital speed in m/s, G = gravitational constant ≈ 6.673×10−11 Nm2/kg2, M = mass of Earth ≈ 5.98×1024 kg. - Approximately 8.6 times when the Moon is nearest (363,104 km ÷ 42,164 km) to 9.6 times when the Moon is farthest (405,696 km ÷ 42,164 km). - orbit (astronomy) – Britannica Online Encyclopedia - The Space Place :: What's a Barycenter - Kuhn, The Copernican Revolution, pp. 238, 246–252 - Encyclopædia Britannica, 1968, vol. 2, p. 645 - M Caspar, Kepler (1959, Abelard-Schuman), at pp.131–140; A Koyré, The Astronomical Revolution: Copernicus, Kepler, Borelli (1973, Methuen), pp. 277–279 - Jones, Andrew. "Kepler's Laws of Planetary Motion". about.com. Retrieved 1 June 2008. - See pages 6 to 8 in Newton's "Treatise of the System of the World" (written 1685, translated into English 1728, see Newton's 'Principia' – A preliminary version), for the original version of this 'cannonball' thought-experiment. - Fitzpatrick, Richard (2 February 2006). "Planetary orbits". Classical Mechanics – an introductory course. The University of Texas at Austin. Archived from the original on 3 March 2001. - Pogge, Richard W.; "Real-World Relativity: The GPS Navigation System". Retrieved 25 January 2008. - Iorio, L. (2011). "Perturbed stellar motions around the rotating black hole in Sgr A* for a generic orientation of its spin axis". Physical Review D. 84 (12): 124001. arXiv:1107.2916. Bibcode:2011PhRvD..84l4001I. doi:10.1103/PhysRevD.84.124001. - Renzetti, G. (2013). "Satellite Orbital Precessions Caused by the Octupolar Mass Moment of a Non-Spherical Body Arbitrarily Oriented in Space". Journal of Astrophysics and Astronomy. 34 (4): 341–348. Bibcode:2013JApA...34..341R. doi:10.1007/s12036-013-9186-4. - Renzetti, G. (2014). "Satellite orbital precessions caused by the first odd zonal J3 multipole of a non-spherical body arbitrarily oriented in space". Astrophysics and Space Science. 352 (2): 493–496. Bibcode:2014Ap&SS.352..493R. doi:10.1007/s10509-014-1915-x. - Peterson, Ivars (23 September 2013). "Strange Orbits". Science News. - "NASA Safety Standard 1740.14, Guidelines and Assessment Procedures for Limiting Orbital Debris" (PDF). Office of Safety and Mission Assurance. 1 August 1995. Archived from the original (PDF) on 15 February 2013., pages 37-38 (6-1,6-2); figure 6-1. - "Orbit: Definition". Ancillary Description Writer's Guide, 2013. National Aeronautics and Space Administration (NASA) Global Change Master Directory. Archived from the original on 11 May 2013. Retrieved 29 April 2013. - Vallado, David A. (2007). Fundamentals of Astrodynamics and Applications. Hawthorne, CA: Microcosm Press. p. 31. - Ferreira, Becky (19 February 2015). "How Satellite Companies Patent Their Orbits". Motherboard. Vice News. Retrieved 20 September 2018. - Abell; Morrison & Wolff (1987). Exploration of the Universe (fifth ed.). Saunders College Publishing. - Linton, Christopher (2004). From Eudoxus to Einstein: A History of Mathematical Astronomy. Cambridge University Press. ISBN 978-1-139-45379-0. - Frank Swetz; John Fauvel; Bengt Johansson; Victor Katz; Otto Bekken (1995). Learn from the Masters. MAA. ISBN 978-0-88385-703-8. - Andrea Milani and Giovanni F. Gronchi. Theory of Orbit Determination (Cambridge University Press; 378 pages; 2010). Discusses new algorithms for determining the orbits of both natural and artificial celestial bodies. \|Look up orbit in Wiktionary, the free dictionary.\| \|Wikimedia Commons has media related to Orbits.\| - Java simulation on orbital motion. Requires Java. - NOAA page on Climate Forcing Data includes (calculated) data on Earth orbit variations over the last 50 million years and for the coming 20 million years - Orbital Mechanics (Rocket and Space Technology) - Orbital simulations by Varadi, Ghil and Runnegar (2003) provide another, slightly different series for Earth orbit eccentricity, and also a series for orbital inclination. Orbits for the other planets were also calculated, by F. Varadi; B. Runnegar; M. Ghil (2003). "Successive Refinements in Long-Term Integrations of Planetary Orbits". The Astrophysical Journal. 592: 620–630. Bibcode:2003ApJ...592..620V. doi:10.1086/375560., but only the eccentricity data for Earth and Mercury are available online. - Merrifield, Michael. "Orbits (including the first manned orbit)". Sixty Symbols. Brady Haran for the University of Nottingham. - Planetary orbit Simulator Astronoo
Are you struggling with solving simultaneous equations? Don’t worry; we’ve got you covered! In this article, we will walk you through the process of solving simultaneous equations graphically. This method offers a visual approach to finding the solution and can be quite useful in certain scenarios. So, let’s dive in and learn how to solve simultaneous equations graphically! - How to Chromecast from Phone: The Ultimate Guide - How Long Does It Take for Dandelion Tea to Work? - How to Leave a Sim at the Altar: A Guide to Handling Relationship Difficulties - How to Get to Cervinia: Your Ultimate Guide to Reaching this Alpine Paradise - How Much Brodifacoum to Kill a Rat: Determining the Right Dosage Understanding Simultaneous Equations Before we delve into the graphical method, let’s quickly understand what simultaneous equations are and why they are important. Simultaneous equations are a set of two or more equations with multiple variables. The goal is to find the values of these variables that satisfy all the given equations simultaneously. Solving simultaneous equations is crucial in various fields, such as physics, engineering, economics, and more. It helps us find the intersection point(s) where multiple lines or curves intersect, representing a common solution for the equations. Graphical Method for Solving Simultaneous Equations The graphical method provides a visual representation of simultaneous equations on a coordinate plane. By plotting the equations and analyzing their intersection point(s), we can determine the solution. Let’s go through the step-by-step process of solving simultaneous equations graphically: 1. Plotting the Equations on the Coordinate Plane To begin, we need to plot the given equations on a coordinate plane. Each equation represents a line or a curve, and their intersection point(s) will be the solution(s) to the simultaneous equations. For instance, let’s consider the following equations: - Equation 1: 2x + 3y = 8 - Equation 2: 4x – y = 7 We can start by assigning arbitrary values to either “x” or “y” in each equation and calculating the corresponding values for the other variable. By repeating this process, we can obtain multiple coordinate points. Plotting these points will help us visualize the lines on the graph. 2. Identifying the Point of Intersection Once we have plotted the equations, we need to identify the point(s) where the lines intersect. This intersection point represents the solution(s) to the simultaneous equations. In our example, by observing the graph, we notice that the lines intersect at a single point. This point represents the values of “x” and “y” that satisfy both equations simultaneously. 3. Reading the Solution from the Graph After identifying the intersection point, we can read the solution from the graph. The “x” and “y” coordinates of the intersection point correspond to the values of the variables that solve the simultaneous equations. In our example, let’s say the intersection point is (2, 1). This means that the values of “x” and “y” that satisfy both equations are x = 2 and y = 1. Frequently Asked Questions (FAQ) Now, let’s address some common questions related to solving simultaneous equations graphically: 1. Can simultaneous equations have no solution or infinite solutions? Yes, it is possible for simultaneous equations to have no solution or infinite solutions. When the lines representing the equations are parallel, they never intersect, resulting in no solution. On the other hand, if the lines coincide or overlap, there are infinite solutions. 2. What should I do if the lines representing the equations are parallel? If the lines are parallel, there is no solution to the simultaneous equations. In such cases, it is advisable to explore alternative methods like substitution or elimination to find a solution. 3. How accurate is the graphical method compared to other methods? The accuracy of the graphical method depends on the precision with which we plot the equations. While it provides a visual representation and is relatively straightforward, it may not yield precise solutions like algebraic methods such as substitution or elimination. However, the graphical method serves as a valuable tool for initial estimations and gaining insights into the simultaneous equations. Solving simultaneous equations graphically offers a visual and intuitive approach to finding solutions. By plotting the equations on a coordinate plane and identifying the intersection point(s), we can determine the values of the variables that satisfy the equations simultaneously. Although the graphical method may not provide the utmost precision, it is a valuable technique for initial estimations and gaining a deeper understanding of simultaneous equations. Now that you have learned how to solve simultaneous equations graphically, give it a try yourself! Practice with different examples to strengthen your skills. Remember, the more you practice, the more confident you will become in solving simultaneous equations. So, grab a pen, a graphing paper, and start solving those equations! For more helpful guides and tutorials on various topics, visit How-To Guides.
By accessing our 180 Days of Math for Fifth Grade Answers Key Day 178 regularly, students can get better problem-solving skills. 180 Days of Math for Fifth Grade Answers Key Day 178 Directions: Solve each problem. Subtract 78 from 143. Subtraction is one of the four basic arithmetic operations in mathematics. We can observe the applications of subtraction in our everyday life in different situations. For example, when we purchase fruits and vegetables for a certain amount of money say Rs. 200 and we have given an Rs. 500 note to the vendor. Now, the vendor returns the excess amount by performing subtraction such as 500 – 200 = 300. Then, the vendor will return Rs. 300. Now we need to calculate the above-given question: we need to subtract 78 from 143. 143 = Minuend; 78 = Subtrahend; 65 = Difference Therefore, the answer is 65. In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life. The major application we can see in multiplication tables. In arithmetic, the multiplication of two numbers represents the repeated addition of one number with respect to another. These numbers can be whole numbers, natural numbers, integers, fractions, etc. If m is multiplied by n, then it means either m is added to itself ‘n’ number of times or vice versa. The formula for multiplication: The multiplication formula is given by: Multiplier × Multiplicand = Product – The multiplicand is the total number of objects in each group – A multiplier is the number of equal groups – Product is the result of multiplication of multiplier and multiplicand Therefore, 76×75 is equal to 5680. 453 ÷ 25 = __________ The division is breaking a number into an equal number of parts. The division is an arithmetic operation used in Maths. It splits a given number of items into different groups. There are a number of signs that people may use to indicate division. The most common one is ÷, but the backslash / and a horizontal line (-) is also used in the form of Fraction, where a Numerator is written on the top and a Denominator on the bottom. The division formula is: Dividend ÷ Divisor = Quotient (or) Dividend/Divisor=quotient Therefore, 453 ÷ 25 = 18 How many digits are in 593,001? Place value in Maths describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on. There are six digits in the number 593,001. 1 is in the unit’s place. 0 is in the tens place 0 is in the hundreds place 3 is in the thousands place 9 is in the ten thousand place 5 is in the hundred thousand places. Write 90% as a fraction. To convert 90% to a fraction follow these steps: Step 1: Write down the per cent divided by 100 like this Step 2: Multiply both top and bottom by 10 for every number after the decimal point. As 90 is an integer, we don’t have numbers after the decimal point. So, we just go to step 3. Step 3: simplify (or reduce) the above fraction by dividing both numerator and denominator by the GCD (greatest common divisor) between them. In this case, GCD(90,100) = 10. So, (90 ÷ 10)/(100 ÷ 10) We can write as 90% as 9/10. 20 + 20 ÷ 4 = ____________ The above-given mathematical computation can be written as: Therefore, the answer is 25. – First, divide 4 and 128 then we get quotient 32 – Now once multiply 4 with 32 then we get 128. If we check like this then we can easily find out the answer. Calculate the volume of a rectangular prism that is 4 m by 2 m by 3 m. In mathematics, the prism is a three-dimensional figure in which the faces of the solid are rectangles. It has six rectangular faces. The rectangular prism is also known as the cuboid. It has a rectangular cross-section. The opposite faces of the rectangular prism are of equal measure. If the length, width, and height are measures of the rectangular prism, then the volume of the rectangular prism is given by the formula, The volume of the rectangular prism, V = Length × Width × Height cubic units The above-given units: 4m, 2m, 3m V=24 cube units. True or false? The diameter of a circle is three times its radius. The diameter of a circle is four its radius. The diameter of a circle is calculated as D=2R where R is the radius of the circle. How much more did it rain in June than in May? The millimetres of rain in june=60 The millimetres of rain in may=25 The millimetres of rain in June than in may=X Therefore, 35 millimetres more rain in June than in May. What is the probability of rolling 3 on a 6-sided die? Probability: Probability means Possibility. It states how likely an event is about to happen. The probability of an event can exist only between 0 and 1 where 0 indicates that event is not going to happen i.e. Impossibility and 1 indicates that it is going to happen for sure i.e. Certainty. The higher or lesser the probability of an event, the more likely it is that the event will occur or not respectively. For example – An unbiased coin is tossed once. So the total number of outcomes can be 2 only i.e. either “heads” or “tails”. The probability of both outcomes is equal i.e. 50% or 1/2. So, the probability of an event is Favorable outcomes/Total number of outcomes. It is denoted with the parenthesis i.e. P(Event). P(Event)=N(Favourable outcomes)/N(Total outcomes) When 6-sided dice are rolled then total outcomes are 6 and Sample space is [1, 2, 3, 4, 5, 6] Probability of getting a 3 on 6-sided dice = favourable outcomes/total outcomes P(getting a 3)=1/6 Complete the chart by rounding the number 837,482 to the specified place. Rounding a number means the process of making a number simpler such that its value remains close to what it was. The result obtained after rounding off a number is less accurate, but easier to use. While rounding a number, we consider the place value of digits in a number. There are some basic rules that need to be followed for rounding numbers. – We first need to know what our rounding digit is. This digit is the one that will ultimately be affected. – After this, we need to check the digit to the right of this place which will decide the fate of the rounding digit. – If the digit to the right is less than 5, we do not change the rounding digit. However, all the digits to the right of the rounding digit are changed to 0. – If the digit to the right is 5 or more than 5, we increase the rounding digit by 1, and all the digits to the right of the rounding digit are changed to 0. Rounding the number nearest to ten: Rounding numbers to the nearest ten means we need to check the digit to the right of the tens place, that is the one’s place. The above-given number is 837,482. Check the number in one’s place, the number in the one’s place is less than 5 so the number in the tens place won’t change and the number in the one’s place becomes zero. Thus, the number is 837,480 – Likewise, we need to round the numbers in hundreds, thousands, ten thousand, hundred thousands.
What Is an Indifference Curve? An indifference curve, with respect to two commodities, is a graph showing those combinations of the two commodities that leave the consumer equally well off or equally satisfied—hence indifferent—in having any combination on the curve. Indifference curves are heuristic devices used in contemporary microeconomics to demonstrate consumer preference and the limitations of a budget. Economists have adopted the principles of indifference curves in the study of welfare economics. - An indifference curve shows a combination of two goods that give a consumer equal satisfaction and utility thereby making the consumer indifferent. - Along the curve, the consumer has an equal preference for the combinations of goods shown—i.e. is indifferent about any combination of goods on the curve. - Typically, indifference curves are shown convex to the origin, and no two indifference curves ever intersect. Understanding an Indifference Curve Standard indifference curve analysis operates on a simple two-dimensional graph. Each axis represents one type of economic good. Along the indifference curve, the consumer is indifferent between any of the combinations of goods represented by points on the curve because the combination of goods on an indifference curve provide the same level of utility to the consumer. For example, a young boy might be indifferent between possessing two comic books and one toy truck, or four toy trucks and one comic book so both of these combinations would be points on an indifference curve of the young boy. Indifference Curve Analysis Indifference curves operate under many assumptions; for example, typically each indifference curve is convex to the origin, and no two indifference curves ever intersect. Consumers are always assumed to be more satisfied when achieving bundles of goods on indifference curves that are farther from the origin. As income increases, an individual will typically shift their consumption level because they can afford more commodities, with the result that they will end up on an indifference curve that is farther from the origin—hence better off. Many core principles of microeconomics appear in indifference curve analysis, including individual choice, marginal utility theory, income, substitution effects, and the subjective theory of value. Indifference curve analysis emphasizes marginal rates of substitution (MRS) and opportunity costs. Indifference curve analysis typically assumes all other variables are constant or stable. Most economic textbooks build upon indifference curves to introduce the optimal choice of goods for any consumer based on that consumer's income. Classic analysis suggests that the optimal consumption bundle takes place at the point where a consumer's indifference curve is tangent with their budget constraint. The slope of the indifference curve is known as the MRS. The MRS is the rate at which the consumer is willing to give up one good for another. If the consumer values apples, for example, the consumer will be slower to give them up for oranges, and the slope will reflect this rate of substitution. Criticisms and Complications of the Indifference Curve Indifference curves, like many aspects of contemporary economics, have been criticized for oversimplifying or making unrealistic assumptions about human behavior. For example, consumer preferences might change between two different points in time rendering specific indifference curves practically useless. Other critics note that it is theoretically possible to have concave indifference curves or even circular curves that are either convex or concave to the origin at various points. Consumer preferences might also change between two different points in time rendering specific indifference curves practically useless.
Ejectives are easier to make at high altitudes since they involve the compression of air, and ejectives also help to reduce the rate of water vapour lost through speech. Certain types of consonant sound are more common in languages spoken at high altitudes, according to anthropological linguist Dr Caleb Everett… Dr Caleb Everett The origin of language has been a hotly debated topic for hundreds of years, and we may never know how, when, where or even exactly why human language first emerged. However, research which recently appeared in the open access journal PLOS ONE provides evidence for at least one of the factors that must have shaped language as it formed and developed. According to Dr Caleb Everett, an associate professor in the Department of Anthropology at the University of Miami, the sounds used in different languages – their phonology – are influenced by geography and, more specifically, topography. In an interview with ScienceOmega.com , Dr Everett explained how he came to investigate the effects of geographic context on the phonology of human language. "Most of my work, which is on language and cognition, is carried out with Amazonian populations," he related. "However, I have also spent some time studying human sound systems, and was led to this research after reading a paper by some anthropologists who suggested that climate could impact sound systems. The data there aren't so convincing, but they got me to thinking about the role of geography." A strong correlation Dr Everett analysed data on around 600 languages, comparing the altitude of the region from which they originated and where they were spoken with the presence or absence of consonants known as ejectives. "I used the World Atlas of Linguistic Structures (WALS) Online, so drawing the comparisons was a matter of extracting the relevant data from the database and using the appropriate geographic and statistical methods," Dr Everett stated. "The confounding variable is relationships between languages of particular language families, but this variable was accounted for in the analysis." Ejective consonants are produced by creating an air pocket in the pharynx before expelling it, and they occur in roughly 20 per cent of the world’s natural languages. Although absent in English and other European tongues, ejectives are common in the native languages of northwestern North America and indeed in most western regions of North and South America. They occur in many languages in southern and eastern Africa, such as Zulu and Tigrinya, and also in the three language families originating from the Caucasus. Na’vi, the constructed language which was created for James Cameron’s film Avatar , was designed to include ejectives. Dr Everett’s analysis uncovered a strong correlation between the presence of ejective consonants in languages and high altitudes. The study found that languages with ejectives are spoken on or near five of the six major high altitude regions which are inhabited by people. Geography and phonology are linked Although he hypothesised that such a relationship might exist, Dr Everett admitted that he was still surprised by the strength of the correlation. But what reason is there for this association to be present? "I think, at this early stage, that there are two possible reasons that the correlation could exist," he said. "Ejectives are easier to make at high altitudes since they involve the compression of air, and ejectives also help to reduce the rate of water vapour lost through speech." Both hypotheses will require further experimental testing, but this is evidence that geography has influenced the phonology of languages in ways that have, for the most part, gone unrecognised. The case of ejectives is not the only one to support this conclusion. "In ongoing research there is evidence that languages in areas with really cold climates rely more heavily on consonants versus vowels, in comparison to languages in warmer climates," Dr Everett confirmed. "Presently I'm analysing data on the relationship between cold climates and syllable structure. Roughly speaking, this means assessing how far languages rely on consonants compared to vowels." Please click here to read the full text of the research paper...
About This Chapter ELM Geometry: Graphing Basics Get ready for the ELM math by watching these online video lessons, then test your knowledge using our interactive online quizzes. The video lessons in this chapter cover the following topics: - Identifying different parts of a graph - Identifying and plotting points on the number line - Identifying and plotting points in the coordinate plane The ELM is a math proficiency exam required for all incoming students to schools in the California State University system. You can learn more about the topics on the ELM. The Graphing Basics chapter is one of many chapters in this course that is focused on Geometry-based skills. Geometry comprises approximately 30% of the entire ELM exam. Other chapters in this courses address other geometry-focused topics, including the following: - Finding the perimeter, area and volume of various geometric figures - Using and applying the Pythagorean Theorem - Solving geometric problems the demonstrate an understanding of essential geometric figures - Determine angles in the plane (using properties of intersecting lines, parallel lines and perpendicular lines) - Graphing linear and quadratic functions - Transferring features of an equation to features of a corresponding graph Mastering the concepts covered in this chapter will provide you with a solid foundation for the corresponding portion of the ELM. 1. What Is a Number Line? A number line is a visual representation of all real numbers. In this lesson, we'll learn how to identify points on a number line. We'll also practice addition and subtraction, letting the number line do all the hard work. 2. What Are the Different Parts of a Graph? Being able to read a graph isn't just vital for an algebra class. Graphs and charts are used everywhere! We'll take a crash course on the basic x/y plane used in algebra and the fundamental vocab you need. 3. Plotting Points on the Coordinate Plane If you'll be working with a graph, otherwise known as the coordinate plane, it's essential to understand how it works. This includes learning the parts of a graph, identifying points and plotting points. Earning College Credit Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level. To learn more, visit our Earning Credit Page Transferring credit to the school of your choice Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you. Other chapters within the ELM: CSU Math Study Guide course - ELM Test - Numbers and Data: Basic Arithmetic Calculations - ELM Test - Numbers and Data: Rational Numbers - ELM Test - Numbers and Data: Decimals and Percents - ELM Test - Numbers and Data: Irrational Numbers - ELM Test - Numbers and Data: Data & Statistics - ELM Test - Algebra: Basic Expressions - ELM Test - Algebra: Exponents - ELM Test - Algebra: Linear Equations & Inequalities - ELM Test - Algebra: Absolute Value Equations & Inequalities - ELM Test - Algebra: Polynomials - ELM Test - Algebra: Rational Expressions - ELM Test - Geometry: Perimeter, Area & Volume - ELM Test - Geometry: Properties of Objects - ELM Test - Geometry: Graphing Functions - About the ELM Test - ELM Flashcards
We have covered quite a number of topics up to this point: the structure of atoms, discrete molecules, complex network solids, and metals; how atoms and molecules interact, through London dispersion forces, dipole-dipole interactions, hydrogen bonds, and covalent and ionic bonds. We have discussed how changes in energy and entropy lead to solid, liquid, and gas state changes. So far, so good, but is this really chemistry? Where are the details about chemical reactions, acids and bases, gas laws, and so forth? Not to worry—we have approached the topics in this order so that you have a strong conceptual foundation before you proceed to the nuts and bolts of chemical reactions. Without this foundation, you would just memorize whatever equations we presented, without making the connections between seemingly disparate reactions. Many of these reactions are complex and overwhelming even for the most devoted student of chemistry. The topics we have covered so far will serve as a tool kit for understanding the behavior of increasingly complex chemical systems. We will continue to reinforce these basic ideas and their application as we move on to the types of reactions that are relevant to most chemical systems. 6.1 What Is a Solution? The first type of complex system that we will consider is a solution. You almost certainly already have some thoughts about what a solution is and you might want to take a moment to think about what these are. This will help you recognize your implicit assumptions if they “get in the way” of understanding what a solution is scientifically. The major difference between a solution and the systems we have previously discussed is that solutions have more than one chemical substance in them. This raises the question: what exactly is a solution and what does it mean to dissolve? You are probably thinking of examples like sugar or salt dissolved in water or soda. What about milk? Is it a solution? Do solutions have to be liquid or can they also include gases and solids? What is the difference between a solution and a mixture? It turns out that we can make solutions from a wide range of materials. Although it is common to think of solutions in terms of a solid dissolved into a liquid, this is not the only type of solution. Other examples of solutions include: gas in liquid (where molecular oxygen, or O2, dissolves in water – important for fish); solid in solid (the alloy brass is a solution of copper and zinc); gas in solid (hydrogen can be dissolved in the metal palladium); and liquid in liquid (beer is a solution of ethanol and water and a few other things). Let us take a closer look at what we mean by a solution, starting with a two-component system. Typically, one of the components is present in a smaller amount than the other. We call the major component the solvent and the minor component(s) the solute(s). The most familiar solutions are aqueous solutions, in which water is the solvent. For example, in a solution of the sugar glucose in water, glucose molecules are the solute and water molecules are the solvent. In beer, which is typically 2–4% ethanol, ethanol is the primary solute and water is the solvent. Once they are thoroughly mixed, solutions have the same composition throughout—they are homogeneous at the macroscopic scale, even though at the molecular level we still find different types of molecules or ions. This is an important point: Once mixed, they remain mixed! If you take a sample from the top of a solution, it has the same composition as a sample from elsewhere in the solution. Solutions, when viewed at the molecular level, have the solute particles evenly (and randomly) dispersed in the solute. Also, because the solute and solvent are in contact with each other, there must be some kind of molecular interaction between the two types of molecules. This is not true for simple mixtures. For example, we tend to describe air as a mixture of gases (N2, O2, H2O, etc.), rather than a solution because the gas molecules do not interact aside from the occasional collision with each other. Molecular Formation of Solutions Let us consider a solution of ethanol and water. Many common solutions contain these two components (usually with minor amounts of other substances as well). Ethanol and water are soluble in each other (what is known as “miscible”) in all proportions. For example, beer is typically about 3% alcohol (6% proof), wine about 6% alcohol (12% proof), and liquors such as whiskey or brandy are about 50% alcohol (100% proof). How do they dissolve into each other at the molecular level, and why? For a process to be thermodynamically favorable, the Gibbs (free) energy change (ΔG) associated with that process must be negative. However, we have learned that Gibbs energy change depends on both enthalpy (H) and entropy (S) changes in the system. It is possible to envision a wide range of situations – involving both positive and negative changes in H and S, and we have to consider the magnitudes of the enthalpy, the entropy and the temperature changes. So what happens when we add a drop of ethanol to a volume of water? The ethanol molecules rapidly disperse and the solution becomes homogeneous. The entropy of the ethanol–water solution is higher than that of either substance on its own. In other words, there are more distinguishable arrangements of the molecules when they are mixed than when they are separate. Using simple entropic arguments we might, at least initially, extend the idea to include all solutions. Everything should be soluble in everything else, because this would to an entropy increase, right? Wrong. We know that this is not true. For example, oil is not soluble in water and neither are diamonds, although for very different reasons. So what are the factors influencing solution formation? We will see that some are entropic (involving ΔS) and some enthalpic (involving ΔH.) Questions to Answer - Make a list of some common solutions you might encounter in everyday life. How do you know they are solutions and not mixtures? - Consider a solution formed from 100 g of water and 5 g sodium chloride: - What would you expect the mass of the solution to be? Why? - What would you expect the volume of the solution to be? Why? - How would you test your hypotheses? What experiments would you do? - What evidence would you collect? 6.2 Solubility: why do some things form solutions and others not? Let us say you have a 100-mL graduated cylinder and you take 50 mL of ethanol and add it to 50 mL of water. You might be surprised to find that the volume of the resulting solution is less than 100 mL. In fact, it is about 98 mL, assuming good technique (no spilling). How can we explain this? Well, we can first reassure ourselves that matter has not been destroyed. If we weigh the solution, it weighs the same as 50 mL of water plus 50 mL of ethanol. This means that the density of the water–ethanol solution must be greater than the density of either the water or ethanol alone. At the molecular level, we can immediately deduce that the molecules are closer together in the ethanol and water mixture than they were when pure (before mixing) –try drawing a molecular level picture of this to convince yourself that this is possible. Now, if you took 50 mL of oil and 50 mL of water, you would find that they do not mix—no matter how hard you tried. They will always separate away from one another into two layers. What factors determine whether or not substances form solutions? First, we need to be aware that solubility is not an all-or-nothing property. Even in the case of oil and water, a very small number of oil molecules are present in the water (the aqueous phase), and a small number of water molecules are present in the oil. There are a number of ways to describe solubility. The most common way is to define the number of moles of solute per liter of solution. This is called the solution’s molarity (M, mol/L). Another common way is to define the number grams of solute per mass of solution. For example: 1 mg (10-3 g) of solute dissolved in 1 kg (103 g) of solution is 1 part per million (106) solute, or 1 ppm. As you might expect, given the temperature term in the free energy equation, solubility data are always reported at a particular temperature. If no more solute can dissolve at a given temperature, the solution is said to be saturated; if more solute can dissolve, it is unsaturated. If we look at the structure of compounds that dissolve in water, we can begin to see some trends: hydrocarbons are not very soluble in water (remember from Chapter 4 that these are compounds composed only of carbon and hydrogen), whereas alcohols (hydrocarbons with an —O–H group attached) with up to 3 carbons are completely soluble. As the number of carbon atoms increases, the solubility of the compound in water decreases. For example, hexanol (CH3CH2CH2CH2CH2CH2OH), is only very slightly soluble in water (0.4 g/L). So perhaps the hydroxyl (—O–H) group is responsible for the molecule’s solubility in water. Evidence supporting this hypothesis can be found in the fact that diols (compounds with 2 —O–H groups) are more soluble than similar alcohols. For example, compared to hexanol, 1,6-hexanediol (HOCH2CH2CH2CH2CH2CH2CH2OH) is quite soluble in water. More familiar water-soluble compounds such as the sugars glucose, fructose, and sucrose (a dimer of glucose and fructose – shown in the figure) are, in fact, polyalcohols. Each of their six carbons is attached to a hydroxyl group. \|Compound\|\|Molar Mass (g/mol)\|\|Structure\|\|Solubility (g/L) 20 ºC\| \|Dimethyl ether\|\|46\|\|CH3OCH3\|\|328 g/L\| \|Diethyl ether\|\|74\|\|CH3CH2OCH2CH3\|\|69 g/L\| \|1,6 Hexanediol\|\|226\|\|HOCH2H2CH2CH2CH2CH2CH2OH\|\|500 g/L\| Questions to Answer - Make a list of substances that you know dissolve in water. - Which of these dissolve: metals, ionic compounds, molecular compounds (polar, non-polar), network solids (diamond graphite)? - Can you make any generalizations about which things dissolve and which don’t? - What must happen in order for something to dissolve in water? - How would you design an experiment to determine the solubility of a solute? - How would you determine whether or not a solution was saturated? - Draw a molecular level picture of a solution of ethanol and water showing why the solution is more dense than the separate liquids. - Draw a molecular level picture of an oil and water mixture. - Draw a molecular level picture of the process of solution - When you try mixing oil and water, which layer ends up on top? Why? Question to Ponder - You have a saturated solution, with some solid solute present. - Do you think the solute particles that are in solution are the same ones over time? - How would you determine whether they were the same? Questions for Later - What would you predict for the sign of ΔS upon the formation of any solution? Why? - What would you predict for the sign of ΔH upon the formation of any solution? Why? - What would you predict for the sign of ΔG upon the formation of any solution? Why? 6.3 Hydrogen Bonding Interactions and Solubility How does adding hydroxyl groups increase the solubility of a hydrocarbon in water? To understand this, we must return to the two components of the free energy equation: enthalpy and entropy. For a solute to dissolve in a liquid, the solute molecules must be dispersed in that liquid. Solubility depends on how many solute molecules can be present within a volume of solution before they begin to associate preferentially with themselves rather than the solvent molecules. When the solute molecules are dispersed, whatever bonds or attractions holding the particles together in the solute are replaced by interactions between solvent and solute molecules. You might deduce that one reason diamonds are not soluble in water is that the C—C bonds holding a carbon atom within a diamond are much stronger (take more energy to break) than the possible interactions between carbon atoms and water molecules. For a diamond to dissolve in water, a chemical reaction must take place in which multiple covalent bonds are broken. Based on this idea, we can conclude that the stronger the interactions between the solute particles, the less favorable it is for the solute to dissolve in water. At the same time, the stronger the interactions between solute and solvent molecules, the greater the likelihood that solubility will increase. So do intermolecular interactions explain everything about solubility? Do they explain the differences between the solubility of hexane, hexanol, and hexanediol in water? Hexanediol (HO(CH2)6OH) is readily soluble, and if we consider its structure we can see that interactions between hexanediol molecules include hydrogen bonding (involving the two hydroxyl groups) and van der Waals interactions (LDFs and dipole-dipole). We can also approach this from a more abstract perspective. If we indicate the non-hydroxyl (—O–H) part of a molecule as R, then an alcohol molecule can be represented as R—O—H, and a diol can be represented as H–O—R—O–H. All alcohols have the ability to form hydrogen bonding interactions with each other as well as with water. So when an alcohol dissolves in water, the interactions between the alcohol molecules are replaced by interactions between alcohol and water molecules—an interaction similar to that between water molecules. Like water molecules, alcohols have a dipole (unequal charge distribution), with a small negative charge on the oxygen(s) and small positive charges on the hydrogen (bonded to the oxygen atoms). It makes sense that molecules with similar structures interact in similar ways. Thus, small molecular-weight alcohols can dissolve in water. But if you look again at the previous table, notice that hexanol (a 6-carbon chain with one —O–H group) is much less soluble than hexanediol (a 6-carbon chain with two —O–H groups—one at each end). As the non-polar carbon chain lengthens, the solubility typically decreases. However, if there are more —O–H groups present, there are more possible interactions with the water. This is also why common sugars, which are really polyalcohols with large numbers of —O–H groups (at least 4 or 5 per molecule), are very soluble in water. Their –O–H groups form hydrogen-bonds with water molecules to form stabilizing interactions. As the length of the hydrocarbon chain increases, the non-polar hydrocarbon part of the molecule starts to become more important and the solubility decreases. This phenomenon is responsible for the “like-dissolves-like” statements that are often found in introductory chemistry books (including this one, apparently). So, do intermolecular interactions explain everything about solubility? If only things were so simple! Entropy and Solubility: Why Don’t Oil and Water Mix? The fact that oil and water do not mix is well known. It has even become a common metaphor for other things that do not mix (people, faiths, etc.) What is not quite so well known is, why? Oil is a generic name for a group of compounds, many of which are hydrocarbons or contain hydrocarbon-like regions. Oils are – well – oily, they are slippery and (at the risk of sounding tedious) unable to mix with water. The molecules in olive oil or corn oil typically have a long hydrocarbon chain of about 16–18 carbons. These molecules often have polar groups called esters (groups of atoms that contain C—O bonds) at one end. Once you get more than six carbons in the chain, these groups do not greatly influence solubility in water, just as the single O—H groups in most alcohols do not greatly influence solubility. So, oily molecules are primarily non-polar and interact with one another as well as with other molecules (including water molecules), primarily through London dispersion forces (LDFs). When oil molecules are dispersed in water, their interactions with water molecules include both LDFs and interactions between the water dipole and an induced dipole on the oil molecules. Such dipole–induced dipole interactions are common and can be significant. If we were to estimate the enthalpy change associated with dispersing oily molecules in water, we would discover ΔH is approximately zero for many systems. This means that the energy required to separate the molecules in the solvent and solute is about equal to the energy released when the new solvent–solute interactions are formed. Remember that the entropy change associated with simply mixing molecules is positive. So, if the enthalpy change associated with mixing oils and water is approximately zero, and the entropy of mixing is usually positive, why then do oil and water not mix? It appears that the only possibility left is that the change in entropy associated with dissolving oil molecules in water must be negative (thus making ΔG positive.) Moreover, if we disperse oil molecules throughout an aqueous solution, the mixed system spontaneously separates (unmixes). This seems to be a process that involves work. What force drives this work? Rest assured, there is a non-mystical explanation but it requires thinking at both the molecular and the systems level. When hydrocarbon molecules are dispersed in water, the water molecules rearrange to maximize the number of H-bonds they make with one another. They form a cage-like structure around each hydrocarbon molecule. This cage of water molecules around each hydrocarbon molecule is a more ordered arrangement than that found in pure water, particularly when we count up and add together all of the individual cages! It is rather like the arrangement of water molecules in ice, although restricted to regions around the hydrocarbon molecule. This more ordered arrangement results in a decrease in entropy. The more oil molecules disperse in the water, the larger the decrease in entropy. On the other hand, when the oil molecules clump together, the area of “ordered water” is reduced; fewer water molecules are affected. Therefore, there is an increase in entropy associated with the clumping of oil molecules—a totally counterintuitive idea! This increase in entropy leads to a negative value for –TΔS, because of the negative sign. Therefore, in the absence of any other factor the system moves to minimize the interactions between oil and water molecules, which leads to the formation of separate oil and water phases. Depending on the relative densities of the substances, the oily phase can be either above or below the water phase. This entropy-driven separation of oil and water molecules is commonly referred to as the hydrophobic effect. Of course, oil molecules are not afraid (phobic) of water, and they do not repel water molecules. Recall that all molecules will attract each other via London dispersion forces (unless they have a permanent and similar electrical charge). The insolubility of oil in water is controlled primarily by changes in entropy, so it is directly influenced by the temperature of the system. At low temperatures, it is possible to stabilize mixtures of water and hydrocarbons. In such mixtures, which are known as clathrates, the hydrocarbon molecules are surrounded by stable cages of water molecules (ice)(→). Recall that ice has relatively large open spaces within its crystal structure. The hydrocarbon molecules fit within these holes, making it possible to predict the maximum size of the hydrocarbon molecules that can form clathrates. For example, some oceanic bacteria generate CH4 (methane), which is then dissolved in the cold water to form methane clathrates. Scientists estimate that between two and ten times the current amount of conventional natural gas resources are present as methane clathrates. Solubility of Ionic Compounds: Salts Polar compounds tend to dissolve in water, and we can extend that generality to the most polar compounds of all—ionic compounds. Table salt, or sodium chloride (NaCl), the most common ionic compound, is soluble in water (360 g/L). Recall that NaCl is a salt crystal composed not of discrete NaCl molecules, but rather of an extended array of Na+ and Cl– ions bound together in three dimensions through electrostatic interactions. When NaCl dissolves in water, the electrostatic interactions within the crystal must be broken. By contrast, when molecular compounds dissolve in water, it is the intermolecular forces between separate molecules that are disrupted. One might imagine that the breaking of ionic interactions would require a very high-energy input (we have already seen that diamonds do not dissolve in water because actual covalent bonds have to be broken). That would be true if all we considered was the energy required to break the ionic interactions, as indicated by the fact that NaCl melts at 801 ºC and boils at 1413 ºC. But we know that substances like NaCl dissolve readily in water, so clearly there is something else going on. The trick is to consider the whole system when NaCl dissolves, just like we did for molecular species. We need to consider the interactions that are broken and those that are formed. These changes in interactions are reflected in the ΔH term (from ΔG = ΔH – TΔS). When a crystal of NaCl comes into contact with water, the water molecules interact with the Na+ and Cl– ions on the crystal’s surface, as shown in the figure. The positive ends of water molecules (the hydrogens) interact with the chloride ions, while the negative end of the water molecules (the oxygen) interacts with the sodium ions. So the ion on the surface of the solid interacts with water molecules from the solution; these water molecules form a dynamic cluster around the ion. Thermal motion (which reflects the kinetic energy of the molecules, that is the motion driven by collisions with other molecules in the system) then moves the ion and its water shell into solution. The water shell is highly dynamic—molecules are entering and leaving it. The ion–dipole interaction between ions and water molecules can be very strongly stabilizing (-ΔH). The process by which solvent molecules interact with and stabilize solute molecules in solution is called solvation. When water is the solvent, the process is known as hydration. Questions to Answer - Draw a molecular-level picture of a solution of NaCl. Show all the kinds of particles and interactions present in the solution. - When we calculate and measure thermodynamic quantities (such as ΔH, ΔS and ΔG), why is it important to specify the system and the surroundings? - When a substance dissolves in water, what is the system and what are the surroundings? Why? What criteria would you use to specify the system and surroundings? - For a solution made from NaCl and water, what interactions must be overcome as the NaCl goes into solution? What new interactions are formed in the solution? - If the temperature goes up when the solution is formed, what can we conclude about the relative strengths of the interactions that are broken and those that are formed? What can we conclude if the temperature goes down? - When you measure the temperature of a solution, are you measuring the system or the surroundings? Questions to Ponder - Why is the water shell around an ion not stable? - What are the boundaries of a biological system? 6.4 Gibbs Energy and Solubility Try adding NaCl to water, you can do this at the dinner table. You will see that the NaCl dissolves and the temperature of the solution goes down. Is this the case with all salts? No, it is not. If you dissolve calcium chloride (CaCl2) or magnesium chloride (MgCl2), the solution gets warmer, not colder. Dissolving CaCl2 or MgCl2 in water clearly involves some kind of energy release (recall that if the temperature increases, the average kinetic energy of the molecules in the solution also increases). How do we explain why dissolving NaCl causes the temperature of the solution to decrease, whereas dissolving CaCl2 or MgCl2 makes the temperature increase? Because both processes (that is the dissolving of NaCl and CaCl2/MgCl2 into water) occur, they must be thermodynamically favorable. In fact, all of these compounds are highly soluble in water, the ΔG for the formation of all three solutions is negative, but the process results in different temperature changes. Let us look at the example of calcium chloride: as a crystal of CaCl2 dissolves in water, interactions between ions are broken and new interactions between water molecules and ions are formed. The table below lists the types of interactions forming in the crystal and the solvent. Within the crystal, there are ion–ion interaction while in the solvent there are H-bonding, dipole–dipole, and LDF interactions. As the crystal dissolves, new ion–dipole interactions form between calcium ions and water molecules, as well as between chloride ions and molecules. At the same time, the majority of the interactions between water molecules are preserved. \|Interactions Present Before Solution\|\|Interactions Present After Solution\| (interactions between Ca2+ and Cl–) interactions between Ca2+ and H2O and Cl– and H2O) \|Interactions Between Water Molecules \| H-bonding, dipole–dipole, and LDFs \|Interactions Between Water Molecules \| H-bonding, dipole–dipole, and LDFs In order to connect our observation that the temperature increases with thermodynamic data, we have to be explicit about what we mean by the system and what we mean by the surroundings. In calcium chloride, the system is CaCl2 and the water molecules it interacts with. The surroundings are the rest of the water molecules (the solution). So when we measure the temperature change, we are actually measuring the temperature change of the surroundings (not the system). If the temperature rises, that means thermal energy is transferred from the CaCl2—H2O system to the water. Therefore, the interactions after the solution is formed are stronger and more stable than those for the solid CaCl2 and water separately. If we look up the enthalpy change for the solution of calcium chloride, it is around -80 kJ/mol: dissolving is exothermic and heat is transferred from the system to the surroundings. So what is going on with NaCl? Solution temperatures decrease when NaCl is dissolved, so the solution (surroundings) loses energy to the ion–solvent interactions (system). Energy from the surroundings breaks up the NaCl lattice and allows ions to move into the solution. That would imply that ion–ion and H2O–H2O interactions are stronger than the ion–water interactions for the NaCl–H2O system. But why does NaCl dissolve at all? The answer is that enthalpy is not the critical factor determining whether solution happens. If we factor in the entropy change for the solution, which in this case is positive, then ΔG is negative. The dissolving of salt is an entropy-driven process! To recap: for a solution to form, the Gibbs energy change must be negative. When calcium chloride dissolves in water, ΔH is negative and as it turns out ΔS is slightly negative (although this cannot be determined from observations). This results in a large negative ΔG and a very high solubility (595 g/L). By contrast, when sodium chloride dissolves, ΔH is positive, but ΔS is positive enough to overcome the effect of ΔH. This means that the Gibbs free energy change is also negative for this process. In fact, many solutes dissolve in water with a decrease in temperature. Ethanol—which is infinitely soluble in water—has an unfavorable enthalpy of solution. Thus, the entropy of mixing is the important factor. Questions to Answer - When ammonium chloride dissolves in water, the temperature of the solution drops. Predict the signs of ΔH, ΔS, and ΔG.and explain your reasoning by drawing molecular level pictures - Calcium phosphate (Ca3(PO4)3) is insoluble in water. The ΔH for solution is about zero. Predict the signs of ΔS and ΔG and explain your reasoning by drawing molecular-level pictures. So far we have considered solutions that are made up of molecules that are either polar or non-polar or ionic species that have properties that are relatively easy to predict. Many substances, however, have more complex structures that incorporate polar, ionic, and non-polar groups. For example, many biomolecules cannot be classified as exclusively polar or non-polar, but are large enough to have distinct regions of differing polarity. They are termed amphipathic. Even though the structures of proteins such as RNA, DNA, and other biomolecules are complex, we can use the same principles involving entropic and enthalpic effects of interacting with water to understand the interactions between biomolecules, as well as within a given biomolecule. Biomolecules are very large compared to the molecules considered in most chemistry courses, and often one part of the molecule interacts with another part of the same molecule. The intramolecular interactions of biological macromolecules, together with their interactions with water, are key factors in predicting their shapes. Let us begin with a relatively simple biomolecular structure. In the previous section we looked at the solubility of oils in water. Oils or fats are also known as a triglycerides. In the figure, R and R’ indicate hydrocarbon chains, which have the generic structure CH3CnH2n, shown in the figure. If you treat an oil or fat with sodium hydroxide (NaOH), the resulting chemical reaction leads to the formation of what is known as a fatty acid (in this example, oxygen atoms are maroon). A typical fatty acid has a long, non-polar hydrocarbon chain and one end that often contains both a polar and ionic group. The polar head of the molecule interacts with water with little or no increase in entropy, unlike a hydrocarbon, where the lack of H-bonding interactions with water forces a more ordered shell of water molecules around the hydrocarbon molecule, leading to a decrease in entropy. On the other hand, in water the non-polar region of the molecule creates a decrease in entropy as water molecules are organized into a type of cage around it—an unfavorable outcome in terms of ΔS, and therefore ΔG as well. So, which end of the molecule “wins”? That is do such molecules dissolve in water or not? The answer is: Both! These amphipathic molecules become arranged in such a manner that their polar groups are in contact with the water, while their non-polar regions are not. (See whether you can draw out such an arrangement, remembering to include the water molecules in your drawing.) In fact, there are several ways to produce such an arrangement, depending in part on the amount of water in the system. A standard micelle is a spherical structure with the polar heads on the outside and the non-polar tails on the inside. It is the simplest structure that can accommodate both hydrophilic and hydrophobic groups in the same molecule. If water is limiting, it is possible to get an inverted micelle arrangement, in which polar head groups (and water) are inside and the non-polar tails point outward (as shown in the figure). Other highly organized structures can form spontaneously depending on the structure of the head group and the tail. For example, lipid molecules have multiple hydrocarbon tails and carbon ring structures called sterols. That structure creates a lipid bilayer—a polar membrane made up of two lipid molecule layers that form cellular and organellar boundaries in all organisms. It should be noted that these ordered structures are possible only because dispersing the lipid molecules in water results in a substantial decrease in the disorder of the system. In fact, many ordered structures associated with living systems, such as the structure of DNA and proteins, are the result of entropy-driven processes, yet another counterintuitive idea. This is one of the many reasons why biological systems do not violate the laws of thermodynamics and why it is scientifically plausible that life arose solely due to natural processes! Questions to Answer - If you had a compound that you suspected might form micelles: - What structural features would you look for? - How might you design an experiment to determine whether the compound would form micelles in water? - What would be the experimental evidence? - Why do you think some amphipathic molecules form spherical clusters (micelles or liposomes) whereas others form sheets (bilayers)? (Hint: consider the shape of the individual molecule itself.) - Amphipathic molecules are often called surfactants. For example, the compounds used to disperse oil spills are surfactants. How do you think they work? Questions to Ponder - If membrane formation and protein folding are entropy-driven processes, does that make the origins of life seem more or less “natural” to you? Solutions, Colloids & Emulsions So, do micelles dissolve in water? Well, micelles are not molecules but rather supramolecular assemblies composed of many distinct molecules. A glucose solution consists of isolated glucose molecules but micelles in solution consist of larger molecular aggregates. Solutions of macromolecular solutes are called colloids. These particles can be aggregates of molecules (like micelles), atoms (nanoparticles), or larger macromolecules (proteins, nucleic acids), among others. When these particles are on the order of the wavelength of visible light, they scatter the light; smaller objects do not. This is why a salt or sugar solution is translucent, whereas a colloidal dispersion of micelles or cells is cloudy. This principle also explains why soap solutions are typically cloudy—they contain particles large enough to scatter the light. When the particles in a solution maintain the structure of a solid, the end result is known as a colloid. The colloid is stable because the thermal movements of these small, solid particles are suspended. As the particles get larger, the colloid becomes unstable; the influence of gravity overcomes the effects of thermal motion and the particles settle out. Before they settle out, such unstable systems are known as suspension But if the suspended particles are liquid, the system is known as an emulsion. For example, if we looked at a salad dressing made of oil and water under a microscope, we would see drops of oil suspended in water. Emulsions are often unstable, and over time the two liquid phases separate. This is why you have to shake up salad dressing just before using it. There are many colloids and emulsions in the world around us. Milk, for example, is an emulsion of fat globules and a colloid of protein (casein) micelles. 6.6 Temperature and Solubility Can you also predict the effect of temperature on solubility? If you raise the temperature, does solubility of a solute increase or decrease? It would be reasonable to assume that increasing temperature increases solubility. But remember that both ΔH and ΔS have a role, and an increase in temperature increases the effect of changes in entropy. Dissolving solute into solvent is likely to increase entropy (if ΔS is positive), but this is not always the case. Consider what happens when you heat up water on the stove. Bubbles of gas are released from the liquid long before the water reaches its boiling point. At low temperatures, these bubbles contain air (primarily N2, O2) that was dissolved in the water. Why? Because the solubility of most gases in water decreases as temperature rises. We can trace the reason for this back to the entropy of solution. Most gases have very small intermolecular attractions – this is the reason why they are gases after all. Gas molecules do not stick together and form solids and liquids. Therefore, they do not have very high solubility in water. As an example, the solubility of O2 in water is 8.3 mg/L (at 25 ºC and 1 atmosphere). Most gases have a slightly favorable (negative) enthalpy of solution and a slightly unfavorable (negative) entropy of solution. The effect on enthalpy can be traced to the dipole–induced dipole attractions formed when the gas dissolves in the solution. The decrease in entropy results from the fact that the gas molecules are no longer free to roam around – their positional entropy is more constrained within the liquid phase than it is in the gas phase. When the temperature is increased the gas molecules have more kinetic energy and therefore more of them can escape from the solution, increasing their entropy as they go back to the gas phase. Thus, the solubility of O2 and other gases decreases as temperature increases. This can produce environmental problems, because less oxygen is available for organisms that live in the water. A common source of thermal pollution occurs when power plants and manufacturing facilities expel warm water into the environment. Solutions of Solids in Solids: Alloys Another type of solution occurs when two or more elements, typically metals, are melted and mixed together so that their atoms can intersperse, forming an alloy. Upon re-solidification, the atoms become fixed in space relative to each other and the resulting alloy has different properties than the two separate metals. Bronze was one of the first known alloys. Its major component is copper (~90%) and its minor component is tin (~10%), although other elements such as arsenic or phosphorus may also be included. The Bronze Age was a significant leap forward in human history. Before bronze, the only metals available were those that occurred naturally in their elemental form—typically silver, copper, and gold, which were not well suited to forming weapons and armor. Bronze is harder and more durable than copper because the tin atoms substitute for copper atoms in the solid lattice. Its structure has stronger metallic bonding interactions, making it harder and less deformable, with a higher melting point than copper itself. Artifacts (weapons, pots, statues, etc.) made from bronze are highly prized. Before bronze, the only metals available were those that occurred naturally in their elemental form– typically silver, copper, and gold. Steel is another example of a solid–solid solution. It is an iron solvent with a carbon solute. The carbon atoms do not replace the iron atoms, but fit in the spaces between them; this is often called an interstitial alloy. Because there are more atoms per unit volume, steel is denser, harder, and less metallic than iron. The carbon atoms are not in the original lattice, so they affect the metallic properties more and make it harder for the atoms to move relative to each other. Steel is more rigid, less malleable, and conducts electricity and heat less effectively than iron. Is the Formation of a Solution a Reaction? We have not yet considered what happens during a chemical reaction: a process where the atoms present in the starting material are rearranged to produce different chemical species. You may be thinking, “Isn’t the formation of a solution a chemical reaction?” If we dissolve ethanol in water, does the mixture contain chemically different species than the two components separately? The answer is no: there are still molecules of ethanol and molecules of water. What about when an ionic substance dissolves in water? For example, sodium chloride must separate into sodium and chloride ions in order to dissolve. Is that a reaction? Certainly interactions are broken (the interactions between Na+ Cl– ions) and new interactions are made (between Na+ ions and water and Cl– ions and water), but the dissolution of a salt has not traditionally been classified as a reaction, even though it seems to fit the criteria. Rather than quibble about what constitutes a reaction, let us move along the spectrum of possible changes and look at what happens when you dissolve a molecular species in water and it forms ions. When you dissolve hydrogen chloride, HCl (a white, choking gas), in water you get an entirely new chemical substance: hydrochloric acid (or muriatic acid as it is known in hardware stores), one of the common strong acids. This reaction can be written: HCl (g) + H2O ➞ HCl (aq) This is a bit of shorthand because we actually begin with lots of water, but not much of it is used in the reaction. We indicate this fact by using the aq symbol for aqueous, which implies that the HCl molecules are dissolved in water (but as we will see they are now no longer molecules). It is important to recognize that hydrochloric acid, HCl (aq), has properties that are quite distinct from those of gaseous hydrogen chloride HCl (g). The processes that form hydrochloric acid are somewhat similar to those that form a solution of sodium chloride, except that in this case it is the covalent bond between H and Cl that is broken and a new covalent bond between H and O is formed at the same time. HCl(g) + H2O ➞ H3O+ + Cl– We call this reaction an acid–base reaction. In the next chapter, we will consider this and other reactions in (much) greater detail. Questions to Answer Can you convert the solubility of O2 in water into molarity (moles solute (O2) / liter solution)? If solubility of gases depends on dipole–induced dipole interactions, what do you think the trend in solubility is for the noble gases (He, Ne, Ar, Kr, Xe)? What else might increase the solubility of a gas (besides lowering the temperature)? (Hint: How are carbonated drinks bottled?) Why do you think silver, copper, and gold often occur naturally as elements (rather than compounds)? Draw an atomic-level picture of what you imagine bronze looks like and compare it to a similar picture of steel. Use these pictures to explain the properties of bronze and steel, as compared to copper and iron. Questions to Ponder - Why do you think the Iron Age followed the Bronze Age? (Hint: Does iron normally occur in its elemental form? Why not?) - How did the properties of bronze and steel influence human history? - Percent proofing of alcoholic beverages can be traced back to the 18th century, when British sailors were partially paid in rum. To prevent it from being watered down, the rum was “proofed” by seeing if it would support the combustion of gunpowder. ↵ - Silverstein, Todd P. J. Chem. Educ. 1998 75 116 ↵ - See additional materials for structures and names of functional groups. ↵ - ACS GenChem materials ↵ - Intramolecular means within the same molecule. Intermolecular means between or among separate molecules. ↵ - For examples, see the internet game “foldit”, which uses intramolecular interactions to predict how proteins will fold into the lowest energy shape. ↵ - Why do you use soap and shampoo? Why not use just water? The answer is, of course, that water doesn’t do a very good job of getting dirt and oil of your skin and hair because grime is just not soluble in water. Soaps and detergents are excellent examples of amphipathic molecules. They both have a polar head and a long non-polar tail, which leads to the formation of micelles. Oily molecules can then be sequestered within these micelles and washed away. ↵ - It is often possible to track the passage of a beam of light through such a solution, known as the Tyndall effect. ↵ - At the boiling point, the bubbles contain only water molecules because all the air has been expelled long before this temperature is reached. ↵ - It has been noted that one reason why chemistry is so difficult is that even experienced chemists cannot agree on the terminology and this is one such example. ↵
SHARE THE ARTICLE ON A correlation coefficient (r) is a statistical measure of the strength of the relationship between two variables; x and y. There are many different types of correlation coefficients, however, Pearson’s correlation coefficient is most widely used in research. Pearson’s correlation coefficient, also known as Pearson’s R, is a correlation coefficient that is generally used in linear regression to find the strength and direction of the linear relationship between two variables. Create an actionable feedback collection process. Pearson’s r can be calculated using the following correlation coefficient formula: The value of r always lies between +1 and -1. Values above 0 indicate a positive relationship; when one value increases, the other increases as well. Values below 0 indicate a negative relationship; when one value increases, the other decreases. When r is 0, there is no correlation between the two variables. More precise interpretations can be made by seeing which one of the following values is closest to your correlation coefficient r: The following image reflects how different r values are reflected on a scatter plot: Get market research trends guide, Online Surveys guide, Agile Market Research Guide & 5 Market research Template The limitations of pearson’s r are: It is important to keep in mind that Pearson’s correlation coefficient connot be used with all types of variables and the two variables must be measured either on the interaval scale or the ratio scale. The variables do not, however, need to be measured on the same scale; Pearson’s r can still be used when one variable is on the interval scale while the other is on the ratio scale. Additionally, the two variables do not have to be measured in the same units. For instance, the correlation coefficient r could be used to correlate a person’s height to their food intake, although these are completely different units of measurement (height is measured in feet while food intake is measured in calories). A correlation coefficient (r) is a statistical measure that reflects the strength of the relationship between two variables; x and y. r values range between -1 and +1. Values above 0 indicate a positive, or direct, relationship while values below 0 indicate a negative, or indirect, relationship. When r is 0, it indicates that there is no relationship between the two variables. The two main limitations of Pearson’s R are; The two main types of correlation coefficients are Pearson’s correlation coefficient (Pearson’s R) and Spearman’s correlation coefficient (Spearman’s p). Pearson’s R indicates the strength and direction of the linear relationship between two variables while Spearman’s p indicates the strength and direction of the monotic relationship between two variables.
Input and Output Boxes \| Division Worksheets Develop division skills employing this collection of worksheets with in and out boxes, hand-picked for 3rd grade, 4th grade, and 5th grade kids. Exercises such as fill the out box using the division rule, understand the pattern and write the division rule, complete the input-output function tables, division function machine and many more; involving 2-digit numbers divided by a single digit in Level 1 and 3-digit numbers divided by divisors up to 20 in Level 2. Solve word problems as well. Click on our free worksheets to start your practice! Work out the quotient by dividing each 2-digit dividend in the in box with the divisor specified in the division rule. Plug it in the out box to complete this set of in-out box pdf worksheets. Level up with this compilation of printable worksheets featuring 3-digit dividends in the input box. Divide each number by the divisor given in the rule and write the answer in the output box. Observe the input-output tables keenly, comprehend the pattern and identify the rule for the six boxes presented in each worksheet along with an interesting in-out function table using shapes, to apply division skills. Recapitulate division skills with this batch of 3rd grade and 4th grade division worksheets. The in-out boxes are filled with the dividends and quotients, figure out the division rule or divisor in each box. This stack of pdf worksheets serves best in testing division skills. Either the input or output of the table is empty, apply the indicated rule and fill in the function table. Involving single-digit and double-digit divisors up to 20 and triple-digit dividends, the in-out boxes featured in this unit provide ample practice in division. Bolster division skills by plugging in the dividend in the in box or the quotient in the out box or by observing the pattern to identify the rule. Fill the empty boxes with the correct 3-digit dividend, identify the rule and using the rule find the quotient. Solve a simple word problem at the end of each sheet. Reaffirm division skills by completing the input and output values in Part A and writing the rule for each function machine in Part B. Test division skills of grade 4 and grade 5 kids with the printable worksheets incorporating the function machine theme. Divide 3-digit numbers with single or double digit divisor up to 20 to find the quotient and also write the rule.
This article was co-authored by Meredith Juncker, PhD. Meredith Juncker is a PhD candidate in Biochemistry and Molecular Biology at Louisiana State University Health Sciences Center. Her studies are focused on proteins and neurodegenerative diseases. There are 10 references cited in this article, which can be found at the bottom of the page. wikiHow marks an article as reader-approved once it receives enough positive feedback. This article received 11 testimonials and 80% of readers who voted found it helpful, earning it our reader-approved status. This article has been viewed 2,461,347 times. In chemistry, the theoretical yield is the maximum amount of product a chemical reaction could create based on chemical equations. In reality, most reactions are not perfectly efficient. If you perform the experiment, you'll end up with a smaller amount, the actual yield. To express the efficiency of a reaction, you can calculate the percent yield using this formula: %yield = (actual yield/theoretical yield) x 100. A percent yield of 90% means the reaction was 90% efficient, and 10% of the materials were wasted (they failed to react, or their products were not captured). Part 1 of 3: Finding the Limiting Reactant 1Start with a balanced chemical equation. A chemical equation describes the reactants (on the left side) reacting to form products (on the right side). Some problems will give you this equation, while others ask you to write it out yourself, such as for a word problem. Since atoms are not created or destroyed during a chemical reaction, each element should have the same number of atoms on the left and right side. X Research source - For example, oxygen and glucose can react to form carbon dioxide and water: → Each side has exactly 6 carbon (C) atoms, 12 hydrogen (H) atoms, and 18 oxygen (O) atoms. The equation is balanced. - Read this guide if you are asked to balance an equation yourself. - For example, oxygen and glucose can react to form carbon dioxide and water: → 2Calculate the molar mass of each reactant. Look up the molar mass of each atom in the compound, then add them together to find the molar mass of that compound. Do this for a single molecule of the compound. - For example, 1 molecule of oxygen () contains 2 oxygen atoms. - Oxygen's molar mass is about 16 g/mol. (You can find a more precise value on a periodic table.) - 2 oxygen atoms x 16 g/mol per atom = 32 g/mol of . - The other reactant, glucose () has a molar mass of (6 atoms C x 12 g C/mol) + (12 atoms H x 1 g H/mol) + (6 atoms O x 16 g O/mol) = 180 g/mol. 3Convert the amount of each reactant from grams to moles. Now it's time to look at the specific experiment you are studying. Write down the amounts of each reactant in grams. Divide this value by that compound's molar mass to convert the amount to moles. X Research source - For example, say you started with 40 grams of oxygen and 25 grams of glucose. - 40 g / (32 g/mol) = 1.25 moles of oxygen. - 25g / (180 g/mol) = about 0.139 moles of glucose. 4Find the ratio of your reactions. A mole is an exact number for the amount of a substance and it is equal to 6.022 times 10 to the 23rd power elementary entities, which could be atoms, ions, electrons, or molecules. You now know how many molecules of each reactant you started with. Divide the moles of 1 reactant with the moles of the other to find the ratio of the 2 molecules. X Research source - You started with 1.25 moles of oxygen and 0.139 moles of glucose. The ratio of oxygen to glucose molecules is 1.25 / 0.139 = 9.0. This means you started with 9 molecules of oxygen for every 1 molecule of glucose. 5Find the ideal ratio for the reaction. Go back to the balanced equation you wrote down earlier. This balanced equation tells you the ideal ratio of molecules: if you use this ratio, both reactants will be used up at the same time. - The left side of the equation is . The coefficients tell you there are 6 oxygen molecules and 1 glucose molecule. The ideal ratio for this reaction is 6 oxygen / 1 glucose = 6.0. - Make sure you list the reactants in the same order you did for the other ratio. If you use oxygen/glucose for 1 and glucose/oxygen for the other, your next result will be wrong. 6Compare the ratios to find the limiting reactant. In a chemical reaction, 1 of the reactants gets used up before the others. The quantity of the product that is created in the reaction is limited by the reagent. Compare the 2 ratios you calculated to identify the limiting reactant: X Research source - If the actual ratio is greater than the ideal ratio, then you have more of the top reactant than you need. The bottom reactant in the ratio is the limiting reactant. - If the actual ratio is smaller than the ideal ratio, you don't have enough of the top reactant, so it is the limiting reactant. - In the example above, the actual ratio of oxygen/glucose (9.0) is greater than the ideal ratio (6.0). The bottom reactant, glucose, must be the limiting reactant. Part 2 of 3: Calculating Theoretical Yield 1Identify your desired product. The right side of a chemical equation lists the products created by the reaction. Each product has a theoretical yield, meaning the amount of product you would expect to get if the reaction is perfectly efficient. X Research source - Continuing the example above, you are analyzing the reaction → . The right-hand side lists 2 products, carbon dioxide and water. Let's calculate the yield of carbon dioxide, . 2Write down the number of moles of your limiting reactant. The theoretical yield of an experiment is the amount of product created in perfect conditions. To calculate this value, begin with the amount of limiting reactant in moles. (This process is described above in the instructions for finding the limiting reactant.) X Research source - In the example above, you discovered that glucose was the limiting reactant. You also calculated that you started with 0.139 moles of glucose. 3Find the ratio of molecules in your product and reactant. Return to the balanced equation. Divide the number of molecules of your desired product by the number of molecules of your limiting reactant. X Research source - Your balanced equation is → . There are 6 molecules of your desired product, carbon dioxide (). There is 1 molecule of your limiting reactant, glucose (). - The ratio of carbon dioxide to glucose is 6/1 = 6. In other words, this reaction can produce 6 molecules of carbon dioxide from 1 molecule of glucose. 4Multiply the ratio by the reactant's quantity in moles. The answer is the theoretical yield of the desired product in moles. - You started with 0.139 moles of glucose and the ratio of carbon dioxide to glucose is 6. The theoretical yield of carbon dioxide is (0.139 moles glucose) x (6 moles carbon dioxide / mole glucose) = 0.834 moles carbon dioxide. 5Convert the result to grams. Multiply your answer in moles by the molar mass of that compound to find the theoretical yield in grams. This is a more convenient unit to use in most experiments. - For example, the molar mass of CO2 is about 44 g/mol. (Carbon's molar mass is ~12 g/mol and oxygen's is ~16 g/mol, so the total is 12 + 16 + 16 = 44.) - Multiply 0.834 moles CO2 x 44 g/mol CO2 = ~36.7 grams. The theoretical yield of the experiment is 36.7 grams of CO2. Part 3 of 3: Calculating Percent Yield 1Understand percent yield. The theoretical yield you calculated assumes that everything went perfectly. In an actual experiment, this never happens: contaminants and other unpredictable problems mean that some of your reactants will fail to convert to the product. This is why chemists use 3 different concepts to refer to yield: X Research source - The theoretical yield is the maximum amount of product the experiment could make. - The actual yield is the actual amount you created, measured directly on a scale. - The percent yield = . A percent yield of 50%, for instance, means you ended up with 50% of the theoretical maximum. 2Write down the actual yield of the experiment. If you performed the experiment yourself, gather the purified product from your reaction and weigh it on a balance to calculate its mass. If you are working on a homework problem or someone else's notes, the actual yield should be listed. X Research source - Let’s say our actual reaction yields 29 grams of CO2. 3Divide the actual yield by the theoretical yield. Make sure you use the same units for both values (typically grams). Your answer will be a unit-less ratio. X Research source - The actual yield was 29 grams, while the theoretical yield was 36.7 grams. . 4Multiply by 100 to convert to a percentage. The answer is the percent yield. - 0.79 x 100 = 79, so the percent yield of the experiment is 79%. You created 79% of the maximum possible amount of CO2. QuestionWhy is percent yield important in chemistry?Percent yield is important because many chemical reactions form byproducts, meaning not all the reactants in the equation actually react. This is important in the manufacturing of products because a low percent yield would indicate that the company is wasting reactants and money. QuestionHow do you increase percent yield in chemistry?To increase percent yield, you can either increase the concentration and/or surface area of your reactants. Adding a catalyst to your reaction may also improve percent yield. QuestionIf in the reaction is below 32 of C2H6 and produces 44 grams of CO2, what is the percent yield?If the reaction you are referring to is 2C2H6 + 7O2 --> 4CO2 + 6H2O then you would find the percent yield as follows: 1) 32g C2H6 * (1mol C2H6/30.08g C2H6)* (4mol CO2/2mol C2H6) (44.01g CO2/1mol CO2) = 93.64g CO2. This is your theoretical yield based on the 32g of C2H6 you started with and the molar ratio between C2H6 and CO2 in your balanced equation. 2) Your experiment produced 44g of CO2, so your actual yield is 44g CO2. % yield = (actual yield/theoretical yield) x 100 (44g CO2/93.64g CO2) x 100 = 46.99% QuestionHow do I calculate theoretical yield?1) Make sure the chemical equation you are working with is balanced. 2) Determine the mole ratios between the desired reactant and product. You can determine this by the coefficients in front of your desired reactant and product in your balanced equation. 3) Use molar mass of reactant to convert grams of reactant to moles of reactant. 4) Use the mole ratio between the reactant and product (step 2) to convert moles of reactant to moles of product. 5) Use the molar mass of the product to convert moles of product to grams QuestionHow do I calculate the percentage yield when I'm only given the volume of the reactants?Community AnswerMultiply the volume by the density of the substance to get the mass. QuestionWhat are the percentages of hydrogen and oxygen in 36g of water?Community AnswerWell water is composed of 3 atoms, 2 hydrogen and 1 oxygen. Therefore the yield should be 2 parts hydrogen for every 1 part oxygen, so it should be 66% hydrogen, and 33% oxygen. QuestionWhat do I do with mols in different atoms when calculating the percentage yield?Community AnswerActual yield divided by theoretical yield. ( actual ÷ theoretical = % yield ) . QuestionHow do I calculate the limiting reactant when calculating the percent yield?Community AnswerFind the number of moles of the reactants and compare them. The reactant with the least number of moles will be your limiting reactant. QuestionHow do I calculate actual yield?Community AnswerActual yield is the mass that will be given to you after the experiment or in the exam question. You can use the Mass = MRMols equation to find the mols of the actual yield given to you. However, the actual yield will nearly always be given. - Some students confuse percent yield (how much you obtained out of the total possible amount) with percent error (how far off an experimental result is from the expected result). The correct percent yield formula is . If you're subtracting the 2 yields, you're using the percent error formula instead. - If you get wildly different results, check your units. If your actual yield is different from your theoretical yield by an order of magnitude or more, you probably used the wrong units at some point in your calculations. Repeat the calculations and keep track of your units each step of the way. - If your percent yield is greater than 100% (and you're sure your math is right), other substances have contaminated your product. Purify the product (such as by drying or filtering) and weigh it again. - ↑ http://www.chemteam.info/Equations/Balance-Equation.html - ↑ http://www.chemteam.info/Stoichiometry/Limiting-Reagent.html - ↑ https://courses.lumenlearning.com/boundless-chemistry/chapter/reaction-stoichiometry/ - ↑ https://www.khanacademy.org/science/chemistry/chemical-reactions-stoichiome/limiting-reagent-stoichiometry/a/limiting-reagents-and-percent-yield - ↑ https://sciencing.com/calculate-theoretical-yields-2658.html - ↑ http://www.softschools.com/formulas/chemistry/theoretical_yield_formula/133/ - ↑ https://www.bbc.com/bitesize/guides/zqcjsrd/revision/1 - ↑ https://www.bbc.com/bitesize/guides/z3n64qt/revision/2 - ↑ https://sciencing.com/how-to-calculate-percent-yield-13710472.html About This Article To calculate a percentage yield in chemistry, start with a balanced chemical equation, with the reactants on the left side and the products on the right. Calculate the molar mass of each reactant and convert the amount of each reactant from grams to moles. Divide the moles of one reactant with the moles of the other to find the ratio of the 2 molecules, then find the ideal ratio for the reaction. Compare the ratios to find the limiting reactant. If you want to learn more, like how to find the theoretical yield of an experiment, keep reading the article!
Moon Phases Lesson Plan Overview: In this hands-on lesson, students learn about and discuss the phases of the moon through a variety of hands-on activities, including making their own moon flipbooks and cookie moons. Fill in your details below or click an icon to log in: You are commenting using your WordPress.com account. The teacher places lava rocks and small piles of crushed lava rock (“moon dust/soil”) on plastic sheeting around the room and turns the … You Teach.” method used in this guide. Change ), You are commenting using your Twitter account. I am not going to go through each page of the teacher instructions since it is neatly written in order in the packet provided, instead I am going to go through each "phase" of the lesson and give you some basic information to help guide you. It's ALL here and it's ALL super awesome!!! Please feel free to use them in your home and home school co-op. I am providing all of the materials I have created with this lesson plan along with some additional lessons I used to get things off on the right foot. Students can work in groups of 2 - 4 for most of the activities. After the challenge students will work on two or more “focus questions” to assess their complete understanding of the topic. Grades: Preschool and K-2 Length of Lesson: 30-45 minutes More Active Astronomy Activities Ask a friend to accurately describe how we can see the lunar phases day in and day out. With phase two of the student packet students will first work on a “what do you think?” to pre-assess their understandings. This science lesson achieves a number of objectives. Letting other students hear these sentences builds vocabulary skills, thinking skills, and confidence. Overview: In this hands-on lesson, students learn about and discuss the phases of the moon through a variety of hands-on activities, including making their own moon flipbooks and cookie moons. We used the longer version and I photocopied a class set and highlighted the different speaking parts for each reader. Lesson Plan Title : Moon Craters. I take 1 more minute to share the (middle) sentences with the class. I have been teaching middle school space science for the past thirteen years and always found the discussions in our class that were centered around the moon to be some of the most meaningful. The main purpose of this is to help students understand why we discuss the explanation for the formation of the Moon as “theoretical” and not fact. Share it with us! Through this short unit, children will develop a deeper understanding of the moon. Or maybe you start with how the moon affects the ocean's tides. Teaching Moon Phases : Summary of Activity: Here we have several hands-on activities to teach the causes of Moon phases. This lesson is aligned to Common Core Standards RST.6-8.1 and RST.6-8.4. See more ideas about Moon lessons, Teaching science, Moon activities. 3. The entire purpose of this phase is to give students a better picture of what the moon looks like and how it has similar geologic composition and structure to that of the Earth. , Thank you for sharing the link to our Readers Theater script “Moon Talk” (based on the NASA transcripts), Liz. Use the lesson plans, activities, worksheets and clip art to help you bring the moon to your classroom. These high school lesson plans have been packaged in a way that meets the learning needs of my children and those I tutor. 1 year ago. To the Moon and Beyond with the Lunar Reconnaissance Orbiter offers a variety of inquiry based, standards-aligned lesson plans. The Sun and Moon work together to make the phases. Varied approaches/ strategies are employed to steer the interest of the students on Astronomy. 1. Sorry, your blog cannot share posts by email. Teachers can access the presentation either through PowerPoint or Google Presentation. I once again use an NSTA article to help reinforce the concept. In this case students will be teaching through writing a book appropriate for fourth grade students. The moon is a perfect object to first get kids excited about space science, mainly because it is so easy to see and investigate (at least visually). Ready to teach your students about moon phases? There is an additional section that focuses on how scientific laws compare to scientific theories. The shape of the moon changes. I ask that you respect my time and energy and do not resell any of the lessons in part of whole. Large area covered with dark material - several pieces of black construction paper taped to the wall or white board work well Aim the light at the dark surface. Cast: 4+ (chorus) Readability: grade 5.8 Many students struggle with geometry at this age and this lesson actually involves a fair amount of geometric reasoning. Moon Story Book” along with the rubric used to grade the final product. Kids always have a level of thoughtful intrigue with the moon because it's just so darn alien to us. The article clearly explains all the materials that you need to create the models but overall it's just paper or plastic plates and some laminated labels. It’s exciting to see a science teacher integrating learning so many different ways. Middle School Science Blog Free lesson plans and resources for grades 5-8 by Liz Belasic (Liz LaRosa) ... Birthday Moons – this is a classic lesson that has I have used over the years. ( Log Out / I end up using local basalt samples and some breccia samples I picked up like these here. 1 1 MULTI-LEVEL LESSON PLAN GUIDE Earth, Moon, and Beyond Jeni Gonzales e-mail: firstname.lastname@example.org SED 5600 Dr. Michael Peterson December 18, 2001 The work I am presenting here took approximately 120 hours to complete and has now been successfully used by numerous colleagues of mine. This first moon landing lesson plan covers the details of that historic event and why it still matters today. 2. One of the best ways to determine if a student completely understands the material is to have the student teach it. Now that the students have an understanding of the positioning of the moon in space and no longer have the misconception that the moon is directly across from the earth at all times you can move on to modeling eclipses. The second phase (“Quarter Moon”) is where the real meat of the curriculum is discovered. My Massive Fail Who has sent home the moon calendar where students are supposed to […] I am happy that you will find good use for the lessons and please do not hesitate to reach out with any questions you might come across. I have found that everything up to this point has moved in such a logical order that this next phase (I know, I gotta stop with that pun) is so simple for the students. Thank you for sharing. It is estimated this lesson will take 20 minutes to teach. I had 2 readers for Armstrong, 2 for Aldrin, 1 for Collins, 5 readers for mission control, 2 readers for the narrator, and one reader for Nixon. I had my students work in pairs to create these books and had our ELA teachers join in on the literary components accompanying the creation of the books. Explain to the students that th… Change ). Post was not sent - check your email addresses! We are lucky to have our elementary school just up the road from us and we have utilized the opportunity for our students to interact and work with the second grade students at the elementary school. You can also find an abundance of resources to help you really delve into teaching everything there is to know about the moon. This final phase can be completed mostly in class with the initial brainstorming and rough draft but I have had students complete the final draft of the book as an out of class project due to the time it takes to create a quality product. This is awesome! Why does the moon … Everyone has gazed at the Moon, but why does it not always look the same to us? Students create Moon Logs to record and sketch how the Moon looks each night in the sky. The moon does not rotate. Free science lesson plans and resources. ( Log Out / ( Log Out / This is comprehensive for sure! To do this, you will need: 1. Participated in the Classroom Science Contest. I plan to use this next school year with my 7th graders. Lesson Plan #4286. • “Moon Talk–Apollo 11 (Quick Version)” grades 4-6, middle school, high school, adults) Time: 13 min. This is probably one of my favorite lessons to teach my students and I was hoping it would benefit other teachers who teach the same curriculum. Most adults can't explain how it is possible that we see only one side of the moon, even more didn't even know that we see only one side of the moon. During this lesson, students are asked to work collaboratively, with a partner, to complete an interactive activity in which they draw and cut out 5 phases of the moon and then glue and label each of the moon’s phases. With this next moon phase you will discuss the moon's composition and general appearance. Moon Area Middle School -- Virtual Nov. 19-20 November 17, 2020 We are experiencing a staffing shortage at the Middle School that makes it impossible for us to return to our Hybrid Model this week. Click to share on Pinterest (Opens in new window), Click to share on Twitter (Opens in new window), Click to share on Facebook (Opens in new window), Click to share on Tumblr (Opens in new window), Click to email this to a friend (Opens in new window), Click to share on Reddit (Opens in new window), Click to share on Pocket (Opens in new window), View middleschoolsciencelessons’s profile on Facebook, Click here to print out the set of cards, ready to laminate, Moon phase images, phases, and descriptions, Laminated placemat, Suns (larger and smaller version), Earth, and 8 Moon Phases, Free Science Starters, Bell Ringers, Warm Ups, Writing Prompts, Charles Darwin Survival Game - Link Updated, How to draw Lewis Structures - a step by step tutorial. After this lesson, students will be able to: 1. name the phases of the moon 2. describe characteristics of lunar phases 3. understand and use key terms Harvest Moon) and some basic ideas surrounding the formation of the moon. Students use math skills to calculate gravity, mass, and weight, as well as, create a solar eclipse in a hands-on activity, and complete an experiment about the law of motion. Description. The entire purpose of the first phase of this lesson is to introduce the students to what they are going to learn about in regards to the moon and hook their interest. The moon is an enigma. ( Log Out / Enter your email address to follow this blog and receive notifications of new posts by email. Love it!!! There will be examples and additional information of extension found in the supplemental information section of this guide. The teacher will present the material using a PowerPoint presentation or Google Presentation. I am providing the entire lesson plan, which, if completed from start to finish, can take an entire month. This a wonderful resource. I would say that after the activity there are at least 80% of the students who "get it" and another 20% that might need the model explained again. It's amazing how much the kids love using the models and solving the problem. I use two binder clips attached to the ceiling with the strings passing through them so that I can adjust the height of the ball and cast a shadow onto them with the opposing ball. Students are introduced to the futuristic concept of the moon as a place people can inhabit. Better yet, start off by asking them when the moon typically rises. Grade: 5 \| ... First Day Activities For Middle School Students . This is a packet of back to school activities for middle school students. We also provide a Powerpoint presentation and extensive teacher guide on how to use Active Engagement to teach and learn Moon phases. Many of my science lessons are based upon and taught using the 5E lesson plan model: Engage, Explore, Explain, Elaborate, and Evaluate.This lesson plan model allows me to incorporate a variety of learning opportunities and strategies for students. After the students create their group models you can model eclipses as a class by using an overhead projector as a light source along with a softball (or similarly sized ball) attached to the ceiling and a ball 1/4 the size (golf ball works well) attached to the ceiling. Change ), You are commenting using your Google account. Is there a shorter version for the “Moon talk”? The moon is an enigma. The challenges will often incorporate applicative thinking and mathematics based upon the information the students just learned. I hope that you find this guide of great use to you and your students and if you have any questions or comments please do not hesitate to email me at email@example.com. ReadWorks – “Climbing Space” has excerpts from Kennedy’s speech and reading comprehension questions. Overhead projector or some other bright light source, Tennis balls or other smooth sports ball (to be used as moon models held by students, you will need at least 9 of these), Marbles (you will need at least 9 of these), Softball attached to a string (to be hung from the ceiling representing the earth), Ball 1/4 size of softball attached to string (to be hung from ceiling representing the moon), Students will use a “student packet” throughout the entire lesson which clearly follows along with the material the teacher presents. I made a Birthday Moon Phases worksheet (pdf) for my students to use based on the original lesson. Everything is clearly explained and detailed in the teacher packet. It is suggested that the teacher uses the focus questions as a form of summative assessment, although some modification might be necessary for students with disabilities. In the book, the reader learns about the moon's composition, eclipses, and moon phases. In this case the student's final assessment is a colorful book that takes the reader on a journey to the moon. Mar 17, 2020 - Explore Pinning Teacher's board "Moon Lesson Plans", followed by 3747 people on Pinterest. The Sun causes the different phases of the Moon. This involves a hefty amount of literacy know-how and application so it is recommended that the teacher acquires the help of any literacy professionals in the school. Let the resources at Teacher Planet help you out. This section relies heavily on student interaction and group work and it is suggest that students work with multiple partners to experience different learning methods and various ideas. Thank you for sharing them! It is suggested that the teacher effectively use this chart by having students go the “L” or “What I Learned” section each time something new is learned to insert the information and keep a sequential timeline of what the class has learned. #4286. You can only see the moon at night. The first phase (“New Moon”) focuses on basic concepts necessary for later understandings along with pre-assessment activities to hook student interest. 5e Lesson Plan Model. There are so many misconceptions surrounding the moon that both kids and adults hold on to, therefore it is so important to get the kids thoughts out there and shared with the group prior to diving into the depths of moon learning. This lesson offers games and activities designed to get even your most stubborn middle school aged student engaged in reviewing information on the sun, moon, and Earth. Designed for the informal learning environment, several of the activities about lunar site selection and lunar geology are appropriate for the middle school classroom. You will need to acquire some moon rocks for this next phase... just joking, that would be some serious $$. There are three distinct sections (phases) separating the curriculum. Laminate, cut apart cards, and store into zip-top bag – 1 bag per 2 students. I love helping teachers! Phases of the Moon Science, level: Middle Posted Sun Dec 7 18:49:36 PST 2008 by Dorothy Puglisi (Dorothy Puglisi). Students follow along with the lessons and activities in their student packet. I have used these these activities for four or more years and have found great success over that time. Code a Traffic Light in Tinkercad Codeblocks & Circuits. You Learn. Some good sentences include: The Moon changes phases because of the Sun. The lesson is an excellent connection between science and math and further reinforces any other scale activities you might do with your students. A light source, a large flahslight or gooseneck lamp would work. Materials Required: Paper, Pencil, Clock, Calendar Concepts Taught: Moon Phases Lesson Plan Lesson Plan Title: Phases of the Moon ... For more lessons about the Moon, visit my Moon Page. I have always found that when a student can clearly explain a concept she/he truly understands it to the utmost extent. Lesson Plans; Moon Phases; Follow Us: Moon Phases Learn all about the different phases of the moon. The Slides - awesome! They brainstorm what people would need to live on the moon and then design a fantastic Moon colony and decide how to power it. I bet that if they don't understand the first question they will answer at sunset for the latter question. Thank you for including so many great resources. , Let me know if you have any ideas for more middle school Readers Theater science scripts, please. There are some materials necessary for this curriculum, which are not included such as rock samples, videos and other various products. With this phase you will discuss the apparent size of the moon, the changing appearance of the moon (i.e. Explain the locations of the Earth, moon and sun and describe their relationship 2. I love this section of the lesson plan since it involves so much interaction with the students. So here's the thing... if you present these ideas and questions to a group of young minds you are bound to get kids excited. Yes, she has them posted on her website: I love seeing the students work together to determine how this is possible and then we do it as an entire class with a couple of students acting as the earth and moon. This does pose some problems with group projects assigned out of class, so this will be at the teacher’s discretion. There are heaps of surprises (one could say craters) one learns when they start diving deep into what we currently know and understand about the moon. Many of the activities are adapted from tested and proven lessons found in the National Science Teachers Association (NSTA) publication Science Scope. Thank you so much! :D. Tinkercad Robotics for School: Evil Zipline Robot! They’ll certainly be seeing the Moon that long. What really blows their mind is the fact that a footprint on the moon remains there for all eternity (barring no meteors find it) due to the low gravity leading to a lack of atmosphere, leading to no weather and no wind. You are welcome to skip sections that might not fit into your curriculum or might seem to advanced for your students. In this lesson students will make craters using small round objects dropped into powder. This lesson plan is designed for middle school science students between the ages of 10 and 15. You'll also find links to helpful worksheets. The first phase starts with a “KWL- What I Know, What I Want to Know, and What I Learned” chart to help jump start the lesson. Cast: 5+ (chorus) Readability: grade 5.1. Once again the students will be using hands on models to help explain this next phenomena. , Thanks Carol! #4286. I just posted a link from the “Moon Talk” script page you used to this wonderful page of resources. It's just too darn big to be orbiting our planet and even with the theories behind its creation, it seems unfathomable that we have this massive object zipping around Earth every day. Learn about the characteristics of the moon, its phases, its craters, and the planets that have moons. 3. Using this format helps keep both the student and teacher organized throughout the entire curriculum. Use this lesson plan to teach students about the Moon's phases. Each activity can be used stand-alone, in or outside the classroom, with students or adults. Lesson Plans Keep your students engaged with our lesson plans. I then use the projector and a tennis ball to help the students visualize the phases in a 360 degree model that allows them to see the changing phases as time passes. The moon incites children's curiosity from a very young age. After the books were fully assembled and finalized we headed up to the elementary school to read the books to the second grade students. NGSS Standard: MS-ESS1.A-1 Patterns of the apparent motion of the sun, the moon, and stars in the sky can be observed, described, predicted, and explained with models. Thank you so much for the comment! Although there are no extension activities taken out of the classroom during the lesson such as homework or short research projects, the curriculum is easily adaptable to additional assignments. With this phase you will model how we are inter tidally locked to the moon and we only see one face of the moon, the near side. Change ), You are commenting using your Facebook account. With this phase you will be teaching students some important facts about the moon's position in space so that they will better understand the next two phases involving eclipses and moon phases. The moon is approximately 1/4 the diameter of Earth, making it one of the larger planetary orbiters out there in proportion to the planet. Phases of the Moon. This article suggests several solar and lunar eclipse activities that can be done in the classroom. (You have my email.) Search Search educational ... Middle school moon experts record several factors, including the altitude above the horizon, the azimuth, the phase, and... Get Free Access See Review. This lesson plan is designed for middle school science students between the ages of 10 and 15. Reply This is a fantastic way to end this hefty lesson and I have loved teaching the entire thing for the past seven years. The student packet completely replaces note-taking and if wanted, summative assessments in the form of quizzes and tests. Sometimes it is a big, bright, circle, but, other times, it is only a tiny sliver. Therefore, o ur Middle School will remain fully virtual on Thursday, November 19 and Friday, November 20 with the goal of returning to school for in person instruction on Monday, November 23. You have a WEALTH of resources here. I ended up using a National Science Teacher's Association article for part of this lesson and I included the link to the article in the teacher packet. Middle School MS-ESS1-1: Develop and use a model of the Earth-sun-moon system to describe the cyclic patterns of lunar phases, eclipses of the sun and moon, and season. The second phase is broken down into five sections: Our Moon's composition Our Moon's period of rotation (day and night cycle) and our Moon's period of revolution (year) Scale: Our Moon's position in space relative to the Earth and the sun (angle and distance) Lunar and solar eclipses and the Moon's involvement Our Moon's apparent "phases" as viewed from Earth and Space Each section is prerequisite to the following section and helps foster a complete understanding of the Moon, ultimately leading up to the final assessment. The other material can be accessed through PDF files and/or Google Documents. Our The Moon lesson plan explores Earth’s moon in a captivating and information packed way. This understanding also helps students understand why much of what they are learning is still up for alterations and changes if new discoveries or findings are made. Mar 22, 2016 - After completing the unit students will be able demonstrate and predict the sequence of events in the lunar cycle.Each lesson plan follows the 5E model and provides you with the exact tools to teach the concept.Essential Questions:1. Because of the obvious level of intrigue my students expressed I thought it would be prudent to create a comprehensive lesson plan that begins with the very basics of the moon and progressively moves along the lines to more complex concepts involving Earth's nearest neighbor.
2. The ability to understand how digital information arrives and how to use search engines effectively The Digital Literacy Framework Explored (with suggested activities and resources) - Evaluate search engines – ability to understand how search engines work and the implications of this - Use different search engines to evaluate results – ability to analyse search results using different search engines and therefore choose high-quality search engines This section introduces and explores how digital information is found, primarily through the use of search engines, and how groups can analyse what makes a story reliable. Activity 2.1 Evaluating search engines Some key questions - How do online searches work? - What does it mean to access high-quality information? 1. Ask your group if they think about how online searches work. Record the responses and discuss them a bit. What search engines do they use? How many do they know of? Do they know of any problems associated with search engines? What is Google or Siri? Note that these engines do not come up with information from nowhere or at random. Programmers designed them to find information using specific criteria and calculations. Explain that just as we often use algorithms (or step-by-step procedures) to solve problems (e.g. in Mathematics), online search engines also use algorithms to locate information for users on the internet. 2. Use the ‘Where Do Search Results Come From?’ handout. Review and discuss the implications of the handout, emphasising that online search engines follow procedures designed by humans. For instance, it is worth noting that search algorithms may take into account where the person who is searching lives or their previous search history. The idea that search algorithm creators have their own motives, such as promoting paying sites at the top of results clearly has implications. It is also worth noting that online searches may have very different features to previous search methodologies. The following questions may help: - How is an online search like or unlike asking an expert? - How is an online search like or unlike checking in a book? - What are some of the reasons people choose one method of searching for information over another? Then, in smaller groups (or pairs), project (or hand out) some screen shots from two to three different search results of the same topic (which your group may be interested in) and then discuss the results. The focus here is simply thinking about what comes up when we put in particular search terms. Some questions for discussion: - What is the same/different about all of the results? - What do you notice about these results? What stands out to you? - Are these search results in any way different from the kinds of answers you might get in a book or by asking an expert? - What might motivate the creators of search algorithms and what might they want you to do following a search? A follow-up activity: Ask your group to talk with friends or family members about what they know about digital searches. Ask them to come up with a list of critical questions everyone should ask when searching online. This can then be discussed in the full group and could even form the basis for a poster for display. Activity 2.2 Exploring what makes a source reliable - How can people work out what is a reliable source on the internet among the many possible search results? - Why are ‘popularity’ and ‘reliability’ important in assessing search engines? - Handout 6: Where do search results come from? - Handout 7: Sample Google search results 1. Use the Sample Google search results handout, ask the group to review the results and then rank them from most to least reliable. Then, in the whole group define the term reliability. Discuss the rankings each group came up with and explain their choices. Divide a chart (or board) into two with the headings ‘Reliable Source’ and ‘Unreliable Source.’ Based on their rankings, place each source in the appropriate column and then list the reasoning behind this. Then note that the handout shows how search results actually appear – not in order of reliability but prioritised based on a variety of factors, including popularity, location and search history. In smaller groups, ask them to create a checklist for evaluating search results. Prompt questions to stimulate deeper discussion: - What kind of website or page is this? (Personal blogs, discussion forums and advice columns aren’t typically reliable sources.) - Is the website connected to an educational institution or organisation? - Is the website from a ‘fact-checked’ news source such as The Guardian, The Irish Times or BBC News? - Does the title of the website use sensational language? - Does the page or site have an author clearly listed and are sources referenced? - Journalists look to verify a ‘fact’ or story from two separate sources. Why might this be important? 2. Pick examples of data/statistics from a mainstream media website (Irish Independent, Irish Times, The Guardian, The Daily Telegraph, Fox News, The New York Times etc. or shared via social media. In pairs, ask participants to research and analyse the data via the 7 questions exercise, and discuss the findings. Seven questions to ask about any piece of data or statistics: 1. Who does this represent? 2. How many people does it represent? 3. How were people reached? 4. How were questions phrased? 5. Has the data been presented in context? 6. Who commissioned the research? 7. When was the study conducted? Activity 2.3 Not all search engines are the same - Why is it important to know how search engines work? - How do search engines affect the way I find information? 1. Start by asking how often they use search engines and which ones do they use most. What are some of the most common problems they experience with search engines? How have they solved any of these problems? - Handout 8: Not all search engines are built alike (by Teaching Tolerance) 2. Review the Not All Search Engines Are Built Alike handout (from Teaching Tolerance), then divide the group into small groups and have them discuss the questions in the handout; then summarise the discussion. Search Google, Bing and Yahoo! for five terms or phrases from a topic of interest to the group – the more specific the terms, the better. Review the results together and then facilitate a discussion using some of the following questions: - Did the three search engines provide results in the same order? If not, how did the orders differ? - Which search engine provided the most understandable page titles? - Did any of the search engines provide information without the user having to click on a link? Which one(s)? - Did all the search engines provide descriptive information about the page titles? Did this information help you decide if the webpage was a source you were looking for? - Did all the search engines provide images of the term or phrase? If not, which one(s) didn’t? Were the images useful? - Did any of the search engines also include ads? Which ones? Were the ads distracting? - Were all the headings on each search engine’s first page of results relevant to the topic? How about the second page? Where in the list did the results seem to go off topic from the searched term or phrase? - Of the three search engines tested, which one do you think provided the best search results and why? A note on algorithms – a challenge to us all Search engines and social media platforms use complex algorithms that shapes what we see online. Relevancy scores are assigned to ‘posts’ and ‘entries’ based on a systematic ranking of what we are likely to prefer, based on historical data collected and mined that has been logged on us. Algorithms, such as the infamous one used in Facebook’s news feed, seek to predict whether we will would ‘like’ a given post and then profile users and classify users on this basis. On the history of the ‘like’ button in particular: “The like button wasn’t just a new way for users to interact on the site. It was a way for Facebook to enlist its users in solving the problem of how best to filter their own news feeds. That users didn’t realize they were doing this was perhaps the most ingenious part. If Facebook had told users they had to rank and review their friends’ posts to help the company determine how many other people should see them, we would have found the process tedious and distracting. Facebook’s news feed algorithm was one of the first to surreptitiously enlist users in personalizing their experience—and influencing everyone else’s.” – Who controls your Facebook feed – and why they keep changing it (January 3, 2016) by Will Ormus, The Slate Sorting social media users into distinctive groups or bubbles, then, makes the role of advertising more specific and customisable in order for social media companies to generate revenue. We see things we already believe in and view content from people who are like us. Therefore: - what does that mean for people who hold views that go against a human rights agenda? - do search engines and social media platforms silence voices from the majority world by design? - as producers of content (and not only consumers), is material we make only potentially available for view/interaction by people who believe in ‘our’ agenda only? - is it more appropriate to re-label ‘social media platforms’ as ‘advertising platforms’ instead? How might we think about our digital footprint, this being the case? Algorithms bring benefits, as well as challenges – something we need to be aware of when using and producing content into social media, in particular. - Recommended reading: The poison in our politics runs deeper than dodgy data (March 22, 2018) by Gary Younge, The Guardian - For more on advertising, see section 6. A final activity Use the answers to the questions above to invite the group to create an advertisement explaining why their favorite search engine is better than others. It might also be useful at some stage in the process to discuss some of the keywords associated with these issues and whether we effectively understand them. - algorithm – a step-by-step procedure for solving a problem, especially by a computer - directory – an organizing unit in a computer’s file system for storing and locating files - index – a method of sorting data by creating keywords or a listing of the data - reliability – the ability to be relied on or depended on, as for accuracy, honesty, or achievement - search engine – a program that searches for keywords that a person is specifically looking for, particularly on the internet
Merging multiple cells into one large cell can give you a better overview of an… Learn how to calculate the difference between two dates in Excel. Maybe you have tried several times, but you are still getting errors. There are a few functions you can use to get the results faster. Find out how you can easily learn to format cells into Date or Number. This article also shows you how to calculate the age difference between two dates in Excel 2007 and more. Table of contents Calculate the difference between two dates in Excel If you need to know the number of days between two dates, you can easily subtract one date from the other in Excel. =End date-Start date If the start date is greater than the end date, the result will be a minus number. The example below shows you how to write the subtraction of cell C2 in the formula bar. It also shows where to format the cell as general. Remember that the cell range (A2:B3) should be formatted into a Date and the cell range (C2:C3) into General or a Number. Otherwise, Excel will not show it correctly. Please notice that writing a date can be different for each country. Some countries write the date in this order day/month/year or the following order month/day/year. Excel uses your computer’s date system. So if a cell’s date is not entered using the same date system, Excel will not see it as a true date. Even if you know how to calculate the difference between two dates in Excel, you can still get #VALUE as a result. How to format cells into different date type Let’s say that your computer’s date system is day/month/year, but you want to show the date in the order month/day/year. Then you can change this by following the steps below. In the formula bar, you always have to write the date order as your computer’s date settings. Then you have to open the Format Cells box, which you can do in many ways. - Select the cells you want to format > Right-click on one of the cells > Choose Format Cells, and the box will open immediately. - Or select the cells and press CTRL + 1 on your keyboard. It will automatically open the box Format Cells. The Format Cells opens automatically, and you are in the tab called Number. Under that, you can see that Category is highlighted. In the list underneath, you have to select Date. Then change the location into English (United States) to get the date order month/day/year. Then choose the type of date above it by scrolling down on the arrow. The date you select will be colored blue. Lastly, click OK. The example below shows you the result of the dates. You can see that the dates are formatted in a different order, months/day/year. At the same time, the date in the formula bar will stay the same as your computer’s date system. Calculate the age difference between two dates in Excel First, you have to make sure that the cells that contain your dates are formatted to Date. To calculate the difference between two dates, you can use the DATEDIF function in Excel. The Excel DATEDIF function returns the difference between two dates in years, months, or days. The DATEDIF function consists of two cells, followed by a year, month, or day. =DATEDIF(start date,end date,unit) Problem using DATEDIF function Some people get an error when using the DATEDIF function. Start to write the formula in the cell you want and click on the start date, cell A2, followed by a comma. The next step is to click on cell B2 (end date). Unfortunately, you can’t continue, and a box shows up, saying that there is a problem with the formula. Even though the instructions in Microsoft Office say that you can use a comma between the cells in the formula bar, you still get this problem. You are trying to calculate the difference between two birth dates in Excel, but it is not working. Even if you follow the instructions as proposed, you might still get errors. That is because the DATEDIF function contains an error. The solution to this problem is to use a semicolon (;) between the cells. So, use the semicolon, and the function should look like the example below. Remember that the start date should be smaller than the end date, or you will get #NUM! as a result. You have successfully learned how to calculate the difference between two dates in Excel. You had encountered some problems when using the DATEDIF function, but you can solve them now. Remember to change the cells that contain your dates are formatted to Date. Now you know how to calculate the difference between two dates in Excel 2007 and more.
They are the associative property, distributive property and the commutative property. The associative property of math refers to grouping. This property states that you can group numbers (move the parenthesis) anyway and the result will remain the same. The associative property in algebra is important for organization of numbers. Rearranging the numbers and parenthesis will not change values but instead make the equation more convenient. when you are only adding or multiplying. Like Associative property All i know is how to remember associative property. In associative property you can have the parentheses in between any numbers and it will be the same answer. The Associative Property in math is how the numbers are associated; ex. 2(34) is the same as (23)4. The associative property is one of those fundamental properties of math that make math work. You probably take this property for granted because it's so ingrained, but it's important to see how the guts of math work, so check out the tutorial and make sure you're solid on your fundamentals. zero property, inverse, commutative, associative, and distributative Commutative Property Identity Property Zero Property Associative Property distributive, associative, commutative, and identity (also called the zero property) The way in which numbers are grouped when added or multiplied does not change the sum or product.In symbols the associative property of addition says that (a+b) +c = a + (b +c) where a,b, and c are any numbers.The associative property for multiplication says that (ab)c=a(bc).Informally, the associative property says that grouping does not matter when applying the operation. facts associative property The parenthesis can be applied to another set of units and the outcome will not change. 2x(3x-1) = 6x2-2x because of the distributive property. there is not division for the associative property associative property example: (a+b)+c = a+(b+c) The associative property does not apply to division but multiplication and addition do. Alternative algebra is a form of algebra such that every subalgebra generated by two elements is associative. It is a result of the associative property of numbers.It is a result of the associative property of numbers.It is a result of the associative property of numbers.It is a result of the associative property of numbers. The associative property is the property that a * (b * c) = (a * b) * c for any binary operation *. Addition and multiplication are associative, but these are definitely not the only two operations that obey this property. The associative property, for example a + b + c = a + c + b The associative property states that the result of an addition or multiplication sentence will be the same no matter the grouping of the terms. Associative: (a + b) + c = a + (b + c) (a × b) × c = a × (b × c) There is only one associative property for multiplication: there is not a separate "regular" version.
Agricultural Literacy Curriculum Matrix Journey 2050 Lesson 3: Water Students will discuss the limited amount of fresh water on earth, identify how best management practices can reduce water consumption, discuss the need for water conservation and protection related to population growth and agriculture, and compare and contrast methods of irrigation for water conservation. Grades 9-12 - Water PowerPoint - Interest Approach Supplies - Option 1: Rain jacket, hat, 5-gallon (18L) bucket of water, tablespoon - Option 2: One-gallon container, clear bowl, ½-cup measuring cup, eyedropper - Map of local watershed (optional) - Journey 2050: Water video - Sustainability Farm Game: Level 3 Water - Computer or tablet device for each student Essential File (map, chart, picture, or document) conservation tillage: farming methods that reduce the intensity or frequency of tilling in order to maintain some ground cover throughout the year and disturb the soil as little as possible while still providing the conditions needed to grow a productive crop crop residue: plant material remaining in a field after harvesting, including leaves, stalks, and roots irrigation: artificial application of water to the land or soil to assist plant growth riparian area: A space between the land and the waterway ideally filled with native grass, bushes and trees watershed: a watershed is the area of land where all of the water that falls in it and drains off of it goes into the same place Did You Know? (Ag Facts) - Over 70% of Earth is covered in water but only a small amount is freshwater. - Only 5% of all the water on Earth is freshwater - Only a small drop (3%) of the freshwater on the earth is accessible because the rest is trapped in groundwater, the atmosphere, glaciers and ice caps.10 - Groundwater is the easiest to access, but that still leaves us with over 68% of our water supply that is salt water or un-accessible. Background Agricultural Connections Journey 2050 takes students on a virtual simulation that explores world food sustainability and answers the question, "How will we sustainably feed nearly 10 billion people by the year 2050?" The lesson plans and online simulation program allows students to make decisions on a virtual farm and witness their impact on society, the environment and the economy at a local and global scale. The lessons engage students with the important concepts regarding sustainable agriculture. The online simulation contextualizes these concepts as students experience the lives of three farm families in Kenya, India and Canada. As students interact with each family, they learn the role of best management practices in feeding the world, reducing environmental impacts, and improving social performance through greater access to education, medical care and community infrastructure. These lessons can be taught individually or as an entire unit. See the links below for the remaining lessons: - Lesson 1: Introduction to Sustainable Agriculture - Lesson 2: Plant Health - Lesson 3: Water - Lesson 4: Economy - Lesson 5: Land Use - Lesson 6: Careers for 2050 and Beyond! - Lesson 7: Technology and Innovations - Take Action: Project-based Learning and Program Summary Imagine a picture of the Earth. All the blue that you see is water, and it makes up 70 percent of Earth’s surface. However, we can only use a tiny fraction of it. Only 2.5 percent of Earth’s water is freshwater, found in glaciers and polar ice caps, groundwater, surface water such as lakes, ponds and rivers, and in the atmosphere. Only 0.3 percent of that is accessible for us to use.1 Water is essential, not just for drinking and keeping clean, but throughout our lives. For example, we need water to make the cars that get us to school and to grow the food that we eat. We can’t live without water. As our population grows, there is even more pressure on our limited supplies. Today, about 1.3 billion people live in regions with an uncertain supply of fresh water.2 With economic and population growth in those areas, more than half the world’s predicted population will face water shortage by 2050 if nothing is done.3 Water is essential and needs to be conserved and protected. Water is an essential part of agriculture. In fact, nearly three-quarters of the world’s freshwater is used in agriculture to produce the food, fiber and products that we need to live.4 For example, it takes 435 liters (115 gallons) of water to grow enough wheat to make just one loaf of bread5 and about 11,000 liters (2,900 gallons) to make a pair of blue jeans.6 This calculation includes the water required to grow the raw materials, process them and manufacture the final product. As our climate changes, the weather is becoming more extreme and unpredictable. In some parts of the world, the climate is becoming drier, and in others it is becoming wetter. The unpredictable availability of water is making it harder for farmers to grow crops, putting our food supply at risk. Through advances in technology and improved best management practices, farmers try to ensure that crops have the right amount of water while conserving water and maintaining water quality. It’s about using the right amounts at the times when crops need water most. Too little and seeds can dry up. Too much and water is wasted as runoff. For example, in countries like Kenya where rainfall can be unpredictable, farmers collect and store rainwater to reuse when it’s needed most. They also utilize drip irrigation where water is delivered close to plant roots through a pipe, drop by drop. This minimizes water losses from evaporation and increases yields by as much as 90 percent compared to plants only receiving rainwater.7 In countries like Canada or the United States, pivot irrigation is a great way to apply water at specific times of the day. Technology plays a key role in water management. Farmers can use their phones to gain information on the soil moisture content of their crops. They can get live weather updates and calculate how much water is needed for the day. They can remotely turn their irrigation systems on and off to use water more efficiently while increasing crop yields. Another best management practice is conservation tillage, which involves covering at least 30 percent of the soil surface with crop residues left after harvesting.8 This helps slow water movement, reducing the risk of erosion. It also provides more organic matter, improving soil health. A healthy soil will hold more moisture and grow better crops. Landowners can also improve water quality by preserving wetland and riparian areas, which are spaces between land and the waterway, ideally filled with native grasses, shrubs and trees. These areas provide many benefits, such as helping filter nutrients that are collected as the water runs over the land; helping control water during floods; and providing habitat for animals. Through innovations such as new seed varieties, scientists are developing crops that are more resistant to change in climates so we can grow crops even when the growing conditions are not ideal. Sharing best practices and providing everyone with the tools they need to use water more efficiently is critical. It is important that every single day of the year we all take the time and make the effort to conserve and protect our precious water supplies. Interest Approach - Engagement This lesson has been adapted for online instruction and can be found on the Journey 2050 eLearning site. Use one of the following demonstrations to help students visualize the amount of freshwater available on earth: - Prior to class, fill a five-gallon bucket with water. - Ask for one volunteer. Dress the volunteer in rain gear, including a rain hat, and have the student sit or stand in front of the class. - Once your volunteer student is in place, bring the bucket of water in front of the class as well. Explain that this bucket represents all the water on the entire earth. - Ask your class what portion of this water they think is usable. As they offer their ideas, help them understand that to be usable, the water cannot be salt water, it can’t be frozen (glaciers), and it can’t be so deep in the ground that we can’t access it. - Tell your class that you are going to show them the answer by dumping how much of our earth’s water is freshwater in a usable form on the student’s head. Pick up the bucket of water and pretend to dump…stop…set it down and grab a tablespoon. Proceed to drop three tablespoons of water on the student’s head.1 - Fill a one-gallon container (such as a plastic ice cream bucket) with water. This represents all the water on Earth. - Pour one half-cup of water out of the one-gallon container and into a clear bowl. The water in the bowl represents all of the freshwater on Earth, which is less than three percent of the total water on Earth. Freshwater is found in lakes, rivers, groundwater, ice and living things. The 15 half-cups that are still in the one-gallon container represent salt water. We cannot use salt water without first removing the salt in a process known as desalination. Though research and technology are improving this process, it is still prohibitively expensive and often impractical. - With an eyedropper, place one drop of water from the half-cup onto a small plate. This one drop represents the freshwater that is available for our use. This water is found in rivers and lakes. Explain that the rest of the water in the half-cup is deep groundwater, water bound up as soil moisture, water in living things or water in the atmosphere. Following the demonstration: - Share the statistics found in the Did You Know? section of the lesson. - Help students conclude from the demonstration that water is a limited natural resource. Ask, “How are water and agriculture related?” Use further guiding questions until students recognize that farmers must use a portion of our water supply to grow the crops and raise the livestock that provide our food supply. Ask students, “What practices can farmers use to conserve and protect freshwater?” Inform students that they will be learning about how water use in agriculture can be managed to provide food more sustainably for our growing population. Three Dimensional Learning Proficiency: Disciplinary Core Ideas Students are able to link key science concepts from the four domains of science: physical science; life science; earth and space science; with problem solving (engineering) and the application of science through technology. Earth and Space Science: The sustainability of human societies and the biodiversity that supports them requires responsible management of natural resources. Preparation: Prior to class, review the Background information, video clip, and PowerPoint slides (including the speaker notes) associated with the lesson. Review the Teacher's Guide: Getting Started document for further information to prepare for class. - Open the Water PowerPoint. - Slide 3: Play the Journey 2050: Water video (5:07). Engage students with the video by asking them to discover three things: 1) How is water used in agriculture? 2) What methods do farmers use to irrigate their crops? 3) What best practices can be implemented to use water more efficiently in agriculture? (Background and discussion prompts are outlined in the steps below and in the PowerPoint notes). - How is water used in agriculture? - Slide 4: Ask students, “What do farmers need to grow a crop?” Use the click animations on the PowerPoint slide to display open space, fertile soil, sunshine, correct climate and seeds. Once these items have been discussed, explain that there is one more item. Without it, the crop will fail completely. Ask students what this could be. (water) - What methods do farmers use to irrigate their crops? Describe these common methods:1 - Slide 6: Drip Irrigation—Using the picture, describe drip irrigation. Water is sent through plastic pipes that are laid along the crop rows. Tiny holes allow water to drip at the base of the plants. This method is most effective for fruit and vegetable crops. - Slide 7: Center-Pivot Irrigation—Using the picture, describe center-pivot irrigation. This is a large sprinkling system on wheels. A line of sprinklers pivots around a center point in a field. This method of irrigation is what creates green crop circles that can be seen from a plane. - Slide 9: Flood/Furrow Irrigation—Using the picture, describe flood or furrow irrigation. To utilize this method of irrigation, farmers dig furrows between their crop rows. Water is delivered to the top of each row using ditches or siphon hoses. The crop is irrigated as the water flows from the top to the bottom of each row. - Slide 10: Ask students, “Besides irrigation, what other ways do farmers use water?” Allow students to offer their answers. Guide the discussion, clarifying that irrigation accounts for the majority of water use in agriculture, but water is also needed to raise livestock and to clean and sterilize facilities such as milk barns or food processing plants in order to prevent food-borne illness. - What best practices can be implemented to use water most efficiently in agriculture? - Help students recall the definition of best practice. Next, apply the principle to water conservation and ask for ideas of how farmers can conserve water as they grow our food and fiber. - Slide 12: Refer back to the video clip they viewed at the beginning of the lesson. It described a practice called conservation tillage. Explain that farmers will leave crop residue (materials such as stalks, stems and seeds) in their fields without plowing it under in the fall. In the spring, they use an air seeder (device that precisely plants the seeds at equal distances and proper depth in the soil and then covers them) to plant the next crop, eliminating the need to plow the soil. Conservation tillage improves water-use efficiency in crops. - Slide 13: Explain that a riparian area is a space between land and a waterway, ideally filled with native grasses, shrubs and trees. Landowners can improve water quality by preserving wetland and riparian areas, which have many benefits. These areas help filter nutrients that are collected as water runs over the land; help control water levels during floods; and provide habitat for animals. If possible, use a local riparian area as an example to help students understand. - Slide 14: Explain to students that some methods of irrigation are more efficient than others. Best practices in irrigation vary by farm and crop, but they will generally enable farmers to decrease water evaporation, deliver water more directly to plant roots (eliminating water loss to other locations or from runoff), and measure precise soil moisture for exact watering. - Slide 15: Ask students, “How can we protect and conserve water at home and in our schools and communities?” As students discuss answers, reinforce the concept that our actions affect our natural resources. Water conservation ideas include: turning off the water while brushing your teeth, using low flow toilets, using water bottles and refill stations, decreasing shower times, etc. Activity 2: Sustainability Farm Game Level 3 Water - Slide 16: Open Level 3 of the Sustainability Farm Game on each student’s computer or device. Explain that in this level of the game they will be farming in all three countries (Kenya, India and Canada). Prepare students for the game by informing them of the following: - In this level of the game you will primarily be managing water use. There will be a water meter on the left side of the screen that you will need to pay close attention to. - The game is simulated for the year 2030. - Stop when you finish farming in Canada - Total game time is 15 minutes (5 minutes in each country) - Slides 17–18: Once students have completed the game, use the following questions to help synthesize what they have learned: - What were your limiting factors? - Did you find it difficult to have enough water for your crops? Why is freshwater conservation and preservation important? How did the weather impact your crops? - What ripple effects did you notice from your investments? Three Dimensional Learning Proficiency: Crosscutting Concepts Students link different domains of science fields into a coherent and scientifically-based view of the world. Cause and Effect: Systems can be designed to cause a desired effect. Summarize the following key points (slide 19): - Water is a natural resource critical to agriculture. - Although the majority of Earth is made up of water, only a small fraction is actually usable. - Farmers improve their water efficiency by using water conservation practices and technologies such as irrigation (with moisture sensors), conservation tillage and riparian areas. - Some regions of the world face greater threats to their water supply than others. Using slide 21 of the attached PowerPoint, consider using the following supplementary videos: Using slide 22 of the attached PowerPoint, break students into small groups. Have each group brainstorm ways we can conserve and protect water. Assign each group one of the specific areas below: - Home – Outside (manage lawn and landscape sprinklers) - Home – Inside (5-minute showers, don’t dump medicine in toilets as treatment plants might not be able to filter them, turn off water while brushing teeth) - School (rain gardens, sensor bathroom taps, water fountains vs water bottles, low flow toilets] - Community [Provide garbage bins and hang posters on impact of dog feces running into river, native tree planting day to stabilize river bank and collect runoff) - Optional – Local Industry such as Oil & Gas, Forestry, Manufacturing (re-use water in processing, clean water used before returning it to the rivers) - Optional – Farm (wetlands, drip irrigation, cell phones that turn irrigation on and off depending on weather) Using slide 23 of the attached PowerPoint, display a map of the world and ask students, “Which countries have the least available freshwater?” Allow students to offer their guesses and proceed to ask, “Which countries have the most available freshwater?” Discuss reasons why. Through class discussion, help students more fully recognize that across the globe not everyone has access to a reliable freshwater source. Discuss factors that impact water availability and daily water use per person (estimate liters or gallons by country). Access data from FAO website. Display a map of your local watershed so students can see where water flows from and to in your area. Every action you take impacts our community and our neighbors downstream. Point out to students that in some countries they can’t drink water from the tap because it is contaminated. Every day we must protect and conserve water. The Journey 2050 program was originally developed by Nutrien in collaboration with Calgary Stampede, Alberta Canola Producers Commission, Nutrients for Life Foundation, and Agriculture in the Classroom Canada. Authors and contributors were drawn from each of these organizations under the direction of Lindsey Verhaeghe (Nutrien) and Robyn Kurbel (Calgary Stampede.) The lessons were updated and revised in 2017 with contributions from the original J2050 Steering Committee, the National Center for Agricultural Literacy, and the National Agriculture in the Classroom Organization. - https://blog.epa.gov/blog/2010/06/my-jeans-are-very-thirsty/ from http://ngm.nationalgeographic.com/2010/04/table-of-contents Suggested Companion Resources - Journey 2050 Program Summary: Project-Based Learning - Agronomy - Grow with It! - Planet Zorcon - Agriculture and the Sustainable Development Goals - How Reducing Food Waste Could Ease Climate Change - The Story of Bottled Water video - World Population History - Wiki Watershed - Food Matters - Project WET - The USGS Water Science School - Using Technology to Save Water \|We welcome your feedback. Please take a minute to share your thoughts on this lesson.\|
When properly implemented, these operations can be performedin constant time. In static hashing, the hash function maps searchkey values to a fixed set of locations. Basically, its a processing unit that takes in data of arbitrary length and gives you the output of a fixed length the hash value. The values returned by a hash function are called hash values, hash codes, hash sums, or simply hashes. Wikipedia has some basic info on both hash tables and hash functions. We present several classes of hash functions which insure that every sample chosen from the input space will be distributed evenly by enough of the functions. A dictionary is a set of strings and we can define a hash function as follows. This socalled hash code or simply hash can then be used as a way to narrow down our search when looking for the item in the map. Since a hash is a smaller representation of a larger data, it is also referred to as a digest. It lets you try out hash functions and collision resolution methods for yourself so that you can really see how they work. One possible hash function is given a string s s 1s2. Hash tables tutorial for complete beginners go4expert. Finding a good hash function it is difficult to find a perfect hash function, that is a function that has no collisions. This is a chapter from the handbook of applied cryptography. Whenever an element is to be searched, compute the hash code of the key passed and locate the element using that. Hashing tutorial welcome to the interactive hashing tutorial. The length of the output or hash depends on the hashing algorithm. There are many hash algorithms that can be implemented, there are a bunch provided in the. In this method, the next available data block is used to enter the new record, instead of overwriting on the older record. A cryptographic hash function is just a mathematical equation. This process is often referred to as hashing the data. It lets you insert, delete, and search for records based on a searchkey value. However, when a more complex message, for example, a pdf file containing the full text of the quixote 471 pages, is run through a hash function, the output of. Hash functions are not quite the previously mentioned oneway functions a oneway function is a function that is easy to compute but computationally hard to reverse easy to calculate f x from hard to invert. But we can do better by using hash functions as follows. Algorithm and data structure to handle two keys that hash to the same index. Hashing techniques hash function, types of hashing. In a hash table, data is stored in an array format, where each data value has its own unique index value. The method that we use to turn an object into a hash code is called the hash function. The password file consists of a table of pairs which are in the form user id, h p. Aug 14, 2018 a brief overview of cryptographic hash functions. The function that does this calculation is called the hash function, and will be denoted by the letter h. Using the key, the algorithm hash function computes an index that suggests where an entry can be found or inserted. Each key is equally likely to hash to any of the m slots, independently of where any other key has hashed to. A hash is usually a hexadecimal string of several characters. The process of logon is depicted in the following illustration. Note that if you do a web search, you can find a lot of good information. Data structure and algorithms hash table tutorialspoint. A cryptographic hash function is more or less the same thing. The conversion function is known as a hash function, hk. The hash function converts the key into the table position. Hashing for message authentication purdue engineering. Oneway hash function an overview sciencedirect topics. In section 5, we show how to hash keys that are strings. This is irritating in that it involves a manual step. A hash table is an array of some fixed size, usually a prime number. The key for a given object can be calculated using a function called a hash function. A cryptographic hash function is something that mechanically takes an arbitrary amount of input, and produces an unpredictable output of a fixed size. A good hash algorithm should be complex enough such that it does not produce the same hash value from two different inputs. Hash functions provide protection to password storage. Jan 27, 2017 sha1 stands for secure hash algorithm 1, a cryptographic hash function developed by the nsa that can be used to verify that a file has been unaltered. Given a key k, our access could then simply be ahashk. Using the hash function, data bucket address is generated for the hash key. A cryptographic hash function also called message digest is a oneway transformation. Sha0 published in 1993 has been compromised many years ago. Obviously, due to its mechanical nature, every time a given input is used the same output will result. Hashing hash table, hash functions and its characteristics. Hashing means using some function or algorithm to map object data to some representative integer value. The strength of hash functions such as md5 and sha1 has been called into. Access of data becomes very fast if we know the index of the desired data. Use a mac derived from any cryptographic hash function hash functions do not use a key, therefore cannot be used directly as a mac motivations for hmac. Secure hash algorithm is a cryptographic hash function designed by the united states nsa. The input to the hash function is of arbitrary length but output is. An integrity service is obtained by running a oneway hash function on the message using a cryptographic key so that the receiver can ensure that the sender of the message possessed a secret key and that no party lacking that cryptographic key modified the message while in transit. As long as i know, the encrypted pdf files dont store the decryption password within them, but a hash asociated to this password when auditing security, a good attemp to break pdf files passwords is extracting this hash and bruteforcing it, for example using programs like hashcat. Hash function hash function is a function which leverages accessing and searching data in the hash table. A hash function h maps keys of a given type to integers in a fixed interval 0. Thus, it becomes a data structure in which insertion and search operations are very fast irrespective of the size of the data. It should be a logic which takes our key as the input, and generally gives out. The hashcode of the message is encrypted with the senders private key. Properties of hash function the properties of a good hash function areit is efficiently computable. The unpredictableness isnt in the operation itself. A hash function, is a mapping function which maps all the set of search keys to the address where actual records are placed. Authentication code mac and the overall hash function as a keyed hash function. Cryptographic hash functions execute faster in software than encryption algorithms such as des no need for the reverseability of encryption. How does sha1 work intro to cryptographic hash functions. Key hash k 9 function hashed value 9 k 17 figure 7. M6 m0hm hm0 i for a secure hash function, the best attack to nd a collision should not be better than the. You can find a decent, easy hash tutorial at hash table tutorial discusses hash functions as well. Collision using a modulus hash function collision resolution the hash table can be implemented either using buckets. Instead of storing password in clear, mostly all logon processes store the hash values of passwords in the file. Hashing tutorial to learn hashing in data structure in simple, easy and step by step way with syntax, examples and notes. So to put an item in the hash table, we compute its hash code in this case, simply count the number of characters, then put the key and value in the arrays at the corresponding. Save items in a keyindexed table index is a function of the key. Hash function h is an arbitrary function which mapped data x. Hashing techniques in data structure pdf gate vidyalay. This function is useful for operations such as analyzing a subset of data and generating a random sample. This tutorial does more than simply explain hashing and collision resolution. Hash function is a function which is applied on a key by which it produces an integer, which can be used as an address of hash table. A hash system stores records in an array called a hash table, which we will call ht. They are used to quickly compare dictionary keys during a dictionary lookup. Hash functions message digest md i4 lehrstuhl fuer. Covers topics like introduction to hashing, hash function, hash table, linear probing etc. Creating a cryptographic hash function lockless inc. Cryptography lecture 8 digital signatures, hash functions. Hashing techniques hash function, types of hashing techniques in hindi and english direct hashing modulodivision hashing midsquare hashing folding hashing foldshift hashing and fold. Hash table is a data structure which stores data in an associative manner. However, if you want to implement one you need to pick an algorithm first. Hash function coverts data of arbitrary length to a fixed length. Hashing techniques hash function, types of hashing techniques. Hashing is a method for storing and retrieving records from a database. Suppose we need to store a dictionary in a hash table. The load factor of a hash table is the ratio of the number of keys in the table to. In general, the hash is much smaller than the input data, hence hash functions are sometimes called compression functions. I hx x mod n is a hash function for integer keys i hx. Another hash function implementation is by davy landman. In this paper, we show that applying a standard technique from the hashing literature can simplify the implementation of bloom. Hashing is also a unidirectional process so you can never work backwards to get back the original data. Deploying a new hash algorithm department of computer. Values returned by a hash function are called message digest or simply. The hash function returns the hash value of the object if it has one. The input to the hash function is of arbitrary length but output is always of fixed length. In the context of message authentication, a hash function takes a variable sized. Well see on the next page that rather than using the string length, we need to use a more adequate hash function. Whenever an element is to be searched, compute the hash code of the key passed and locate the element using that hash code as index in the array. Perfect hashing computer science university of otago. In this the integer returned by the hash function is called hash key. It depends on the user which hash function he wants to use. Hash function a hash function is any function that can be used to map a data set of an arbitrary size to a data set of a fixed size, which falls into the hash table. Skein512224 512 224 sha256 skein256256 256 256 skein512256 512 256 sha384 skein512384 512 384 skein1024384 1024 384 sha512 skein512512 512 512 skein1024512 1024 512 table 1. In dynamic hashing a hash table can grow to handle more items. The associated hash function must change as the table grows. Hence one can use the same hash function for accessing the data from the hash table. Choosing best hashing strategies and hash functions. A hash function takes a finite amount of time to map a potentially large key space to a feasible amount of storage space searchable in a bounded amount of time regardless of the number of keys. How can i extract the hash inside an encrypted pdf file. Hash function a good hash function satisfies approximately the assumption of simple uniform hashing. Linear probing linear probing is a fixed interval between probes. And let us suppose that our hash function is to simply take the length of the string. It discusses the hash table, its basic operations and typical hash function operations and the. Define a hashing method to compute the hash code of the key of the data item. However, there is a technical difficul ty in defining collisionresistance for a hash funfixed ct hard to define collisionresistant hash functions x h x ion. Python immutable builtins, such as integers, strings, or. The scheme in figure 1c is a publickey encryption version of the scheme shown in figure 1b. We will discuss such applications of hash functions in greater detail in section 15. Sha1 stands for secure hash algorithm 1, a cryptographic hash function developed by the nsa that can be used to verify that a file has been unaltered. Skeins novel idea is to build a hash function out of a tweakable block cipher. Its typically rendered as a 40 digits long hexadecimal number. The array has size mp where m is the number of hash values and p. In the next sections, well explore how to generate more adequate hash codes. Note that the hash value of foo in an array of 29 elements may be different than the hash value of foo in an array of 23 elements. Oct 15, 2016 hashing techniques hash function, types of hashing techniques in hindi and english direct hashing modulodivision hashing midsquare hashing folding hashing foldshift hashing and fold. In most applications, it is highly desirable that the hash function be computable with minimum latency and secondarily in a minimum number of instructions. Hashing works by performing a computation on a search key k in a way that is intended to identify the position in ht that contains the record with key k. Hash functions and hash tables a hash function h maps keys of a given type to integers in a. It could be any algorithm customised and optimised as per a particular scenario. This table can be searched for an item in o1 amortized time meaning constant time, on average using a hash function to form an address from the key. Instead, we need to use the hash function to ensure they get put in the right place. Hash function, cryptographic hash functions, examples of crypto hash functions, applications of crypto hash fn, birthday problem, probability of hash collisions, hash function cryptanalysis, block ciphers as hash functions, secure hash algorithm sha, sha1 algorithm, sha2, sha512 sha512 round function, 80word input sequence, sha3, sha3. It has been compromised in 2005 as theoretical collisions were.106 754 1609 43 1610 468 30 615 511 823 1171 426 67 1395 1149 1005 1417 667 973 426 1217 343 563 799 200 345 401 1473 18 74 388 877 1561 569 721 560 355 318 294 56 783 1018 966 1214 557 210
Compounds react in a certain ratio in a chemical reaction. There will be a residual reactant if the ratio is uneven. To grasp this, you must be familiar with the molar or mole ratio. What exactly do you mean by molar ratio? A mole ratio is the ratio of the mole quantities of any two compounds in a chemical process. In many chemical situations, mole ratios are employed as conversion factors between products and reactants. Examining the coefficients in front of formulae in a balanced chemical equation, can provide the mole ratio. The significance of molar ratio Chemical equations are representations of chemical processes in symbolic form.The reacting components are written on the left side of a chemical equation, and the products are written on the right; the two sides are generally divided by an arrow indicating the direction of the reaction. The absolute stoichiometric quantity employed in the reaction is denoted by the number coefficient next to each entity. Because the rule of conservation of mass states that the amount of each element must remain constant during a chemical reaction, each side of a balanced chemical equation must have the same amount of each element. The coefficients in a balanced chemical equation can be used to calculate the relative quantity of molecules, formula units, or moles of chemicals involved in the reaction. The coefficients in a balanced equation may be used to calculate molar ratios, which can then be utilized as conversion factors to connect the reactants to the products. These conversion factors state the ratio of reactants participating in the reaction but do not specify how much of each component is really engaged in the process. Units of Molar Ratio Molar ratio units are either mole: mole or a dimensionless number since the units cancel each other out. For example, it is acceptable to state that a 3:1 ratio of 3 moles of O2 to 1 mole of H2 is correct, or it can also be stated as 3 mol O2: 1 mol H2. Example of a Mole Ratio: A Balanced Equation In response to the reaction: 2 H2(g) + O2(g) → 2 H2O(g) The mole ratio of O2 to H2O is 1:2. For every mole of O2 consumed, two moles of H2O are produced. H2 and H2O have a mole ratio of 1:1. 2 moles of H2O are generated for every 2 moles of H2. If four moles of hydrogen are utilized, four moles of water are generated. Example of an Unbalanced Equation Let's take another imbalanced equation as an example: O3 → O2 This equation is not balanced since mass is not conserved, as may be seen by inspection. Ozone (O3) has more oxygen atoms than oxygen gas (O2). A mole ratio cannot be calculated for an imbalanced equation. When this equation is balanced, the following results: 2O3 → 3O2 You may now calculate the mole ratio by plugging the coefficients in front of ozone and oxygen. The ozone-to-oxygen ratio is 2:3. How will you put this to use? Assume you are requested to calculate how many grams of oxygen are created when 0.2 grams of ozone are reacted! The first step is to determine how many moles of ozone are contained in 0.2 grams. (Because it's a molar ratio, the ratio for grams isn't the same in most calculations.) Look up the atomic weight of oxygen in the periodic table to convert grams to moles. Per mole, there are 16.00 grams of oxygen. To determine how many moles are in 0.2 grams, solve for: X moles = 0.2 g * (1 mole/16.00 g) You will receive 0.0125 moles Calculate how many moles of oxygen are created by 0.0125 moles of ozone using the mole ratio: * (3 moles oxygen/2 moles ozone) moles of oxygen = 0.0125 moles ozone When you solve this, you obtain 0.01875 moles of oxygen gas Finally, for the solution, convert the amount of moles of oxygen gas into grams: 0.01875 moles * (16.00 grams/mole) = grams of oxygen gas 0.3 gram = 0.3 gram of oxygen gas Because just one sort of atom was present on both sides of the equation, it should be very evident that you could have put the mole fraction straight away in this specific example. However, knowing the technique is useful for, when you encounter more difficulties to tackle. Netsol Water is Greater Noida-based leading water & wastewater treatment plant manufacturer. We are industry's most demanding company based on client review and work quality. We are known as best commercial RO plant manufacturers, industrial RO plant manufacturer, sewage treatment plant manufacturer, Water Softener Plant Manufacturers and effluent treatment plant manufacturers. Apart from this 24x7 customer support is our USP. Call on +91-9650608473, or write us at firstname.lastname@example.org for any support, inquiry or product-purchase related query.
Early middle ages Early Middle Ages or early Middle Ages is a modern term for the first of the three large sections of the Middle Ages , based on Europe and the Mediterranean for the period from approx. 500 to 1050. The early Middle Ages are preceded by late antiquity (approx. 300 to 600) represents a time of transformation and partly overlaps with the beginning of the early Middle Ages. The two periods following the Early Middle Ages are the High and the Late Middle Ages . The early Middle Ages are important as a transition from antiquity to the Middle Ages and as an independent epoch. The beginning and the end are dated differently in historical research, so that transition periods of different widths are considered. Contrary to the older interpretation as a “dark” or “backward” epoch, the early Middle Ages are viewed in a much more differentiated manner in modern research. It is characterized by continuities as well as changes in the political, cultural and social spheres, which have effects right up to modern times. Thus began the continuous division of Europe and the Mediterranean region into a Christian and an Islamic part, as well as the Christian part into a Latin and an Orthodox , which included the cultural area of Byzantium . Several of the empires that arose in the early Middle Ages also formed the basis for states that still exist today. The beginning of the early Middle Ages is linked to the so-called migration of peoples , in the course of which the Western Roman Empire perished in 476. The Roman administrative structures in the west disappeared only slowly, and new Germanic - Romanic empires emerged on the soil of the western empire. The Franconian empire founded by the Merovingians in the late 5th century developed into the most important successor empire in the west. In the east, on the other hand, Ostrom held its own, which in the 6th century even managed to recapture some lost territories in the west. However, large parts of the conquered areas were soon lost again. East or Byzantium was also in a defensive battle against the Persian Sāsānids until the early 7th century . In the 7th / 8th In the 19th century, the political order in the Mediterranean changed fundamentally as a result of the Arab conquests . This marked the final end of antiquity . The former Byzantine controlled area in the Middle East and North Africa was occupied by the Muslim Arabs and slowly Islamized. Islamic rule also existed for a long time on the Iberian Peninsula and Sicily . In the east, the Arabs conquered Persia and advanced as far as Central Asia . In the 8th century the Carolingians took over rule in the Franconian Empire . Under them, the Franconian Empire developed into a hegemonic power in the west. Associated with this was a shift in the political focus from the Mediterranean to Western and Central Europe and a new phase of the “state order” in Europe. Under Charlemagne , who linked up with the western empire in 800, the Franconian Empire comprised the core part of Latin Christianity from northern Spain to the right bank of the Rhine and central Italy. From the Carolingian Empire , which fell apart in the 9th century, the West and East Franconia emerged , from which France and Germany later developed. In Eastern Franconia, the Liudolfingers rose in the 10th century , achieved the western imperial dignity and laid the foundation for the Roman-German Empire , which also included imperial Italy . France and England eventually developed into territorially closed rulers. Politically, the 10th and 11th centuries were a phase of consolidation in the Carolingian successor empires, on the Iberian Peninsula and in England; the transition into the High Middle Ages took place. In the north, the Viking Age began in the 8th century and lasted until the 11th century . From the 7th century onwards, Slavic domains emerged in Eastern Europe , partly on a tribal basis and partly in the form of empires. Byzantium was able to assert itself after heavy defensive battles and also overcame the iconoclasm in the 8th / 9th centuries. Century. In 10./11. In the 19th century Byzantium rose again to become a great power in the eastern Mediterranean. The Arab caliphate , on the other hand, has repeatedly been weakened by internal struggles. The Umayyad dynasty, ruling since 661, was overthrown by the Abbasids in 750 . Under them the caliphate experienced a cultural boom, but also had to accept the separation of parts of it. With regard to state institutions and the organization of more complex tasks based on them, Byzantium and the Caliphate were for a long time superior to the weaker monarchies in the West. Likewise, the local economic power and, above all, the cultural milieu were more pronounced, especially since more of the ancient cultural assets and the scientific tradition were preserved there. In Latin Europe, a new social order was established in the early Middle Ages, with the nobility and the high clergy as the leading classes. An important role was played by the manorial system . After a period of decline, culture in Western Europe flourished noticeably in the course of the Carolingian educational reform in the late 8th and early 9th centuries, before a temporary decline again occurred. Education was largely restricted to the clergy. After a slump in the 7th / 8th Century again a phase of the boom, in which the cities played a part, although the early Middle Ages was predominantly agrarian economically. In the religious sphere, the Christianization of the pagan areas in the interior of Europe was promoted. This slow process sometimes dragged on into the High Middle Ages, but expanded the Christian culture considerably to include Northern and Eastern Europe. The papacy and monasticism , which were initially not politically relevant , became increasingly important. The church also played an important role in the cultural field. With Islam, a new, large monotheistic religion emerged at the beginning of the 7th century . Term and temporal delimitation The Middle Ages are often equated with the millennium from around 500 to around 1500. The term primarily refers to Europe and the Mediterranean area as a cultural area and can therefore only be applied to a limited extent to non-European history, although in historical research, specific historical periods are also referred to as the respective Middle Ages with regard to the cultural areas of India, China and Japan. The term Middle Ages is particularly relevant for the Christian-Latin part of Europe, as there was a political and cultural break there in late antiquity . But the Byzantine-Greek and Islamic-Arab regions are also essential for understanding the Middle Ages, as all three regions were in a mutual relationship. History is still debating how to delimit the early Middle Ages from late antiquity and the high Middle Ages . With the end of antiquity and the beginning of the early Middle Ages, a time set in that was often viewed as a rather "dark period" in older research. This began with the appearance of the term “Middle Ages” (medium aevum) in humanism and was finally consolidated with the historical model of the Enlightenment in the 18th century, in which this form of periodization became predominant and history processes in a certain sense (a “middle time “Between antiquity and modern times). This was a deliberate devaluation from the outset. In comparison to antiquity and the Renaissance, the early Middle Ages, in particular, were considered to be a “dark epoch”. This view of history was formative until the 20th century. In modern research, however, the problematic of such general judgments is pointed out and a more differentiated view is advocated. For the beginning of the early Middle Ages, different times and events have been suggested from different perspectives: - 306–337: Reign of Constantine , Constantinian turning point in religious policy - around 375: The Huns invade East Central Europe; this is considered to be the beginning of the migration of peoples and the resulting transformation of Western and Central Europe. - 476: The last Western Roman emperor, Romulus Augustus , is deposed by Odoacer . - 486/87: The Merovingian King Clovis I defeats Syagrius , the last representative of Roman rule in Gaul. - 529: Benedict of Nursia founds the Montecassino Abbey in southern Italy, which becomes the cradle of medieval monasticism. In the same year Justinian I bans the Platonic Academy in Athens . - 565: The Eastern Roman Emperor Justinian , who sought to restore Roman rule in the West, dies. - 568: With the Lombards invading Italy, the last significant successor empire for the early Middle Ages was founded on Roman soil. - 632: The spread of Islam begins. The early dates are hardly represented in recent research. Rather, one regards the period from approx. 500 to the middle of the 7th century as a flowing transition period from late antiquity to the early Middle Ages with overlaps. It is taken into account that this process was very different from region to region and that several ancient elements were preserved. The development in late antiquity from the 4th century onwards is also often taken into account, insofar as important prerequisites for the later development of Western Europe were created in this phase. Because late antiquity was a transitional period that anticipated individual characteristics of the Middle Ages. While older, classicism- oriented research emphasized a break between antiquity, which is considered exemplary, and the supposedly “dark” Middle Ages (“catastrophe theory”), today's research therefore emphasizes the aspects of continuity and gives greater weight. The large number of current publications shows the significant increase in research interest in the transition period from late antiquity to the early Middle Ages, although the research approaches vary widely. In recent research, what happened in the Eurasian area in the first millennium - the emergence of the late Roman Empire with all the upheavals associated with it, the "migration of peoples", the conflicts with Persia, the emergence of the Islamic world and the Romance-Germanic world in the west of the former empire - increasingly viewed in a temporal and spatial context. In this context, a model called " long late antiquity " emerged from the 3rd to 9th century, which is represented by a minority in research. It is now undisputed that late antiquity and the early Middle Ages should not be understood as rigid chronological structures. In recent research, early medieval Europe is no longer viewed in isolation, but is embedded in a global historical context. The end of the Early Middle Ages and the beginning of the High Middle Ages are not fixed on any single date. The cornerstones are the final disintegration of the Carolingian Empire and the formation of the successor kingdoms around and after 900, the adaptation of the Western Roman imperial idea by Emperor Otto I in 962 (including the following development that led from Eastern Franconia to the later so-called Holy Roman Empire ), the End of the Ottonian imperial family (1024) or generally the period around 1050. The structural approaches in German-language research are primarily based on the history of the Central European dynasty; English, French and Italian research focus on other aspects. This is related to the different scientific traditions. In Great Britain, for example, the conquest of England by the Normans in 1066 is considered a turning point. From a Byzantine point of view, the year 1054, with which the Eastern Schism began between Rome and Constantinople, and the conquest of Anatolia by Turkish nomads from 1071 are important turning points. The dating approaches therefore vary in the specialist literature, including in the “European” -oriented overview presentations, between around 900 and the middle of the 11th century. Requirements: Rome in late antiquity Even after the extinction of the Western Roman Empire in 476, the Roman legacy continued to be important in the Middle Ages. Latin remained the central lingua franca and scholarly language, and Roman offices continued to exist long after the end of Western Rome in the Germanic-Romanic successor realms. Many contemporaries therefore did not perceive 476 as a turning point. Material remains were omnipresent and some of them continued to be used. The emperors of the Eastern Empire residing in Constantinople were recognized as overlords in most regions of the West throughout the sixth century (although mostly without practical consequences). Because the idea of the Roman Empire had a lasting impact on scholarly thinking: Since the church fathers had taught that the Roman Empire was the last before the end of the world, many Christian authors concluded from this, conversely, that the Roman Empire would continue to exist. This empire, however, changed in many ways long before 476, and these tendencies continued after the fall of the central imperial authority. The Roman Empire went through a process of transformation in late antiquity , which for a long time was equated with decadence or decline and which has only been analyzed in more differentiated fashion in modern research. Following on from the reforms of Emperor Diocletian , Constantine the Great reorganized the administration and army to a large extent at the beginning of the 4th century. Even more momentous was the turn in religious policy pursued by Constantine, which is often referred to as the Constantinian turn , especially the clear privilege of Christianity after 312 . With the exception of Julian, the emperors who followed Constantine were all Christians. This development culminated at the end of the 4th century with the elevation of Christianity to the state religion by Theodosius I. The pagan (pagan) cults lasted into the 6th century, but lost more and more importance after 400 at the latest and were only of one practiced by a shrinking minority. In contrast, the Christian imperial church gained more and more influence, even though the various internal Christian disputes (→ First Council of Nicaea , Arianism , Nestorianism , Monophysitism ) sometimes caused considerable social and political problems. As early as the 3rd century, monasticism first developed in the east of the empire , which was of great importance in the Middle Ages. In contrast to an older doctrine, the development of the Roman state and society in late antiquity was no longer viewed as a process of decline. Rather, the economy, art, literature and society showed signs of noticeable vitality, albeit differently regionally. In the east of the empire, which remained largely stable internally, the overall situation was significantly more favorable than in the crisis-ridden west. The “classical heritage” was cultivated in late antique culture, but at the same time Christian influence grew. Christian and pagan authors created important writings of various stripes (see Late Antiquity # Cultural Life ). In the Middle Ages, the so-called Corpus iuris civilis was of great importance from a legal perspective . The Roman state had been more centralized since Constantine than before, with the now purely civil Praetorian prefects at the head of the administration. However, one cannot speak of a coercive state, especially since the administration with its around 30,000 officials for the approx. 60 million inhabitants was weakly staffed by modern standards. In the military field, Germanic tribes and other “barbarians” were often recruited for the army; since, unlike in the past, they no longer served in separate units ( auxiliary troops ), but in the regular army, the army now appeared to be more “un-Roman” than before. The foederati , foreign warriors who were considered allies and were only indirectly subject to Roman orders , played a special role . In terms of foreign policy, the situation of the late ancient empire deteriorated from around 400 onwards. Teutons on the Rhine and Danube, and above all the New Persian Sāsānid Empire , Rome's great rival in the east, had already caused constant pressure, but the situation remained relatively stable until the late 4th century . The Romans were often able to take the initiative themselves. After the actual division of the empire in 395 , however, both imperial courts were repeatedly involved in territorial disputes and in conflicts over the priority in the entire empire. The economically stronger and more populous Eastern Empire was able to solve the external and internal problems better, but from the 6th century it was involved in an ongoing conflict with the Sāsānids (→ Roman-Persian Wars ). Westrom, however, experienced internal turmoil and a chain of civil wars. There, the army masters also increasingly gained political influence (which, unlike in the Eastern Empire, they could also maintain) and in the end effectively controlled the emperors. From antiquity to the Middle Ages: the migration of peoples The so-called migration of peoples (approx. 375 to 568) forms a link between late antiquity and the beginning of the European early Middle Ages. The increasingly weakly defended western Roman borders were now increasingly crossed by looters of Germanic tribes from the Barbaricum , while warrior groups wandered about inside the empire. Foederati (non-imperial warrior groups with their own commanders who were in Roman service on the basis of contracts) were particularly involved in the internal battles that lasted for decades in West Rome. Partly in cooperation and through contracts (foedera) with the Roman authorities, partly with military force, their leaders gained control over ever larger parts of the empire, often filling the power vacuum created by the progressive disintegration of imperial rule. In this way, in turn, they contributed to a destabilization of the Western Roman Empire . The process of dissolution, combined with the successive loss of the western provinces (especially Africa and Gaul), progressed rapidly until the middle of the 5th century and ended in 476 with the deposition of the last emperor in Italy, while the east was able to assert itself. According to the traditional view, this development began as early as the 4th century: In 376 the Goths on the Danube, fleeing from the Huns, asked for admission to the east of the empire. The Romans recruited the warriors as mercenaries. Tensions that soon emerged, however, led to a mutiny and in 378 to the Battle of Adrianople , in which the Eastern Roman Emperor Valens and much of his army fell. In the decades that followed, these Gothic groups in the Empire sometimes acted as foederati and sometimes as opponents of Rome. Under their leader Alaric , Gothic foederati demanded increasingly desperate supply (annona militaris) from the western emperor Flavius Honorius since 395 ; when no agreement was reached, they plundered Rome in 410 , which had long since ceased to be an imperial residence, but was an important symbol of the empire. In the years 416/18 the warriors were finally settled in Aquitaine . In the following time they acted as Roman foederati and fought against the Huns under the powerful Western Roman army master Flavius Aëtius 451. The Visigoth rex Eurich (II.) Broke the treaty with the weakened western empire soon after taking office in 466 and pursued an expansive policy in Gaul and Hispania . From these conquests the new Visigoth Empire arose , which until 507 comprised large parts of Hispania and the south-west of Gaul. For Westrom, which was shaken by internal power struggles and usurpations, the situation became more and more threatening due to the crossing of the Rhine in 406 and the development it triggered: At the turn of the year 406/07, vandals , Suebi and Alans crossed the Rhine , probably in the Mogontiacum area ( Mainz ). The Roman defense of the Rhine temporarily collapsed and "barbaric groups" raided Gaul and plundered before moving on to Hispania. The Romans, who were at war with each other, accused each other of having called the foreign warriors into the country. The Burgundians also advanced to the Rhine and interfered briefly in Roman politics before entering the service of the Romans and establishing an empire that lasted until 436 on the central Rhine. The Burgundians were then relocated to what is now Savoy , where they established a new empire that was conquered by the Franks in the 530s . The Franconian Empire played an important role in the context of the “Great Migration” and in the further course of the early Middle Ages . Franks functioned as Roman foederati in northeastern Gaul at the beginning of the 5th century . They benefited most from the collapse of Roman rule in Gaul, where they established a new empire in the late 5th and early 6th centuries ( see below ). The warriors' association of the Vandals crossed under the rex Geiseric in 429 from southern Spain to North Africa, where the warriors conquered the whole of Africa , the richest western Roman province, by 439 . With a new fleet, the Vandals became a serious threat to the Western Roman government, which had resided in Ravenna instead of Milan since late 402 . In the period that followed, Geiserich repeatedly intervened in the Western Roman power struggles. In 455 he sacked Rome , in 468 he fought off an all-Roman naval expedition. Inside, like many other foederati , the vandals turned out to be not barbarians, but rather followers of Roman culture, which was further cultivated in Africa . However, there was considerable religious tension between the Arian Vandals and the Catholic Romans, which was not overcome until Eastern Roman troops conquered the Vandal Empire in 533/534. In Britain , meanwhile, the Roman order fell as early as the first half of the 5th century. Around 440, Saxons rebelled here , later also Jutes and Angles , who had served as foederati , and founded their own small empires after Westrom had practically left the island to itself. Only a few Roman-British troops were able to offer resistance to the invaders, but little is known about the details ( see below ). The (later so-called) Ostrogoths came under Hunnic rule after 375. Under Attila , the Hun empire on the Danube achieved the greatest development of power: both western and eastern currents tried to maintain the best possible relationships (see, for example, the detailed report by Priskos on an eastern Roman legation 449). Then around 450 there came a conflict with Flavius Aëtius . After failed forays into Gaul (451) and Italy (452), after Attila's death in 453 and the Battle of Nedao in the following year (454), the very loosely organized Hun Empire fell apart . The Ostrogoths benefited from this after they had been victorious in the Battle of the Bolia (469) against Gepids and Skiren . First in Pannonia , then in Thrace , they lived as Roman foederati . In the meantime, the ever-shrinking Western Roman Empire, that is, the area controlled by the court in Ravenna, was finally limited to Italy, after Westrom had effectively lost Africa , Hispania and Gaul to the various warrior groups. This entailed considerable tax losses, which had an impact on military resources. Furthermore, only "shadow emperors" had ruled in the last decades, while the real power lay with the army masters and the army could no longer be effectively controlled by the emperors. The now almost completely “barbaric” Western Roman army had claimed land from the Western Roman government in 476; when the demand was not met, the troops mutinied. Their leader Odoacer deposed the last Roman emperor in Italy, Romulus Augustulus , in August 476. This left only the emperor in Constantinople as head of the empire reduced to the Eastern Empire (although the emperor Julius Nepos, who was expelled from Italy in 475, stayed in Dalmatia until 480) . In the year 488 the Eastern Roman Emperor Zenon proposed an invasion of Italy to the Ostrogothic King Theodoric , who seemed to him to be more and more dangerous. A year later (489) Theodoric invaded Italy and defeated and killed Odoacer in 493. Italy prospered under Theodoric's rule, but after his death in 526 a time of crisis began. Ostrom took advantage of dynastic battles to conquer the former heartland of the empire in the Gothic War (from 535). This succeeded until the year 552, but Italy was then devastated. The incursion of the Lombards in 568, who set out from Pannonia and soon ruled large parts of northern and central Italy, only marked the end of this. In contrast to older research, today the problem of the term mass migration and the associated historical image is pointed out. Not whole peoples "migrated", rather it was differently sized, heterogeneously composed warrior groups that only grew together in the course of time into associations and claimed their own identity. This process cannot be recorded using biological categories; Rather, identities emerged in a changeable social process in which several factors play a role. The members of these groups were united not least by the effort to share in the prosperity of the empire, which they neither wanted to destroy nor conquer. For a long time they tried to achieve this goal by entering the service of the Romans and fighting for them against external and internal enemies. In this context, the process of ethnogenesis plays an important role, i.e. the emergence of new groups that were fictitious communities of descent, but whose unity was in reality politically and socially justified. However, this influential research approach (represented by Herwig Wolfram and, with modifications, Walter Pohl ) has been questioned by several Anglo-American researchers in recent years. The migration of peoples was also much more than just a defensive struggle by the Roman Empire. Above all, it was a transformation of the previous Roman Mediterranean world into a Germanic-Roman world in the west and a Greco-Roman world in the east. The sometimes dramatic changes at the end of late antiquity should not be overlooked, but neither should they be overestimated, as numerous signs of continuity can be discerned. The “post-Roman world” that emerged in the course of the Great Migration was in many ways still closely linked to antiquity, although it was changing more and more. Johannes Fried summarizes this as follows: “So antiquity shrank and disappeared in a long, uneven process of transformation. [...] But the dwindling left its traces everywhere like melted glaciers [...] " Little by little, larger and larger parts of the usual Roman institutions disappeared in the West, first (as early as the 5th century) the army, then the Roman administrative order. Roman education and cultural traditions, which were closely related to urban society in late antiquity, were also in decline, but by no means everywhere (apart from the special case of Britain, which collapsed very quickly): especially in North Africa, in the Visigoth Empire as well in Italy and partly in Gaul, the culture of late antiquity flourished well into the 6th century. The church played an important mediating role in this context, in whose monasteries ancient texts were kept and later copied, starting with Cassiodorus . The loss of books in late antiquity , however, meant that numerous ancient works could only be received on the basis of quotations and summaries in the writings of the church fathers. The Roman-trained administration also functioned in these areas for a long time. The minority of the Germanic tribes, which in any case was vanishingly small, often resembled the native Romansh population with their superior Roman civilization, but was largely religiously separated from the Romans. The Germanic tribes, if they were not in Pagan religious tradition beforehand, were predominantly Arian Christians, while the population was Roman Catholic, which often led to tensions, especially in the Vandal Empire and partly in Ostrogothic and Longobard Italy. The Franks, on the other hand, avoided such problems by adopting the Catholic creed under Clovis I. The changing Mediterranean world: from Justinian to the onset of Islam In the 6th century the Mediterranean and the Middle East were dominated by two rival great powers: the Eastern Roman Empire and the New Persian Sāsānid Empire , which the Eastern Roman Empire had grown militarily and culturally. The (Eastern) Roman Emperor Justinian (r. 527-565) emphasized the Christian-sacred component of his empire internally, while externally he strove to regain territories in the west since the 530s. Even though Justinian's time was of a transitional nature, the emperor continued to orient himself politically towards the Roman tradition. He took great care of religious policy and took action against the remnants of the pagan cults and against heretical Christian groups. A solution to the sometimes difficult theological problems (see under Monophysitism ) and the implementation of a uniform Christian creed for the entire empire did not succeed, however. He also pursued a vigorous building and legal policy (see Corpus iuris civilis ). In terms of foreign policy, the empire went on the offensive in the West during its reign and, at first glance, had impressive successes. Thanks to capable commanders such as Belisarius , the rapid conquest of the Vandal Empire in North Africa succeeded in 533/34. From 535 to 552 the Ostrogoth Empire in Italy was conquered after hard fighting in the Gothic War . Even in southern Spain, Ostrom had temporarily regained a foothold since 552. The Roman Empire thus extended again from the Atlantic to Mesopotamia . However, this expansion claimed all resources of the empire, which was weakened internally by natural disasters and epidemics (→ Justinian plague ). In the east, Justinian also suffered setbacks against the Sāsānids and was only able to make peace with the important Persian king Chosrau I in 562 after changing and costly battles . When Justinian died in 565, the empire was weakened by the long wars in the west and east, but it was undoubtedly the most important power in the Mediterranean. After it came to war with Persia again in the reign of Justin II. 572 , whereby neither side achieved a decisive success, Emperor Maurikios (r. 582-602) was able to benefit from a conflict over the Persian succession to the throne and with King Chosrau II. 591 Make peace. Chosrau II used the murder of the emperor in 602 as an excuse to invade Roman territory. From 603 to 628 the “last great war of antiquity” raged. By 619, Persian troops conquered Syria and Egypt, the breadbasket of the empire, and in 626, together with the Avars (who had established an empire in the Balkans at the end of the 6th century), even besieged Constantinople . The realm was in an extremely difficult situation, and complete annihilation did not seem ruled out. The counter-attack of Herakleios (ruled 610-641) in the years 622 to 628 saved the empire and finally forced the Persians to retreat. In 628 Persia asked for peace in the face of internal turmoil, and Herakleios, who is considered one of the most important emperors in Eastern Roman-Byzantine history, was at the height of his reputation; He even received congratulations on his great victory from the Frankish Empire. But the empire was extremely weakened by the heavy fighting over the past decades, the extent of the destruction is clearly expressed in the sources. Inside, Herakleios completed the Graecization of the state, but he was unable to end the religious disputes (→ monotheleticism ) nor to consolidate the empire again. When the Islamic expansion began in the 630s , East Stream and Persia were no longer able to offer effective resistance after the long wars, which was an important reason for the rapid Arab successes. The desert border could hardly be controlled for Eastern Current and Persia anyway (in the form of the Lachmids and Ghassanids one had rather relied on Arab allies) and larger troops were not stationed there after the Persian War; Added to this was the mobility of the Muslim Arabs. The Sāsānid Empire, weakened by civil wars, suffered two heavy defeats against the Arabs (638 in the Battle of Kadesia and 642 in the Battle of Nehawend ). Although the Persians offered resistance and were able to win a major battle at the beginning and lead several successful smaller counter-offensives, their empire finally collapsed in 651; the sons of the last Persian great king Yazdegerd III. fled to the Chinese imperial court of the Tang Dynasty . Persia was largely able to retain its cultural identity under Islamic rule and was Islamized relatively slowly, similar to the Christian areas in Egypt and Syria. At the beginning of the 8th century, the Arabs conquered Sogdia (see also Ghurak and Dēwāštič ) and pushed further into Central Asia . In the west, Eastern Roman troops were subject to the Arabs in the Battle of Yarmuk in 636 and had to completely evacuate Syria after Damascus surrendered in 635 . From then on, Syria served as the starting point for Arab attacks on Asia Minor , which the Eastern Romans, however, were able to hold and which now became the heartland of the empire. Jerusalem surrendered in 638. Most painful was the loss of Egypt in 640/42 (due to its economic strength, tax revenue and grain). Soon after, the Arabs took Armenia, Cyprus (649) and Rhodes (654). They advanced along the North African coast to the west and occupied what is now Tunisia around 670; Carthage was held until 698. 711–725 was followed by the conquest of the Visigoth Empire in Hispania and southwestern Gaul. Forays into the Franconian Empire were unsuccessful. In 655, the Eastern Roman fleet under Constantine II suffered a heavy defeat against the Arabs in the Battle of Phoinix , who now emerged as a sea power and thus threatened the trade and maritime domination of Eastern Europe. The Eastern Romans / Byzantines also achieved some important successes: in the defense of Constantinople from 674 to 678, they destroyed the Arab fleet; However, whether there was a real siege in this context is controversial in recent research. In 677/678 the eastern Romans were able to go on an offensive despite limited resources and even temporarily land troops in Syria. Eastern Byzantium could not prevent or reverse the loss of the eastern provinces and was put on the defensive. The ancient unity of the Mediterranean (which was both politically and economically of great importance for the stability of the Roman state) ended with the Arab conquests. 100 years after Justinian's death, the Roman Empire had lost more than half of its territory and population, while on the east and south coast of the Mediterranean a new empire with a new faith had emerged with the Arab caliphate . The old world order, which had existed between East and Persia throughout late antiquity, was broken as a result of the Arab conquests and replaced by a new order in which East-Byzantium had to fight against the caliphate for pure existence. The Eastern Roman Empire, which around 700 was finally limited to Asia Minor, Greece, Constantinople including the surrounding area and some areas in Italy, now finally changed to the Greek Byzantium of the Middle Ages. The period from the middle of the 7th to the 8th century was still characterized by heavy defensive battles. The finally successful defense prevented the Arabs from advancing further into south-eastern Europe. The Herakleios dynasty ruled until 711. Under Emperor Leo III. , who came to power in 717, Byzantium went back on a limited offensive against the Arabs ( see below ). For the history of Western and Central Europe, it was crucial that from the 7th century the emperors were effectively forced to largely leave the former west of the Roman Empire to its own devices: unlike in the 6th century, military interventions were no longer to be expected . Constantinople moved into the distance. The Franconian Empire of the Merovingians The Frankish empire , which emerged in the late 5th century, was to develop into the most important of the Germanic-Romanic successor empires in the west. The rise of the Franks from a regional power in northeastern Gaul to a great empire began under the leadership of kings from the Merovingian dynasty . The Sal-Franconian king (rex) Childerich I , who resided in Tournai , established his own sphere of influence in northern Gaul, where he could fall back on the still working local armories (fabricae) . It is often assumed that he cooperated with the Gallo-Roman general Aegidius , who rose against the Western Roman government in 462/463, but the details are unclear. Aegidius himself established an independent domain in the Soissons area ; after his death he was soon followed by his son Syagrius . Childerich's son Clovis destroyed the other small Franconian empires (including Ragnachars and Chararichs ) and thus became the founder of the Franconian Empire. 486/487 Clovis conquered the kingdom of Syagrius. In 507, the Visigoths were defeated at the Battle of Vouillé and effectively driven out of Gaul. Clovis also took action against the Alemanni , while a preliminary rapprochement was reached with the Burgundians. The originally pagan Clovis converted to Christianity at an unspecified point in time (probably towards the end of his rule). The decisive factor was that he opted for the Catholic creed and thus avoided problems that sometimes arose in the other Germanic-Romanic empires between the conquerors and the Roman population. The skilful and at the same time unscrupulous actions by Clovis secured the Franks a dominant position in Gaul. After the death of Clovis in 511, the Franconian Empire was divided among his four sons Theuderich , Chlodomer , Childebert and Chlotar , each receiving a share of the Franconian ancestral land in northern Gaul and the conquered areas in the south. The widespread practice among the Franks of dividing rulership among their sons after the death of a king caused the central royal power to be fragmented. Conflicts for the throne were not uncommon, especially since most of the Merovingians did not reach old age and often had children of several women, which made succession arrangements difficult. Clovis had already called on the Gallo-Roman upper class for administrative tasks, and especially the bishops (such as Gregory of Tours , whose history is the most important source of the Franconian history of the 6th century). He had also used the system of Roman civitates , which were particularly widespread in southern Gaul , where the Gallo-Roman senatorial nobility (whose ancestors once held Roman state offices and now functioned as local and above all ecclesiastical dignitaries) can be traced for a long time. The administration was initially based largely on late Roman institutions, before these disappeared and the influence of counts (comites) and duces (duces) increased . The Franconian expansion was pushed further: In 531/534 the Thuringians and in 534 the Burgundians were subjected. The Franks used the Gothic War in Italy to occupy parts of the Eastern Gothic territory. Theuderich's son Theudebert I saw his position in the east of the Merovingian Empire as so solid that he is said to have even toyed with the idea of challenging Emperor Justinian. However, as early as the 6th century there were signs of divisions in the Frankish domain, which repeatedly played a role in later battles between rulers. The Gallo-Roman south with the centers on the Rhône and Saône retained its elite, which emerged from the Gallo-Roman senate nobility, and its late antique urban structures with a strong position of bishops and Roman law (droit écrit) . On the other hand, in the more Germanized north the elites changed, the urban culture partially declined and the customary law rooted in Germanic tribal law (droit coutumier) played a growing role. It was not until the 15th century that the legal systems gradually converged. Visigothic influences persisted in the southwest. So fights flared up inside between the individual Merovingian rulers. After the death of Chlothar I in 561 a Merovingian fratricidal war broke out , which only ended in 613 with the reunification of the entire empire under Chlothar II . Dagobert I , who took over the rule of Austrasia in 623 and ruled over the entire empire from 629 to 639, is generally considered to be the last strong Merovingian king, although he too had to make some concessions to the powerful nobility. According to the common doctrine, after Dagobert's death, the royal power declined more and more and the real power lay in the hands of the caretakers (originally only administrators of the royal court, but who gained more and more influence over time). This assessment is based on the view of the Carolingian Frankish historiography, such as the Reichsannalen and Einhard's Vita Karoli Magni . In the presentation of these sources, the transfer of the Franconian royal dignity to the Carolingians in 751 appears as a necessary consequence of the powerlessness of the last Merovingians, which was reflected in their rather ridiculous appearance. The negative attitude of the Carolingian authors towards the late Merovingians makes an unbiased assessment difficult. In more recent research it is sometimes doubted that the last Merovingian kings were really as powerless as Carolingian historiography suggests. It can be assumed that the partisan sources have deformed at least parts of the historical narrative. What is certain is that after Grimoald the Elder's failed attempt to bring about a change of dynasty as early as the 7th century , the Carolingians long shied away from disempowering the Merovingians, be it because of sacred ideas of the king or because of deeply rooted dynastic thinking. After the Battle of Tertry in 687 the final rise of the Carolingians began, whose name goes back to the powerful Franconian housekeeper Karl Martell . Karl Martell was able to prevail against competing house keepers and functioned as the true power behind the throne until his death in 741, where he was able to secure and expand the borders of the empire (among other things by subjugating the Frisians ). From then on, the Carolingians controlled the affairs of state in the empire and finally achieved the Franconian royal dignity in 751 when the last Merovingian king Childerich III. was discontinued. From the Carolingian Empire to West and East Franconia In 751, in consultation with Pope Zacharias Pippin the Younger, he was the first Carolingian to be raised to the rank of Frankish king (ruled 751–768). The anointing of Pippin by the Pope in 754 apparently served as additional legitimation and laid the foundation for the role of the Frankish kings as the new patrons of the Pope in Rome. The early Carolingian kings proved capable rulers. Pippin intervened in Italy, where he took action against the Lombards, led campaigns in Aquitaine and secured the Pyrenees border. When he died in 768, he enjoyed a reputation far beyond the borders of the Franconian Empire. The empire was divided between his two sons Karlmann and Karl. Apparently there was great tension between the brothers; After the unexpected death of Karlmann at the end of 771, Karl ignored the inheritance claims of Karlmann's sons (which were later probably removed on Karlmann's orders) and occupied his part of the empire. Karl , later called Carolus Magnus ("Charlemagne"), is considered the most important Carolingian and one of the most important medieval rulers (ruled 768–814). After securing rule in the interior, Karl began campaigns against the Saxons in the summer of 772 . The resulting Saxon Wars lasted with interruptions until 804 and were fought with extreme brutality. The goal was not only the conquest of the country, but also the forcible Christianization of the previously pagan Saxons. From a military point of view, the Franconian tank riding played an important role. At the same time, at the papal request, Charles intervened in Italy in 774 and conquered the Longobard Empire, which he united with the Frankish Empire. The Spanish campaign against the Moors in 778 was less successful , although at least the Spanish mark was established later. Karl's diplomatic contacts extended to the caliph Hārūn ar-Raschīd . In the east of his empire, he ended the independence of the tribal duchy of Bavaria in 788 . There were also battles with the Danes and several Slavic tribes, as well as the ultimately successful Imperial War against the Avars (791–796). In decades of fighting, Karl had expanded the borders of the empire considerably and established the Frankish empire as a new great power alongside Byzantium and the caliphate. The Carolingian Empire now encompassed large parts of Latin Christianity and was the most important state structure in the West since the fall of Western Rome. Karl made Aachen his main residence. He used comites (so-called "county constitution") and the church he sponsored to organize the rulership system more efficiently . The so-called Carolingian renaissance (which should be better described as the "Carolingian educational reform") brought about a cultural revitalization of Christian Western Europe, after an educational decline in the Franconian Empire from the 7th century. The high point of Charles's reign was his coronation as emperor at Christmas in the year 800 by Pope Leo III. in Rome. The details of this process and its history are disputed in research. What is certain is that, from the point of view of contemporaries, the empire was renewed, which, however, led to conflicts with Byzantium ( two- emperor problem ). This event is of great importance for the history of the Middle Ages as it laid the foundation for the western medieval empire . Karl left a lasting impression on the following generations. In the anonymous epic of Charles , the emperor is even praised as pater Europae , the father of Europe. In the Middle Ages he was considered an ideal emperor. With this the myths about Karl began, which resulted in different historical images up to modern times. After Karl's death in January 814, he was succeeded by his son Ludwig the Pious , whom Karl had already crowned co-emperor in 813. The first few years of Ludwig's reign were mainly shaped by his will to reform in the ecclesiastical and secular areas. Programmatically, he proclaimed the Renovatio imperii Francorum , the renewal of the Frankish Empire. In 817 Ludwig decided that after his death the empire should be divided. However, his eldest son Lothar was to be given priority over his other sons Ludwig (in Bavaria) and Pippin (in Aquitaine). A difficult situation arose when, in 829, Emperor Ludwig also assured Karl , his son from his second marriage to Judith , who was influential at court , a share in the inheritance. There had been opponents of the new imperial order before; they now openly opposed the emperor. With the uprising of the three eldest sons against Ludwig the Pious in 830, the time of crisis in the Carolingian Empire began, which eventually led to its dissolution. The rebellion was primarily directed against Judith and her advisors, but in 833 it led to the capture of the emperor on the " Lies Field near Colmar", with Ludwig's army overflowing to the enemy. Then Ludwig had to agree to a humiliating act of penance. But with that the arch was overstepped and the three older sons of Ludwig fell out again. In 834 several supporters turned away from Lothar, who withdrew to Italy. While the empire was increasingly besieged from the outside by Vikings, Slavs and Arabs, internal tensions persisted. Ludwig endeavored to secure Karl's inheritance. After Pippin's death in 839, Karl was given the western part of the empire, but the situation at Ludwig's death in 840 was still unclear. In the eastern part had Louis the German secured his position, similar to Karl in the West, so that the pressure on Kaiser Lothar rose. Karl and Ludwig formed an alliance against Lothar and defeated him in the Battle of Fontenoy on June 25, 841. In February 842 they reaffirmed their alliance with the Strasbourg oaths . At the urging of the Franconian nobles, the Treaty of Verdun was signed in 843 , which basically confirmed the division of the empire: Charles ruled the west, Ludwig the east, while Lothar was given a middle empire and Italy. The question about the beginnings of “German” history, which is often discussed in research in this context, is rather misleading, as it was a long-term process that stretched into the 11th century; The name Regnum Teutonicorum can only be proven with certainty from the 10th century . Apparently, however, the Carolingian parts of the empire were becoming more and more separated from each other in the 9th century, and imperial unity could only be restored temporarily. After Lothar's death in 855, his eldest son Lothar II inherited the Middle Kingdom. After his death in 869, there was a conflict between Karl and Ludwig over the inheritance, which led to the division in the Treaty of Meerssen in 870 . This finally formed the West and East Franconia , while in Italy from 888 to 961 kings ruled separately . The idea of imperial unity still had some supporters. Under Charles III. who won the imperial crown in 881 and ruled over all of Eastern Franconia since 882, the entire empire was reunited for a few years when he also acquired the west Franconian royal crown in 885. But this unification of the empire remained an episode, especially since Karl could not effectively repel the increasing Viking attacks (peace of Asselt in 882 and siege of Paris in 885-886 ) and East Franconia lost to his nephew Arnolf in late 887 (r. 887-899). In the "Regensburg continuation" of the annals of Fulda for the year 888 it is disparagingly noted that after the death of Charles (in January 888) many reguli (minor kings) in Europe would have seized power. Arnolf confirmed the rule of the new kings, for example in West Franconia, Burgundy and Italy. His base of rule was Bavaria. He limited his rule explicitly to Eastern Franconia, where he fought off Slavs and Vikings. Arnolf initially rejected a train to Italy. Not until 894 did he go to Italy following a papal call for help; In 896 he even acquired the imperial crown. Nevertheless, the collapse of the Carolingian Empire was obvious. Culturally, too, there was a decline in the late 9th century, especially in Eastern Franconia, where there was a noticeable decline in literary production. In the east, the last Carolingian Ludwig the child died in 911; he was succeeded by I. Konrad after. Konrad tried to stabilize Eastern Franconia, where he had to assert himself against the powerful nobility and at the same time had to fend off the Hungarians who had founded an empire a few years earlier. In the end, his rule, which was entirely based on Carolingian traditions, turned out to be a mere transition period to the Ottonians , who were the East Franconian kings from 919 to 1024. In West Franconia the Carolingians ruled with interruptions until the death of Ludwig V in 987, but had already largely lost their power. They were replaced by the Capetians , who then became the French kings until the 14th century. However, the French kingship was initially largely restricted to its core area in the Ile de France and only exercised nominal supremacy over the spheres of power of self-confident dukes. The Empire of the Ottonians After the death of the East Franconian King Konrad in 919, Heinrich I, the first member of the Saxon house of the Liudolfinger ("Ottonen"), ascended the East Franconian royal throne; they were able to hold their own in the empire until 1024. In more recent research, the importance of the Ottonian period for the formation of Eastern Franconia is emphasized, but it is no longer considered the beginning of actual “German” history. The complex process associated with it dragged on at least until the 11th century. Heinrich I was confronted with numerous problems. The rulership, based on Carolingian patterns, reached its limits, especially since the written form, a decisive administrative factor, was now falling sharply. With regard to the greats of the empire, Heinrich, like several other rulers after him, seems to have practiced a form of consensual rule: While he formally insisted on his higher rank, he tied the dukes into his politics through friendship alliances (amicitia) and let them in their duchies extensive political leeway. Swabia and Bavaria were thereby integrated into the royal rule of Henry, but remained regions remote from the king until around the year 1000, in which the influence of the kingship was weak. The empire was still in a defensive battle against the Hungarians, with whom an armistice was concluded in 926. Heinrich used the time and had the border security intensified; the king was also successful against the Elbe Slavs and Bohemia. In 932 he refused to pay tribute to the Hungarians; In 933 he defeated them in the battle of Riyadh . In the west, Heinrich had initially given up the claim to Lorraine, which was disputed between West and East Franconia , in 921 before he could win it in 925. Even before his death in 936, Heinrich had made a succession plan within the framework of "house rules", so that his son Otto could be the designated successor as early as 929/30 and the empire remained undivided. In the reign of Otto I (r. 936–973), Eastern Franconia was to assume a hegemonic position in Latin Europe. Otto proved to be an energetic ruler. In 948 he transferred the important Duchy of Bavaria to his brother Heinrich . Otto's rulership was not without problems, however, because he deviated from the consensual rule of his father. At times Otto behaved inconsiderately and came into conflict with close relatives several times. Otto's eldest son Liudolf, for example, acted against the king and was even connected to the Hungarians. They took advantage of the situation in the empire and openly attacked in 954. Liudolf's situation became untenable and he submitted to the king. Otto succeeded in organizing a defense against the Hungarians and in 955 defeating them in the battle of the Lechfeld . His reputation in the empire was increased considerably by this success and opened up new options for him. In the east he won victories over the Slavs, with which the Elbe Slavic areas (Sclavinia) were increasingly involved in Ottonian politics. Otto promoted the establishment of the Archdiocese of Magdeburg , which he finally succeeded in 968. The goal was the Slavic mission in the east and the expansion of the East Franconian area of dominion, for which border marks were set up based on the Carolingian model. Otto's strengthened position made it possible to intervene in Italy that was never completely out of sight of the East Franconian rulers. During the first Italian campaign in 951, his attempt to renew the western empire in Rome failed, even though Italian nobles paid homage to him as "King of the Lombards". He set out for Italy again in 961 and was crowned emperor by the Pope in Rome on February 2, 962, in return he confirmed the rights and possessions of the church. The western empire, based on the ancient Roman imperial dignity, was now connected to the East Franconian (or Roman-German) kingship. In addition, large parts of Upper and Central Italy were annexed to the East Franconian Empire ( Imperial Italy ). However, effective domination of imperial Italy required the personal presence of the ruler, and government from afar was hardly possible at this time. This structural deficit should also cause problems for his successors. A third Italian campaign (966–972) followed a papal call for help, but at the same time served to secure the Ottonian rule. Inside Otto, like many early medieval rulers in general, relied primarily on the church for administrative tasks. When Otto died on May 7, 973, after difficult beginnings, the empire was consolidated and the empire once again a political power factor. Otto's son Otto II (r. 973–983) was crowned co-king in 961 and co-emperor in 967 at a very young age. In April 972 he had married the educated Byzantine princess Theophanu . Otto himself was also educated and, like his wife Theophanu, he was also interested in intellectual matters. In the north he fended off attacks by the Danes, while in Bavaria Heinrich der Zänker (a relative of the emperor) acted against him and received support from Bohemia and Poland. The conspiracy was uncovered, but it wasn't until 976 that Heinrich's (provisional) submission was achieved. The Ostmark was separated from Bavaria and transferred to the Babenbergers . In the west there was fighting with West Franconia (France) before an agreement could be reached in 980. Unlike his father, Otto planned the conquest of southern Italy, where Byzantines, Lombards and Arabs ruled. The campaign began at the end of 981, but in July 982 the imperial army suffered a crushing defeat against the Arabs in the battle of Cape Colonna . Otto managed to escape only with difficulty. In the summer of 983 he planned a new campaign to southern Italy when, under the leadership of the Liutizen, parts of the Elbe Slavs rose up ( Slav uprising of 983 ) and the Ottonian mission and settlement policy suffered a severe setback. The emperor died in Rome on December 7, 983, where he was buried. In medieval historiography Otto II was heavily criticized due to military setbacks and church political decisions (such as the abolition of the diocese of Merseburg ), while modern research takes into account his difficult starting position without overlooking the military failures. He was succeeded by his son of the same name, Otto III. (ruled 983–1002), who had been elected co-king before his father's death when he was not quite three years old. Due to his young age, his mother Theophanu took over the reign , after whose death in 991 his grandmother Adelheid of Burgundy took over the reign. In 994 Otto III. at the age of 14 the government. The ruler, highly educated for his time, surrounded himself over the years with scholars, including Gerbert von Aurillac . Otto was particularly interested in Italy. Disputes in Rome between Pope John XV. and the powerful aristocratic family of the Crescentier were the occasion for Otto's Italian move in 996. Pope Johannes, however, had already died, so that Otto appointed his relative Bruno as Gregory V as the new Pope, who on May 21, 996 crowned him emperor. Then Otto returned to Germany. However, Gregor was expelled from Rome, so that Otto set out again for Italy in 997 and brutally suppressed the uprising in early 998. The emperor stayed in Italy until 999 and, in cooperation with the Pope, sought a church reform. During this time, Otto's government motto is documented: Renovatio imperii Romanorum , the renewal of the Roman Empire, the continuation of which was considered to be the medieval Roman-German Empire. However, the details are controversial; a closed concept is rather unlikely, which is why the importance is relativized in recent research. After Gregory's death, the Emperor made Gerbert von Aurillac the new Pope on New Year's Eve II. Both appointments to the papacy illustrate the distribution of power between the empire and papacy at this time. Otto also made contact with the Polish ruler Bolesław I and went to Gniezno . The emperor spent the next few months in Germany before returning to Italy. In 1001 an uprising broke out in Rome. Otto retired to Ravenna , the emperor died at the end of January 1002 during the renewed advance to Rome. In the sources, his great commitment in Italy is rated rather negatively; Modern research emphasizes that Otto's early death makes a final assessment difficult because his politics did not go beyond the beginnings. Successor of Otto III. was Heinrich II (ruled 1002-1024), who came from the Bavarian branch of the Ottonians and whose accession to power was controversial. Henry II set different priorities than his predecessor and concentrated primarily on the exercise of power in the northern part of the empire, although he moved to Italy three times. On his second Italian campaign in 1014, he was crowned emperor in Rome. In the south there were also clashes with the Byzantines in 1021/22, which in the end were unsuccessful and brought the emperor no profit. In the east he led four campaigns against Bolesław of Poland, which involved property claimed by Poland and questions of honor and honor, before the Treaty of Bautzen was concluded in 1018 . Inside, Heinrich presented himself as a ruler permeated by the sacred dignity of his office. He founded the diocese of Bamberg and favored the imperial church, on which he relied in the sense of the "imperial church system", although this aspect has been evaluated differently in recent times. Some researchers consider Heinrich's approach in this regard as realpolitically motivated; Heinrich ruled over the imperial church, ruled with it and thus tried to intensify the royal rule. What is certain is the close interlinking of royal rule with the church in the empire. With this, Heinrich was hoping for a counterweight to the aristocratic opposition, which repeatedly rose against the king, who emphasized his leadership role over the greats in the empire. His reign is valued very differently; Only in retrospect was he, promoted by the Bamberg Church, stylized as a "holy emperor" and canonized in 1146. His marriage remained childless, instead of the Ottonians, the Salians came to rule. France and Burgundy Although in West Franconia (France) the Carolingians formally provided the kings until 987, apart from the reign of some (quite assertive) kings from other families such as Odo , they had already lost most of their power. Politics was dominated by the great nobles in the 10th century, such as B. from Duke Hugo Magnus from the house of the Robertines . The contrast between Carolingians and Robertinians was formative at this time. In the late phase of the western Carolingians, King Lothar even became dependent on the more powerful Ottonians. He tried to break away from it militarily and made advances to Eastern Franconia, which were unsuccessful. In 987 the Robertine Hugo Capet was elected the new king. This began the rule of the Capetians, later named after Hugo's nickname . All later French kings descended from Hugo Capet in direct male line until the final abolition of kingship in the 19th century. Hugo's contemporaries did not, however, perceive his assumption of government as a significant turning point, and his uprising turned out to be a permanent change of dynasty only later. In the same year Hugo made his son Robert co-king; he was to succeed his father as Robert II in 996 and rule until 1031. The change of dynasty in 987 was not without conflicts. Duke Karl of Lower Lorraine , a Carolingian king's son, asserted his claim to the throne. He had some successes before falling into the hands of the Capetians through betrayal. An attempted coup by the Blois family in 993 also failed. The Capetians emphasized the sacredness of their royal dignity and the associated reputation (auctoritas) . The core of the royal rule was the crown domain with the center of Paris ; the royal property was systematically expanded in the following decades. In addition, the Capetians could count on a fairly broad church support. The establishment of the royal rule did not succeed completely, however, because the greats of the empire dealt with the early Capetians on a relatively equal level. Although they were obliged to travel to court and the army, there were occasional anti-royal coalitions. Princely rule consolidated in several regions in the early 11th century. Attempts by Roberts II to increase the king's power in areas that have become domesticated were only successful in the Duchy of Burgundy, while he failed in the counties of Troyes and Meaux . His son and successor Heinrich I had to assert himself against the House of Blois and had very good connections to the Salian rulers. In terms of foreign policy, the early Capetians were not successful; the attempt to regain Lorraine from the Ottonians failed. However, the French kings tried to emphasize the equality of their empire with the empire. In the 12th century, there were conflicts with the powerful House of Plantagenet , which, in addition to extensive land holdings in France, also provided the English kings until the late Middle Ages . It was only under Philip II August (r. 1180–1223) that the Capetians succeeded in gaining the upper hand. The Kingdom of Burgundy came into being during the fall of the Carolingian Empire. In 879 Boso von Vienne was elected King of Lower Burgundy , his son Ludwig the Blind briefly expanded the Burgundian domain. Even before Ludwig's death in 928, the Lower Burgundian rulership fell apart, from which Hugo von Vienne initially benefited , but ultimately Hochburgund . Rudolf I was crowned king there in 888 . In the period that followed, there were repeated tensions with the local nobility; a strong kingdom could never develop, the royal power remained rather regionally limited. Rudolf II. , Whose expansion to the north-east into the Swabian region had been stopped in 919, made contacts with the Ottonians. He recognized the East Franconian sovereignty and initiated the unification of Hoch- and Niederburgund (allegedly contractually agreed in 933, although this is partly disputed in research), but he died in 937. His son Konrad was able to claim power in Niederburgund with Ottonian support bring to bear. The close relationship between the Burgundian Rudolfinger and the Ottonians was expressed in the Succession Treaty of 1016, which benefited the Salian rulers who united Burgundy with the Empire in 1033. After the end of Western Rome in 476, there was initially no cultural or economic breakdown in Italy. Under Theodoric's rule of the Goths (489/93 to 526), the country experienced a flourishing of late ancient culture, as can be seen in the philosophers Boethius and Symmachus . Theodoric paid respect to the senatorial elite and strove to rule in agreement with the Romans. He used the knowledge of the senatorial ruling class in Italy and used Romans for civil administration, but separated civil and military violence according to ethnic principles. His Goths exercised the military administration and were also assigned land. It seems as if the privilege of the Ostrogoths prevented or even prevented the merging of the Roman nobility with the Gothic leadership group. After Theodoric's death in 526, there was a turmoil of the throne, with Ostrom taking the opportunity and intervening in Italy. The subsequent Gothic War (535–552) devastated the peninsula, which was now again an Eastern Roman province for the time being. The Lombards who broke into Italy under their King Alboin in 568 profited from the state of the exhausted country and the few imperial occupation troops. Resistance to the conquerors was only sporadic, so that Milan fell in 569, but Pavia not until 572. The Lombard conquest of upper and parts of central Italy, however, turned out to be devastating for the remains of ancient culture and the local economy. Alboin had already established a ducat (duchy) in Cividale del Friuli shortly after the invasion began; this form of rulership organization (a combination of late Roman administration and the Lombard military order) was to become typical of the Lombards. The king's power fell after the assassination of Alboin in 572 and that of his successor Cleph in 574, and the Lombard rule was split up into relatively independent ducats. The Longobard Empire was still under great external pressure. Only in the face of a threat from the Franks did the Lombards elect Authari again in this position for the first time after ten years of kingship in 584 . The East Romans / Byzantines were also able to hold several of the seaside towns, as well as Ravenna, Rome and southern Italy. Domestically, the tensions between the mostly Arian Longobards and the Catholic Romans remained a burden for the mutual relationship, even though Catholic Longobard kings also ruled. Worth mentioning among the Lombard kings of the 7th century are Agilulf , under whom the Lombards were able to achieve some successes again, and Rothari , who in 643 had the Lombard legal customs systematically collected and recorded. Liutprand (ruled 712-744) also acted as a legislator and was even able to exercise his power against the Duces of Spoleto and Benevento, the two southern Lombard dominions. By this time the Lombards had finally become Catholic and reappeared expansively, for example against Byzantium, and also intervened in Rome. In 774 the Franks defeated King Desiderius and conquered the Longobard Empire. Italy in the early Middle Ages was a politically fragmented area. During the process of disintegration of the Carolingian Empire in the 9th century, local rulers rose. They ruled independently as kings in Northern Italy from 888 to 961 , until this region (except for the Republic of Venice ) was integrated into Eastern Franconia under Otto I. As Imperial Italy , it remained part of the Roman-German Empire until the end of the Middle Ages. In this context, the bishops sponsored by the emperors were an important factor in securing rule. However, the Roman-German kings since Otto I did not pursue a stringent Italian policy , but had to enforce their rights of rule ( regalia ), especially in later times, militarily. The domination of Northern Italy was relevant to real politics, above all because of the comparatively high economic and financial strength of the cities there, which have flourished again since the 11th century; The maritime republics played a special role . At first, many cities in imperial Italy were under the influence of the bishops, before they gradually gained political autonomy. In addition to the still relatively strong urban culture, parts of the ancient culture had also been preserved there. The writing level was higher than in the north, which was advantageous for an effective exercise of power, although the personal presence of the ruler was still an important factor. On the other hand, Northern Italy benefited from the now more stable political conditions. In the 8th century had in Central Italy Papal States established with its scope and the status of the city of Rome was controversial even among the popes and emperors often. Politically, the popes gained leeway for a short time during the decline of the Carolingians, on the other hand, in Rome, attacks by the Normans and Arabs on papal property had to be fended off repeatedly. For this reason alone, the later intervention of the Ottonians in Italy was welcomed. In the 10th century, however, the papacy also came into conflict with influential urban Roman families who exploited it for their own purposes, which meant a loss of reputation for the Bishop of Rome. Since the Ottonian period, like the Carolingians before, the Roman-German rulers exercised a patronage over the papacy, although in the Salian period there was an open, politically motivated conflict in the investiture dispute . Byzantium had bases in Italy until the 11th century. After Ravenna was lost to the Lombards in 751 and it was no longer possible to intervene effectively in central Italy, the Byzantines concentrated on controlling their possessions in southern Italy. These were threatened by Arab raids, especially since the conquest of Sicily from North Africa in the 9th century (fall of Syracuse in 878, fall of Taorminas in 902), and from the 10th century also by the Roman-German rulers. With the fall of Baris in 1071, Byzantine rule in Italy ended for good. The Normans played a leading role in this in southern Italy . At the beginning of the 11th century they had been recruited as warriors by the Lombard local rulers there, but they soon established their own rulers. They took advantage of the complicated political situation in the space between Byzantium, papacy and local rulers, whereby the alliances were changeable. In the following years Norman principalities emerged in Aversa , Capua and Salerno . From 1061 the Normans also expanded to Sicily, which in the meantime had been partially and briefly recaptured by the Byzantines, and won the island for themselves. The Hauteville family played a leading role . As early as 1059 the Duchy of Apulia and Calabria had been created for them as a papal fiefdom; they obtained the royal dignity of Sicily and southern Italy in 1130 until the Kingdom of Sicily fell to the Hohenstaufen in 1194 . The Visigoth Empire had established itself in Hispania and southern Gaul at the end of the 5th century . However, after the heavy defeat in the Battle of Vouillé against the Franks in 507, the Visigoths had to evacuate Gaul to the region around Narbonne . Toledo became the new capital of the Visigoths (Toledan Empire) and in the course of the 6th century a Visigothic imperial idea developed. The relationship between the king and the influential nobles was not infrequently tense and there were repeated arguments. The Visigoths were also Arians, which led to conflicts with the Catholic majority population. Like his son and successor Rekkared I, Leovigild was an important ruler. In 585 he conquered the Suebian Empire in northwestern Hispania, but failed in his attempt to establish the ecclesiastical unity of the empire through a moderate Arianism. Rekkared I, who converted to the Catholic faith in 587, solved the problem by achieving the conversion of the Visigoths at the 3rd Council of Toledo in 589. This favored the already great influence of the Visigoth kings on their imperial church. The Eastern Romans were expelled from southern Spain at the beginning of the 7th century and the Franks no longer posed an immediate threat. Nevertheless, the following Visigoth kings failed to establish a permanent dynasty. The reason for this was the internal power struggles in the 7th century. There were repeated rebellions and power struggles between rival noble families, with the court aristocracy being particularly influential. More than half of the Visigoth kings of the 7th century were deposed or murdered. Nevertheless, individual kings managed to assert themselves, such as Chindaswinth (642–653) or King Rekkeswinth (653–672). Under Rekkeswinth the empire was largely at peace again. He ruled in harmony with the nobility and in 654 issued a uniform code of law for Goths and Romans. The empire profited from the connection to late Roman traditions and proved to be more stable overall. The Christian idea of kings of the early Middle Ages, on the other hand, was influenced by the Visigothic idea of sacred kingship. In terms of culture, the empire flourished around 600, and Isidore of Seville was its most important representative . The Visigoth Empire achieved considerable cultural radiance, not least through the transmission of knowledge in the monastery schools there. In the early 8th century the empire was conquered by the Arabs; they defeated King Roderich in 711 in the battle of the Río Guadalete . The political situation on the Iberian Peninsula was quite complicated in the further course of the early Middle Ages. After the fall of the Visigoths Empire, the Moors even penetrated the southern Franconian Empire for a time. All parts of the peninsula initially came under Islamic rule, but a few years after the Muslim invasion, resistance formed in the north-west. There, Christian nobles elected the noble Goth Pelagius as their king in 718 . Thus the Kingdom of Asturias was founded. This is considered to be the starting point of the Reconquista , the reconquest by the Christians, with some Christian rulers emphasizing the connection to the Visigoths (Neo-Gothic). Until the late 15th century, there was a Christian north and an Islamic ruled south ( Al-Andalus ) that was much more powerful for a long time and (but not in the early days of the conquest) culturally more developed . In addition to the existing Kingdom of Asturias-León , which flourished in the 10th century and was connected to Castile in the 11th century, other Christian empires emerged in northern Spain: in the 9th century the county (from Ferdinand I in the early 11th century: Kingdom) Castile and the Kingdom of Navarre ; Added to this were the former Franconian Spanish Mark , from which the county of Barcelona developed, and in the 11th century the Kingdom of Aragon . The Christians profited from the domestic political crises in the emirate and the later Caliphate of Cordoba and had been more aggressive since the 9th century; despite some setbacks and Moorish counter-attacks, they pushed Islamic rule back south, piece by piece. In addition, there were always phases of coexistence. In Al-Andalus, Muslims, Christians and Jews lived together largely peacefully, although there were also some attacks by Muslims on Christians and coexistence should not be idealized. The culture in Islamic Spain was in full bloom in the 10th century. Cordoba was one of the largest and richest cities in the Mediterranean at that time. A cultural exchange process also took place, which was very beneficial for the Christian side. The majority of the population in Moorish Spain was still Christian ( Mozarab ) in the 10th century . However, there were emigration to the Christian kingdoms and conversions to Islam, especially when the tolerant Muslim religious policy changed in part later. Under Sancho III. from Navarre, which had expanded its empire considerably, Christian Spain experienced a political and cultural strengthening in the early 11th century (supported by a monastery reform). Sancho divided his kingdom among his sons, but these kingdoms were now ruled by descendants of the same dynasty. After the fall of the Caliphate of Córdoba in 1031, the Islamic south split into numerous small and small pranks ( Taifa kingdoms ), which the Christian rulers took advantage of. In 1085 the former Visigoth royal city of Toledo fell to Alfonso VI. of León-Castile, whereupon the Muslim rulers in Seville and Granada called the Almoravids from North Africa for help, who defeated Alfons in 1086 in the Battle of Zallaqa , but soon established their own rulers. The British Isles There is almost no written evidence of what happened in Britain immediately after the Romans left at the beginning of the 5th century, which is why little details are known. The rough frame can be reconstructed at least approximately on the basis of the few written and archaeological sources. The field army had the island in 407/8 under the counter-emperor Constantine III. probably completely evacuated, but it is difficult to imagine that at least a minimum of garrison troops were not left behind, since the island as a whole should not be abandoned. The few associations are likely to have only disbanded in the course of time, when the island was in fact left to its own devices, which is why there was an uprising in Britain in 409. The local administration seems to have functioned at least partially for a longer period of time, and finally several small Romano-British empires (Sub-Roman Britain) emerged . During this time, Anglo-Saxons came to Britain as mercenaries in relatively small numbers and took on defensive tasks instead of Roman soldiers. Around the middle of the 5th century they rose up against the Romano-British rulers, although the reasons are not entirely clear. Around 500 the Anglo-Saxons seem to have been forced to a temporary settlement freeze after they were defeated by Ambrosius Aurelianus in the battle of Mons Badonicus , which cannot be precisely dated or localized . In the following years, however, they pushed the Romano-British back. Although details have not been passed on, the Anglo-Saxons succeeded in bringing large parts of the area south of the Firth of Forth under their control by the end of the 7th century , with repeated heavy fighting apparently. Individual British territories, however, were able to retain their independence, such as Wales and what is now Cornwall . There were also hardly any mass expulsions of the Romano-British population. The Christianization of the Anglo-Saxons achieved a breakthrough in the 7th century. During this time, the so-called heptarchy also formed, the seven Anglo-Saxon kingdoms that dominated until the 9th century ( Essex , Sussex , Wessex , Kent , East Anglia , Mercia and Northumbria ), of which Mercia and Northumbria were the most powerful and repeatedly fought over fought out the supremacy. Mercia defeated Northumbria in 679 in the Battle of the River Trent, which established Mercia's supremacy; The Anglo-Saxon empires were also threatened by incursions by the Picts . In the first half of the 8th century, the southern Anglo-Saxon empires became dependent on Mercia, which under Offa temporarily rose to become the most powerful empire in England, while Northumbria expanded northwards due to the Mercian resistance. Mercia's supremacy among the Anglo-Saxon empires was short-lived. As early as the early 9th century, East Anglia and Kent freed themselves from mercian domination. Under Egbert , Wessex gained increasing influence again. With the victory over Mercia at the Battle of Ellendun in 825, the mercian hegemony was finally broken and Wessex annexed several other Anglo-Saxon areas. By the mid-9th century, Wessex controlled all of England south of the Thames when the great Viking invasion began in 866 . Anglo-Saxon England was associated with Scandinavia , especially in the early days . In 865/66, however, several Viking leaders (including Ivar Ragnarsson , a hero of Scandinavian saga literature) joined forces and invaded north-east England from Denmark with a large army, plundering and killing numerous residents. The incursion is probably connected with the increased defense efforts in the Franconian Empire, so that England was an easier target. The Viking army evidently outnumbered the Anglo-Saxon troops. In 871 the Vikings controlled the east of England, from York in the north to the London area . But they did not begin to settle there until the 870s, although some of them used Anglo-Saxon shadow kings. This broke the previous political order of the Anglo-Saxon empires, only Wessex initially remained relatively unscathed. With Alfred von Wessex (r. 871–899), later called "Alfred the Great", the Vikings began to be pushed back and an important period of Anglo-Saxon England began. After initial setbacks, Alfred defeated the Vikings in 878 at the Battle of Edington. His opponent Guthrum was baptized and withdrew from Wessex; In 886 the border between Anglo-Saxons and Danelag was established in a treaty . In fact, at this point in time, Alfred ruled over all Anglo-Saxons who did not live under Danish rule. For further defense against the Vikings, who attacked again towards the end of his reign, burhs (fortified places) were set up and a navy was set up. Inside, he operated an effective cultural promotion based on the Carolingian model. Alfred's successors (like his son Edward the Elder ) pushed the Danish rule back further and further, until only the Kingdom of York remained. Eduards son Æthelstan , like Alfred, promoted culture intensively and was also able to record military successes. However, some kings of Wessex did not find universal recognition of all Anglo-Saxons. In Northumbria, for example, attempts were made to preserve independence with the help of the Danes. In the 10th century, therefore, there were repeated battles for rule over the entire Anglo-Saxon England. The relatively long reign of Edgar had a stabilizing effect, but after his death in 975 tensions reemerged. Subsequent attempts to further consolidate the royal power were hardly successful, mainly because there were again major Viking incursions since 980. The climax of this development was reached under Canute the Great , who briefly established a maritime empire in the early 11th century that included large parts of western Scandinavia and England. In England, Edward the Confessor ascended the throne in 1042 , but he had to contend with strong domestic political resistance, which left him only relatively little room for maneuver. When he died in 1066, the West Saxon dynasty ended. In the follow-up struggle, the Norman William the Conqueror finally prevailed, who won the Battle of Hastings in 1066 . This marked the end of Anglo-Saxon England. In the north of Britain, the Kingdom of Scotland emerged in the middle of the 9th century from the union of the Picts with the Celtic Scots ( Dál Riada ), although the kingship was rather weak. Although an area-wide penetration of rule was not or hardly succeeded, Lothian was gained around 950, Cumbria 1018. Under Malcolm II (d. 1034) the kingdom of Alba (Scotland) slowly took shape. Fights with the Anglo-Saxons were relatively rare, but Viking attacks had to be repelled repeatedly. In Ireland , besides tribal kings , mainly regional petty kings ruled . The persistence of Irish dynasties over long periods of time is remarkable. The Hochkönigsamt , which is said to have been ahistorically ancient, was repeatedly claimed by various groups. Above all the Uí Néill , whose rise began as early as the 5th century and was at the expense of the provincial kingdom of Ulaid, tried to use it to legitimize their claim to rule and claimed the "kingdom of Tara " since the 7th century . There were repeated fighting between the individual groups. Until the High Middle Ages, no strong kingship that encompassed the entire island was able to establish itself. At the end of the 8th century, the Vikings appeared in Ireland and established bases; Viking settlements and battles with them are documented in the 10th century. This was the first time in history that Ireland was exposed to external military attacks. Several Germanic tribes of the Migration Period claimed in their history of origin a descent from Scandinavia , but in modern research this is usually viewed as a topos that primarily served to establish identity and provide additional legitimation. The beginning of the early Middle Ages in Scandinavia is referred to in modern research as the Vendel period (Sweden, after the rich grave finds in Vendel ), Merovingian period (Norway) or the younger Germanic Iron Age (Denmark). Few details are known about this period, mainly based on archaeological finds. Research has often assumed that the late 6th and 7th centuries declined, with several settlements falling into disrepair. More recent studies, however, show that numerous settlements remained continuously inhabited. Around 600 additional areas were cultivated and finds indicate that the political centers of chiefs and petty kings continued to be active ; however, some studies are still lacking for individual regions. The exercise of power in Scandinavia (as in other parts of early medieval Europe) was closely related to the ability of the respective ruler to gain prestige and wealth through struggles and to let his followers participate in it. This eventually led to raids in other regions. The Viking Age began in Scandinavia in the late 8th century . In 793 Scandinavian sailors, the so-called Vikings , attacked the Lindisfarne monastery off the coast of England. In the following years they repeatedly invaded the Franconian Empire and England and Ireland in search of booty, where they built partially fortified places for wintering or settlements. The Vikings were active as both robbers and traders. Their trains took them to the Mediterranean and Eastern Europe, and finally to the North Atlantic. The first settlements appeared there on Iceland at the end of the 9th century, and Greenland was settled at the end of the 10th century ; finally there were even trips to North America ( Vinland ). In the east, Scandinavian seafarers, the so-called Varangians , advanced across various rivers into the interior of Russia , engaged in trade and were also politically active, as reported in the Nestor Chronicle (see Kievan Rus ). Other groups made it to the Arab and Byzantine regions. The contemporary sources, such as the Anglo-Saxon Chronicle or the Frankish Reichsannals and their later continuations, describe the devastating raids of the Vikings several times. This was also followed by the formation of rulers. In the late 9th century they established themselves in the north of England, while in 911 the Viking Rollo was enfeoffed with Normandy by the King of West Franconia . The Romanized Normans were to become active in southern Italy in the 11th century and conquered England in 1066. The political history of Scandinavia in the early Middle Ages is quite confused and the sources are not always reliable. Sweden , where the Svear kingship took shape at the end of the 10th century , had a close economic relationship with Eastern Europe. The Swedish kingship was poorly developed in the early Middle Ages and was mainly of a cultic character in Pagan times. Presumably Olof Skötkonung (d. 1022) was the first king to rule over all of Sweden. He was a Christian and apparently used religion in an attempt to establish authority for his rule, but met with opposition. For this he won 999 or 1000 in alliance with Denmark in the naval battle of Svold over the Norwegian King Olav I. Tryggvason . Little is known about the Swedish kings who immediately followed him. Anund Jakob , together with Norwegian support, opposed Danish supremacy under King Canute . In Norway , a kingship around 900 under Harald I is documented in the sources. He seems to have ruled large parts of south-west Norway directly and to have exercised a more formal supremacy in other parts, but details are hardly known (see the history of Norway from Harald Hårfagre to the unification of the empire ). Harald's eldest son and successor Erik had to go into exile (presumably to England), where he also died. Then in the early 11th century Olav II. Haraldsson promoted Christianity in Norway. He had to fight both domestic political opponents and the claims of the Danish king Knut . Olav was able to repel a first attack by Knut, but in 1028 he had to flee to the court of Yaroslav of Kiev and fell in 1030 while trying to regain the Norwegian throne. Olav's son Magnus was called to Norway at a young age in 1035, where he eventually took action against political opponents. At the end of his reign, Magnus had to share rule with his uncle Harald Hardråde , who succeeded him in 1047. Harald gained control of all of Norway and completed the unification of the empire, but died in England in 1066. Norway was able to maintain its independence from Denmark during this time, Magnus and Harald even claimed the Danish royal crown. In Denmark , kings, who may have had a relatively strong position at a fairly early age, are documented as early as the early 9th century when there was fighting with the Franks. However, it seems to have been small kings who were initially unable to establish a dynastically legitimized exercise of rule. In the 9th century, when kings such as Gudfred and Horik I are mentioned in the sources, Denmark temporarily exercised supremacy in southern Scandinavia, which was shaken around 900. In the early 10th century there is evidence of King Gorm , during whose reign the Danish power was consolidated again. Little is known about Gorm himself, but unlike him, his son Harald Blauzahn did not refuse the baptism. Harald's son Sven Gabelbart tried his hand at becoming a Viking leader and invaded England; there he was recognized as king in 1013, but died in 1014. His son was the aforementioned Knut (also known as Canute the Great), who briefly linked England and Denmark in a kind of personal union. Canute invaded England in 1015 and achieved military success there. He came to an understanding with King Edmund II and, after his death in 1016, also took over Wessex. So Knut effectively ruled all of England. Since 1014/1015 he called himself rex Danorum ("King of the Danes"), he was sole ruler in Denmark since 1019. In Sweden and Norway his expansion met with stiff resistance, with Knut acting more successfully against Norway. The North Sea region he established did not exist after his death in 1035. Eastern and Southeastern Europe In the early Middle Ages, the east and south-east of Europe were politically fragmented. Even in the course of the end of the migration of peoples in the 6th century, Slavs invaded the area east of the Elbe and north of the Danube, which had largely been abandoned by Germanic tribes . Their origin or the process of their ethnogenesis is controversial and problematic to this day. Archaeological findings and literary sources (e.g. Jordanes and Prokopios from Kaisareia ) only confirm their appearance for the 6th century. A record of the Slavic tribes from the 9th century can be found in the so-called Bavarian geographer . Details about the further expansion of the Slavs and their first rule formations are hardly known; only when they came into contact or conflict with the neighboring kingdoms does this change. The Anten appeared in the Danube region during Justinian's time . In the period that followed, several Slavic groups apparently crossed the Danube, initially under the rule of the Avars . They had established their own empire in the Balkans at the end of the 6th century before the power of the Avarenkhagans declined noticeably in the 7th century. Since the 580s, the Byzantine border defense in the Danube region came under massive pressure and finally gave way at the beginning of the 7th century, especially since the troops in the east were needed to fight the Persians. Slavs then invaded the Roman Balkan provinces and Greece. In 626 Slavs besieged Constantinople as Avar subjects in vain . After the collapse of Avar domination, several Slavic domains formed in the Balkans, which the Byzantines referred to as slave lines . A de facto conquest of land took place, and Slavs also settled in parts of Greece, where, however, after the Byzantine reconquest, rehellenization took place. The Byzantine cities in the Balkans shrank, economically and demographically this also meant a considerable loss, although only a few details are known. On the other hand, Byzantium exercised a great cultural influence on the Balkan empires in the following period. It was not until the 8th century that Byzantium was able to go on the offensive again in this area, when a new enemy emerged with the (later Slavicized) proto- Bulgarians who also posed a threat to Byzantium, while the Volga-Bulgarians were building their own empire. Despite Byzantine military operations (a Byzantine army was already defeated in 679, while operations in the 8th century were sometimes very successful), the Bulgarian empire was able to assert itself in the battles with the Byzantines, as the successes of Krum prove. The proto-Bulgarian and Slavic groups increasingly merged in the Bulgarian dominion. Under Omurtag there was intensive building activity in the empire. Bulgaria was also shaped by Byzantine influences. Under Boris I , who was baptized Michael in 865, Christianization intensified in the 9th century despite some resistance from Bulgarian boyars . The constant Slavicization of Bulgaria culminated in the adoption of the liturgy in the Slavic language and the Cyrillic alphabet . The high point of early medieval Bulgarian history was the reign of Simeon I in the early 10th century, who was educated and militarily successful. He was the first Bulgarian and Slavic ruler with the title of Tsar , the Slavic equivalent for a (regionally limited) imperial title. The fighting with Byzantium flared up again and again before Emperor Basil II defeated the Bulgarians decisively in 1014 after brutal fighting and conquered the Bulgarian Empire in 1018. A Slavic westward movement into the area of today's Czech Republic and the Eastern Alps is archaeologically documented for the 6th century, the Baltic coast was probably reached in the 7th century. The “Slavic expansion” favored the collapse of the Avar Empire. A Frankish merchant named Samo took advantage of this , who headed a Slav uprising and established a Slavic empire (probably in the Bohemian region) in the first half of the 7th century, which also resisted an attack by the Franks, but after Samo's death collapsed. In the 9th century in particular, several Slavic dominions, some of which existed for a longer period, emerged, for example in Bohemia, which was soon Christianized and had belonged to the Roman-German Empire since the 10th century. Furthermore Croatia (whereby the Croats immigrated to Dalmatia in the 7th century ) and Serbia (which soon came under Byzantine influence). Further to the east, new rulers emerged in Poland and today's Ukraine, which played an important role in the further history of Europe. These included the Kievan Rus , who was Christianized in the 10th century and experienced a first heyday under Vladimir I. Around 900 there was also the conquest of the (non-Slavic) Hungarians , who repeatedly undertook far-reaching raids and invaded Italy and Eastern Franconia several times before they were defeated in 955. The first Hungarian king became Stephen I in 1001 , the founder of the Árpáden dynasty. Stephan was a Christian and submitted his kingdom to the Holy See, for which he received the ecclesiastical organizational sovereignty. He created a royal administration inside and strengthened the church and royal power in Hungary. In terms of foreign policy, there were conflicts with the Roman-German Empire in the early 11th century, while Hungary, which rose to become a major power in south-eastern Europe, had very good relations with Byzantium and Poland. In the 9th century, the border in the Elbe region was secured by the Franks. Several Slavic tribes had established themselves here in Carolingian times, including the Abodrites and Wilzen . In Ottonian times, attempts were made to subjugate and Christianize the pagan Elbe Slavs , but this project suffered a considerable setback due to the Slav uprising of 983 . Poland, in the 8th / 9th Century established with the core area of the Polanen , strengthened under the Piasts in the 10th century. Mieszko I accepted Christianity, from then on the Polish rulers promoted the proselytizing of the pagan areas. With the Ottonian and Salian rulers, there were repeated collaborations (combined with tribute payments) and conflicts; the three royal coronations in the 11th century are to be understood as a demarcation to the Roman-German Empire. Bolesław I was crowned king in 1024/25, but Poland eventually had to cede territories to the Salian rulers. The main residence of the reduced kingdom became Krakow . The Eastern Roman Empire had changed profoundly in the course of the 7th century. The Latin still spoken in the army and administration had finally given way to Greek; Due to the Arab conquests and the threat to the Balkans, military provinces, the so-called themes , emerged on the borders around the middle of the 7th century . Medieval Byzantium emerged from the foundations of the Roman state, Greek culture and Christian Orthodox belief . The defensive battles against the Arabs lasted until the 8th and 9th centuries. Century on. Byzantium, along with the Oriental and African provinces, lost more than half of its population and tax revenue to the caliphate by the end of the 7th century. The loss of these provinces, in which the majority Christian churches were represented with a different attitude to the imperial church , also ensured greater religious uniformity in the empire. The Arab sea power and regular raids on land initially continued to threaten Byzantium, while the Balkans and Greece were besieged by Bulgarians and Slavs. Slavic groups settled in Greece in the late 6th (or perhaps early 7th) century, but the details are controversial in recent research. Several coastal regions remained in Byzantine hands. The areas ruled by Slavs in Greece ( slave lines ) were gradually recaptured and Hellenized again until around 800. Fortress towns, called Kastra , arose in the Balkans and in Asia Minor, the now central region of the empire . The empire was able to survive this struggle for existence through a military reorganization with capable generals, aided by internal Arab power struggles, after which the Byzantine state was consolidated again. A not unimportant ally against the caliphate was the powerful Khazar empire on the north coast of the Black Sea. Justinian II was the last ruler of the dynasty founded by Herakleios , which had ruled the empire since 610. After his death in 711, anarchy followed for a few years, before another capable emperor ascended the throne in 717 with the theme general Leo. Leo (n) III. in 717–718 repulsed the last and most serious Arab advance on Constantinople . The new emperor even went on a limited offensive and won a great victory at Akroinon in 740 . Leo secured the borders and began reforms internally; for example a new code of law (eclogue) was published. In 741 he was followed by his son Constantine V (r. 741–775), who first had to put down a usurpation. In the years that followed, the emperor took offensive action against the Arabs, Bulgarians and Slavs and achieved several successes. Inside, Byzantium was shaken in the 8th and 9th centuries by the so-called iconoclast . In modern research, however, this important period of the Middle Byzantine period is viewed in a much more differentiated manner. Compared with the foreign policy threat, the (image-friendly) sources obtained seem to convey a rather distorted picture of this internal conflict that does not correspond to reality. So it is already very questionable whether the “iconoclastic” (image-hostile) emperors led to a downright ban on images or bloody persecutions due to the worship of images ( see below ). The of Leo III. established Syrian dynasty held power until 802; it was followed by the Amorian dynasty (820–867) and the Macedonian dynasty (867–1057). In terms of foreign policy, the empire had to cope with a number of setbacks in the early 9th century. The Bulgarenkhan Krum defeated a Byzantine army in 811, killed the emperor and made a drinking vessel out of his skull. In 813 there was another defeat against the Bulgarians, before calm returned to the Balkan border for the time being. In the middle of the 9th century, the Byzantines began proselytizing the Balkan Slavs and Bulgarians. Nevertheless, at the end of the 9th and the beginning of the 10th century, the conflict with Bulgaria came up again, and Byzantium even had to pay tribute at times. The ambitious goal of Simeon I , to obtain the Byzantine imperial crown and to establish a large Bulgarian-Byzantine empire, was not achieved; But Bulgaria remained a threatening power factor in the region for Byzantium. In the 10th century, the Byzantines won several victories. Its fleet dominated again Aegean and in the reign of Emperor Nikephoros II. And John Tzimiskes were Crete , Cyprus , Cilicia and parts of Syria recaptured; Byzantine troops even advanced as far as Palestine for a short time. At the same time, however, the Byzantine influence in the west, where Sicily was lost around 900, declined noticeably. After a cultural collapse in the middle of the 7th century, although more ancient substance was preserved than in many regions of the West, the empire recovered and the so-called Macedonian Renaissance began in the 9th century . This phase of increased recollection of the ancient heritage in Byzantium was promoted by several emperors, including Leo VI. and Constantine VII. Inside, the generals and leaders of the large families determined the politics of the 10th century to a large extent, before a new emperor came to power in 976 and was able to assert himself after a difficult beginning. Basil II (ruled 976-1025) not only conquered the Bulgarian Empire, but also secured the Byzantine eastern border. He made Byzantium once again a great power in the eastern Mediterranean. His successors were less successful, however; the consequences of the defeat of Manzikert (1071) were devastating, since Byzantium lost the interior of Asia Minor to the Turks and from then on was again forced into a defensive battle. The Islamic world In Arabia , a new monotheistic religion emerged in the early 7th century with Islam . Their prophet and religious founder was Mohammed , who came from a leading Meccan family. The Islamic tradition on Mohammed ( Koran , Hadith literature , biographies and Islamic historiography ) is rich, but various statements are contradictory; Individual aspects are therefore viewed more critically in modern research and are controversial. The early history of Islam, for which the source situation is problematic (among other things, primarily because of the oral tradition of Arabic reports), is being increasingly discussed in more recent research. This includes the statement that the development of the new religion took place in the historical context of the end of late antiquity and was influenced by various contemporary currents. Mohammed was working as a merchant when he had a revelation experience at the age of about 40. He then advocated a strict belief in an almighty god of creation ( Allah ), who required the believers to lead a moral life. With this, however, he encountered resistance in Mecca. The city benefited as a Pagan pilgrimage site with the Kaaba as its center. At the same time, however, there were also Jewish and Christian influences in Arabia who favored monotheistic currents such as the new faith; Mohammed was also not the only person who appeared as a prophet during this period. In 622 Mohammed went to Medina with his followers ; the excerpt from Mecca ( Hijra ) is the beginning of the Islamic calendar. However, he also had to overcome resistance in Medina. Then came the war with Mecca, which Mohammed finally won in 630. Converted Meccans and, above all, Muhammad's own tribe, the Koreishites , played an important role in the new Islamic empire. In contrast to Christianity, for example, a claim to political rule was formulated very early in Islam; this was also held on later. Up to his death in 632, Mohammed was able to achieve several successes and unite most of Arabia under his rule and on the basis of the new faith. The northern outskirts were still under the control of Eastern Rivers and the Sāsānid Empire. After Muhammad's death in 632, the leadership fell to the first caliph (successor, deputy) Abu Bakr , a close confidante of Muhammad. Abu Bakr was the first of the four so-called "rightly guided" caliphs. There was an apostasy movement ( Ridda ) among the Muslim Arabs , as many tribes believed that they were only obliged to the Prophet himself; the insurgents were finally subdued ( Ridda Wars ). Under Abu Bakr, the Islamic expansion in the real sense began in the 630s : the conquest of the Christian Middle East and North Africa as well as the Persian Empire of the Sāsānids (for details see above ). The Arabs, motivated by religion and the prospect of rich booty, achieved great successes in the following years over the two great powers, weakened by long battles; the last war between East and Persia was only ended in 628 after a good 25 years. By 651, the Sāsānid Empire had been conquered in the east, but only after heavy fighting. In the west, East / Byzantium lost its oriental and north African possessions: 636 Syria, 640/42 Egypt, up to 698 all of North Africa. In 717/18 the Arabs, now also appearing as a sea power, besieged Constantinople in vain. The Arabs embarked on raids in Asia Minor, while the Iberian Peninsula was conquered in the west (711) and the border with India was reached in the east; a (probably limited) campaign into the Franconian Empire failed in 732 in the battle of Tours and Poitiers . Then there was the threat to the Christian empires from the new Arab sea power. From 888 to 972, for example, Arab pirates established themselves on the coast of Provence in Fraxinetum (today's La Garde-Freinet) and undertook extensive robberies; in the eastern Mediterranean they threatened Byzantine territory (see, for example, Leon of Tripoli ). However, the sources of the early conquests are problematic. The later Arabic reports ( Futuh ) are not always reliable, while only relatively sparse Christian reports are available for the 7th century. The Arabs built new cities in the conquered areas, such as Kufa , Basra , Fustat or Kairouan . In terms of administration, they initially relied largely on the existing, well-functioning bureaucracy. Until the end of the 7th century, Greek (for the former Eastern Roman areas, the administrative seat was Damascus) and Middle Persian (for the former Persian areas, the administrative seat was Kufa) were common in the financial administration of the caliphate, which was initially quite loosely organized; the possibilities of a centralized imperial administration were limited. The administration of Egypt was organized from Fustat. Christians who were familiar with the effective late Roman administrative practice were therefore active in the administration of the caliphate for a long time. They also held high-ranking posts such as the influential Sarjun ibn Mansur and his son, who later became known as John of Damascus . It was not until 700 that the ousting of Christians from the administration began, but this was a slow process, so that the caliphs continued to rely on Christians in the former Byzantine territories for some time. In cultural terms, too, the former Eastern Roman and Persian regions were more developed than the Arab heartland. The majority of the population in the Caliphate was non-Muslim for a long time and was Islamized relatively slowly. Followers of the book religions (Christians, Jews and Zoroastrians ) had to pay a special poll tax ( jizya ), were not allowed to practice their faith in public and were not allowed to carry weapons, but otherwise remained largely unmolested. In the following period, however, there were attacks against Christians, for example, as the pressure had increased overall since the late 7th century, so that there was discrimination and suppressive measures on the part of the caliphs and governors against the Christian majority population (see below ). Later on, Zoroastrians were persecuted by Muslim rulers. Despite the spectacular foreign policy successes, there were repeated unrest inside the caliphate's empire. After Abu Bakr's death in 634, two more caliphs ( Umar ibn al-Chattab and Uthman ibn Affan ) followed, until in 656 Mohammed's son-in-law Ali became caliph. His claim within the community ( Umma ) was controversial, however, and civil war broke out. Ali was murdered in 661; The winner was Muawiya (ruled 661–680), who brought the Umayyad dynasty to power, which was to rule the caliphate until 750. The followers of Ali, however, remained active ( Schia ), which led to a split in the Islamic religious community. The Umayyads made Damascus the capital of the caliphate, pushed ahead with the expansion (described above) and reorganized the administration according to the model in Byzantium and Persia. However, her claim to power was not undisputed even after Ali's death. Resistance arose in Mecca and Medina, and in Abdallah ibn az-Zubair a counter-caliph appeared. However, he was killed during the Umayyad conquest of Mecca in 692, which ended the second civil war. Abd al-Malik (ruled 685–705) secured Umayyad rule and created a new Islamic gold and silver currency; In administration, Arabic finally replaced Greek and Persian. However, the caliphate remained relatively loosely structured, and the Umayyad's control power was all in all quite limited. Hisham, who died in 743, is considered the last important Umayyad caliph . In the late phase of the Umayyads internal tensions increased; This led to a conflict between Arab and non-Arab Muslims, the unresolved tax problem (as there were more conversions and therefore no money) became a serious burden and internal unrest shook the empire. In 750 the Umayyads were overthrown by the Abbasids , who had started a successful revolt in the east of the empire. Most of the Umayyads were murdered, but Abd ar-Rahman I managed to escape to Spain in an adventurous way, where he founded the Emirate of Córdoba in 756 and in fact broke away from the caliphate. Under the Abbasids, who formally ruled until 1258, the caliphate increasingly lost its specifically Arab character. The political focus shifted to Mesopotamia in the east, where a new capital, Baghdad, was founded in 762 ( Round City Baghdad ). Originally supported by the Shiite movement, the Abbasids soon tried to distance themselves, which, however, led to resistance. Ali's supporters were fought and pre-Abbasid caliphs were viewed as usurpers. The new caliphs tried to achieve a religious unification of the empire, but this did not prevent the emergence of regional dynasties in the peripheral areas from around 800, such as the Aghlabids in North Africa or the Samanids in Iran. The early Abbasid period was a cultural heyday in art, literature, philosophy, theology, and law. The court of caliphs in Baghdad was extremely splendid, based on the model of the Sāsānid Empire, the last great empire of the ancient Orient. The Arabs' monopoly on high posts in the empire was ended; Persians from then on played an important role at court in political and cultural terms. Exemplary was the court holding of Hārūn ar-Raschīd (r. 786-809), whose reputation even extended into the Frankish Empire. Politically, however, the situation deteriorated dramatically in the 9th century when various Turkish mercenary leaders seized power in the provinces. They eventually gained influence at the court of the caliph, which led to the political decline of the caliphate. In the middle of the 10th century the Abbasids were under the control of the Buyids , who exercised true power in Baghdad for a good 100 years, while the caliph was only the spiritual leader. 929 had Abd ar-Rahman III in Spain . proclaimed caliph; this was the beginning of the Caliphate of Cordoba , which existed until 1031 . In the 10th and 11th centuries, the Fatimids also threatened the rule of the Abbasids in Egypt. The power of the caliphs in Baghdad was already broken at this point and only a pseudo-rule. System of rule and exercise of rule Form of rule The "state development" proceeded differently in the various early medieval empires. Central administrative structures from the late Roman period initially persisted in the kingdoms of the migration period (especially in the Goths, but also in the Vandal and Franconian empires). Certain elements (finances, coins and documents) were largely preserved in the West in the period that followed; However, compared to the Roman period, the state structures were only rudimentary or eventually collapsed. Most problematic was that the Roman tax system ceased to exist in the west and land ownership was now the most important factor. The incomes of the post-Roman empires were therefore far lower than they were in the time of the empire. In early medieval Latin Europe, “state power” was not derived from a central authority (like the king), but from everyone in whatever form who ruled. In the early Middle Ages, rulership was therefore essentially tied to individual persons; in fact, there were no “state institutions” (and thus no abstract term such as statehood) apart from these rulership structures of an association of persons. During the migration period, the military skills of leaders in particular gained in importance ( army king ), who built their own rulers on this basis. However, in the course of time there was a “condensation” of rule, in that kingship no longer existed as a central point of reference, but also the empire itself gained strength as an idea, thus making it possible to stabilize the structures of rule, such as the Franconian Empire . This structural deficit affected almost all early medieval rulers in Europe - in Scandinavia as well as with the Slavs, the royal rule had developed relatively late in comparison to the Germanic-Romanic empires and Anglo-Saxon England - only in Byzantium and the Caliphate were the state structures more tightly organized . Although many aspects of medieval rule are controversial in recent research (a distinction must be made between royal rule, church rule, village and city rule, etc.), it can generally be considered an important feature that rule was essentially based on reciprocity and that it was a ruling association . The ruler and the ruled were bound by oaths: support was promised in exchange for protection and certain services. This was especially true in the military field, since the early medieval empires (except Byzantium and the Caliphate) did not maintain standing armies as in Roman times, but were dependent on followers for military actions. Subject loyalties were basically only valid for the respective ruler and therefore had to be secured again when a new rule came to power. It was not a pure ruler-subject relationship, because the nobility had a right to share in the rule, which was to be respected. Friendship ties were used for this purpose, which is why the sources often refer to amicitia . The importance of Roman law was comparatively minor in the early Middle Ages, but it never completely broke off, especially in Italy, especially since legal collections were also created in the Germanic-Romanic empires. The Germanic popular rights (Leges) , which are attested from the 5th to the 8th century, played an important role , for example among the Goths, Franks, Burgundians, Alemanni, Bavarians and Lombards. In addition, there was canon law , which was later increasingly received . The question of feudalism In the Germanic-Romanic successor empires of West Rome, the Germanic allegiance system of the Migration Period, in which the army king played an important role, developed further and was influenced by the contact with the Roman statehood. The rule over a free retinue finally expanded to rule over the land and people ( manorial rule , see below). According to the traditional view of research, this led to the feudal system as a form of political organization in early medieval Latin Europe . Both sides could benefit from the feudal relationship, because while the feudal lord gained additional power, the prestige of the feudal bearer also increased when he took the feudal oath to a socially superior. Such oaths could also be taken as a reward for service rendered. In modern research, however, the traditional conception of the feudal system, which, among others, had a decisive influence on François Louis Ganshof , has been questioned. For a long time it was assumed that the later widespread practice of vassalage and fiefdom was already common in Carolingian times. The roots of the vassal are probably Gallo-Roman / Frankish, but the interpretation of the relevant sources is problematic. So was z. For example, the term vassus that appears there was often interpreted as a vassal, as was fidelis , while beneficium was often interpreted as a fiefdom. The terms are ambiguous, however, so vassus does not necessarily mean “vassal”. Fidelis initially only means “faithful”, beneficium as “beneficence” could describe a gift that was not linked to anything in return. In the sources of the 9th century, no high Franconian office bearer is also referred to as vassus , which should actually be the case in the context of a fully developed feudal system. In the past, this is a central point of criticism in recent research, terms in the sources were often interpreted as indications of vassal status, the assignment of which is not certain. Personal ties were therefore very diverse in the Carolingian Empire, which earlier research in relation to the formation of the feudal system had often examined, and did not follow a rigid pattern. An oath of allegiance by a loyal lover was therefore not necessarily a fealty. For this reason, more recent research emphasizes how uncertain many older interpretations are and how the system in which fiefdoms and vassals were closely linked and the relationship of fidelity was often less respected due to hereditary fiefdoms developed later and did not develop in this form in the early Middle Ages was common. This discussion is still ongoing. Royal and nobility power The ideal foundations of early medieval kingship in the west of the old Roman Empire were the army kingship of the Migration Period , ancient Roman ideas of rulership and Christianity. The importance of a Germanic sacred kingdom in this context is viewed very skeptically or rejected in recent research. The army kingship, on the other hand, apparently played a decisive role, as did the Roman ideology of rule. The political contacts between the Germanic-Romanic kings of the early Middle Ages and the Roman emperor formed the basis for establishing contacts between states in the context of representing and staging Roman rule; this path led "from the army kingship to the vice-imperial royal monarch". Finally, there were also influences from Christianity, which had already influenced the late ancient Roman Empire. Accordingly, every worldly rulership was dependent on divine will, because God would stand above the kings of this world. At the same time, the kings also represented God's rule on earth ( divine right ); the kingship was thus "Christianized" in the Christian early medieval empires. The closest possible proximity of the king to his subjects was an important factor in the intensification of royal rule. The early medieval kings, especially in the Carolingian empire and its successor empires , were often traveling kings who traveled from Palatinate to Palatinate and regulated the necessary government business along the way. This was essential in an increasingly oral, "archaic" society, in which the written form in the administrative area declined in different regions after the early Carolingian period (especially in the 10th century); it wasn't very effective, however. The center of royal rule was the royal court with the attached chancellery; however, several documents issued in the early Middle Ages are not preserved today and can only partly be accessed indirectly ( Deperdita ). The situation in Eastern Franconia was problematic in that no specific residential town developed there, unlike, for example, previously in the Western and Ostrogoths or later in England and France. The Carolingians relied on extensive and economically efficient possessions, while in the Ottonian period the travel kingship was already more pronounced, although the rulers preferred areas near the kings in Saxony and Franconia. In the Carolingian Empire and its successor kingdoms there were always rooms close to and remote from the kings, where an effective exercise of rule was sometimes more, sometimes less successful. Likewise, the nobility and high clergy in the respective empires had different degrees of relationship to royalty. The interaction between king and church was of particular importance in the early Middle Ages. Already the Merovingians and later the Carolingians had integrated the church into their conception of rule. The court orchestra played an important role among the Carolingians . In the Franconian Empire, offices were generally not inheritable until the late Carolingian period, but were conferred by the king; this changed at the end of the 9th century, so that offices conferred became hereditary titles (as with the counts and dukes), under which the authority of kingship suffered. Inside, the Ottonians also relied on the imperial church due to the poorly trained structures for administrative tasks . Only the Church had enough trained staff to read and write; the episcopal churches also provided troop contingents. In return for taking on these secular tasks, the church was increasingly given sovereign rights and received extensive donations. In older research, this interplay was called the Ottonian-Salian imperial church system. However, the practice of exercising power is not unusual in comparison to other Christian-Latin rulers and was hardly carried out according to plan. In recent research it is pointed out that the Ottonian and Early Sali kings, because of their position of power, only succeeded more effectively than other rulers in integrating the church into secular rule. Assertiveness and acceptance of royal rule varied. In the Visigoth Empire z. B. there were always conflicts between the king and the influential nobility, but the kingship in the Visigoths was already strongly religiously legitimized. The sacred aspect of rulership was also significant later in the other early medieval empires. Sacred anointing was used, among other things, to support royal rule, and the "kingship by the grace of God" gained in importance. The ideal of the king is always tangible in the sources where the ideal king is just, virtuous and religious and defends the kingdom. While the late Merovingians were less able to act freely or not at all due to the strong position of the housekeepers, which were dominated by the high nobility , the early Carolingians were able to better assert their rule, tellingly they abolished the office of housekeeper. However, the various divisions of power made a consolidated rule difficult. The dynastic connection was often there, but in Eastern Franconia, for example, the electoral character of kingship was very pronounced. The choice of king or king's elevation was accordingly different in the respective empires. In western Franconia, however, the royal power finally declined in the struggle with the influential greats, in eastern Franconia the Ottonians succeeded in stabilizing the royal rule, even though the tribal duchies (re) established in the late Carolingian period represented their own interests. In addition to the effective personal ties and the interaction with the church, the availability of the crown property was also important. In Anglo-Saxon England, however, after the time of Alfred the Great, it was only possible for a time to unite the entire country under one king. In France in the 11th century the Capetians could only exercise royal rule within narrow limits; they were essentially limited to their own crown domain, the relationship with the high nobility was based on extensive equality. The royal court was the center of manorial activity. If the nobility or different groups within the nobility succeeded in enforcing their own rulership in the territories or largely eliminating the king politically at court, then the power of the king declined at the same time. But the nobility was also differentiated; so there were local aristocratic groups and, as in the Carolingian era, nobility operating across the empire (such as the Robertines and the Guelphs ); accordingly, the various interests of the nobility varied. In the case of a relatively strong royal power, it was again of central importance for the great to have the best possible access to the court and thus to the king. This was the only way to guarantee that your own needs and desires could be specifically articulated and thus implemented as far as possible. It was therefore important who had the “ear of the king” and thus had the opportunity to present requests, wishes and demands or to act as an advocate. The importance of the triangle of forces (king, nobility and church) is emphasized in research for the Franconian Empire and Eastern Franconia. At the farm days there were always important consultations, which were mainly about advice and support. The consensus between the king and the high nobility played an important role in the effective exercise of rule (" consensual rule "): The king and the greats of the empire, who were in a reciprocal relationship, respected each other's rank and tried to avoid confrontation if possible act. In modern Medieval Studies, research on rituals and the representation of power are also given great importance. It is about the description and interpretation of ritualized processes in medieval politics, which are summarized under the term " symbolic communication ". This concerns, among other things, the ceremonial reception or conflict behavior, such as the staging of the deditio (submission) of rebel princes. Rituals were also important in this context because they are to be understood at least partially as an expression of the respective hierarchy between the greats . If this approach is followed, z. B. lordship defamation satisfaction (satisfactio) , for example in the form of deditio . Conflicts at different courts in the early Middle Ages are documented several times. The amicable settlement (compositio) , however, turned out to be more difficult the more the conflict had escalated beforehand. Recently, ritual research has come under fire in some cases. Claims to power and reality The western (“Roman”) empire, which was renewed by the Carolingians and Ottonians, played a special role; it was in the late antique tradition and introduced a new universal component ( imperial idea ). The two emperor problem with Byzantium only had realpolitical consequences until 812, when Venice was recognized as part of the Byzantine Empire in the Peace of Aachen . The Carolingian and Ottonian emperors exercised a hegemonic position in Latin Europe. However, this very rarely resulted in actual political influence in other empires, because justified rights of intervention did not exist for the empire. Ultimately, it was primarily a matter of formal priority. The relationship between the emperors and the papacy changed, however: while the early Carolingians had made “oath friendship”, the emperors later only made promises of protection and, since the Ottonian era, security oaths. In connection with more recent studies it can also be seen how relatively limited the creative power of the empire was even in the Carolingian Empire (after all the most powerful rulership in Latin Europe since the fall of Western Rome) compared to other great empires of this time. This becomes clear with a simple example: In 792 Charlemagne ordered the construction of a 3 km long canal in Middle Franconia, which would have connected the river systems Rhine and Danube. However, the construction work soon got stuck, so that in 793 the construction was canceled. In contrast, in 767 far more extensive construction projects in Byzantium (where water pipes were repaired over a distance of more than 100 km) and in the Caliphate ( round city of Baghdad , the construction of which over 100,000 workers were involved) succeeded without major problems. In the China of the Tang Dynasty, on the other hand, a canal around 150 km in length was built according to plan in 742/43. All of these empires had universal claims to rule, similar to the Carolingian empire; however, the resources and the creative leeway based on them were much more limited in the case of the western empire. That did not change significantly during the Ottonian era. In Byzantium, however, the late ancient statehood had survived to a greater extent. The Byzantine Emperor largely ruled absolutely and could still rely on an apparatus of officials (see offices and titles in the Byzantine Empire ), although the Byzantine state also changed significantly in the 7th and 8th centuries compared to the late Roman Empire in the 6th century would have. The emperor's possibilities of influence were higher in Byzantium due to the more differentiated and clearly regulated political infrastructure that was geared towards the emperor; Unlike in the West (during the investiture controversy ), he was not so much subject to the danger of church reprimand. In the caliphate, the functioning Byzantine and Persian bureaucracy was largely taken over, Greek and Middle Persian remained the administrative languages until the end of the 7th century. The Dīwān functioned as a central administrative body, headed by the vizier in the Abbasid period . The caliph himself was regarded as a political leader after the time of the “rightly guided caliphs”, but was subject to religious law. His secular claim to rule was also not all-encompassing. After in the 8th / 9th When local rulers had increasingly formed in the 19th century, the political theory was advocated that the caliph could delegate his power, which meant giving up an absolute claim to rule. In the Abbasid period, actual power at court was also increasingly transferred to the high officials. Society and economy People and the environment Modern knowledge of early medieval society in Latin Europe is very sketchy. The narrative sources report only very rarely about the life of the "common people", while archaeological research sometimes allows more precise insights. In the early Middle Ages, according to modern estimates, over 90% of the people lived in the countryside and from agriculture. Demographic data are quite speculative, for the period around 1000 it is assumed that the total population in Europe will be around 40 million, which increased in the following period. The general life expectancy, especially in the poorer population, was much lower than in modern times. Some areas had to be made arable and cultivated in the course of time; even areas that were used in Roman times had to be cleared again and made usable. The difficulties of living conditions that arose from the natural environment should therefore not be underestimated. In addition, the various geographical areas differed from one another culturally and economically, such as the regions that were heavily urbanized in the late Roman period and oriented towards the Mediterranean Sea and the regions further north. But there were still contiguous urban areas, especially in Italy and southern Gaul. Due to wars, epidemics and other reasons, these also recorded a decline in population, but were still relatively densely populated. Stronger lines of continuity from late antiquity to the Middle Ages can also be seen here. The eastern Mediterranean is again a special case due to the different development. However, the further one moved away from the old Roman centers, especially east of the Rhine, the lower the population density became. In the period that followed, however, new settlement centers emerged and settlements and cities were rebuilt on the basis of older predecessors. Intercultural contacts between the Latin as well as the Byzantine and Arab regions existed in some cases, but were not infrequently made more difficult by numerous factors (such as poor knowledge of foreign languages and poor spatial conceptions). The church, which was visibly represented in the congregations, was of central social importance. The respective communities were mostly manageable. An overarching sense of community can hardly be ascertained and manifested itself through special "sponsorships" (nobility and clergy). Ethnic identifications, that is, an overarching “we-consciousness”, were largely missing and only developed over time. The development in the individual regions was rather heterogeneous. Comparable living conditions, technical knowledge as well as intellectual and religious developments ensured a certain uniformity of post-Roman Europe. The dissolution of the Roman order in the west set in motion a development that led to new social conditions. Early medieval society in Latin Europe was not a religious caste or economic class society , but a class society . It was hierarchically ordered and social advancement was relatively seldom possible. Social and legal inequality caused by birth was not the exception, but the rule. The aristocratic ruling class at the top was very small. Proximity to the king and the extent of ownership played an important role for the aristocratic class consciousness, although the respective territorial ownership often shifted in one direction or the other and was not always geographically constant. Noble memoria , purposeful memory maintenance, and noble focus formation therefore had an important function. Roman law already distinguished two groups of people: free (liberi) and unfree (servi) , this was also done in the early Middle Ages. A kind of middle position between the nobility and the unfree were occupied by the free with property who were not part of the manorial system. One layer below that were small, self-employed peasants or agricultural workers and artisans at the court of a gentleman, who had to pay taxes. In general, according to recent research, it is wrong to emphasize a tendency towards impoverishment in the early Middle Ages. There was definitely a trend towards greater freedom. Socially inferior people sometimes eluded their masters and emigrated, for example. Since the 9th century, there have been legal improvements and tax reductions in the Franconian Empire. However, the nobility often endeavored to maintain and strengthen relationships of dependency. Even in the “lower” social class, however, there are parallels to the aristocratic rulership, such as B. the farmer who has the right of disposal over his house and his family. In the social hierarchy followed the poor without possessions (pauperes) , who were often dependent on begging. The church often intervened, but it never succeeded (even in the early modern period) in solving this social problem in a satisfactory manner. The slaves were right at the bottom, but the question of early medieval slavery poses a research problem. This is due, among other things, to the unclear source statements about the slaves, so that one sometimes tries to describe this as “unfree” or “dependent”. At first there were also slaves in the true sense of the word, which were usually "spoils of war". Scandinavians (Vikings) in particular engaged in brisk trade in slaves, who were mainly shipped to the Arab region. Under Christian influence, the simple right of the landlord to kill was later revoked, but he was still able to freely dispose of the "household". But unfree servi could also rise and be liberated. In any case, there were different degrees of dependency (see also serfdom ). More recently, the thesis has also been put forward that research had emphasized the peasants' dependence on the landlord in the early Middle Ages and that one had to examine the regional source material more closely. Women, children and Jews The patriarchal society of the Middle Ages assumed a subordinate role for women. From the sources in which women are mentioned again and again with respect, however, no real misogyny can be deduced. The role of women in the early Middle Ages is not entirely clear. Legally, they were formally underage; Father, husband or guardian were superordinate to them, and the power of disposal over property is denied to women in several laws. In practice, however, there were certainly opportunities for self-development, but this depended largely on your current status. Above all in the aristocratic milieu there are examples of women who had considerable influence and in some cases were even able to assert themselves politically. This potential influence of aristocratic women, but especially of some queens, which can be found in several sources, could well meet resistance at the court. This did not necessarily have to be related to the female person, but could also be politically justified, as Brunichild's political work shows, while the reign of Theophanus was accepted. Because even as a woman, masculine behavior (viriliter) was exemplary in order to receive recognition in a dominant position. A woman then had political influence by marrying accordingly or being born into a high-ranking aristocratic family. In contrast, male applicants for the office of king were often elected or came to power as a result of inheritance. Both women and men of the upper classes had to secure rule and thereby strengthen the family and the dynasty. It was therefore not uncommon for the roles of women and men to complement each other. The wives of the anointed kings were obliged to give birth to a suitable successor under the sign of fertility. So you had a similarly crucial role as the king's wife. Royal couples were on their way to maintain power in their rulership. If the king and queen were present at the same place, it was expected that the wife would show herself to her husband, although the queen might also be politically active. There were often disputes within the family, so that both women and men had to mediate in positions of power. They then did this together at the same place or chose different places of presence to mediate and mediate. The king and queen held court on their travels in palaces or castles. These disputes, for example between fathers and sons, but also other disputes, were often violent. Royal women were mentioned in documents as well as their male counterparts. Theophanu was included in the royal balance of power through the marriage certificate by the designation consortium imperii (participation in the rule). Around 989 Theophanu was using the male surnames Kaiser and Augustus in addition to female titles. It is also wrong, as sometimes happened, to speak of hostility towards children in the early Middle Ages. Concern and love for the well-being of children are repeatedly expressed in various sources; corporal punishment was not seen as the opposite of this in contemporary thinking. However, due to the lower life expectancy, childhood ended very early. The Jews held a special position as a religious fringe group in the Christian empires. Relatively strong Jewish minorities existed in Byzantium, Italy, southern Gaul and Spain in the early Middle Ages. In later Germany there were Jewish communities in some episcopal cities, including Mainz. Already in the Franconian Empire they held a special position secured by privileges. Its role as a long-distance trader was economically significant, but Jewish craftsmen and doctors are also documented. The Jews were legally restricted and there were occasionally anti-Jewish statements, violent attacks (which were relatively rare in the early Middle Ages) and attempts at (rejected by the church) forced baptisms. At the Synod of Elvira there was a first ban on marriage between Jews and Christians as early as 300 ( canones 16/78), with the Codex Theodosianus (III, 7.2; IX, 7.5), this ban applied throughout the empire Death penalty. In addition, clothing bans were imposed on the Jews, slavery (thus access to latifundia property and manor) was denied, and public office was forbidden. However, their practice of religion was not permanently and systematically prevented; they were often largely tolerated. Almost nothing is known about the cultural development of the Jews in the Diaspora in the early Middle Ages; only a few conclusions can be drawn from the later shape. The Midrash literature and the Babylonian Talmud played a larger role in religious life . Early medieval society was predominantly shaped by agriculture. The basis of the social and economic order in the west was the manorial rule , in which most of the people in the countryside were involved ( bondage ). The largest landowners were the king, the nobility and the church. Whether the aristocratic and ecclesiastical manorial rule went back to Germanic or late Roman roots or to both, or whether it rather represents an original early medieval development, is disputed in research. In late Roman times, the extensive imperial and senatorial estates (latifundia) dominated with the corresponding villae rusticae . Large villa estates are still in evidence until the 6th century, before the system collapsed. The collapse of the Roman structures thus had far-reaching consequences for the great senatorial landowners who were closely connected to the Roman state. Typical for the early Middle Ages was the villication , the two-part manorial rule: on the one hand the lord's labor yard , on the other hand the farms dependent on the landlord. The landlord made land available to the farmer for cultivation and he was placed under his protection, the farmer had to pay different taxes. There was consequently a reciprocal relationship, from which the landlord, of course, benefited most. The manors, however, were not closed economic areas; rather, there was brisk trade. Agriculture was the most important branch of the economy. In the Carolingian Empire, attempts were made to record the arable land more precisely and to divide it into parcels (hooves) as far as possible. The population, which finally increased in the early Middle Ages, was problematic for the system of manorial rule, especially since a systematic written record did not succeed in the long term. However, business-related computing now took place. This process of economic recording is not stringent, but rather connected with numerous breaks, especially since the decline of the Carolingian Empire, but has been definitely noticeable since that time. In agriculture, a distinction must be made between arable land and pasture land, although arable farming probably dominated, and viticulture was also important. Grain represented the most important food source for the general population and was used in a variety of ways. Meat and fish were consumed differently from region to region, but also as a supplement. However, there were repeated regional famines, especially with increasing populations or as a result of military conflicts. Animals were not only kept on manor farms but also on farms. A variety of everyday products were made at home. The yields of the sowing were relatively low, they amounted to only 1.6 to 1.8 times according to one source; however, it is questionable how representative this is. The beginnings of the three-field economy seem to go back to the 8th century, but it was not widespread in the early Middle Ages. An innovation process began in the early Middle Ages, but technically many ancient forerunners were initially adopted, such as the well-known plow for tillage. As a rule, oxen were used as draft animals, as horses were too expensive for them. The collar came only in the 11th / 12th. Increased use in the 19th century and only in regions with sufficient horses; According to recent studies, the ancient tensioning systems were not inferior in principle to the collar, which only brought a real increase in efficiency in conjunction with other innovations. Mills played an important role in grain processing, with water mills already being widely used in late antiquity. In handicrafts, Roman traditions were followed, such as in ceramic, glass and metal processing. Although specialized craftsmen did not enjoy a particularly prominent social position, they were certainly respected because of their skills. One of the few relevant sources, the Carolingian Capitulare de villis vel curtis imperii , lists, among other things, the craft specialists in the royal domains of the Franconian Empire. The monasteries played a not unimportant role in the economic cycle. Several had their own, sometimes very substantial, property and used it economically. The larger monastic manors could include over a thousand farming positions. The most important means of transport was the ship, regardless of whether it was inland or sea shipping. Contrary to older assumptions, the money economy still played an important role in the early Middle Ages; the importance of the natural exchange economy must therefore not be overestimated. Coins were minted almost continuously from late antiquity to the Middle Ages, but their precise purchasing power is difficult to assess today. In some cases, however, a considerable lack of material can be identified. There has been evidence of mining in the Franconian Empire since the late Merovingian period, and in the 7th century there was a transition from gold to silver coins. Trade and traffic in the early Middle Ages represent a much discussed research problem, especially since the relatively few sources on early medieval economic history are quite scattered. In older research it was often assumed that long-distance trade had come to a standstill as a result of the upheavals in late antiquity (see Pirenne thesis ). However, recent studies have shown that there was a decrease in long-distance trade, but not a complete breakdown. The late antiquity trade network had encompassed the entire Mediterranean area, with the further trade network reaching over Persia to Central Asia, China and India (see the explanations on Central Asia in the article Late antiquity and trade in India ). After the collapse of the Roman state order in the west (the trade contacts of the Eastern Empire were not affected until the end of the 6th century), regional developments took place; in this context the local aristocracy, except in the Francia (the Frankish dominion) and in the Levant , was even poorer and politically more regionally restricted than in Roman times. State power declined as a result of the lower financial strength. The fiscal structure was simpler than in Roman times and even collapsed completely in the West. In this context, however, nothing can be generalized; the regions must be considered individually. The late antique economic system in the Mediterranean area suffered severe setbacks in the 6th century, not least due to the so-called Justinian plague and the subsequent waves of plague. However, the consequences of the plague are difficult to assess in detail. The decline in population in the early Middle Ages is not necessarily due to the plague due to the inconsistent sources. it can also be the result of political crises. Around the middle of the 7th century there was probably an economic low in Mediterranean trade. Around 700, however, new trade routes developed. The individual regions (also in the west) were not completely isolated, but were still in trade contact with one another. Contrary to the older doctrine, there was already a not inconsiderable economic boom in the late 8th century. In the Mediterranean region, too, there was evidence of a lively exchange of goods between the Latin-Christian empires, Byzantium and the Caliphate, from luxury goods (such as furs and silk) to salt, honey and, last but not least, slaves. In this sense, a new networked and wide-ranging trading system emerged. In the west, there was also a trade shift to the north during the Merovingian era, with Franconian traders advancing into the Slavic region in the east as early as the 7th century. Trade routes to Scandinavia were added later. The most important Franconian port for northern trade was Quentovic . After the Arab expansion, the northern regions were by no means cut off from the cultural area of the Mediterranean, because there was a mutual exchange process and corresponding communication. Long-distance traders crossed the narrower regional boundaries, and some fairs seem to have been visited continuously since late antiquity. Nevertheless, it makes sense to consider the western and eastern Mediterranean regions separately with regard to the exchange of goods, as there were definitely differences. The cities, which had often shrunk, were important for the handling of goods and long-distance trade even after the 6th century, especially in the ancient cultural landscapes in the west, for example in Italy and partly in southern Gaul. Venice negotiated with Islamic rulers for timber and traded in salt and, above all, slaves, who were sold to Byzantium and the Islamic region. Gaeta , Amalfi and Bari also benefited from long-distance trading. Milan , which had already played an important role in late antiquity, gained importance again in the late 10th century, for example in the area of the money economy. In contrast, ancient urban culture in the Danube region and in Britain virtually collapsed. As before and long afterwards, smaller cities could only trade with the surplus of local production. The trade in bulk goods was particularly important for domestic trade. Most of the trade is likely to have taken place within the regions anyway, so most goods were transported over relatively short distances. Byzantium ran through in the 7th / 8th centuries. Century a transformation, whereby important ancient structures were preserved, but society and economy changed in some cases fundamentally. Due to the tense foreign policy situation, society became increasingly militarized in the 7th century. Since that time, a class of nobility has formed from the ranks of the influential bureaucracy and the large landowners, and surnames have emerged - families that in some cases became very important. In the late 9th century, the ruling class increasingly recruited from these sexes. At the same time, the free peasantry decreased, and many eventually became dependent on large landowners. Nevertheless, Byzantine society remained much more open than Western European, and the imperial throne was not reserved for the high nobility. Social advancement to the top of the state was therefore basically open to everyone, as the example of Basil I shows. The Byzantine economy slowly recovered after the crisis of the 6th and 7th centuries. During this time she had suffered from the consequences of the plague and war, combined with a decline in population. The sources on Central Byzantine economic history, especially for the 8th / 9th centuries. Century, but are not particularly productive. Some cities were abandoned, others were reduced to their core centers, but Constantinople remained an important metropolis in the Mediterranean area and the most important city in the empire. The richest provinces of the empire were lost after 700, but Asia Minor could at least to some extent serve as a replacement base. In contrast to the West, the state bureaucracy remained fully functional, although tax revenues fell. The economic power rose again in the following period; while the Byzantine state was almost impoverished in the 8th century, it again had considerable resources at its disposal in the 10th century. In general, the rural economic area played an important but not the dominant role in Byzantium, as in Latin Europe, since urban economic production continued to be an important factor. In contrast to Latin Europe, the economy was also more strictly regulated by the state and financed the ruling apparatus more through the treasury. Education system and development Early medieval society was largely an oral society in which few people could read and write. An even smaller minority was literarily educated, consisting predominantly, but not exclusively, of clergymen. The ancient cultural assets formed the basis. However, only a small part of ancient literature was preserved in early medieval western Europe. The medieval Latin ( Medieval Latin ) also differed from the classical Latin, the knowledge of Greek had in the Late Antiquity accepted in the West. Nevertheless, even after the collapse of Western Rome, the Latin language connected large parts of Europe with one another, as there was a common communicative basis. The late ancient three-tier education system (elementary instruction, grammar and rhetoric) had gradually disappeared as a result of the political upheavals of the migration period in the west. Older research often equated the transition from antiquity to the Middle Ages with "barbarization". Ultimately, however, it is about a transition to a new culture in which divergent interests and a new cultural ideal can also be identified. For the Romansh upper class, education was important for a long time anyway. The historian and bishop Gregory of Tours in the late 6th century came from a noble Gallo-Roman senatorial family and clearly attached importance to education, because he lamented its decline. Schools in southern Gaul and Italy gradually went under, but education continued to be provided in private circles. The development of the written culture in the early Middle Ages was very heterogeneous and was influenced by different factors. Nor were education and intellectual life uniform in the Latin West. In the early Merovingian times, profane lessons were apparently still given, because the Merovingians had a rudimentary bureaucracy that required written knowledge. In the early Merovingian period, the noble Gallo-Roman families played an important role as intermediaries with regard to classical teaching content. For a long time the Merovingian chancellery consisted mainly of lay people, not of clerics. The royal family and members of the high nobility were expected to have literacy skills. Some kings like Chilperic I had a high education and demonstrated it. Only after the middle of the 7th century did the Merovingian power struggles with the nobility lead to further decline. Reading and writing skills fell sharply among laypeople, but also among clergy. In the Visigoths there are still traces of late antique education in the 7th century. The same applies to Italy after the Lombard invasion in the late 6th century; In the Italian cities, written laypeople are still attested. A new culture of writing developed in the British Isles in the 7th and 8th centuries. In the Merovingian Empire, literary production broke in the 7th / 8th. Century dramatically, but still a few works such as the Merovingian saints' lives were created. After all , the monastery , cathedral and collegiate schools, and thus the church, were of central importance for medieval education and the transfer of knowledge in the Latin West . Most of the ancient literature has not survived, but the ancient knowledge still available in the West was collected and passed on in the monasteries; this tradition began in the 6th century with Cassiodorus . Texts were read according to fixed rules and some were learned by heart and copied in the church scriptoria . Papyrus was still sometimes used as writing material (as in the Merovingian administration), but parchment became increasingly popular ; the scroll increasingly gave way to the book ( codex ). In addition to clerics, nuns also received a Latin education, and some schools were also open to lay people (from the aristocratic upper class). As a rule, however, the laypeople were unlearned, and in church circles the opposition to the illiterati (people unfamiliar with reading) was sometimes emphasized. Rosamond McKitterick , however, advocates the controversial thesis that in Carolingian times the written form among lay people was higher than was often assumed earlier. In the church schools, in addition to the Bible and the texts of the church fathers , profane late antique texts were also used for teaching. Martianus Capella had written a textbook in late antiquity in which the canon of the seven liberal arts (the artes liberales ) was summarized: Trivium and the further quadrivium . In addition, Boethius and Isidore of Seville played an important role. The writings of Boethius enjoyed a tremendous reputation in the Middle Ages. He had also reworked the liberal arts and thus created an important basis for the medieval teaching canon. In the 7th century, Isidore had systematically collected large parts of the known knowledge of late antiquity in 20 books in the Encyclopedia Etymologiae . The work was of great importance for imparting knowledge in the early Middle Ages. Carolingian educational reform In the Franconian Empire, the Latin language was stylistically increasingly wild, and the church educational institutions also fell into disrepair. This process has been stopped in the Carolingian Empire since the end of the 8th century through targeted measures to promote culture. This new boom phase is often referred to as the Carolingian renaissance . The term “ renaissance ” is very problematic for methodological reasons. This also applies to the so-called Macedonian Renaissance in Byzantium, as there was a cultural continuity with antiquity there. Although weakening occurred here, there was never a complete break. In the Franconian Empire it was not a question of a “rebirth” of classical ancient knowledge, but rather a purification and unification. For this reason one speaks of the Carolingian educational reform for the Carolingian period . The impetus for this was probably the reform of the Frankish Church by Boniface in the middle of the 8th century. Before that, there was also a revival of intellectual life in England and Ireland, where the written culture was growing stronger. The writings of the well-read Beda Venerabilis (d. 735) cover a wide range, such as church history, hagiography , chronology and the liberal arts, and convey the image of a lively spiritual life. Charlemagne himself was evidently quite interested in culture and deliberately assembled several scholars from Latin Europe at his court. The most respected of them was the Anglo-Saxon Alcuin (d. 804). Alcuin had previously been director of the famous cathedral school in York; he owned an extensive library and enjoyed an excellent reputation. He met Karl in Italy and in 782 followed the call to his court, where he not only worked as an influential advisor, but also rose to head the court school. Einhard (d. 840) came from a noble Franconian family and was initially a pupil of Alkuin, later head of the court school and a confidante of Charles. He was also active as a builder for Charles and after 814 wrote a biography of the king based on ancient models, which has been described as the "ripe fruit of the Carolingian Renaissance". Peter of Pisa was a Latin grammarian who taught Karl in Latin. The Lombard scholar Paulus Diaconus had served as a king in Italy and had come to Charles's court in 782, where he stayed and worked for four years. Theodulf von Orléans was a Gothic theologian and poet. He was well-read and educated; for Karl he also wrote the Libri Carolini . The Karl court and the court school gave impulses for a cultural renewal, whereby the Carolingian church was reformed as the central cultural carrier. The implementation of the following educational reform was largely due to Alkuins. The key term for this was correctio , according to which the Latin script and language as well as the worship service were to be "corrected". The existing educational material should be systematically collected, maintained and disseminated; the establishment of a court library also served for this purpose. The educational program is also addressed in the famous Admonitio Generalis from 789. The monasteries were exhorted to set up schools. The reform of the monastery and cathedral schools was also important for religious reasons, as the clergy relied on the most precise language and scripture possible in order to be able to interpret the Bible and prepare theological writings. The written Latin language has been cleaned up and improved. Great emphasis was placed on correct grammar and spelling, which raised the stylistic level. The Carolingian minuscule became the new font . In the ecclesiastical field, among other things, the liturgy was revised, collections of homilies created and compliance with ecclesiastical rules demanded. Several changes have also been made in the administrative area. The church educational institutions received increased support, and a revised version of the Latin Bible edition was prepared (so-called Alcuin Bible ). Older writings were looked through and corrected, copies made and distributed. The court school became a teaching center, which radiated across the entire Franconian Empire. In the Fulda monastery, for example, a distinct literary culture developed under Alkuin's pupil Rabanus Maurus . In addition, Corbie and St. Gallen were also important. Research has identified 16 “written provinces” in addition to the Karlshof for the period around 820, each with several scriptoria. The educational reform ensured a significant strengthening of intellectual life in the Franconian Empire. After the sharp decline since the 7th century, literary production increased noticeably, and art and architecture also benefited from it. Ancient texts by both pagan and Christian authors were now increasingly being used, read and, above all, copied. Ovid and Virgil were particularly in demand, and Sallust , Quintus Curtius Rufus , Suetonius and Horace , among others , were increasingly being read again. The Carolingian educational reform was therefore of great importance for the transmission of ancient texts. However, there were regional differences in the Franconian Empire. West Franconia was culturally further developed due to the Gallo-Roman heritage. The court of Charles the Bald acted as a cultural center, and the so-called Auxerre School was also of importance . In Eastern Franconia, on the other hand, literary production stagnated in the middle / end of the 9th century before there was a renewed upswing in the 10th century. In Ottonian times, the cathedral schools gained increasing importance. In the 10th century reading and writing skills are rarer in the aristocracy, the aristocratic-warlike upbringing was decisive. On the other hand, both Otto II and Otto III. a very good education. Culture in the Eastern Mediterranean The east, Byzantium and the Islamic world, where ancient Greek knowledge was preserved and cultivated, formed a cultural center. In Byzantium, the preoccupation with ancient works did not cease completely, even in the period from the middle of the 7th century to the 9th century, often referred to as the “dark period”; the best example of this is Photios . Not only clergy, but also lay people who could afford it, continued to enjoy an education there, which was indispensable for civil service anyway. Elementary classes in reading and writing lasted two to three years and were also open to the middle classes. However, little is known about the exact details of how the lessons were given. The higher education was sometimes promoted and monitored by the state. The relevant lessons were given at imperial universities, in Central Byzantine times thus primarily in Constantinople; however, there also seem to have been some institutions in the provinces. There were several extensive libraries, and the training could include law, theology or medicine. The Arab conquerors profited considerably from the already existing higher cultural development in the former Eastern Roman areas and in Persia, something which Muslim scholars later followed. In the Islamic world, classes were held in the Masǧid ( mosque ), which had an attached hostel for the students. Higher education (except in Al-Andalus) was taught in the guild-like organized madrasa , where mainly Islamic theology and law (also with knowledge of the Koran) were taught. The lessons were financed by private donations. Numerous Arabic translations of Greek works were created ( House of Wisdom ). In Damascus, Baghdad, and later also in Sicily and Al-Andalus, they dealt extensively with ancient scripts, which gave impetus for new considerations. In the Umayyad period , the cultural orientation was still strongly based on late antique models. Magnificent hunting castles in the late antique architectural style were built (such as Chirbat al Mafdschar north of Jericho and Qasr al-Hair al-Gharbi in Syria). Mention should also be made of Christian Syrian scholars who lived under Arab rule, such as Jacob of Edessa , John of Damascus and Theophilos of Edessa . Syrians generally played a not unimportant role in imparting ancient knowledge to the Arabs. Knowledge from the East also found its way into Latin Europe. Indo-Arabic numerals have been used since the late 10th century. Especially Spain and later Sicily played an important mediating role. Early medieval literature The last significant and largely preserved late antique historical work in Latin was written by Ammianus Marcellinus in the late 4th century. The names of some Latin historians in the West up to the end of antiquity are known, but in fact nothing of their works has survived. This also applies to the Gothic story of Cassiodorus (who also wrote a preserved chronicle), which formed the basis for the Getica des Jordanes . At the end of the 6th century, the educated Bishop Gregory of Tours , who came from a senatorial Gallo-Roman family, wrote his main work, the histories of up to 591 in 10 books. It is an important Christian universal history with the Franconian Empire in the center, with contemporary history being described in particular in detail. The level of Gregory was not reached for a long time. The Fredegar Chronicle from the 7th century, for example, is written in a wild Latin and also poor in content. In addition to the chronicle (local chronicles and Christian world chronicles , which are of late antique origin), the annals are typical of early medieval historiography . They originated in the Carolingian monasteries and developed from very short, annual entries to sometimes detailed, chronicle-like descriptions. The most important of these were the Reichsannals , which lasted up to 829 and were followed by various sequels in West and East Franconia ( Annals of St. Bertin , Annals of Fulda ). In terms of content, they were close to the Carolingian dynasty and can in a certain way be regarded as court historiography. In addition, there were other annals and chronicles, which were often geared towards their own diocese, monastery or imperial territory. Several narrative historical works were also written in the Carolingian period. Paulus Diaconus wrote a Lombard story in 6 books (his main work), a Roman story in 16 books and a story of the bishops of Metz, who praised the Carolingian ancestors. Nithard , unlike most early medieval writers in the West no clergyman, wrote four books histories about the history of the Carolingian brother fighting after the death of Charlemagne. The Carolingian court scholar Einhard wrote the first medieval biography of a secular ruler: Inspired by the emperor's biographies Suetons , he wrote the Vita Karoli Magni after the death of Charlemagne . Karl's son and successor Ludwig the Pious were even dedicated to two biographies: the Thegans and that of an anonymous author known as Astronomus . In the late Carolingian period, Regino von Prüm wrote a world chronicle that went up to 906. In the early 10th century, no major historical works were created, just as the written form in Eastern Franconia had declined during this time. Widukind von Corvey wrote a Saxon history in three books, which is important for Ottonian history. The bishop's chronicle of Thietmar von Merseburg , written at the end of the 10th century, expanded into an important history of the empire, which is an important source for the Ottonian period. In West Franconia, Flodoard von Reims (annals and a history of the Church of Reims) and Richer von Reims ( histories , partly with reference to Flodoard) wrote historical works that contain important information for the events in late Carolingian West Franconia. In Britain, the important church history of Beda Venerabilis (early 8th century), which also goes into the political and cultural history of Britain, the Anglo-Saxon Chronicle and Aser's biography of Alfred the Great emerged in the early Middle Ages ; Local histories are documented for Ireland and Wales ( Annales Cambriae ) . Already in late antiquity, the steadily continued Liber Pontificalis , a continuous papal history , was created in Rome . Otherwise, there are several more locally oriented chronicles from Italy. In Hispania, during the Visigothic period, the important scholar Isidore of Seville wrote a universal chronicle and a history of the Goths. Later, the Mozarabic Chronicle and the Crónica Albeldense were written in Spain . Individual early medieval works were also lost in the following period (e.g. the Historiola des Secundus von Trient ). Several of the works mentioned are problematic in some respects from the point of view of modern research. What should be emphasized, however, is the diversity of early medieval Latin historiography. Although this had moved away from late antique historiography, the ancient foundations had not completely disappeared. Since the Carolingian educational reform, the focus has again been turned more towards antiquity, for example ancient authors often served as stylistic models or reference was made to past events (exempla) . The early medieval historiography was pervaded by a solid Christian historical thought, z. B. with regard to a linear course in which the Imperium Romanum was the goal of history; divine work and Christian ethical action also played an important role. The Byzantine historiography in Greek was likewise Christian influences in the early Middle Ages, but the ancient terms was far greater than in the West, especially since the ancient heritage remained more preserved and history was not confined to the clergy. Significant Byzantine chronicles have come down to us from Georgios Synkellos and Theophanes . The tradition of ancient historiography ended in Byzantium in the early 7th century, but was increasingly received again in the 10th century. The imitation ( mimesis ) of the classical texts was sought in many subsequent Byzantine works of profane history. Under Constantine VII , texts by ancient historians were excerpted in an enormous undertaking; Only small remains of it have survived today, but they contain valuable material that would otherwise not have been handed down. (Christian) Armenian and Syrian histories continued to emerge in the Orient, some of which provide very valuable information. To be mentioned are z. B. the work of the pseudo- Sebeos in the 7th century and the now lost chronicle of Theophilos of Edessa in the 8th century, which has served as a source for several later authors. The beginnings of Islamic historiography go back to the 8th century, but many details are disputed, especially since compilations of the older material only survived from the 9th / 10th centuries. Century. Particularly noteworthy is the universal history of the learned at-Tabarī , which goes back to the early 10th century. Hagiography plays a special role . It was also included in the genus of historia (storytelling) and was more widespread than “secular historiography” in the narrower sense. The vita of St. Martin of Tours , which Sulpicius Severus wrote, was an important model . Already in the Merovingian period there were stories of martyrs and lives as examples of an exemplary way of life, as well as bishops' vites, and miracula reports were added . In addition to Gaul, Italy should be mentioned above all: Pope Gregory the Great wrote dialogues in the late 6th century in which contemporary saints were represented; later, the patronage was increasingly thought of in several cities. In the Carolingian period, influenced by the educational reform, several vites were rewritten or rewritten. While the hagiographic tradition from Hispania is relatively poor, vites have been passed down from England since the early 8th century. In Byzantine literature, the genre boundary is fluid, since theological literature was widely developed there (homilies, letters, historical works, etc.). In the Slavic area, after the adoption of Christianity, various hagiographic works were created, for example in Bulgaria in the 10th century through the translation and processing of Byzantine works. Middle Latin poetry was quite heavily influenced by ancient works. Venantius Fortunatus , who lived in the late 6th / early 7th century , was the first early medieval poet , who received his training in Italy and worked at the Merovingian royal court in Austrasia , where he made good contacts and finally became a bishop. Venantius Fortunatus was poetic in the late antique tradition and wrote over 200 poems of praise, lamentation and consolation songs as well as obituaries, which is an expression of a need for traditional education still existing around 600 in the Franconian Empire. The early medieval court poetry was particularly important, especially at the Carolingian royal court. More than 300 metrical poems have come down to us from Charles' already mentioned learned advisor Alkuin . Angilbert , court chaplain of Charlemagne and father of the historian Nithard , wrote not only prose but also poems and was called Charles " Homerus ". Paulinus II of Aquileia wrote a lamentation poem in honor of Eric, the Marquis of Friuli; other poems are also ascribed to him. Paulus Diaconus , who also worked as a historian and worked for some time at the court of Charles, wrote several poems, including praise poems and epitaphs. About 80 poems by Theodulf von Orléans have survived , which testify to his extensive education. In the further course of the 9th century, Ermoldus Nigellus and the very learned Johannes Scottus Eriugena worked in West Franconia . There were also monastic poems, some of which were very important. These include poems by Walahfrid Strabos and the Liber Ymnorum Notkers (written around 884 and dedicated to the influential Liutward von Vercelli ). The cultural revival after the end of antiquity was favored by the Carolingian educational reform. The most important early medieval poet was Hrotsvit in the 10th century. In the area of Middle Latin epic, the Waltharius , an epic heroic poem from the 9th or 10th century, should be mentioned above all . In the transition from the early to the high Middle Ages, the poem about the knight Ruodlieb was created , which is considered the first fictional novel of the Middle Ages. Biblical poems were widespread, especially since the Bible already played a central role as the basis of material in Middle Latin literature. Historical poems were also created, for example the verse epic Karolus Magnus et Leo papa around 800 and the work of Poeta Saxo at the end of the 9th century . Cædmon and Aldhelm von Sherborne worked in England in the 7th century, and some important poems were also written in Italy and the Spanish Visigothic Empire. Since the middle of the 8th century, not only Latin, but also vernacular works have been documented in the West; however, the number of authors known by name is manageable. The range of vernacular early medieval literature is quite considerable, it includes, among other things, books of magic and blessings, heroic tales, historical and battle poems. Church texts were also translated, particularly with a view to conveying Christian messages of faith. Much of the vernacular poetry was of a spiritual nature, such as B. Bible poems. The earliest surviving evidence of the Old High German Bible poetry is the Wessobrunn creation poem from the 9th century. The Carolingian educational reform not only resulted in an increasing preoccupation with Latin texts and the existing ancient tradition, it also strengthened the development of Old High German. Centers of old German tradition included the monasteries Fulda, Reichenau, St. Gallen and Murbach. The Hildebrandslied , an Old High German hero song from the early 9th century, has been preserved in fragments . Charlemagne is said to have ordered old pagan heroic songs to be recorded, but nothing has survived. Under the direction of the learned Rabanus Maurus , a translation of the Gospels was created around 830 with the Old High German Tatian . The first German poet is Otfrid von Weißenburg , who worked in the 860s and 870s. The Liber Evangeliorum , written by him around 870, is an Old High German Bible epic (in the South Rhine-Franconian dialect) and comprises 7104 long lines in five books, with the life of Jesus Christ at the center. The Strasbourg oaths of 842 have been handed down in Old High German and Old French and are considered early language certificates. The Old High German Ludwigslied originated in the late 9th century. In the Ottonian period, Old High German literature production ended for some time, for which research has not yet found a satisfactory explanation. Around 1000, for example, Notker von St. Gallen worked , who translated several ancient texts into Old High German and thus created an important basis for scientific texts in this language. At the Anglo-Saxon royal court of Alfred the Great, individual works by Latin scholars (such as Boethius and Orosius ) were translated into Old English . The bulk of Old English literature (which includes several Latin texts in addition to Old English) has been preserved in four manuscripts (Junius manuscript, also called Cædmonhandschrift , Exeter book, Vercelli book and Beowulf manuscript ). In Ireland, in the 6./7. Century a lively written culture with initially Latin, soon also Old Irish works, which included heroic tales, poetry, annals, saints and kings genealogies, hagiographic and spiritual literature. In Old French few early medieval texts are occupied, such as the Sequence of Saint Eulalia (in honor of St Eulalia) in the late 9th century and the Leodegarlied from the 10th century. The old French poetic processing of a Latin legend, the so-called Alexius song, dates from the 11th century . In Italy, the history of vernacular literature does not begin until the 13th century. There is hardly any evidence of Romanesque works from the early Middle Ages on the Iberian Peninsula. Romanesque glosses (10th century) come from the monastery of San Millán de la Cogolla , while Romanesque final stanzas are documented in Arabic and Hebrew poems (the so-called Jarchas , 11th century). However, fully developed vernacular works were not written until the High Middle Ages; this includes the epic Cantar de Mio Cid . In Scandinavian literature, the transition from oral narratives and poems ( scald poetry and preliminary stages of the Edda in the 9th century) to written language is also associated with Christianization and the adoption of the Latin alphabet (instead of runes ). With the development of Church Slavonic in the 9th century, a rich literature emerged in the Slavic cultural area in the period that followed. After the Christianization of Bulgaria, several Old Church Slavonic translations of Greek works were made, especially theological works (liturgical and biblical texts), chronicles and lives. In Byzantium itself, in addition to writings in the ancient Greek standard language, several vernacular ( Middle Greek ) works were created. One of the most important is the epic Digenis Akritas . The philosophy of the Middle Ages was based heavily on ancient foundations, however, unlike in late antiquity, now firmly embedded in the Christian worldview. In this sense the theologically oriented patristic was important, which in the 7./8. Century ended. Already in late antiquity, Neoplatonism was received by Christian scholars who combined the Platonic doctrine of ideas with Christian considerations, especially since Plato's ideas were already transcendent through Neoplatonism. Statements in the Bible were partly interpreted with the help of Platonic ideas, among other things with reference to the good and the being / being. Little was known of the writings of Plato and Aristotle in the West in the early Middle Ages. Platonic influenced philosophers were influential. Augustine of Hippo and Boethius are both historically part of late antiquity, but historically they stand on the threshold of the Middle Ages. Both had a strong lasting influence on medieval philosophy, especially in the early Middle Ages. This also applies to the works of the pseudo-Dionysius Areopagita , an anonymous late antique Christian neo-Platonist, which was translated into Latin as early as the Carolingian period. Pseudo-Dionysius also elaborated the concept of negative theology . Around the middle of the 9th century there is evidence of the important philosopher Johannes Scottus Eriugena , who came from Ireland and who spent some time at the West Franconian royal court. He worked there as a learned advisor, also gave classes in the liberal arts and apparently enjoyed a great reputation. Eriugena is exceptional in that, without his writings, there would be a large gap in Latin philosophical literature between Boethius and Anselm of Canterbury . He had some knowledge of Greek, which was very unusual in the West at the time, and advocated strictly logical thinking, which also came into conflict with church authorities. His main work with the Greek title Periphyseon ("About Natures") deals in the form of a dialogue, divided into five books, above all the cosmological world order and the relationship between creator and creation. In a logical and systematic way, Christian revelation should be studied and interpreted in order to discern the truth it contains. The work is based on a fairly extensive source base and is influenced by the Neoplatonic movement. Eriugena also wrote a (only fragmentary) commentary on John's Gospel and Martianus Capella . In the Byzantine area, Stephanos of Alexandria is the last philosopher of late antiquity in the early 7th century. The Reich's military struggle for survival at the time resulted in a noticeable decline in the level of cultural interest. The tradition regarding intellectual development in Byzantium is not favorable for the late 7th and 8th centuries, but byzantium has retained more of the cultural heritage than in the West. In the 9th / 10th In the 19th century, the very learned Photios worked , who had a large library and wrote philosophical treatises that are now lost. One of his students, Zacharias of Chalkedon, wrote a little pamphlet "About Time" in the 860s. Leon the mathematician and Arethas von Kaisareia also collected classical Greek texts and partly re-edited them. From scattered fragments it can also be deduced that Aristotle and Plato were also read in Byzantium in the 9th century and probably partly reissued. As a result of the picture dispute , there were also writings in which philosophical arguments were put forward. The basis of Islamic philosophy was initially the systematic translation of Greek philosophical or scientific texts, whereby the still living Christian-Syrian tradition of studying Greek science also played a role. Al-Kindī gained importance in the 9th century , whose works are thematically diversified and include astronomy, mathematics, optics, medicine and music. Al-Kindī dealt with Plato and Aristotle and made translations of Greek works. His treatise on definitions and descriptions of things, in which he prepared the Greek philosophical vocabulary, was influential. The Jewish philosopher Isaak ben Solomon Israeli based his book on definitions closely on al-Kindī. The Persian philosopher Abu Bakr Muhammad ibn Zakariya ar-Razi and al-Farabi, who came from Central Asia, worked in the 10th century . The latter was able to fall back on practically the entire still preserved ancient tradition of Greek philosophers; he regarded philosophy as the basis of all science and also related this to religion. The important Persian philosopher Avicenna (d. 1037) fundamentally asked the question of the task and the possibility of philosophy. His very influential considerations concerned, among other things, logic and intellect. In his canon of medicine , he also systematically summarized the medical knowledge of the time. There are also other scholars to be mentioned, for example: B. al-Khwarizmi in the 9th century. In the early Middle Ages, the royal courts, but above all the Franconian royal court with the court school, and the church played a key role in cultural and artistic promotion. Christian symbolism dominates the motifs. Early medieval art was initially based on late antique models before new art styles developed. The Byzantine art , also influenced the West where in research, the degree of this influence is controversial. Whereas early medieval culture was previously seen as more receptive and less as creative, it has recently been emphasized again that there were already late antiquity models in the west and that the influence between east and west was more subtle. The Carolingian educational reform and the so-called Ottonian Renaissance (10th / 11th centuries) brought about a renewed cultural upswing. In medieval scholarly thought, the question of beauty is detached from art and is based on Platonic and Neoplatonic considerations. In the art theory of the early Middle Ages, the statements of Augustine and the Pseudo-Dionysius Areopagita were influential. A work of art and the associated aesthetic beauty was therefore not an end in itself; Rather, beauty also had a transcendental purpose. For Johannes Scottus Eriugena z. B. the perceptible was considered a symbol of the divine. In architecture, pre-Romanesque forms a transition between late antique and Romanesque architectural forms. In the church dominated Hispania and Britain hall churches of stone, east of the Rhine were initially distributed Holzkirchen, almost none of which has been preserved. In Italy, on the other hand, basilicas were common. New types of construction developed, often inspired by Italy and decorated with mosaics , which was already common in late antiquity. The monumental architecture has been cultivated again since the time of Charlemagne, the mass construction with several pillars was based on ancient knowledge. In the Carolingian period, several rulers' palaces were finally built, such as the Aachen Royal Palace , whose overall composition was also based on Roman models. After 814 there was a certain break in monumental architecture in the Franconian Empire. Initially, rather small-scale church buildings composed of individual room cells were preferred. Although the Hildebold Cathedral was built later in the 9th century, the Lorsch westwork form was also adopted in Corvey or, for example, the transverse cell construction was carried out in larger dimensions in Hersfeld, but this was not the rule. In the Ottonian times, the Carolingian tradition was consciously followed, and several large churches were built again. The problem with the evaluation of early medieval architecture, however, is that hardly any remains of manorial secular buildings from the 10th and 11th centuries have survived, but mainly church buildings. In Italy, due to the relative cultural continuity, the transition to the early Middle Ages was less pronounced, but square pillars and hall crypts were new. In Hispania, ancient, early Christian and popular motifs merged during the Visigothic period; after 711 the Mozarabic architecture developed . In England, as a result of the Christianization of the Anglo-Saxons, there were several wooden churches as well as larger church buildings, of which only small remains have survived. In the different Anglo-Saxon empires different types of buildings can be found in church construction. The Carolingian book illumination , which was also influenced by Byzantine influence, meant an increase compared to the Merovingian book illumination and is one of the results of the Carolingian educational reform. Examples of this include the Lorsch Gospels , the Coronation Gospels , and the Ada manuscript (see also Ada group ) from the time of Charlemagne or the Codex aureus of St. Emmeram from the late 9th century. In addition to the royal court school, the centers of Carolingian book illumination were later Reims , St. Martin in Tours and Metz . The court school of Charles II in West Franconia gained importance in the later 9th century. Pictorial manuscripts were also created in the large imperial monasteries and important bishop's residences, partly in imitation of the royal court schools (according to the Fulda Gospel ). The decisive factor here was that the spiritual institutions had good scriptories and received cultural impulses, which was initially hardly the case on the secular side. In the Ottonian period in 10./11. In the 19th century, after a cultural downturn at the end of the Carolingian era, older models were followed. This is how the equally important Ottonian book illumination came into being in Eastern Franconia , the centers of which were the monasteries of Corvey, Hildesheim, Fulda and Reichenau; later Cologne, Regensburg and Salzburg also gained in importance. One of their most important products is Otto III's prayer book. and the Gospel Book of Otto III . Furthermore, book illuminations from other regions of Europe have been preserved. The Aethelwold Benedictionale from the late 10th century represents a high point of Anglo-Saxon book illumination. The richly decorated “First Bible” of St. Martial (Limoges) was created in West Franconia around 1000. The Beatus Commentary on the Revelation of John (8th century) comes from Spain , while numerous illustrative manuscripts were also produced in Italy, especially on the life of well-known saints and important clergymen. Some ancient art knowledge was lost in the early Middle Ages. This applies, for example, to the three-dimensionality and the representation of people in their natural proportions. A rather static structure developed and a certain fear of emptiness ( horror vacui ) . In addition, there were new artistic objectives and other artistic characteristics, such as Celtic and Germanic ornamentation (see also Germanic animal style ). The basis of the early medieval wall painting is the late antique monumental painting, of which more was preserved in the early Middle Ages than today. How strong the concrete connections are between late antique and early medieval wall painting can hardly be determined today, as there are often more recent interventions. In addition, only parts of various early medieval wall paintings have survived. A picture of monumental painting in Carolingian times around 800 is conveyed by the preliminary drawings for the original dome decor of Charlemagne's Palatine Chapel in Aachen , which are lost today, but known through descriptions and sketches . Wall paintings depicting the life of Jesus Christ were particularly popular in churches, but numerous other biblical scenes were also used. This was reinforced by eschatological expectations for the time around 1000. In Ottonian times, the Carolingian tradition was initially used. The central nave of St. Georg in Reichenau-Oberzell (10th century) is probably the best example of the interior decoration of a church, which was quite common in Carolingian and Ottonian times. Several bishops appeared as patrons of art, such as Gebhard von Konstanz in his own church in Petershausen or Egbert von Trier , under whose patronage the master of the registrum Gregorii worked. The handicrafts produced, among other things, fibulae , belt buckles, but also carvings made of ivory , gold sheet work and richly decorated book cover work. In the small sculpture , many reliquary containers were made due to the strong religious need . Numerous liturgical devices were also created; One of the most beautiful is the Lothar cross , made around 1000 . The Gero Cross , created in Ottonian times, is one of the first monumental sculptures of the Middle Ages. The cultural centers were also mainly in the east. In Byzantium, icon painting is one of the highlights of early medieval art, and Byzantine book illumination also produced important works. The so-called Macedonian Renaissance in the 9th / 10th centuries. The 19th century led in Byzantium, after the defensive struggles against the Arabs that threatened existence had been overcome, to a stronger focus on ancient motifs and ancient literature. In Byzantium, the iconoclasm raged in the 8th and 9th centuries , which had an impact on art. In the late 8th century, the admirers of images were able to prevail for a short time and then they were finally victorious in the 9th century. In the West, at the Synod of Frankfurt in 794 , religious worship of images was dealt with, which was ultimately rejected ( Libri Carolini ). In the west, however, Byzantine art influences were taken up, e. B. in illuminating or with regard to forms of central building in Romanesque churches. In terms of architecture, the Byzantine style inspired, among other things, St. Mark's Basilica in Venice and the Carolingian Palatine Chapel in Aachen Cathedral ( octagon shape ). In the early Middle Ages religion was a determining factor in life in Latin Europe, Byzantium and the Caliphate. However, it is very questionable whether one can speak of a unity in culture and religiosity for each of these cultural areas; on the contrary, there was a difference between learned ideas and popular piety . This also affected Latin Europe, although popular ideas often assume a monolithic block. The general history of Latin Europe and the Byzantine cultural area in the early Middle Ages is nevertheless closely linked to the history of Christianity during this period. Church, state and culture were already closely linked in late antiquity . Christianity was elevated to the state religion under Theodosius I , the pagan ("pagan") cults lost more and more followers and finally sank into insignificance, although small pagan minorities in Byzantium are documented until the 6th century. After the fall of West Rome, political unity in the Mediterranean was abolished, but the new Germanic empires were Christian empires - either when they were founded or shortly afterwards (like the Frankish empire). While the majority of Christian Teutons inclined towards Arianism , the Romansh majority population consisted of Catholic Christians, which in some cases led to considerable tensions. In Eastern Gothic Italy, the denominational difference even had an impact on foreign policy in relation to Byzantium ( Akakian schism ). The Lombards, who invaded Italy in 568, were also predominantly Arians, but took place in the 7th / 8th centuries. Century increasingly the turn to the Catholic faith. Clovis I was baptized a Catholic around 500 and was followed by numerous Franks; in the Visigoths the conversion took place in 589. Despite political fragmentation, a certain cultural and religious unity remained, which only ended with the Arab expansion in the 7th century. Popes and secular rule In the early Middle Ages, the papacy did not play such a decisive role politically as it did in the further course of the Middle Ages. The bishop of Rome enjoyed great prestige as the successor to the apostles Peter and Paul , but he did not exercise any suzerainty over the Byzantine Church, for example. The Patriarch of Constantinople, on the other hand, never got the same importance as the Pope in the West, where the Popes finally also claimed full secular authority , and at no time determined Byzantine politics. During the transition from antiquity to the Middle Ages, the popes were politically strongly influenced by Byzantine influence. As a result of the Byzantine loss of power in the west, the popes slowly but increasingly gained political leeway. Gregory the Great, for example, who came from a distinguished Roman family, was very learned and was one of the most important medieval popes, was also politically active. Nevertheless, the popes were formally subject to the Byzantine emperor, who could even try them. In the middle of the 8th century, the Lombard threats forced the popes to look for support. Pope Stephan II traveled to the Frankish King Pippin in 753/54 and entered into an alliance with him. The Carolingians took on the role of the new papal protective power, which the Ottonians and the following Roman-German kings also took over later . Through this alliance, the papal claims were protected not least, which, as the resulting located Kirchenstaat shows articulated in secular form. The in the 8./9. A forged gift of Constantine from the 19th century was intended to provide a basis for these claims. Since Charlemagne's coronation as emperor in 800, the Pope and Franconian Empire were even more closely intertwined. The connection was problematic in that both the papacy and the empire were universal powers, whose interests did not always run parallel, like the investiture controversy in 11/12. Century clearly shows; but already in the 9th century there were conflicts between the Pope and the Carolingian emperors. As a counterbalance to secular power, the church developed the two-sword theory , although in the High Middle Ages the popes themselves sometimes emphatically claimed secular supremacy. The papal prestige increased so that various rulers in Latin Europe requested the support of the Pope. In the 9th century, papal authority under Nicholas I reached its first climax, a "world position" before it fell into disrepair in the late 9th century. The papacy became a plaything of the interests of urban Roman families in the early 10th century. In the Ottonian times it played no political role. The connection between the western and eastern churches, in turn, dwindled more and more and ultimately led to the schism of 1054 . The Carolingian educational reform around 800 already had an impact on the church in the Franconian Empire due to the close connection between Christian religion and culture in the early Middle Ages and promoted its renewal. A revised version of the Latin Bible edition was created and the church educational institutions (schools, scriptoria and libraries) promoted, which led to a cultural boom. The imperial church in the Franconian Empire was politically closely linked to the monarchy. Since the Carolingian times, the Franconian kings had to rely on the church to take on secular administrative tasks after the administrative practice of the Merovingian era, which was based on late Roman patterns, collapsed. This tradition was maintained in West and East Franconia until the High Middle Ages. Because of the effective connection between empire and church in the Ottonian and Salier times , older research spoke of an imperial church system in Eastern Franconia. In fact, the Church had also taken on administrative tasks in other Christian empires in Latin Europe. The Christian kings and, above all, the emperors exercised a protective rule over the church and often endeavored to at least formally correspond to the image of a just Christian ideal ruler. Church councils and synods were often convened by secular rulers, precisely to demonstrate the close cooperation between ruler and church. In the middle of the 4th century, Martin von Tours founded the first monastic community in western Europe. The monasticism won the early Middle Ages in the course increasingly important. The monastic rules of Benedict of Nursia became influential . Everyday life in the monasteries was characterized by fixed processes. The monks, largely shielded from the outside world, devoted their lives and work entirely to God, but the monasteries were also an important economic factor, as they had goods and possessions. Monasticism is also to be understood as a corrective to a church that increasingly turned to worldly affairs. The church was hierarchical and had a fairly effective administration. In the early medieval Latin Church, the individual bishops enjoyed far-reaching powers. After the collapse of the Roman administrative order in the west, the episcopal seats were given an important administrative task. Especially in southern Gaul, in Italy and also in Spain, bishops took on political tasks, which led to the establishment of de facto autonomous so-called “episcopal republics”. Piety and worship The spiritual and religious life in Latin Europe was extremely diverse in the early Middle Ages and numerous Christian scholars worked. Examples for the Latin West include: Gregory of Tours and Gregory the Great in the late 6th century, Alkuin , Einhard , Rabanus Maurus and Hinkmar von Reims in the 9th century, and Notker of St. Gallen around 1000. Christian piety was ubiquitous in the early Middle Ages, but expressed itself quite differently and changed from time to time. Belief in a kingdom of God in the hereafter was a common idea, whereby death and the devil should be overcome. Acceptance into the Christian community took place through baptism ; even in late antiquity it had not had this meaning. As a rule, this was preceded by the catechumenate as a training period. In principle, voluntary acceptance was a prerequisite, forced conversion (although in part practiced) was not permitted under canon law and was repeatedly rejected by various popes (such as Gregory the Great). The power of God's omnipotence should be obtained by doing good in the present. God was considered good and just, but he certainly punishes wrongdoing. Misconduct therefore required appropriate penance. The divine service was characterized by fixed rituals which, within the liturgy , had primarily a symbolic meaning. Even though Christianity is a book religion, spoken word worship was very important in the early Middle Ages due to poor reading skills. In addition to the Latin services, there were also vernacular prayers. The Creed and the Lord's Prayer were central and translated into several vernacular languages. In popular piety, superstition, the veneration of saints and relics played an important role. Social work such as caring for the poor was a religious duty. As a result of the armed conflicts, an increasing expectation of peace emerged, the realization of which was hoped for by church measures and which was partially fulfilled ( God's peace movement ). Eschatological ideas of the end of the world did exist, but it is controversial in recent research how strong the end-time expectations were around 1000. Mission and Diversity of Faith During the entire early Middle Ages, the Christianization promoted by the popes , including the German mission, was promoted in the pagan areas of Europe. These included regions where the Germanic religion was practiced in its various forms. This affected areas on the right bank of the Rhine that had not yet been Christianized (such as the settlement areas of the Bavarians and Thuringians in the 6th century, as well as Saxony in northwest Germany), Scandinavia (with the main god Odin and important secondary gods such as Thor and Tyr , see North Germanic religion ) and parts of Britain (see Anglo-Saxon Religion ). There were also cults in the Slavic region, where Perun , Svarog , Svarožić (Dazbog) and Veles represented important deities. In addition to older ancient reports, runic inscriptions and later processing ( Edda ), many of the related reports come from Christian authors. Pagan deities were considered by Christians to be creatures of the devil and demons. As with the pagan Teutons, the Slavs had an important role to play in their worship of nature, and there was also a widespread conception of the afterlife with regard to life after death. The Slavic cults were strongly influenced by Gentile religion, i.e. related to the respective tribal area. The Christianization of previously Pagan areas had an impact on the living conditions there: manslaughter or abandonment of children were made more difficult by the new religious rules, which thus had a mitigating effect; The compulsory welfare work also fundamentally differentiated the Christian faith from the pagan cults, in which charitable measures outside of the families were not common. The missionary work of Ireland by monks, which began in late antiquity, was completed in the 6th century. In the 7th century, the Christianization of the Anglo-Saxons was largely complete, but the invasion of the Vikings in the 9th century meant a setback and sometimes required new missionaries. Ireland, although never part of the Roman Empire itself, took up ancient culture and eventually carried it back to continental Europe. So it is no coincidence that Irish scholars worked in the Frankish Empire during the Carolingian period. Irish monks like Columban also actively participated in Christianization ( Iro-Scottish mission ), even in areas that were still pagan in the former Germania magna . Bonifatius was very active in the right bank of the Rhine in the 8th century and founded the later important Fulda monastery . The Saxons , for whom the Irminsul was an important sanctuary, were not violently Christianized until the bloody Saxon Wars of Charlemagne in the late 8th and early 9th centuries. Around 900 the Elbe formed the border to the pagan area. The Ottonen operated in 10/11. Century an active missionary policy in the Slavic country , but with significant setbacks as the Slavs revolt of 983 was connected. In many regions Christianization in the early Middle Ages was not violent but peaceful, which means that the Christian profession was accepted voluntarily. Furthermore, the forced baptism was very controversial in the church; it was repeatedly rejected by the papal side and was also forbidden by canon law, although according to the same rulings forced baptized people were urged to remain Christians. The Bulgarians and Serbs adopted Christianity in the second half of the 9th century, Kievan Rus was Christianized in the late 10th century, the Poles and (non-Slavic) Hungarians were Christianized around 1000. At the turn of the millennium, Christianization was largely successful in Denmark and Norway. The missionary activity in the north was in the 9./10. Century largely taken over by the Archdiocese of Hamburg-Bremen. The Christianization of these areas usually took place through conversion of the upper class. This process was slow and not always free of tension. Pagan customs persisted in everyday life for a long time. The Christianization of the Slavs, Hungarians and Scandinavians meant a considerable expansion of the Christian cultural area. Byzantine missionaries worked mainly in eastern and south-eastern Europe, where in the 9th century the brothers Methodios and Kyrill were successful in the Slav mission; They also created the basis for Church Slavonic (see Glagolitic script ). In Eastern Europe, Latin and Greek missionaries competed as the jurisdiction of the new Christian territories fell to either Rome or Constantinople. So Serbia and Bulgaria submitted to the Patriarchate of Constantinople. Bulgaria established its own patriarchate in 927, which was demoted to an archbishopric after the Byzantine conquest in the early 11th century. In Byzantium, there were considerable religious tensions between the representatives of the Orthodox Imperial Church and the Nestorians and the Miaphysites within the territory of the empire until the 7th century . Several imperial attempts to solve the problem failed. This religious-political problem was in fact "solved" by the Arab conquest of the Byzantine eastern provinces in the 7th century, because the remaining imperial population (including refugees pouring into Asia Minor) was predominantly of the Orthodox faith. The Christian church in North Africa, which had produced great thinkers such as Augustine of Hippo , increasingly lost its importance and eventually died out. There, from 645 onwards, a denominational survey prepared for Islamization. Maximus Confessor had been polemic against monotheletism , which was often brought with them by refugees from territories conquered by the Arabs, from around 640 AD . In 645 he was able to convince the former patriarch of Constantinople Pyrrhus I of his dyotheletic teaching in a public disputation . Their teachings agreed that Jesus Christ had two natures, namely a divine and a human, but in Constantinople at that time the belief in only one will or goal prevailed, while Carthage and Rome in the work of two separate wills prevailed believed in the person of Christ. The Christian churches in Egypt, Syria and Mesopotamia, on the other hand, retained their importance for a long time (Christian minorities are still present in Egypt and Syria) and the majority of the population under Arab rule remained Christian for a long time. Some Christians were even active as scholars at the court of the caliphs. B. Theophilos of Edessa in the middle of the 8th century . The relatively tolerant Arab rule did not seem to meet with any significant resistance. Followers of the book religions (Christians, Jews and Zoroastrians ) had to pay a special poll tax ( jizya ), were not allowed to practice their beliefs in public and were not allowed to carry weapons, but otherwise remained largely unmolested. In some cases, Christians were required to wear special clothing. At the end of the 7th century, however, the pressure on the Christian majority population increased: In 699, Arabic replaced the previous administrative languages of Greek and Middle Persian in the Caliphate, and Christians were excluded from state positions. Social life was increasingly oriented towards the new faith and there was increased discrimination against non-Muslims. This was due to the respective religious policy of the ruling caliph, which since the late 7th century increased the pressure on the non-Muslim population not insignificantly, interfered in internal Christian affairs and also confiscated church property. Iconoclasm in Byzantium With the reign of the Byzantine Emperor Leo III. and Constantine V are traditionally linked to an important section of Byzantine history, the beginning of the so-called iconoclast that only ended in the middle of the 9th century. Leo is said to have sparked the iconoclasm when he removed the Christ icon above the Chalketor at the imperial palace in 726 and soon after passed a law that allegedly forbade the worship of icons . Various possible motives for this have been discussed in research. The result was an "iconoclasm", combined with the destruction of images of saints and persecution. According to modern research, this description by no means corresponds to reality. Above all, the source situation is extremely problematic, since almost exclusively reports from the ultimately victorious side, the picture friends (icon modules), have been preserved and historically reinterpretations have been made in them. Several of these works polemicize against the militarily successful and by no means unpopular emperors Leo and Constantine (as in Byzantine historical works such as the Chronicle of Theophanes ). But it is not even certain whether Leo III. actually took concrete measures against the veneration of images, because there is no reliable evidence of a legal ban. Constantine V, on the other hand, wrote theological treatises against the veneration of images and convened the Council of Hiereia in 754 , but then hardly took any serious steps. Although Constantine was evidently not a supporter of the worship of images, allegations against him are not made in contemporary, but in the later iconodule sources. Several tough measures against political opponents of the emperor were therefore only retrospectively rewritten as measures against friends of pictures. The controversy over the pictures took place in the middle of the 8th century, but not in the traditional form; It is also not certain that the majority of the population would have rejected iconoclasm. In general, it is questionable whether the iconoclastic dispute in Byzantium had the meaning as suggested by later sources. The second council of Nikaia in 787 allowed the worship of images only within certain limits, the majority of the bishops must have been iconoclastically oriented. In the early 9th century, the iconoclasm flared up again under Leo V (r. 813–820), although the public confession was most important. The background is likely to have been the memory of the military successes of the "iconoclastic emperors", which could not be repeated until then. The new imperial policy was, as apparently before, supported by numerous church leaders and monks. Emperor Michael III. (r. 842–867), however, allowed icons to be worshiped again in 843, thus ending the iconoclastic dispute. General presentations and overview works The New Cambridge Medieval History . Edited by Paul Fouracre et al. Vol. 1–3. Cambridge University Press, Cambridge 1995-2005. (Probably the most comprehensive account of the early Middle Ages with an extensive bibliography.) Arnold Angenendt : The early Middle Ages. Western Christianity from 400 to 900 . Kohlhammer, Stuttgart et al. 1990; 3. Edition. Kohlhammer, Stuttgart / Berlin / Cologne 2001, ISBN 3-17-017225-5 . (Overall presentation with a focus on the history of the church and mentality.) Peter Brown : The Rise of Western Christendom . 2nd, expanded edition. Blackwell, Oxford 2003, ISBN 0-631-22138-7 . (Depiction of the development from late antiquity to the Middle Ages with a focus on Christianity and cultural history.) Roger Collins : Early Medieval Europe 300-1000 . 3rd, revised edition. Palgrave, Basingstoke, et al. a. 2010, ISBN 0-230-00673-6 . (Up-to-date and easily readable presentation with a focus on political history, including religious and cultural history.) - Johannes Fried : The formation of Europe 840-1046 (= Oldenbourg outline of history . Volume 6). 3. Edition. Oldenbourg, Munich 2008. Hans-Werner Goetz : Europe in the early Middle Ages. 500–1050 (= Handbook of the History of Europe. Volume 2). Ulmer, Stuttgart 2003, ISBN 3-8001-2790-3 . (Overview with a focus on structural history.) - Matthew Innes: Introduction to Early Medieval Western Europe, 300-900: The Sword, the Plow and the Book . Routledge, London et al. 2007. - Reinhold Kaiser : The Mediterranean world and Europe in late antiquity and early Middle Ages (= New Fischer World History . Volume 3). S. Fischer, Frankfurt am Main 2014, ISBN 978-3-10-010823-4 . - Franz Neiske: Europe in the early Middle Ages 500-1050: A history of culture and mentality . Primus, Darmstadt 2006. Johannes Preiser-Kapeller : Beyond Rome and Charlemagne. Aspects of the global entanglement in the long late antiquity, 300-800 AD. Mandelbaum Verlag, Vienna 2018. (Global historical overview of the entanglements in the Eurasian and East African region in the context of a “long late antiquity”. Discussions at H-Soz-Kult von Lutz Berger , Stefan Esders and Marcus Bingenheimer .) Friedrich Prinz : From Constantine to Charlemagne. Development and change of Europe . Artemis and Winkler, Düsseldorf / Zurich 2000, ISBN 3-538-07112-8 . (Well-founded and easily legible presentation, which mainly works out the continuities and breaks of late antiquity towards the Middle Ages.) Peter Sarris : Empires of Faith. The Fall of Rome to the Rise of Islam, 500-700. Oxford University Press, Oxford 2011. (On the transition from Late Antiquity to the Early Middle Ages, with a strong focus on political history.) Rudolf Schieffer : Christianization and empire building. Europe 700–1200. CH Beck, Munich 2013, ISBN 978-3-406-65375-9 . (Brief, up-to-date overview work that dates back to the High Middle Ages and focuses on political history.) Chris Wickham : The Inheritance of Rome. A History of Europe from 400 to 1000 . Penguin, London 2009. (Up-to-date and easily legible overview of the early Middle Ages.) Literature on individual subject areas - Kunibert Bering: Art of the early Middle Ages (= art epochs. Volume 2). 2nd Edition. Reclam, Stuttgart 2008, ISBN 978-3-15-018169-0 . Franz Brunhölzl : History of the Latin Literature of the Middle Ages . Wilhelm Fink Verlag, Munich 1975 (Volume 1); Munich 1992 (Volume 2). (Overview of Latin literature from late antiquity to the middle of the 11th century.) Florin Curta : Eastern Europe in the Middle Ages (500-1300). Brill, Leiden / Boston 2019. (Current presentation on Eastern Europe up to the High Middle Ages with a comprehensive bibliography.) Falko Daim (Ed.): Byzanz. Historical and cultural studies manual (= Der Neue Pauly, Supplements. Vol. 11). Metzler, Stuttgart 2016, ISBN 978-3-476-02422-0 . (Current manual on the history of Byzantium.) - Gilbert Dragon, Pierre Riché and André Vauchez (eds.): The history of Christianity. Volume 4: Bishops, Monks and Emperors (642–1054) . Herder, Freiburg (Breisgau) et al. 1994. (Comprehensive presentation of Christianity in the early Middle Ages, including the Eastern churches.) - Stefan Esders , Yaniv Fox, Yitzhak Hen (Eds.): East and West in the Early Middle Ages. The Merovingian Kingdoms in Mediterranean Perspective. Cambridge University Press, Cambridge 2019. Johannes Fried : The way into history. The origins of Germany up to 1024 (= Propylaea history of Germany. Vol. 1). Propylaea, Berlin 1994, ISBN 3-549-05811-X . (Comprehensive and legible, but quite unconventional presentation.) Hugh N. Kennedy : The Prophet and the Age of the Caliphates. The Islamic Near East from the sixth to the eleventh century . 2nd Edition. Pearson Longman, Harlow et al. 2004, ISBN 0-582-40525-4 . (Introduction to Early Islamic History.) Ralph-Johannes Lilie : Byzantium - The second Rome. Siedler, Berlin 2003, ISBN 3-88680-693-6 . (Clearly legible overview of Byzantine history.) Mischa Meier : History of the Great Migration. Europe, Asia and Africa from the 3rd to the 8th centuries. CH Beck, Munich 2019, ISBN 978-3-406-73959-0 . (The current and most comprehensive presentation of the Great Migration Period.) - Lutz E. von Padberg : The Christianization of Europe in the Middle Ages . 2nd Edition. Reclam, Stuttgart 2009, ISBN 3-15-017015-X . - Walter Pohl (ed.): The search for the origins - From the importance of the early Middle Ages (= research on the history of the Middle Ages, Volume 8). Austrian Academy of Sciences, Vienna 2004, ISBN 3-7001-3296-4 . Reinhard Schneider : The Franconian Empire (= Oldenbourg outline of history, volume 5). 4th edition. Oldenbourg, Munich 2001. (Concise presentation with research overview and comprehensive bibliography) - Klaus von See (ed.), Peter Foote (co-author): European early Middle Ages . In: Klaus von See (ed.): New handbook of literary studies. Vol. 6. Aula-Verlag, Wiesbaden 1985, ISBN 3-89104-054-7 . - Juliet MH Smith: Europe after Rome. A New Cultural History 500-1000 . Oxford University Press, Oxford 2005. (Problem-oriented cultural history overview.) - Christoph Stiegemann u. a. (Ed.): CREDO. Christianization of Europe in the Middle Ages. 2 volumes, Michael Imhof Verlag, Petersberg 2013. (Catalog and volume of essays in which the Christianization of Europe is comprehensively described.) Chris Wickham : Framing the Early Middle Ages. Europe and the Mediterranean, 400-800. Oxford University Press, Oxford 2005. (Basic economic and social history presentation.) - Hermann Kulke: Is there an Indian Middle Ages? In: Saeculum 33, 1982, pp. 221-239. - Kai Vogelsang: History of China. 3rd, reviewed and updated edition, Stuttgart 2013, pp. 171 ff. - The Cambridge History of Japan. Volume 3. Ed. By Kozo Yamamura. Cambridge 1990. - Cf. with further references: Alfred Haverkamp : Perspektiven des Mittelalters . In: Gebhardt. Handbook of German History . Vol. 1. 10., completely revised edition, Stuttgart 2004, pp. 1–137, here: pp. 31 ff. - See in detail Paul Fouracre (Ed.): The New Cambridge Medieval History : Volume 1, c. 500-c. 700 . Cambridge 2005. - For example in Roger Collins: Early Medieval Europe 300–1000. 3rd edition, Basingstoke et al. 2010; Friedrich Prinz: From Constantine to Charlemagne . Düsseldorf / Zurich 2000; Chris Wickham: The Inheritance of Rome: A History of Europe from 400 to 1000 . London 2009. - On the character of the transition period, see the detailed articles in Theo Kölzer , Rudolf Schieffer (Ed.): From Spätantike zum early Mittelalter: Continuities and breaks, conceptions and findings. Stuttgart 2009, and the summary presentation by Hans-Werner Goetz: Europe in the early Middle Ages. 500-1050. Stuttgart 2003, pp. 280-284. - See for an overview the review article by Roger Collins: Making Sense of the Early Middle Ages . In: English Historical Review 124, 2009, pp. 641-665. In it, Collins criticizes some of the recent research trends and emphasizes what he believes is narrative form, including political history, that is still necessary. - See, among others, Mark Humphries: Late Antiquity and World History. Challenging Conventional Narratives and Analyzes. In: Studies in Late Antiquity 1, 2017, pp. 8–37; Mischa Meier: Late antiquity, redefined in terms of time and space. An interim balance of current searches. In: Historische Zeitschrift 304, 2017, pp. 686–706; Johannes Preiser-Kapeller: Beyond Rome and Charlemagne. Aspects of global interdependence in the long period of late antiquity, 300-800 AD Vienna 2018. - See for example Arnaldo Marcone: A long late antiquity? Considerations on a controversial periodization . In: Journal of Late Antiquity 1, 2008, pp. 4-19. - See for example Erik Hermans (Ed.): A Companion to the Global Early Middle Ages. Leeds 2020; Johannes Preiser-Kapeller: Beyond Rome and Charlemagne. Aspects of global interdependence in the long period of late antiquity, 300-800 AD Vienna 2018. - Alfred Haverkamp: Perspectives of the Middle Ages . In: Gebhardt. Handbook of German History. Volume 1. Stuttgart 2004, p. 45. - See The New Cambridge Medieval History Vol. 1-3. Cambridge 1995-2005; Roger Collins: Early Medieval Europe 300-1000. 3rd edition, Basingstoke et al. a. 2010; Hans-Werner Goetz: Europe in the early Middle Ages. 500-1050. Stuttgart 2003; Chris Wickham: The Inheritance of Rome. A History of Europe from 400 to 1000. London 2009; Theodor Schieder (Hrsg.): Handbook of European history. Vol. 1. Stuttgart 1976. - For a first orientation, refer to The Oxford Dictionary of Late Antiquity . The presentation by Arnold Hugh Martin Jones : The Later Roman Empire 284–602 is fundamental . A Social, Economic and Administrative Survey. 3 vols., Oxford 1964 (reprinted in two volumes, Baltimore 1986). Recent overview presentations: Douglas Boin: A Social and Cultural History of Late Antiquity. Hoboken (NJ) 2018; Alexander Demandt : The late antiquity. Handbook of Classical Studies III.6 . 2nd edition, Munich 2007; Hugh Elton: The Roman Empire in Late Antiquity. A Political and Military History. Cambridge 2018; Scott Fitzgerald Johnson (Ed.): The Oxford Handbook of Late Antiquity . Oxford et al. a. 2012; Reinhold Kaiser : The Mediterranean World and Europe in Late Antiquity and the Early Middle Ages. Frankfurt am Main 2014; AD Lee: From Rome to Byzantium Ad 363 to 565: The Transformation of Ancient Rome. Edinburgh 2013; Stephen Mitchell: A History of the Later Roman Empire. AD 284-641. 2nd ed., Oxford u. a. 2015; Rene Pfeilschifter: Late Antiquity. The one God and the many rulers. Munich 2014; Johannes Preiser-Kapeller: Beyond Rome and Charlemagne. Aspects of global interdependence in the long late antiquity, 300-800 AD Vienna 2018; Philip Rousseau (Ed.): A Companion to Late Antiquity. Malden (Massachusetts) et al. a. 2009; Cambridge Ancient History , 2nd Edition, Cambridge 1997-2005, Volumes 12-14. - Current overview for the development in the 4th century with Alan Cameron : The Last Pagans of Rome. Oxford / New York 2011, which relativizes the importance of pagan cults for the late 4th century. - Review of modern research in The Oxford Dictionary of Late Antiquity and Scott Fitzgerald Johnson (Ed.): The Oxford Handbook of Late Antiquity. Oxford et al. a. 2012; Philip Rousseau (Ed.): A Companion to Late Antiquity . Malden (Massachusetts) et al. a. 2009. - Overview in Scott McGill, Edward Watts (Ed.): A Companion to Late Antique Literature. Hoboken, NJ 2018. - The detailed overview by Arnold Hugh Martin Jones: The Later Roman Empire is fundamental . In summary, Stephen Mitchell: A History of the Later Roman Empire. AD 284-641. 2nd ed., Oxford u. a. 2015, p. 165 ff. - See AHM Jones: The Later Roman Empire. 2 vols. Baltimore 1986, p. 1057. - On the Sāsānidenreich see now Michael Bonner: The Last Empire of Iran. Piscataway 2020 and cf. introductory Touraj Daryaee: Sasanian Iran 224–651 CE. Portrait of a Late Antique Empire. Costa Mesa (Calif.) 2008; Touraj Daryaee: Sasanian Persia. The Rise and Fall of an Empire. London 2009; Khodadad Rezakhani: ReOrienting the Sasanians. East Iran in Late Antiquity. Edinburgh 2017; Eberhard Sauer (Ed.): Sasanian Persia. Between Rome and the Steppes of Eurasia. Edinburgh 2017; Klaus Schippmann : Basic features of the history of the Sassanid Empire. Darmstadt 1990; Josef Wiesehöfer: The Late Sasanian Near East. In: Chase Robinson (Ed.): The New Cambridge History of Islam. Vol. 1. Cambridge 2010, pp. 98-152. - Wolfgang Kuhoff : The temptation of power. Late Roman army masters and their potential reach for the empire . In: Silvia Serena Tschopp, Wolfgang EJ Weber (Hrsg.): Power and communication . Berlin 2012, pp. 39-80; Anne Poguntke: The Roman army master's office in the 5th century. Reflections on the relationship between emperor and army master in East and West. In: Carola Föller, Fabian Schulz (eds.): East and West 400-600 AD. Communication, cooperation and conflict. Stuttgart 2016, pp. 239–262. - The most comprehensive presentation based on current research is provided by Mischa Meier : Geschichte der Völkerwanderung. Europe, Asia and Africa from the 3rd to the 8th centuries. Munich 2019. Also see Guy Halsall: Barbarian Migrations and the Roman West, 376-568. Cambridge 2007; Walter Pohl : The Great Migration. 2nd edition, Stuttgart a. a. 2005; Peter J. Heather : Empires and Barbarians: Migration, Development and the Birth of Europe. London 2009; Verena Postel : The origins of Europe. Migration and Integration in the Early Middle Ages. Stuttgart 2004; Herwig Wolfram : The Roman Empire and its Germanic Peoples: A narrative of origin and arrival. Vienna / Cologne / Weimar 2018. The exhibition catalog Rome and the Barbarians is richly illustrated and equipped with numerous (brief) specialist articles . Europe at the time of the Great Migration. Munich 2008. - See Henning Börm : Westrom. From Honorius to Justinian. Stuttgart 2013 (2nd edition 2018). - Cf. with further literature: Gerd Kampers: Geschichte der Westgoten . Paderborn 2008; Roger Collins: Visigothic Spain 409-711. Oxford 2004. - summary Peter J. Heather: Why Did the Barbarian Cross the Rhine? In: Journal of Late Antiquity 2, 2009, pp. 3-29. Occasionally, a date of 405/06 is also suggested, but this raises additional problems. - Reinhold Kaiser: The Burgundy. Stuttgart u. a. 2004. - Helmut Castritius : The Vandals. Stuttgart et al. 2007; Andy Merrills, Richard Miles: The Vandals. Oxford / Malden, MA 2010; Roland Steinacher: The vandals. The rise and fall of a barbarian empire. Stuttgart 2016; Konrad Vössing : The Kingdom of the Vandals. Darmstadt 2014. - See generally Herwig Wolfram : Die Goten. 4th edition, Munich 2001. - On Attila cf. (each with further literature) Michael Maas (Ed.): The Cambridge Companion to the Age of Attila. Cambridge 2014; Klaus Rosen : Attila. The horror of the world. Munich 2016; Timo Stickler : The Huns. Munich 2007. - On the history of the late antique Alpine and Danube regions cf. also Roland Steinacher: Rome and the barbarians. Peoples in the Alpine and Danube region (300–600). Stuttgart 2017. - For the process of the dissolution of the Western Roman Empire see Henning Börm: Westrom. From Honorius to Justinian . Stuttgart 2018; Peter J. Heather : The Fall of the Roman Empire. London u. a. 2005; Dirk Henning: Periclitans res Publica. Empire and elites in the crisis of the Western Roman Empire 454 / 5–493. Stuttgart 1999. - Roland Steinacher: Migration of the Barbarians? On the origin and meaning of the epoch term 'migration of peoples' up to the 19th century. In: Felix Wiedemann, Kerstin P. Hofmann, Hans-Joachim Gehrke (eds.): From the wandering of the peoples. Migration narratives in ancient studies. Berlin 2017, pp. 67–95. - Michael Kulikowski: Barbaric Identity. Current research and new interpretive approaches. In: Michaela Konrad, Christian Witschel (eds.): Roman legionary camps in the Rhine and Danube provinces - nuclei of late antiquity and early medieval life? Munich 2011, pp. 103–111. - On this process of change see for example Thomas FX Noble (Ed.): From Roman Provinces to Medieval Kingdoms . London / New York 2006. For the development after 476, see also Peter J. Heather: The Restoration of Rome: Barbarian Popes and Imperial Pretenders. London 2013. - Friedrich Prinz: From Constantine to Charlemagne. Düsseldorf / Zurich 2000, p. 251 ff. - Current overview by Michael Bonner: The Last Empire of Iran. Piscataway 2020. For mutual relationships, see Henning Börm : Prokop and the Persians. Investigations into the Roman-Sasanid contacts in late antiquity. Stuttgart 2007; Matthew P. Canepa: The Two Eyes of the Earth. Art and Ritual of Kingship between Rome and Sasanian Iran. Berkeley 2009; Engelbert Winter , Beate Dignas: Rome and the Persian Empire. Two world powers between confrontation and coexistence. Berlin 2001. - For Justinian see now Hartmut Leppin : Justinian. The Christian experiment . Stuttgart 2011; Michael Maas (Ed.): The Cambridge Companion to the Age of Justinian . Cambridge 2005. See also Peter Heather: Rome Resurgent. War and Empire in the Age of Justinian. Oxford 2018. - Geoffrey B. Greatrex , Samuel NC Lieu: The Roman Eastern Frontier and the Persian Wars. Part II AD 363-630. A narrative sourcebook . London / New York 2002, p. 142 ff. - Geoffrey B. Greatrex, Samuel NC Lieu: The Roman Eastern Frontier and the Persian Wars. Part II AD 363-630. A narrative sourcebook . London / New York 2002, p. 182 ff. See also James Howard-Johnston : Witnesses to a World Crisis. Historians and Histories of the Middle East in the Seventh Century . Oxford 2010; Peter Sarris: Empires of Faith . Oxford 2011, p. 242 ff. - On Herakleios see Walter E. Kaegi: Heraclius - Emperor of Byzantium . Cambridge 2003; Gerrit Jan Reinink, Bernard H. Stolte (eds.): The Reign of Heraclius (610-641). Crisis and Confrontation . Leuven 2002. - The dating 638 seems more sensible than the older one (636 or 637); see. James Howard-Johnston: Witnesses to a World Crisis . Oxford 2010, p. 116 f. - Generally see with further literature Hugh Kennedy: The Great Arab Conquests . Philadelphia 2007. See also James Howard-Johnston: Witnesses to a World Crisis . Oxford 2010. - Ekkehard Eickhoff : Sea War and Sea Politics between Islam and the West. Berlin 1966. - Marek Jankowiak: The first Arab siege of Constantinople. In: Travaux et Mémoires du Center de Recherche d'Histoire et Civilization de Byzance. Vol. 17. Paris 2013, pp. 237-320. - James Howard-Johnston: Witnesses to a World Crisis . Oxford 2010, p. 226 f. - Franz Georg Maier : The Metamorphosis of the Mediterranean World still offers a good overview of the development from the 6th to the early 8th century . Frankfurt am Main 1968, p. 172 ff. See also Ernst Pitz : The Greco-Roman Ecumenism and the Three Cultures of the Middle Ages . Berlin 2001, p. 305 ff. Current overview, for example at: Roger Collins: Early Medieval Europe 300–1000. 3rd edition, Basingstoke et al. 2010, pp. 114 ff .; Reinhold Kaiser: The Mediterranean World and Europe in Late Antiquity and the Early Middle Ages. Frankfurt am Main 2014; Peter Sarris: Empires of Faith . Oxford 2011, p. 125 ff .; Chris Wickham: The Inheritance of Rome . London 2009, pp. 111-202 and pp. 255-297. - See James Howard-Johnston: Witnesses to a World Crisis. Historians and Histories of the Middle East in the Seventh Century. Oxford 2010, p. 488ff. - Basically John Haldon: Byzantium in the Seventh Century. The Transformation of a Culture . 2nd edition, Cambridge 1997. See also John F. Haldon: The Empire That Would Not Die. The Paradox of Eastern Roman Survival, 640-740. Cambridge (Massachusetts) 2016; Mischa Meier : Eastern Byzantium, Late Antiquity-Middle Ages. Reflections on the “end” of antiquity in the east of the Roman Empire. In: Millennium 9, 2012, pp. 187-253. - General overview up to the early Carolingians in Friedrich Prinz: European foundations of German history (4th – 8th centuries). Gebhardt. Handbook of German History. Vol. 1. 10. completely revised edition. Stuttgart 2004, p. 147–616, here: p. 286 ff. For Franconian early history see Ulrich Nonn: Die Franken . Stuttgart 2010 and Erich Zöllner : History of the Franks up to the middle of the sixth century . Munich 1970. See also the various articles in Alfried Wieczorek, Patrick Périn, Karin von Welck, Wilfried Menghin (eds.): Die Franken. Pioneer of Europe. 5th to 8th centuries. 2 volumes. Mainz 1996 (1997). - Eugen Ewig: The Merovingians and the Franconian Empire . 5th edition, Stuttgart 2006; Ian N. Wood: The Merovingian Kingdoms . London 1994; Sebastian Scholz : The Merovingians. Stuttgart 2015. See also the articles in Stefan Esders u. a. (Ed.): The Merovingian Kingdoms and the Mediterranean World. Revisiting the Sources. London u. a. 2019; Stefan Esders u. a. (Ed.): East and West in the Early Middle Ages. The Merovingian Kingdoms in Mediterranean Perspective. Cambridge 2019. - good current overview from Matthias Becher : Clovis I. The Rise of the Merovingians and the End of the Ancient World . Munich 2011; Mischa Meier , Steffen Patzold (Ed.): Chlodwigs Welt. Organization of rule around 500th Stuttgart 2014. - For the following see Eugen Ewig: The Merovingians and the Franconian Empire . 5th edition, Stuttgart 2006, p. 31ff .; Ian N. Wood: The Merovingian Kingdoms . London 1994, pp. 88ff .; Sebastian Scholz: The Merovingians. Stuttgart 2015, p. 35ff. - See also Karl Friedrich Stroheker : The senatorial nobility in late antique Gaul. Tübingen 1948 (ND Darmstadt 1970). - See Andrew Gillett: Telling Off Justinian: Theudebert I, the Epistolae Austrasicae, and Communication Strategies in Sixth-Century Merovingian – Byzantine Relations. In: Early Medieval Europe . Volume 27, 2019, pp. 161-194. - Gerhard Dilcher, Eva-Marie Distler (ed.): Leges - Gentes - Regna: On the role of Germanic legal habits and Latin writing tradition in the development of the early medieval legal culture. Berlin 2006. - On regional centrifugal forces, cf. Patrick J. Geary: The Merovingians: Europe before Charlemagne. Munich 2003, p. 157 ff. - On Dagobert's reign see Sebastian Scholz: The Merowinger. Stuttgart 2015, p. 204 ff. - Annales regni Francorum , anno 749; Einhard: Vita Karoli Magni. cap. 1 f. - So z. B. Johannes Fried: The Middle Ages. History and culture . Munich 2008, p. 53. - At this time see introductory Andreas Fischer: Karl Martell. The beginning of Carolingian rule. Stuttgart 2012. - On these see John Hines, Nelleke IJssennager (ed.): Frisians and their North Sea Neighbors. From the Fifth Century to the Viking Age. Woodbridge 2017. - For the time from Pippin the Younger see Pierre Riché : Die Karolinger. One family makes Europe. Stuttgart 1987, p. 87 ff .; Rudolf Schieffer: The Carolingians . 4th edition, Stuttgart 2006, p. 50 ff. In general, see also Jörg W. Busch: Die Herrschaft der Karolinger 714–911. Munich 2011; Rudolf Schieffer: The time of the Carolingian empire (714-887). Stuttgart 2005. - See introductory Johannes Fried: Karl der Grosse. Munich 2013; Dieter Hägermann : Charlemagne. Ruler of the west . Berlin 2000; Wilfried Hartmann : Charlemagne . Stuttgart 2010; Rosamond McKitterick : Charlemagne. The Formation of a European Identity . Cambridge 2008 (German Charlemagne , Darmstadt 2008); Stefan Weinfurter : Charlemagne. The holy barbarian. Munich 2013. - Current overview from Matthias Becher: The empire of Charlemagne between reconsideration and innovation. In: Hartmut Leppin, Bernd Schneidmüller , Stefan Weinfurter (eds.): Empire in the first millennium. Regensburg 2012, pp. 251-270. Cf. also Jörg W. Busch: The Lords of the Carolingians 714-911. Munich 2011, p. 79 ff. - Egon Boshof : Ludwig the Pious . Darmstadt 1996; Mayke de Jong: The Penitential State. Authority and Atonement in the Age of Louis the Pious, 814-840 . Cambridge 2009. - Egon Boshof: Ludwig the Pious . Darmstadt 1996, p. 108 ff. - See for example Johannes Fried: The way in the story. The origins of Germany up to 1024. Berlin 1994, p. 366 ff .; Pierre Riché: The Carolingians. One family makes Europe. Stuttgart 1987, pp. 195 ff .; Rudolf Schieffer: The time of the Carolingian empire (714-887). Stuttgart 2005, p. 136 ff .; Rudolf Schieffer: The Carolingians. 4th edition, Stuttgart 2006, p. 139 ff. - On the rebellion against Ludwig see Egon Boshof: Ludwig der Fromme . Darmstadt 1996, p. 182 ff. - On Ludwig see Eric J. Goldberg: Struggle for Empire. Kingship and Conflict under Louis the German. 817-876 . Ithaca 2006; Wilfried Hartmann: Ludwig the German . Darmstadt 2002. - At this time see also Carlrichard Brühl : The birth of two peoples. Germans and French (9th-11th centuries) . Cologne et al. 2001, p. 115 ff. Carlrichard Brühl: Germany - France is much more detailed on the development of the two Franconian sub-kingdoms after 843 . The birth of two peoples . 2nd edition, Cologne / Vienna 1995. - Cf. Carlrichard Brühl: The birth of two peoples. Cologne et al. 2001, p. 69 ff. - See Simon MacLean, Kingship and Politics in the Late Ninth Century: Charles the Fat and the End of the Carolingian Empire . Cambridge 2003, especially p. 123 ff. - On Arnolf see Franz Fuchs, Peter Schmid (ed.): Kaiser Arnolf. The East Franconian Empire at the end of the 9th century . Munich 2002. - For the following in general see Gerd Althoff: Die Ottonen. Royal rule without a state . 2nd edition, Stuttgart et al. 2005; Helmut Beumann : The Ottonians . 5th edition Stuttgart u. a. 2000; Gerd Althoff, Hagen Keller: Late Antiquity to the End of the Middle Ages. The time of the late Carolingians and Ottonians. Crises and Consolidations 888–1024. Stuttgart 2008. - On the classification of Ottonian history in general Hagen Keller, Gerd Althoff: The time of the late Carolingians and the Ottonians . Stuttgart 2008, p. 18 ff. - For the different research approaches see Joachim Ehlers: The emergence of the German Empire . 4th edition, Munich 2012; see. generally also Johannes Fried: The way into history . Berlin 1994, especially p. 9 ff. And p. 853 ff. Carlrichard Brühl is fundamental: Germany - France. The birth of two peoples . 2nd edition Cologne / Vienna 1995. - general on Heinrich's reign, see now Wolfgang Giese : Heinrich I. Founder of Ottonian rule . Darmstadt 2008. - Gerd Althoff: Amicitiae and pacta. Alliance, unification, politics and prayer commemoration in the early 10th century. Hanover 1992. - In addition to the general literature on the Ottonians mentioned, see Matthias Becher: Otto der Große. Emperor and Empire . Munich 2012; Johannes Laudage : Otto the Great (912–973). A biography . Regensburg 2001. - Johannes Laudage: Otto the Great . Regensburg 2001, p. 110 ff. - On this aspect, see Hartmut Leppin , Bernd Schneidmüller , Stefan Weinfurter (eds.): Kaisertum in the first millennium. Regensburg 2012. - Hagen Keller: The "legacy" of Otto the Great . In: Frühmittelalterliche Studien 41, 2007, pp. 43–72, especially pp. 62 ff. - See in summary Hagen Keller, Gerd Althoff: The time of the late Carolingians and the Ottonians. Stuttgart 2008, p. 239 ff. - General overview in Hagen Keller, Gerd Althoff: The time of the late Carolingians and the Ottonians . Stuttgart 2008, p. 273 ff. See also Gerd Althoff: Otto III. Darmstadt 1997; Ekkehard Eickhoff : Theophanu and the King. Otto III. and his world. Stuttgart 1996; Ekkehard Eickhoff: Emperor Otto III. The first millennium and the development of Europe. 2nd edition, Stuttgart 2000. - Gerd Althoff: Otto III. Darmstadt 1997, p. 100 ff. - Cf. for example Hagen Keller, Gerd Althoff: The time of the late Carolingians and the Ottonians . Stuttgart 2008, p. 292 ff. (With further evidence); Knut Görich: Otto III. Romanus Saxonicus et Italicus: Imperial Rome politics and Saxon historiography. Sigmaringen 1995, p. 267 ff. - Cf. Ekkehard Eickhoff: Kaiser Otto III. The first millennium and the development of Europe. 2nd edition Stuttgart 2000, pp. 271-273. - Stefan Weinfurter: Heinrich II. (1002-1024). Rulers at the end of time. 3rd edition, Regensburg 2002. - Knut Görich: A turning point in the east: Heinrich II. And Boleslaw Chrobry . In: Bernd Schneidmüller, Stefan Weinfurter (Ed.): Otto III. - Heinrich II. A turning point? . Sigmaringen 1997, pp. 95-167. - Johannes Fried: The way into history. Berlin 1994, p. 630 f. - general on the history of France at this time, see Bernd Schneidmüller: The emergence of France. In: Ernst Hinrichs (Ed.): History of France. Stuttgart 2014, p. 13 ff .; Jean Dunbabin: West Francia: The Kingdom. In: Timothy Reuter (Ed.): The New Cambridge Medieval History. Volume 3. Cambridge 1999, p. 372 ff .; Rolf Große: From the Franconian Empire to the origins of the nation states 800 to 1214. Darmstadt 2005 (each with further literature). - Joachim Ehlers: History of France in the Middle Ages. Stuttgart et al. 1987; Joachim Ehlers: The Capetians. Stuttgart et al. 2000. - Constance Brittain Bouchard: Burgundy and Provence. In: Timothy Reuter (Ed.): The New Cambridge Medieval History. Volume 3. Cambridge 1999, p. 328 ff. - Carlrichard Brühl: Germany - France. The birth of two peoples . 2nd edition, Cologne / Vienna 1995, p. 454 ff. - On Theoderich see now up-to-date and in detail Hans-Ulrich Wiemer : Theoderich der Große. King of the Goths, ruler of the Romans. Munich 2018. Cf. also Frank M. Anbüttel: Theoderich der Große. Darmstadt 2004; Wilhelm Enßlin : Theodoric the Great. 2nd Edition. Munich 1959. For the sources and their evaluation see Andreas Goltz: Barbar - König - Tyrann. The image of Theodoric the Great in tradition from the 5th to 9th centuries. Berlin / New York 2008. - Marco Aimone this question: Romani e Ostrogoti fra integrazione e separazione. Il contributo dell'archeologia a un dibattito storiografico . In: Reti Medievali Rivista 13, 2012, pp. 1-66, for the first time based on archaeological research. - General overview of the history of Italy in the Middle Ages with further literature from Elke Goez : History of Italy in the Middle Ages . Darmstadt 2010. On the Lombards see, among others, Roger Collins: Early Medieval Europe 300–1000. 3rd ed., Basingstoke et al. a. 2010, p. 198 ff .; Peter Erhart, Walter Pohl (ed.): The Longobards: Rule and identity . Vienna 2005; Wilfried Menghin : The Lombards . Stuttgart 1985. On early medieval Italy see, among others: Cristina La Rocca (Ed.): Italy in the Early Middle Ages: 476–1000. Oxford 2002; Chris Wickham: Early Medieval Italy. Central Power and Local Society 400-1000 . London / Basingstoke 1981; Giovanni Tabacco: Sperimentazioni del potere nell'alto medioevo . Turin 1993. - On this process see Chris Wickham: Early Medieval Italy . London / Basingstoke 1981, p. 174 ff. - Elke Goez: History of Italy in the Middle Ages . Darmstadt 2010, p. 76 f. - Elke Goez: History of Italy in the Middle Ages . Darmstadt 2010, p. 71 f. - Elke Goez: History of Italy in the Middle Ages . Darmstadt 2010, p. 91 ff. - general on the Visigothic Empire from the 6th century, see Gerd Kampers: History of the Visigoths . Paderborn 2008, pp. 140 ff .; Roger Collins: Visigothic Spain 409-711 . Oxford 2004, p. 38 ff. Cf. also Manuel Koch: Ethnic Identity in the Development Process of the Spanish Visigoth Empire . Berlin / Boston 2012. - Gerd Kampers: History of the Visigoths. Paderborn 2008, p. 173 ff. - Gerd Kampers: History of the Visigoths . Paderborn 2008, p. 188 ff. - Gerd Kampers: History of the Visigoths . Paderborn 2008, p. 222 ff. - Especially on Spain in the early Middle Ages, see Roger Collins: Caliphs and Kings: Spain, 796-1031. Chichester et al. a. 2012. General overview, for example from Klaus Herbers : History of Spain in the Middle Ages . Stuttgart 2006; Ludwig Vones : History of the Iberian Peninsula in the Middle Ages (711-1480) . Sigmaringen 1993 (each with further literature). - Nikolaus Jaspert: The Reconquista. Munich 2019. - On Islamic Spain cf. currently about Brian A. Catlos: Kingdoms of Faith. A New History of Islamic Spain. New York 2018. - Roger Collins: Caliphs and Kings: Spain, 796-1031. Chichester et al. a. 2012, p. 50 ff. And p. 138 ff. - To the Christian empires summarizing Klaus Herbers: History of Spain in the Middle Ages . Stuttgart 2006, p. 102 ff. - See Darío Fernández-Morera: The Myth of the Andalusian Paradise . In: The Intercollegiate Review 41, 2006, pp. 23-31. - For a summary of the situation of Christians in Islamic Spain, see Roger Collins: Caliphs and Kings: Spain, 796-1031. Chichester et al. a. 2012, pp. 83-103. - Cf. in summary Evangelos Chrysos: The Roman rule in Britain and its end. In: Bonner Jahrbücher 191 (1991), pp. 247-276. - See Peter Salway: A History of Roman Britain. Oxford 2001, p. 323ff. - See David Dumville: Sub-Roman Britain: History and Legend. In: History 62, 1977, pp. 173-192. For general information on the Anglo-Saxons, see: Michael Lapidge, John Blair, Simon Keynes, Donald Scragg (Eds.): The Blackwell Encyclopaedia of Anglo-Saxon England. 2nd edition Chichester 2014; James Campbell (Ed.): The Anglo-Saxons . Oxford 1982 (several NDe); Roger Collins: Early Medieval Europe 300-1000. 3rd ed., Basingstoke et al. a. 2010, p. 173ff .; Nicholas J. Higham, Martin J. Ryan: The Anglo-Saxon World. New Haven 2013 [quite comprehensive current overview]; Harald Kleinschmidt: The Anglo-Saxons . Munich 2011 [brief introduction]; Henrietta Leyser: A Short History of the Anglo-Saxons. London / New York 2017 [current introduction]. Frank M. Stenton: Anglo-Saxon England . 3rd edition Oxford 1971 [important older, but partly outdated representation]. - Nicholas J. Higham, Martin J. Ryan: The Anglo-Saxon World. New Haven 2013, pp. 103ff. - Roger Collins: Early Medieval Europe 300-1000. 3rd ed., Basingstoke et al. a. 2010, p. 176. - Current overview in Nicholas J. Higham, Martin J. Ryan: The Anglo-Saxon World. New Haven 2013, p. 126 ff. - Roger Collins: Early Medieval Europe 300-1000 . 3rd ed., Basingstoke et al. a. 2010, p. 177. - Peter Sarris: Empires of Faith . Oxford 2011, pp. 361f. - See Nicholas J. Higham, Martin J. Ryan: The Anglo-Saxon World. New Haven 2013, pp. 179ff .; Henrietta Leyser: A Short History of the Anglo-Saxons. London / New York 2017, pp. 71ff. - General overview in Simon Keynes: England, 700–900 . In: Rosamond McKitterick (Ed.): New Cambridge Medieval History . Volume 2. Cambridge 1995, pp. 18-42; Barbara Yorke: Kings and Kingdoms of early Anglo-Saxon England . London / New York 1990. - For the history of Wessex during this period, see Barbara Yorke: Wessex in the Early Middle Ages. London / New York 1995, p. 94 ff. - James Campbell (Ed.): The Anglo-Saxons . Oxford 1982, p. 61. - Current overview in Nicholas J. Higham, Martin J. Ryan: The Anglo-Saxon World. New Haven 2013, p. 232ff. and with Henrietta Leyser: A Short History of the Anglo-Saxons. London / New York 2017, pp. 93ff. See also James Campbell (ed.): The Anglo-Saxons . Oxford 1982, pp. 132ff .; Roger Collins: Early Medieval Europe 300-1000. 3rd ed., Basingstoke et al. a. 2010, p. 359 ff. - Richard Abels: Alfred the Great . London 1998. - See James Campbell (Ed.): The Anglo-Saxons . Oxford et al. a. 1982, p. 192 ff. - Timothy Bolton: Cnut the Great. New Haven 2017. - Jörg Peltzer : 1066. The fight for England's crown. Munich 2016. - Comprehensive description by Alex Woolf: From Pictland to Alba 789-1070 . Edinburgh 2007. For a summary, see Andrew DM Barrell: Medieval Scotland . Cambridge 2000, pp. 1-15. - Dáibhí Ó Cróinín (Ed.): A New History of Ireland provides a comprehensive account of the history of Ireland up to the 12th century . Volume 1. Oxford et al. a. 2005. Also see Clare Downham: Medieval Ireland. Cambridge 2018; Seán Duffy (Ed.): Medieval Ireland: An Encyclopedia. London / New York 2005; Michael Richter: Ireland in the Middle Ages. Münster u. a. 2003 (ND). - Alheydis Plassmann : Origo gentis. Establishing identity and legitimacy in early and high medieval narratives of origin . Berlin 2006. - introduction see Lotte Hedeager: Scandinavia . In: Paul Fouracre (Ed.): New Cambridge Medieval History . Volume 1. Cambridge 2005, pp. 496-523; Bjørn Myhre: The Iron Age . In: Knut Helle (Ed.): The Cambridge History of Scandinavia . Volume 1. Cambridge 2003, pp. 60–93, here p. 83 ff. - Cf. Carsten Jahnke: History of Denmark. Ditzingen 2017, p. 29f. - introduction see for example Robert Ferguson: The Hammer and the Cross. A New History of the Vikings. London 2009; Gwyn Jones : A History of the Vikings. 2nd edition Oxford 1984 (several NDs); F. Donald Logan: The Vikings in History. 2nd edition, London / New York 1991; Birgit Sawyer, Peter Sawyer: The world of the Vikings. The Germans and the European Middle Ages. Berlin 2002; Peter Sawyer (Ed.): The Vikings. History and culture of a seafaring people . Stuttgart 2000 (several NDe); Not so Winroth: The Age of the Vikings. Princeton 2014. - Wladyslaw Duczko: Viking Rus. Studies on the Presence of Scandinavians in Eastern Europe. Leiden / Boston 2004. - Overview in Niels Lund: Scandinavia, c. 700-1066 . In: Rosamond McKitterick (Ed.): New Cambridge Medieval History . Volume 2. Cambridge 1995, pp. 202-227; Birgit Sawyer, Peter Sawyer: The world of the Vikings . Berlin 2002. - For the history of the Swedish kings in the Middle Ages, cf. about Jörg-Peter Findeisen : The Swedish Monarchy. Volume 1. Kiel 2010, p. 61ff. - Niels Lund: Scandinavia, c. 700-1066 . In: Rosamond McKitterick (Ed.): New Cambridge Medieval History . Volume 2. Cambridge 1995, here p. 220. - Birgit Sawyer, Peter Sawyer: Die Welt der Wikinger . Berlin 2002, p. 186 f. - On Knut, see Timothy Bolton: Cnut the Great. New Haven 2017. - Niels Lund: Scandinavia, c. 700-1066 . In: Rosamond McKitterick (Ed.): New Cambridge Medieval History . Volume 2. Cambridge 1995, here p. 226. - Birgit Sawyer, Peter Sawyer: Die Welt der Wikinger . Berlin 2002, p. 78. - Birgit Sawyer, Peter Sawyer: Die Welt der Wikinger . Berlin 2002, p. 120 ff. - Carsten Jahnke: History of Denmark. Ditzingen 2017, p. 28ff. - Birgit Sawyer, Peter Sawyer: Die Welt der Wikinger . Berlin 2002, p. 171 ff. - Timothy Bolton: Cnut the Great. New Haven 2017. See also Timothy Bolton: The Empire of Cnut the Great . Leiden 2009, p. 9 ff. - Timothy Bolton: The Empire of Cnut the Great . Leiden 2009, p. 155 f. - Fritz Mitthof, Peter Schreiner, Oliver Jens Schmitt (eds.): Handbuch zur Geschichte Südosteuropas is now fundamental . Volume 1: Rule and Politics in Southeast Europe from Roman Antiquity to 1300. de Gruyter, Berlin / Boston 2019. See also the online handbook on the history of Southeast Europe . For more information on the period covered, see Florin Curta: Eastern Europe in the Middle Ages (500–1300). Leiden / Boston 2019; Florin Curta: The Making of the Slavs. History and Archeology of the Lower Danube Region, c . 500-700 . Cambridge 2001; Florin Curta: Southeastern Europe in the Middle Ages, 500-1250 . Cambridge 2006; Christian Lübke: Eastern Europe. The Germans and the European Middle Ages . Munich 2004. See also Florin Curta: The Beginning of the Middle Ages in the Balkans. In: Millennium . Yearbook on culture and history of the first millennium AD 10, 2013, pp. 145ff. - Overview with documents in Florin Curta: The Making of the Slavs . Cambridge 2001, p. 335 ff .; Florin Curta: Southeastern Europe in the Middle Ages, 500-1250 . Cambridge 2006, p. 56 ff. Curta questions the older thesis of a Slavic “original home”; a Slavic identity developed later. Cf. also the brief overview in Eduard Mühle : The Slavs in the Middle Ages. Berlin / Boston 2016. - Florin Curta: The Making of the Slavs . Cambridge 2001, p. 36 ff .; Christian Lübke: Eastern Europe . Munich 2004, pp. 42–46. - On Justinian's Balkan policy see now Alexander Sarantis: Justinian's Balkan Wars. Campaigning, Diplomacy and Development in Illyricum, Thace and the Northern World AD 527-65. Prenton 2016. - On the Avars see above all Walter Pohl: The Avars . 2nd Edition. Munich 2002. - Florin Curta: The Making of the Slavs . Cambridge 2001, p. 120 ff. - Cf. Florin Curta: Southeastern Europe in the Middle Ages, 500-1250 . Cambridge 2006, p. 70 ff. - Current overview of the Bulgarian empire formation with Daniel Ziemann: From Wandering People to Great Power. The emergence of Bulgaria in the early Middle Ages. Cologne u. a. 2007, p. 180 ff. - Christian Lübke: Eastern Europe . Munich 2004, p. 47 ff. - Walter Pohl: The Avars. 2nd edition, Munich 2002, p. 256 ff. - Simon Franklin, Jonathan Shepard: The Emergence of the Rus 750-1200 . London / New York 1996. - Christian Lübke: Eastern Europe . Munich 2004, p. 123 ff. On medieval Hungary see the overview in Pál Engel: The Realm of St Stephen. A History of Medieval Hungary, 895-1526. London / New York 2001. - Christian Lübke: Eastern Europe . Munich 2004, p. 52 ff. - On the history and culture of “Central Europe” around 1000, including the Slavic world and Hungary, see introductory Alfried Wieczorek, Hans-Martin Hinz (Ed.): Europe center around 1000 . 3 vol., Stuttgart 2000. See also Joachim Herrmann (Ed.): The Slavs in Germany. Berlin 1985. - Eduard Mühle: The Piasts. Poland in the Middle Ages. Munich 2011. - For a summary of the (controversial) origin of the topics, see John Haldon: Military Service, Military Lands, and the Status of Soldiers. Current Problems and Interpretations . In: Dumbarton Oaks Papers 47, 1993, pp. 1-67. - On the so-called Middle Byzantine period see, in addition to the various general manuals, especially Leslie Brubaker, John F. Haldon: Byzantium in the Iconoclast era. c. 680-850. A history . Cambridge et al. 2011; Michael J. Decker: The Byzantine Dark Ages. London / New York 2016; John F. Haldon: The Empire That Would Not Die. The Paradox of Eastern Roman Survival, 640-740. Cambridge (Massachusetts) 2016; John F. Haldon: Byzantium in the Seventh Century . 2nd edition Cambridge 1997; Mark Whittow: The Making of Byzantium, 600-1025 . Berkeley 1996. Cf. also generally Falko Daim (Ed.): Byzanz. Historical and cultural studies manual (Der Neue Pauly, Supplements, Vol. 11). Stuttgart 2016. The prosopography of the Middle Byzantine period is also important . - Ralph-Johannes Lilie: The Byzantine reaction to the expansion of the Arabs. Studies on the structural change of the Byzantine state in the 7th and 8th centuries . Munich 1976. For diplomatic contacts up to the middle of the 8th century see Andreas Kaplony: Konstantinopel und Damascus. Embassies and treaties between emperors and caliphs 639-750. Berlin 1996 ( Menadoc Library, University and State Library Saxony-Anhalt, Halle ). - On the Slavs in Greece see (with some new interpretations) Florin Curta: Still waiting for the barbarians? The making of the Slavs in "Dark-Age" Greece . In: Florin Curta (Ed.): Neglected Barbarians . Turnhout 2010, pp. 403-478. See also Florin Curta: The Edinburgh History of the Greeks, c. 500 to 1050. The Early Middle Ages. Edinburgh 2011, pp. 97ff. - Peter Benjamin Golden a. a. (Ed.): The World of the Khazars. New Perspectives. Leiden / Boston 2007. - Ilse Rochow: Emperor Konstantin V (741–775). Materials on his life and afterlife . Frankfurt am Main u. a. 1994, p. 73 ff. - See especially Leslie Brubaker: Inventing Byzantine Iconoclasm . London 2012; Leslie Brubaker, John F. Haldon: Byzantium in the Iconoclast era, ca 680-850. A history. Cambridge 2011. - On Basil, see especially Catherine Holmes: Basil II and the Governance of Empire, 976-1025 . Oxford 2005. - Josef Matuz : The Ottoman Empire. Baseline of its history. 7th edition. Darmstadt 2012, p. 14ff. - General overview of the following by Ulrich Haarmann (Ed.): History of the Arab World . 4th revised and expanded edition Munich 2001; Hugh Kennedy: The Prophet and the Age of the Caliphates . 2nd edition Harlow et al. 2004; Chase F. Robinson (Ed.): The New Cambridge History of Islam. Volume 1. Cambridge et al. a. 2010. See also the general article in the Encyclopaedia of Islam (2nd edition). - On Mohammed see in detail Tilman Nagel : Mohammed. Life and legend . Munich 2008; Tilmann Nagel: Allah's Favorite: Origin and manifestations of the belief in Mohammed. Munich 2008. For historical development see also Lutz Berger: The emergence of Islam. The first hundred years. Munich 2016; Fred M. Donner: Muhammad and the Believers. At the Origins of Islam. Cambridge MA et al. a. 2010 (with partly new interpretations). Introductory cf. Hartmut Bobzin : Mohammed. 5th edition Munich 2016 and the article Muhammad in: Oxford Islamic Studies Online . - On the current state of research cf. Tilman Nagel: Mohammed. Life and legend . Munich 2008, p. 835 ff. - See for example Fred M. Donner: Muhammad and the Believers. At the Origins of Islam. Cambridge MA et al. a. 2010 (according to which Mohammed originally stood up for a monotheistic “ecumenical movement” to which Christians and Jews could also belong, and Islam in its current form did not develop until the Umayyad period; summarizing ibid., P. 194 ff.); Robert G. Hoyland : New Documentary Texts and the Early Islamic State. In: Bulletin of the School of Oriental and African Studies. Volume 69, 2006, pp. 395-416; Robert G. Hoyland: The Identity of the Arabian Conquerors of the Seventh-Century Middle East. In: Al-ʿUṣūr al-Wusṭā 25, 2017, pp. 113–140. - Glen Bowersock : The Cradle of Islam. Mohammed, the Koran and the ancient cultures. Munich 2019. - Extensive overview in Chase F. Robinson (Ed.): The New Cambridge History of Islam . Volume 1. Cambridge et al. a. 2010. See also Aziz Al-Azmeh: The Emergence of Islam in Late Antiquity. Allah and His People. Cambridge 2014; Lutz Berger: The Origin of Islam. The first hundred years. Munich 2016. - Tilman Nagel: Mohammed. Life and legend . Munich 2008, p. 180 ff. - Tilman Nagel: Mohammed. Life and legend. Munich 2008, p. 352 ff. - Rudi Paret : The Islamic World Empire . In: Historische Zeitschrift 187, 1959, pp. 521-539. - See Wilferd Madelung: The Succession to Muhammad . Cambridge 1997. - For details on Islamic expansion see Fred M. Donner: The Early Islamic Conquests . Princeton 1981; Robert G. Hoyland : In God's Path. The Arab Conquests and the Creation of an Islamic Empire. Oxford 2015; Walter E. Kaegi: Byzantium and the Early Islamic Conquests. Cambridge 1992; Hugh Kennedy: The Great Arab Conquests . Philadelphia 2007. See also Lutz Berger: The emergence of Islam. The first hundred years. Munich 2016, pp. 141ff. - James Howard-Johnston: Witnesses to a World Crisis . Oxford et al. a. 2010. - On the non-Islamic sources see above all Robert G. Hoyland: Seeing Islam as Others Saw It. A Survey and Evaluation of Christian, Jewish and Zoroastrian Writings on Early Islam. Princeton 1997. - summary, see Lutz Berger: The emergence of Islam. The first hundred years. Munich 2016, pp. 255ff. - For the case study of Egypt see Petra M. Sijpesteijn: Shaping a Muslim State. The World of a Mid-Eighth-Century Egyptian Official. Oxford 2013. - Wolfgang Kallfelz: Non-Muslim subjects in Islam. Wiesbaden 1995, p. 46 ff .; Milka Levy-Rubin: Non-Muslims in the Early Islamic Empire: From Surrender to Coexistence. Cambridge 2011, p. 100 ff. - General on the history of the caliphate until the 11th century: Hugh Kennedy: The Prophet and the Age of the Caliphates . 2nd ed. Harlow et al. a. 2004, especially p. 50 ff .; Chase F. Robinson (Ed.): The New Cambridge History of Islam. Volume 1. Cambridge et al. a. 2010 (Part 2, from p. 173 ff.). - Hugh Kennedy: The Prophet and the Age of the Caliphates . 2nd ed. Harlow et al. a. 2004, p. 75 ff .; Wilferd Madelung: The Succession to Muhammad . Cambridge 1997, p. 141 ff. - GR Hawting: The First Dynasty of Islam: The Umayyad Caliphate . 2nd edition, London / New York 2000; Hugh Kennedy: The Prophet and the Age of the Caliphates . 2nd ed., Harlow et al. 2004, p. 82 ff. - Hugh Kennedy: The Prophet and the Age of the Caliphates . 2nd ed., Harlow et al. a. 2004, p. 123 ff .; Hugh Kennedy: When Baghdad ruled the Muslim world. The rise and fall of Islam's greatest dynasty . Cambridge MA 2005; B. Lewis: Abbasids . In: Encyclopaedia of Islam . 2nd ed. Volume 1, pp. 15-23. - Heinz Halm : The caliphs of Cairo . Munich 2003. - Detailed comparative overview in Walter Pohl, Veronika Wieser (ed.): The early medieval state - European perspectives . Vienna 2009. - Chris Wickham: The Inheritance of Rome . London 2009, p. 103 f. - See in summary Peter Moraw : Herrschaft II. In: Geschichtliche Grundbegriffe . Volume 3, pp. 5-13, especially p. 7 f. - introduction see Arnold Bühler: Herrschaft im Mittelalter. Ditzingen 2013. For a summary of the following, see Johannes Fried: The formation of Europe 840-1046. 3rd edition, Munich 2008, p. 58 ff .; Hans-Werner Goetz: Europe in the early Middle Ages. 500-1050 . Stuttgart 2003, p. 118 ff. For specific information on Eastern Franconia, see Roman Deutinger : Royal rule in the East Franconian Empire . Ostfildern 2006. - See Johannes Fried: The formation of Europe 840-1046 . 3rd edition Munich 2008, p. 59 f. - Johannes Fried: The formation of Europe 840-1046 . 3rd edition Munich 2008, p. 172 f. - Sharply criticized by Susan Reynolds in her extensive study Fiefs and Vassals: The Medieval Evidence Reinterpreted . Oxford 1994; see. also Susan Reynolds: The Middle Ages Without Feudalism. Essays in Criticism and Comparison on the Medieval West. Farnham 2012. For an introduction see Steffen Patzold: Das Lehnwesen . Munich 2012. - summary Steffen Patzold: Das Lehnwesen . Munich 2012, p. 25 ff. - Current introduction to royalty by Andreas Büttner: Royal rule in the Middle Ages. Berlin / Boston 2017. See also Franz-Reiner Erkens (Hrsg.): The early medieval monarchy. Idea and religious foundations. Berlin 2005. - Stefanie Dick: The myth of the "Germanic" kingship. Studies on the organization of rule among the Germanic barbarians up to the beginning of the migration period. Berlin 2008. - Andreas Büttner: King's rule in the Middle Ages. Berlin / Boston 2017, p. 39 f. - Andreas Büttner: King's rule in the Middle Ages. Berlin / Boston 2017, p. 40 f. - See Johannes Fried: The formation of Europe 840-1046. 3rd edition, Munich 2008, p. 60 f. - Monika Suchan: The good shepherd. Religion, power and rule in the politics of the Carolingian and Ottonian times . In: Frühmedalterliche Studien 43, 2009, pp. 95–112. - Cf. Rudolf Schieffer: The historical place of the Ottonian-Salic imperial church politics . Opladen 1998. - Franz-Reiner Erkens: Rulers' sacredness in the Middle Ages . Stuttgart 2006. - Johannes Fried: The formation of Europe 840-1046 . 3rd edition Munich 2008, pp. 61–64. - For the early medieval court from the Migration Period to the Carolingian Period, see Yitzhak Hen: Roman Barbarians. The Royal Court and Culture in the Early Medieval West . New York 2007. - Hagen Keller, Gerd Althoff: The time of the late Carolingians and the Ottonians . Stuttgart 2008, p. 348 ff. - Bernd Schneidmüller: Consensual rule. An essay on forms and concepts of political order in the Middle Ages. In: Paul-Joachim Heinig (Ed.): Empire, regions and Europe in the Middle Ages and modern times. Festschrift for Peter Moraw . Berlin 2000, pp. 53-87. - Gerd Althoff was pioneering: On the importance of symbolic communication for understanding the Middle Ages . In: Frühmittelalterliche Studien 31, 1997, pp. 370–389. - See introductory Gerd Althoff: Die Macht der Rituale. Symbolism and rule in the Middle Ages . Darmstadt 2003. - Matthias Becher, Alheydis Plassmann (ed.): Dispute at the court in the early Middle Ages . Göttingen 2011. - Cf. Gerd Althoff: Compositio. Restoration of injured honor in the context of amicable conflict resolution . In: Klaus Schreiner, Gerd Schwerhoff (ed.): Injured honor. Conflicts of Honor in Medieval and Early Modern Societies . Cologne u. a. 1995, p. 63 ff. - Geoffrey Koziol: The dangers of polemic: Is ritual still an interesting topic of historical study? In: Early Medieval Europe 11, 2002, pp. 367-388. Sometimes very pointed Peter Dinzelbacher : Why is the king crying: A critique of medievalist pan ritualism . Badenweiler 2009. - Hartmut Leppin, Bernd Schneidmüller, Stefan Weinfurter (eds.): Empire in the first millennium . Regensburg 2012. - Johannes Fried: The formation of Europe 840-1046 . 3rd edition, Munich 2008, p. 190. - Johannes Preiser-Kapeller: Beyond Rome and Charlemagne. Aspects of global interdependence in late antiquity, 300–800 AD Vienna 2018, p. 8f. - Johannes Preiser-Kapeller: Beyond Rome and Charlemagne. Aspects of global interdependence in late antiquity, 300–800 AD Vienna 2018, pp. 9–11. - Ralph-Johannes Lilie: Introduction to Byzantine History . Stuttgart u. a. 2007, p. 132 ff. - Martin Forstner: Kalif, Kalifat . In: Lexicon of the Middle Ages . Volume 5 (1991), Col. 868 f. On the caliphate in general, see Patricia Crone , Martin Hinds: God's Caliph. Religious Authority in the First Centuries of Islam . Cambridge 1986. - To summarize the following, see Johannes Fried: Die Formierung Europa 840-1046 . 3rd edition Munich 2008, p. 8 ff .; Hans-Werner Goetz: Europe in the early Middle Ages. 500-1050. Stuttgart 2003, p. 160 ff. See also the comprehensive social and economic history study by Chris Wickham ( Framing the Early Middle Ages . Oxford 2005, p. 80 ff.). - Johannes Fried: The formation of Europe 840-1046. 3rd edition, Munich 2008, p. 18 f. - See Johannes Fried: The formation of Europe 840-1046. 3rd edition, Munich 2008, p. 17 f. - Johannes Fried: The formation of Europe 840-1046 . 3rd edition Munich 2008, pp. 21-23. - See Johannes Fried: The formation of Europe 840-1046 . 3rd edition Munich 2008, p. 20. - Johannes Fried: The formation of Europe 840-1046 . 3rd edition Munich 2008, p. 31 f. - summary see Friedrich Prinz: European Foundations of German History (4th – 8th Century). In: Gebhardt, Handbuch der deutschen Geschichte Vol. 1. 10., completely revised edition Stuttgart 2004, pp. 147–616, here: p. 503 ff. - Friedrich Prinz: From Constantine to Charlemagne . Düsseldorf / Zurich 2000, p. 415 ff. - See Chris Wickham: Framing the Early Middle Ages . Oxford 2005, p. 533 ff. - Hans-Werner Goetz: Europe in the early Middle Ages. 500-1050 . Stuttgart 2003, p. 182. - detail on the role of Mrs. Edith Ennen: Women in the Middle Ages . 6th edition, Munich 1999. On the early Middle Ages, ibid., P. 32 ff. See also Julia Smith: Europe after Rome. Oxford 2005, p. 115 ff. - Cordula Nolte: Men and women in society in the Middle Ages. Darmstadt 2011, p. 119. - Cordula Nolte: Men and women in society in the Middle Ages. Darmstadt 2011, p. 120. - Cordula Nolte: Men and women in society in the Middle Ages. Darmstadt 2011, p. 118. - Cordula Nolte: Men and women in society in the Middle Ages. Darmstadt 2011, p. 121. - Cordula Nolte: Men and women in society in the Middle Ages. Darmstadt 2011, p. 123. - Cordula Nolte: Men and women in society in the Middle Ages. Darmstadt 2011, p. 124. - Heike Hawicks: Theophanu. In: Amalie Fößel (Ed.): The Empresses of the Middle Ages. Regensburg 2011, pp. 60–77, here p. 64. - Heike Hawicks: Theophanu. In: Amalie Fößel (Ed.): The Empresses of the Middle Ages. Regensburg 2011, pp. 60–77, here p. 70. - Johannes Fried: The formation of Europe 840-1046. 3rd edition, Munich 2008, p. 28 f. - comparative overview of the position of the Jews in the Christian Middle Ages and the early Islamic world in Mark R. Cohen: Under Crescent and Cross. The Jews in the Middle Ages . Princeton 1994. - Michael Borgolte, Juliane Schiel, Annette Seitz, Bernd Schneidmüller (eds.): Middle Ages in the Laboratory. Medieval Studies tests ways to a transcultural European science. Berlin 2008, p. 446 f. - summary, Hans-Werner Goetz: Europe in the early Middle Ages. 500-1050 . Stuttgart 2003, pp. 172-174; Friedrich Prinz: From Constantine to Charlemagne . Düsseldorf / Zurich 2000, pp. 377–381. - Johannes Fried: The formation of Europe 840-1046. 3. Edition. Munich 2008, pp. 158–162. - For a first orientation cf. about Hans-Jörg Gilomen : Economic History of the Middle Ages. Munich 2014. - Hans-Werner Goetz: Europe in the early Middle Ages. 500-1050. Stuttgart 2003, p. 198. - Marcus Popplow: Technology in the Middle Ages. Munich 2010, p. 48 ff. - Marcus Popplow: Technology in the Middle Ages . Munich 2010, p. 77 f. - Dieter Hägermann: The abbot as landlord. Monastery and economy in the early Middle Ages . In: Friedrich Prinz (ed.): Dominion and Church . Stuttgart 1988, pp. 345-385. - Karl-Heinz Ludwig: Mining, metal and coins in the early Middle Ages . In: Brigitte Kasten (Hrsg.): Fields of activity and horizons of experience of rural people in the early medieval rulership . Stuttgart 2006, pp. 235-247. - Hans-Werner Goetz: Europe in the early Middle Ages. 500-1050. Stuttgart 2003, p. 200 ff .; Michael McCormick: Origins of the European Economy. Communications and Commerce, A.D. 300-900 . Cambridge 2001. Chris Wickham: Framing the Early Middle Ages is of fundamental importance for the period up to around 800 . Oxford 2005. - On the exchange of goods in general, cf. especially Chris Wickham: Framing the Early Middle Ages . Oxford 2005, especially p. 693 ff. - Cf. with further literature Johannes Preiser-Kapeller: Jenseits von Rom und Charlemagne. Aspects of global interdependence in the long period of late antiquity, 300-800 AD Vienna 2018. - Wickham has done this extensively in his study ( Framing the Early Middle Ages . Oxford 2005). - On this wave of epidemics see Mischa Meier: The 'Justinianic Plague': the economic consequences of the pandemic in the eastern Roman empire and its cultural and religious effects. In: Early Medieval Europe 24, 2016, pp. 267–292. - Chris Wickham: Framing the Early Middle Ages . Oxford 2005, pp. 548-550. - summary Michael McCormick: Origins of the European Economy. Communications and Commerce, A.D. 300-900 . Cambridge 2001, p. 778 ff. - For details on this, Chris Wickham: Framing the Early Middle Ages . Oxford 2005, p. 708 ff. - Michael McCormick: Origins of the European Economy. Communications and Commerce, A.D. 300-900 . Cambridge 2001, p. 761 ff. - Chris Wickham: Framing the Early Middle Ages . Oxford 2005, pp. 707 f. - summary, cf. Michael J. Decker: The Byzantine Dark Ages. London / New York 2016; Ralph-Johannes Lilie: Introduction to Byzantine History. Stuttgart u. a. 2007, p. 91 ff. - Angeliki E. Laiou, Cécile Morrison: The Byzantine Economy . Cambridge 2007, p. 43 ff. - Angeliki E. Laiou, Cécile Morrison: The Byzantine Economy . Cambridge 2007, p. 54. - Angeliki E. Laiou, Cécile Morrison: The Byzantine Economy . Cambridge 2007, p. 70 ff. - On the education system of late antiquity cf. summarizing Alexander Demandt: The late antiquity . 2nd edition, Munich 2007, p. 467 ff. - Hans-Werner Goetz: Europe in the early Middle Ages. 500-1050. Stuttgart 2003, p. 250 f. - Rosamond McKitterick (Ed.): The Uses of Literacy in Early Mediaeval Europe . Cambridge et al. a. 1990. - Ian Wood: Administration, law and culture in Merovingian Gaul . In: Rosamond McKitterick (Ed.): The Uses of Literacy in Early Mediaeval Europe . Cambridge et al. a. 1990, p. 63 ff. - Wolfgang Haubrichs : Education . In: Reallexikon der Germanischen Altertumskunde . Volume 2 (1975), p. 599. - an introduction to (early) medieval education, see for example Martin Kintzinger: Knowledge becomes power. Education in the Middle Ages . Ostfildern 2003; Ulrich Nonn: Monks, scribes and scholars: Education and science in the Middle Ages . Darmstadt 2012. Research overview with Johannes Fried: The formation of Europe 840-1046 . 3rd edition, Munich 2008, p. 202 ff .; Hans-Werner Goetz: Europe in the early Middle Ages. 500-1050 . Stuttgart 2003, pp. 250-260. Cf. also Wolfgang Haubrichs: Bildungswesen . In: Reallexikon der Germanischen Altertumskunde . Volume 2 (1975), p. 598 ff. - Rosamond McKitterick: The Carolingians and the Written Word. Cambridge et al. 1989, p. 211 ff. - Ulrich Nonn: On the prehistory of the educational reform of Charlemagne . In: Charlemagne and his aftermath . Volume 1. Turnhout 1997, pp. 63-77. - Quotation from Reinhold Rau ( Einhard. The life of Charlemagne . In: Reinhold Rau (Hrsg.): Selected sources on the German history of the Middle Ages . Volume 5. Darmstadt 1955, p. 159). - Introductory to the educational reform see among others Arnold Angenendt: The early Middle Ages . Stuttgart u. a. 1990, p. 304 ff .; Franz Brunhölzl: History of the Latin Literature of the Middle Ages . Volume 1. Munich 1975, p. 243 ff .; Philippe Depreux: Ambitions et limits des réformes culturelles à l'époque carolingienne . In: Revue Historique 307 (2002), pp. 721-753; Wilfried Hartmann: Charlemagne . Stuttgart 2010, p. 177 ff .; Rosamond McKitterick: Charlemagne. The Formation of a European Identity . Cambridge 2008, p. 292 ff .; Rosamond McKitterick (Ed.): Carolingian Culture. Emulation and innovation. Cambridge et al. a. 1994; Friedrich Prinz: From Constantine to Charlemagne . Düsseldorf / Zurich 2000, p. 464 ff .; Bernd Roeck : The morning of the world. History of the renaissance. Munich 2017, p. 129 ff. - Compact overview from Arnold Angenendt: The early Middle Ages. Stuttgart u. a. 1990, p. 317 ff. - Reinhard Schneider: The Franconian Empire . 4th edition, Munich 2001, p. 90. - Rosamond McKitterick: The Carolingians and the Written Word. Cambridge et al. a. 1989, especially p. 169 ff .; Leighton D. Reynolds, Nigel G. Wilson : Scribes and scholars. A guide to the transmission of Greek and Latin literature . 3rd edition Oxford 1991, p. 92 ff. - summary, cf. Johannes Fried: The way into history . Berlin 1994, pp. 413-416. - Wolfgang Haubrichs: Education . In: Reallexikon der Germanischen Altertumskunde . Volume 2 (1975), p. 603. - summary, Peter Schreiner : Byzanz. 4th updated edition. Munich 2011, pp. 113–115. - See introductory Thomas Bauer : Why there was no Islamic Middle Ages. The legacy of antiquity and the Orient. Munich 2018. - George Makdisi: Madrasa . In: Lexicon of the Middle Ages . Volume 6, Col. 65-67; Article madrasa . In: Encyclopaedia of Islam . Volume 5. 2nd edition, p. 1123 ff. - On the transfer of knowledge from ancient times, see for example John Freely: Plato in Baghdad: How ancient knowledge came back to Europe . Stuttgart 2012. - On Latin literature in the Middle Ages see basically Franz Brunhölzl : History of Latin Literature of the Middle Ages (Volume 1, Munich 1975 and Volume 2, Munich 1992); Max Manitius: History of Latin Literature in the Middle Ages. Munich 1974 ff. (ND). See also the various related articles in the Lexicon of the Middle Ages and in the author's lexicon (2nd edition). - Richard W. Burgess , Michael Kulikowski: Mosaics of Time. The Latin Chronicle Traditions from the First Century BC to the Sixth Century AD. Volume I: A Historical Introduction to the Chronicle Genre from its Origins to the High Middle Ages. Turnhout 2013. - See Thomas M. Charles-Edwards (Ed.): The Chronicle of Ireland . Liverpool 2006. - Overview of individual authors and lines of development in Deborah Mauskopf Deliyannis (Ed.): Historiography in the Middle Ages . Leiden / Boston 2003 (there Part One, p. 17 ff.); Anton Scharer , Georg Scheibelreiter (Ed.): Historiography in the early Middle Ages . Munich / Vienna 1994. - On Byzantine historiography in the Middle Byzantine period, see introductory (albeit partially outdated) Herbert Hunger : Die hochsprachliche Profane Literatur der Byzantiner. 2 Bde., Munich 1978, here Volume 1, p. 331 ff. Cf. also Warren Treadgold: The Middle Byzantine Historians. Basingstoke 2013. - Overview of Christian-Syrian historiography, for example at Syri.ac (scientifically supervised). - Chase F. Robinson: Islamic Historiography . Cambridge 2003. - Overview with Claudio Leonardi a . a .: Hagiography. In: Lexicon of the Middle Ages . Volume 4, Col. 1840-1862. - On Byzantine theological literature see still Hans-Georg Beck : Church and theological literature in the Byzantine Empire. Munich 1959. See now also Thomas Pratsch: The hagiographical topos. Greek lives of saints in the Middle Byzantine period. Berlin / New York 2005. - summary, Hans-Werner Goetz: Europe in the early Middle Ages. 500-1050. Stuttgart 2003, p. 260 f. - introduction to old German literature, see Heinz Sieburg: Literatur des Mittelalters. Berlin 2010, p. 69 ff. - Heinz Sieburg: Literature of the Middle Ages. Berlin 2010, p. 73. - For an overview, see the corresponding articles in the Lexicon of the Middle Ages : Old English Literature (Bd. 1, Sp. 467–469); Irish language and literature III. (Vol. 5, Col. 647-649); French Literature I. (Vol. 4, Col. 836); Church Slavonic Language and Literature II. (Vol. 5, Sp. 1179 f.). - Overview of early medieval philosophy, taking into account the development from the 4th century, by Kurt Flasch : The philosophical thinking in the Middle Ages. From Augustine to Machiavelli. 2nd edition, Stuttgart 2000; Richard Heinzmann: Philosophy of the Middle Ages . 3rd edition, Stuttgart 2008. See also John Marenbon (Hrsg.): Medieval Philosophy. Routledge History of Philosophy 3 . New York 1998. - Deirdre Carabine: John Scottus Eriugena . Oxford et al. 2000; Kurt Flasch: Philosophical Thinking in the Middle Ages. 2nd edition, Stuttgart 2000, p. 173 ff .; Richard Heinzmann: Philosophy of the Middle Ages . 3rd edition, Stuttgart 2008, p. 123 ff. - Katerina Ierodiakonou , Börje Bydén: Byzantine Philosophy. In: Edward N. Zalta (Ed.): Stanford Encyclopedia of Philosophy . - Cristina D'Ancona : Greek Sources in Arabic and Islamic Philosophy. In: Edward N. Zalta (Ed.): Stanford Encyclopedia of Philosophy . - Peter Adamson: Al-Kindi. Oxford et al. 2007. - Jon McGinnis: Avicenna . Oxford et al. 2010. - Thomas Labusiak : "He gave the church many sacred vessels made of gold and silver." Goldsmithing in the time of Charlemagne. In: Peter van den Brink, Sarvenaz Ayooghi (ed.): Charlemagne - Charlemagne. Karl's art. Dresden 2014, pp. 74–93, here p. 92. - Overview of the following by Kunibert Bering: Art of the early Middle Ages. 2nd Edition. Stuttgart 2008; Beat Brenk: Late Antiquity and Early Christianity . Berlin 1977; Hermann Fillitz : The Middle Ages 1 . Berlin 1969; Jean Hubert, Jean Porcher, Wolfgang Fritz Volbach : Early Middle Ages: From the Migration Period to the threshold of the Carolingian era . Munich 1968; Jean Hubert, Jean Porcher, Wolfgang Fritz Volbach: The art of the Carolingians: from Charlemagne to the end of the 9th century . Munich 1969; Lawrence Nees: Art and architecture . In: Rosamond McKitterick (Ed.): New Cambridge Medieval History . Volume 2. Cambridge 1995, pp. 809 ff .; Henry Mayr-Harting: Artists and Patrons. In: Timothy Reuter (Ed.): The New Cambridge Medieval History. Volume 3. Cambridge 1999, p. 212 ff. - Lawrence Nees: Art and architecture . In: Rosamond McKitterick (Ed.): New Cambridge Medieval History. Volume 2, Cambridge 1995, here p. 810 f. - summary Ulrike Mörschel: Art theories in the Middle Ages . In: Lexicon of the Middle Ages . Volume 5, Col. 1573-1576. - Günther Pöltner: Philosophical Aesthetics . Stuttgart 2008, p. 49 ff. - Kenneth J. Conant: Carolingian and Romanesque Architecture, 800-1200 . 4th ed., New Haven 1978. - Architecture A II 1 . In: Lexicon of the Middle Ages. Volume 1, Col. 1632 ff. - summary of the early medieval wall painting (with further literature) see Matthias Exner : Wall painting . In: Reallexikon der Germanischen Altertumskunde . Volume 33 (2006), pp. 220-231. - For further examples see Matthias Exner: Wandmalerei . In: Reallexikon der Germanischen Altertumskunde . Volume 33 (2006), here p. 224 ff. And the article Fresko . In: Real Lexicon on German Art History . Women at the grave fresco . Delivery 114, here Sp. 747 f. - Wolfgang Fritz Volbach, Jacqueline Lafontaine-Dosogne: Byzantium and the Christian East . Berlin 1968. - Lawrence Nees: Art and architecture . In: Rosamond McKitterick (Ed.): New Cambridge Medieval History . Volume 2. Cambridge 1995, p. 817 ff. - See for example Aaron Gurjewitsch: The world view of medieval man . 5th edition, Munich 1997, p. 352 ff. - For the history of Christianity in the early Middle Ages see among others: Arnold Angenendt: Das Frühmittelalter . Stuttgart u. a. 1990; Peter Brown: The Rise of Western Christendom . 2nd ed., Oxford 2003; Judith Herrin: The Formation of Christendom . Princeton 1987. Luce Pietri et al. (Ed.): Die Geschichte des Christianentums offer a comprehensive presentation (including the Eastern Churches) . Volume 3: The Latin West and the Byzantine East (431–642). Freiburg i. Br. Et al. 2001; Gilbert Dragon, Pierre Riché and André Vauchez (eds.): The history of Christianity. Volume 4: Bishops, Monks and Emperors (642–1054). Freiburg i. Br. Et al. 1994; The Cambridge History of Christianity . Volume 2-3. Cambridge 2007-2008. For individual personalities, institutions and terms, see the entries in the Lexicon of the Middle Ages , in the Real Theological Encyclopedia and in the Lexicon for Theology and Church (3rd edition). - Friedrich Prinz: From Constantine to Charlemagne. Düsseldorf / Zurich 2000, p. 17 ff. - Brief summary of the development at Arnold Angenendt: The early Middle Ages. Stuttgart u. a. 1990, p. 238 ff. On the individual popes see for example Franz Xaver Seppelt : History of the Popes. Vol. 2, 2nd edition, Munich 1955. For the papacy, see Klaus Herbers: History of the Papacy in the Middle Ages . Darmstadt 2012. - Heike Johanna Mierau: Emperor and Pope in the Middle Ages . Cologne 2010, p. 26 ff. - Peter Eich : Gregor the Great. Bishop of Rome between antiquity and the Middle Ages. Paderborn 2016. - Arnold Angenendt: The spiritual alliance of the popes with the Carolingians 754-796 . In: Historisches Jahrbuch 100, 1980, pp. 1-94. - Heike Johanna Mierau: Emperor and Pope in the Middle Ages . Cologne 2010, p. 41 ff. - Johannes Fried: The formation of Europe 840-1046 . 3rd edition, Munich 2008, p. 98. - Friedrich Prinz: From Constantine to Charlemagne . Düsseldorf / Zurich 2000, p. 66. For general information on the Gallic episcopal rule see Martin Heinzelmann: Bischofsherrschaft in Gallien . Munich / Zurich 1976. - summarize, see Arnold Angenendt: Basic forms of piety in the Middle Ages . Munich 2004; Johannes Fried: The formation of Europe 840-1046 . 3rd edition, Munich 2008, p. 100 ff. - Knut Görich: The year 999 and the fear of the turn of the millennium . In: Ernst Halter, Martin Müller (Ed.): The end of the world . Zurich 1999, pp. 31-40. - See generally Christoph Stiegemann u. a. (Ed.): CREDO: Christianization of Europe in the Middle Ages. 2 vols., Petersberg 2013. - Bernhard Maier: The religion of the Germanic peoples . Munich 2003. - Article Slavic Religion . In: Theological Real Encyclopedia . Volume 31. Berlin 2000, p. 396 ff. - Arnold Angenendt: The early Middle Ages. Stuttgart u. a. 1990, p. 204 ff. - Friedrich Prinz: From Constantine to Charlemagne . Düsseldorf / Zurich 2000, pp. 305–309. - Resolutions of the 4th Council of Toledo 633, c. 57. - Product Africa I . In: Theological Real Encyclopedia . Volume 1. Berlin / New York 1977, here p. 687 f. - Overview with Gilbert Dragon, Pierre Riché and André Vauchez (eds.): The history of Christianity. Volume 4: Bishops, Monks and Emperors (642–1054) . Freiburg i. Br. U. a. 1994, p. 391 ff. - Wolfgang Kallfelz: Non-Muslim subjects in Islam. Wiesbaden 1995, p. 46 ff .; Milka Levy-Rubin: Non-Muslims in the Early Islamic Empire: From Surrender to Coexistence. Cambridge 2011, p. 100 ff. - Cf. in summary Wolfgang Kallfelz: Non-Muslim subjects in Islam. Wiesbaden 1995, p. 49 ff. - On the iconoclasm, see Leslie Brubaker: Inventing Byzantine Iconoclasm . London 2012; Leslie Brubaker, John F. Haldon: Byzantium in the Iconoclast era, ca. 680-850. A history. Cambridge 2011; see. also the balancing representation in Judith Herrin: The Formation of Christendom . Princeton 1987, p. 307 ff. - summary, Leslie Brubaker: Inventing Byzantine Iconoclasm . London 2012, p. 32 ff. - Ralph-Johannes Lilie: Byzanz - The second Rome. Berlin 2003, p. 122 f. - Ralph-Johannes Lilie: Byzanz - The second Rome . Berlin 2003, p. 122. - Leslie Brubaker: Inventing Byzantine Iconoclasm. London 2012, p. 90 f. - Leslie Brubaker: Inventing Byzantine Iconoclasm . London 2012, p. 93. - For classification and evaluation cf. Leslie Brubaker: Inventing Byzantine Iconoclasm. London 2012, p. 107 ff.
In Chapter 3, you have read about the two types of human reasoning, “deductive” and “inductive.” Deductive reasoning relies on logical relationships between claims and tells us, given what we know or assume to be true, what must necessarily be true. Consider the following example of a deductive argument in the form of modus ponens: Premise 1: If it is raining outside, then I have an umbrella. Need assignment help for this question? If you need assistance with writing your essay, we are ready to help you! Premise 2: It is raining outside. Conclusion: Therefore, I have an umbrella. In this example, if the premises are both true, then the conclusion is guaranteed to be true. What this means is that premise 1 and premise 2 are logically related such that if both are true, then the truth of the conclusion is required. In other words, if it is true that “if it is raining outside, then I have an umbrella,” and it is true that “it is raining outside,” then it cannot be false that “I have an umbrella”….because that’s just what it means to say “if it is raining outside, then I have an umbrella.” You may be thinking, though, that it is quite possible that it is raining outside but I forget my umbrella. But notice that this would make the first premise false. It is false that “if it is raining outside, then I have an umbrella,” when it is raining outside, but I don’t have an umbrella. In fact, that are no conditions under which it is true that “if it is raining outside, then I have an umbrella,” and it is raining outside, but I don’t have an umbrella. This is because, again, that’s just what it means to say that “if it is raining outside, then I have an umbrella.” On pp. 45-46, you read about some of the most common deductive argument forms and you saw examples of each. These are: modus ponens, modus tollens, and the hypothetical syllogism.You may see more deductive argument forms here: Deductive Argument Forms Because moral arguments are always deductive, you read more about them than about inductive arguments. Still, inductive arguments are an important part of human reasoning so I will say a bit more about them here. Rather than relying on logical relationships between claims, inductive arguments draw conclusions on the basis of observation and experimentation. Inductive reasoning, then, is the backbone of the scientific method. While deductive reasoning is characteristic of logic and mathematics, inductive reasoning is characteristic of the applied sciences. At a very basic level, we are taking inductive reasoning for granted when we assume that the world really is the way we observe it to be. For instance, I observe a computer screen in front of me, so I assume that there really is a computer screen in front of me. But is it guaranteed that there is a computer screen in front of me simply because I observe it? You might reply, “Well, of course, and you can touch it too!” However, if you have ever had a very vivid dream, or if you have seen the 1999 movie, “The Matrix,” then you will admit that there are situations we can imagine in which I observe a computer screen, but there really isn’t one there. (A note: This question of whether, and to what extent, we can rely on our observations will become relevant again in our module on environmental and animal ethics. It will be discussed further there, along with ethical issues related to scientific claims. It is also a topic we discuss in my Introduction to Philosophy class quite a bit.) For a critical thinking class, though, our goal is to determine what is most likely true, or what is most reasonable to believe. I typically say to students at this point, “It is not most reasonable to believe that we are in the Matrix, so we will leave this problem of induction behind for now…” Then one semester, a student replied, “Yeah, I bet that’s what people in the Matrix think too.” Indeed! Yet, at some point, if we need to decide what we should do, we must make that decision about what is most reasonable to believe. Overall, there just aren’t enough things we know with the strength of deductive reasoning to rely only on what is guaranteed to be true. When we don’t know what is guaranteed, we must still decide what is most likely true. That is exactly what science helps us to do. In particular, the scientific method helps us to make good generalizations and is indispensable to causal reasoning. Read more about inductive reasoning here: Kris Barton & Barbara G. Tucker: Inductive Reasoning ______________________________________________________ For this assignment, you will be demonstrating your understanding of deductive and inductive reasoning. First, create your own example of each of the three deductive argument forms discussed on pp. 45-46: modus pones, modus tollens, and hypothetical syllogism. I gave an example of one, modus ponens, above, about it raining outside and me having an umbrella. That’s exactly what I’m asking you to do. Don’t use my example or an example from the book or internet. Just think of your own example to show you can create the argument forms. It is only necessary to create one example of each argument. Please state the argument so that the logical form is apparent rather than discussing your argument in a passage. You may use this format: Your examples should look just like my example of modus ponens above, only with your own original content. To show your understanding of inductive reasoning, answer the following using the reading in the textbook and the link provided above: 1. What is inductive reasoning? 2. How does inductive reasoning differ from deductive reasoning? 3. What is a generalization? 4. What is causal reasoning? 5. What is sign reasoning? 6. What is analogical reasoning? 7. Describe a situation where you have used one of the types of inductive reasoning that you defined in questions 2-5. To be clear, your submission to this dropobox should include: 1) one original example for each of the three deductive argument forms, and 2) your answers to the seven questions above.
1 Introduction to MATLABThis chapter is intended to get the user started using MATLAB through simple exercises innumerical calculations. The chapter starts by describing how to download and install MATLAB ina Windows environment. Installation of the software in other operating systems is very similarand is explained in detail in the MATLAB website.What is MATLAB?MATLAB is a numerical, programming and graphics environment with a variety of applications inscience and engineering. MATLAB is a self-contained package including a large number ofintrinsic numeric, programming and graphics functions.Getting started with MATLABTo get started, launch the MATLAB application.To load a value into a variable use an assignment statement (one that includes the equal sign),e.g., a = 3.2. Try the following exercises for simple arithmetic operations. Type the commandsshown in front of the MATLAB prompt. In this chapter, the prompt EDU» is used. This promptbelongs to a student version of MATLAB.a = 3.2 <return>b = 6.4 <return>a+b <return>a-b <return>ab <return>a/b <return>a^b <return>who <return>The last command will return a list of the active variables in your worksheet. Many of them aresystem variables that cannot be modified by the user.MATLAB has a number of special constants, such as i and pi, corresponding to the unitimaginary number, and π = ratio of circumference to diameter, respectively. The base of thenatural logarithms, e can be obtained by evaluating exp(1). The value eps is another specialconstant corresponding to the maximum value for which 1 + exp(1)ps = 1. Other importantconstants are inf = infinity, and nan = not-a-number. Boolean (i.e., logical ) constants are 1(true) and 0 (false).Try the following exercises to see what values are returned by MATLAB:exp(1) <return>i <return>j <return>pi <return>eps <return>inf <return>nan <return>3>2 <return>3<2 <return> Comments in MATLAB are represented by the percentage sign (%). Anything in front of %/ istaken as a comment. For example, enter:a = 4.5 % redefining a <return>MATLAB will return the value of 4.5 for a and ignore the comment after the % character.Simple operations with MATLABSimple scalar operations: the following exercises will get you acquainted with a few ofMATLABs abilities for operating with scalar values.a = 2 <return>b = 3 <return>Save(‘a’) <return>clear a <return>a <return>b <return>load(‘a’) <return>a <return>exp(a) + exp(b) <return>sin(api/b) <return>(Note: the clear command is used to eliminate variables, as in clear a, as shown above. Byitself, clear deletes all variables recently defined. Therefore, be very careful when using thiscommand).Vectors: • To enter vectors use the square brackets and separate the elements with commas or blanks for a row vector, e.g.: v = [-1. , 2., pi]. • The transpose of a vector (or matrix) is expressed using the apostrophe, for example,type: v • To enter a column vector, use any of the following procedures: w = [3; -2; 5] <return>Or, user = [6 <return>-2 <return>10 ] <return> • You can create a row vector by indicating a starting value, an increment (or decrement), and an ending value, all separated by the colon (:) operator as follows: vector_name = starting_value : increment : ending valuefor example: x = -10.0 : 0.5 : 10.0 <return> • If you prefer to store it as a column vector, try the following: xt = x <return> • Lets apply a function to the vector x, try: y = sin(xpi/10) <return> • We can plot the vectors x,y using: plot(x,y) <return> . [Type help plot <return> for more information] • Lets clear the MATLAB variables and operate with other vectors: Type clear <enter> followed by clc <enter>. The command clc clears the Matlab interface. • Enter the row vectors, u = [-1. 2. 3.] and v = [6. -10. 0.] • Perform the following operations:u + v <return>u - v <return>uv <return>uv <return>uv <return> • To extract elements of the vectors, try:u(3) <return>u(2) + v(1) <return> • Try the following exercise: a = 1; b = 2; c = 3; r = [a, b, c] <return> • To suppress MATLAB responses use the semi-colon after entering a command. Forexample, try: s = [-1., 2.]; <return> • Vectors can also contain characters as their elements, e.g.,letters = [a, b, c, d] <return>Note: Expressions such as ‘a’, ‘b’, etc., are referred to as strings. Therefore, only those stringoperations such as concatenation, part, etc. are allowed for vectors with character elements.MATLAB strings and string operations are presented in a subsequent chapter.Matrices: • Here are several ways to enter matrices: (use clear and clc to clear the memory and the screen)A = [1. 2. 3.; 4. 5. 6.; 1. -1. 0.] <return>B = [ 1. 1. 1. <return>2. 3. -1. <return>5. 7. -2. ] <return>u = [1. 3. -5. ]; v = [4. 2. 3. ]; w = [-1. 0. 1.]; <return>C = [u; v; w] <return>r = [u, v, w] <return>D = [u v w] <return> • Matrix operations: try the following operations: •A + B <return>C - D <return>AB <return>BA <return>Cu <return>Dv <return>rank (A) <return>inv(A) <return> cond(B) <return>det(C) <return>Ainv(A) <return>inv(B)B <return>eig(A) <return> (calculates eigenvalues)trace(C) <return>(Note: to find out more about any of the commands listed here type help followed bythe command name, e.g., help spec).Solution of linear systems: some possibilities are (use clear and clc to restart memory andscreen):A = [1. 3. 2.; 2. 1. -1.; 5. 2. 1.]; b = [2; 3; 4]; <return>xa = inv(A)b <return>xb = linsolve(A,b)<return>xc = Ab <return>(Note: type help linsolve to learn more about this command).Simple MATLAB Input and OutputOutput: To get a list of your current session use the function diary. The format is asfollows: diary (output_filename), where the filename is written within quotes. To endcollecting output in the current diary output file use diary off. For example, try thefollowing session:clear; clc; <return>diary (session1.txt) <return>A = [1. 2. 3.; 2. 3. 1.; 3. 2. 1.];b=[5; 4; -1.];<return>A <return>b <return>x = linsolve(A,b) <return>diary(0) <return>Next, use NOTEPAD, or other text editor, to open the file session1.txt to see the contentsof the file. The default directory for storing a diary file is the current working directory, i.e.,typically the work subdirectory within the MATLAB directory.Cutting and pasting: You can also copy statements or results from the Matlab interface into atext file by cutting and pasting.Command Input: you can read MATLAB commands from a script file, which is basically atext file listing all the commands you want to use. As an example, create the followingtext file in the work subdirectory of the MATLAB directory using NOTEPAD, and call itsession2.m:clearA = [1. 2. -3. % entering3. 4. 5. % elements of7. 8. 9.] % matrix Ab = [1.; 2.; 3.] % enter vector bxa = inv(A)b % calculate x using matrix inversexb = linsolve(A,b) % calculate x using MATLABs own linsolve functionThen, press clc in MATLAB, and type: session2You will see MATLAB execute all the commands in your file, stopping at the end of the file. MATLAB command historyAll commands entered in a given MATLAB session get stored into a MATLAB command historybuffer. The commands are thus accessible for re-use or edition. All the command historyfunctions are available through the option History under the File menu in theMATLAB worksheet. The most useful commands are cntl-P and cntl-N, which lets you access theprevious command or the next command, respectively, in the command history buffer. (As analternative, you could use the up and down arrow keys in your keyboard to move about thecommand history buffer in Matlab). Once a command is recalled from the command historybuffer it can be edited by using the backspace or delete keys, or by inserting new characters bysimply typing at the proper location.For example, try the following MATLAB session:1 – Use clear; clc; to clear memory and interface in Matlab.2 - Enter the following commands (you don’t need to enter the comments):EDU>> x = [0:pi/20:2pi];EDU>> y = sin(x) + sin(2x);3 - Use cntl-P and edit the previous command (y = sin(x) + sin(2x);) to read:EDU>> z = sin(x) + cos(x);4 - Use cntl-P once more to edit the previous command (z = sin(x) + cos(x); ) to read:EDU>> p = cos(x) + cos(2x);5 - So far you have created vectors x, y, z, and p. Next, we use the following commands toproduce a plot of y-vs.-x:EDU>> figure(1); plot(x,y)6 - Use cntl-P to edit the previous command to read:EDU>> xset(window,1); plot(x,z)7 - Continue using cntl-P to edit the last commands and produce the following plots:EDU>> figure(2); plot(x,p)EDU>> figure(3); plot(y,z)EDU>> figure(4); plot(y,p)EDU>> figure(5); plot(z,p)Selective worksheet outputSuppose you have been working on a lengthy MATLAB session whose command history buffercontains some results that produced errors as well as some intermediary results that are not ofinterest to you for output. For your output, you can select only those commands relevant toyour final results by using Cntl-P and Cntl-N, or the up and down arrow keys. Try the followingMATLAB session that explores some basic vector operations using vectors x and y:1 - Use clear; clc; to clear memory and interface in Matlab.2 - Enter the following MATLAB commands:EDU>> x = [1, 2, 5, -4]EDU>> y = [0, 2, 3,-5]EDU>> xy EDU>> x.yEDU>> sum(ans)EDU>> sum(x.y)EDU>> xyEDU>> xyEDU>> yxEDU>> xy + yxEDU>> b = xy + yxNote: These commands and their corresponding results represent an exploratory session forvector operations.3 - Suppose that you are only interested in the commands defining vectors x and y, in theoperations that produce the dot product of the vectors (i.e., sum(x.y) and xy), and in thevery last command (b = xy + yx). Using the diary command create the filec:myVectors.txt and collect only the commands of interest out of the command history bufferby using cntl-P and cntl-N as needed. The resulting MATLAB session should look like this:EDU» diary(c:myVectors)EDU» x = [1, 2, 5, -4]x = 1 2 5 -4EDU» y = [0, 2, 3, -5]y = 0 2 3 -5EDU» sum(x.y)ans = 39EDU» xyans = 39EDU» b = xy + yxb = 39 39 39 39 41 43 49 31 42 45 54 27 34 29 14 59EDU» diary offThe session, except for the very first command (diary(c:myVectors) is stored in filec:myVectors.txt. This file can be edited or printed from a text editor such as NOTEPAD, theeditor available with Matlab. Current directory / creating a work directoryMATLAB uses a current directory where files are saved by default, for example when usingthe function diary. To see the current directory use:EDU>> pwdUnder a Windows operating system, the default current directory is typically the work sub-directory within the Matlab installation. The command pwd stands for print working directory.A preview of MATLAB functionsHere are some useful functions in MATLAB that we will explore in more details in subsequentchapters: • Elementary functions: sum, prod, sqrt, diag, cos, max, round, sign, fft • Sorting: sort, find • Specific matrices: zeros, eye, ones • Linear algebra: det, inv, qr, svd, eig, schur, trace • Random numbers: rand • Programming: function, for, if, end, while, warning, error, break, return • Comparison symbols: ==, >=, >, <=, <, =, & (and), \| (or), ~ (not) • Debugging: pause, returnTo find out more about these functions use the help command. For example, try:EDU>> help rootsEDU>> help eyeEDU>> help traceExercisesDetermine the result of the following calculations using MATLAB if a = 2.3, b = -2.3, c= π/2, x =2/ π, and y = √3. Produce a diary file, e.g., c:Exercises1.txt, showing the calculations inproblems through .. (a2 + bc + x). sin(c) + y/c. (a+c)/(x+y). 1/(cos(c) + ln(x)). (a+c)3/bEnter the matrices A = [1 -1 3; 2 5 –6; 0 7 1], and B = [0, 2, 3; -1, 1, 2; 1,2, 3]. Then calculate the following:. sum(A) . sum(B’)’ . prod(A) . prod(B’)’. A’, transpose . diag(A) . rank(B) . inv(B). eig(A’) . C = A + B . D = A-B . P = AB. Q = BA . R = BA’Enter the following vectors: u = [2, -1, 3, 5], v = [1:5:16], w = [10:-2:4].Then calculate the following:. u’ . z = u + v . y = u – v . S = u’v. q = uv’ . r = u.v . k = Sv’ . m = VS Using A = [1 -1 3; 2 5 –6; 0 7 1] and b = [-14, 46, 9]’, solve the system oflinear equations represented by the matrix equation A⋅x = b, where x = [x1, x2, x3]’, using:. The inverse of matrix A, i.e., x = A-1⋅b. MATLAB function linsolve. MATLAB left-division, i.e., x = AbEnter a vector x = [0:0.1:20]; then create the vectors, y = sin(x); z = sin(x/2);w = y + x; r = y-x; and. Plot y vs. x . Plot z vs. x . Plot w vs. x . Plot r vs. x
Ancient Indian astronomers knew the real scientific causes of the eclipses. Even before Aryabhata (AD 476), the celestial phenomena were explained correctly without any traditional myths, as evident from the extant Panca Sidhantas. India’s Chandrayaan-1 continues this tradition of scientific observation and understanding of the natural phenomena. The best view of the Moon was available only after Galileo saw it through his telescope. Even the first picture of the crescent Moon he drew with its craters along the line of lunar sunrise matched well with a photograph taken 350 years later. His telescope demolished the traditional idea of the Moon as a smooth celestial body and incurred the wrath of the Church, even as it quietly triggered a scientific revolution in our understanding of the cosmos. Science fiction seems to have revived people’s interest in the study of the Moon and other celestial objects without reference to myths. Jules Verne (1828-1905), a founder of modern science fiction, inspired the founders of astronautics like Tsiolkovsky, Goddard and Oberath. Verne’s classic novels, A Trip to the Moon (1865) and its sequel, Around the Moon (1870), triggered serious studies on real journeys into space. Despite all the modern telescopes and lunar mission, the Moon has yet to yield much of its secrets. India’s first unmanned lunar mission, Chandrayaan-1, joins the worldwide exploratory journey to the Moon in the International Lunar Decade, which began in 2007. Chandrayaan’s scientific payloads (525 kg in 100 km lunar orbit) are designed for simultaneous photo, geological and chemical mapping of the lunar surface (Box 20.1). The data will test the early evolutionary history of the Moon and help in determining the nature of the lunar crust. The Mission Sequence Chandrayaan-1 was launched on October 22, 2008 from Sriharikota on the east coast, initially into a highly oval-shaped Earth orbit. In order to get the speed and the angle of the final orbit correctly, the spacecraft’s onboard liquid rocket was fired five times on different days, raising the On November 8, 2008, it entered into the lunar orbit Earlier, at about 500 km from the Moon, the velocity of the spacecraft was reduced so that the Moon’s gravity would capture it. The elliptical lunar orbit was later made circular at 100 km from the surface of the Moon. The experiments have since been switched on and the data are being received and processed by the Deep Space Network. En route, the Terrain Mapping Camera took pictures of Earth and the Moon. The satellite weighed 1,304 kg at launch and 590 kg in lunar orbit. It is three-axis stabilized to keep itself in correct position with the help of star sensors, four reaction wheels, attitude control thrusters inertial reference unit, accelerometers. The spacecraft has bipropellant propulsion system for use in maintaining its altitude. The propellant is designed for a mission of two years but it can last for some more time. Its deployable solar array has a single panel that generates 700 W of peak power. When the spacecraft does not get sunlight, it is powered by lithium ion batteries. Its parabolic antenna (0.7 m in diameter) transmits data to the Earth station. The satellite has three solid state recorders on board to store data from various payloads. The recorder can store 32 giga bits. Another recorder has 8 giga bits of capacity, mostly for attitude information and “house-keeping”. The Moon Mineralogy Mapper on board the satellite has an independent recorder with 10 giga bit capacity. A Deep Space Network has been set up to communicate with the satellite. A fully steerable 18-m and a 32-m antenna (for both up and down links) function at Byalalu near Bangalore. The Deep Space Network will support the spacecraft at a slant range of upto 4,00,000 km. The existing ISTRAC network (8 in S-band) stations that support other missions of ISRO, were used during launch and early orbit phase. The network has been strengthened with stations in Bearslake (Russia), and Jet Propulsion Laboratory (USA) and other stations so that the satellite’s “visibility” lasts longer. Dedicated communications links connect the ground stations and the antennae. A National Science Data Centre to process the data into user friendly format will be set up. The design, development and fabrication as well as installation of the 32-m antenna constitute a totally indigenous effort.
3rd Grade Addition, Subtraction, and Place Value Addition, Subtraction, Properties of Addition, Rounding to the tens and hundreds place, and Estimation. Multiplication and Division with large numbers. Answer questions correctly to make music and get new band members. Add, Subtract, Mix n' Max Practice Your Addition & Subtraction For Fun! What is the square root for the number given? Have U herd! Fractions! 25 problems about fractions! Practice using number spellings. Choose the correct answer and enjoy the concert! NUMBERS 1 - 20 : Addition and Subtraction Choose the correct answer for every match operation. 2 digits multipication1. 请点击带有正确答案的气球。2. 限时每题各4秒内回答题目。 Game about dependent events and probability CIjferen + en - zonder onthouden (Addition and Subtraction) Maak alle cijferoefeningen zonder te onthouden.
We met Dr Matthew Campbell, Mechanical Engineer, Postdoctoral Researcher of the Department of Mechanical Engineering and Applied Mechanics of the “Bargatin Group” of the University of Pennsylvania (USA). The goal of the “Bargatin Group” is to create a sail that does not tear and does not melt during interstellar travel. There are currently two different sails: the solar sail, powered by the sun; and the sail powered by laser photons. A solar sail probe is propelled by the solar rays charged with photons, which “bumping” against the sail fabric, push it forward (just like sailing boats, which are pushed by the wind). Instead, the chips/sails pushed by powerful laser beams must have a different fabric, just to withstand the enormous laser power. The laser beams are able to provide the small chip/sail with a frightening boost, capable of significantly reducing interstellar travel. The big dream is to send a chip/sail, the size of a microchip, pushed by powerful laser beams, up to Alpha Centauri (the Star closest to us, only 4 light years away from Earth). With traditional technology it would take 80,000 years of travel to reach it, but with sailing powered by laser photons, the journey would be reduced to just 20 years. To create a technology of the future you are looking to the past, taking up the famous sail. This time, instead of being blown by the wind, she will be blown by the light. Will the light come from a series of lasers mounted on the surface of the Earth? Yes – the idea is to have a very large array of lasers on Earth. The lasers might be arranged in a square pattern, and the side length of the square would be several kilometers, so think of it like thousands of individual lasers linked together. The power required would be around 100 gigawatts, which is about five times the output of the Three Gorges Dam in China. Fortunately, these lasers would not need to be turned on for very long – only 10-30 minutes per chip/sail launch, and it may be that only some of the lasers would need to be turned on at a given time. These lasers would probably be powered by large banks of capacitors or batteries that were charged slowly via solar panels over the course of days or weeks. When the spacecraft has moved million or billion of kilometers away from us, will it continue to be pushed by the lasers mounted on Earth? The lasers are used only to accelerate the chips/sails to high velocities; once a chip/sail reaches its target velocity (around one fifth the speed of light), it no longer needs any light to accelerate it more. The term “acceleration length” is used to denote the distance that a chip/sail travels before it reaches that target velocity. Typical acceleration lengths are on the order of 10 million kilometers. So, the answer is no – once the chip is around 10 million kilometers from Earth, the laser light is no longer needed. Actually, a fun fact is that the lasers can be turned off before the chip/sail reach their target velocity, because it the final photons released from the laser take several minutes to reach the moving sail and propel it to its final speed. What is the difference between your sail, propelled with lasers, and the sail of space agencies, propelled by the sun’s rays? Does the sail fabric have to be different? There are several noteworthy differences between solar sails (powered by the sun) and light sails (powered by laser photons). Solar sails generally have very large areas (100 square meters) in order to capture more of the sun’s photons, whereas light sails must have small areas (less than 10 square meters) in order to be lightweight and accelerate quickly. Solar sails have higher areal densities (about 10 grams per square meter) compared to light sails (about 0.1 gram per square meter). Solar sails are generally designed to travel at low velocities (less than 0.1% the speed of light), whereas light sails aim to travel very fast (20% or more of the speed of light). Many of the existing solar sail designs are planar (flat) and are supported by a frame, whereas the design we propose is curved much like a traditional gas-inflated parachute. Also, solar sails are designed to reflect the entire solar spectrum (many photon wavelengths), whereas light sails are designed for a much narrower range of photons (only the photon wavelengths from the laser – of course compensated for the fact that the incoming photon wavelengths are longer the faster the sail is moving). These differences, as well as others that I have not mentioned here, motivate substantial differences in the sail fabric for solar sails and light sails. To name a few, relative to solar sail films, light sail films must be more reflective, absorb less light (at the laser wavelength), emit more light (at all wavelengths except those near the laser), tolerate greater stress/strain, be more lightweight, etc. This technology will allow a spacecraft to reach the closest star to us, Alpha Centauri, which is 4 light years away, in just 20 years of travel, instead of 80,000 years with traditional technology. Could your laser powered glider also be used for travel in our Solar System, to shorten the duration of the voyage? Solar sails could certainly be used for travel within our solar system. Mission specialists would need to consider whether it would be worthwhile to send gram-sized probes to other planets in minutes or better to wait several years to have full-scale satellites sent using traditional rockets. Do you think that one day, it will be possible to build a spaceship with a sail propelled with lasers, to bring humans close to the star Alpha Centauri? In that case, human beings will have to suffer the effects of Albert Einstein’s Relativity. Others have proposed using laser-propelled light sails for this purpose. Several significant challenges exist for this effort, however, including the enormous laser power required (millions of gigawatts) and the long travel times (40-50 years for a return trip). Even if it were technically possible, it is unclear whether humankind would choose to invest in such a venture. Improvements in microchip and sensor technology promise to greatly improve the capabilities of space probes, perhaps undermining the purpose of human visits to other star systems. Your creation could give us, within a few decades, the first photo taken of a planet belonging to another Solar System! The first close-up photo of an exoplanet, or of another star! What is the advice you would give to the young people of 2050, when they will be thrilled to see the first spacecraft reach another star, for the first time? Interestingly, it may be that, if we are able to construct 50-kilometer-diameter reflectors for space telescopes, we could image foreign planets from Earth without needing to send probes closer. I am a person of faith, believing in a loving God who created our planet and fills it with life. As I imagine exploring further away from Earth and discovering other parts of the cosmos, I sense more and more that our planet is uniquely and specially designed for us to live. Considering that, I would encourage everyone to be thankful for planet Earth, to try to preserve it as best they can, and perhaps even to search out answers for big questions about who created them and what their purpose is in life. Interview made by Fabio Meneghella
A circle (black) which is measured by its circumference (C), diameter (D) in cyan, and radius (R) in red; its centre (O) is in magenta. A circle is a simple closed shape in Euclidean geometry. It is the set of all points in a plane that are at a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves so that its distance from a given point is constant. The distance between any of the points and the centre is called the radius. A circle is a simple closed curve which divides the plane into two regions: an interior and an exterior. In everyday use, the term "circle" may be used interchangeably to refer to either the boundary of the figure, or to the whole figure including its interior; in strict technical usage, the circle is only the boundary and the whole figure is called a disc. A circle may also be defined as a special kind of ellipse in which the two foci are coincident and the eccentricity is 0, or the two-dimensional shape enclosing the most area per unit perimeter squared, using calculus of variations. - 1 Terminology - 2 History - 3 Analytic results - 4 Properties - 5 Compass and straightedge constructions - 6 Circle of Apollonius - 7 Circles inscribed in or circumscribed about other figures - 8 Circle as limiting case of other figures - 9 Squaring the circle - 10 See also - 11 References - 12 Further reading - 13 External links A circle is a plane figure bounded by one line, and such that all right lines drawn from a certain point within it to the bounding line, are equal. The bounding line is called its circumference and the point, its centre.— Euclid. Elements Book I.:4 - Annulus: the ring-shaped object, the region bounded by two concentric circles. - Arc: any connected part of the circle. - Centre: the point equidistant from the points on the circle. - Chord: a line segment whose endpoints lie on the circle. - Circumference: the length of one circuit along the circle, or the distance around the circle. - Diameter: a line segment whose endpoints lie on the circle and which passes through the centre; or the length of such a line segment, which is the largest distance between any two points on the circle. It is a special case of a chord, namely the longest chord, and it is twice the radius. - Disc: the region of the plane bounded by a circle - Lens: the intersection of two discs - Passant: a coplanar straight line that does not touch the circle. - Radius: a line segment joining the centre of the circle to any point on the circle itself; or the length of such a segment, which is half a diameter. - Sector: a region bounded by two radii and an arc lying between the radii. - Segment: a region, not containing the centre, bounded by a chord and an arc lying between the chord's endpoints. - Secant: an extended chord, a coplanar straight line cutting the circle at two points. - Semicircle: an arc that extends from one of a diameter's endpoints to the other. In non-technical common usage it may mean the diameter, arc, and its interior, a two dimensional region, that is technically called a half-disc. A half-disc is a special case of a segment, namely the largest one. - Tangent: a coplanar straight line that touches the circle at a single point. The word circle derives from the Greek κίρκος/κύκλος (kirkos/kuklos), itself a metathesis of the Homeric Greek κρίκος (krikos), meaning "hoop" or "ring". The origins of the words circus and circuit are closely related. The circle has been known since before the beginning of recorded history. Natural circles would have been observed, such as the Moon, Sun, and a short plant stalk blowing in the wind on sand, which forms a circle shape in the sand. The circle is the basis for the wheel, which, with related inventions such as gears, makes much of modern machinery possible. In mathematics, the study of the circle has helped inspire the development of geometry, astronomy, and calculus. Early science, particularly geometry and astrology and astronomy, was connected to the divine for most medieval scholars, and many believed that there was something intrinsically "divine" or "perfect" that could be found in circles. Some highlights in the history of the circle are: - 1700 BCE – The Rhind papyrus gives a method to find the area of a circular field. The result corresponds to 256/ (3.16049...) as an approximate value of π. - 300 BCE – Book 3 of Euclid's Elements deals with the properties of circles. - In Plato's Seventh Letter there is a detailed definition and explanation of the circle. Plato explains the perfect circle, and how it is different from any drawing, words, definition or explanation. - 1880 CE – Lindemann proves that π is transcendental, effectively settling the millennia-old problem of squaring the circle. Length of circumference The ratio of a circle's circumference to its diameter is π (pi), an irrational constant approximately equal to 3.141592654. Thus the length of the circumference C is related to the radius r and diameter d by: As proved by Archimedes, in his Measurement of a Circle, the area enclosed by a circle is equal to that of a triangle whose base has the length of the circle's circumference and whose height equals the circle's radius, which comes to π multiplied by the radius squared: Equivalently, denoting diameter by d, that is, approximately 79% of the circumscribing square (whose side is of length d). This equation, known as the Equation of the Circle, follows from the Pythagorean theorem applied to any point on the circle: as shown in the diagram to the right, the radius is the hypotenuse of a right-angled triangle whose other sides are of length \|x − a\| and \|y − b\|. If the circle is centred at the origin (0, 0), then the equation simplifies to An alternative parametrisation of the circle is: In this parametrisation, the ratio of t to r can be interpreted geometrically as the stereographic projection of the line passing through the centre parallel to the x-axis (see Tangent half-angle substitution). However, this parametrisation works only if t is made to range not only through all reals but also to a point at infinity; otherwise, the bottom-most point of the circle would be omitted. It can be proven that a conic section is a circle exactly when it contains (when extended to the complex projective plane) the points I(1: i: 0) and J(1: −i: 0). These points are called the circular points at infinity. In polar coordinates the equation of a circle is: where a is the radius of the circle, is the polar coordinate of a generic point on the circle, and is the polar coordinate of the centre of the circle (i.e., r0 is the distance from the origin to the centre of the circle, and φ is the anticlockwise angle from the positive x-axis to the line connecting the origin to the centre of the circle). For a circle centred at the origin, i.e. r0 = 0, this reduces to simply r = a. When r0 = a, or when the origin lies on the circle, the equation becomes In the general case, the equation can be solved for r, giving Note that without the ± sign, the equation would in some cases describe only half a circle. In the complex plane, a circle with a centre at c and radius (r) has the equation . In parametric form this can be written . The slightly generalised equation for real p, q and complex g is sometimes called a generalised circle. This becomes the above equation for a circle with , since . Not all generalised circles are actually circles: a generalised circle is either a (true) circle or a line. The tangent line through a point P on the circle is perpendicular to the diameter passing through P. If P = (x1, y1) and the circle has centre (a, b) and radius r, then the tangent line is perpendicular to the line from (a, b) to (x1, y1), so it has the form (x1 − a)x + (y1 – b)y = c. Evaluating at (x1, y1) determines the value of c and the result is that the equation of the tangent is If y1 ≠ b then the slope of this line is This can also be found using implicit differentiation. When the centre of the circle is at the origin then the equation of the tangent line becomes and its slope is - The circle is the shape with the largest area for a given length of perimeter. (See Isoperimetric inequality.) - The circle is a highly symmetric shape: every line through the centre forms a line of reflection symmetry and it has rotational symmetry around the centre for every angle. Its symmetry group is the orthogonal group O(2,R). The group of rotations alone is the circle group T. - All circles are similar. - The circle which is centred at the origin with radius 1 is called the unit circle. - Through any three points, not all on the same line, there lies a unique circle. In Cartesian coordinates, it is possible to give explicit formulae for the coordinates of the centre of the circle and the radius in terms of the coordinates of the three given points. See circumcircle. - Chords are equidistant from the centre of a circle if and only if they are equal in length. - The perpendicular bisector of a chord passes through the centre of a circle; equivalent statements stemming from the uniqueness of the perpendicular bisector are: - If a central angle and an inscribed angle of a circle are subtended by the same chord and on the same side of the chord, then the central angle is twice the inscribed angle. - If two angles are inscribed on the same chord and on the same side of the chord, then they are equal. - If two angles are inscribed on the same chord and on opposite sides of the chord, then they are supplementary. - An inscribed angle subtended by a diameter is a right angle (see Thales' theorem). - The diameter is the longest chord of the circle. - If the intersection of any two chords divides one chord into lengths a and b and divides the other chord into lengths c and d, then ab = cd. - If the intersection of any two perpendicular chords divides one chord into lengths a and b and divides the other chord into lengths c and d, then a2 + b2 + c2 + d2 equals the square of the diameter. - The sum of the squared lengths of any two chords intersecting at right angles at a given point is the same as that of any other two perpendicular chords intersecting at the same point, and is given by 8r 2 – 4p 2 (where r is the circle's radius and p is the distance from the centre point to the point of intersection). - The distance from a point on the circle to a given chord times the diameter of the circle equals the product of the distances from the point to the ends of the chord.:p.71 - A line drawn perpendicular to a radius through the end point of the radius lying on the circle is a tangent to the circle. - A line drawn perpendicular to a tangent through the point of contact with a circle passes through the centre of the circle. - Two tangents can always be drawn to a circle from any point outside the circle, and these tangents are equal in length. - If a tangent at A and a tangent at B intersect at the exterior point P, then denoting the centre as O, the angles ∠BOA and ∠BPA are supplementary. - If AD is tangent to the circle at A and if AQ is a chord of the circle, then ∠DAQ = 1/arc(AQ). - The chord theorem states that if two chords, CD and EB, intersect at A, then CA × DA = EA × BA. - If a tangent from an external point D meets the circle at C and a secant from the external point D meets the circle at G and E respectively, then DC2 = DG × DE. (Tangent-secant theorem.) - If two secants, DG and DE, also cut the circle at H and F respectively, then DH × DG = DF × DE. (Corollary of the tangent-secant theorem.) - The angle between a tangent and chord is equal to one half the angle subtended at the centre of the circle, on the opposite side of the chord (Tangent Chord Angle). - If the angle subtended by the chord at the centre is 90 degrees then l = r √2, where l is the length of the chord and r is the radius of the circle. - If two secants are inscribed in the circle as shown at right, then the measurement of angle A is equal to one half the difference of the measurements of the enclosed arcs (DE and BC). This is the secant-secant theorem. An inscribed angle (examples are the blue and green angles in the figure) is exactly half the corresponding central angle (red). Hence, all inscribed angles that subtend the same arc (pink) are equal. Angles inscribed on the arc (brown) are supplementary. In particular, every inscribed angle that subtends a diameter is a right angle (since the central angle is 180 degrees). - The sagitta (also known as the versine) is a line segment drawn perpendicular to a chord, between the midpoint of that chord and the arc of the circle. - Given the length y of a chord, and the length x of the sagitta, the Pythagorean theorem can be used to calculate the radius of the unique circle which will fit around the two lines: Another proof of this result which relies only on two chord properties given above is as follows. Given a chord of length y and with sagitta of length x, since the sagitta intersects the midpoint of the chord, we know it is part of a diameter of the circle. Since the diameter is twice the radius, the "missing" part of the diameter is (2r − x) in length. Using the fact that one part of one chord times the other part is equal to the same product taken along a chord intersecting the first chord, we find that (2r − x)x = (y / 2)2. Solving for r, we find the required result. Compass and straightedge constructions There are many compass-and-straightedge constructions resulting in circles. The simplest and most basic is the construction given the centre of the circle and a point on the circle. Place the fixed leg of the compass on the centre point, the movable leg on the point on the circle and rotate the compass. Construct a circle with a given diameter - Construct the midpoint M of the diameter. - Construct the circle with centre M passing through one of the endpoints of the diameter (it will also pass through the other endpoint). Construct a circle through 3 noncollinear points - Name the points P, Q and R, - Construct the perpendicular bisector of the segment PQ. - Construct the perpendicular bisector of the segment PR. - Label the point of intersection of these two perpendicular bisectors M. (They meet because the points are not collinear). - Construct the circle with centre M passing through one of the points P, Q or R (it will also pass through the other two points). Circle of Apollonius Apollonius of Perga showed that a circle may also be defined as the set of points in a plane having a constant ratio (other than 1) of distances to two fixed foci, A and B. (The set of points where the distances are equal is the perpendicular bisector of A and B, a line.) That circle is sometimes said to be drawn about two points. The proof is in two parts. First, one must prove that, given two foci A and B and a ratio of distances, any point P satisfying the ratio of distances must fall on a particular circle. Let C be another point, also satisfying the ratio and lying on segment AB. By the angle bisector theorem the line segment PC will bisect the interior angle APB, since the segments are similar: Analogously, a line segment PD through some point D on AB extended bisects the corresponding exterior angle BPQ where Q is on AP extended. Since the interior and exterior angles sum to 180 degrees, the angle CPD is exactly 90 degrees, i.e., a right angle. The set of points P such that angle CPD is a right angle forms a circle, of which CD is a diameter. Second, see:p.15 for a proof that every point on the indicated circle satisfies the given ratio. A closely related property of circles involves the geometry of the cross-ratio of points in the complex plane. If A, B, and C are as above, then the circle of Apollonius for these three points is the collection of points P for which the absolute value of the cross-ratio is equal to one: Stated another way, P is a point on the circle of Apollonius if and only if the cross-ratio [A,B;C,P] is on the unit circle in the complex plane. If C is the midpoint of the segment AB, then the collection of points P satisfying the Apollonius condition is not a circle, but rather a line. Thus, if A, B, and C are given distinct points in the plane, then the locus of points P satisfying the above equation is called a "generalised circle." It may either be a true circle or a line. In this sense a line is a generalised circle of infinite radius. Circles inscribed in or circumscribed about other figures A hypocycloid is a curve that is inscribed in a given circle by tracing a fixed point on a smaller circle that rolls within and tangent to the given circle. Circle as limiting case of other figures The circle can be viewed as a limiting case of each of various other figures: - A Cartesian oval is a set of points such that a weighted sum of the distances from any of its points to two fixed points (foci) is a constant. An ellipse is the case in which the weights are equal. A circle is an ellipse with an eccentricity of zero, meaning that the two foci coincide with each other as the centre of the circle. A circle is also a different special case of a Cartesian oval in which one of the weights is zero. - A superellipse has an equation of the form for positive a, b, and n. A supercircle has b = a. A circle is the special case of a supercircle in which n = 2. - A Cassini oval is a set of points such that the product of the distances from any of its points to two fixed points is a constant. When the two fixed points coincide, a circle results. - A curve of constant width is a figure whose width, defined as the perpendicular distance between two distinct parallel lines each intersecting its boundary in a single point, is the same regardless of the direction of those two parallel lines. The circle is the simplest example of this type of figure. Squaring the circle In 1882, the task was proven to be impossible, as a consequence of the Lindemann–Weierstrass theorem which proves that pi (π) is a transcendental number, rather than an algebraic irrational number; that is, it is not the root of any polynomial with rational coefficients. Specially named circles Of a triangle Of certain quadrilaterals Of certain polygons Of a conic section Of a sphere Of a torus - OL 7227282M - krikos, Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus - Arthur Koestler, The Sleepwalkers: A History of Man's Changing Vision of the Universe (1959) - Proclus, The Six Books of Proclus, the Platonic Successor, on the Theology of Plato Tr. Thomas Taylor (1816) Vol. 2, Ch. 2, "Of Plato" - Chronology for 30000 BC to 500 BC. History.mcs.st-andrews.ac.uk. Retrieved on 2012-05-03. - Squaring the circle. History.mcs.st-andrews.ac.uk. Retrieved on 2012-05-03. - Katz, Victor J. (1998), A History of Mathematics / An Introduction (2nd ed.), Addison Wesley Longman, p. 108, ISBN 978-0-321-01618-8 - Posamentier and Salkind, Challenging Problems in Geometry, Dover, 2nd edition, 1996: pp. 104–105, #4–23. - College Mathematics Journal 29(4), September 1998, p. 331, problem 635. - Johnson, Roger A., Advanced Euclidean Geometry, Dover Publ., 2007. - Harkness, James (1898). Introduction to the theory of analytic functions. London, New York: Macmillan and Co. p. 30. - Ogilvy, C. Stanley, Excursions in Geometry, Dover, 1969, 14–17. - Altshiller-Court, Nathan, College Geometry, Dover, 2007 (orig. 1952). - Incircle – from Wolfram MathWorld. Mathworld.wolfram.com (2012-04-26). Retrieved on 2012-05-03. - Circumcircle – from Wolfram MathWorld. Mathworld.wolfram.com (2012-04-26). Retrieved on 2012-05-03. - Tangential Polygon – from Wolfram MathWorld. Mathworld.wolfram.com (2012-04-26). Retrieved on 2012-05-03. - Pedoe, Dan (1988). Geometry: a comprehensive course. Dover. - "Circle" in The MacTutor History of Mathematics archive \|Wikimedia Commons has media related to:\| \|Wikiquote has quotations related to: Circles\| - Hazewinkel, Michiel, ed. (2001), "Circle", Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4 - Circle (PlanetMath.org website) - Weisstein, Eric W. "Circle". MathWorld.
PARTS AND MATERIALS It would be ideal in this experiment to have two meters: one voltmeter and one ammeter. For experimenters on a budget, this may not be possible. Whatever ammeter is used should be capable measuring at least a few amps of current. A 6-volt “lantern” battery essentially short-circuited by a long piece of wire may produce currents of this magnitude, and your ammeter needs to be capable of measuring it without blowing a fuse or sustaining other damage. Make sure the highest current range on the meter is at least 5 amps! Lessons In Electric Circuits, Volume 1, chapter 8: “DC Metering Circuits” Although this experiment is best performed with two meters, and indeed is shown as such in the schematic diagram and illustration, one multimeter is sufficient. Most ohmmeters operate on the principle of applying a small voltage across an unknown resistance (Runknown) and inferring resistance from the amount of current drawn by it. Except in special cases such as the megger, both the voltage and current quantities employed by the meter are quite small. This presents a problem for measurement of low resistances, as a low resistance specimen may be of much smaller resistance value than the meter circuitry itself. Imagine trying to measure the diameter of a cotton thread with a yardstick, or measuring the weight of a coin with a scale built for weighing freight trucks, and you will appreciate the problem at hand. One of the many sources of error in measuring small resistances with an ordinary ohmmeter is the resistance of the ohmmeter’s own test leads. Being part of the measurement circuit, the test leads may contain more resistance than the resistance of the test specimen, incurring significant measurement error by their presence: One solution is called the Kelvin, or 4-wire, resistance measurement method. It involves the use of an ammeter and voltmeter, determining specimen resistance by Ohm’s Law calculation. A current is passed through the unknown resistance and measured. The voltage dropped across the resistance is measured by the voltmeter, and resistance calculated using Ohm’s Law (R=E/I). Very small resistances may be measured easily by using large current, providing a more easily measured voltage drop from which to infer resistance than if a small current were used. Because only the voltage dropped by the unknown resistance is factored into the calculation—not the voltage dropped across the ammeter’s test leads or any other connecting wires carrying the main current—errors otherwise caused by these stray resistances are completely eliminated. First, select a suitably low resistance specimen to use in this experiment. I suggest the electromagnet coil specified in the last chapter or a spool of wire where both ends may be accessed. Connect a 6-volt battery to this specimen, with an ammeter connected in series. The ammeter used should be capable of measuring at least 5 amps of current so that it will not be damaged by the (possibly) high current generated in this near-short circuit condition. If you have a second meter, use it to measure the voltage across the specimen’s connection points, as shown in the illustration, and record both meters’ indications. If you have only one meter, use it to measure current first, recording its indication as quickly as possible, then immediately opening (breaking) the circuit. Switch the meter to its voltage mode, connect it across the specimen’s connection points, and re-connect the battery, quickly noting the voltage indication. You don’t want to leave the battery connected to the specimen for any longer than necessary for obtaining meter measurements, as it will begin to rapidly discharge due to the high circuit current, thus compromising measurement accuracy when the meter is re-configured and the circuit closed once more for the next measurement. When two meters are used, this is not as significant an issue, because the current and voltage indications may be recorded simultaneously. Take the voltage measurement and divide it by the current measurement. The quotient will be equal to the specimen’s resistance in ohms. by Ikimi .O by Jake Hertz
Linear programming is a branch of mathematics and statistics that allows researchers to determine solutions to problems of optimization. Linear programming problems are distinctive in that they are clearly defined in terms of an objective function, constraints and linearity. The characteristics of linear programming make it an extremely useful field that has found use in applied fields ranging from logistics to industrial planning. All linear programming problems are problems of optimization. This means that the true purpose behind solving a linear programming problem is to either maximize or minimize some value. Thus, linear programming problems are often found in economics, business, advertising and many other fields that value efficiency and resource conservation. Examples of items that can be optimized are profit, resource acquisition, free time and utility. As the name hints, linear programming problems all have the trait of being linear. However, this trait of linearity can be misleading, as linearity only refers to variables being to the first power (and therefore excluding power functions, square roots and other non-linear functions). Linearity does not, however, mean that the functions of a linear programming problem are only of one variable. In short, linearity in linear programming problems allows the variables to relate to each other as coordinates on a line, excluding other shapes and curves. All linear programming problems have a function called the “objective function.” The objective function is written in terms of the variables that can be changed at will (e.g., time spent on a job, units produced and so on). The objective function is the one that the solver of a linear programming problem wishes to maximize or minimize. The result of a linear programming problem will be given in terms of the objective function. The objective function is written with the capital letter “Z” in most linear programming problems. All linear programming problems have constraints on the variables inside the objective function. These constraints take the form of inequalities (e.g., “b < 3” where b may represent the units of books written by an author per month). These inequalities define how the objective function can be maximized or minimized, as together they determine the “domain” in which an organization can make decisions about resources.
We will understand the basic concepts of Place Value, Carrying and Borrowing. Dr. Maya Saran We will use numbers less than 100 throughout. STAGE 1: UNDERSTANDING NUMBERS AS GROUPS OF 10’s PLUS SOME UNITS How to get there: through games, drills, activities. (Getting away from mechanical repetition without understanding.) Suggested game for 2-‐4 players: Show me a numbe · A cup of small tiles with 1 shown on each tile, or beads, or other small objects · Cards with numbers written on them · Pencil and paper The game: One card is put face up. Children try to take that number of tiles from the cup. Whoever does it the fastest wins. (If there are several players in the group, you might have to provide one cup per child to make it easier.) Start with numbers less than 10. Move on the numbers upto 20, then 30. Now the game will become harder. Now change the game. Add a cup of tiles to the table with a “10” marked on each tile. Tell students that one of these can be used in place of 10 of the 1-‐tiles (or beads, whatever you’re using.) Don’t give any other instructions. Now see what happens -‐-‐ children will try to save time by taking the 10-‐ tiles. Now you can give cards with larger numbers, upto 99. Another way to play the game, with 2 players: Start with the unit tiles only. The players are playing as a team, not against each other. Player 1 picks up a card, doesn’t show it to Player 2. Player 1 puts that number of tiles on the table. Player 2 has to count the tiles and write down that number. Then Player 1 shows the original card – the number should match. If the number match, the team is successful. When you move on to larger numbers, upto 30, the game become harder. The team will make mistakes. Now introduce the cup of 10-‐tiles on the table. Tell students that one of these can be used in place of 10 of the 1-‐tiles (or beads, whatever you’re using.) Don’t give any other instructions. Now see what happens -‐-‐ suddenly the game will become easy again. Note: if some students are not getting the idea of replacing groups of ten 1-‐tiles with a single 10-‐tile, then you can control the process by placing on the table 2 cups that contain, respectively, exactly 9 unit-‐tiles and exactly 9 ten-‐tiles. Then they will be forced to use the ten-‐tiles to show numbers greater than 9. STAGE 2: GETTING READY TO CARRY Idea: recognize groups of ten. How to get there: Again, we use games and activities. Some suggested games: Game 1: Khana time! Groups of 3-‐4 students. · 3 dice and a cup of beads or other small objects The game: One player will roll the dice. For each number shown, they will take out that many beads from the cup (if the dice say 1, 4, 2 then they will take out 1 plus 4 plus 2 beads.) the other players watch. The other players watch. When the total crosses more than 10, they yell Khana time! and take away ten beads and put them back in the cup. After one round, when everyone has had one turn, the player with the most beads wins. Notes: Instead of dice, you can use number cards, or non-‐standard dice, or just use 2 dice if the kids are just new to addition. Also a good game to practice addition for beginners. Game 2: Too many mice (taken from mathpickle.com) 2 players · 6 cards showing the numbers 1 to 6. (Can use playing cards.) · 21 small objects (these are mice.) The game: Place the mice in groups of 1, 2, 3, 4, 5 and 6 on the table. Lay the cards face up, with 1 on the bottom, going upwards to 6, which will be face up on the top of the pile. Players take turns to take the top card. When you take a card, let us say 6, then you pick up the pile of 6 mice and you have a choice: you can keep the whole pile or you can give it to the other player. The second player will pick up the card that says 5. Again, he or she will pick up the pile of 5 mice and make a choice: either keep the whole pile or give it to the other player. The catch is: as soon as your mice cross ten, then the cat will come and eat up ten mice! After the last card has gone, the player with the most remaining mice wins. Notes: too many mice is a two player game, but you can add an additional role: one student can play the part of the cat. 1) If your students find the game is always won by the person who goes first, then increase the number of cards from 6 to 9. 2) Is a tie possible with 6 cards? With 7? 8? 9? 10? 3) How many different ways are there to play the game with 2 cards? With 3? 4? 5? 6? 4) If both players play very well, who will win -‐ the first player, the second player -‐ or will it end in a tie? With 1 card? 2 cards? 3? 4? 5? 6? (Taken from mathpickle.com) STAGE 3: CARRYING How to get there: use a grid showing a tens column and a ones column to carry out addition using physical tiles This game is just one possibility – depending on your resources, your particular class, your mood, their mood – you can come up with all kinds of other games and activities! The main idea is that the games whould help the children understand that a group of ten units/beads/objects can be replaced with a single token/tile/bundle representing TEN. Set up for activity: Place on each table 2 cups that contain, respectively, a large number of unit-‐tiles and ten-‐tiles. Place both cups on a paper marked BANK. Give each child a grid of their own. Step 1: get students comfortable showing numbers on this grid using 10-‐tiles and 1-‐tiles. Ask students to show, for example, 42, by placing 4 10-‐tiles in the 10’s column and 2 1-‐tiles in the unit column. You can do this as a whole-‐class activity: let each student have their own pesonal grid in front of them, along with a bank on each table. Call out the numbers one by one, and let all the children show the numbers on their own grids. Let them take their time and get really comfortable with this. You can make a game out of it too… anything you like. IMPORTANT: The process should go both ways: they should take a number and show it on the grid, and if they see a number shown in the grid with tiles, they should be able to write down the number. You can make a game out of this: pair up the students. On each table place a number of cards with numbers shown on them, face down. The first student takes a card and looks at it without showing it to the other student. He or she shows the number on the grid. The second student looks at the grid and writes down the number shown. The team is successful if the number is matching with the original card. Then the students switch roles. Step 2: try addition on this grid without carrying. Simple sums like: You can make cards with one sum each. They pick up the cards and do the addition on their grid. Get them to write down the answers (maybe on the card itself, if you have enough copies.) Again, you can make a game out if it (e.g., timed contest.) Step 3: Now try addition with carrying, very very very simple sums like this: 14+7 The problem is; where to put the extra units? DON’T TELL THEM! Let them think about it. Some students will figure this out themselves: they have to go to the bank to exchange the groups of ten tiles. Other students will copy those who figured it out. You can give a hint to the class like this: · Can you go to the bank? · Can you make an exchange? · If you have too many unit tiles, can the bank help you by making an exchange? Your hints should be as small as possible! Let them have the pleasure of figuring it out. Step 4: addition with two 2-‐digit numbers. The sum should be less than 100 in all cases. Give lots of practice with this (several sessions) before moving on the column-‐wise addition in the standard way. STAGE 4: BORROWING Again we use the same format of the grid, and the same process. Set up the table in the same way as for carrying, with a bank and a grid in front of each child. Step 1: Start with simple subtraction without borrowing. Sums like 26-‐3 You can make activites out of this with 2 children: they can take a card that says 26-‐12, then one of them will show 23 on the grid and the second one will take away 12. They should write down the answer. Step 2: Moving on to simple sums that need borrowing, the idea is the same as before: you need to go to the bank! Start with a simple sum where you only have to subtract a single digit number from a two-‐digit number, like this: You have to take away 4 units. How can you do it? You have to go to the bank. Give them time to think about it, to figure it out by themselves. DON’T TELL THEM WHAT TO DO! Let them struggle. Give small hints only when needed (don’t be in a hurry to give hints.) The hints are the same as for carrying. Step 3: Finally, move on to subtraction using two 2-‐digit numbers. GOING FORWARD: THREE DIGIT NUMBERS The basic ideas are all present when you work with 2 digit numbers. There should be no sush to go on to 3 digits. Once students are really comfortable with 2 digits, then 3 digits will be easy. The entire sequence of activities can be repeated with 3 columns – the activites will be much quicker as they will already be familiar with the processes. Again, give lots of time, and remember to encourage thinking and to keep a playful atmosphere in your classroom!
It is inferred from the empirical study of natural satellites in the Solar System that they are likely to be common elements of planetary systems. The majority of detected exoplanets are giant planets. In the Solar System, the giant planets have large collections of natural satellites (see Moons of Jupiter, Moons of Saturn, Moons of Uranus and Moons of Neptune). Therefore, it is reasonable to assume that exomoons are equally common. Though exomoons are difficult to detect and confirm using current techniques, observations from missions such as Kepler have observed a number of candidates, including some that may be habitats for extraterrestrial life and one that may be a rogue planet. To date there are no confirmed exomoon detections. Nevertheless, in September 2019, astronomers reported that the observed dimmings of Tabby's Star may have been produced by fragments resulting from the disruption of an orphaned exomoon. Definition of satellites around brown dwarfs and free-floating planets Although traditional usage implies moons orbit a planet, the discovery of brown dwarfs with planet-sized satellites, blurs the distinction between planets and moons, due to the low mass of brown dwarfs. This confusion is resolved by the International Astronomical Union (IAU) declaration that "Objects with true masses below the limiting mass for thermonuclear fusion of deuterium that orbit stars, brown dwarfs or stellar remnants and that have a mass ratio with the central object below the L4/L5 instability (M/Mcentral < 2/(25+√) are planets." The IAU definition does not address the naming convention for the satellites of free-floating objects that are less massive than brown dwarfs and below the deuterium limit (the objects are typically referred to as free-floating planets, rogue planets, low-mass brown dwarfs or isolated planetary-mass objects). The satellites of these objects are typically referred to as exomoons in the literature. Characteristics of any extrasolar satellite are likely to vary, as do the Solar System's moons. For extrasolar giant planets orbiting within their stellar habitable zone, there is a prospect a terrestrial planet-sized satellite may be capable of supporting life.[clarification needed] In August 2019, astronomers reported that an exomoon in the WASP-49b exoplanet system may be volcanically active. For impact-generated moons of terrestrial planets not too far from their star, with a large planet–moon distance, it is expected that the orbital planes of moons will tend to be aligned with the planet's orbit around the star due to tides from the star, but if the planet–moon distance is small it may be inclined. For gas giants, the orbits of moons will tend to be aligned with the giant planet's equator because these formed in circumplanetary disks. Lack of moons around planets close to their stars Planets close to their stars on circular orbits will tend to despin and become tidally locked. As the planet's rotation slows down the radius of a synchronous orbit of the planet moves outwards from the planet. For planets tidally locked to their stars, the distance from the planet at which the moon will be in a synchronous orbit around the planet is outside the Hill sphere of the planet. The Hill sphere of the planet is the region where its gravity dominates that of the star so it can hold on to its moons. Moons inside the synchronous orbit radius of a planet will spiral into the planet. Therefore, if the synchronous orbit is outside the Hill sphere, then all moons will spiral into the planet. If the synchronous orbit is not three-body stable then moons outside this radius will escape orbit before they reach the synchronous orbit. A study on tidal-induced migration offered a feasible explanation for this lack of exomoons. It showed the physical evolution of host planets (i.e. interior structure and size) plays a major role in their final fate: synchronous orbits can become transient states and moons are prone to be stalled in semi-asymptotic semimajor axes, or even ejected from the system, where other effects can appear. In turn, this would have a great impact on the detection of extrasolar satellites. Proposed detection methods The existence of exomoons around many exoplanets is theorized. Despite the great successes of planet hunters with Doppler spectroscopy of the host star, exomoons cannot be found with this technique. This is because the resultant shifted stellar spectra due to the presence of a planet plus additional satellites would behave identically to a single point-mass moving in orbit of the host star. In recognition of this, there have been several other methods proposed for detecting exomoons, including: - Direct imaging - Pulsar timing - Transit timing effects - Transit method Direct imaging of an exoplanet is extremely challenging due to the large difference in brightness between the star and exoplanet as well as the small size and irradiance of the planet. These problems are greater for exomoons in most cases. However, it has been theorized that tidally heated exomoons could shine as brightly as some exoplanets. Tidal forces can heat up an exomoon because energy is dissipated by differential forces on it. Io, a tidally heated moon orbiting Jupiter, has volcanoes powered by tidal forces. If a tidally heated exomoon is sufficiently tidally heated and is distant enough from its star for the moon's light not to be drowned out, it would be possible for future telescopes (such as the James Webb Space Telescope) to image it. Doppler spectroscopy of host planet Doppler spectroscopy is an indirect detection method that measures the velocity shift and result stellar spectrum shift associated with an orbiting planet. This method is also known as the Radial Velocity method. It is most successful for main sequence stars The spectra of exoplanets have been successfully partially retrieved for several cases, including HD 189733 b and HD 209458 b. The quality of the retrieved spectra is significantly more affected by noise than the stellar spectrum. As a result, the spectral resolution, and number of retrieved spectral features, is much lower than the level required to perform doppler spectroscopy of the exoplanet. Detection of radio wave emissions from the magnetosphere of host planet During its orbit, Io's ionosphere interacts with Jupiter's magnetosphere, to create a frictional current that causes radio wave emissions. These are called "Io-controlled decametric emissions" and the researchers believe finding similar emissions near known exoplanets could be key to predicting where other moons exist. In 2002, Cheongho Han & Wonyong Han proposed microlensing be used to detect exomoons. The authors found detecting satellite signals in lensing light curves will be very difficult because the signals are seriously smeared out by the severe finite-source effect even for events involved with source stars with small angular radii. In 2008, Lewis, Sackett, and Mardling of the Monash University, Australia, proposed using pulsar timing to detect the moons of pulsar planets. The authors applied their method to the case of PSR B1620-26 b and found that a stable moon orbiting this planet could be detected, if the moon had a separation of about one fiftieth of that of the orbit of the planet around the pulsar, and a mass ratio to the planet of 5% or larger. Transit timing effects In 2007, physicists A. Simon, K. Szatmáry, and Gy. M. Szabó published a research note titled 'Determination of the size, mass, and density of “exomoons” from photometric transit timing variations'. In 2009, David Kipping published a paper outlining how by combining multiple observations of variations in the time of mid-transit (TTV, caused by the planet leading or trailing the planet–moon system's barycenter when the pair are oriented roughly perpendicular to the line of sight) with variations of the transit duration (TDV, caused by the planet moving along the direction path of transit relative to the planet–moon system's barycenter when the moon–planet axis lies roughly along the line of sight) a unique exomoon signature is produced. Furthermore, the work demonstrated how both the mass of the exomoon and its orbital distance from the planet could be determined using the two effects. Transit method (star-planet-moon systems) When an exoplanet passes in front of the host star, a small dip in the light received from the star may be observed. The transit method is currently the most successful and responsive method for detecting exoplanets. This effect, also known as occultation, is proportional to the square of the planet's radius. If a planet and a moon passed in front of a host star, both objects should produce a dip in the observed light. A planet–moon eclipse may also occur during the transit, but such events have an inherently low probability. Transit method (planet-moon systems) If the host planet is directly imaged, then transits of an exomoon may be observable. When an exomoon passes in front of the host planet, a small dip in the light received from the directly-imaged planet may be detected. Exomoons of directly imaged exoplanets and free-floating planets are predicted to have a high transit probability and occurrence rate. Moons as small as Io or Titan should be detectable with the James Webb Space Telescope using this method, but this search method requires a substantial amount of observation time. Orbital sampling effects If a glass bottle is held up to the light it is easier to see through the middle of the glass than it is near the edges. Similarly a sequence of samples of a moon's position will be more bunched up at the edges of the moon's orbit of a planet than in the middle. If a moon orbits a planet that transits its star then the moon will also transit the star and this bunching up at the edges may be detectable in the transit light curves if a sufficient number of measurements are made. The larger the star the greater the number of measurements are needed to create observable bunching. The Kepler spacecraft data may contain enough data to detect moons around red dwarfs using orbital sampling effects but won't have enough data for Sun-like stars. Indirect detection around white dwarfs The atmosphere of white dwarfs can be polluted with metals and in a few cases the white dwarfs are surrounded by a debris disk. Usually this pollution is caused by asteroids or comets, but tidally disrupted exomoons were also proposed in the past for a source of white dwarf pollution. In 2021 Klein et al. discovered that the white dwarfs GD 378 and GALEXJ2339 had an unusually high pollution with beryllium. The researchers conclude that that oxygen, carbon or nitrogen atoms must have been subjected to MeV collisions with protons in order to create this excess of beryllium. In one proposed scenario the beryllium excess is caused by a tidally disrupted exomoon. In this scenario a moon-forming icy disk exists around a giant planet, which orbits the white dwarf. The strong magnetic field of such a giant planet accelerates stellar wind particles, such as protons and directs them into the disk. The accelerated proton collides with water ice in the disk, creating elements like beryllium, boron and lithium in a spallation reaction. These three elements are under-abundant in the universe, because they are destroyed in stars. A moonlet forming in this kind of disk would have a higher beryllium, boron and lithium abundance. The study also predicted that the mid-sized moons of Saturn, for example Mimas, should be enriched in Be, B and Li. In December 2013, a candidate exomoon of a free-floating planet MOA-2011-BLG-262, was announced, but due to degeneracies in the modelling of the microlensing event, the observations can also be explained as a Neptune-mass planet orbiting a low-mass red dwarf, a scenario the authors consider to be more likely. This candidate also featured in the news a few months later in April 2014. In October 2018, researchers using the Hubble Space Telescope published observations of the candidate exomoon Kepler-1625b I, which suggest that the host planet is likely several Jupiter masses, while the exomoon may have a mass and radius similar to Neptune. The study concluded that the exomoon hypothesis is the simplest and best explanation for the available observations, though warned that it is difficult to assign a precise probability to its existence and nature. However, a reanalysis of the data published in April 2019 concluded that the data was fit better by a planet-only model. According to this study, the discrepancy was an artifact of the data reduction, and Kepler-1625b I likely does not exist. A paper by Chris Fox and Paul Wiegert examined the Kepler dataset for indications of exomoons solely from transit timing variations. Eight candidate signals were found that were consistent with an exomoon, however the signals could also be explained by the presence of another planet. Fox & Wiegert's conclusion was more and higher quality transit timing data would be required to establish whether these are truly moons or not. However, in August 2020 David Kipping re-derived the timings of six of the eight targets (based on a pre-peer review version) and evaluated the TTV evidence as uncompelling. The same study finds that Kepler-1625b I remains an exomoon candidate. In January 2022, an exomoon candidate was reported around the planet Kepler-1708b, and because it is orbiting a planet at approximately 1.6 AU from a star that is slightly more luminous than our Sun, it too could be within the habitable zone. However, this candidate is based on limited observations (only 2 transits) and some consider the data to be non-convincing. \|Planet designation\|\|Planet mass\|\|Planet \|1SWASP J140747.93-394542.6\|\|J1407b\|\|020 14–26\|\|3.9 2.2–5.6 \|\|0.24 AU\|\|<0.3\|\|Two possible exomoons residing in small ring gaps around J1407b.\| \|0.40 AU\|\|00.8 <0.8\|\|Possible exomoon residing in a large ring gap around J1407b.\| \|N/A\|\|2MASS J1119-1137A or B\|\|3.7 [[Astronomy:Jupiter mass\|\|J}}}}}}]]\|\|3.6 ± 0.9 separation from each other \|0.004 - 0.009 AU\|\|0.5 - 1\|\|Found using the transit method. A habitable-zone exomoon candidate transiting a directly imaged free-floating planet or isolated planetary-mass object.\| \|HD 189733\|\|HD 189733 b\|\|1.13 [[Astronomy:Jupiter mass\|\|J}}}}}}]]\|\|0.031\|\|0.0087 AU\|\|?\|\|Found by studying periodic increases and decreases in light given off from HD 189733 b. Outside of planet's Hill sphere.\| \|<0.00112 AU\|\|~ 0.015\|\|Exo-Io candidate; The sodium and potassium data at HD189733b is consistent with evaporating exomoons and/or their corresponding gas torus.\| \|Kepler-409\|\|Kepler-409b\|\|1.00 M⊕\|\|0.320\|\|0.222 RHill\|\|0.300\|\|Possible exomoon from transit timing variations, since deemed unlikely.\| \|Kepler-517\|\|Kepler-517b\|\|7.59 M⊕\|\|0.298\|\|0.278 RHill\|\|0.499\|\|Possible exomoon from transit timing variations, since deemed unlikely.\| \|Kepler-809\|\|Kepler-809b\|\|38.02 M⊕\|\|0.308\|\|0.289 RHill\|\|2.931\|\|Possible exomoon from transit timing variations.\| \|Kepler-857\|\|Kepler-857b\|\|14.13 M⊕\|\|0.376\|\|0.208 RHill\|\|1.636\|\|Possible exomoon from transit timing variations.\| \|Kepler-1000\|\|Kepler-1000b\|\|19.95 M⊕\|\|0.534\|\|0.235 RHill\|\|1.551\|\|Possible exomoon from transit timing variations, since deemed unlikely.\| \|Kepler-1326\|\|Kepler-1326b\|\|24.55 M⊕\|\|0.2691\|\|0.295 RHill\|\|6.057\|\|Possible exomoon from transit timing variations, since deemed unlikely.\| \|Kepler-1442\|\|Kepler-1442b\|\|14.13 M⊕\|\|0.405\|\|0.208 RHill\|\|1.586\|\|Possible exomoon from transit timing variations, since deemed unlikely.\| \|KOI-268\|\|KOI-268.01\|\|9.33 M⊕\|\|0.47\|\|0.217 RHill\|\|0.817\|\|Possible exomoon from transit timing variations, since deemed unlikely.\| \|♃\|J}}}}}} \|\| 1.64 \|\| 0.005 AU \|Possible Neptune-sized exomoon or double planet, indicated by transit observations.\| \|WASP-12\|\|WASP-12b\|\|1.465 [[Astronomy:Jupiter mass\|\|J}}}}}}]]\|\|0.0232\|\|6 RP\|\|03.485 0.57–6.4\| \|WASP-49\|\|WASP-49b\|\|0.37 [[Astronomy:Jupiter mass\|\|J}}}}}}]]\|\|0.0379\|\|< 1.74 RP\|\|~ 0.015\|\|Exo-Io candidate; The sodium exosphere around WASP-49b could be due to a volcanically-active Io-like exomoon. ).\| \|WASP-76\|\|WASP-76b\|\|0.92 [[Astronomy:Jupiter mass\|\|J}}}}}}]]\|\|0.033\|\|1.125 RP\|\|~ 0.015\|\|Exo-Io candidate; Sodium detected via absorption spectroscopy around WASP-76b is consistent with an extrasolar toroidal atmosphere generated by an evaporating exomoon.\| \|WASP-121\|\|WASP-121b\|\|1.184 [[Astronomy:Jupiter mass\|\|J}}}}}}]]\|\|0.02544\|\|~ 1.9 RP\|\|~ 0.015\|\|Exo-Io candidate; The sodium detected via absorption spectroscopy around WASP-121b is consistent with an extrasolar gas torus possibly fueled by a hidden exo-Io.\| Habitability of exomoons has been considered in at least two studies published in peer-reviewed journals. René Heller & Rory Barnes considered stellar and planetary illumination on moons as well as the effect of eclipses on their orbit-averaged surface illumination. They also considered tidal heating as a threat for their habitability. In Sect. 4 in their paper, they introduce a new concept to define the habitable orbits of moons. Referring to the concept of the circumstellar habitable zone for planets, they define an inner border for a moon to be habitable around a certain planet and call it the circumplanetary "habitable edge". Moons closer to their planet than the habitable edge are uninhabitable. In a second study, René Heller then included the effect of eclipses into this concept as well as constraints from a satellite's orbital stability. He found that, depending on a moon's orbital eccentricity, there is a minimum mass for stars to host habitable moons at around 0.2 solar masses. Taking as an example the smaller Europa, at less than 1% the mass of the Earth, Lehmer et al. found if it were to end up near to Earth orbit it would only be able to hold onto its atmosphere for a few million years. However, for any larger, Ganymede-sized moons venturing into its solar system's habitable zone, an atmosphere and surface water could be retained pretty much indefinitely. Models for moon formation suggest the formation of even more massive moons than Ganymede is common around many of the super-Jovian exoplanets. Earth-sized exoplanets in the habitable zone around M-dwarfs are often tidally locked to the host star. This has the effect that one hemisphere always faces the star, while the other remains in darkness. An exomoon in an M-dwarf system does not face this challenge, as it is tidally locked to the planet and it would receive light for both hemispheres. Martínez-Rodríguez et al. studied the possibility of exomoons around planets that orbit M-dwarfs in the habitable zone. While they found 33 exoplanets from earlier studies that lie in the habitable zone, only four could host Moon- to Titan-mass exomoons for timescales longer than 0.8 Gyr (HIP 12961 b, HIP 57050 b, Gliese 876 b and c). For this mass range the exomoons could probably not hold onto their atmosphere. The researchers increased the mass for the exomoons and found that exomoons with the mass of Mars around IL Aquarii b and c could be stable on timescales above the Hubble time. The CHEOPS mission could detect exomoons around the brightest M-dwarfs or ESPRESSO could detect the Rossiter–McLaughlin effect caused by the exomoons. Both methods require a transiting exoplanet, which is not the case for these four candidates. Like an exoplanet, an exomoon can potentially become tidally locked to its primary. However, since the exomoon's primary is an exoplanet, it would continue to rotate relative to its star after becoming tidally locked, and thus would still experience a day/night cycle indefinitely. The possible exomoon candidate transiting 2MASS J1119-1137AB lies in the habitable zone of its host (at least initially until the planet cools), but it is unlikely complex life has formed as the system is only 10 Myr old. 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Bibcode: 2018SciA....4.1784T. - Laura Kreidberg; Rodrigo Luger; Megan Bedell (24 April 2019), No Evidence for Lunar Transit in New Analysis of HST Observations of the Kepler-1625 System, doi:10.3847/2041-8213/ab20c8 - Fox, Chris; Wiegert, Paul (23 November 2020). "Exomoon Candidates from Transit Timing Variations: Eight Kepler systems with TTVs explainable by photometrically unseen exomoons". Monthly Notices of the Royal Astronomical Society 501 (2): 2378–2393. doi:10.1093/mnras/staa3743. Bibcode: 2020MNRAS.tmp.3526F. - Kipping, David (8 August 2020). "An Independent Analysis of the Six Recently Claimed Exomoon Candidates". The Astrophysical Journal 900 (2): L44. doi:10.3847/2041-8213/abafa9. Bibcode: 2020ApJ...900L..44K. - Kipping, David et al. (13 January 2022). "An exomoon survey of 70 cool giant exoplanets and the new candidate Kepler-1708 b-i". Nature 6 (3): 367–380. doi:10.1038/s41550-021-01539-1. PMID 35399159. - "Astronomers may have found a huge moon around a Jupiter-like exoplanet". https://www.newscientist.com/article/2304546-astronomers-may-have-found-a-huge-moon-around-a-jupiter-like-exoplanet/. - "1SWASP J1407 b". exoplanet.eu. http://exoplanet.eu/catalog/1swasp_j1407_b/. - Ben-Jaffel, Lotfi; Ballester, Gilda (3 April 2014). "Transit of Exomoon Plasma Tori: New Diagnosis". The Astrophysical Journal 785 (2): L30. doi:10.1088/2041-8205/785/2/L30. Bibcode: 2014ApJ...785L..30B. - Oza, Apurva V.; Johnson, Robert E.; Lellouch, Emmanuel; Schmidt, Carl; Schneider, Nick; Huang, Chenliang; Gamborino, Diana; Gebek, Andrea et al. (2019-08-28). "Sodium and Potassium Signatures of Volcanic Satellites Orbiting Close-in Gas Giant Exoplanets". The Astrophysical Journal 885 (2): 168. doi:10.3847/1538-4357/ab40cc. Bibcode: 2019ApJ...885..168O. - Wyttenbach, A.; Ehrenreich, D.; Lovis, C.; Udry, S.; Pepe, F. (5 May 2015). "Spectrally resolved detection of sodium in the atmosphere of HD 189733b with the HARPS spectrograph". Astronomy & Astrophysics 577: A62. doi:10.1051/0004-6361/201525729. Bibcode: 2015A&A...577A..62W. https://www.aanda.org/articles/aa/full_html/2015/05/aa25729-15/aa25729-15.html. - Keles, Engin; Mallonn, Matthias; von Essen, Carolina; Carroll, Thorsten; Alexoudi, Xanthippi; Pino, Lorenzo; Ilyin, Ilya; Poppenhager, Katja et al. (October 2019). "The potassium absorption on HD189733b and HD209458b". Monthly Notices of the Royal Astronomical Society: Letters 489 (1): L37-L41. doi:10.1093/mnrasl/slz123. Bibcode: 2019MNRAS.489L..37K. - Gebek, Andrea; Oza, Apurva (29 July 2020). "Alkaline exospheres of exoplanet systems: evaporative transmission spectra". Monthly Notices of the Royal Astronomical Society 497 (4): 5271–5291. doi:10.1093/mnras/staa2193. Bibcode: 2020MNRAS.497.5271G. https://academic.oup.com/mnras/article-abstract/497/4/5271/5877918?redirectedFrom=fulltext. Retrieved 8 December 2020. - "WASP-12 b". exoplanet.eu. http://exoplanet.eu/catalog/wasp-12_b/. - Seidel, J.V.; Ehrenreich, D.; Wyttenbach, A.; Allart, R.; Lendl, M.; Pino, L.; Bourrier, V.; Cegla, H.M. et al. (27 March 2019). "Hot Exoplanet Atmospheres Resolved with Transit Spectroscopy (HEARTS)★ II. A broadened sodium feature on the ultra-hot giant WASP-76b". Astronomy & Astrophysics 623: A166. doi:10.1051/0004-6361/201834776. Bibcode: 2019A&A...623A.166S. - Johnson, Robert E.; Huggins, Patrick (August 2006). "Toroidal Atmospheres around Extrasolar Planets". Publications of the Astronomical Society of the Pacific 118 (846): 1136–1143. doi:10.1086/506183. Bibcode: 2006PASP..118.1136J. - Hoeijmakers, H.J.; Seidel, J.V.; Pino, L.; Kitzmann, D.; Sindel, J.P.; Ehrenreich, D.; Oza, A.V.; Bourrier, V. et al. (18 September 2020). "Hot Exoplanet Atmospheres Resolved with Transit Spectroscopy (HEARTS) - IV. A spectral inventory of atoms and molecules in the high-resolution transmission spectrum of WASP-121 b". Astronomy & Astrophysics 641: A123. doi:10.1051/0004-6361/202038365. Bibcode: 2020A&A...641A.123H. - Lozano, Sharon; Dunbar, Brian (30 January 2015). "NASA Supercomputer Assists the Hunt for Exomoons". NASA. http://www.nasa.gov/ames/nasa-supercomputer-assists-the-hunt-for-exomoons. - Nesvorny, David (June 2012). "The Detection and Characterization of a Nontransiting Planet by Transit Timing Variations". Science 336 (6085): 1133–1136. doi:10.1126/science.1221141. PMID 22582018. Bibcode: 2012Sci...336.1133N. - Heller, René; Rory Barnes (January 2013). "Exomoon habitability constrained by illumination and tidal heating". Astrobiology 13 (1): 18–46. doi:10.1089/ast.2012.0859. PMID 23305357. Bibcode: 2013AsBio..13...18H. - Heller, René (September 2012). "Exomoon habitability constrained by energy flux and orbital stability". Astronomy and Astrophysics 545: L8. doi:10.1051/0004-6361/201220003. Bibcode: 2012A&A...545L...8H. - http://iopscience.iop.org/article/10.3847/1538-4357/aa67ea/meta The Longevity of Water Ice on Ganymedes and Europas around Migrated Giant Planets - Martínez-Rodríguez, Héctor; Caballero, José Antonio; Cifuentes, Carlos; Piro, Anthony L.; Barnes, Rory (December 2019). "Exomoons in the Habitable Zones of M Dwarfs" (in en). Astrophysical Journal 887 (2): 261. doi:10.3847/1538-4357/ab5640. ISSN 0004-637X. Bibcode: 2019ApJ...887..261M. - Shadow Moons: The Unknown Sub-Worlds that Might Harbor Life - Likely First Photo of Planet Beyond the Solar System - Working Group on Extrasolar Planets – Definition of a "Planet" Position statement on the definition of a planet. (IAU) - The Hunt for Exomoons with Kepler (HEK): I. Description of a New Observational Project Original source: https://en.wikipedia.org/wiki/Exomoon. Read more
9.1: The Same But Different (5 minutes) In previous grades, students learned the formula for the volume of a cylinder. In this task, students compare and contrast methods for finding volumes of cylinders and prisms. Monitor for vocabulary such as diameter and radius, and for expressions like $Bh$, $\pi r^2$, and $\ell w h$. Arrange students in groups of 2. Tell students there are many possible answers for the questions. After quiet work time, ask students to compare their responses to their partner’s and decide if they are both correct, even if they are different. Follow with a whole-class discussion. Here are two solids. - What information would you need to calculate the volume of each solid? - What is the same and different about how you would find the volume of each solid? In the discussion, be sure the expressions $Bh$ and $\pi r^2$ come up. Ask students if they’ve seen the expression $\ell w h$, and to describe how this relates to $Bh$. Make sure they can describe what the formula $V=Bh$ means in words—to find the volume of a prism or cylinder, we multiply the area of the solid’s base by the height of the solid. 9.2: Water Transfer (15 minutes) In previous grades, students learned how to calculate the volume of a cylinder. In this activity, they revisit that process. Students are prompted to think about volume in 1-unit layers. This will be helpful in upcoming lessons when students learn about Cavalieri’s Principle, or the idea that if two solids have equal-area cross sections at all heights, the solids have equal volumes. Cavalieri’s Principle will be used to derive a formula for the volume of a pyramid. Note that in this activity, “volume of a container” is used as shorthand for “the volume of the region enclosed by the container.” Monitor for students who calculate the volume of the water in the prism then work backward to find the height of the water in the cylinder, and for those who use deductive logic (for example, reasoning that because the two bases have equal area, the height of the water must be equal in both solids) to arrive at the same answer. Students reason abstractly and quantitatively (MP2) when they compare the prism and cylinder volumes. Design Principle(s): Maximize meta-awareness; Support sense-making Supports accessibility for: Language; Social-emotional skills Here are two containers. All measurements are in centimeters. - Suppose the prism contains water that reaches a height of 1 cm. - Draw a representation of this situation. - The water is poured from the prism into the cylinder. What is the height of the water in the cylinder? Explain your reasoning. - Suppose the prism contained water that reached a height of 3 cm instead of 1 cm. If the water were poured into the empty cylinder, what would the height of the water in the cylinder be? Students may be unsure how to work with the prism measurement $4\pi$ cm. Invite them to write out the area calculation as $9\boldcdot4\pi$. Alternatively, they can use an approximation of $\pi$ to get rounded answers. If students struggle to find the height of the water in the cylinder, ask them what they already know about the cylinder, and to consider what additional information they would need to find the height. Prompt them to use their responses to the first question to help them answer this one. The goal is to make connections between methods of calculating volumes for prisms and cylinders. Ask previously identified students to share their reasoning, starting with those who did volume calculations and worked backward, and ending with those who used deductive reasoning. Connect these methods by asking these questions: - “Describe what volume formulas you used. Do they apply to just one of the containers, or to both?” (Sample responses: The expression $\ell wh$ applies to the prism. The expression $\pi r^2 h$ applies to the cylinder. The expression $BH$ applies to both.) - “Consider the volume formula $V=Bh$. How does this formula help explain why the heights were the same for the same volume of water in each container?” (The area of the base, $B$, is the same for each container: $36\pi$ square centimeters. The volume formula can be rewritten $h=V\div B$, so if the containers have the same volume of water in each and have bases with the same area, the height will be the same.) Invite students to describe how the volumes of the two containers compare (they are equal), and challenge them to describe another solid that has the same volume as these two. 9.3: Revisiting Rotation (15 minutes) Students combine their experience with solids of rotation and their understanding of cylinder volume. No specific directions are given in regard to specifying how students should express their volume answer. Monitor for students who leave their answers in terms of $\pi$ and those who found an approximate decimal answer. Supports accessibility for: Memory; Language Suppose each two-dimensional figure is rotated around the vertical axis shown. Each small square in the grid represents 1 square centimeter. For each solid: - Either sketch or describe in words the three-dimensional solid that would form. - Find the solid’s volume. Are you ready for more? - Given a cylinder with radius $r$ and height $h$, write an expression for the volume if each of these changes were made. - The height is tripled to $3h$ and the radius remains $r$. - The radius is tripled to $3r$ and the height remains $h$. - Given a cube of side length $s$, write an expression for the volume if the side length were tripled to $3s$. - Which change affected the shape’s volume the most? The least? Explain or show your reasoning. Teachers with a valid work email address can click here to register or sign in for free access to Extension Student Response. Students may struggle to visualize the rotated figures. For the L shape, encourage them to divide it into smaller pieces and consider each independently. For the rectangle, remind them of the doughnut cross section they drew in a previous lesson. In the discussion, explore different aspects of the calculations students made. Invite one student who left the answer in terms of $\pi$ and another who found a decimal answer to share their results. Remind students that the former is called an exact answer, while the latter is called an approximate answer because the value of $\pi$ needs to be approximated and rounded to find a decimal answer. Emphasize that the choice of expression depends on the situation at hand. If time permits, ask students would would happen if the first figure were rotated around the horizontal axis formed by the bottom edge of the figure. Challenge them to decide if the volume would be the same as with the rotation around the given vertical axis. (The volume of this figure would actually be $99\pi$ cubic centimeters.) Design Principle(s): Support sense-making; Optimize output (for justification) Display the images for all to see, or bring in similar objects. Ask students to identify which solids’ volumes can be found by using the processes from this lesson. Challenge them to explain their reasoning using precise geometric language. Invite them to describe the types of solids for which the formula $V=Bh$ applies. Sample responses: We could find the volumes of the stick of butter, the bolt and nut, and the pencil using the formula $V=Bh$. These shapes are all made of prisms and cylinders, so you can think of them as being built from stacked, congruent layers. The pyramid, traffic cone, and sphere can’t use the formula $V=Bh$. If we think about stacking layers to form these shapes, the shape and size of the layers would change as you move through the object. 9.4: Cool-down - Cylinder Strategies (5 minutes) Teachers with a valid work email address can click here to register or sign in for free access to Cool-Downs. Student Lesson Summary Cylinder and prism volumes can be found by multiplying the area of the figure’s base by its height. The formula $V=Bh$, where $V$ represents volume, $B$ is the area of the base, and $h$ is height, captures this concept. Consider the solid formed by rotating this rectangle around the horizontal axis shown. The result is a hollow cylinder of height 5 units with inner radius 1 unit and outer radius 4 units. To calculate the volume of the outer cylinder, start by finding the area of the circular base. The circle’s radius measures 4 units, so its area is $16 \pi$ square units because $\pi(4)^2=16\pi$. Multiply that by the cylinder’s height of 5 units to get $80\pi$ cubic units. For the inner cylinder, the area of the base is $\pi$ square units, because $\pi (1)^2 = \pi$. The volume is therefore $5\pi$ cubic units. Now subtract the volume of the inner, hollow part from the volume of the outer cylinder to get the volume of the solid: $75 \pi$ cubic units because $80\pi - 5\pi = 75\pi$ .
The North Pole and South Pole look stable on maps. In reality, both poles are gradually drifting because the Earth wobbles slightly as it spins on its axis. The North Pole has drifted slightly toward North America throughout most of the 20th century due to this wobbling. But scientists found something anomalous in 2000. The North Pole mysteriously switched direction and started moving east toward the Greenwich meridian at almost twice its previous speed—at a rate of seven inches a year. In other words, the North Pole is no longer moving toward Hudson Bay but rather toward the British Isles. This was a mystery that baffled geologists for years. Researchers Surendra Adhikari and Erik Irvins of the Jet Propulsions Laboratory at NASA finally figured out why. Their study involved analysing data from the NASA GRACE satellites to determine whether water mass across the planet was related to the spin axis of the Earth. The GRACE satellites pinpointed positive gravity anomalies. These anomalies are indicator that there is more mass in a particular region. The only explanation for this apparent sudden shift of mass is the movement of water on a huge scale. Findings revealed that the movement of water around the world contributes to the rotational wobble of the Earth. There is thereby a strong link between water mass and the wobbles in the spin axis of the Earth. The findings also revealed that human activities are pretty much to blame of the current wobble or movement of the North Pole toward the Greenwich meridian. These activities have been affecting the movement and distribution of water across the globe. Some scientists have already hypothesised that water was playing a role in the wobbling of the Earth and the movement of the North Pole. Some evidences suggested that this phenomenon was due to climate change and the melting of the Greenland Ice Sheet. The study of Adhikari and Irvins demonstrated that the changes in Greenland alone were not enough to generate the gigantic amount of energy needed to pull the spin axis as far as it has shifted. Of course, in the Southern Hemisphere, the ice mass loss from West Antarctica is pulling and the ice mass gain in East Antarctica is pushing in the spin axis of the Earth in the same direction that Greenland is pulling it from the north. But the combined effect was not enough to account for the new direction and the speedup. The NASA researchers realized that something east of Greenland has to be exerting an additional pull. Further analysis of the data revealed that the water deficit in Eurasia—particularly the Indian subcontinent and the Caspian Sea area—was contributing considerably to the phenomenon. This was surprising. Accordingly, Eurasia has lost water mass due to drought and the depletion of aquifers. However, this loss was nowhere near as massive as the changes in the ice sheets. The theory of rotating objects explains why this relative minimal loss of water in Eurasia has considerably affected the spin axis of the Earth. Adhikari and Irvins explained that the spin axis is very sensitive to changes occurring around 45 degrees latitude. A notable takeaway from this study is that it provides a new model for explaining the wobbling of the Earth. Take note that the spin axis wobbles about 20 to 60 inches either east or west of its general direction drift every six to 14 years. By comparing the GRACE data and the graph of changes in continental water storage collected for the same period, Adhikari and Irvins concluded that changes in polar ice appeared to have no relationship to the wobble. Changes in water on land appeared to have contribution to the wobble instead. For example, analysis of the two sets of data revealed that dry years in Eurasia corresponded to eastward swings while wet years corresponded to westward swings. The results suggested that the relationship between land water mass in Eurasia and spin axis wobble is more than a simple correlation. The NASA researchers have isolated the cause. Another takeaway from this study is that it provides insights about the water distribution across the Earth in the past. In addition, the study also introduces a novel model for predicting the movement of the North Pole and South Pole in the future. The wobble of the Earth does not have far-reaching effect on daily lives. However, it is important take into account that moving poles could affect the accuracy of GPS and other satellite or observation tools. Further details of the study of Adhikari and Irvins are in the article “Climate-driven Polar Motion: 2003-2015” published in April 2016 in the journal Science Advances.
Radiochemistry is the chemistry of radioactive materials, where radioactive isotopes of elements are used to study the properties and chemical reactions of non-radioactive isotopes (often within radiochemistry the absence of radioactivity leads to a substance being described as being inactive as the isotopes are stable). Much of radiochemistry deals with the use of radioactivity to study ordinary chemical reactions. This is very different from radiation chemistry where the radiation levels are kept too low to influence the chemistry. Radiochemistry includes the study of both natural and man-made radioisotopes. Main decay modes 1. α (alpha) radiation—the emission of an alpha particle (which contains 2 protons and 2 neutrons) from an atomic nucleus. When this occurs, the atom's atomic mass will decrease by 4 units and atomic number will decrease by 2. These three types of radiation can be distinguished by their difference in penetrating power. Alpha can be stopped quite easily by a few centimetres in air or a piece of paper and is equivalent to a helium nucleus. Beta can be cut off by an aluminium sheet just a few millimetres thick and are electrons. Gamma is the most penetrating of the three and is a massless chargeless high energy photon. Gamma radiation requires an appreciable amount of heavy metal radiation shielding (usually lead or barium-based) to reduce its intensity. By neutron irradiation of objects it is possible to induce radioactivity; this activation of stable isotopes to create radioisotopes is the basis of neutron activation analysis. One of the most interesting objects which has been studied in this way is the hair of Napoleon's head, which have been examined for their arsenic content. A series of different experimental methods exist, these have been designed to enable the measurement of a range of different elements in different matrices. To reduce the effect of the matrix it is common to use the chemical extraction of the wanted element and/or to allow the radioactivity due to the matrix elements to decay before the measurement of the radioactivity. Since the matrix effect can be corrected for by observing the decay spectrum, little or no sample preparation is required for some samples, making neutron activation analysis less susceptible to contamination. The effects of a series of different cooling times can be seen if a hypothetical sample which contains sodium, uranium and cobalt in a 100:10:1 ratio was subjected to a very short pulse of thermal neutrons. The initial radioactivity would be dominated by the 24Na activity (half-life 15 h) but with increasing time the 239Np (half-life 2.4 d after formation from parent 239U with half-life 24 min) and finally the 60Co activity (5.3 yr) would predominate. One biological application is the study of DNA using radioactive phosphorus-32. In these experiments stable phosphorus is replaced by the chemical identical radioactive P-32, and the resulting radioactivity is used in analysis of the molecules and their behaviour. Another example is the work which was done on the methylation of elements such as sulfur, selenium, tellurium and polonium by living organisms. It has been shown that bacteria can convert these elements into volatile compounds, it is thought that methylcobalamin (vitamin B12) alkylates these elements to create the dimethyls. It has been shown that a combination of Cobaloxime and inorganic polonium in sterile water forms a volatile polonium compound, while a control experiment which did not contain the cobalt compound did not form the volatile polonium compound. For the sulfur work the isotope 35S was used, while for polonium 207Po was used. In some related work by the addition of 57Co to the bacterial culture, followed by isolation of the cobalamin from the bacteria (and the measurement of the radioactivity of the isolated cobalamin) it was shown that the bacteria convert available cobalt into methylcobalamin. Radiochemistry also includes the study of the behaviour of radioisotopes in the environment; for instance, a forest or grass fire can make radioisotopes become mobile again. In these experiments, fires were started in the exclusion zone around Chernobyl and the radioactivity in the air downwind was measured. It is important to note that a vast number of processes are able to release radioactivity into the environment, for example the action of cosmic rays on the air is responsible for the formation of radioisotopes (such as 14C and 32P), the decay of 226Ra forms 222Rn which is a gas which can diffuse through rocks before entering buildings and dissolve in water and thus enter drinking water in addition human activities such as bomb tests, accidents, and normal releases from industry have resulted in the release of radioactivity. Chemical form of the actinides The environmental chemistry of some radioactive elements such as plutonium is complicated by the fact that solutions of this element can undergo disproportionation and as a result many different oxidation states can coexist at once. Some work has been done on the identification of the oxidation state and coordination number of plutonium and the other actinides under different conditions. This includes work on both solutions of relatively simple complexes and work on colloids Two of the key matrixes are soil/rocks and concrete, in these systems the chemical properties of plutonium have been studied using methods such as EXAFS and XANES. Movement of colloids While binding of a metal to the surfaces of the soil particles can prevent its movement through a layer of soil, it is possible for the particles of soil which bear the radioactive metal can migrate as colloidal particles through soil. This has been shown to occur using soil particles labeled with 134Cs, these have been shown to be able to move through cracks in the soil. Radioactivity is present everywhere (and has been since the formation of the earth). According to the International Atomic Energy Agency, one kilogram of soil typically contains the following amounts of the following three natural radioisotopes 370 Bq 40K (typical range 100–700 Bq), 25 Bq 226Ra (typical range 10–50 Bq), 25 Bq 238U (typical range 10–50 Bq) and 25 Bq 232Th (typical range 7–50 Bq). Action of microorganisms The action of micro-organisms can fix uranium; Thermoanaerobacter can use chromium(VI), iron(III), cobalt(III), manganese(IV) and uranium(VI) as electron acceptors while acetate, glucose, hydrogen, lactate, pyruvate, succinate, and xylose can act as electron donors for the metabolism of the bacteria. In this way the metals can be reduced to form magnetite (Fe3O4), siderite (FeCO3), rhodochrosite (MnCO3), and uraninite (UO2). Other researchers have also worked on the fixing of uranium using bacteria , Francis R. Livens et al. (Working at Manchester) have suggested that the reason why Geobacter sulfurreducens can reduce UO2+ 2 cations to uranium dioxide is that the bacteria reduce the uranyl cations to UO+ 2 which then undergoes disproportionation to form UO2+ 2 and UO2. This reasoning was based (at least in part) on the observation that NpO+ 2 is not converted to an insoluble neptunium oxide by the bacteria. Despite the growing use of nuclear medicine, the potential expansion of nuclear power plants, and worries about protection against nuclear threats and the management of the nuclear waste generated in past decades, the number of students opting to specialize in nuclear and radiochemistry has decreased significantly over the past few decades. Now, with many experts in these fields approaching retirement age, action is needed to avoid a workforce gap in these critical fields, for example by building student interest in these careers, expanding the educational capacity of universities and colleges, and providing more specific on-the-job training. Nuclear and Radiochemistry (NRC) is mostly being taught at university level, usually first at the Master- and PhD-degree level. In Europe, as substantial effort is being done to harmonize and prepare the NRC education for the industry's and society's future needs. This effort is being coordinated in a projects funded by the Coordinated Action supported by the European Atomic Energy Community's 7th Framework Program: The CINCH-II project - Cooperation in education and training In Nuclear Chemistry. This project has set up a wiki dedicated to NRC teaching: NucWik. Although NucWik is primarily aimed at teachers, anyone interested in Nuclear and Radiochemistry is welcome and can find a lot of information and material explaining topics related to NRC. - H. Smith, S. Forshufvud and A. Wassén, Nature, 1962, 194(26 May), 725–726 - N. Momoshima, Li-X. Song, S. Osaki and Y. Maeda, "Biologically induced Po emission from fresh water", Journal of Environmental Radioactivity, 2002, 63, 187–197 - N. Momoshima, Li-X. Song, S. Osaki and Y. Maeda, "Formation and emission of volatile polonium compound by microbial activity and polonium methylation with methylcobalamin", Environmental Science and Technology, 2001, 35, 2956–2960 - Yoschenko VI et al. (2006) Resuspension and redistribution of radionuclides during grassland and forest fires in the Chernobyl exclusion zone: part I. 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C. Duff, D. B. Hunter, I. R. Triay, P. M. Bertsch, D. T. Reed, S. R. Sutton, G. Shea-McCarthy, J. Kitten, P. Eng, S. J. Chipera, and D. T. Vaniman, "Mineral Associations and Average Oxidation States of Sorbed Pu on Tuff", Environ. Sci. Technol, 1999, 33, 2163–2169 - R. D. Whicker and S. A. Ibrahim, "Vertical migration of 134Cs bearing soil particles in arid soils: implications for plutonium redistribution", Journal of Environmental Radioactivity, 2006, 88, 171–188. - "Generic Procedures for Assessment and Response during a Radiological Emergency", International Atomic Energy Agency TECDOC Series number 1162, published in 2000 - Yul Roh, Shi V. Liu, Guangshan Li, Heshu Huang, Tommy J. Phelps, and Jizhong Zhou, "Isolation and Characterization of Metal-Reducing Thermoanaerobacter Strains from Deep Subsurface Environments of the Piceance Basin, Colorado", Applied and Environmental Microbiology, 2002, 68, 6013–6020. - Joanna C. Renshaw, Laura J. C. Butchins, Francis R. 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Vectors are a data structure that's useful for storing information like position and velocity. A vector is something that describes both magnitude and direction. In order to illustrate this idea imagine that you live in a city with a grid-based system. You're located at point A and you're trying to get to point B. You're new in town so you stop somebody on the street and ask them. The person tells you that you need to go 3 blocks East, then 4 blocks South. The person gave you two sets of information and each set of information contained a distance and a direction. One set was 3 blocks East, and the other set was 4 blocks South. This is all a vector is, it's really that simple. In this case the person gave you two vectors to follow. Notice that both pieces of each vector are necessary in order for you to reach your destination. If the person had just told you to go 3 blocks, then 4 blocks, you'd naturally want to know in which direction you should travel those distances. Likewise, if he had told you to go East, then South, you'd want to know how far to travel in each direction. Vectors require both a magnitude (or length) and a direction. You should also notice that the order in which he gave you the directions doesn't matter. He could have just as easily told you to go 4 blocks South first, then 3 blocks East. He could have also sent you in all sorts of directions before reaching your destination, so you can see that there are actually an infinite number of paths to travel from A to B. It would have been a lot easier if you could just go straight to point B cutting across all of the blocks. This is always the shortest path and usually the one we're most interested in. But this vector isn't purely East and it isn't purely South. It's a combination of both of these directions. If we could use shorthand to describe this vector it would be 3E + 4S for 3 blocks East and 4 blocks South. Don't let the addition symbol confuse you, this isn't like adding 2 + 2 where we get a single result. We can add vectors together as we'll see below, but we can't add orthogonal directions such as East and South so we keep them separated with the addition symbol. We can add same directions together like 3N + 5N = 8N and if the directions are opposite each other then we can add them together as well like 4N + 6S = 2S. Adding opposite directions is basically subtraction. We don't even need special symbols for South and West since South = -North and West = -East. Then it makes more sense how we got the previous result if we write it as 4N - 6N = -2N. Start by creating a file called vector.py. You can organize the code any way you want, but for this tutorial I'm just going to have all of the code in a single folder called 'Pacman'. What I will then do is create this vector.py file inside the 'Pacman' folder and then copy the following code to the file. To start we import the math package so we can use some predefined math functions. Then we create the Vector class. The x and y variables should be easy to understand based on the explanation above. They are just the coordinates that the vector is pointing towards. The 'thresh' variable will be explained below when we actually use it. These are the methods that will allow us to add and subtract vectors, as well as multiply and divide a vector by a scalar. Notice in our division code that we first need to check that we are not dividing by 0. Very important! Also when multiplying and dividing a vector by a scalar, order matters. Not in general, but just here. The scalar always has to be on the right side. So something like 'Vector2 * 5' and not '5 * Vector2'. What's the difference between the __div__ and the __truediv__ methods? It appears that the __truediv__ just calls the __div__ method, so what gives? Python 3 does away with the __div__ method in favor of the __truediv__ method and Python 2 uses the __div__ method. That's really it. I'm trying to make this work for both Python 2 and Python 3. These methods allow us to check for equality between two vectors. This is also where we use the thresh variable. In computer-land two values can be nearly equal like 2 and 2.00000000001. If we were doing scientific computing, then that difference could be significant. However, we aren't doing science and we need to be able to say that those two values are the same. So we do that by subtracting the two values and then seeing if it's less than our theshold value, which is just a really small number. So in our game the two vectors <3,4> is equal to <3.000004, 4.000001>. We have two types of magnitude methods here. The 'magnitude' method returns the actual length of the vector which requires a square root (which is why we had to import the math package). The 'magnitudeSquared' method, however, is the one we'll use more often in our game. The reason is because it does not require us to take a square root. It's good practice to avoid taking the square root in your games whenever you can avoid it. If all you need to do is compare the length of two vectors, then comparing their length squared is just as valid as comparing their length. For example, if m and n are the lengths of two vectors and if m > n, then it's also true that m2 > n2. The copy method allows us to copy any vector so we get a new instance of it. The reason we want to do this is because of how Python stores its variables in memory. I'll explain more when we get to an example. The reasoning though is that we want to create a new instance of this object, then we can modify the new object without touching this object. The last two methods are just nice to have. They just convert our vector into a tuple and an int tuple. They really just make code cleaner later. This method doesn't affect the functionality of the game or anything, it's really a convenience function so we can easily print out the vector. So let's say we create a vector with 'v = Vector(3,4)'. Then we want to print out the vector at some point. Naturally we want to say something like: 'print(v)'. However, at this point if you do that you'll get something like the following printed out: '<vector.Vector object at 0x03020F70>' That's not terribly useful, it just tells you where that object is in memory. So if we include the following function we can tell the class how we want the printout of the objects to look. So now if we say 'print(v)' we'll get the following: '<3, 4>'. That's a lot more useful, so this method is good to have especially for debugging. You can add a __str__ method to all of your classes and have it output whatever you want.
If you've ever wondered how two or more pieces of data relate to each other (e.g. how GDP is impacted by changes in unemployment and inflation), or if you've ever had your boss ask you to create a forecast or analyze predictions based on relationships between variables, then learning regression analysis would be well worth your time. In this article, you'll learn the basics of simple linear regression, sometimes called 'ordinary least squares' or OLS regression—a tool commonly used in forecasting and financial analysis. We will begin by learning the core principles of regression, first learning about covariance and correlation, and then moving on to building and interpreting a regression output. Popular business software such as Microsoft Excel can do all the regression calculations and outputs for you, but it is still important to learn the underlying mechanics. - Simple linear regression is commonly used in forecasting and financial analysis—for a company to tell how a change in the GDP could affect sales, for example. - Microsoft Excel and other software can do all the calculations, but it's good to know how the mechanics of simple linear regression work. At the heart of a regression model is the relationship between two different variables, called the dependent and independent variables. For instance, suppose you want to forecast sales for your company and you've concluded that your company's sales go up and down depending on changes in GDP. The sales you are forecasting would be the dependent variable because their value "depends" on the value of GDP and the GDP would be the independent variable. You would then need to determine the strength of the relationship between these two variables in order to forecast sales. If GDP increases/decreases by 1%, how much will your sales increase or decrease? The formula to calculate the relationship between two variables is called covariance. This calculation shows you the direction of the relationship. If one variable increases and the other variable tends to also increase, the covariance would be positive. If one variable goes up and the other tends to go down, then the covariance would be negative. The actual number you get from calculating this can be hard to interpret because it isn't standardized. A covariance of five, for instance, can be interpreted as a positive relationship, but the strength of the relationship can only be said to be stronger than if the number was four or weaker than if the number was six. We need to standardize the covariance in order to allow us to better interpret and use it in forecasting, and the result is the correlation calculation. The correlation calculation simply takes the covariance and divides it by the product of the standard deviation of the two variables. This will bind the correlation between a value of -1 and +1. A correlation of +1 can be interpreted to suggest that both variables move perfectly positively with each other and a -1 implies they are perfectly negatively correlated. In our previous example, if the correlation is +1 and the GDP increases by 1%, then sales would increase by 1%. If the correlation is -1, a 1% increase in GDP would result in a 1% decrease in sales—the exact opposite. Now that we know how the relative relationship between the two variables is calculated, we can develop a regression equation to forecast or predict the variable we desire. Below is the formula for a simple linear regression. The "y" is the value we are trying to forecast, the "b" is the slope of the regression line, the "x" is the value of our independent value, and the "a" represents the y-intercept. The regression equation simply describes the relationship between the dependent variable (y) and the independent variable (x). The intercept, or "a," is the value of y (dependent variable) if the value of x (independent variable) is zero, and so is sometimes simply referred to as the 'constant.' So if there was no change in GDP, your company would still make some sales. This value, when the change in GDP is zero, is the intercept. Take a look at the graph below to see a graphical depiction of a regression equation. In this graph, there are only five data points represented by the five dots on the graph. Linear regression attempts to estimate a line that best fits the data (a line of best fit) and the equation of that line results in the regression equation. Regressions in Excel Now that you understand some of the background that goes into a regression analysis, let's do a simple example using Excel's regression tools. We'll build on the previous example of trying to forecast next year's sales based on changes in GDP. The next table lists some artificial data points, but these numbers can be easily accessible in real life. Just eyeballing the table, you can see that there is going to be a positive correlation between sales and GDP. Both tend to go up together. Using Excel, all you have to do is click the Tools drop-down menu, select Data Analysis and from there choose Regression. The popup box is easy to fill in from there; your Input Y Range is your "Sales" column and your Input X Range is the change in GDP column; choose the output range for where you want the data to show up on your spreadsheet and press OK. You should see something similar to what is given in the table below: Regression Statistics Coefficients The major outputs you need to be concerned about for simple linear regression are the R-squared, the intercept (constant) and the GDP's beta (b) coefficient. The R-squared number in this example is 68.7%. This shows how well our model predicts or forecasts the future sales, suggesting that the explanatory variables in the model predicted 68.7% of the variation in the dependent variable. Next, we have an intercept of 34.58, which tells us that if the change in GDP was forecast to be zero, our sales would be about 35 units. And finally, the GDP beta or correlation coefficient of 88.15 tells us that if GDP increases by 1%, sales will likely go up by about 88 units. The Bottom Line So how would you use this simple model in your business? Well if your research leads you to believe that the next GDP change will be a certain percentage, you can plug that percentage into the model and generate a sales forecast. This can help you develop a more objective plan and budget for the upcoming year. Of course, this is just a simple regression and there are models that you can build that use several independent variables called multiple linear regressions. But multiple linear regressions are more complicated and have several issues that would need another article to discuss.
There is no standard definition, but in the United States (where the terminology was devised in the 1970s from the engineering term light railway), light rail operates primarily along exclusive rights-of-way and uses either individual tramcars or multiple units coupled to form a train that is lower capacity and lower speed than a long heavy passenger train or metro system. A few light rail networks tend to have characteristics closer to rapid transit or even commuter rail; some of these heavier rapid transit-like systems are referred to as light metros. Other light rail networks are tram-like in nature and partially operate on streets. Light rail systems are found throughout the world, on all inhabited continents. They have been especially popular in recent years due to their lower capital costs and increased reliability compared with heavy rail systems. - 1 History - 2 Definition - 3 Types - 4 Track gauge - 5 Comparison to other rail transit modes - 6 Tram and other light rail transit systems worldwide - 7 Capacity - 8 Safety - 9 Health impact of light rail - 10 Integration with bicycles - 11 Construction and operation costs - 12 Variations - 13 See also - 14 References - 15 External links Many original tram and streetcar systems in the United Kingdom, United States, and elsewhere were decommissioned starting in the 1950s as the popularity of the automobile increased. Britain abandoned its last tram system, except for Blackpool, by 1962. Although some traditional trolley or tram systems exist to this day, the term "light rail" has come to mean a different type of rail system. Modern light rail technology has primarily West German origins, since an attempt by Boeing Vertol to introduce a new American light rail vehicle was a technical failure. After World War II, the Germans retained many of their streetcar networks and evolved them into model light rail systems (Stadtbahnen). Except for Hamburg, all large and most medium-sized German cities maintain light rail networks. The basic concepts of light rail were put forward by H. Dean Quinby in 1962 in an article in Traffic Quarterly called "Major Urban Corridor Facilities: A New Concept". Quinby distinguished this new concept in rail transportation from historic streetcar or tram systems as: - having the capacity to carry more passengers - appearing like a train, with more than one car connected together - having more doors to facilitate full utilization of the space - faster and quieter in operation The term light rail transit (LRT) was introduced in North America in 1972 to describe this new concept of rail transportation. The first of the new light rail systems in North America began operation in 1978 when the Canadian city of Edmonton, Alberta, adopted the German Siemens-Duewag U2 system, followed three years later by Calgary, Alberta, and San Diego, California. The concept proved popular, and although Canada has few cities big enough for light rail, there are now at least 30 light rail systems in the United States. Britain began replacing its run-down local railways with light rail in the 1980s, starting with the Tyne and Wear Metro and followed by the Docklands Light Railway (DLR) in London. The historic term light railway was used because it dated from the British Light Railways Act 1896, although the technology used in the DLR system was at the high end of what Americans considered to be light rail. The trend to light rail in the United Kingdom was firmly established with the success of the Manchester Metrolink system in 1992. The term light rail was coined in 1972 by the U.S. Urban Mass Transportation Administration (UMTA; the precursor to the Federal Transit Administration) to describe new streetcar transformations that were taking place in Europe and the United States. In Germany the term Stadtbahn (to be distinguished from S-Bahn, which stands for Stadtschnellbahn) was used to describe the concept, and many in UMTA wanted to adopt the direct translation, which is city rail (the Norwegian term, bybane, means the same). However, UMTA finally adopted the term light rail instead. Light in this context is used in the sense of "intended for light loads and fast movement", rather than referring to physical weight. The infrastructure investment is also usually lighter than would be found for a heavy rail system. The Transportation Research Board (Transportation Systems Center) defined "light rail" in 1977 as "a mode of urban transportation utilizing predominantly reserved but not necessarily grade-separated rights-of-way. Electrically propelled rail vehicles operate singly or in trains. LRT provides a wide range of passenger capabilities and performance characteristics at moderate costs." The American Public Transportation Association (APTA), in its Glossary of Transit Terminology, defines light rail as: ...a mode of transit service (also called streetcar, tramway, or trolley) operating passenger rail cars singly (or in short, usually two-car or three-car, trains) on fixed rails in right-of-way that is often separated from other traffic for part or much of the way. Light rail vehicles are typically driven electrically with power being drawn from an overhead electric line via a trolley [pole] or a pantograph; driven by an operator on board the vehicle; and may have either high platform loading or low level boarding using steps." However, some diesel-powered transit is designated light rail, such as the O-Train Trillium Line in Ottawa, Canada, the River Line in New Jersey, United States, and the Sprinter in California, United States, which use diesel multiple unit (DMU) cars. Light rail is similar to the British English term light railway, long-used to distinguish railway operations carried out under a less rigorous set of regulation using lighter equipment at lower speeds from mainline railways. Light rail is a generic international English phrase for these types of rail systems, which means more or less the same thing throughout the English-speaking world. The use of the generic term light rail avoids some serious incompatibilities between British and American English. The word tram, for instance, is generally used in the UK and many former British colonies to refer to what is known in North America as a streetcar, but in North America tram can instead refer to an aerial tramway, or, in the case of the Disney amusement parks, even a land train. (The usual British term for an aerial tramway is cable car, which in the US usually refers to a ground-level car pulled along by subterranean cables.) The word trolley is often used as a synonym for streetcar in the United States, but is usually taken to mean a cart, particularly a shopping cart, in the UK and elsewhere. Many North American transportation planners reserve streetcar for traditional vehicles that operate exclusively in mixed traffic on city streets, while they use light rail to refer to more modern vehicles operating mostly in exclusive rights of way, since they may operate both side-by-side targeted at different passenger groups. The difference between British English and American English terminology arose in the late 19th century when Americans adopted the term "street railway", rather than "tramway", with the vehicles being called "streetcars" rather than "trams". Some have suggested that the Americans' preference for the term "street railway" at that time was influenced by German emigrants to the United States (who were more numerous than British immigrants in the industrialized Northeast), as it is the same as the German term for the mode, Straßenbahn (meaning "street railway"). A further difference arose because, while Britain abandoned all of its trams except Blackpool after World War II, seven major North American cities (Toronto, Boston, Philadelphia, San Francisco, Pittsburgh, Newark, and New Orleans) continued to operate large streetcar systems. When these cities upgraded to new technology, they called it light rail to differentiate it from their existing streetcars since some continued to operate both the old and new systems. Since the 1980s, Portland, Oregon, has built all three types of system: a high-capacity light rail system in dedicated lanes and rights-of-way, a low-capacity streetcar system integrated with street traffic, and an aerial tram system. The opposite phrase heavy rail, used for higher-capacity, higher-speed systems, also avoids some incompatibilities in terminology between British and American English, as for instance in comparing the London Underground and the New York City Subway. Conventional rail technologies including high-speed, freight, commuter/regional, and metro/subway/elevated urban transit systems are considered "heavy rail". People movers and personal rapid transit are even "lighter," at least in terms of capacity. Monorail is a separate technology that has been more successful in specialized services than in a commuter transit role. Due to varying definitions, it is hard to distinguish between what is called light rail, and other forms of urban and commuter rail. A system described as light rail in one city may be considered to be a streetcar or tram system in another. Conversely, some lines that are called "light rail" are in fact very similar to rapid transit; in recent years, new terms such as light metro have been used to describe these medium-capacity systems. Some "light rail" systems, such as Sprinter, bear little similarity to urban rail, and could alternatively be classified as commuter rail or even inter-city rail. In the United States, "light rail" has become a catch-all term to describe a wide variety of passenger rail systems. There is a significant difference in cost between these different classes of light rail transit. Tram-like systems are often less expensive than metro-like systems by a factor of two or more. The most difficult distinction to draw is that between light rail and streetcar or tram systems. There is a significant amount of overlap between the technologies, many of the same vehicles can be used for either, and it is common to classify streetcars or trams as a subcategory of light rail rather than as a distinct type of transportation. The two general versions are: - The traditional type, where tracks and trains run along the streets and share space with road traffic. Stops tend to be very frequent, but little effort is made to set up special stations. Because space is shared, the tracks are usually visually unobtrusive. - A more modern variation, where the trains tend to run along their own right-of-way, separated from road traffic. Stops are generally less frequent, and the vehicles are often boarded from a platform. Tracks are highly visible, and in some cases significant effort is expended to keep traffic away through the use of special signaling, level crossings with gate arms, or even a complete separation with non-level crossings. At the highest degree of separation, it can be difficult to draw the line between light rail and metros, as in the case of Wuppertal's Schwebebahn hanging rail system, the "D" Branch of Boston's Green Line, or London's Docklands Light Railway, which would likely not be considered "light" were it not for the contrast between it and the London Underground. These may be considered to be light metro lines rather than "light rail" lines. In Europe, however, the term light rail is increasingly used to describe any rapid transit system with a fairly low frequency or short trains compared to heavier mass rapid systems such as the London Underground or Singapore's Mass Rapid Transit. For instance, the LRT-1 and MRT-3 in Manila are often referred to as "light rail", despite being fully segregated, mostly elevated railways. This phenomenon is quite common in Chinese cities, where elevated light metro lines in Shanghai, Wuhan, and Dalian are called light rail lines. In North America, such systems are not considered light rail. Many systems have mixed characteristics. Indeed, with proper engineering, a rail line could run along a street, then go underground, and then run along an elevated viaduct. For example, the Los Angeles Metro Rail's Gold Line "light rail" has sections that could alternatively be described as a tramway, a light metro, and, in a narrow sense, rapid transit. This is especially common in the United States, where there is not a popularly perceived distinction between these different types of urban rail systems. It is even possible to have high-floor rapid transit cars run along a street, like a tram; this is known as street running. Speed and stop frequency In some areas, "light rail" may also refer to any rail line with frequent low speeds or many stops in a short distance. This inherits the old definition of light railway in the UK. Hong Kong's Light Rail is an example of this, although it is also called "light rail" because it is a lower-scale system than the rest of the MTR. Sprinter in the San Diego area uses DMUs and is targeted towards a commuter rail audience; however, because of the large number of stops along the line, it is called light rail. Reference speed from major light rail systems, including station stop time, is shown below. \|System\|\|Average speed (mph)\| \|Dallas (Red Line)\|\|21\| \|Dallas (Blue Line)\|\|19\| \|Los Angeles (Blue Line)\|\|24\| \|Los Angeles (Green Line)\|\|38\| \|Salt Lake City\|\|24\| However, low top speed is not always a differentiating characteristic between light rail and other systems. For example, the Siemens S70 LRVs used in the Houston METRORail and other North American LRT systems have a top speed of 106 kilometres per hour (66 mph) while the trains on the all-underground Montreal Metro can only reach a top speed of 72 kilometres per hour (45 mph). Los Angeles Metro light rail vehicles have higher top and average speeds than Montreal Metro or New York City Subway trains. The main difference is that Montreal Metro and New York City Subway trains carry far more passengers than any North American LRT system, and the trains have faster acceleration, making station-to-station times relatively short in their densely populated urban areas. Most light rail systems serve less densely populated cities and suburbs where passenger traffic is not high, but low cost combined with high top speed may be important to compete with automobiles. Many light rail systems—even fairly old ones—have a combination of both on- and off-road sections. In some countries (especially in Europe), only the latter is described as light rail. In those places, trams running on mixed rights-of-way are not regarded as light rail, but considered distinctly as streetcars or trams. However, the requirement for saying that a rail line is "separated" can be quite low—sometimes just with concrete "buttons" to discourage automobile drivers from getting onto the tracks. Some systems such as Seattle's Link are truly mixed but closed to traffic, with light rail vehicles and traditional buses both operating along a common right-of-way. Some systems, such as the AirTrain JFK in New York City, the DLR in London, and Kelana Jaya Line in Kuala Lumpur, Malaysia, have dispensed with the need for an operator. The Vancouver SkyTrain was an early adopter of driverless vehicles, while the Toronto Scarborough rapid transit operates the same trains as Vancouver, but uses drivers. In most discussions and comparisons, these specialized systems are generally not considered light rail. Historically, the track gauge has had considerable variations, with narrow gauge common in many early systems. However, most light rail systems are now standard gauge. Older standard-gauge vehicles could not negotiate sharp turns as easily as narrow-gauge ones, but modern light rail systems achieve tighter turning radii by using articulated cars. An important advantage of standard gauge is that standard railway maintenance equipment can be used on it, rather than custom-built machinery. Using standard gauge also allows light rail vehicles to be moved around, conveniently using the same tracks as freight railways. Another factor favoring standard gauge is that accessibility laws are making low-floor trams mandatory, and there is generally insufficient space for wheelchairs to move between the wheels in a narrow-gauge layout. Furthermore, standard-gauge rolling stock can be switched between networks either temporarily or permanently and both newly built and used standard-gauge rolling stock tends to be cheaper to buy, as more companies offer such vehicles. Comparison to other rail transit modes With its mix of right-of-way types and train control technologies, LRT offers the widest range of latitude of any rail system in the design, engineering, and operating practices. The challenge in designing light rail systems is to realize the potential of LRT to provide fast, comfortable service while avoiding the tendency to overdesign that results in excessive capital costs beyond what is necessary to meet the public's needs. \|Rapid transit\|\|Light rail vehicles (LRVs) are distinguished from rapid rail transit (RRT) vehicles by their capability for operation in mixed traffic, generally resulting in a narrower car body and articulation in order to operate in a street traffic environment. With their large size, large turning radius, and often an electrified third rail, RRT vehicles cannot operate in the street. Since LRT systems can operate in existing streets, they can often avoid the cost of expensive grade-separated subway and elevated segments that would be required with RRT.\| \|Streetcars or trams\|\|Conversely, LRVs generally outperform traditional streetcars in terms of capacity and top-end speed, and almost all modern LRVs are capable of multiple-unit operation. The latest generation of LRVs is considerably larger and faster, typically 29 metres (95 ft) long with a maximum speed of around 105 kilometres per hour (65 mph).\| \|Heritage streetcars\|\|A variation considered by many cities is to use historic or replica cars on their streetcar systems instead of modern LRVs. A heritage streetcar may not have the capacity and speed of an LRV, but it will add to the ambiance and historic character of its location.\| \|Light metro\|\|A derivative of LRT is light rail rapid transit (LRRT), also referred to as light metro. Such railways are characterized by exclusive rights of way, advanced train control systems, short headway capability, and floor-level boarding. These systems approach the passenger capacity of full metro systems, but can be cheaper to construct due to LRVs generally being smaller in size, turning tighter curves and climbing steeper grades than standard RRT vehicles, and having a smaller station size.\| \|Interurbans\|\|The term interurban mainly refers to rail cars that run through streets like ordinary streetcars (trams), but also between cities or towns, often through rural environments. In the period 1900–1930, interurbans were very common in the US, especially in the Midwest. Some of them, like the Red Devils, the J. G. Brill Bullets, and the Electroliners, were the high-speed railcars of their time, with an in-service speed of up to about 145 km/h (90 mph). In Europe interurbans are making a comeback as "tram-trains" (locally known under different names) that operate on both railway and light rail tracks, often with different voltage. The Karlsruhe Stadtbahn is one well known example.\| Typical rolling stock \|Type\|\|Rapid transit (heavy rail)\|\|Light rail\|\|Tram, or streetcar\|\|Heritage streetcar\| \|Manufacturer\|\|Rohr\|\|Siemens\|\|Skoda\|\|Gomaco Trolley Co.\| \|Model\|\|BART A-Car\|\|S70\|\|10T\|\|Replica Birney\| \|Width\|\|3.2 metres (10 ft)\|\|2.7 metres (8.9 ft)\|\|2.6 metres (8.53 ft)\|\|2.62 metres (8.6 ft)\| \|Length\|\|22.9 metres (75 ft)\|\|27.7 metres (91 ft) articulated\|\|20.13 metres (66.0 ft) articulated\|\|15.16 metres (49.7 ft)\| \|Weight (empty)\|\|TBD\|\|48.6 t\|\|28.8 t\|\|23.5 t\| \|Capacity\|\|150 max.\|\|72 seats, 220 max.\|\|30 seats, 157 max.\|\|40 seats, 50 max.\| \|Top speed\|\|125 km/h (78 mph)\|\|106 km/h (66 mph)\|\|70 km/h (43 mph)\|\|48 km/h (30 mph)\| \|Typical consist\|\|4–10 vehicles\|\|2–5 vehicles\|\|1 vehicle\|\|1 vehicle\| An important factor crucial to LRT is the train operator. Unlike rail rapid transit, which can travel unattended under automatic train operation (ATO), safe, high-quality LRT operation relies on a human operator as a key element. The reason that the operator is so important is because the train tracks often share the streets with automobiles, other vehicles, and pedestrians. If trains were fully automated on roads, nobody would be there to stop the train if a car pulled in front of it. Light rail trains are actually very sturdily built for passenger safety, and to reduce damage from impacts with cars. The latest generation of LRVs has the advantage of partially or fully low-floor design, with the floor of the vehicles only 300 to 360 mm (11.8 to 14.2 in) above the top of the rail, a feature not found in either rapid rail transit vehicles or streetcars. This allows them to load passengers, including those in wheelchairs or strollers, directly from low-rise platforms that are little more than raised sidewalks. This satisfies requirements to provide access to disabled passengers without using expensive and delay-inducing wheelchair lifts, while also making boarding faster and easier for other passengers. Overhead lines supply electricity to the vast majority of light rail systems. This avoids the danger of passengers stepping on an electrified third rail. The Docklands Light Railway uses an inverted third rail for its electrical power, which allows the electrified rail to be covered and the power drawn from the underside. Trams in Bordeaux, France, use a special third-rail configuration where the power is only switched on beneath the trams, making it safe on city streets. Several systems in Europe and a few recently opened systems in North America use diesel-powered trains. Tram and other light rail transit systems worldwide Around the world there are many tram and streetcar systems. Some date from the beginning of the 20th century or earlier, but many of the original tram and streetcar systems were closed down in the mid-20th century, with the exceptions of many Eastern Europe countries. Even though many systems closed down over the years, there are still a number of tram systems that have been operating much as they did when they were first built over a century ago. Some cities (such as Los Angeles and Jersey City) that once closed down their streetcar networks are now restoring, or have already rebuilt, at least some of their former streetcar/tram systems. Most light rail services are currently committed to articulated vehicles like modern LRVs, i.e. trams, with the exception of large underground metro or rapid transit systems. The table below illustrates the capacity of a light rail train (the Siemens S70) compared to that of a standard car with five seats. The average length of a standard five-seat car is about 4.74 metres. The length of a Siemens S70 light rail vehicle is 27.7 meters, approximately the same length as 5.8 cars. The maximum occupancy of a five-seat automobile car is five people. The maximum capacity of the Siemens S70 is 220 people. This means that one metre in a car has a capacity of one person and one metre in a light rail vehicle has a capacity of almost eight persons, so the capacity of light rail is about eight times as high as that of an average consumer car, if only the length of the vehicles is taken into consideration. The average width of an automobile is about 1.77 metres, while the average width of the Siemens S70 is about 2.7 metres. The area of an average consumer car is about 8.4 m², while the area taken up by a light rail car is about 74.8 m². In an automobile car, each square metre has room for only 0.6 persons, while each square metre in a light rail car has room for 2.9 persons. This means that a light rail vehicle is significantly more capacity-effective than a consumer car is. Height is not taken into consideration, because it is not normally a problem given minimum-clearance regulations for underpasses. \|Length\|\|Width\|\|Area\|\|Maximum passengers\|\|Passenger density\| \|Car\|\|4.74 m\|\|1.77 m\|\|8.4 m²\|\|5\|\|0.6/m²\| \|Siemens S70\|\|27.7 m\|\|2.7 m\|\|74.8 m²\|\|220\|\|2.9/m²\| Comparison with high capacity roads While the table above compares the maximum capacity of each mode, the average use of a lane might be quite different, based on a number of factors. One line of light rail (requires 25' Right of Way) has a theoretical capacity of up to 8 times more than one 12' lane of freeway (not counting buses) during peak times. Roads have ultimate capacity limits that can be determined by traffic engineering. They usually experience a chaotic breakdown in flow and a dramatic drop in speed (colloquially known as a traffic jam) if they exceed about 2,000 vehicles per hour per lane (each car roughly two seconds behind another). Since most people who drive to work or on business trips do so alone, studies show that the average car occupancy on many roads carrying commuters is only about 1.5 people per car during the high-demand rush hour periods of the day. This combination of factors limits roads carrying only automobile commuters to a maximum observed capacity of about 3,000 passengers per hour per lane. The problem can be mitigated by introducing high-occupancy vehicle (HOV) lanes and ride-sharing programs, but in most cases the solution adopted has been to add more lanes to the roads. By contrast, light rail vehicles can travel in multi-car trains carrying a theoretical ridership up to 20,000 passengers per hour in much narrower rights-of-way, not much more than two car lanes wide for a double track system. They can often be run through existing city streets and parks, or placed in the medians of roads. If run in streets, trains are usually limited by city block lengths to about four 180-passenger vehicles (720 passengers). Operating on two-minute headways using traffic signal progression, a well-designed two-track system can handle up to 30 trains per hour per track, achieving peak rates of over 20,000 passengers per hour in each direction. More advanced systems with separate rights-of-way using moving block signalling can exceed 25,000 passengers per hour per track. Most light rail systems in the United States are limited by demand rather than capacity (by and large, most North American LRT systems carry fewer than 4,000 persons per hour per direction), but Boston's and San Francisco's light rail lines carry 9,600 and 13,100 passengers per hour per track during rush hour. Elsewhere in North America, the Calgary C-Train and Monterrey Metro have higher light rail ridership than Boston or San Francisco. Systems outside North America often have much higher passenger volumes. The Manila Light Rail Transit System is one of the highest capacity ones, having been upgraded in a series of expansions to handle 40,000 passengers per hour per direction, and having carried as many as 582,989 passengers in a single day on its Line 1. It achieves this volume by running four-car trains with a capacity of up to 1,350 passengers each at a frequency of up to 30 trains per hour. However, the Manila light rail system has full grade separation and as a result has many of the operating characteristics of a metro system rather than a light rail system. A capacity of 1,350 passengers per train is more similar to heavy rail than light rail. A bus rapid transit (BRT) system using dedicated lanes can have a theoretical capacity of 3,600 passengers per hour per direction (30 buses per direction, 120 passengers in articulated buses). BRT is an alternative to LRT, at least if very high capacity is not needed. Using buses, roads can achieve a much higher commuter capacity than is achievable with passenger cars. To have 30 buses per direction an hour, buses must have priority at traffic lights and have their own dedicated lanes. Buses can travel closer to each other than rail vehicles because of better braking capability. However, each bus vehicle requires a single driver, whereas a light rail train may have three to four cars of much larger capacity in one train under the control of one driver, or no driver at all in fully automated systems, increasing the labor costs of high-traffic BRT systems compared to LRT systems. The peak passenger capacity per lane per hour depends on which types of vehicles are allowed at the roads. Typically roadways have 1,900 passenger cars per lane per hour (pcplph). If only cars are allowed, the capacity will be less and will not increase when the traffic volume increases. When there is a bus driving on this route, the capacity of the lane will be more and will increase when the traffic level increases. And because the capacity of a light rail system is higher than that of a bus, there will be even more capacity when there is a combination of cars and light rail. Table 3 shows an example of peak passenger capacity. \|Car\|\|Car + bus\|\|Car + light rail\| (Edson & Tennyson, 2003) While many claim that light rail is safe, research by car bloggers[which?] suggest otherwise. For example, an analysis of data from the 505-page National Transportation Statistics report published by the US Department of Transportation shows that light rail fatalities are higher than all other forms of transportation except motorcycle travel (31.5 fatalities per 100 million miles). However, the National Transportation Statistics report published by the US Department of Transportation states that "Caution must be exercised in comparing fatalities across modes because significantly different definitions are used. In particular, Rail and Transit fatalities include incident-related (as distinct from accident-related) fatalities, such as fatalities from falls in transit stations or railroad employee fatalities from a fire in a workshed. Equivalent fatalities for the Air and Highway modes (fatalities at airports not caused by moving aircraft or fatalities from accidents in automobile repair shops) are not counted toward the totals for these modes. Thus, fatalities not necessarily directly related to in service transportation are counted for the transit and rail modes, potentially overstating the risk for these modes." Health impact of light rail Integration with bicycles Light rail lines have various policies on bicycles. Some fleets restrict bicycles on trains during peak hours. Some light rail systems, such as the St. Louis MetroLink, allow bicycles on the trains, but only in the rear sections of cars. Some light rail lines, like San Francisco's, allow only folding bicycles on board. In some systems dedicated bike parking is available at select stations and others are integrated with local bike share systems. Construction and operation costs The cost of light rail construction varies widely, largely depending on the amount of tunneling and elevated structures required. A survey of North American light rail projects shows that costs of most LRT systems range from $15 million to over $100 million per mile. Seattle's new light rail system is by far the most expensive in the US, at $179 million per mile, since it includes extensive tunneling in poor soil conditions, elevated sections, and stations as deep as 180 feet (55 m) below ground level. This results in costs more typical of subways or rapid transit systems than light rail. At the other end of the scale, four systems (Baltimore, Maryland; Camden, New Jersey; Sacramento, California; and Salt Lake City, Utah) incurred construction costs of less than $20 million per mile. Over the US as a whole, excluding Seattle, new light rail construction costs average about $35 million per mile. By comparison, a freeway lane expansion typically costs $1.0 million to $8.5 million per lane mile for two directions, with an average of $2.3 million. However, freeways are frequently built in suburbs or rural areas, whereas light rail tends to be concentrated in urban areas, where right of way and property acquisition is expensive. Similarly, the most expensive US highway expansion project was the "Big Dig" in Boston, Massachusetts, which cost $200 million per lane mile for a total cost of $14.6 billion. Since a light rail track can carry up to 20,000 people per hour as compared with 2,000–2,200 vehicles per hour for one freeway lane, light rail is comparable in construction cost to freeways on a per passenger-mile basis. For example, in Boston and San Francisco, light rail lines carry 9,600 and 13,100 passengers per hour, respectively, in the peak direction during rush hour. Combining highway expansion with LRT construction can save costs by doing both highway improvements and rail construction at the same time. As an example, Denver's Transportation Expansion Project rebuilt interstate highways 25 and 225 and added a light rail expansion for a total cost of $1.67 billion over five years. The cost of 17 miles (27 km) of highway improvements and 19 miles (31 km) of double-track light rail worked out to $19.3 million per highway lane-mile and $27.6 million per LRT track-mile. The project came in under budget and 22 months ahead of schedule. LRT cost efficiency improves dramatically as ridership increases, as can be seen from the numbers above: the same rail line, with similar capital and operating costs, is far more efficient if it is carrying 20,000 people per hour than if it is carrying 2,400. The Calgary, Alberta, C-Train used many common light rail techniques to keep costs low, including minimizing underground and elevated trackage, sharing transit malls with buses, leasing rights-of-way from freight railroads, and combining LRT construction with freeway expansion. As a result, Calgary ranks toward the less expensive end of the scale with capital costs of around $24 million per mile. However, Calgary's LRT ridership is much higher than any comparable US light rail system, at 300,000 passengers per weekday, and as a result its capital efficiency is also much higher. Its capital costs were one-third those of the San Diego Trolley, a comparably sized US system built at the same time, while by 2009 its ridership was approximately three times as high. Thus, Calgary's capital cost per passenger was much lower than that of San Diego. Its operating cost per passenger was also much lower because of its higher ridership. A typical C-Train vehicle costs only CA$163 (equivalent to $192 in 2016) per hour to operate, and since it averages 600 passengers per operating hour, Calgary Transit estimates that its LRT operating costs are only 27 cents per ride, versus $1.50 per ride on its buses. Compared to buses, costs can be lower due to lower labor costs per passenger mile, higher ridership (observations show that light rail attracts more ridership than a comparable bus service) and faster average speed (reducing the number of vehicles needed for the same service frequency). While light rail vehicles are more expensive to buy, they have a longer useful life than buses, sometimes making for lower life-cycle costs. Trams operating on mainline railways Around Karlsruhe, Kassel, and Saarbrücken in Germany, dual-voltage light rail trains partly use mainline railroad tracks, sharing these tracks with heavy rail trains. In the Netherlands, this concept was first applied on the RijnGouweLijn. This allows commuters to ride directly into the city centre, rather than taking a mainline train only as far as a central station and then having change to a tram. In France, similar tram-trains are planned for Paris, Mulhouse, and Strasbourg; further projects exist. In some cases, tram-trains use previously abandoned or lightly used heavy rail lines in addition to or instead of still in use mainline tracks. Some of the issues involved in such schemes are: - compatibility of the safety systems - power supply of the track in relation to the power used by the vehicles (frequently different voltages, rarely third rail vs overhead wires) - width of the vehicles in relation to the position of the platforms - height of the platforms There is a history of what would now be considered light rail vehicles operating on heavy rail rapid transit tracks in the US, especially in the case of interurban streetcars. Notable examples are Lehigh Valley Transit trains running on the Philadelphia and Western Railroad high-speed third rail line (now the Norristown High Speed Line). Such arrangements are almost impossible now, due to the Federal Railroad Administration refusing (for crash safety reasons) to allow non-FRA compliant railcars (i.e., subway and light rail vehicles) to run on the same tracks at the same times as compliant railcars, which includes locomotives and standard railroad passenger and freight equipment. Notable exceptions in the US are the NJ Transit River Line from Camden to Trenton and Austin's Capital MetroRail, which have received exemptions to the provision that light rail operations occur only during daytime hours and Conrail freight service only at night, with several hours separating one operation from the other. The O-Train Trillium Line in Ottawa also has freight service at certain hours. Third-rail power for trams When electric streetcars were introduced in the late 19th century, conduit current collection was one of the first ways of supplying power, but it proved to be much more expensive, complicated, and trouble-prone than overhead wires. When electric street railways became ubiquitous, conduit power was used in those cities that did not permit overhead wires. In Europe, it was used in London, Paris, Berlin, Marseille, Budapest, and Prague. In the United States, it was used in parts of New York City and Washington, DC. Third rail technology was investigated for use on the Gold Coast of Australia for the G:link light rail, though power from overhead lines was ultimately utilized for that system. In the French city of Bordeaux, the tramway network is powered by a third rail in the city centre, where the tracks are not always segregated from pedestrians and cars. The third rail (actually two closely spaced rails) is placed in the middle of the track and divided into eight-metre sections, each of which is powered only while it is completely covered by a tram. This minimises the risk of a person or animal coming into contact with a live rail. In outer areas, the trams switch to conventional overhead wires. The Bordeaux power system costs about three times as much as a conventional overhead wire system, and took 24 months to achieve acceptable levels of reliability, requiring replacement of all the main cables and power supplies. Operating and maintenance costs of the innovative power system still remain high. However, despite numerous service outages, the system was a success with the public, gaining up to 190,000 passengers per day. - Automated guideway transit - Cater MetroTrolley - Capa vehicle - General Motors streetcar conspiracy - Light rail in North America - Light Rail Transit Association - List of North American light rail systems by ridership - List of rail transit systems in the United States - List of town tramway systems (all-time lists) - List of tram and light rail transit systems (operational systems only) - List of United States light rail systems by ridership - Medium-capacity rail transport system - Passenger rail terminology - Railway electrification system - Rubber-tyred trams - Streetcars in North America - Tram and light rail transit systems - Urban rail transit - "Fact Book Glossary - Mode of Service Definitions". American Public Transportation Association. 2015. Retrieved 2015-01-06. - "National Transit Database Glossary". U.S. Department of Transportation Federal Transit Administration. 18 October 2013. Retrieved 2015-01-06. - "What is light rail?". Public transport A-Z. International Association of Public Transport. 2008. Archived from the original on 13 October 2008. Retrieved 2015-07-29. - "This Is Light Rail Transit" (PDF). Transportation Research Board. pp. 7–9. Retrieved 2015-01-06. - "What is Light Rail?". Light Rail Transit Association (LRTA). Retrieved 2015-01-06. - "Welcome to Saskrailmuseum.org". Saskatchewan Railway Museum. BlackNova Internet Services. 11 September 2008. Archived from the original on 15 October 2008. Retrieved 2009-12-26. - Courtenay, Peter (2006). "Trams in the UK". thetrams.co.uk. Retrieved 26 December 2009. - Bottoms, Glen (2000). Continuing Developments in Light Rail Transit in Western Europe (PDF). 9th National Light Rail Transit Conference. Portland, Oregon: Light Rail Transit Association. Retrieved 26 December 2009. - Thompson, Gregory L. (2003). "Defining an Alternative Future: The Birth of the Light Rail Movement in North America". Transportation Research Circular. Transportation Research Board (E-C058). Retrieved 26 December 2009. From: 9th National Light Rail Transit Conference - Gregory L. Thompson (2003), Defining an Alternative Future: Birth of the Light Rail Movement in North America (PDF), Transportation Research Board. - "Tram (definition)". Merriam-Webster Online Dictionary. Retrieved 2007-07-18. - "The Yesterland Hotel Tram". Yesterland.com. Retrieved 2013-02-07. - "Trolley (definition)". Merriam-Webster Online Dictionary. Retrieved 2007-07-18. - "Light Rail Transit". Encyclopædia Britannica. Retrieved 2007-07-18. - Smiler, Simon P. "Trams, Streetcars, and Light Rail Vehicles". citytransport.info. Retrieved 2007-07-18. - Plous, Jr, F.K. (June 1984). "A Desire Named Streetcar". Planning. American Planning Association. Archived from the original on 3 March 2006. Retrieved 2007-08-14. - "Light Rail Schedule Speed – Faster Than Bus, Competitive With Car". - "Link Light Rail in the North American Context". 30 December 2009. - Fazio, A. E.; Hickey, T. R. (2003). "Designing New Light Rail – Taking Engineering Beyond Vanilla". Circular E-C058: 9th National Light Rail Transit Conference. Transportation Research Board. Retrieved 2006-11-10. - "Technical Data". Light Rail Vehicle System Houston/Texas, USA. Siemens. 2008. Archived from the original on 27 April 2008. Retrieved 2008-03-18. - "Siemens S70 Low-floor Light Rail Vehicle" (PDF). Siemens. - "Gomaco Trolley Company". Gomaco Trolley Company. - Comparison of Energy Use & CO2 Emissions From Different Transportation Modes page 7, Results of Analysis. M.J. Bradley & Associates, May 2007 - Matt Lorenz and Lily Elefteriadou (2000) A Probabilistic Approach to Defining Freeway Capacity and Breakdown (PDF), Transportation Research Board. - "Highlights of the 2001 National Household Travel Survey: A-15 Vehicle Occupancy Per Vehicle Mile by Time of Day and Weekend Status". US Department of Transportation. - Tom Parkinson and Ian Fisher (1996) Rail Transit Capacity, Transportation Research Board. - Transit Capacity and Quality of Service Manual, Transportation Research Board. - Hanson, Susan; Giuliano, Genevieve (2004). The geography of urban transportation. Guilford Press. ISBN 1-59385-055-7. - "LRT-1 sets 25-year high record ridership". Manilla Light Rail Transit Authority. 12 January 2009. Archived from the original on 26 March 2009. Retrieved 2009-03-14. - "NCHRP Report 599: Default Values for Highway Capacity and Level of Service Analyses" (PDF). NATIONAL COOPERATIVE HIGHWAY RESEARCH PROGRAM. - "National Transportation Statistics 2013" (PDF). U.S. Department of Transportation. - "Dissected: How're Ya Dying? Charting transportation mayhem in its many gory varieties". - "Bikes on Muni". San Francisco Municipal Transportation Agency. Retrieved 2013-08-14. - "Status of North American Light Rail Projects". Light Rail Now. 2002. Retrieved 2006-11-23. - "Link Light Rail Projects". Sound Transit (Central Puget Sound Regional Transit Authority). 2006. Archived from the original on 2006-11-17. Retrieved 2006-11-23. - "Highway Construction Cost Comparison Survey Final Report" (PDF). Washington State Department of Transportation. April 2002. p. 3. Archived from the original (PDF) on 2009-09-05. - Traffic and Highway Engineering By Nicholas J. Garber, Lester A. Hoel, p. 37 - Shaw, Mark (May–June 2006). "Reinventing a Corridor: Denver's T-REX project nears completion after five years". Constructor. McGraw-Hill Construction. Archived from the original on 19 October 2006. Retrieved 2006-11-20. - Flynn, Kevin (17 November 2006). "T-REX trains ready to roll". Rocky Mountain News (Denver, CO). Retrieved 2006-11-20. - McKendrick; et al. (2006). "Calgary's C-Train – Effective Capital Utilization" (PDF). Joint International Light Rail Conference, St. Louis, Missouri. Calgary Transit. Retrieved 2008-02-11. - "LRT technical data". Calgary Transit. 2006. Archived from the original on 2006-10-23. Retrieved 2006-10-14. - Post, Robert C. (2007). Urban Mass Transit: The Life Story of a Technology. Greenwood Press. pp. 45–47. ISBN 0-313-33916-3. - "Gold Coast Light Rail Feasibility Study". Commonwealth Government, Gold Coast City Council & Queensland Government Queensland Transport. 23 December 2004. Archived from the original on 19 March 2003. - "Bordeaux Light Rail Route Will Operate Without Overhead Lines" (Press release). American Public Transportation Association. 2003. Archived from the original on 1 December 2008. Retrieved 2007-12-21. - "99% AVAILABILITY AND EXCEPTIONALLY HIGH PASSENGER LEVELS : THE BORDEAUX URBAN TRAMWAY IS A RESOUNDING SUCCESS". Railway-Technology.com. Net Resources International. Archived from the original on 2008-06-13. Retrieved 2009-12-26. \|Wikimedia Commons has media related to Light rail.\| - Light Rail Transit Committee of the Transportation Research Board (US) - Light Rail Transit Association (UK-based, international organization) - Light Rail Now! (US) A pro-light rail web site, opposing monorails, Bus Rapid Transit (busways), and other less common transportation systems - Light Rail Netherlands (NL) in English, Nederlands, Русский, Deutsch, Français, Español - "This Is Light Rail Transit" (PDF) brochure by the American Public Transportation Association (APTA) (2000; updated 2003) - Photo gallery of the world's light rail
How to teach operations with integers including printable summary fact sheets to download - Number line. Addition of integers on a number line is presented as a movement of so many units either right or left. The first number in the expression is your "starting point". If you add a positive integer, you move that many units right. If you add a negative integer, you move that many units left. For example, 5 + (-6) means you start at 5, and you move 6 units to the left. -9 + 5 means you start at -9, and move 5 units to the right. This idea is usually relatively simple for students to grasp. Counters. These are represented as little balls with + or - sign drawn inside them, or something similar. For example: + + + + + − − − This represents 5 + (-3). Each plus-minus pair cancels, and so the answer is positive 2. − − − − − − − − + + + This represents (-8) + 3. Each plus-minus pair cancels, and so the answer is -5. You have several options how to present subtraction of integers. Personally, I think of situations where we subtract a positive integer in terms of the number line, and the situations where we subtract a negative integer ("the double negative"), I change those to additions. One is the familiar number line. Try split it to two cases: Number line. Here, 2 − 5 would mean that you start at 2, and you move 5 units to the left, ending at -3. This is identical to interpreting the addition 2 + (-5) on the number line. Similarly, -4 − 3 would mean that you start at -4, and you move 3 units to the left, ending at -7. This is identical to interpreting the addition -4 + (-3) on the number line. Subtracting a negative integer using number line movements is a bit trickier. Problem such as -4 − (-8) would mean that you start at -4, you get ready to move 8 units to the left (the "minus sign"), but the second minus sign reverses your direction, and you go 8 units to the right instead, ending at 4. Please also see these animations that illustrate adding and subtracting integers on a number line. - Patterns can be used to justify the common rules for subtracting integers. First, consider subtracting a positive integer. For example, consider 2 − 5. Do a little pattern for the student to solve, and observe what happens with the answers: 3 − 1 = 3 − 2 = 3 − 3 = 3 − 4 = 3 − 5 = 3 − 6 = Also here you can use the number line. For example, 5 − 8. Place your finger at 5, and show or draw an arrow that is 8 units long towards the left. You will 'end up' at (-3). Then do the same when your starting point is a negative number, such as (-4) − 5. Start at (-4) and move 5 units to the left. Even when subtracting from a negative integer you can use a pattern, and ask the student to observe the answers, and then continue the pattern: (-4) + 2 = (-4) + 1 = (-4) + 0 = (-4) − 1 = (-4) − 2 = etc. Also use temperature dropping examples: 5 - 9 means temperature is 5 degrees and drops 9 degrees. (-4) - 8 means temperature is -4 now and drops 8 degrees. Pattern to justify the rule for subtracting a negative number. This is the case with a problem such as 7 − (-2) or (-4) − (-3). Observe the pattern and see what happens: 3 − 3 = 3 − 2 = 3 − 1 = 3 − 0 = 3 − (-1) = 3 − (-2) = 3 − (-3) = 3 − (-4) = Students are led to discover the shortcut that two negatives turns into a positive!. - Counters. These are trickier to use with subtraction, but the basic idea is to interpret subtraction as "taking away". For example, for (-4) − (-2), you start out with 4 negative counters, and you take away two negative counters. So you are left with 2 negative counters. In other situations, you may not initially have the counters that you are supposed to take away. For example, in 5 − (-3), you start out with 5 positive counters, but you are supposed to take away 3 negative counters. How to do that? The trick is to first add enough pairs of negative-positive counters to the situation - this amounts to adding zero, so it is alright. Then you can take away what you need. + + + + + 5 − (-3). We cannot take away three negative counters, so we'll add three negative-positive pairs (which amounts to adding zero). + + + + + + + + − − − Now, taking away three negatives leaves +8. - Difference. Remind the students that 5 − 2 denotes the difference of 5 and 2, which is 3. You can think of the difference as the distance between the two numbers on the number line. However, you need to write the greater number first! If we wrote 2 − 5 instead, we'd have to take the distance as a negative number. Using this model, (-2) − (-9) would mean the distance between -2 and -9, which is 7. However, (-9) − (-2) would be -7, because the numbers wouldn't be in the order of having the greater number first. Similarly, 4 − (-2) would be 6 since that is the distance between 4 and -2. -6 − (-3) would have the numbers in the "wrong" order, so we'd take their distance as a negative number and the answer would be -3. The video below shows how to use THREE of the different models for subtraction of integers: 1) the number line model, 2) Concept of difference, and 3) counters. Multiplying with negative numbers is EVENTUALLY quickest to do by just memorizing the little rules: negative x negative is positive positive x positive is positive negative x positive is negative positive x negative is negative. In other words, if the two integers have a different sign, then the product is negative, and otherwise it's positive. But if your student or you would like to know a little bit as to WHY it all works that way, use this: - 3 × (-8) or when you have positive × negative: This can be written as repeated addition: (-8) + (-8) + (-8) = -24 See also this clever animation about a pattenr in multiplying 2 x (a number), and when it goes to the negative numbers. - (-5) × 4 or negative times positive. By the fact that multiplication is commutative, you can turn this around and then by 1) above, it is negative: (-5) × 4 = 4 × (-5) = (-5) + (-5) + (-5) + (-5) = -20. - Negative times negative. Make a pattern: (-3) x 3 = (-3) x 2 = (-3) x 1 = (-3) x 0 = (-3) x (-1) = (-3) x (-2) = (-3) x (-3) = (-3) x (-4) = and observe how the products continually increase by 3 in each step. You can also see it in this animation. Another justification for this rule can be seen using distributive property. Distributive property of arithmetic states that a(b + c) = ab + ac. So, if a = (-1), b = 3, and c = (-3), it should still hold: (-1)(3 + (-3)) = (-1)(3) + (-1)(-3) Now, since 3 + (-3) is zero, the whole left side is zero. So (-1)(3) + (-1)(-3) must be zero as well. (-1)(3) is -3. So it follows that (-1)(-3) has to be opposite of -3, or 3. This last part might be too difficult for 6-7th graders to grasp. But they don't have to grasp it all; you can say that sometimes we have to just follow the rules and understand the "why" fully later. They can probably understand it partially now. The negative x negative makes positive rule has to do with the fact that IF we made it to he positive, then all these neat rules/properties of arithmetic wouldn't hold for negative numbers... but since we want them to hold, since we DO want mathematics to be a very consistent system, then we make negative x negative to be positive. Division of integers Division follows because it's the opposite operation of multiplication: What is (-21) ÷ (-7) ? I call the answer A. (-21) ÷ (-7) = A. It follows that A × (-7) = (-21) Knowing the multiplication rules, the only number that fits A is 3. And so on. Just make a similar case for (-21) ÷ 7 and 21 ÷ (-7). (In reality, mathematicians would not use specific numbers like 21 and 7 but just variables; I wrote this with specific numbers to make it easier to grasp the argument, plus this is the way you'd probably explain it to a 6th or 7th grader.) Of course with division too the student will just memorize the little rules and use those in practical computations. But studying the logic behind all this is very enlightening. Integers fact sheets You're welcome to download and print these integer operations fact sheets for your students. All I require is that you not modify them. These fact sheets are pulled out from Math Mammoth Grade 7 Worksheets Collection. A self-teaching worktext for 5th-7th grade that covers integers, addition, subtraction, multiplication, and division of integers, coordinate grid, some graphing, and reflecting figures. The book uses both counters and number line consistently to help students visualize the concepts. Download ($3.70). Also available as a printed copy.
The majority (90%) of children with hearing loss are born to parents with normal hearing11. 50% of hearing loss is due to genetics while the other 50% is due to non-genetic and unknown causes2. Genetic/ hereditary hearing loss (HL) may present at birth/ at a later age (e.g. in adulthood) and may/ may not occur as part of a syndrome (e.g. Down syndrome). A non-syndromic HL means there is no other deficit except with hearing. Non-genetic HL is most often a result of illness (e.g. mumps, scarlet fever, jaundice), bacterial and viral infections or trauma that damages the hearing system4. This can occur before, during or after birth11. Some examples of infections include Rubella (German measles), Herpes, Syphillis, Toxoplasmosis (Cat-scratch disease), Cytomegalovirus (CMV) and Meningitis. Birth complications, such as, prematurity, low birth weight, breathing problems, heart abnormality and prolonged mechanical ventilation are also risk factors. Unfortunately, some medications used to treat these complications or infections can produce a permanent hearing loss11,12. Genetic testing and careful questioning (case history) may help identify the cause of the HL, but sometimes, this remains unclear or unknown5. Types of Hearing Loss Hearing loss is described and managed according to which part of the ear is affected. As you can see below, the ear is divided into outer, middle and inner ear segments. 1. Conductive Hearing Loss (CHL) HL caused only by outer and/or middle ear problems is called a CHL. This can be temporary (e.g. excessive earwax, middle ear infection) or permanent (absent ear canal/ middle ear bones). Middle ear infections are a common cause of temporary CHL among young children. This is because the Eustachian Tube (see Figure 2 above), which connects the middle ear to the throat, is easily blocked during a cold or flu. In comparison to adults, children are at greater risk because their tube is shorter and more horizontal. When this tube is closed, middle ear pressure is not equal to the outer air pressure, giving the sensation of ‘blocked ears’ (like when you are in the plane). This can cause a build up of fluid, which may/ may not be infected by the cold, to produce a temporary HL. Sometimes, infections can persist to produce more severe consequences3. Therefore, a GP consultation is advised if your child demonstrates any sign of ear infections or hearing difficulties. As management of CHL is usually medical and/or surgical, hearing aids are often unnecessary if hearing returns to normal after treatment11. 2. Sensorineural Hearing Loss (SHL) SHL is due to a problem in the inner ear, that is, damage to the cochlea (hearing organ) or the hearing nerve. This may be due to genetics, medication, bacterial/ viral infections, birth complications or a malformed inner ear. SHL is the most common type of permanent HL and cannot be medically treated11. Besides reducing loudness, it also reduces sound clarity. A hearing aid can help by making sounds louder. However, as it cannot replace the intricate workings of the cochlea, hearing will still not be perfect1. When only the hearing nerve is affected, the HL is called Auditory Neuropathy/ Dysynchrony. It is not as common as SHL and unlike SHL; the problem lies in the delivery and processing of sound by the brain. There are many causes for this condition, including, genetics, head trauma, severe jaundice, lack of oxygen, infectious disease and neurological disorders5. 3. Mixed Hearing Loss (MHL) A MHL is when both a CHL and SHL exist. Although medical treatment of the CHL will improve hearing, a hearing loss will still present due to the permanent sensorineural component11. 4. Unilateral Hearing Loss (UHL) UHL means that the hearing loss is in only one ear. UHL can be present at birth (genetic/ pregnancy complications), acquired from illness (mumps/ meningitis) or due to unknown causes. Medical investigation is required as UHL is sometimes a sign of other more serious health conditions. Depending on the situation, a hearing aid may/ may not be required. However, monitoring and protection of the normal ear is very important. Communication/ listening strategies, to be used at home and school, will also help with difficulties locating sounds and hearing in noisy situations1, 11.
Students and parents/guardians will find information related specifically to my Geometry classes in this area. The fundamental purpose of the course in Geometry a one-credit course, is to formalize and extend students’ geometric experiences from the middle grades. Students explore more complex geometric situations and deepen their explanations of geometric relationships, moving towards formal mathematical arguments. Important differences exist between this Geometry course and the historical approach taken in Geometry classes. Close attention should be paid to the introductory content for the Geometry conceptual category found in the high school MS CCRS. The Mathematical Practice Standards apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations. The six critical areas of this course include (1) building a thorough understanding of translations, reflections, and rotations; (2) developing the understanding of similarity and several theorems; (3) extension of formulas for 2-dimensional and 3-dimensional objects (4) extension of 8th grade geometric concepts of lines; (5) prove basic theorems about circles; and (6) work with experimental and theoretical probability. Each critical area is described below: - In previous grades, students were asked to draw triangles based on given measurements. They also have prior experience with rigid motions: translations, reflections, and rotations and have used these to develop notions about what it means for two objects to be congruent. In this unit, students establish triangle congruence criteria, based on analyses of rigid motions and formal constructions. They use triangle congruence as a familiar foundation for the development of formal proof. Students prove theorems—using a variety of formats—and solve problems about triangles, quadrilaterals, and other polygons. They apply reasoning to complete geometric constructions and explain why they work. - Students apply their earlier experience with dilations and proportional reasoning to build a formal understanding of similarity. They identify criteria for similarity of triangles, use similarity to solve problems, and apply similarity in right triangles to understand right triangle trigonometry, with particular attention to special right triangles and the Pythagorean Theorem. Students develop the Laws of Sines and Cosines in order to find missing measures of general (not necessarily right) triangles, building on students’ work with quadratic equations done in the first course. They are able to distinguish whether three given measures (angles or sides) define 0, 1, 2, or infinitely many triangles. - Students’ experience with two-dimensional and three-dimensional objects is extended to include informal explanations of circumference, area and volume formulas. Additionally, students apply their knowledge of two-dimensional shapes to consider the shapes of cross-sections and the result of rotating a two-dimensional object about a line. - Building on their work with the Pythagorean theorem in 8th grade to find distances, students use a rectangular coordinate system to verify geometric relationships, including properties of special triangles and quadrilaterals and slopes of parallel and perpendicular lines, which relates back to work done in the first course. Students continue their study of quadratics by connecting the geometric and algebraic definitions of the parabola. - Students prove basic theorems about circles, such as a tangent line is perpendicular to a radius, inscribed angle theorem, and theorems about chords, secants, and tangents dealing with segment lengths and angle measures. They study relationships among segments on chords, secants, and tangents as an application of similarity. In the Cartesian coordinate system, students use the distance formula to write the equation of a circle when given the radius and the coordinates of its center. Given an equation of a circle, they draw the graph in the coordinate plane, and apply techniques for solving quadratic equations, which relates back to work done in the first course, to determine intersections between lines and circles or parabolas and between two circles. - Building on probability concepts that began in the middle grades, students use the languages of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for compound events, attending to mutually exclusive events, independent events, and conditional probability. Students should make use of geometric probability models wherever possible. They use probability to make informed decisions.
Source: The Library of Congress Country Studies With the exception of Saudi Arabia and Iraq, the Arab coast of the gulf was ruled by ten families: in Kuwait the Al Sabah; in Bahrain the Al Khalifa; in Qatar the Al Thani; in the present-day UAE the Al Nuhayyan in Abu Dhabi, the Al Nuaimi in Ajman, the Al Sharqi in Al Fujayrah, the Al Maktum in Dubayy, the Al Qasimi in Ras al Khaymah and Sharjah, and the Al Mualla in Umm al Qaywayn; and the Al Said in present-day Oman. These families owed their positions to tribal leadership; it was on this traditional basis that the British had negotiated treaties with their leaders in the nineteenth century and the early twentieth century. A major provision of these treaties was the recognition of sovereignty. The British were concerned that rulers of the weaker gulf families would yield some of their territory under pressure from more powerful groups, such as the Al Saud or the Ottomans. Accordingly, the treaties signed between 1820 and 1916 recognized the sovereignty of these rulers within certain borders and specified that these borders could not be changed without British consent. Such arrangements helped to put tribal alliances into more concrete terms of landownership. This meant that the Al Nuhayyan of Abu Dhabi, for example, not only commanded the respect of tribes in the hinterland but also owned, as it were, the land that those tribes used--in this case, about 72,000 square kilometers of Arabia. Controlling, or owning, land became more important with the discovery of oil. When oil companies came to explore for oil, they looked for the "owner" of the land; in accordance with British treaties, they went to the area's leading families and agreed to pay fees to the heads of these families. As oil revenues increased, the leaders became rich. Although the leaders spent much of their new wealth on themselves, they also distributed it in the area they controlled according to traditional methods, which initially consisted mostly of largesse: gifts for friends and food for whomever needed it. As time passed, the form of largesse became more sophisticated and included, for example, the construction of schools, hospitals, and roads to connect principal cities to towns in the interior. Oil revenues did not change traditional tribal ideas about leadership. New money, however, increased the influence of area leaders by giving them more resources to distribute. Because of oil exploration, tribal boundaries became clearer, and areas were defined more precisely. Distinctions among tribes also became more evident. A new sense of identity appeared in gulf shaykhdoms and aroused a growing expectation that they should rule themselves. To do this, shaykhs had to cut themselves off from British control and protection. By the early 1960s, this was something to which the British had little objection. India and Pakistan won their independence in 1947; this meant that Britain no longer had to worry about protecting the western flank of the subcontinent. Britain was also burdened by the tremendous sacrifices it made during World War II and could not be as globally involved as it had been before the war. Therefore, Britain yielded many of its strategic responsibilities to the United States in the postwar period or gave them up entirely. However, the British were bound to the gulf by treaties and so remained in the region, but it was clear by the 1960s that they sought to leave the gulf. Kuwait was the first state to terminate the agreement connecting it with Britain. Oil production in Kuwait had developed more quickly than in neighboring states; as a result, Kuwaitis were better prepared for independence. They declared independence in 1961 but ran into immediate trouble when Iraq claimed the territory. The Iraqis argued that the British had recognized Ottoman sovereignty over Kuwait before World War I and, because the Ottomans had claimed to rule Kuwait from what was then the province of Iraq, the territory should belong to Iraq. The British immediately sent troops to Kuwait to deter any Iraqi invasion. British and Kuwaiti positions were supported by the newly formed League of Arab States (Arab League), which recognized the new state and sent troops to Kuwait. The Arab League move left the Iraqis isolated and somewhat intimidated. Accordingly, when a new Iraqi government came to power in 1963, one of its first steps was to give up its claim and recognize the independence of Kuwait. The experience of Kuwait may have increased the anxiety of other gulf leaders about declaring their independence. Even into the 1970s, Iran and Saudi Arabia continued to make claims on territory in Bahrain and the UAE, although by the end of 1971 those states were independent, and nothing came of those claims. Gulf leaders also faced uncertainty about the form their state should take. Should they all, with the exception of Oman whose situation was different in that its treaty relationship with Britain did not guarantee its borders as did treaties of the other gulf states, band together in the largest entity possible? Or should they break up into nine separate states, the smallest of which had little territory, few people, and no oil? British action forced gulf leaders to decide. Because of domestic financial concerns, Britain decided in the late 1960s to eliminate its military commitments east of Suez. As a result, the gulf shaykhs held a number of meetings to discuss independence. Initially, leaders considered a state that would include all nine shaykhdoms; Qatar had even drawn up a constitution to this effect. In the end, however, so large a federation proved unworkable. An obstacle to creating a "superstate" was the status of Bahrain, which had been occupied by Iran at various times. The shah of Iran argued that he had a stronger claim to the island than the Al Khalifa, who had only come to Bahrain in the eighteenth century. Furthermore, the shah indicated that Iran would not accept a federation of Arab states that included Bahrain. In the end, the United Nations (UN) considered the issue of Bahrain; it decided to deny the Iranian claim to the island and to allow the Bahrainis to form an independent state. Bahrain was better suited to independence than some of the other shaykhdoms because the island had been a center of British administration and had a more developed infrastructure and education system than its neighbors. Ironically, the greater British presence on Bahrain made residents more resentful of treaty ties to Britain. Bahrain was the only place in the gulf where demonstrations against Britain occurred. Backed by the UN decision, Bahrain declared its independence on August 15, 1971. On September 3, 1971, Qatar followed, removing another state from any potential federation. Although Qatar had minimal contact with Britain, it was well suited to independence because it had a history of support from the Al Saud that went back to the beginnings of the Wahhabi state. Accordingly, at independence, Qatar could expect continued support from Saudi Arabia. It could also anticipate substantial oil revenues that had been increasing since the 1950s. The same was not true for the other gulf states. The five southern shaykhdoms--Ajman, Al Fujayrah, Ras al Khaymah, Sharjah, and Umm al Qaywayn--had little oil in their territory and so could not afford self-sufficiency as countries. Although substantial deposits had been discovered in Abu Dhabi and Dubayy, these two states preferred the security of a confederation rather than independence. Abu Dhabi, for example, had an outstanding border dispute with Saudi Arabia and a history of poor relations with that country because of Abu Dhabi's opposition to Wahhabi Islam. Abu Dhabi might have protected itself by forming a federation with the five southern shaykhdoms, but this would not have suited Dubayy. Although Dubayy had oil of its own, its rulers, the Al Maktum, had a history of hostility toward their relatives in Abu Dhabi, the Al Nuhayyan, from whom they split in the early nineteenth century. The Al Maktum would not have liked the Al Nuhayyan to dominate a confederation of gulf leaders while they were isolated in Dubayy. Powers beyond the gulf coast also had an interest in the state to be formed. The Saudis no longer sought to control the gulf coast, but they remained concerned about stability on the eastern border. The British and other oil-consuming countries in the West were similarly concerned, and all parties believed that the largest state would also be the most stable. Accordingly, many forces were applying pressure in 1970 to convince the seven shaykhs to stay together. Thus, in 1971 soon after Qatar became independent, the remaining shaykhs, with the exception of the Al Qasimi in Ras al Khaymah, took the preliminary constitution that Qatar had originally drawn up for a nine-member confederation and adapted it to a six-member body. On December 2, 1971, one day after the British officially withdrew, these six shaykhdoms declared themselves a sovereign state. Ras al Khaymah originally refused to join the confederation. The Al Qasimi, who ruled the area, claimed a number of islands and oil fields within the gulf to which Iran laid claim as well. In the negotiations to form the UAE, the Al Qasimi sought support for their claims from Arab states on the peninsula as well as from some Western powers. When their efforts proved unsuccessful, the Al Qasimi pulled out of the negotiations. They quickly realized, however, that they could not exist on their own and joined the union in February 1972. Oman was never considered a possible confederation member. Always geographically separate from its neighbors to the north, Oman had never entered into the agreements with Britain that governed other gulf rulers. The British had been closely involved in Oman since the middle of the nineteenth century, but they were under no official obligation to defend it. The issue in Oman was one of internal unity rather than of sovereignty over foreign affairs. The historical split between coast and interior had continued through the second half of the nineteenth century and the first part of the twentieth. In 1920 the Al Said sultan, Taimur ibn Faisal, came to terms with this split by granting limited sovereignty to the tribes of the interior. Because of ambiguous language, the peoples of the interior believed that the treaty cut them off from the Al Said; the Al Said, however, never gave up their claim to all of Oman. The dispute between the two groups was exacerbated by the exploration for oil, which began in Oman in 1924. The oil fields lay in the interior, and the oil companies negotiated for access to them with the Al Said in Muscat. This Al Said sultan gladly sold them rights to the Omani oil fields, although the tribes of the interior claimed sovereignty over the area. When the oil men went inland to explore, they were attacked by the tribes, whom the sultan considered to be rebels, leading the oil companies to complain to the British government. Their complaints encouraged the British to continue their aid to the sultan, hoping that he would pacify the area and ensure Western access to Omani oil. The sultan was eventually successful. In 1957 forces loyal to Said ibn Taimur captured the town of Nazwah, which the Al Said had not controlled since the nineteenth century. In 1958 the sultan withdrew to his palace in the coastal city of Salalah in Dhofar, a southern province that the Al Said had annexed in the nineteenth century, and took little interest in maintaining stability in the country. While keeping his military relationship with the British, he restricted Oman's contact with the rest of the world, discouraged development, and prohibited political reform. In the end, the Al Said control over a united Oman survived, but Said ibn Taimur did not. Although the sultan had partially reestablished his authority in the Omani interior, he was unable to handle the increasing complexity of domestic politics. By the 1960s, Omani affairs had become international issues. Western oil companies sought to work in the interior of the country, and foreign governments, such as the Marxist state of the People's Democratic Republic of Yemen, were sending arms to the rebels in Dhofar. The Al Said hold over the region remained problematic, however, and in 1964 another rebellion arose, this time in Dhofar. The Dhofar rebellion, which was not brought under control until 1976, obliged the sultan to seek foreign military assistance; therefore, British forces, particularly the air force, resumed action in the country. The rebels pointed to British involvement as an indication of the sultan's illegitimacy and brought their case to the UN, which eventually censured Britain for its continuing involvement in Oman. Said ibn Taimur's policies frustrated many, not only in Oman but also in Britain, whose citizens were heavily involved in the sultan's military and intelligence apparatus. By 1970 these elements decided they could bear with the situation no longer; a coalition of Omani military and civilian forces, as well as British forces, attacked the palace and forced Said ibn Taimur to abdicate. They replaced him with his son, Qabus ibn Said Al Said, who had played no role in Said ibn Taimur's government. The sultan had actually locked his son in the palace for fear that Qabus ibn Said, who had been educated in Britain, would challenge his archconservative policies. On his release, Qabus ibn Said consolidated the sultanate's hold over the interior and then solicited regional rather than British help to put down the rebellion in Dhofar. Other Arab leaders, as well as the shah of Iran, sent troops to Oman in response to Qabus ibn Said's requests; with the help of this coalition, by 1976 the sultan ended the Dhofar rebellion. Qabus ibn Said was not an Ibadi imam as the first rulers in his line had been, but in 1970 this was less important than it had been in earlier times. Only about 60 percent of Oman's population was Ibadi, concentrated in the northern mountains. Furthermore, the province of Dhofar had a relatively short history of association with the rest of Oman. Data as of January 1993 NOTE: The information regarding Bahrain on this page is re-published from The Library of Congress Country Studies. No claims are made regarding the accuracy of Bahrain INDEPENDENCE information contained here. All suggestions for corrections of any errors about Bahrain INDEPENDENCE should be addressed to the Library of Congress.
A black hole is a theoretical entity predicted by the equations of general relativity. How do black holes form? Black holes are thought to form from stars or other massive objects if and when they collapse from their own gravity to form an object whose density is infinite (a singularity). During most of a star’s lifetime, nuclear fusion in the core generates electromagnetic radiation, including photons, the particles of light. This radiation exerts an outward pressure that exactly balances the inward pull of gravity caused by the star’s mass. As the nuclear fuel is exhausted, the outward forces of radiation diminish, allowing the gravitation to compress the star inward. The contraction of the core causes its temperature to rise and allows remaining nuclear material to be used as fuel. The star is saved from further collapse. So: a black hole is formed when a star of sufficient mass undergoes gravitational collapse, with most or all of its mass compressed into a sufficiently small area of space, causing infinite spacetime curvature at that point (a “singularity”). Such a massive spacetime curvature allows nothing, not even light, to escape from the “event horizon,” or border. An area of space so dense the degenerate neutronic forces/pressures can not withstand the combined force per unit area of the gravitons from the stellar mass. This creates an implosion whereby the collapse only stops when the body occupies a space of infinitesimal dimension. The mass needed to overcome the degeneracy pressure must be above the Oppenheimer-Volkoff limit. The area around the degenerate mass above the Oppenheimer-Volkoff is warped in a manner consistent with Einstein’s General Theory of Relativity (1916) whereby space times folds about the object. The physicist Karl Schwartzchild produced a solution to Einstein’s equation for a spherical mass (called the Schwartzchild metric). The term expressing the radius had a disturbing feature. This radius, known as the Schwartzchild radius, rs, is defined as: rs = 2GM/c2 G is the gravitational constant, M is the mass, and c is the speed of light. An object whose entire mass M lies within rs is considered to be a black hole. The Schwarzschild surface, the sphere at one Schwarzschild radius, is also called the event horizon of a black hole (Event horizon is the name given to rs). For stellar masses less than about 1.44 solar masses, the energy from the gravitational collapse is not sufficient to produce the neutrons of a neutron star, so the collapse is halted by electron degeneracy to form white dwarfs. This maximum mass for a white dwarf is called the Chandrasekhar limit (it’s 1,44 solar masses). Hawking radiation (also called Bekenstein-Hawking radiation) is a theoretical prediction from British physicist Stephen Hawking. Smaller primordial black holes can actually emit more energy than they absorb, which results in them losing net mass. Larger black holes, such as those that are one solar mass, absorb more cosmic radiation than they emit through Hawking radiation. Astronomers in England have discovered a singing black hole in a distant cluster of galaxies. “Starlight” from Muse.
Article One of the United States Constitution describes the powers of Congress, the legislative branch of the federal government. The Article establishes the powers of and limitations on the Congress, consisting of a House of Representatives composed of Representatives, with each state gaining or losing representation in proportion to its population, and a Senate, composed of two Senators from each state. The article details the manner of election and qualifications of members of each House. It outlines legislative procedure and enumerates the powers vested in the legislative branch. Finally, it establishes limits on the powers of both Congress and the states. There are ten sections in the article. The Vesting Clause (Section One) vests "all legislative powers herein granted" to the Congress. Sections Two and Three deal with the House of Representatives and Senate respectively. The sections set the composition, term lengths, qualifications of members, officers, and methods of filling vacancies for both Houses. Section Two also requires direct taxes to "be apportioned among the several States... according to their respective Numbers" and that a census be held every ten years. Section Three also provides that the Vice President of the United States shall be President of the Senate but shall have only a tie-breaking vote. The House of Representatives is given the sole power of impeachment while the Senate is given the sole power of the trial of impeachments. Section Four gives to state legislatures the power to set the "times, Places and Manner of holding elections for Senators and Representatives," but provides for Congressional oversight of elections. The section also provides that Congress shall assemble "at least once in every year" and sets a default date for the initial assembly, later modified by the Twentieth Amendment. Section Five deals with procedure, providing that "Each House shall be the Judge of the Elections, Returns and Qualifications of its own Members, and a Majority of each shall constitute a Quorum to do Business," although a small number may adjourn and compel the attendance of absent members. The section also gives to each house the power to "determine the rules of its proceedings," including the power to punish or expel a member". Each house is required to "keep a journal of its proceedings" and publish it from time to time except in special circumstances. The section also provides that neither House may adjourn without the consent of the other for more than three days or change its meeting place, without the consent of the other House. Section Six provides that members of Congress shall receive salaries, have a limited privilege from arrest during sessions of Congress, and immunity "for any Speech or Debate in either House." The section also provides that no member may simultaneously serve in Congress and "be appointed to any civil Office under the Authority of the United States", and also may not serve in any such office "which shall have been created, or the Emoluments whereof shall have been increased" during the member's term in office. Section Seven deals with legislative procedure, providing that all bills for revenue must originate in the House of Representative. The section also introduces the veto power of the President of the United States, and describes its powers and limitations. Section Eight gives to the Congress certain broad enumerated powers. Among these are the power to lay and collect taxes and provide for the common defense and general welfare of the United States; to borrow money on the credit of the United States, to regulate interstate, foreign, and Indian commerce; (5) To coin money, regulate the value thereof, and of foreign coin, and fix the standard of weights and measures; and to create courts inferior to the Supreme Court among many others. The section also gives to Congress the power to "make all laws which shall be necessary and proper for carrying into execution the foregoing powers, and all other powers vested by this Constitution in the government of the United States." Section Nine places limits on powers of Congress and the government. The section provides that the writ of habeas corpus shall not be suspended "except when in cases of rebellion or invasion the public safety may require it"; prohibits bills of attainder or ex post facto laws; bars the imposition of taxes or duties on articles exported from any state or the granting of preference to ports of one state over another; and prohibits civil officers from accepting titles of nobility without the consent of Congress. The section also provides that "No money shall be drawn from the treasury, but in consequence of appropriations made by law," and that a statement of receipts and expenditures of public money "be published from time to time." This section barred Congress from banning the import of slaves from abroad or from laying a duty of more than 10 dollars on each imported slave until 1808; Congress banned the slave trade on January 1, 1808, as soon as constitutionally allowed. Section Ten sets limits on states, reserving certain powers exclusively to the Congress. States are prohibited from coining money or making anything other than gold or silver coin legal tender for payment of debts and are prohibited from entering into treaties or alliances, although compacts with other states are allowed with the permission of Congress. States are also not permitted to lay duties, keep troops or warships in peacetime with Congressional approval, or engage in war unless actually invaded or in imminent danger. States also are barred from laying imposts or duties on imports or exports except for the fulfillment of state inspection laws, which may be revised by Congress, and any net revenue of such duties is remitted to the federal treasury. Finally, states, like Congress, may not pass bills of attainder or ex post facto laws, nor grant any title of nobility. Section 1: Legislative power vested in Congress Section 1 is a vesting clause, granting all the federal government's legislative authority to Congress. Similar vesting clauses are found in Articles II and III, which grant "the executive power" to the President and "the judicial power" to the federal judiciary. In legal garb, the working definition of "herein" connotes specificity and exclusivity. The Vesting Clauses thus establishes the principle of separation of powers by specifically giving to each branch of the federal government only those powers it can exercise and no others. This means that no branch may exercise powers that properly belong to another (e.g., since the legislative power is vested in Congress, the executive and judiciary may not enact laws). The language "herein granted" in Article I's vesting clause has been interpreted to mean that the powers Congress are to exercise are exclusively those specifically provided for in Article I. The clause "herein granted" was further defined and elaborated by the tenth amendment. Thus, this congressional clause is contrasted by the general vesting of the executive and judicial powers in Articles II and III in the branches of government those articles govern, which has been interpreted to mean that those branches enjoy "residual" or "implied" powers beyond those specifically mentioned, as contrasted with the Congress, which is vested with those legislative powers "herein granted;" however, there is substantial contemporary disagreement about the precise extent of the powers conferred by the general vesting clauses. As a corollary to the fact that Congress, and only Congress, is vested with the legislative power, Congress (in theory) cannot delegate legislative authority to other branches of government (e.g., the Executive Branch), a rule known as the nondelegation doctrine. However, the Supreme Court has ruled that Congress does have latitude to delegate regulatory powers to executive agencies as long as it provides an "intelligible principle" which governs the agency's exercise of the delegated regulatory authority. In practice, the Supreme Court has only invalidated four statutes on non-delegation grounds in its history, three of which were invalidated in the mid-1930s. The fourth, the Line Item Veto Act of 1996, was invalidated in 1998. The nondelegation doctrine is primarily used now as a way of interpreting a congressional delegation of authority narrowly, in that the courts presume Congress intended only to delegate that which it certainly could have, unless it clearly demonstrates it intended to "test the waters" of what the courts would allow it to do. Although not specifically mentioned in the Constitution, Congress has also long asserted the power to investigate and the power to compel cooperation with an investigation. The Supreme Court has affirmed these powers as an implication of Congress's power to legislate. Since the power to investigate is an aspect of Congress's power to legislate, it is as broad as Congress's powers to legislate. However, it is also limited to inquiries that are "in aid of the legislative function;" Congress may not "expose for the sake of exposure." It is uncontroversial that a proper subject of Congress's investigation power is the operations of the federal government, but Congress's ability to compel the submission of documents or testimony from the President or his subordinates is often-discussed and sometimes controversial (see executive privilege), although not often litigated. As a practical matter, the limitation of Congress's ability to investigate only for a proper purpose ("in aid of" its legislative powers) functions as a limit on Congress's ability to investigate the private affairs of individual citizens; matters that simply demand action by another branch of government, without implicating an issue of public policy necessitating legislation by Congress, must be left to those branches due to the doctrine of separation of powers. The courts are highly deferential to Congress's exercise of its investigation powers, however. Congress has the power to investigate that which it could regulate, and the courts have interpreted Congress's regulatory powers broadly since the Great Depression. Additionally, the courts will not inquire into whether Congress has an improper motive for an investigation (i.e., using a legitimate legislative purpose as a cover for "expos[ing] for the sake of exposure"), focusing only on whether the matter is within Congress's power to regulate and, thus, investigate. Persons called before a congressional investigatory committee are entitled to the constitutional guarantees of individual rights, such as those in the Bill of Rights. Congress can punish those who do not cooperate with an investigation via holding violators in contempt of Congress. Section 2: House of Representatives Clause 1: Composition and election of Members Section Two provides for the election of the House of Representatives every second year. Since Representatives are to be "chosen... by the People," State Governors are not allowed to appoint temporary replacements when vacancies occur in a state's delegation to the House of Representatives; instead, the Governor of the state is required by clause 4 to issue a writ of election calling a special election to fill the vacancy. The Constitution does not directly guarantee the franchise to anyone; rather, it provides that those qualified to vote in elections for the largest chamber of a state's legislature may vote in congressional elections as well. Amendments to the Constitution, however, have restricted the states' ability to set such qualifications. The Fifteenth Amendment and Nineteenth Amendment bar the use of race or sex as qualifications to vote in both federal and state elections. Furthermore, the Twenty-sixth Amendment provides that states may not set age requirements higher than eighteen years. The Twenty-fourth Amendment bars states from using the payment of a tax as a voter qualification in federal elections. Moreover, since the Supreme Court has recognized voting as a fundamental right, the Equal Protection Clause places very tight limitations (albeit with uncertain limits) on the states' ability to define voter qualifications; it is fair to say that qualifications beyond citizenship, residency, and age are usually questionable. Since clause 3 provides that Members of the House of Representatives are apportioned state-by-state and that each state is guaranteed at least one Representative, exact population equality between all districts is not guaranteed and, in fact, is currently impossible, because while the size of the House of Representatives is fixed at 435, several states had less than 1/435 of the national population at the time of the last reapportionment in 2000. However, the Supreme Court has interpreted the provision of Clause One that Representatives shall be elected "by the People" to mean that, in those states with more than one member of the House of Representatives, each congressional election district within the state must have nearly identical populations. Clause 2: Qualifications of Members The Constitution provides three requirements for Representatives: A Representative must be at least 25 years old, must be an inhabitant of the state in which he or she is elected, and must have been a citizen of the United States for the previous seven years. There is no requirement that a Representative reside within the district in which he represents; although thus is usually the case, there have been occasional exceptions. The Supreme Court has interpreted the Qualifications Clause as an exclusive list of qualifications that cannot be supplemented by a house of Congress exercising its Section 5 authority to "judge...the...qualifications of its own members" or by a state in its exercise of its Section 4 authority to prescribe the "times, places and manner of holding elections for Senators and Representatives." The Supreme Court, as well as other federal courts, have repeatedly barred states from additional restrictions, such as imposing term limits on members of Congress, allowing members of Congress to be subject to recall elections, or requiring that Representatives live in the congressional district in which they represent. However, the United States Supreme Court has ruled that certain ballot access requirements, such as filing fees and submitting a certain number of valid petition signatures do not constitute additional qualifications and thus few Constitutional restrictions exist as to how harsh ballot access laws can be. Clause 3: Apportionment of Representatives and taxes The Constitution does not fix the size of the House of Representatives; instead, this clause empowers Congress to determine the size of the House as part of the apportionment process, so long as the size of the House does not exceed 1 member for every 30,000 of the country's total population and the size of the state's delegation does not exceed 1 for every 30,000 of the state's population (although these limits have not been approached since the Founding). The number is currently fixed at 435, which is around a 1 Representative: 700,000 Citizen ratio. A particular number of Representatives is assigned to each State according to its share of the national population; election districts are not drawn nationally and do not cross state boundaries. Congress additionally has the authority to prescribe what method shall be used to allocate Representatives to each state; currently, Congress has prescribed the use of the Equal Proportions method. The Constitution mandates that a Census be conducted every ten years to determine the populations of the States, and this clause provided for a temporary apportionment of seats until the first Census could be conducted. The population of a state originally included (for congressional apportionment purposes) all "free persons", three-fifths of "other persons" (i.e., slaves) and excluded untaxed Native Americans. Presently, the Census counts illegal immigrants, and Census figures are used to determine congressional seats. The three-fifths clause was a compromise between Southern and Northern states in which three-fifths of the population of slaves would be counted for enumeration purposes regarding both the distribution of taxes and the apportionment of the members of the United States House of Representatives. This compromise had the effect of increasing the political power of slave-holding states by increasing their share of seats in the House of Representatives, and consequently their share in the Electoral College (where a state's influence over the election of the President is tied to the size of its congressional delegation). Following the Civil War, the Thirteenth and Fourteenth Amendments changed this arrangement by (respectively) abolishing slavery, and superseding the three-fifths clause by requiring that a state's population for apportionment purposes was to be determined by "counting the whole number of Persons" in the state, "excluding Indians not taxed." Since there are at present no such untaxed Native Americans (Indians), all persons inhabiting a state whether citizens or not count towards the population of that state in determining the state's congressional apportionment. Originally, the amount of direct taxes that could be collected from any State was tied directly to its share of the national population. On the basis of this requirement, application of the income tax to income derived from real estate and specifically income in the form of dividends from personal property ownership such as stock shares was found to be unconstitutional because it was not apportioned among the states; that is to say, there was no guarantee that a State with 10% of the country's population paid 10% of those income taxes collected, because Congress had not fixed an amount of money to be raised and apportioned it between the States according to their respective shares of the national population. To permit the levying of such an income tax, Congress proposed and the states ratified the Sixteenth Amendment, which superseded this requirement by specifically providing that Congress could levy a tax on income "from whatever source derived" without it being apportioned among the States or otherwise based on a State's share of the national population. Clause 4: Vacancies Section 2, Clause 4, provides that when vacancies occur in the House of Representatives, it is not the job of the House of Representatives to arrange for a replacement, but the job of the State whose vacant seat is up for refilling. Moreover, the State Governor may not appoint a temporary replacement, but must instead arrange for a special election to fill the vacancy. The original qualifications and procedures for holding that election are still valid. Clause 5: Speaker and other officers; Impeachment Section Two further provides that the House of Representatives may choose its Speaker and its other officers. Though the Constitution does not mandate it, every Speaker has been a member of the House of Representatives. The Speaker rarely presides over routine House sessions, choosing instead to deputize a junior member to accomplish the task. Finally, Section Two grants to the House of Representatives the sole power of impeachment. Although the Supreme Court has not had an occasion to interpret this specific provision, the Court has suggested that the grant to the House of the "sole" power of impeachment makes the House the exclusive interpreter of what constitutes an impeachable offense. Impeachments are tried in the Senate (as discussed below). Section 3: Senate Clause 1: Composition; Election of Senators Section Three provides that each state is entitled to two Senators chosen for a term of six years. The state legislatures originally chose the means of choosing the Senators. This provision has been superseded in 1913 by the Seventeenth Amendment, which provides for the direct election of Senators by the respective states' voters. Generally, Article Five requires that a proposal to amend the Constitution garner a two-thirds majority in both Houses of Congress, and then be ratified by three-fourths of the state legislatures. Section Three of Article I is one of a handful of clauses on which Article Five places special restrictions to be amended; in this case, Article Five provides that "no State, without its Consent, shall be deprived of its equal Suffrage in the Senate." Thus, no individual state may have its representation in the Senate adjusted without its consent unless all other states have an identical change. That is to say, an amendment that changed this clause to provide that all states would get only one Senator (or three Senators, or any other number) could be ratified through the normal process, but an amendment that provided for some basis of representation other than strict numerical equality (for example, population, wealth, or land area) would require the assent of every state. Clause 2: Classification of Senators; Vacancies After the first group of Senators was elected to the First Congress (1789 1791), the Senators were divide into three "classes" as nearly equal in size as possible, as required by this section. This was done in May 1789 by lot. Those Senators grouped in the first class had their term expire after only two years; those Senators in the second class had their term expire after only four years, instead of six. After this, all Senators from those States have been elected to six-year terms, and as new States have joined the Union, their Senate seats have been assigned to one of the three classes, maintaining each grouping as nearly equal in size as possible. In this way, election is staggered; approximately one-third of the Senate is up for re-election every two years, but the entire body is never up for re-election in the same year (as contrasted with the House, where its entire membership is up for re-election every 2 years). As originally established, Senators were elected by the Legislature of the State they represented in the Senate. If a senator died, resigned, or was expelled, the legislature of the state would appoint a replacement to serve out the remainder of the senator's term. If the State Legislature was not in session, its Governor could appoint a temporary replacement to serve until the legislature could elect a permanent replacement. This was superseded by the Seventeenth Amendment, which provided for the Popular Election of Senators, instead of their appointment by the State Legislature. In a nod to the less populist nature of the Senate, the Amendment tracks the vacancy procedures for the House of Representatives in requiring that the Governor call a special election to fill the vacancy, but (unlike in the House) it vests in the State Legislature the authority to allow the Governor to appoint a temporary replacement until the special election is held. Note, however, that under the original Constitution, the Governors of the states were expressly allowed by the Constitution to make temporary appointments. The current system, under the Seventeenth Amendment, allows Governors to appoint a replacement only if their state legislature has previously decided to allow the Governor to do so; otherwise, the seat must remain vacant until the special election is held to fill the seat, as in the case of a vacancy in the House. Clause 3: Qualifications of Senators A Senator must be at least 30 years of age, must have been a citizen of the United States for at least nine years before being elected, and must reside in the State he or she will represent at the time of the election. The Supreme Court has interpreted the Qualifications Clause as an exclusive list of qualifications that cannot be supplemented by a House of Congress exercising its Section. 5. authority to "Judge... the... Qualifications of its own Members," or by a state in its exercise of its Section. 4. authority to prescribe the "Times, Places and Manner of holding Elections for Senators and Representatives,..." Clause 4: Vice President as President of Senate; Voting power Section Three provides that the Vice President is the President of the Senate. In modern times, the Vice President usually presides over the Senate only when a tie in the voting is anticipated. (The following section provides for the President pro tempore of the Senate, a Senator elected to the post by the Senate, to preside in the Absence of the Vice President, or when he shall exercise the Office of the President of the United States, but like the Vice President the President pro tempore, traditionally the longest-serving member of the majority party, rarely actually presides over the chamber; typically the President pro tempore deputizes junior Senators of the majority party to act as presiding officers). As a non-member of the assembly, the Vice President has only a "casting" (tie-breaking) vote. This is contrasted with the Speaker of the House, who has always been chosen from the Members of the House of Representatives, and as a member of the House is entitled to participate in debate vote on all measures, not just when ties occur, although customarily the speaker votes only rarely, and often to make or break a tie. The tie-breaking vote has been cast 243 times by 35 different Vice Presidents. Clause 5: President pro tempore and other officers The Senate may elect a President pro tempore to act in the Vice President's absence. Although the Constitutional text seems to suggest to the contrary, the Senate's practice has been to elect a full-time President pro tempore at the beginning of each Congress, as opposed to making it a temporary office only existing during the Vice President's absence. As is true of the Speaker of the House, the Constitution does not require that the President pro tempore be a senator, but by convention, a senator is always chosen; since World War II, the senior member of the majority party has filled this position. The President pro tempore, as a member of the Senate, is free to make or break a tie vote like the Speaker of the House, but in the event that the possibility of a tie vote is anticipated the Vice President is routinely on hand to ensure that the Executive Branch's policy preference prevails. Clause 6: Trial of Impeachments The Senate is granted the sole power to try impeachments, just as the House of Lords could try impeachments in Great Britain. The Supreme Court has interpreted the Constitution's provision that the Senate has the "sole" power to try impeachments to mean that the Senate has exclusive and unreviewable authority to determine what constitutes an adequate impeachment trial. The senators must sit on oath or affirmation, unlike the lords who voted upon their honor. The Chief Justice presides whenever the President of the United States is tried, to avoid the Vice President exercising his duties as President of the Senate and presiding over the trial of the President of the United States. Although this was probably originally intended to avoid a situation where the Vice President was presiding over a debate that could ultimately result in his promotion to the presidency (were the President convicted and removed from office), it also prevents a possibly more likely contemporary scenario, where a President accused of some offense is being tried by the Senate presided over by a Vice President who may well be sympathetic to the President, reducing the independence of the Senate's consideration of the delicate question of whether to remove a sitting chief executive. On the other hand, nothing prevents the curious circumstance of a Vice President presiding over his own impeachment trial as President of the Senate, should he be impeached (although this has never happened). A two-thirds supermajority of those Senators "present" is required to convict, although given the obvious importance of impeachment proceedings, there are generally few absent members. In addition, requiring a two-thirds majority of those members "present" has the net effect of making a present member's decision not to cast a vote either way the same as a vote against conviction. This is as contrasted with typical practice, where a proposition passes, or not, based on whether it receives the appropriate majority of however many votes were cast, irrespective of how many members were present but chose not to vote. However, much as impeachment trials generally have few members absent, the importance of impeachment trials is unlikely to produce many abstentions (i.e., non-votes) by present members. Clause 7: Judgment in cases of impeachment; Punishment on conviction If any officer is convicted on impeachment, he or she is immediately removed from office, and may be barred from holding any public office in the future. No other punishments may be inflicted pursuant to the impeachment proceeding, but the convicted party remains liable to trial and punishment in the courts for civil and criminal charges. Section 4: Congressional elections Clause 1: Time, place, and manner of holding This clause generally commits to the States the authority to determine the "times, places and manner of holding elections," which includes the preliminary stages of the election process (such as a primary election), while reserving to Congress the authority to preempt State regulations with uniform national rules. Congress has exercised this authority to determine a uniform date for federal elections: the Tuesday following the first Monday in November. Because Congress has not enacted any on-point regulations, States still retain the authority to regulate the dates on which other aspects of the election process are held (registration, primary elections, etc.) and where elections will be held. As for regulating the "manner" of elections, the Supreme Court has interpreted this to mean "matters like notices, registration, supervision of voting, protection of voters, prevention of fraud and corrupt practices, counting of votes, duties of inspectors and canvassers, and making and publication of election returns." The Supreme Court has held that States may not exercise their power to determine the "manner" of holding elections to impose term limits on their congressional delegation. One of the most significant ways that States regulate the "manner" of elections is their power to draw election districts. Although in theory Congress could draw the district map for each State, it has not exercised this level of oversight. Congress has, however, required the States to conform to certain practices when drawing districts. States are currently required to use a single-member district scheme, whereby the State is divided into as many election districts for Representatives in the House of Representatives as the size of its representation in that body (that is to say, Representatives cannot be elected at-large from the whole State unless the State has only one Representative in the House, nor can districts elect more than 1 Representative). Congress once imposed additional requirements that districts be composed of contiguous territory, be "compact," and have equal populations within each State. Congress has allowed those requirements to lapse, but the Supreme Court has re-imposed the population requirement on the States under the Equal Protection Clause and is suspicious of districts that do not meet the other "traditional" districting criteria of compactness and contiguity. The restriction on Congress's inability to "make or alter" regulations pertaining to the places of choosing Senators is largely an anachronism. When State Legislatures selected Senators, if Congress had been able to prescribe the place for choosing Senators, it could have in effect told each State where its state capital must be located. This would have been offensive to the concept of each State being sovereign over its own internal affairs. Now that Senators are popularly elected, it is largely a moot point. Clause 2: Sessions of Congress Clause 2 requires that Congress must assemble at least once each year. This was designed to force Congress to make itself available at least once in a year to provide the legislative action the country needed in the face of the transportation and communication challenges present in the 18th century. In modern practice, Congress is in session virtually year-round. Originally, the Constitution provided that the annual meeting was to be on the first Monday in December unless otherwise provided by law. The government under the Articles of Confederation had determined, as a transitional measure to the new constitution, that the date for "commencing proceedings" under the U.S. Constitution would be March 4, 1789. Since the first term of the original federal officials began on this date and ended 2, 4, or 6 years later, this became the date on which new federal officials took office in subsequent years. This meant that, every other year, although a new Congress was elected in November, it did not come into office until the following March, with a "lame duck" Congress convening in the interim. As modern communications and travel made it less necessary to wait 4 months from Election Day to the swearing-in of the elected officials, it became increasingly cumbersome to elect officials in November but wait until March for them to take office. Congress eventually proposed that elected officials take office in January, instead of March; since this required cutting short (by a couple of months) the terms of the elected federal officials at the time of the proposal, Congress proposed the Twentieth Amendment, which established the present dates for when federal officials take office. While the Constitution always granted Congress the authority to meet on a different day without the need to pass an amendment, 2 of the Twentieth Amendment "tidied up" the constitutional text by paralleling the original provision requiring that the Congress meet at least once a year in December, and changing it to January 3 (unless changed by law). Although the original Constitution allowed Congress to change its annual meeting date by statute, this change eliminated any reference to a requirement in the Constitution that a lame duck Congress meet in the period between the election of a new Congress and its taking office. Section 5: Procedure Clause 1: Qualifications of Members Section Five states that a majority of each House constitutes a quorum to do business; a smaller number may adjourn the House or compel the attendance of absent members. In practice, the quorum requirement is all but ignored. A quorum is assumed to be present unless a quorum call, requested by a member, proves otherwise. Rarely do members ask for quorum calls to demonstrate the absence of a quorum; more often, they use the quorum call as a delaying tactic. Sometimes, unqualified individuals have been admitted to Congress. For instance, the Senate once admitted John Henry Eaton, a twenty-eight-year-old, in 1818 (the admission was inadvertent, as Eaton's birth date was unclear at the time). In 1934, a twenty-nine-year-old, Rush Holt, was elected to the Senate; he agreed to wait six months, until his thirtieth birthday, to take the oath. The Senate ruled in that case that the age requirement applied as of the date of the taking of the oath, not the date of election. Clause 2: Rules Each House can determine its own Rules (assuming a quorum is present), and may punish any of its members. A two-thirds vote is necessary to expel a member. Section 5, Clause 2 does not provide specific guidance to each House regarding when and how each House may change its rules, leaving details to the respective chambers. Clause 3: Record of proceedings Each House must keep and publish a Journal, though it may choose to keep any part of the Journal secret. The decisions of the House not the words spoken during debates are recorded in the Journal; if one-fifth of those present (assuming a quorum is present) request it, the votes of the members on a particular question must also be entered. Clause 4: Adjournment Neither House may adjourn, without the consent of the other, for more than three days. Often, a House will hold pro forma sessions every three days; such sessions are merely held to fulfill the constitutional requirement, and not to conduct business. Furthermore, neither House may meet in any place other than that designated for both Houses (the Capitol), without the consent of the other House. Section 6: Compensation, privileges, and restrictions on holding civil office Clause 1: Compensation and legal protection Senators and Representatives set their own compensation. Under the Twenty-seventh Amendment, any change in their compensation will not take effect until after the next congressional election. Members of both Houses have certain privileges, based on those enjoyed by the members of the British Parliament. Members attending, going to or returning from either House are privileged from arrest, except for treason, felony or breach of the peace. One may not sue a Senator or Representative for slander occurring during Congressional debate, nor may speech by a member of Congress during a Congressional session be the basis for criminal prosecution. The latter was affirmed when Mike Gravel published over 4,000 pages of the Pentagon Papers in the Congressional Record, which might have otherwise been a criminal offense. This clause has also been interpreted in Gravel v. United States, 408 U.S. 606 (1972) to provide protection to aides and staff of sitting members of Congress, so long as their activities relate to legislative matters. Clause 2: Independence from the executive Senators and Representatives may not simultaneously serve in Congress and hold a position in the executive branch. This restriction is meant to protect legislative independence by preventing the president from using patronage to buy votes in Congress. It is a major difference from the political system in the British Parliament, where cabinet ministers are required to be members of parliament. Furthermore, Senators and Representatives cannot resign to take newly created or higher-paying political positions; rather, they must wait until the conclusion of the term for which they were elected. If Congress increases the salary of a particular officer, it may later reduce that salary to permit an individual to resign from Congress and take that position (known as the Saxbe fix). The effects of the clause were discussed in 1937, when Senator Hugo Black was appointed an Associate Justice of the Supreme Court with some time left in his Senate term. Just prior to the appointment, Congress had increased the pension available to Justices retiring at the age of seventy. It was therefore suggested by some that the office's emolument had been increased during Black's Senatorial term, and that therefore Black could not take office as a Justice. The response, however, was that Black was fifty-one years old, and would not receive the increased pension until at least 19 years later, long after his Senate term had expired. Section 7: Bills Clause 1: Bills of revenue This establishes the method for making Acts of Congress. Accordingly, any bill may originate in either House of Congress, except for a revenue bill, which may originate only in the House of Representatives. In practice, the Senate can simply circumvent this requirement by substituting the text of any bill previously passed by the House with the text of a revenue bill. When the Senate sends an appropriation bill to the House, the House may return it to the Senate with a blue slip, thereby settling the question in practice. Either House may amend any bill, including revenue and appropriation bills. The Origination Clause stemmed from an English parliamentary convention that all money bills must have their first reading in the House of Commons. It was intended to ensure that the "power of the purse" lies with the legislative body responsible to the people. The clause was also part of a compromise between small and large states. The latter were unhappy with equal representation in the Senate. Clause 2: From bills to law This clause is known as the Presentment Clause. Before a bill becomes law, it must be presented to the President, who has ten days (excluding Sundays) to act upon it. If the President signs the bill, it becomes law. If he disapproves of the bill, he must return it to the House in which it originated together with his objections. This procedure has become known as the veto, although that particular word does not appear in the text of Article One. The bill does not then become law unless both Houses, by two-thirds votes, override the veto. If the President neither signs nor returns the bill within the ten-day limit, the bill becomes law, unless the Congress has adjourned in the meantime, thereby preventing the President from returning the bill to the House in which it originated. In the latter case, the President, by taking no action on the bill towards the end of a session, exercises a "pocket veto", which Congress may not override. In the former case, where the President allows a bill to become law unsigned, there is no common name for the practice, but recent scholarship has termed it a "default enactment." What exactly constitutes an adjournment for the purposes of the pocket veto has been unclear. In the Pocket Veto Case (1929), the Supreme Court held that "the determinative question in reference to an 'adjournment' is not whether it is a final adjournment of Congress or an interim adjournment, such as an adjournment of the first session, but whether it is one that 'prevents' the President from returning the bill to the House in which it originated within the time allowed." Since neither House of Congress was in session, the President could not return the bill to one of them, thereby permitting the use of the pocket veto. In Wright v. United States (1938), however, the Court ruled that adjournments of one House only did not constitute an adjournment of Congress required for a pocket veto. In such cases, the Secretary or Clerk of the House in question was ruled competent to receive the bill. Clause 3: Presidential veto In 1996, Congress passed the Line Item Veto Act, which permitted the President, at the time of the signing of the bill, to rescind certain expenditures. The Congress could disapprove the cancellation and reinstate the funds. The President could veto the disapproval, but the Congress, by a two-thirds vote in each House, could override the veto. In the case Clinton v. City of New York, the Supreme Court found the Line Item Veto Act unconstitutional because it violated the Presentment clause. First, the procedure delegated legislative powers to the President, thereby violating the nondelegation doctrine. Second, the procedure violated the terms of Section Seven, which state, "if he approve [the bill] he shall sign it, but if not he shall return it." Thus, the President may sign the bill, veto it, or do nothing, but he may not amend the bill and then sign it. Every bill, order, resolution, or vote that must be passed by both Houses, except on a question of adjournment, must be presented to the President before becoming law. However, to propose a constitutional amendment, two-thirds of both Houses may submit it to the states for the ratification, without any consideration by the President, as prescribed in Article V. Some Presidents have made very extensive use of the veto, while others have not used it at all. Grover Cleveland, for instance, vetoed over four hundred bills during his first term in office; Congress overrode only two of those vetoes. Meanwhile, seven Presidents have never used the veto power. There have been 2,560 vetoes, including pocket vetoes. Section 8: Powers of Congress Congress's powers are enumerated in Section Eight: Many powers of Congress have been interpreted broadly. Most notably, the Taxing and Spending, Interstate Commerce, and Necessary and Proper Clauses have been deemed to grant expansive powers to Congress. Congress may lay and collect taxes for the "common defense" or "general welfare" of the United States. The U.S. Supreme Court has not often defined "general welfare," leaving the political question to Congress. In United States v. Butler (1936), the Court for the first time construed the clause. The dispute centered on a tax collected from processors of agricultural products such as meat; the funds raised by the tax were not paid into the general funds of the treasury, but were rather specially earmarked for farmers. The Court struck down the tax, ruling that the general welfare language in the Taxing and Spending Clause related only to "matters of national, as distinguished from local, welfare". Congress continues to make expansive use of the Taxing and Spending Clause; for instance, the social security program is authorized under the Taxing and Spending Clause. Congress is permitted to borrow money on the credit of the United States. In 1871, when deciding Knox v. Lee, the Court ruled that this clause permitted Congress to emit bills and make them legal tender in satisfaction of debts. Whenever Congress borrows money, it is obligated to repay the sum as stipulated in the original agreement. However, such agreements are only "binding on the conscience of the sovereign", as the doctrine of sovereign immunity prevents a creditor from suing in court if the government reneges its commitment. The Supreme Court has seldom restrained the use of the commerce clause for widely varying purposes. The first important decision related to the commerce clause was Gibbons v. Ogden, decided by a unanimous Court in 1824. The case involved conflicting federal and state laws: Thomas Gibbons had a federal permit to navigate steamboats in the Hudson River, while the other, Aaron Ogden, had a monopoly to do the same granted by the state of New York. Ogden contended that "commerce" included only buying and selling of goods and not their transportation. Chief Justice John Marshall rejected this notion. Marshall suggested that "commerce" included navigation of goods, and that it "must have been contemplated" by the Framers. Marshall added that Congress's power over commerce "is complete in itself, may be exercised to its utmost extent, and acknowledges no limitations other than are prescribed in the Constitution". Chief Justice John Marshall established a broad interpretation of the Commerce Clause. The expansive interpretation of the Commerce Clause was restrained during the late nineteenth and early twentieth centuries, when a laissez-faire attitude dominated the Court. In United States v. E. C. Knight Company (1895), the Supreme Court limited the newly-enacted Sherman Antitrust Act, which had sought to break up the monopolies dominating the nation's economy. The Court ruled that Congress could not regulate the manufacture of goods, even if they were later shipped to other states. Chief Justice Melville Fuller wrote, "commerce succeeds to manufacture, and is not a part of it." The U.S. Supreme Court sometimes ruled New Deal programs unconstitutional because they stretched the meaning of the commerce clause. In Schechter Poultry Corp. v. United States, (1935) the Court unanimously struck down industrial codes regulating the slaughter of poultry, declaring that Congress could not regulate commerce relating to the poultry, which had "come to a permanent rest within the State." As Chief Justice Charles Evans Hughes put it, "so far as the poultry here in question is concerned, the flow of interstate commerce has ceased." Judicial rulings against attempted use of Congress's Commerce Clause powers continued during the 1930s. It was only in 1937 that the Supreme Court gave up the laissez-faire doctrine as it decided a landmark case, National Labor Relations Board v. Jones & Laughlin Steel Company. The legislation in question, the National Labor Relations Act, prevented employers from engaging in "unfair labor practices" such as firing workers for joining unions. The Court ruled to sustain the Act's provisions. The Court, returning to the theories propounded by John Marshall, ruled that Congress could pass laws regulating actions that even indirectly influenced interstate commerce. Further decisions expanded the Congress's powers under the commerce clause. This dramatic change in the Court's thinking was influenced by the threat of President Franklin D. Roosevelt's Court Packing scheme. In the 1990s, the Court acted to restrain Congress's exercise of its power to regulate commerce. In United States v. Lopez, the Court found that Congress could not exercise "Police power" reserved to the States by use of the Commerce Clause. In contrast to United States v. Lopez , the powers defined in the Commerce Clause have been elastically re-interpreted to cover non-commercial activity not just between but within the states. In 2005, the Supreme Court controversially ruled in Gonzales v. Raich, that the Commerce Clause granted Congress the authority to regulate Cannabis plants grown, processed, and consumed within the state on private property. The court reclassified the plant as a commodity even though it was not sold or exchanged in any transaction. Other powers of Congress Congress may establish uniform laws relating to naturalization and bankruptcy. It may also coin money, regulate the value of American or foreign currency and punish counterfeiters. Congress may fix the standards of weights and measures. Furthermore, Congress may establish post offices and post roads (the roads, however, need not be exclusively for the conveyance of mail). Congress may promote the progress of science and useful arts by granting copyrights and patents of limited duration. Section eight, clause eight of Article One, known as the Copyright Clause, is the only instance of the word "right" used in the original constitution (though the word does appear in several Amendments). Though perpetual copyrights and patents are prohibited, the Supreme Court has ruled in Eldred v. Ashcroft (2003) that repeated extensions to the term of copyright do not constitute perpetual copyright; also note that this is the only power granted where the means to accomplish its stated purpose is specifically provided for. Courts inferior to the Supreme Court may be established by Congress. Congress has several powers related to war and the armed forces. Under the War Powers Clause, only Congress may declare war, but in several cases it has, without declaring war, granted the President the authority to engage in military conflicts. Five wars have been declared in American history: the War of 1812, the Mexican-American War, the Spanish-American War, World War I and World War II. Some historians argue that the legal doctrines and legislation passed during the operations against Pancho Villa constitute a sixth declaration of war. Congress may grant letters of marque and reprisal. Congress may establish and support the armed forces, but no appropriation made for the support of the army may be used for more than two years. This provision was inserted because the Framers feared the establishment of a standing army, beyond civilian control, during peacetime. Congress may regulate or call forth the state militias, but the states retain the authority to appoint officers and train personnel. Congress also has exclusive power to make rules and regulations governing the land and naval forces. Although the executive branch and the Pentagon have asserted an ever-increasing measure of involvement in this process, the U.S. Supreme Court has often reaffirmed Congress's exclusive hold on this power (e.g. Burns v. Wilson, 346 U.S. 137 (1953)). Congress used this power twice soon after World War II with the enactment of two statutes: the Uniform Code of Military Justice to improve the quality and fairness of courts martial and military justice, and the Federal Tort Claims Act which among other rights had allowed military service persons to sue for damages until the U.S. Supreme Court repealed that section of the statute in a divisive series of cases, known collectively as the Feres Doctrine. Congress has the exclusive right to legislate "in all cases whatsoever" for the nation's capital, the District of Columbia. Congress chooses to devolve some of such authority to the elected mayor and council of District of Columbia. Nevertheless, Congress remains free to enact any legislation for the District so long as constitutionally permissible, to overturn any legislation by the city government, and technically to revoke the city government at any time. Congress may also exercise such jurisdiction over land purchased from the states for the erection of forts and other buildings. Necessary and Proper clause Finally, Congress has the power to do whatever is "necessary and proper" to carry out its enumerated powers and, crucially, all others vested in it. This has been interpreted to authorize criminal prosecution of those whose actions have a "substantial effect" on interstate commerce in Wickard v. Filburn ; however, Thomas Jefferson, in the Kentucky Resolutions, supported by James Madison, maintained that a penal power could not be inferred from a power to regulate, and that the only penal powers were for treason, counterfeiting, piracy and felony on the high seas, and offenses against the law of nations. The necessary and proper clause has been interpreted extremely broadly, thereby giving Congress wide latitude in legislation. The first landmark case involving the clause was McCulloch v. Maryland (1819), which involved the establishment of a national bank. Alexander Hamilton, in advocating the creation of the bank, argued that there was "a more or less direct" relationship between the bank and "the powers of collecting taxes, borrowing money, regulating trade between the states, and raising and maintaining fleets and navies". Thomas Jefferson countered that Congress's powers "can all be carried into execution without a national bank. A bank therefore is not necessary, and consequently not authorized by this phrase". Chief Justice John Marshall agreed with the former interpretation. Marshall wrote that a Constitution listing all of Congress's powers "would partake of a prolixity of a legal code and could scarcely be embraced by the human mind". Since the Constitution could not possibly enumerate the "minor ingredients" of the powers of Congress, Marshall "deduced" that Congress had the authority to establish a bank from the "great outlines" of the general welfare, commerce and other clauses. Under this doctrine of the necessary and proper clause, Congress has sweepingly broad powers (known as implied powers) not explicitly enumerated in the Constitution. However, the Congress cannot enact laws solely on the implied powers, any action must be necessary and proper in the execution of the enumerated powers. Section 9: Limits on Congress The next section of Article One provided limits on Congress's powers: Although the international slave trade was allowed until 1808, Congress prohibited it on January 1, 1808, the first day it was permitted to do so. Until 1808, however, the Constitution permitted Congress to levy a maximum duty of ten dollars per slave imported into the United States. A writ of habeas corpus is a legal action against unlawful detainment that commands a law enforcement agency or other body that has a person in custody to have a court inquire into the legality of the detention. The court may order the person released if the reason for detention is deemed insufficient or unjustifiable. The Constitution further provides that the privilege of the writ of habeas corpus may not be suspended "unless when in cases of rebellion or invasion the public safety may require it". In Ex parte Milligan (1866), the Supreme Court decided that the suspension of habeas corpus was lawful, but military tribunals did not apply to citizens in states that had upheld the authority of the Constitution and where civilian courts were still operating. A bill of attainder is a law by which a person is immediately convicted without trial. An ex post facto law is a law which applies retroactively, punishing someone for an act that was only made criminal after it was done. The ex post facto clause does not apply to civil matters. Section Nine reiterates the provision from Section Two that direct taxes must be apportioned by state populations. Furthermore, no tax may be imposed on exports from any state. Congress may not, by revenue or commerce legislation, give preference to ports of one state over those of another; neither may it require ships from one state to pay duties in another. All funds belonging to the Treasury may not be withdrawn except according to law. Modern practice is that Congress annually passes a number of appropriation bills authorizing the expenditure of public money. The Constitution requires that a regular statement of such expenditures be published. The Title of Nobility Clause prohibits Congress from granting any title of nobility. In addition, it specifies that no civil officer may accept, without the consent of Congress, any gift, payment, office or title from a foreign ruler or state. However, a U.S. citizen may receive foreign office before or after their period of public service. Section 10: Limits on the States Clause 1: Contracts Clause States may not exercise certain powers reserved for the federal government: they may not enter into treaties, alliances or confederations, grant letters of marque or reprisal, coin money or issue bills of credit (such as currency). Furthermore, no state may make anything but gold and silver coin a tender in payment of debts, which expressly forbids any state government (but not the federal government) from "making a tender" (i.e., authorizing something that may be offered in payment) of any type or form of money to meet any financial obligation, unless that form of money is coins made of gold or silver (or a medium of exchange backed by and redeemable in gold or silver coins, as noted in Farmers & Merchants Bank v. Federal Reserve Bank). Much of this clause is devoted to preventing the States from using or creating any currency other than that created by Congress. In Federalist no. 44, Madison explains that "... it may be observed that the same reasons which shew the necessity of denying to the States the power of regulating coin, prove with equal force that they ought not to be at liberty to substitute a paper medium in the place of coin. Had every State a right to regulate the value of its coin, there might be as many different currencies as States; and thus the intercourse among them would be impeded." Moreover, the states may not pass bills of attainder, ex post facto laws, impair the obligation of contracts or grant titles of nobility. The Contract Clause was the subject of much contentious litigation in the 19th century. It was first interpreted by the Supreme Court in 1810, when Fletcher v. Peck was decided. The case involved the Yazoo land scandal, in which the Georgia legislature authorized the sale of land to speculators at low prices. The bribery involved in the passage of the authorizing legislation was so blatant that a Georgia mob attempted to lynch the corrupt members of the legislature. Following elections, the legislature passed a law that rescinded the contracts granted by the corrupt legislators. The validity of the annulment of the sale was questioned in the Supreme Court. In writing for a unanimous court, Chief Justice John Marshall asked, "What is a contract?" His answer was: "a compact between two or more parties." Marshall argued that the sale of land by the Georgia legislature, though fraught with corruption, was a valid "contract". He added that the state had no right to annul the purchase of the land, since doing so would impair the obligations of contract. The definition of a contract propounded by Chief Justice Marshall was not as simple as it may seem. In 1819, the Court considered whether a corporate charter could be construed as a contract. The case of Trustees of Dartmouth College v. Woodward involved Dartmouth College, which had been established under a Royal Charter granted by King George III. The Charter created a board of twelve trustees for the governance of the College. In 1815, however, New Hampshire passed a law increasing the board's membership to twenty-one with the aim that public control could be exercised over the College. The Court, including Marshall, ruled that New Hampshire could not amend the charter, which was ruled to be a contract since it conferred "vested rights" on the trustees. The Marshall Court determined another dispute in Sturges v. Crowninshield. The case involved a debt that was contracted in early 1811. Later in that year, the state of New York passed a bankruptcy law, under which the debt was later discharged. The Supreme Court ruled that a retroactively applied state bankruptcy law impaired the obligation to pay the debt, and therefore violated the Constitution. In Ogden v. Saunders (1827), however, the court decided that state bankruptcy laws could apply to debts contracted after the passage of the law. State legislation on the issue of bankruptcy and debtor relief has not been much of an issue since the adoption of a comprehensive federal bankruptcy law in 1898. Clause 2: Export Clause Still more powers are prohibited of the states. States may not, without the consent of Congress, tax imports or exports except for the fulfillment of state inspection laws (which may be revised by Congress). The net revenue of the tax is paid not to the state, but to the federal Treasury. Clause 3: Compact Clause Under the Compact Clause, states may not, without the consent of Congress, keep troops or armies during times of peace. They may not enter into alliances nor compacts with foreign states, nor engage in war unless invaded. States may, however, organize and arm a militia. Currently the National Guard and State Militias with federal oversight fulfill this function. The idea of allowing Congress to have say over agreements between states traces back to the numerous controversies that arose between various colonies. Eventually compromises would be created between the two colonies and these compromises would be submitted to the Crown for approval. After the American Revolutionary War, the Articles of Confederation allowed states to appeal to Congress to settle disputes between the states over boundaries or "any cause whatever". The Articles of Confederation also required Congressional approval for "any treaty or alliance" in which a state was one of the parties. There have been a number of Supreme Court cases, especially Virginia v. Tennessee, , concerning what constitutes valid congressional consent to an interstate compact. The Court found that some agreements among states stand even without Congress consent. According to the Court, the Compact Clause requires congressional consent only if the agreement among the states is "directed to the formation of any combination tending to the increase of political power in the States, which may encroach upon or interfere with the just supremacy of the United States". The National Popular Vote Interstate Compact, which is not yet effective, might be the first modern case that truly stretches the limits of the Compact Clause. es:Art culo I de la Constituci n de los Estados Unidos fr:Article I de la Constitution des tats-Unis he: 1 nl:Artikel 1 van de grondwet van de Verenigde Staten pt:Artigo Primeiro da Constitui o dos Estados Unidos ro:Articolul nt i al Constitu iei Statelor Unite ale Americii zh:
Routing is the process of selecting a path for traffic in a network, or between or across multiple networks. Routing is performed for many types of networks, including circuit-switched networks, such as the public switched telephone network (PSTN), computer networks, such as the Internet, as well as in networks used in public and private transportation, such as the system of streets, roads, and highways in national infrastructure. In packet switching networks, routing is the higher-level decision making that directs network packets from their source toward their destination through intermediate network nodes by specific packet forwarding mechanisms. Packet forwarding is the transit of logically addressed network packets from one network interface to another. Intermediate nodes are typically network hardware devices such as routers, bridges, gateways, firewalls, or switches. General-purpose computers also forward packets and perform routing, although they have no specially optimized hardware for the task. The routing process usually directs forwarding on the basis of routing tables, which maintain a record of the routes to various network destinations. Thus, constructing routing tables, which are held in the router's memory, is very important for efficient routing. Most routing algorithms use only one network path at a time. Multipath routing techniques enable the use of multiple alternative paths. Routing, in a narrower sense of the term, is often contrasted with bridging in its assumption that network addresses are structured and that similar addresses imply proximity within the network. Structured addresses allow a single routing table entry to represent the route to a group of devices. In large networks, structured addressing (routing, in the narrow sense) outperforms unstructured addressing (bridging). Routing has become the dominant form of addressing on the Internet. Bridging is still widely used within localized environments. Routing schemes differ in how they deliver messages: - unicast delivers a message to a single specific node - anycast delivers a message to anyone out of a group of nodes, typically the one nearest to the source - multicast delivers a message to a group of nodes that have expressed interest in receiving the message - geocast delivers a message to a geographic area - broadcast delivers a message to all nodes in the network Unicast is the dominant form of message delivery on the Internet. This article focuses on unicast routing algorithms. In static routing (or non-dynamic routing), small networks may use manually configured routing tables. Larger networks have complex topologies that can change rapidly, making the manual construction of routing tables unfeasible. Nevertheless, most of the public switched telephone network (PSTN) uses pre-computed routing tables, with fallback routes if the most direct route becomes blocked (see routing in the PSTN). Dynamic routing attempts to solve this problem by constructing routing tables automatically, based on information carried by routing protocols, allowing the network to act nearly autonomously in avoiding network failures and blockages. Dynamic routing dominates the Internet. Examples of dynamic-routing protocols and algorithms include Routing Information Protocol (RIP), Open Shortest Path First (OSPF) and Enhanced Interior Gateway Routing Protocol (EIGRP). Distance vector algorithms Distance vector algorithms use the Bellman–Ford algorithm. This approach assigns a cost number to each of the links between each node in the network. Nodes send information from point A to point B via the path that results in the lowest total cost (i.e. the sum of the costs of the links between the nodes used). The algorithm operates in a very simple manner. When a node first starts, it only knows of its immediate neighbours, and the direct cost involved in reaching them. (This information — the list of destinations, the total cost to each, and the next hop to send data to get there — makes up the routing table, or distance table.) Each node, on a regular basis, sends to each neighbour node its own current assessment of the total cost to get to all the destinations it knows of. The neighbouring nodes examine this information and compare it to what they already 'know'; anything that represents an improvement on what they already have, they insert in their own routing table(s). Over time, all the nodes in the network discover the best next hop for all destinations, and the best total cost. When one network node goes down, any nodes that used it as their next hop discard the entry, and create new routing-table information. These nodes convey the updated routing information to all adjacent nodes, which in turn repeat the process. Eventually all the nodes in the network receive the updates, and discover new paths to all the destinations they can still "reach". When applying link-state algorithms, a graphical map of the network is the fundamental data used for each node. To produce its map, each node floods the entire network with information about the other nodes it can connect to. Each node then independently assembles this information into a map. Using this map, each router independently determines the least-cost path from itself to every other node using a standard shortest paths algorithm such as Dijkstra's algorithm. The result is a tree graph rooted at the current node, such that the path through the tree from the root to any other node is the least-cost path to that node. This tree then serves to construct the routing table, which specifies the best next hop to get from the current node to any other node. Optimised Link State Routing algorithm A link-state routing algorithm optimised for mobile ad hoc networks is the Optimised Link State Routing Protocol (OLSR). OLSR is proactive; it uses Hello and Topology Control (TC) messages to discover and disseminate link state information through the mobile ad hoc network. Using Hello messages, each node discovers 2-hop neighbor information and elects a set of multipoint relays (MPRs). MPRs distinguish OLSR from other link state routing protocols. Path vector protocol Distance vector and link state routing are both intra-domain routing protocols. They are used inside an autonomous system, but not between autonomous systems. Both of these routing protocols become intractable in large networks and cannot be used in Inter-domain routing. Distance vector routing is subject to instability if there are more than a few hops in the domain. Link state routing needs huge amount of resources to calculate routing tables. It also creates heavy traffic due to flooding. Path vector routing is used for inter-domain routing. It is similar to distance vector routing. Path vector routing assumes that one node (there can be many) in each autonomous system acts on behalf of the entire autonomous system. This node is called the speaker node. The speaker node creates a routing table and advertises it to neighboring speaker nodes in neighboring autonomous systems. The idea is the same as distance vector routing except that only speaker nodes in each autonomous system can communicate with each other. The speaker node advertises the path, not the metric, of the nodes in its autonomous system or other autonomous systems. Path vector routing is discussed in RFC 1322; the path vector routing algorithm is somewhat similar to the distance vector algorithm in the sense that each border router advertises the destinations it can reach to its neighboring router. However, instead of advertising networks in terms of a destination and the distance to that destination, networks are advertised as destination addresses and path descriptions to reach those destinations. A route is defined as a pairing between a destination and the attributes of the path to that destination, thus the name, path vector routing, where the routers receive a vector that contains paths to a set of destinations. The path, expressed in terms of the domains (or confederations) traversed so far, is carried in a special path attribute that records the sequence of routing domains through which the reachability information has passed. Path selection involves applying a routing metric to multiple routes to select (or predict) the best route. In computer networking, the metric is computed by a routing algorithm, and can cover information such as bandwidth, network delay, hop count, path cost, load, MTU (maximum transmission unit), reliability, and communication cost (see e.g. this survey for a list of proposed routing metrics). The routing table stores only the best possible routes, while link-state or topological databases may store all other information as well. In case of overlapping or equal routes, algorithms consider the following elements to decide which routes to install into the routing table (sorted by priority): - Prefix-Length: where longer subnet masks are preferred (independent of whether it is within a routing protocol or over different routing protocol) - Metric: where a lower metric/cost is preferred (only valid within one and the same routing protocol) - Administrative distance: where a route learned from a more reliable routing protocol is preferred (only valid between different routing protocols) Because a routing metric is specific to a given routing protocol, multi-protocol routers must use some external heuristic to select between routes learned from different routing protocols. Cisco routers, for example, attribute a value known as the administrative distance to each route, where smaller administrative distances indicate routes learned from a supposedly more reliable protocol. A local network administrator, in special cases, can set up host-specific routes to a particular device that provides more control over network usage, permits testing, and better overall security. This is useful for debugging network connections or routing tables. In some small systems, a single central device decides ahead of time the complete path of every packet. In some other small systems, whichever edge device injects a packet into the network decides ahead of time the complete path of that particular packet. In both of these systems, that route-planning device needs to know a lot of information about what devices are connected to the network and how they are connected to each other. Once it has this information, it can use an algorithm such as A* search algorithm to find the best path. In high-speed systems, there are so many packets transmitted every second that it is infeasible for a single device to calculate the complete path for each and every packet. Early high-speed systems dealt with this by setting up a circuit switching relay channel once for the first packet between some source and some destination; later packets between that same source and that same destination continue to follow the same path without recalculating until the channel teardown. Later high-speed systems inject packets into the network without any one device ever calculating a complete path for that packet—multiple agents. In large systems, there are so many connections between devices, and those connections change so frequently, that it is infeasible for any one device to even know how all the devices are connected to each other, much less calculate a complete path through them. Such systems generally use next-hop routing. Most systems use a deterministic dynamic routing algorithm: When a device chooses a path to a particular final destination, that device always chooses the same path to that destination until it receives information that makes it think some other path is better. A few routing algorithms do not use a deterministic algorithm to find the "best" link for a packet to get from its original source to its final destination. Instead, to avoid congestion in switched systems or network hot spots in packet systems, a few algorithms use a randomized algorithm—Valiant's paradigm—that routes a path to a randomly picked intermediate destination, and from there to its true final destination. In many early telephone switches, a randomizer was often used to select the start of a path through a multistage switching fabric. In some networks, routing is complicated by the fact that no single entity is responsible for selecting paths; instead, multiple entities are involved in selecting paths or even parts of a single path. Complications or inefficiency can result if these entities choose paths to optimize their own objectives, which may conflict with the objectives of other participants. A classic example involves traffic in a road system, in which each driver picks a path that minimizes their travel time. With such routing, the equilibrium routes can be longer than optimal for all drivers. In particular, Braess' paradox shows that adding a new road can lengthen travel times for all drivers. In another model, for example, used for routing automated guided vehicles (AGVs) on a terminal, reservations are made for each vehicle to prevent simultaneous use of the same part of an infrastructure. This approach is also referred to as context-aware routing. The Internet is partitioned into autonomous systems (ASs) such as internet service providers (ISPs), each of which controls routes involving its network, at multiple levels. First, AS-level paths are selected via the BGP protocol, which produces a sequence of ASs through which packets flow. Each AS may have multiple paths, offered by neighboring ASs, from which to choose. Its decision often involves business relationships with these neighboring ASs, which may be unrelated to path quality or latency. Second, once an AS-level path has been selected, there are often multiple corresponding router-level paths, in part because two ISPs may be connected in multiple locations. In choosing the single router-level path, it is common practice for each ISP to employ hot-potato routing: sending traffic along the path that minimizes the distance through the ISP's own network—even if that path lengthens the total distance to the destination. Consider two ISPs, A and B. Each has a presence in New York, connected by a fast link with latency 5 ms—and each has a presence in London connected by a 5 ms link. Suppose both ISPs have trans-Atlantic links that connect their two networks, but A's link has latency 100 ms and B's has latency 120 ms. When routing a message from a source in As London network to a destination in Bs New York network, A may choose to immediately send the message to B in London. This saves A the work of sending it along an expensive trans-Atlantic link, but causes the message to experience latency 125 ms when the other route would have been 20 ms faster. A 2003 measurement study of Internet routes found that, between pairs of neighboring ISPs, more than 30% of paths have inflated latency due to hot-potato routing, with 5% of paths being delayed by at least 12 ms. Inflation due to AS-level path selection, while substantial, was attributed primarily to BGP's lack of a mechanism to directly optimize for latency, rather than to selfish routing policies. It was also suggested that, were an appropriate mechanism in place, ISPs would be willing to cooperate to reduce latency rather than use hot-potato routing. As the Internet and IP networks become mission critical business tools, there has been increased interest in techniques and methods to monitor the routing posture of networks. Incorrect routing or routing issues cause undesirable performance degradation, flapping and/or downtime. Monitoring routing in a network is achieved using route analytics tools and techniques. - RFC 3626 - Michael Mitzenmacher; Andréa W. Richa; Ramesh Sitaraman. "The Power of Two Random Choices: A Survey of Techniques and Results". Section "Randomized Protocols for Circuit Routing". p. 34. - Stefan Haas. "The IEEE 1355 Standard: Developments, Performance and Application in High Energy Physics". 1998. p. 15. quote: "To eliminate network hot spots, ... a two phase routing algorithm. This involves every packet being first sent to a randomly chosen intermediate destination; from the intermediate destination it is forwarded to its final destination. This algorithm, referred to as Universal Routing, is designed to maximize capacity and minimize delay under conditions of heavy load." - Jonne Zutt, Arjan J.C. van Gemund, Mathijs M. de Weerdt, and Cees Witteveen (2010). Dealing with Uncertainty in Operational Transport Planning. In R.R. Negenborn and Z. Lukszo and H. Hellendoorn (Eds.) Intelligent Infrastructures, Ch. 14, pp. 355–382. Springer. - Matthew Caesar and Jennifer Rexford. BGP routing policies in ISP networks. IEEE Network Magazine, special issue on Interdomain Routing, Nov/Dec 2005. - Neil Spring, Ratul Mahajan, and Thomas Anderson. Quantifying the Causes of Path Inflation. Proc. SIGCOMM 2003. - Ratul Mahajan, David Wetherall, and Thomas Anderson. Negotiation-Based Routing Between Neighboring ISPs. Proc. NSDI 2005. - Ratul Mahajan, David Wetherall, and Thomas Anderson. Mutually Controlled Routing with Independent ISPs. Proc. NSDI 2007. - Ash, Gerald (1997). Dynamic Routing in Telecommunication Networks. McGraw–Hill. ISBN 0-07-006414-8. - Doyle, Jeff & Carroll, Jennifer (2005). Routing TCP/IP, Volume I, Second Ed. Cisco Press. ISBN 1-58705-202-4.Ciscopress ISBN 1-58705-202-4 - Doyle, Jeff & Carroll, Jennifer (2001). Routing TCP/IP, Volume II,. Cisco Press. ISBN 1-57870-089-2.Ciscopress ISBN 1-57870-089-2 - Huitema, Christian (2000). Routing in the Internet, Second Ed. Prentice–Hall. ISBN 0-321-22735-2. - Kurose, James E. & Ross, Keith W. (2004). Computer Networking, Third Ed. Benjamin/Cummings. ISBN 0-321-22735-2. - Medhi, Deepankar & Ramasamy, Karthikeyan (2007). Network Routing: Algorithms, Protocols, and Architectures. Morgan Kaufmann. ISBN 0-12-088588-3. \|Wikiversity has learning materials about Routing\| \|Wikimedia Commons has media related to Routing.\| - Count-To-Infinity Problem - "Stability Features" are ways of avoiding the "count to infinity" problem. - Cisco IT Case Studies about Routing and Switching - good example at event-helix
Although we may not feel motion, the Earth is currently moving 67,000 mph (link) around the sun, the solar system is moving 514,000 mph around the center of the Milky Way Galaxy (link), and the Milky Way is moving a staggering 1.3 million mph (link) around the gravitational field of a supercluster. Therefore, it is fair to say that our galaxy is in constant motion, being pushed apart and pulled together by the acceleration of the universe (link) and gravity (link) respectively. In 2011, Saul Perlmutter, Brian Schmidt and Adam Riess (link) were awarded the Nobel Prize in Physics for their discovery of the accelerating universe. As Royal Swedish Academy’s Olga Botner described, “This discovery is fundamental and a milestone for cosmology.Before their discovery, cosmologists made the assumption that the universe was static, non-moving, and all the galaxies were at a fixed position in space. We normally associate moving objects to be blurry in pictures as they are in motion; however, if we look at the Hubble Deep Space image, we are able to see that the image is very clear and most of the galaxies are distinguishable. Therefore, the assumption that the universe was static made sense at the time because our knowledge of the universe was based on the images and visuals that were available to us at the time. However, we are now aware that the universe is in fact not static, but is expanding and accelerating. (link)How do we know that the universe is accelerating? Adam Riess et al. were one of two research teams that started using the technique of calibrating type Ia supernovae to measure distances. They needed to measure two things to confirm the acceleration of the universe (Appendix 1):- The distance of type Ia supernovae from the Milky Way.- The rate at which the space between supernovae and the Milky Way is expanding; this was done by measuring the redshift of light being emitted by the supernovae. Measuring DistanceIn order to measure the expansion of space, Adam Riess et al. had to measure how far galaxies in our local group were from the Milky Way, then this was done over a period of time so that they could measure the rate at which the galaxies are moving away from us. In a lecture presented at Loyola University Maryland (link), Adam Riess used the analogy:”A ship captain at night wants to figure out how far away the rocky shore is, so they look for a lighthouse. They use the knowledge that a lighthouse is very luminous, so if the lighthouse looks very faint they know they’re very far from shore they’re very safe.”Much like a captain, astrophysicists can measure distances using the light emitted from an exploding star in a galaxy; otherwise known as a supernova. Astrophysicists know how luminous these supernovae are; therefore they are able to use the Inverse Square Law of brightness and distance to determine how far away the supernova is by simply measuring the faintness of the supernova.The inverse square law, tells us that the brightness decreases as the inverse of the distance squared increases (1/D2). This is because the same magnitude of light is required to fill the surface of a larger sphere of distance. Therefore, if the supernova is twice as faint, it’ll be four times as far.)Riess et al. created a chart that is similar to the one above; the magnitude of the type Ia supernovae was compared to the redshift from our perspective from Earth. In 1998, Riess et al. announced their results, the values they had measures were closely aligned to the model they had created of the accelerating universe – they had found that the universe was expanding.What Causes Acceleration of the Universe? (cite book)The acceleration of the universe can be explained by the idea that the expansion of the universe is speeding up (as it is not a constant expansion); therefore, there must be an unknown force of repulsion that counteracts the force of gravity.What Is a Supercluster?If the universe was viewed under a microscope, we would see a network of many fibres, extending out and clumping together. These are galaxies. Due to the nature of chaos in the universe, galaxies naturally form clusters (link), that are more concentrated in some parts and less so in others. These clusters of galaxies further clump together to form superclusters of galaxies.
Quadrilaterals and Other Polygons In this polygon worksheet, 5th graders name 6 polygons, tell if each one is a regular polygon or not and tell if it is a special quadrilateral. 7 Views 51 Downloads A Five Day Approach to Using Technology and Manipulatives to Explore Area and Perimeter Young mathematicians build an understanding of area and perimeter with their own two hands in a series of interactive geometry lessons. Through the use of different math manipulatives, children investigate the properties of rectangles,... 3rd - 6th Math CCSS: Adaptable Polygons-Changing Area Versus Changing Perimeter Investigate the area and perimeter of polygons in this geometry instructional activity. Young geometers use grid paper to draw a quadrilateral and calculate its area and perimeter. They also read The Greedy Triangle to identify the... 5th - 8th Math CCSS: Designed
Can you tell me about gamma-ray bursts? At least once a day, the sky lights up with a spectacular flash of gamma-rays coming from deep space. The brightness of this flash of gamma-rays can temporarily overwhelm all other gamma-ray sources in the universe. The burst can last from a fraction of a second to over a thousand seconds. The time that the burst occurs and the direction from which it will come cannot be predicted. Gamma-ray bursts (GRBs) can release more energy in 10 seconds than the Sun will emit in its entire 10 billion-year lifetime! In order to understand what a gamma-ray burst is, you must recognize gamma-rays as the most energetic form of light. Light, or electromagnetic radiation, can be thought of as coming in tiny packets of energy called photons. These photons come with a wide range of energies. At the low-energy end, we find radio waves. At the high-energy end, we find gamma-rays. The human eye is blind to nearly the entire electromagnetic spectrum, except for the very narrow range light that falls in what we call the "visible" (or "optical") range. If an astronomer were to study the universe only in the visible range of the spectrum, the large majority of cosmic events would go unobserved. Events such as star birth and star death emit photons that occur across the entire electromagnetic spectrum. Within the past 30 years, astronomers have developed the ability to view the universe in radio waves, gamma-rays, and all energies in between. This ability has allowed us to discover amazing events in our universe such as GRBs. The first gamma-ray bursts were detected while scientists were using satellites to look for gamma-rays that would result from violations of the Nuclear Test Ban Treaty during the Cold War Era of the 1960s. Gamma-rays were found, but the gamma-rays were coming from outer space and not from a nuclear bomb exploding in the Earth's atmosphere. There are several current theories about the possible causes of gamma-ray bursts. One explanation proposes that they are the result of colliding neutron stars -- corpses of massive stars (5 to 10 times the mass of our Sun) that have blown up as supernovae. A second theory proposes that gamma-ray bursts are the result of a merging between a neutron star and a black hole or between two black holes. Black holes result when supermassive (greater than 20 times the mass of our Sun) stars die. A theory that is attracting considerable attention states that gamma-ray bursts occur as the result of material shooting towards Earth at almost the speed of light as the result of a hypernova. A hypernova explosion can occur when the largest of the supermassive stars come to the end of their lives and collapse to form black holes. Hypernova explosions can be at least 100 times more powerful than supernova explosions. One of the greatest difficulties in finding gamma ray bursts is that they are so short-lived. Once a burst is detected, it takes too long to rotate a satellite to face the burst and collect data. Recently, scientists were able to observe the visible light from a burst as the burst was occurring. This extraordinary event occurred as the result of a great deal of planning, cooperation, and luck. On January 23, 1999, a network of scientists was notified within 4 seconds of the start of a burst that a burst was in progress. Thanks to the coordinated efforts of scientists and observatories all around the world, data were collected on the burst from start to finish in several different energy ranges of the electromagnetic spectrum. It had the optical brightness of 10 million billion Suns, which was only one-thousandth of its gamma-ray brightness! The future looks good for solving the mystery of GRBs. Swift, a NASA satellite with the capacity to study the universe in a multitude of wavelengths, is expected to launch 2003. The satellite is aptly named because, once a burst is detected, the satellite can be repositioned to face the gamma-ray source within 50 seconds. By observing the burst in the optical, ultraviolet, X-ray, and gamma-ray ranges of the electromagnetic spectrum, scientists hope to finally be able to answer the many questions surrounding gamma-ray bursts. The StarChild site is a service of the High Energy Astrophysics Science Archive Research Center (HEASARC), Dr. Alan Smale (Director), within the Astrophysics Science Division (ASD) at NASA/GSFC. The StarChild Team StarChild Graphics & Music: Acknowledgments StarChild Project Leader: Dr. Laura A. Whitlock Responsible NASA Official: Phil Newman
By Monica Grady - Professor of Planetary and Space Sciences, The Open University When Guiseppe Piazzi reported his observations of a minor planet in 1801, he originally thought it might be a comet. But follow-up observations by fellow astronomers suggested that Ceres was actually an asteroid. So it’s somewhat ironic that the latest results from NASA’s Dawn mission suggest this asteroid is confusingly similar to a comet. Dawn has found a number of mysterious features on Ceres so far, including bright white spots on its surface. Its latest results suggest that these are salts left behind as ice vaporised from the surface by sublimation – a process often seen in comets. They also suggest Ceres may have formed far away from its current location in orbit between Mars and Jupiter. This would be surprising as many astronomers believe that a key difference between comets and asteroids is that asteroids form closer to the sun. Ceres is the largest asteroid we know of – it is also classified as a dwarf planet. Its bright spots were first discovered when Dawn started orbiting Ceres in 2014, the largest at a latitude of around 25°N. There was intense speculation about what these features were, as they had the characteristics of ice. The Herschel Space Observatory later found that water vapour was being produced at specific locations on Ceres. It therefore seemed that Ceres was acting like a comet, with ice-rich regions releasing dust and vapour during daylight hours. If that were the case, then ice might be a major component of the asteroid, buried below a surface of dust and rubble. But the two new studies (see here and here), using information from different instruments on the Dawn spacecraft, did not record any ice on the surface. However, one article speculates that ice may still be buried just below the surface while the other suggests that water bound in minerals is abundant. The researchers also investigated the bright feature at the bottom of Occator Crater, the brightest of the white spots, and concluded that they may be hydrated magnesium salts. The salts are deposits left behind from recent sublimation of water ice that have not yet been covered by soil. Other bright spots, although not as prominent, may also be salt deposits, but that material is likely to be older. A Kuiper Belt Object? The researchers also identified a mixture of minerals on the surface of Ceres, which they think are ammonia-bearing clay minerals and magnesium carbonate. The clay minerals could have been produced by silicates reacting with ammonia ice. However, if Ceres had formed where it is now, it would not have been able to pick up any ammonia ice to enable such a reaction, because the ice would not be stable. This means that Ceres may have originally formed in the Kuiper Belt on the outskirts of the solar system and then scattered inwards as the giant planets migrated outwards. Alternatively, Ceres could have formed more or less where it is, and incorporated nitrogen-containing organic molecules, which, like the water ice, were transported inwards from beyond Neptune. While this might not sound all that significant, it does have quite profound ramifications for our understanding of how material has been mixed to form planets, minor planets, comets and Kuiper Belt Objects. This year has been an amazing one for small icy bodies. Images from the New Horizons mission to Pluto have shown us the variety of landscapes that can be sculpted on an icy surface. Similarly, pictures of the surface of comet 67P Churyumov Gerasimenko taken by Rosetta have revealed canyons and pits probably caused by fracturing and ice sublimation. Now we can add a third small body where a combination of ice, water and salts have left behind an environment in which there is the potential for an active, sub-surface chemistry that might, eventually, result in formation of complex molecules. It is also becoming more clear than ever that strict division between comets and asteroids is no longer realistic, and that they represent a spectrum of objects of varying activity and orbit. Just one last word about the surface of Ceres. I might not be much of a farmer – but I’m fairly certain that magnesium salts and nitrogen-bearing clays are important ingredients in a good, rich soil for raising crops. So naming Ceres after a harvest deity was more appropriate than Piazzi could have imagined! Source: The Conversation
An equation in one variable can be easily represented on a number line by plotting the value of the variable on it. We can also represent the equation on a graph by considering the coefficient of the missing variable as zero, and then assuming the different values of the missing variable we can find the solutions and then plot the solutions on the graph. Illustration: Plot the equation x= 4 on the graph Solution: Let the coefficient of the missing variable be zero. The equation can be written as ; x + 0y = 4 For y=2 , the equation becomes x + 0(2)=4 or x = 4 For y=4 , the equation becomes x + 0(4)=4 or x = 4 For y=6 , the equation becomes x + 0(6)=4 or x = 4 So (4,2), (4,4) and (4,6) are the solution of the equation plotting them on the graph we get We get a line parallel to Y- Axis Similarly if we plot the equation y=4, we get a line parallel to X- Axis We can further generalize that an equation in one variable represents a line parallel to the axis whose variable is missing in the equation.
This page is being written live. To get an email when it’s done, jump onto the list here. String theory is the leading theory that attempts to explain the mystery of the Planck length, the incredibly tiny length at which the force of gravity starts to interact with the quantum world. Although it has never been experimentally proven, it remains the leading theory for the world of the Planck length, and its predictions are astonishing. Three of the four fundamental forces (electromagnetism, and the two nuclear forces) have been explained and experimentally demonstrated with the framework called the Standard model. The fourth force, gravity, remains an outlier. Compared to the other forces it is exceptionally weak, but it has a much further range. This has meant that it plays a negligible role in the quantum world, but as you approach the large scales of moons, planets, stars, and galaxies, it becomes by far the dominant force. So far we have been able to split our models of the universe in two: The Standard Model explains the small, and Einstein’s general relativity explains the large. Both models are exceptionally accurate. General relativity has been the knowledge base with which we have put men on the moon, robots on Mars, Jupiter, Venus, and Titan, and flown probes past Pluto and into interstellar space. Richard Feynman compared the accuracy of the experimental predictions from Quantum mechanics as akin to specifying the width of North America to within one hair’s breadth of accuracy. But the two theories are mathematically incompatible. In areas where the two overlap, such as in black holes or in the early seconds of the universe following the big bang, applying the two theories at once produce illegible and mathematically impossible outcomes. Part of the reason for this is that, at the Planck length, general relativity assumes that the universe is smooth and uniform, while quantum mechanics assumes it to be chaotic and warped. Using the two together produces strange results like lengths that somehow have less than one dimension. This means that the world of the Planck length and the secret that lies there is a new frontier of science. String Theory is the leading theory that attempts to unify all four fundamental forces of the universe into a single framework. A theory of everything that explains the basis of all known phenomena in the universe. What is String Theory? Instead of a smooth or warped surface at the planck length, string theory speculates that every particle contains planck length-sized string-like structures that vibrate in different ways. The vibrations of these strings create the particles described in the Standard Model, like plucking a guitar string can create the musical notes G, A, B, C, etc. It is through these different vibrations that properties like mass, and force charge is created. So an up quark is created by one set of vibrations, an electron is created by another, and the explanation for how gravity comes about at the quantum level is that there is another set of vibrations that create a particle called a graviton. These strings are really weird. They don’t just move in four dimensions (three for space, one for time) like a tiny piece of regular string, they move in up to eleven dimensions. This concept is absolutely wild. An artist’s conception of a vibrating string. The diameter of the string is equal to the Planck Length.
Experiment: Does the Heads or Tails Side of a Quarter Hold More Drops of Water? Lesson 7 of 16 Objective: SWBAT follow the steps of the scientific method to test whether the heads or tails side of a quarter will hold the most drops of water. The Why Behind Teaching This: Over the past week, students have been building their foundation of science tools and procedures and skills that scientists use. Now it is time for the students to put what they have learned to practice by becoming the scientists. They will follow the steps of the scientific method to test whether the heads or tails side of a quarter will hold the most drops of water. This activity is linked to standard 3-5-ETS1-3: Plan and carry out fair tests in which variables are controlled and failure points are considered to identify aspects of a model or prototype that can be improved. I chose this experiment as the first to have my students conduct because I like to begin with an experiment they can do independently. This is a fairly easy experiment that even the ESE and ELL students can complete independently. The majority of the experiments done throughout the year are done in cooperative groups. I like to begin with an opportunity for each student to work through the steps alone first, without having to take others opinions into account. I also require students to repeat experiments three time to ensure valid results. In this experiment, each student applies drops of water differently which is a variable that must be controlled. The same student has to add the drops, which would mean the other group members would not get the opportunity to use the dropper, which students enjoy. The goal of today’s lesson is for students to follow the steps of the scientific method, to test a whether the heads or tails side of a quarter hold the most drops of water. I will be reviewing some of the science tools and we will be identifying the variables in the experiment as well. I will follow up this lesson with a lesson on graphing so students can share their results with the class. Students will demonstrate success on this activity by following the steps of the scientific method we outline together to conduct the experiment accurately. They will need to control all variables except the independent variable in order to accurate results. Students will also need to collect and record accurate data. I will be assessing all of this through obseravtion during the experiment. Students will also be assessed through the explanations they write on the model they are required to draw during the wrap up section. They are asked to draw a model of the experiment, label each part, and write an explanation of what is happening. This will provide me with information as to whether they understand the procedures they just completed. - A quarter - A hand lens for each student - Foldable, trifold, made from copy paper for each student - Print out of the procedure for quarter experiment for each student - Dropper for each student - Cup of water for each pair of students - Paper towel for each student Making Observations Before Experimenting: I begin the lesson today by having students take out their science notebooks and title the page Experiment: Does the heads or tails side of a quarter hold more drops of water? I have my notebook displayed on the overhead with the title written already for students to refer to as a reference. This helps the ESE and ELL students who may struggle with spelling and writing quickly. As students record the title of the lesson, I pass out a quarter and a hand lens to each student and ask them not to pick them up until I give them directions. I draw a T-chart in my science notebook with one side titled Heads, and the other side titled Tails. Students know that anything I write in my notebook they should copy into theirs so they are already copying this as I begin to discuss the T-chart. I explain that a T-chart is used to compare two things, in this case the heads side of a quarter versus the tails side. I ask students why they think they have a hand lens to use as a tool for this activity. They explain that they will be using it to help them observe the quarter (this is review from a previous lesson). I ask them why we are not using a different tool for observing, such as a microscope. This helps me note a clear understanding of the difference between the two tools, as well as identify and correct any misconceptions. After our discussion, I ask students to make observations about their quarter and write characteristics of both sides in their T-chart. I tell them that they can discuss these differences in their groups as they observe. I give them about 3 minutes to make and record their observations. I circulate to observe and ask questions. We discuss some of the answers the students came up with and I record some of the examples in my notebook. Observations Lead to Experiments: I explain to students that observations are what often lead to the first step of the scientific method. I ask them what that step is and they are able to tell me, it is the questions or purpose. I explain to them that several years ago I used to have students test how many drops of water a penny, a nickel, a dime, and a quarter could hold. Then one of my previous students observed some of the same differences they just filled in their T-chart with, and asked me if it mattered which side of the coins he used. I told him to test it out and find out. By him making those observations, it has led me to change the activity into an experiment to test his question. I provide each student with a piece of copy paper that has the sides folded in like a trifold display board (the same set up we used for the previous scientific method foldables). I place my example under the overhead and we all write Question in the upper left hand corner as the section heading. I write Does the heads or tails side of a quarter hold more drops of water? Again, the modeling is important for my students because I have both ESE and ELL students which need that visual reference for copying. As we complete more experiments together, groups will be responsible for completing all of this together without my assistance. I then ask students what the next step of the scientific method is and they are able to tell me the hypothesis follows the question. We all record Hypothesis as the heading for this section. I ask them how making observations of the quarter first, will help them with their hypothesis. I am looking for answers such as “It helped me see the differences”, and “It helped me see characteristics that may allow more water to build up on that side”. I ask students for examples of what the hypothesis may be. We have already discussed that in 5th grade we write our hypothesis as a cause and effect sentence so I am looking for examples of that. There are really three possible options: If I place drops of water on the heads side and tails side of a quarter, then I predict/hypothesize/believe, that the __________(heads or tails) side of the quarter will hold more drops. Or they might choose to end that statement with both sides will hold the same number of drops. Students choose which hypothesis they believe is correct and they record it on their foldable. I leave mine blank as I do not want to influence students to choose what I have written. I remind students that the next step is to plan a way to test our hypothesis to find out if we are correct. I ask what two things our plan will consist of and they are able to tell me, materials and procedure. We write Materials as the heading in the lower left hand corner of the foldable, and Procedure as the heading in the upper right hand corner. To save time, I have the procedure for quarter experiment typed, printed, and cut out for each student. I pass one out to each student and ask them to glue it in under that section. I do this for the first few experiments because some have several steps and it takes a lot of my students a long time to write, plus they get tired of writing. I am assessing their ability to follow the steps, not their ability to copy information. As they glue in the procedure, I read the steps out loud while they follow along. We then move over to the materials section. After hearing the procedure, they are able to tell me all of the materials we will be using: a dropper, one quarter, a cup, water, paper towel. After we have our plan written out, I ask students what the next step is, and they are excited to tell me they get to conduct the experiment now. I ask them what they should be doing while they conduct the experiment and they know they should be recording data in a chart. We move to the center section of the foldable and draw a data chart together. Before students begin, we discuss the variables in the experiment. We record this information in their notebooks under the T-chart. We begin with the independent variable which they tell me is the side of the quarter (the one thing they are changing). Next, I ask what the dependent variable will be and they tell me the number of drops the side holds (data they are collecting). Finally, we try to name at least four control variables which students usually have a more difficult time coming up with. They tell me: the person adding the drops, the quarter being used, the dropper, the height the dropper is held from, the surface the quarter sits on, and no bumping or shaking the desks. They were able to tell me six variables to control which I thought was great. Conducting the Experiment: After we identify the variables, I ask a student to explain again what the steps of the experiment are. I like to do this right before they begin so the directions are fresh in their mind. I call on a student that I know often times needs directions repeated, and ask him to repeat the steps again. This allows students to hear the directions for a third time, and I can make sure he is clear on the expectations. I pass out a cup of water with two droppers in it to each pair of students and choose a student to pass out a paper towel to each student. I tell them to set the quarter on the paper towel so when the water overflows it does not make a mess and tell them they may begin testing. I circulate to observe and to remind students to count quietly as this is distracting to those around them. I also remind them to include the unit of measure, in this case, drops. I am watching as students conduct the experiment to make sure they are collecting data accurately, and to make sure they are testing the heads then the tails, then moving on to trial two and doing the heads and tails again. I find that many students try to do all three trials on the heads side, then move on to the tails side. If they do this, and time runs out, they will not have completed trials they may only have the heads side done and not any on the tails side. Students should always do the experiment once, then move on to completed trial two all the way through, and then completed trial three. As students are working, I go ahead and label the rest of my headings in my foldable. I write Conclusion in the bottom right section of the foldable and Graph in the bottom center section. As students begin finishing up their experiment, I collect their materials, and ask them to analyze their data and write their conclusion on their foldable. As I collect materials, I review the conclusions being written in foldables. I am checking what they have written for their conclusion to see that they restated their hypothesis and told whether it was accepted or denied by the data collected. Often times they will just write, "my hypothesis was/was not correct" and not explain it. They have to include an explanation indicating they analyzed their data. When all students are finished, and I have collected all materials, I call on a couple of students I saw had their conclusion written correctly. The conclusion should have the hypothesis restated, whether the hypothesis was correct or incorrect, and what evidence they collected to support that. I try to find at least one student whose hypothesis was correct, and one whose hypothesis was incorrect. As students read their conclusion, I point these things out and give positive reinforcement. I ask students to rewrite their conclusion if they did not include all of these details and glue them into their science notebook with glue on the back of the center section only, not on the flaps. Identifying Factors that Affected the Outcome: The results of the class were about 70% tails and 30% heads. We discuss what factors may have affected some student outcomes. The students give me suggestions such as, the drops they added were larger, someone bumped the table causing it to spill over quickly, not all tails side of the quarters are the same, some students held their droppers closer or father away, etc. Some of the items mentioned were variables that we identified before beginning the experiment we I mention again how important it is to keep all those variables constant when testing because they may cause the outcome to be different. We also use this time to discuss why it is so important to repeat experiments several times, and not just do it once. On the ouside of the foldable (flaps closed) I ask students to draw a model of the experiment, label the drawing, and explain what is happening at each part. I ask them to do this on their foldable, in their science notebooks, so they can refer to it as a reference instead of being handed into me. The exit activity reviews what we have learned about models, while also pulling in other science skills such as diagraming and labeling, and connects writing to the activity as well. They can then open the foldable to see details about each step and to see the data that was collected. If students do not finish this in the time given, they will take it home to finish as homework and I will check it in the morning the following day.
Gravitational theory is a theory that states any two particles attract each other with a force that is equal to the product of the two masses. Before Newton, the views on gravity and the motion of the planets, were quite different. Aristotle believed the universe never had a beginning and would never end; he believed it was eternal. Kepler’s view on gravity and motion was that the planets orbited around the sun and orbits faster the closer it becomes to the sun. Galileo believed if something started at the same speed, the speed will stay constant. Whereas the previous models heavily depended on which component was moving. The ether model, disproved in the 1887 Michelson-Morley experiment along with the previously mentioned magnet/conductor setup, suggests that “the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest” (Einstein, On the Electrodynamics of Moving Bodies 1). Furthermore, Einstein postulates that the laws of physics (he specifically mentions electrodynamics and optics) are the same in any frame of reference. This is what he calls the “Principle of Relativity.” He also postulates that light in vacuum will always propagate with velocity c, regardless of the motion of the reference frame. He abandons the idea of the luminous ether here because ether necessitates the absolute rest that Einstein argues against. They have not yet been directly detected on earth, although astronomers Joe Taylor and Russell Hulse received the 1993 Nobel Prize for proof of their existence, by showing that a star system is losing energy by producing gravitational waves. Gravitational waves are a completely new spectrum. If electromagnetic waves let us see the universe, gravitational waves will let us hear the universe. They will provide us with a new sense, the sense of hearing, with which to explore the universe. Gravity is a very complicated subject, but scientists are learning more and more about it as time goes on. His second law is about the acceleration of an object is equal to the net force acting on it divided by the object’s mass. Newton’s third law is whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object. The momentum is mass × velocity. The kinetic energy is the mass × velocity. Momentum is a property of any moving object. According to his original theory, the relationship between time and light, time actually slows down for objects that are moving at near light speeds.The object themselves will become shorter and heavier. This crazy theory has since then been proven with various experiments showing the trueness in this theory. This plays an important role in astronomical observation. Relativity comes in two forms, one known as Special and one known as General. The first postulate of Einstein’s theory states that if two frame that are moving relative to one another at a constant velocity or speed, the laws regarding physics are the same in one as it is in the other. Mass-Energy Equivalence In 1905, Albert Einstein confirmed the Theory of Special Relativity. This stated that objects moving at a constant speed move in relation to each other. This discovery managed to unify space and time, as a concept, because of how things appear differently in space depending on the speed someone is going. This wasn’t the only concept that was a result of the Theory of Special Relativity, however. Another idea that came about as a result of the Theory of Special Relativity was the Mass-Energy Equivalence. If string theory is a theory of gravity, then how does it compare with Einstein's theory of gravity? What is the relationship between strings and spacetime geometry? Strings and gravitons The simplest case to imagine is a single string traveling in a flat spacetime in d dimensions, meaning that it is traveling across space while time is ticking, so to speak. A string is a one-dimensional object, meaning that if you want to travel along a string, you can only go forwards or backwards in the direction of the string, there is no sideways or up and down on a string. The string can move sideways or up and down in spacetime, though, and as the string moves around in spacetime, it sweeps out a surface in spacetime called the string worldsheet, a two-dimensional surface with one dimension of space and one dimension of time. Investigation of Falling Cake Cases Planning and Introduction: To begin I will explain the term terminal velocity. Terminal velocity is the maximum speed that a given fallen object can obtain. Terminal velocity is obtained in this way; when an object first starts falling, it accelerates for some while after starting. Eventually the force upwards due to the air flowing over the objects body is equal to the weight acting downwards, and it no longer accelerates. We can also obtain by using Newton's 2nd law how there is no acceleration on the falling object. The path of the electrons is circular because of this fact. The ratio of e/m can be found by the relationships between the measured accelerating potential difference, the diameter of the circular path described by the electron, and the magnetic flux density. Theory: British scientist Sir J.J. Thompson (1856-1940) first discovered that the electron was a discrete particle of electricity. From his discoveries came the accepted value for e/m which is 1.75890*10^11 coulombs/kg. With this information we could then accurately determine the mass of the electron.
1. Transformer Basics Transformers are electrical devices consisting of two or more coils of wire used to transfer electrical energy by means of a changing magnetic field. One of the main reasons that we use alternating AC voltages and currents in our homes and workplace’s is that AC supplies can be easily generated at a convenient voltage, transformed (hence the name transformer) into much higher voltages and then distributed around the country using a national grid of pylons and cables over very long distances. The reason for transforming the voltage to a much higher level is that higher distribution voltages implies lower currents for the same power and therefore lower I2R losses along the networked grid of cables. These higher AC transmission voltages and currents can then be reduced to a much lower, safer and usable voltage level where it can be used to supply electrical equipment in our homes and workplaces, and all this is possible thanks to the basic Voltage Transformer. A Typical Voltage Transformer The Voltage Transformer can be thought of as an electrical component rather than an electronic component. A transformer basically is very simple static (or stationary) electro-magnetic passive electrical device that works on the principle of Faraday’s law of induction by converting electrical energy from one value to another. The transformer does this by linking together two or more electrical circuits using a common oscillating magnetic circuit which is produced by the transformer itself. A transformer operates on the principals of “electromagnetic induction”, in the form of Mutual Induction. Mutual induction is the process by which a coil of wire magnetically induces a voltage into another coil located in close proximity to it. Then we can say that transformers work in the “magnetic domain”, and transformers get their name from the fact that they “transform” one voltage or current level into another. Transformers are capable of either increasing or decreasing the voltage and current levels of their supply, without modifying its frequency, or the amount of electrical power being transferred from one winding to another via the magnetic circuit. A single phase voltage transformer basically consists of two electrical coils of wire, one called the “Primary Winding” and another called the “Secondary Winding”. For this tutorial we will define the “primary” side of the transformer as the side that usually takes power, and the “secondary” as the side that usually delivers power. In a single-phase voltage transformer, the primary is usually the side with the higher voltage. These two coils are not in electrical contact with each other but are instead wrapped together around a common closed magnetic iron circuit called the “core”. This soft iron core is not solid but made up of individual laminations connected together to help reduce the core’s losses. The two coil windings are electrically isolated from each other but are magnetically linked through the common core allowing electrical power to be transferred from one coil to the other. When an electric current passed through the primary winding, a magnetic field is developed which induces a voltage into the secondary winding as shown. Single Phase Voltage Transformer In other words, for a transformer there is no direct electrical connection between the two coil windings, thereby giving it the name also of an Isolation Transformer. Generally, the primary winding of a transformer is connected to the input voltage supply and converts or transforms the electrical power into a magnetic field. While the job of the secondary winding is to convert this alternating magnetic field into electrical power producing the required output voltage as shown. Transformer Construction (single-phase) · VP – is the Primary Voltage · VS – is the Secondary Voltage · NP – is the Number of Primary Windings · NS – is the Number of Secondary Windings · Φ (phi) – is the Flux Linkage Notice that the two coil windings are not electrically connected but are only linked magnetically. A single-phase transformer can operate to either increase or decrease the voltage applied to the primary winding. When a transformer is used to “increase” the voltage on its secondary winding with respect to the primary, it is called a Step-up transformer. When it is used to “decrease” the voltage on the secondary winding with respect to the primary it is called a Step-down transformer. However, a third condition exists in which a transformer produces the same voltage on its secondary as is applied to its primary winding. In other words, its output is identical with respect to voltage, current and power transferred. This type of transformer is called an “Impedance Transformer” and is mainly used for impedance matching or the isolation of adjoining electrical circuits. The difference in voltage between the primary and the secondary windings is achieved by changing the number of coil turns in the primary winding ( NP ) compared to the number of coil turns on the secondary winding ( NS ). As the transformer is basically a linear device, a ratio now exists between the number of turns of the primary coil divided by the number of turns of the secondary coil. This ratio, called the ratio of transformation, more commonly known as a transformers “turns ratio”, ( TR ). This turns ratio value dictates the operation of the transformer and the corresponding voltage available on the secondary winding. It is necessary to know the ratio of the number of turns of wire on the primary winding compared to the secondary winding. The turns ratio, which has no units, compares the two windings in order and is written with a colon, such as 3:1 (3-to-1). This means in this example, that if there are 3 volts on the primary winding there will be 1 volt on the secondary winding, 3 volts-to-1 volt. Then we can see that if the ratio between the number of turns changes the resulting voltages must also change by the same ratio, and this is true. Transformers are all about “ratios”. The ratio of the primary to the secondary, the ratio of the input to the output, and the turns ratio of any given transformer will be the same as its voltage ratio. In other words for a transformer: “turns ratio = voltage ratio”. The actual number of turns of wire on any winding is generally not important, just the turns ratio and this relationship is given as: A Transformers Turns Ratio Assuming an ideal transformer and the phase angles: ΦP ≡ ΦS Note that the order of the numbers when expressing a transformers turns ratio value is very important as the turns ratio 3:1 expresses a very different transformer relationship and output voltage than one in which the turns ratio is given as: 1:3. Transformer Basics Example No1 A voltage transformer has 1500 turns of wire on its primary coil and 500 turns of wire for its secondary coil. What will be the turns ratio (TR) of the transformer. This ratio of 3:1 (3-to-1) simply means that there are three primary windings for every one secondary winding. As the ratio moves from a larger number on the left to a smaller number on the right, the primary voltage is therefore stepped down in value as shown. Transformer Basics Example No2 If 240 volts rms is applied to the primary winding of the same transformer above, what will be the resulting secondary no load voltage. Again, confirming that the transformer is a “step-down” transformer as the primary voltage is 240 volts and the corresponding secondary voltage is lower at 80 volts. Then the main purpose of a transformer is to transform voltages at preset ratios and we can see that the primary winding has a set amount or number of windings (coils of wire) on it to suit the input voltage. If the secondary output voltage is to be the same value as the input voltage on the primary winding, then the same number of coil turns must be wound onto the secondary core as there are on the primary core giving an even turns ratio of 1:1 (1-to-1). In other words, one coil turn on the secondary to one coil turn on the primary. If the output secondary voltage is to be greater or higher than the input voltage, (step-up transformer) then there must be more turns on the secondary giving a turns ratio of 1:N (1-to-N), where N represents the turns ratio number. Likewise, if it is required that the secondary voltage is to be lower or less than the primary, (step-down transformer) then the number of secondary windings must be less giving a turns ratio of N:1 (N-to-1). We have seen that the number of coil turns on the secondary winding compared to the primary winding, the turns ratio, affects the amount of voltage available from the secondary coil. But if the two windings are electrically isolated from each other, how is this secondary voltage produced? We have said previously that a transformer basically consists of two coils wound around a common soft iron core. When an alternating voltage ( VP ) is applied to the primary coil, current flows through the coil which in turn sets up a magnetic field around itself, called mutual inductance, by this current flow according to Faraday’s Law of electromagnetic induction. The strength of the magnetic field builds up as the current flow rises from zero to its maximum value which is given as dΦ/dt. As the magnetic lines of force setup by this electromagnet expand outward from the coil the soft iron core forms a path for and concentrates the magnetic flux. This magnetic flux links the turns of both windings as it increases and decreases in opposite directions under the influence of the AC supply. However, the strength of the magnetic field induced into the soft iron core depends upon the amount of current and the number of turns in the winding. When current is reduced, the magnetic field strength reduces. When the magnetic lines of flux flow around the core, they pass through the turns of the secondary winding, causing a voltage to be induced into the secondary coil. The amount of voltage induced will be determined by: NdΦ/dt (Faraday’s Law), where N is the number of coil turns. Also this induced voltage has the same frequency as the primary winding voltage. Then we can see that the same voltage is induced in each coil turn of both windings because the same magnetic flux links the turns of both the windings together. As a result, the total induced voltage in each winding is directly proportional to the number of turns in that winding. However, the peak amplitude of the output voltage available on the secondary winding will be reduced if the magnetic losses of the core are high. If we want the primary coil to produce a stronger magnetic field to overcome the cores magnetic losses, we can either send a larger current through the coil, or keep the same current flowing, and instead increase the number of coil turns ( NP ) of the winding. The product of amperes times turns is called the “ampere-turns”, which determines the magnetizing force of the coil. So assuming we have a transformer with a single turn in the primary, and only one turn in the secondary. If one volt is applied to the one turn of the primary coil, assuming no losses, enough current must flow and enough magnetic flux generated to induce one volt in the single turn of the secondary. That is, each winding supports the same number of volts per turn. As the magnetic flux varies sinusoidally, Φ = Φmax sinωt, then the basic relationship between induced emf, ( E ) in a coil winding of N turns is given by: emf = turns x rate of change · ƒ – is the flux frequency in Hertz, = ω/2π · Ν – is the number of coil windings. · Φ – is the amount of flux in webers. This is known as the Transformer EMF Equation. For the primary winding emf, N will be the number of primary turns, ( NP ) and for the secondary winding emf, N will be the number of secondary turns, ( NS ). Also please note that as transformers require an alternating magnetic flux to operate correctly, transformers cannot therefore be used to transform or supply DC voltages or currents, since the magnetic field must be changing to induce a voltage in the secondary winding. In other words, transformers DO NOT operate on steady state DC voltages, only alternating or pulsating voltages. If a transformers primary winding was connected to a DC supply, the inductive reactance of the winding would be zero as DC has no frequency, so the effective impedance of the winding will therefore be very low and equal only to the resistance of the copper used. Thus the winding will draw a very high current from the DC supply causing it to overheat and eventually burn out, because as we know I = V/R. Transformer Basics Example No3 A single phase transformer has 480 turns on the primary winding and 90 turns on the secondary winding. The maximum value of the magnetic flux density is 1.1T when 2200 volts, 50Hz is applied to the transformer primary winding. Calculate: a). The maximum flux in the core. b). The cross-sectional area of the core. c). The secondary induced emf. Electrical Power in a Transformer Another one of the transformer basics parameters is its power rating. The power rating of a transformer is obtained by simply multiplying the current by the voltage to obtain a rating in Volt-amperes, ( VA ). Small single phase transformers may be rated in volt-amperes only, but much larger power transformers are rated in units of Kilo volt-amperes, ( kVA ) where 1 kilo volt-ampere is equal to 1,000 volt-amperes, and units of Mega volt-amperes, ( MVA ) where 1 mega volt-ampere is equal to 1 million volt-amperes. In an ideal transformer (ignoring any losses), the power available in the secondary winding will be the same as the power in the primary winding, they are constant wattage devices and do not change the power only the voltage to current ratio. Thus, in an ideal transformer the Power Ratio is equal to one (unity) as the voltage, V multiplied by the current, I will remain constant. That is the electric power at one voltage/current level on the primary is “transformed” into electric power, at the same frequency, to the same voltage/current level on the secondary side. Although the transformer can step-up (or step-down) voltage, it cannot step-up power. Thus, when a transformer steps-up a voltage, it steps-down the current and vice-versa, so that the output power is always at the same value as the input power. Then we can say that primary power equals secondary power, ( PP = PS ). Power in a Transformer Where: ΦP is the primary phase angle and ΦS is the secondary phase angle. Note that since power loss is proportional to the square of the current being transmitted, that is: I2R, increasing the voltage, let’s say doubling ( ×2 ) the voltage would decrease the current by the same amount, ( ÷2 ) while delivering the same amount of power to the load and therefore reducing losses by factor of 4. If the voltage was increased by a factor of 10, the current would decrease by the same factor reducing overall losses by factor of 100. Transformer Basics – Efficiency A transformer does not require any moving parts to transfer energy. This means that there is no friction or windage losses associated with other electrical machines. However, transformers do suffer from other types of losses called “copper losses” and “iron losses” but generally these are quite small. Copper losses, also known as I2R loss is the electrical power which is lost in heat as a result of circulating the currents around the transformers copper windings, hence the name. Copper losses represents the greatest loss in the operation of a transformer. The actual watts of power lost can be determined (in each winding) by squaring the amperes and multiplying by the resistance in ohms of the winding (I2R). Iron losses, also known as hysteresis is the lagging of the magnetic molecules within the core, in response to the alternating magnetic flux. This lagging (or out-of-phase) condition is due to the fact that it requires power to reverse magnetic molecules; they do not reverse until the flux has attained sufficient force to reverse them. Their reversal results in friction, and friction produces heat in the core which is a form of power loss. Hysteresis within the transformer can be reduced by making the core from special steel alloys. The intensity of power loss in a transformer determines its efficiency. The efficiency of a transformer is reflected in power (wattage) loss between the primary (input) and secondary (output) windings. Then the resulting efficiency of a transformer is equal to the ratio of the power output of the secondary winding, PS to the power input of the primary winding, PP and is therefore high. An ideal transformer is 100% efficient because it delivers all the energy it receives. Real transformers on the other hand are not 100% efficient and at full load, the efficiency of a transformer is between 94% to 96% which is quite good. For a transformer operating with a constant voltage and frequency with a very high capacity, the efficiency may be as high as 98%. The efficiency, η of a transformer is given as: Where: Input, Output and Losses are all expressed in units of power. Generally, when dealing with transformers, the primary watts are called “volt-amps”, VA to differentiate them from the secondary watts. Then the efficiency equation above can be modified to: It is sometimes easier to remember the relationship between the transformers input, output and efficiency by using pictures. Here the three quantities of VA, W and η have been superimposed into a triangle giving power in watts at the top with volt-amps and efficiency at the bottom. This arrangement represents the actual position of each quantity in the efficiency formulas. Transformer Efficiency Triangle and transposing the above triangle quantities gives us the following combinations of the same equation: Then, to find Watts (output) = VA x eff., or to find VA (input) = W/eff., or to find Efficiency, eff. = W/VA, etc. Transformer Basics Summary Then to summarize this transformer basics tutorial. A Transformer changes the voltage level (or current level) on its input winding to another value on its output winding using a magnetic field. A transformer consists of two electrically isolated coils and operates on Faraday’s principal of “mutual induction”, in which an EMF is induced in the transformers secondary coil by the magnetic flux generated by the voltages and currents flowing in the primary coil winding. Both the primary and secondary coil windings are wrapped around a common soft iron core made of individual laminations to reduce eddy current and power losses. The primary winding of the transformer is connected to the AC power source which must be sinusoidal in nature, while the secondary winding supplies electrical power to the load. Having said that, a transformer could be used in reverse with the supply connected to the secondary winding provided the voltage and current ratings are observed. We can represent the transformer in block diagram form as follows: Basic Representation of the Transformer The ratio of the transformers primary and secondary windings with respect to each other produces either a step-up voltage transformer or a step-down voltage transformer with the ratio between the number of primary turns to the number of secondary turns being called the “turns ratio” or “transformer ratio”. If this ratio is less than unity, n < 1 then NS is greater than NP and the transformer is classed as a step-up transformer. If this ratio is greater than unity, n > 1, that is NP is greater than NS, the transformer is classed as a step-down transformer. Note that single phase step-down transformer can also be used as a step-up transformer simply by reversing its connections and making the low voltage winding its primary, and vice versa as long as the transformer is operated within its original VA design rating. If the turns ratio is equal to unity, that is n = 1, then both the primary and secondary have the same number of coil turns so therefore the voltages and currents will be the same for both the primary and secondary windings. This type of 1:1 transformer is classed as an isolation transformer as both the primary and secondary windings of the transformer have the same number of volts per turn. The efficiency of a transformer is the ratio of the power it delivers to the load to the power it absorbs from the supply. In an ideal transformer there are no losses so no loss of power then PIN = POUT. In the next tutorial to do with Transformer Basics, we will look at the physical Construction of a Transformer and see the different magnetic core types and laminations used to support the primary and secondary windings. This article is reprinted from Electronics Tutorials - Transformer Basics.
. OBJECTIVES The purpose of this lab is to familiarize the student with techniques of measurement and also with the concept of density. B. BACKGROUND Density is defined as MASS divided by VOLUME. Volume can be measured as liquid volume (liters, pints, quarts) or as cubic linear volume (I x w x ht, cm3, in3). If a geometric object has regular dimensions, there may be a formula for calculating the volume (rectangular solid is length x width x height; cylinder is pr2 x height). The mass is determined by weighing. In the metric system, mass is expressed in grams (or kilograms). Once mass and volume are determined, density is calculated directly from the formula D = M / V. C. EQUIPMENT You will need a ruler marked in centimeters, a kitchen scale for weighing in grams, 2 blocks of wood that are different sizes but made of the same type of wood, and a brick. If you have a scale that only measures in ounces and pounds, you can convert to grams. Take the weight in pounds, divide by 2.2, and then multiply by 1,000. If you have a friendly grocer, you may be able to weigh your wood blocks on the scale in the vegetable section. D. PROCEDURES 1. Determine the mass of the first wood block to the nearest gram. If your scale is metric, read the mass directly in grams. Otherwise, convert ounces to pounds, pounds to kilograms, and kilograms to grams. (Example: You weigh the block to be 5 oz. To change ounces to pounds, divide by 16 oz. in a pound. So your measurement of 5 oz. divided by 16 oz/lb equals 0.31 pounds. Next, divide 0.31 by 2.2 and get .1409 kilograms. Finally, multiply .1409 by 1,000 to get 140.9 g. Your measurement to the nearest gram is 141 g.) 2. Measure dimensions of the block in centimeters: Length ____________ Width ____________ Height ____________ Calculate the volume from the formula: V = 1 x w x h Volume cm3 Calculate density by dividing volume into mass: Density g/cm3 Repeat measurements and calculations for the second wood block. The density of pure water is 1.0 g/cm3. If an object has a density lower than water, it will float. From your calculations, predict whether the blocks will float. Now put them in a pan of water and verify your answer. If the two blocks were made of the same material, they should have the same density no matter what sizes they are. Are your calculations for density the same for both blocks? If not, consider some sources of error in your measurements. Calculate the density of a brick or other heavy rectangular solid. Should it float? It is possible to determine the volume of objects that are irregular. Instead of measuring dimensions, the object is immersed in water in a container that has accurate markings for liquid volume on its walls. This could be done with a glass measuring cup or a graduated cylinder (from a chemistry laboratory). Fill the measuring cup to the halfway mark. Carefully lower an object into the water, being careful not to splash. After the water surface is calm, read the new water level. The increase in water volume is the volume of the immersed object. This method is only accurate if you have an accurately marked cup or cylinder. OPTIONAL: DETERMINE THE DENSITY OF A SPARK PLUG OR OTHER IRREGULAR OBJECT. RESULTS AND CONCLUSIONS Record all your calculations neatly for your lab report. Answer any questions that were raised in the above discussion. Try to think of some practical applications to using density. Could density be a useful measurement for identifying different metals or other substances? Solve this problem: Archimedes had to protect the king from being swindled. If the king’s new crown had a mass of 2790 g, and he knew the density of gold to be 15g/cm3, how much water must the crown displace when submerged if the crown is pure gold? laboratory report should contain the following sections: (1) Hypothesis, (2) Procedures, (3) Observations and Results, and (4) Conclusions. Make certain you include all four headings with at least a short paragraph for each. In addition, tables, graphs, and answers to questions may be necessary in the latter two sections. Scientific research should contain a preliminary statement of the expected outcome of the experiment. This can include predictions of the specific experiment or the general anticipated result. If you are merely doing an observation and have no idea of the outcome, you cannot make an actual hypothesis. Instead, make a short statement of the purpose of the observation. However, if you have preconceived ideas of the outcome, include them in this section, and then see how they compare to the results. Even though you are told what to do, write a paragraph of the specific steps you actually took in doing the experiment or observation. Because you are coming up with your own equipment, your procedures will be of particular interest. OBSERVATIONS AND RESULTS This is where you should make a detailed statement of the outcome of your experiment. Record all your pertinent observations in a clear, readable form. Arrange your data in tables (such as measurements and calculations you make). Answer any questions asked in this Study Guide, marking these clearly so that they can be easily found. Your conclusions should include a comparison between the outcome of the experiment and your initial predictions made in the hypothesis. In cases where you are attempting to recreate a physical constant, compare your number to the accepted value, using the formula for experimental error: Experimental Error Equation If you find a large difference in your results from the expected value or if your anticipated observations are not the same as your actual observations, try to identify possible sources of error or reasons for the difference in the hypothesis and results
Updated May 4, 2023 What is OFFSET Function in Excel The offset function helps to get the value stored in a selected row or column or array of a row-column matrix by calling out the row and column number concerning the cell value. The offset function starts counting the row and column number once we fix the reference cell, and that cell will become its first point to start counting. Below is the OFFSET Syntax in Excel: OFFSET Function in Excel consists of the following arguments: - Reference: It is the argument on which we want to base the offset. It could be a cell reference or a range of adjacent cells; if not, Offset returns the #VALUE! Error value. - Rows: It is the no. of rows to offset. If we use a positive number, it offsets the rows below; if a negative number is used, it offsets the above. - Columns: It is for no. of columns to offset. So, it is the same concept as Rows; if we use a positive number, it offsets the columns to the right, and if a negative number is used, it offsets the columns on the left. - Height: This argument is optional. It should be a positive number. It is a number that represents the number of rows in the returned reference. - Width: This is also an optional argument. It must be a positive number. It is a number that represents the number of columns in the returned reference. - The OFFSET Function in Excel returns the #REF! Error value if rows and columns offset reference over the edge of the worksheet. - The OFFSET function is supposed to be the same height or width as a reference if height or width is omitted. - OFFSET returns a reference; it does not move any cells or range of cells or change the selection. It can be used with any function expecting a reference argument. How to Use the OFFSET Function in Excel? OFFSET Function in Excel is straightforward to use. Let us understand the working of the OFFSET Function in Excel by some OFFSET Formula examples. The Offset formula returns a cell reference based on a starting point, rows, and columns that we specify. We can see it in the given below example: =OFFSET (A1, 3, 1) The formula tells Excel to consider cell A1 for starting point (reference), then move three rows down (rows) and 1 column to the left (columns argument). After this, the OFFSET formula returns the value in cell B4. The picture on the left shows the route of the function, and the screenshot on the right demonstrates how we can use the OFFSET formula in real time. The difference between the two formulas is that the second (on the right) includes a cell reference (D1) in the row’s argument. But since cell D1 contains number 1, and the same number appears in the rows argument of the first formula, both would return an identical result – the value in B2. In the above picture, suppose we have to find out the number of marks, then we can also use the OFFSET function. The formula is below: So, in the above formula, D5 is the first cell where the data begins, which is a reference as starting cell. After that, the rows and column value is 0, so we can put it as 0,0. Then there is 4, which means four rows below the reference for which Excel needs to calculate the sum, and then, at last, it is 1, which means there is 1 column as width. We can refer to the above pic to co-relate the explained example. And below is the result: We have to press Enter after entering a formula in the required cell, and then we have the result. Things to Remember - The OFFSET Function in Excel returns a reference; it does not move any cells or range of cells. - If the OFFSET Formula returns a range of cells, the rows and columns always refer to the upper-left cell in the returned range. - The reference should include a cell or range of cells; otherwise, the formula will return the #VALUE error. - If the rows and columns are specified over the edge of the spreadsheet, the Offset formula in Excel will return the #REF! Error. - OFFSET function can be used within any other Excel function which accepts a cell or range reference in its arguments. For example, if we use the formula = OFFSET (A1, 3, 1, 1, 3) on its own, it will give a #VALUE! Error, since a range of returns (1 row, three columns) does not fit in a cell. However, if we collate it into the SUM function like below: =SUM (OFFSET (A1, 3, 1, 1, 3)) The Offset formula returns the sum of values in a 1-row by a 3-column range of three rows below and 1 column to the right of cell A1, i.e., the total values in cells B4:D4. As we can see, 36+63+82 of highlighted Mar equals 181, resulting in G2 after applying the sum and Offset formula. (highlighted in yellow) Use of OFFSET Function in Excel As we have seen what the OFFSET function does with the help of the above example, we may have questions Why bother to use the OFFSET formula that is a bit complex? Why not simply use a direct reference like sum or B4:D4? The OFFSET function in Excel is perfect for below: - Getting the range from the starting cell: Sometimes, we do not know the exact or actual address of the range; we only know where it starts from a particular cell. In this case, we can use the OFFSET Function, which is easy. - Creating Dynamic Range: The references like the above example B1:C4 are static, which means they always refer to a given or fixed range. But in some cases, the tasks are easier to perform with dynamic ranges. It especially helps when we work with changing data. For example, we could have a spreadsheet where a new row or column is inserted or added every day/week/month; in this case, the OFFSET function will help. Limitations and Alternatives of the OFFSET Function in Excel As every formula in Excel has limitations and alternatives, we have seen how and when to use the OFFSET Function in Excel. Below are the critical limitations of the OFFSET function in Excel: - Resource-hungry Function: The formula will be recalculated for the entire set whenever there is a change in the source data, which keeps Excel busy for a longer time. A small spreadsheet will not affect that much, but Excel may take time to recalculate if there are many spreadsheets. - Difficulty in review: As we know, the references returned by the Offset function are dynamic or changing and may contain a big formula, which may find tricky to correct or edit as per requirement. Alternatives of the OFFSET Function in Excel: - INDEX function: The INDEX function in Excel may also create a dynamic range of references. It is not the same as OFFSET. But like OFFSET, the INDEX function is not that volatile; hence it won’t slow down Excel, which is a limitation for OFFSET. - INDIRECT Function: We can also use the INDIRECT function to create a dynamic range of references from many sources like cell values, text, and the named ranges. This has been a guide to OFFSET in Excel. Here we discuss the OFFSET Formula in Excel and How to use the OFFSET Function in Excel, along with practical examples and a downloadable Excel template. 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Tired of ads? Join today and never see them again. Advertisement - Guide continues below Let's take a look at (surprise, surprise) a circle. We don't know anything about this circle. Sure, we've spent almost a whole chapter learning about properties of circles in general, but we don't know anything about this circle in particular. What's its favorite color? How does it spend its leisure time? Does it like artificial banana flavor or not? For example, we learned at the beginning of the chapter that two things define a circle: 1. Where it is (center) 2. How big it is (radius) But without any context, we don't know where this circle is or how big it is. We know that it has some center and some radius, and for many mathematicians that's enough. But if we're practical people who want to put this circle to work, we need to get some specifics (and probably a résumé of some kind). We need to know whether the circle is in Chile or China. We need to know if it's the right size to be a wheel on a shopping cart or a fence around the Smiths' disk-shaped ranch. Maybe it's not even on Earth. Maybe it's as big as Earth. After all, scale is pretty important. Fortunately, in this case, since we simply made up the circle, we can make up its characteristics. Let's say its radius is 5 km and it's located at a point 4 km east and 3 km north of the center of Sydney, Australia. Now if we want to give that information to somebody else, we can tell them using those cumbersome English words, or we can take a leaf from Descartes's sketch pad and use a coordinate plane with appropriate labels. Isn't that nice? And we didn't even have to pay for airfare. We can describe a circle in the coordinate plane with an equation. But before we go there, we'll make things a little easier. Let's start by considering a circle with its center at the origin and radius 5 units. Here it is, on the coordinate plane. Notice that the circle goes through the points (5, 0), (0, 5), (-5, 0), and (0, -5). We're trying to find an equation relating the coordinates of a generic point on the circle (x, y). Notice that by nature of the Cartesian system, we can easily draw a right triangle based on any point (x, y). One leg is horizontal and has length x. The other leg is vertical and has length y. The hypotenuse connects (x, y) and the origin. If (x, y) is on the circle and the circle's center is at the origin, then the hypotenuse has a length equal to the circle's radius. In this case, it's 5 units. Pythagoras tells us that x2 + y2 = 52. But the radius of a circle centered at the origin doesn't have to be 5 units. It could be 6, or 7, or 50, or even a million units. Let's cover all our bases and call it r units. So we have the equation x2 + y2 = r2. There you have it. We now have an equation that relates the x- and y-coordinates of any point on a circle with radius r centered at the origin. Wasn't that easy? You may notice that we left the x and y terms on the same side of the equation, rather than solving for y as we like to do for linear equations. (Remember those from algebra?) A formula with all the variables on one side is called implicit, while a formula that has been solved for one variable in terms of the other (such as y = mx + b) is called explicit. Go ahead and try solving our implicit equation for y. You'll end up with a messy plus-or-minus square root. We'll stick with the nice, clean, simple equation we've got here. Besides, this is a family website. We don't want any explicit content here. What is the formula for a circle centered at the origin with a circumference of 25.1 inches? We know the formula for a circle is x2 + y2 = r2. All we need to complete it is the length of the radius, which we can find using the circumference. If we just recall the formula C = 2πr, we can plug in 25.1 inches for C and solve for r ≈ 4 inches. Our final equation, then, is x2 + y2 = 42 or x2 + y2 = 16. Our formula is certainly nice, clean, and simple, but it's only useful if our circle is at the origin. How do we describe a circle like that one outside of Sydney? We can still draw a right triangle, so Pythagoras can still help us out. The hypotenuse still has length equal to the radius of the circle, since its endpoints are the center of the circle and a point on the circle. We know the Sydney Circle's radius is 5 km. But the lengths of the legs aren't just plain old x and y anymore. We have to adjust for the "shifting" of the center of the circle from the origin. So the lengths of the horizontal and vertical legs of our right triangle are x – 4 and y – 3, respectively. Now we can plug these lengths into the Pythagorean Theorem to get (x – 4)2 + (y – 3)2 = 52. And there's our formula for the Sydney Circle, with x and y in kilometers (because Aussies, like the rest of the world, use the metric system). In general, the implicit formula for a circle with center (h, k) and radius r is: (x – h)2 + (y – k)2 = r2 Now we have all the information we need to define any circle in a nice, compact formula. You can use it to describe anything from the orbit of a spacecraft to a cookie on a cookie sheet. That's right: the mathematical technology necessary to put a satellite into orbit is no more complex than that necessary to make snickerdoodles at home. More or less. What is the equation for a circle with center (6, -2) and radius 18 units? The implicit formula for a circle with center (h, k) and radius r is (x – h)2 + (y – k)2 = r2. We're given the center and radius, so all we need to do is plug the information into the right places. We should end up with (x – 6)2 + (y – (-2))2 = 182, or (x – 6)2 + (y + 2)2 = 324 when simplified. We just learned how to represent a circle with an equation. We've known for a long time how to represent a line with an equation. So let's use equations to examine what happens when circles and lines interact. We represent a generic circle with (x – h)2 + (y – k)2 = r2and a generic line with y = mx + b. Let's put a line and a circle together in the same system of equations. (x – h)2 + (y – k)2 = r2 y = mx + b Don't get too worried (or excited). We won't make you solve systems like this, even though you could do it. The algebra is a little tough and we're trying to focus on the geometry here. Besides, focusing on the geometry might actually help us understand the algebra. Remember that the solution of a system of two equations like this one is the set of all points (x, y) that make both equations true at the same time. In other words, the solution of that system is the set of all points that are both on the circle and on the line. In other other words, the solution of that system is the set of points where the circle and the line intersect. We already know that a line can intersect a circle at two, one, or zero points (it can be a secant of the circle, a tangent to the circle, or neither). Therefore, this system of equations must always have two, one, or zero solutions, depending on whether the line is a secant, a tangent, or neither. As we said before, we won't make you solve a system like this. But we will make you do some algebra, because it's fun. And maybe we're a little sadistic. We've talked before about cutting up a pizza, but never in Australia. Each cut made by a pizza knife stretches from one side of the pizza to the other, intersecting the crust of the pizza at two points. So each cut is a secant. Hopefully, each cut is also a diameter, so that the pizza ends up looking like this: and not like this: Suppose we put a coordinate grid over that pizza so you can see the coordinates of the points where the sloppy pizza man's cut intersects the edge of the pizza as well as find the equation of the circle. Could you find the equation of the line made by the cut? Of course you could. You actually don't need to consider the circle at all: it's just finding the equation of a line given two points on the line, which is algebra-level stuff. But let's say the pizza man is really sloppy and makes a cut that's not a secant of the pizza, but rather a tangent to the pizza. He's basically cutting the box, only touching the tiniest nub of pizza. Could you find the equation of the line then? Let's draw a diagram of the situation. The pizza has a radius of 25 cm. Let's consider the center of the pizza to be at the origin. This sloppy pizza man, who is seriously liable to damage himself, his co-workers, or his place of employment, makes a cut tangent to the pizza at the point (7, 24). We know one point on the line already, so let's see if we can find the slope of the line. Then we'll have enough information to write the equation of the line. We know that the tangent line is perpendicular to the radius of the circle at the point of tangency. So if we find the slope of the radius, we can take the negative reciprocal and we have the slope of the tangent line. Ingenious! What is the equation of the tangent line that intersects a circle centered at the origin with radius 25 at the point (7, 24)? In this case, the radius is the line segment with endpoints (0, 0) and (7, 24). The slope of the radius is Taking the negative reciprocal, we get a slope of for the tangent line. We now have enough to write the equation of the tangent line in point-slope form:
Algebraic Expressions and In Equalities PDF In this we have given Algebraic Expressions and In Equalities Pdf for those who are preparing for Competitive Examination. This, we believe shall be useful in preparing and gearing up for taking the exams. - The unknown, quantities used in any equation are known as variables. Generally, they are denoted by the last English alphabet x, y, z etc. - An equation is a statement of equality of two algebraic expressions, which involve one or more unknown quantities, called the variables. An equation in which the highest power of variables is one, is called a linear equation. These equations are called linear be-cause the graph of such equations on the x-y Cartesian plane is a straight line. Linear Equation in one variable: - A linear equation which contains only one variable is called linear equation in one variable. - The general form of such equations is a x+b=c, where a, b and c are constants and a 0. - All the values of x which satisfy this equation are called its solution(s). Applications of Linear Equations With One Variables The sum of the digits of a two digit number is 16, If the number formed by reversing the digits is less than the original number by 18. Find the original number. Let unit digit be x. Then tens digit = 16- x ∴Original number =10 × (16 – x)+x = 160 -9x. On reversing the digits, we have x at the tens place and (16-x)at the unit place. ∴New number=10x+(16-x) = 9x+16 Original number-New number = 18 (160-9x) – (9x+16)= 18 -18x+144 = 18 – 18x = 18 – 144 ⇒18x=126 ⇒ x = 7 ∴In the original number, we have unit digit = 7 Tens digit = (16 – 7) = 9 Thus, original number=97 Linear equation in two variables: General equation of a linear equation in two variables is ax + by + c = 0, where a, b 0 and c is, a constant,’ and x and y are the two variables The sets of values of x and y satisfying any equation are called its solution(s). Consider the equation 2x+ y=4. Now, if we substitute x = – 2 in the equation, we obtain 2.(-2) +y = 4or-4 + y = 4 or y = 8. Hence (-2,8) is a solution. If we substitute x = 3 in the equation, we obtain 2.3 + y = 4 or 6 + y = 4 or y = -2 Hence (3, -2) is a solution. The following table lists six possible values for x and the corresponding values for y, i.e. six solutions of the equation. If we plot the solutions of the equation 2x+y – 4which appear in the above table then we see that they all lie on the same line. We call .this line the graph of the equation since it corresponds precisely to the solution set of the equation. 4x + 3y = 25 ….. (i) x + 5y =19 ….. (ii) Multiply equation (ii) by 4 on both sides. We find 4x+20y =76 Subtracting equation (i) from equation (iii), we have 4x+ 20y =76 4x + 3y=25 − − − 17 y = 51 ⇒ y = = 3 Substituting value of y in equation (i), we get 4x + 3 × 3 = 25 4x =16 ⇒ x = = 4 ∴ x=4 and y=3 is the solution. Now consider two linear equations in two unknowns, a1x + b1y = c1 ….. (i) a2x + b2y = c2 ….. (ii) The above equations arc nothing else but equations of 2 lines. Any pair (x, y) which satisfy both the equation is called a solution to the above system of equations. Systems of Linear Equation Consistent System: A system (of 2 or.3 or more equations taken together) of linear equations is said to be consistent, if it has at least one solution. Inconsistent System: A system of simultaneous linear equations is said to be inconsistent, if it has no solutions at all e.g. X+Y = 9; 3X+3Y = 8 Clearly there are no values of X & Y which simultaneously satisfy the given equations. So the system is inconsistent. An equation of the degree two of one variable is called quadratic equation. General form: ax2+bx+c =0….. (l) where a,b and c are all real number and a ≠ 0. For Example: 2x2–5x+3=0; 2x2–5=0; x2 + 3x = 0 A quadratic equation gives two and only two values of the unknown variable and both these values are called the roots of the equation. Nature of Roots: The nature of roots of the equation depends upon the nature of its discriminant D. - If D < 0, then the roots are non-real complex, Such roots are always conjugate to one another. That is, if one root is p + iq then other is p-iq,q ≠ 0. - If D = 0, then the roots are real and equal. Each root of the equation becomes . Equal roots are referred as repeated roots or double roots also: - If D > 0 then, the roots are real and unequal. - In particular, if a, b, c are rational number, D> 0 and D is a perfect square, then the roots of the equation are rational number and unequal. - If a, b, c, are rational number, D>0 but D is not a perfect square, then the roots of the equation are irrational (surd). Surd roots are always conjugate to one another, that is if one root is then the other is ,q>0. - If a = 1, b and c are integers, D > 0 and perfect square, then the roots of the equation are integers. Sign of Roots: Let are real roots of the quadratic equation ax2+bx + c = 0 that is D = b2-4ac≤0. Then - Both the roots are positive if a and c have the same sign and the sign of b is Opposite. - Both the roots are negative if a, b and c all have the same sign. - The Roots have opposite sign if sign of a and c are opposite. - The Roots are equal in magnitude and opposite in sign if b = 0 [that is its roots and ] - The roots are reciprocal if a = c. [that Is the roots are α and ¹⁄∝] - If c = 0. then one root is zero. - If b = c = 0. then both the roots are zero. - If a = 0, then one root is infinite. - If a = b = 0, then both the roots are infinite. - If a = b = c = 0, then the equation becomes an identity - If a + b + c =0 then one root is always unity and the other root is , Hence the roots are rational provided a, b, c, are rational. Symmetric Functions of Roots: An expression in is called asymmetric function of α, β if the function is not affected by inter changing and . If are the roots of the quadratic equation ax2+bx + c = 0, a ≠ 0 t Formation of Quadratic Equation With Given Roots - An equation whoso roots are and can be written as (x – )(x – ) = 0 or x2– x + = 0 or x2-(sum of the roots) x. + product of the roots = 0. - Further If and are the roots of a quadratic equation ax2 + bx + c = 0, then ax2+bx+c = a(x- )(x- ) is an identity. A number of relations between the roots can be derived using this identity by substituting suitable values of x real or imaginary. Condition of a Common Root between two quadratic equations: Consider two quadratic equations a1x2 + b1x + c1 = 0 ….. (i) and a2x2 + b2x + c2 = 0 ….. (ii) Let be a common root of the two equations On solving we get If a, b are two roots of a quadratic equation such that a + b = 24 and a – b = 8, then find a quadratic equation having a and b as its roots. a + b = 24 and a – b = 8 ⇒ a = 16 and b = 8 ⇒ 16 × 8 = 128 A quadratic equation with roots a and b is x2 – (a + b) x + ab = 0 or x2 – 24x + 128 = 0 In equations: A statement or equation which states that one thing is not equal to another, is called an in equation. ‘<’ means “is less than” ‘>’ means “is greater than” ‘≤’ means “is less than or equal to” ‘≥’ means “is greater than or equal to” - x < 3 means x is less than 3. - y ≥ 9 means y is greater than or equal to 9. - Adding the same number to each side of an equation does not effect the sign of inequality, it remains same, i.e. if x > y then, x + a > y + a. - Subtracting the same number to each side of an inequation does not effect the sign of inequality, i.e. if x < y then, x – a < y – a. - Multiplying each side of an inequality with same number does not effect the sign of inequality, i.e., if x ≤ 1 then ax ≤ ay (where, a> 0). - Multiplying each side of an inequality with a negative number effects the sign of inequality or sign of inequality reverses, i.e., if x < y then ax > ay (where a < 0) - Dividing each side of an inequation by a positive number does not effect the sign of inequality, i.e., if x ≤ y then (where, a> 0). - Dividing each side of an inequation by a negative number reserves the sign of inequality, i.e., if x > y then (where, a < 0). - If a is positive real number, x and y be the fixed real numbers, then (i) \|x – y\| < a ⇔ y –a < x < y + a (ii) \|x – y\| ≤ a ⇔ y –a ≤ x ≤ y + a (iii) \|x – y\| > a ⇔ x> y + a or x < y – a (iv) \|x – y\| ≥ a ⇔ x ≥ y + a or x ≤ y – a - Triangle Inequality: (i) \|x + y\| ≤ \|x\| + \|y\|, ∀ x, y ∈ R (ii) \|x – y\| ≥ \|x\| – \|y\|, ∀ x, y ∈ R \|IMPORTANT ALGEBRAIC FORMULAE\| \|1. (a + b)2 = a2 + 2ab + b2\| \|2. (a – b)2 = a2 – 2ab + b2\| \|3. (a – b) (a + b) = a2 – b2\| \|4. (a + b)2 + (a – b)2 = 2 (a2 + b2)\| \|5. (a + b)2 – (a – b)2 = 4ab\| \|6. (a + b)3 = a3 + b3 + 3ab (a + b)\| \|7. (a – b)3 = a3 – b3 – 3ab (a – b)\| \|8. a3 + b3 = (a + b) (a2 – ab + b2)\| \|9. a3 – b3 = (a – b) (a2 + ab + b2)\| \|10. (a + b + c)2 = (a2 + b2 +c 2) +2 (ab + bc + ca)\| \|11. a3 + b3 +c3 – 3abc = (a + b+ c) (a2 + b2 + c2 – ab – bc – ca)\| \|12. a4 – b4 = (a2 – b2) (a2 + b2)\| IMPORTANT SERIES TYPE FORMULA Value of √(P+√(P+√(P+⋯∞)) ) =(√(4P+1)+1)/2 Value of √(P-√(P-√(P-…∞)) ) =(√(4P+1)-1)/2 Value of √(P.√(P.√(P…∞)) ) =P Value of √(P√(P√(P√(P√P) ) ) ) = P^((2^n-1)+2^n ) Where n ¬→ no. of times P repeated. SOME SPECIAL SERIES - Sum of first n natural numbers 1 + 2 + 3 +…n = ((n)(n+1))/2 - Sum of the squares of first n natural numbers 12 + 22 + 32 + …. b2 = ((n)(n+1)(2n+1))/6 - Sum of the cubes of first n natural numbers 13 + 23 + 33 + … n3 = (((n)(n+1))/2)^2 RRB WhatsAPP Group – Click Here Telegram Channel – Click Here Join Us on FB – Examsdaily Join Us on Twitter – Examsdaily
acceleration due to gravity Want to see an object accelerate? - Pick something up with your hand and drop it. When you release it from your hand, its speed is zero. On the way down its speed increases. The longer it falls the faster it travels. Sounds like acceleration to me. - But acceleration is more than just increasing speed. Pick up this same object and toss it vertically into the air. On the way up its speed will decrease until it stops and reverses direction. Decreasing speed is also considered acceleration. - But acceleration is more than just changing speed. Pick up your battered object and launch it one last time. This time throw it horizontally and notice how its horizontal velocity gradually becomes more and more vertical. Since acceleration is the rate of change of velocity with time and velocity is a vector quantity, this change in direction is also considered acceleration. In each of these examples the acceleration was the result of gravity. Your object was accelerating because gravity was pulling it down. Even the object tossed straight up is falling — and it begins falling the minute it leaves your hand. If it wasn't, it would have continued moving away from you in a straight line. This is the acceleration due to gravity. What are the factors that affect this acceleration due to gravity? If you were to ask this of a typical person, they would most likely say "weight" by which the actually mean "mass" (more on this later). That is, heavy objects fall fast and light objects fall slow. Although this may seem true on first inspection, it doesn't answer my original question. "What are the factors that affect the acceleration due to gravity?" Mass does not affect the acceleration due to gravity in any measurable way. The two quantities are independent of one another. Light objects accelerate more slowly than heavy objects only when forces other than gravity are also at work. When this happens, an object may be falling, but it is not in free fall. Free fall occurs whenever an object is acted upon by gravity alone. Try this experiment. - Obtain a piece of paper and a pencil. Hold them at the same height above a level surface and drop them simultaneously. The acceleration of the pencil is noticeably greater than the acceleration of the piece of paper, which flutters and drifts about on its way down. Something else is getting in the way here — and that thing is air resistance (also known as aerodynamic drag). If we could somehow reduce this drag we'd have a real experiment. No problem. - Repeat the experiment, but before you begin, wad the piece of paper up into the tightest ball possible. Now when the paper and pencil are released, it should be obvious that their accelerations are identical (or at least more similar than before). We're getting closer to the essence of this problem. If only somehow we could eliminate air resistance altogether. The only way to do that is to drop the objects in a vacuum. It is possible to do this in the classroom with a vacuum pump and a sealed column of air. Under such conditions, a coin and a feather can be shown to accelerate at the same rate. (In the olden days in Great Britain, a guinea coin was used and so this demonstration is sometimes still called the "guinea and feather".) A more dramatic demonstration was done on the surface of the moon — which is as close to a true vacuum as humans are likely to experience any time soon. Astronaut David Scott released a rock hammer and a falcon feather at the same time during the Apollo 15 lunar mission in 1971. In accordance with the theory I am about to present, the two objects landed on the lunar surface simultaneously (or nearly so). Only an object in free fall will experience a pure acceleration due to gravity. the leaning tower of Pisa Let's jump back in time for a bit. In the Western world prior to the Sixteenth Century, it was generally assumed that the acceleration of a falling body would be proportional to its mass — that is, a 10 kg object was expected to accelerate ten times faster than a 1 kg object. The ancient Greek philosopherAristotle of Stagira(384–322 BCE), included this rule in what was perhaps the first book on mechanics. It was an immensely popular work among academicians and over the centuries it had acquired a certain devotion verging on the religious. It wasn't until the Italian scientist Galileo Galilei (1564–1642) came along that anyone put Aristotle's theories to the test. Unlike everyone else up to that point, Galileo actually tried to verify his own theories through experimentation and careful observation. He then combined the results of these experiments with mathematical analysis in a method that was totally new at the time, but is now generally recognized as the way science gets done. For the invention of this method, Galileo is generally regarded as the world's first scientist. In a tale that may be apocryphal, Galileo (or an assistant, more likely) dropped two objects of unequal mass from the Leaning Tower of Pisa. Quite contrary to the teachings of Aristotle, the two objects struck the ground simultaneously (or nearly so). Given the speed at which such a fall would occur, it is doubtful that Galileo could have extracted much information from this experiment. Most of his observations of falling bodies were really of bodies rolling down ramps. This slowed things down enough to the point where he was able to measure the time intervals with water clocks and his own pulse (stopwatches and photogates having not yet been invented). This he repeated "a full hundred times" until he had achieved "an accuracy such that the deviation between two observations never exceeded one-tenth of a pulse beat." With results like that, you'd think the universities of Europe would have conferred upon Galileo their highest honor, but such was not the case. Professors at the time were appalled by Galileo's comparatively vulgar methods even going so far as to refuse to acknowledge that which anyone could see with their own eyes. In a move that any thinking person would now find ridiculous, Galileo's method of controlled observation was considered inferior to pure reason. Imagine that! I could say the sky was green and as long as I presented a better argument than anyone else, it would be accepted as fact contrary to the observation of nearly every sighted person on the planet. Galileo called his method "new" and wrote a book called Discourses on Two New Sciences wherein he used the combination of experimental observation and mathematical reasoning to explain such things as one dimensional motion with constant acceleration, the acceleration due to gravity, the behavior of projectiles, the speed of light, the nature of infinity, the physics of music, and the strength of materials. His conclusions on the acceleration due to gravity were that… the variation of speed in air between balls of gold, lead, copper, porphyry, and other heavy materials is so slight that in a fall of 100 cubits a ball of gold would surely not outstrip one of copper by as much as four fingers. Having observed this I came to the conclusion that in a medium totally devoid of resistance all bodies would fall with the same speed. For I think no one believes that swimming or flying can be accomplished in a manner simpler or easier than that instinctively employed by fishes and birds. When, therefore, I observe a stone initially at rest falling from an elevated position and continually acquiring new increments of speed, why should I not believe that such increases take place in a manner which is exceedingly simple and rather obvious to everybody? I greatly doubt that Aristotle ever tested by experiment. Galileo Galilei, 1638 Despite that last quote, Galileo was not immune to using reason as a means to validate his hypothesis. In essence, his argument ran as follows. Imagine two rocks, one large and one small. Since they are of unequal mass they will accelerate at different rates — the large rock will accelerate faster than the small rock. Now place the small rock on top of the large rock. What will happen? According to Aristotle, the large rock will rush away from the small rock. What if we reverse the order and place the small rock below the large rock? It seems we should reason that two objects together should have a lower acceleration. The small rock would get in the way and slow the large rock down. But two objects together are heavier than either by itself and so we should also reason that they will have a greater acceleration. This is a contradiction. Here's another thought problem. Take two objects of equal mass. According to Aristotle, they should accelerate at the same rate. Now tie them together with a light piece of string. Together, they should have twice their original acceleration. But how do they know to do this? How do inanimate objects know that they are connected? Let's extend the problem. Isn't every heavy object merely an assembly of lighter parts stuck together? How can a collection of light parts, each moving with a small acceleration, suddenly accelerate rapidly once joined? We've argued Aristotle into a corner. The acceleration due to gravity is independent of mass. Galileo made plenty of measurements related to the acceleration due to gravity but never once calculated its value (or if he did, I have never seen it reported anywhere). Instead he stated his findings as a set of proportions and geometric relationships — lots of them. His description of constant speed required one definition, four axioms, and six theorems. All of these relationships can now be written as the single equation in modern notation. Algebraic symbols can contain as much information as several sentences of text, which is why they are used. Contrary to the common wisdom, mathematics makes life easier. location, location, location The generally accepted value is… g = 9.8 m/s2 or in non-SI units… g = 35 kph/s = 22 mph/s = 32 feet/s2 It is useful to memorize this number (as millions of people around the globe already have), however, it should also be pointed out that this number is not a constant. Although mass has no effect on the acceleration due to gravity, there are other factors that do. Everyone reading this should be familiar with the images of the astronauts hopping about on the moon and should know that the gravity there is weaker than it is on the Earth — about one sixth as strong or approximately 1.6 m/s2. That is why the astronauts were able to hop around on the surface easily despite the weight of their space suits. In contrast, gravity on Jupiter is stronger than it is on the Earth — about two and a half times stronger or 25 m/s2. Astronauts cruising through the top of Jupiter's thick atmosphere would find themselves struggling to stand up inside their space ship. The acceleration due to gravity varies with location. Furthermore, even on the Earth, this value varies with latitude and altitude (to be discussed in later chapters). The acceleration due to gravity is greater at the poles than at the equator and greater at sea level than atop Mount Everest. There are also local variations that depend upon geology. The value of 9.8 m/s2 is thus merely a convenient average over the entire surface of the Earth. This value is accurate to two significant digits up to the altitude at which commercial jets fly (18 km, 29,000 feet, or 5.5 miles). The acceleration due to gravity is effectively 9.8 m/s2 over the entire surface of the Earth. How crazy are you for accuracy? For most applications, the value of 9.8 m/s2 is more than sufficient. If you're in a hurry, or don't have access to a calculator, or just don't need to be that accurate; rounding g to 10 m/s2 is often acceptable. During a multiple choice exam where calculators aren't allowed, this is often the way to go. If you need greater accuracy, consult a comprehensive reference work to find the accepted value for your latitude and altitude. If that's not good enough, then obtain the required instruments and measure the local value to as many significant digits as you can. You may learn something interesting about your location. I once met a geologist whose job it was to measure g across a portion of West Africa. When I asked him who he worked for and why he was doing this, he basically refused to answer other than to say that one could infer the interior structure of the Earth from a gravimetric map prepared from his findings. Knowing this, one might then be able to identify structures where valuable minerals or petroleum might be found. Like all professions, those in the gravity measuring business (gravimetry) have their own special jargon. The SI unit of acceleration is the meter per second squared [m/s2]. Split that into a hundred parts and you get the centimeter per second squared [cm/s2] also known as the gal [Gal] in honor of Galileo. (Note that the unit is written in lowercase as a word but is capitalized as a symbol.) Split that into a thousand parts and you get a milligal [mGal]. Since earth's gravity produces a surface acceleration of about 10 m/s2, a milligal is about 1 millionth of the value we're all used to. Measurements with this precision can be used to study changes in the Earth's crust, sea levels, ocean currents, polar ice, and groundwater. Push it a little bit further and it should be possible to detect changes in earth's atmosphere. Gravity is a heavy subject that will be discussed in more detail later in this book. As was discussed earlier, don't confuse the phenomena of acceleration due to gravity with the unit of the same name. While the quantity g has a value that depends on location and is approximately 9.8 m/s2 on earth, the unit gravity has the defined value of… g = 9.80665 m/s2 You may also have noticed they use slightly different symbols. The unit uses the roman or upright g while the natural phenomena uses the italic or oblique g. Don't confuse g with g. The unit g is often used to measure the acceleration of a reference frame. "Say what?" This is technical language that will be elaborated upon later in another section of this book, but I will explain it with examples for now. As I write this, I'm sitting in front of my computer in my home office. Gravity is drawing my body down into my office chair, my arms toward the desk, and my fingers toward the keyboard. This is the normal 1 g (one gee) world we're all accustomed to. I could take a laptop computer with me to an amusement park, get on a roller coaster, and try to get some writing done there. Gravity works on a roller coaster just as it does at home, but since the roller coaster is accelerating up and down (not to mention side to side) the sensation of normal earth gravity is lost. There will be times when I feel heavier than normal and times when I fell lighter than normal. These correspond to periods of more than one g and less than one g. I could also take my laptop with me on a trip to outer space. After a brief period of 2 or 3 g (two or three gees) accelerating away from the surface of the Earth, most space journeys are spent in conditions of apparent weightlessness or 0 g (zero gee). This happens not because gravity stops working (gravity has infinite range and is never repulsive), but because a spacecraft is an accelerating reference frame. As I said earlier, this concept will be discussed more thoroughly in a later section of this book.
Here are some examples of division word problems that can be solved in two steps. We will illustrate how block diagrams can be used to help you to visualize the division word problems in terms of the information given and the data that needs to be found. Block diagrams are used in Singapore Math. We also learn how to solve multiplication and division word problems by identifying key terms. Marcus had 700 marbles. He gave away 175 marbles and put the remaining marbles equally into 5 bags. How many marbles were there in each bag? Step 1: Find how many marbles he had left. 700 – 175 = 525 He had 525 marbles left. Step 2: Find the number of marbles in each box. 525 ÷ 5 = 105 There were 105 marbles in each box. Rosalind made 364 donuts. She put 8 donuts into each box. a) How many boxes of donuts were there? How many donuts were left over? b) If she sold each box for $3, how much money would she receive? Step 1: Find the number of boxes of donuts. 364 ÷ 8 = 45 remainder 4 There were 45 boxes of donuts. 4 donuts were left over. Step 2: Find how much money she would receive. 45 x 3 = 135 She would receive $135. Translate multiplication and division word problems by identifying key terms Solve multiplication and division word problems by identifying key vocabulary (part 1) How to translate multiplication and division mathematic operations in word problems by first identifying the key term, and then pairing that term with the appropriate operation. Solve multiplication and division word problems by identifying key vocabulary (part 2) How to solve real-world problems involving multiplication and division, by using the given one-step equations. (1) Ms. Smith bought one piece of candy for each of the 22 students in her class. The total cost of her candy was $1.10. Solve the equation 22c= 1.10 to determine the cost of each piece of candy. (2) Three friends went out to dinner together. They split the total bill evenly, amongst the three of them. Solve the equation b ÷ 3 = 7 to determine the amount of the total bill. (3) Deja bought several books at her school's book sale. Each book cost $2. Deja spent a total of $14. Solve the equation 2b = 14 to determine how many books Deja purchased. Example: Jeremy bought 8 identical pens and 5 identical notebooks. The cost of 8 pens is the same as the cost of 5 notebooks. Each notebook costs 30 cents more than each pen. How much did Jeremy spend altogether? Solve multi step problems using multiple operations Example: If a class has three cakes and each cake has 5 pieces with one piece for each student, how many pieces will be left over after each of the 12 students had a slice? Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations. You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.
Any opinions, findings, conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of UK Essays. Environmental Monitoring- Survey techniques for life and Earth sciences - Describe the three different types of volcanic eruptions that have given rise to Iceland’s volcanic landforms. - Effusive: An effusive eruption is a volcanic eruption characterized by the flow of lava onto the ground. Lava flows generated by effusive eruptions vary in shape, thickness, length, and width depending on the type of lava that erupted, the type of discharge, the slope of the ground over which the lava travels, and the duration of the volcanic eruption. - Explosive: This is a violent, explosive type of eruption. This is a result of when sufficient gas has dissolved under pressure within a viscous magma, such that the discharged lava violently bubbles up into volcanic ash as pressure is suddenly lowered at the vent. Explosive eruptions can send rocks, dust, gas and lava fragments into the atmosphere. A cloud is then created which then collapses, creating a flow of hot volcanic matter (gas + rocks). - Mixed: This eruption is a mixture of both lava and tephra (fragmental material produced by a volcanic eruption). - Describe the characteristics of a Tuya. How does this acquire its distinctive shape? A Tuyais a flat-topped, steep-sided volcano formed when lava erupts through a thick glacier or ice sheet. Such volcanic formations are restricted to regions which were covered by glaciers and had volcanic activity during the same period. Their formation is due to lava that erupts under a glacier and cools very quickly. It cannot travel far, so it piles up into a steep-sided hill. - Define the term jökulhlaup and explain its significance to Iceland. Jökulhlaups in Iceland may originate from marginal or subglacial sources of water melted by atmospheric processes, permanent geothermal heat or volcanic eruptions. Glacier-volcano interactions produce meltwater that either drains toward the glacier margin or accumulates in subglacial lakes. Iceland is a unique and valuable study-site for glacio-volcanic interactions. The jökulhlaups can be seen as modern analogues of past mega floods on the earth and their exploration may improve understanding of ice-volcano processes on other planets. Jo¨kulhlaups, both those draining meltwater stored in subglacial lakes and meltwater produced during a volcanic eruption, have significant landscaping potential: they erode large canyons and transport enormous quantities of sediment and icebergs over vast outwash plains. - What are the origins of Icelandic river waters? Describe the relevant main characteristics. Icelandic rivers are of three general types: - The glacial-fed rivers which carry large quantities of fine silt and are typically brown in colour. Their runoff, being conditioned by ice melt, is high in the summer and low in the winter. Glacial rivers are close to freezing at source but warm up considerably in lowland areas. They typically divide into many interlinked distributaries which constantly change direction. - The direct runoff rivers; are relatively clear. They are characteristic of old basaltic areas where the bedrock is impermeable. They have their greatest flows in the spring during snowmelt and in autumn following heavy rains. Water temperature in these streams generally follows the air temperature. - The spring-fed stream drains areas covered by permeable post-glacial lava fields. In these zones the ground is more porous; therefore water emerges in springs at lower levels to supply the rivers with a constant flow of generally clear water. These spring-fed rivers have a water temperature of 3–5°C at source and never freeze over at that point. Their beds and banks are usually stable. - Explain the following terms: - Tephrochronology: A geo-chronological technique that uses discrete layers of tephravolcanic ash from a single eruption to create a chronological framework in which archaeological records can be placed. - Cryptotephra: Very few studies have looked in detail at the sedimentation and distribution of cryptotephra deposits within sequences and, more importantly, the criteria for defining the correct stratigraphic position of the volcanic event. Cryptotephra is a tephra-derived glass shard which is not that visible to the naked human eye since they are less than 125micrometers. - Isopachs: Lines on a map or diagrams which connect points beneath which a particular stratum or group of strata has the same thickness. - One measure used to tackle the problem of soil erosion is re-seeding with appropriate floral species. What characteristics of a plant would make it suitable for such a purpose? Soil stabilizing plants range in size, root type (ideally long), degree of ground cover (fast growth) and visual appeal, and selecting a variety of plants is essential for combating the impact of wind and water erosion. Low plants provide ground cover from wind, while higher trees slow down the force of rain before it hits the ground or more delicate ground cover plants. Once plants are established, their life cycles help return nutrients to the soil to encourage future plant growth (important to have an easy seed dispersal process as well) and maintain adequate moisture levels to avoid soil drying or oversaturation. - Describe one method that could be used to measure the profile of a beach. - Select sampling points for beach profiles across the width of the beach. - At each sample point in turn, place a pole at the start and finish. The first point should ideally be the low tide mark, or as close to it. - The next step is to note the main changes in slope angle up the beach, each change is to inform the ‘sections’ for the profile. - For each change in slope, use a clinometer to take a bearing to record the slope angle (It is important to ensure that the bearing is taken from a point on the pole that corresponds with the eye level of the person using the clinometer). - Measure the distance along the ground of the section, and record this information alongside the slope angle. - Repeat processes for each break in slope that you have identified. - Explain the following: - Lateral moraines: Parallel ridges of debris deposited along the sides of a glacier. The unconsolidated debris can be deposited on top of the glacier by frost shattering of the valley walls or tributary streams flowing into the valley. Because lateral moraines are deposited on top of the glacier, they do not experience the postglacial erosion of the valley floor and therefore, as the glacier melts, lateral moraines are usually preserved as high ridges. Lateral moraines stand high because they protect the ice under them from the elements, causing it to melt or sublime less than the uncovered parts of the glacier. Multiple lateral moraines may develop as the glacier advances and retreats. - Kettle Lake: Kettles are depressions left behind after partially-buried ice blocks melt. “Kettle Lake” describes the way the lake basin was formed. While glaciers were forming, a block of ice broke of, and found a uniform position. As the glacier continued to melt, the debris from the glacier (soil, rocks, stones, gravel, etc.) filled in around the block of ice. When the block of ice finally melted, all the debris surrounding it fell into the hole, creating the kettle type basin, which when filled with water, became a lake as we know it. - Outwash plain: is a flat region formed of glacial sediments deposited by melt water outwash at the terminus of a glacier. - Explain the presence of wave-cut platforms in areas of Iceland presently distant from the coast. A wave-cut platform is the narrow flat area often found at the base of a sea cliff or along the shoreline of a lake, bay, or sea that was created by the erosion of waves. Wave-cut platforms are often most obvious at low tide when they become visible as huge areas of flat rock. In Iceland, some cases, the rock is relatively easy to erode. Sea-level changes have left a stamp on the coast, and wave-cut platforms can be seen in many around Iceland. - Distinguish between mafic and felsic lava: These words are used to indicate the chemical composition of silicate minerals, magmas, and igneous rocks. Mafic is used for silicate minerals, magmas, and rocks which are relatively high in the heavier elements. The minerals are usually dark in color and have relatively high specific gravities and also represent material which is newly differentiated from the upper mantle. Our academic experts are ready and waiting to assist with any writing project you may have. From simple essay plans, through to full dissertations, you can guarantee we have a service perfectly matched to your needs.View our services Felsic is used for silicate minerals, magmas, and rocks which have a lower percentage of the heavier elements, and are correspondingly enriched in the lighter elements, such as silicon and oxygen. Felsic minerals are usually light in color and have specific gravities. The most common felsic rock is granite, which represents the purified end product of the earth’s internal differentiation process. - What is the nominal fix accuracy of a GPS? Why can a DGPS improve this nominal accuracy? The nominal fix accuracy of a GPS is of 100 meters with a selective availability enabled on the system. The GPS has a number of small errors (e.g signal delay), so a DGPS can be used to improve nominal accuracy since it transmits messages from local stations that are connected to satellites, producing better and accurate data readings. - In cartographic terms, explain why the datum used by a GPS navigation set must be the same as for the reference chart being used. A datum is a set of reference points on the Earth’s surface against which their position can be associated with a model of the shape of the Earth to define a geodetic coordinate system. Horizontal datum is used to describe a point in latitude and longitude. A vertical datum measures elevations or depths. Because the Earth is an imperfect ellipsoid, all localized datums can give a more accurate representation of the area which is being covered than the latest version of the World Geodetic System datum (84). Cite This Work To export a reference to this article please select a referencing style below: Related ServicesView all DMCA / Removal Request If you are the original writer of this essay and no longer wish to have the essay published on the UK Essays website then please:
The Pythagorean Theorem describes the lengths of the sides of a right triangle in a practical way and is still widely used today. The theorem states that for any right triangle, the sum of the squares of the non-hypotenuse sides is equal to the square of the hypotenuse (Padovan, 2002). In other words, for a right triangle with perpendicular sides of length a and b and hypotenuse of length c, a2 + b2 = c2. The Pythagorean Theorem is one of the fundamental pillars of basic geometry, having countless practical applications such as finding the distance between two points on a coordinate plane. During their workday, architects and carpenters’ find themselves using a special type of right triangle where the lengths of the triad are always integers. In correlation, the Pythagorean Theorem is a useful and necessary tool in measuring surface areas and volumes of various geometric shapes; and calculating maxima and minima of perimeters, or surface areas and volumes of various geometric shapes. Often, when builders want to lay the foundation for the corners of a building, one of the methods they use is based on the Pythagorean Theorem. The carpenters and architectures use tape measures to calculate corner right angle (Eli , 2007) Builders use this special triangle when they don’t have a carpenter’s square. Builders often need to construct a square corner. The Pythagorean Theorem tells us that if a corner is square, then the Sides of a triangle built on that corner will satisfy the formula a2 + b2 = c2, but we can also prove that the converse of the theorem is true. If the sides of a triangle satisfy the formula a2 + b2 = c2, then the triangle is a right triangle, with a square to prove converse concept. The online Pythagorean Theorem Calculator is used to calculate the length of third side of right triangle based on the other two sides using the Pythagorean Theorem. This animated PowerPoint presentation uses shearing and the invariance of the area of triangles with congruent bases and heights to show a step-by-step geometric proof of the Pythagorean Theorem. Eli, M. (2007). The Pythagorean Theorem: A 4,000-year history. (p. 166). New York: Princeton University Press Padovan, R. (2002). Proportion: Science, philosophy, architecture. (pp. 116-125). New York: Taylor & Francis,..
If a quantity x is proportional (directly) to another quantity y, then x is written as x = ky, where k is called the _____________ Direct Proportion (Direct Variation) Two quantities are said to be in direct proportion (or directly proportional), if one is a constant multiple of the other, i.e. y is said to be directly proportional to x if y = kx where k is a constant. Division Property of Equality states that dividing both sides of an equation by a non-zero number doesn't affect the equation a mathematical sentence that uses the equal sign (=) to show that two expressions are equal. a mathematical sentence that uses symbols such as <, ≤,="">, or ≥ to compare two quantities. if one operation undoes the effect of the other operation. Multiplication Property of Equality The two sides of an equation remain equal if they are multiplied by the same number. That is: for any real numbers a, b, and c, if a = b, then ac = bc. an equation written in the form a/b=c/d stating that two ratios are equivalent. Subtraction Property of Equality If the same number is subtracted from both sides of an equation, then the two sides remain equal. That is, if x = y, then x - z = y - z. A number, a variable, or a product of numbers and variables. A letter or symbol used to represent a number or quantities that vary. Addition Property of Equality If the same number is added to both sides of an equation, the two sides remain equal. That is, if x = y, then x + z = y + z. a variable whose value depends on the values of one or more independent variables. in an equation may have its value freely chosen regardless the values of any other variable. the set of all values which, when substituted for unknowns, make an equation true. the process of replacing a variable in an expression with its actual value. YOU MIGHT ALSO LIKE... Expressions, Equations, & Properties Math 7th Finals 2 Flashcards MATH VOCAB FOR EXAM Alg. 1 S1: Terms to Know OTHER SETS BY THIS CREATOR Unit 6: Statistics Unit 7: Rational Explorations: Numbers and Unit 4-Equations and Equalities Unit 5: Area and Volume THIS SET IS OFTEN IN FOLDERS WITH... Unit 1: Number System Fluency Unit 2: Rate, Ratio and Proportional Reasoning Using Equivalent Fractions
credit: galaxy zoo.org Astronomers know that there are galaxies that contain not only one supermassive black hole, but two! In this case, the two black holes are usually 3,000 light years apart from each other, a distance that roughly corresponds to the 1/8 of distance from our solar system to the center of our galaxy. Only a small number of such systems have been detected so far. Using observations from the Hubble Space Telescope and Chandra Observatory, astrophysicist Julie Comerford at the University of Colorado recently announced the discovery of 6 galaxies that host dual supermassive black holes. Supermassive black holes reside at the cores of galaxies and have mass a few million times that of the sun. They grow by consuming nearby material, but no one really knows how they reach their enormous weight. A possible scenario is that they mainly grow through black hole mergers when two galaxies collide. In this occasion a lot of fuel becomes available and is funneled toward the black holes. The two black holes finally form into a larger supermassive black hole, releasing huge amounts of energy in the form of gravitational waves. The exact details of this mechanism are unclear though. Understanding this impressive phenomenon will help us understand not only how black holes grow and evolve but also their host galaxies.
Sampling and Data 4 Levels of Measurement Once you have a set of data, you will need to organize it so that you can analyze how frequently each datum occurs in the set. However, when calculating the frequency, you may need to round your answers so that they are as precise as possible. Levels of Measurement The way a set of data is measured is called its level of measurement. Correct statistical procedures depend on a researcher being familiar with levels of measurement. Not every statistical operation can be used with every set of data. Data can be classified into four levels of measurement. They are (from lowest to highest level): - Nominal scale level - Ordinal scale level - Interval scale level - Ratio scale level Data that is measured using a nominal scale is qualitative (categorical). Categories, colors, names, labels and favorite foods along with yes or no responses are examples of nominal level data. Nominal scale data are not ordered. For example, trying to classify people according to their favorite food does not make any sense. Putting pizza first and sushi second is not meaningful. Smartphone companies are another example of nominal scale data. The data are the names of the companies that make smartphones, but there is no agreed upon order of these brands, even though people may have personal preferences. Nominal scale data cannot be used in calculations. Data that is measured using an ordinal scale is similar to nominal scale data but there is a big difference. The ordinal scale data can be ordered. An example of ordinal scale data is a list of the top five national parks in the United States. The top five national parks in the United States can be ranked from one to five but we cannot measure differences between the data. Another example of using the ordinal scale is a cruise survey where the responses to questions about the cruise are “excellent,” “good,” “satisfactory,” and “unsatisfactory.” These responses are ordered from the most desired response to the least desired. But the differences between two pieces of data cannot be measured. Like the nominal scale data, ordinal scale data cannot be used in calculations. Data that is measured using the interval scale is similar to ordinal level data because it has a definite ordering but there is a difference between data. The differences between interval scale data can be measured though the data does not have a starting point. Temperature scales like Celsius (C) and Fahrenheit (F) are measured by using the interval scale. In both temperature measurements, 40° is equal to 100° minus 60°. Differences make sense. But 0 degrees does not because, in both scales, 0 is not the absolute lowest temperature. Temperatures like -10° F and -15° C exist and are colder than 0. Interval level data can be used in calculations, but one type of comparison cannot be done. 80° C is not four times as hot as 20° C (nor is 80° F four times as hot as 20° F). There is no meaning to the ratio of 80 to 20 (or four to one). Data that is measured using the ratio scale takes care of the ratio problem and gives you the most information. Ratio scale data is like interval scale data, but it has a 0 point and ratios can be calculated. For example, four multiple choice statistics final exam scores are 80, 68, 20 and 92 (out of a possible 100 points). The exams are machine-graded. The data can be put in order from lowest to highest: 20, 68, 80, 92. The differences between the data have meaning. The score 92 is more than the score 68 by 24 points. Ratios can be calculated. The smallest score is 0. So 80 is four times 20. The score of 80 is four times better than the score of 20. Twenty students were asked how many hours they worked per day. Their responses, in hours, are as follows: 56332475235654435253. (Figure) lists the different data values in ascending order and their frequencies. A frequency is the number of times a value of the data occurs. According to (Figure), there are three students who work two hours, five students who work three hours, and so on. The sum of the values in the frequency column, 20, represents the total number of students included in the sample. A relative frequency is the ratio (fraction or proportion) of the number of times a value of the data occurs in the set of all outcomes to the total number of outcomes. To find the relative frequencies, divide each frequency by the total number of students in the sample–in this case, 20. Relative frequencies can be written as fractions, percents, or decimals. \|Data value\|\|Frequency\|\|Relative frequency\| The sum of the values in the relative frequency column of (Figure) is , or 1. Cumulative relative frequency is the accumulation of the previous relative frequencies. To find the cumulative relative frequencies, add all the previous relative frequencies to the relative frequency for the current row, as shown in (Figure). \|Data value\|\|Frequency\|\|Relative frequency\|\|Cumulative relative frequency\| \|3\|\|5\|\|or 0.25\|\|0.15 + 0.25 = 0.40\| \|4\|\|3\|\|or 0.15\|\|0.40 + 0.15 = 0.55\| \|5\|\|6\|\|or 0.30\|\|0.55 + 0.30 = 0.85\| \|6\|\|2\|\|or 0.10\|\|0.85 + 0.10 = 0.95\| \|7\|\|1\|\|or 0.05\|\|0.95 + 0.05 = 1.00\| The last entry of the cumulative relative frequency column is one, indicating that one hundred percent of the data has been accumulated. Because of rounding, the relative frequency column may not always sum to one, and the last entry in the cumulative relative frequency column may not be one. However, they each should be close to one. (Figure) represents the heights, in inches, of a sample of 100 male semiprofessional soccer players. \|Heights (inches)\|\|Frequency\|\|Relative frequency\|\|Cumulative relative frequency\| \|61.95–63.95\|\|3\|\|= 0.03\|\|0.05 + 0.03 = 0.08\| \|63.95–65.95\|\|15\|\|= 0.15\|\|0.08 + 0.15 = 0.23\| \|65.95–67.95\|\|40\|\|= 0.40\|\|0.23 + 0.40 = 0.63\| \|67.95–69.95\|\|17\|\|= 0.17\|\|0.63 + 0.17 = 0.80\| \|69.95–71.95\|\|12\|\|= 0.12\|\|0.80 + 0.12 = 0.92\| \|71.95–73.95\|\|7\|\|= 0.07\|\|0.92 + 0.07 = 0.99\| \|73.95–75.95\|\|1\|\|= 0.01\|\|0.99 + 0.01 = 1.00\| \|Total = 100\|\|Total = 1.00\| The data in this table have been grouped into the following intervals: - 59.95 to 61.95 inches - 61.95 to 63.95 inches - 63.95 to 65.95 inches - 65.95 to 67.95 inches - 67.95 to 69.95 inches - 69.95 to 71.95 inches - 71.95 to 73.95 inches - 73.95 to 75.95 inches In this sample, there are five players whose heights fall within the interval 59.95–61.95 inches, three players whose heights fall within the interval 61.95–63.95 inches, 15 players whose heights fall within the interval 63.95–65.95 inches, 40 players whose heights fall within the interval 65.95–67.95 inches, 17 players whose heights fall within the interval 67.95–69.95 inches, 12 players whose heights fall within the interval 69.95–71.95, seven players whose heights fall within the interval 71.95–73.95, and one player whose heights fall within the interval 73.95–75.95. All heights fall between the endpoints of an interval and not at the endpoints. From (Figure), find the percentage of heights that are less than 65.95 inches. If you look at the first, second, and third rows, the heights are all less than 65.95 inches. There are 5 + 3 + 15 = 23 players whose heights are less than 65.95 inches. The percentage of heights less than 65.95 inches is then or 23%. This percentage is the cumulative relative frequency entry in the third row. (Figure) shows the amount, in inches, of annual rainfall in a sample of towns. \|Rainfall (inches)\|\|Frequency\|\|Relative frequency\|\|Cumulative relative frequency\| \|4.97–6.99\|\|7\|\|= 0.14\|\|0.12 + 0.14 = 0.26\| \|6.99–9.01\|\|15\|\|= 0.30\|\|0.26 + 0.30 = 0.56\| \|9.01–11.03\|\|8\|\|= 0.16\|\|0.56 + 0.16 = 0.72\| \|11.03–13.05\|\|9\|\|= 0.18\|\|0.72 + 0.18 = 0.90\| \|13.05–15.07\|\|5\|\|= 0.10\|\|0.90 + 0.10 = 1.00\| \|Total = 50\|\|Total = 1.00\| From (Figure), find the percentage of rainfall that is less than 9.01 inches. 0.56 or 56% From (Figure), find the percentage of heights that fall between 61.95 and 65.95 inches. Add the relative frequencies in the second and third rows: 0.03 + 0.15 = 0.18 or 18%. From (Figure), find the percentage of rainfall that is between 6.99 and 13.05 inches. 0.30 + 0.16 + 0.18 = 0.64 or 64% Use the heights of the 100 male semiprofessional soccer players in (Figure). Fill in the blanks and check your answers. - The percentage of heights that are from 67.95 to 71.95 inches is: ____. - The percentage of heights that are from 67.95 to 73.95 inches is: ____. - The percentage of heights that are more than 65.95 inches is: ____. - The number of players in the sample who are between 61.95 and 71.95 inches tall is: ____. - What kind of data are the heights? - Describe how you could gather this data (the heights) so that the data are characteristic of all male semiprofessional soccer players. Remember, you count frequencies. To find the relative frequency, divide the frequency by the total number of data values. To find the cumulative relative frequency, add all of the previous relative frequencies to the relative frequency for the current row. - quantitative continuous - get rosters from each team and choose a simple random sample from each Nineteen people were asked how many miles, to the nearest mile, they commute to work each day. The data are as follows: 25732101815207101851213124510. (Figure) was produced: \|Data\|\|Frequency\|\|Relative frequency\|\|Cumulative relative frequency\| - Is the table correct? If it is not correct, what is wrong? - True or False: Three percent of the people surveyed commute three miles. If the statement is not correct, what should it be? If the table is incorrect, make the corrections. - What fraction of the people surveyed commute five or seven miles? - What fraction of the people surveyed commute 12 miles or more? Less than 12 miles? Between five and 13 miles (not including five and 13 miles)? - No. The frequency column sums to 18, not 19. Not all cumulative relative frequencies are correct. - False. The frequency for three miles should be one; for two miles (left out), two. The cumulative relative frequency column should read: 0.1052, 0.1579, 0.2105, 0.3684, 0.4737, 0.6316, 0.7368, 0.7895, 0.8421, 0.9474, 1.0000. - , , (Figure) represents the amount, in inches, of annual rainfall in a sample of towns. What fraction of towns surveyed get between 11.03 and 13.05 inches of rainfall each year? (Figure) contains the total number of deaths worldwide as a result of earthquakes for the period from 2000 to 2012. \|Year\|\|Total number of deaths\| Answer the following questions. - What is the frequency of deaths measured from 2006 through 2009? - What percentage of deaths occurred after 2009? - What is the relative frequency of deaths that occurred in 2003 or earlier? - What is the percentage of deaths that occurred in 2004? - What kind of data are the numbers of deaths? - The Richter scale is used to quantify the energy produced by an earthquake. Examples of Richter scale numbers are 2.3, 4.0, 6.1, and 7.0. What kind of data are these numbers? - 97,118 (11.8%) - 67,092/823,356 or 0.081 or 8.1 % - Quantitative discrete - Quantitative continuous (Figure) contains the total number of fatal motor vehicle traffic crashes in the United States for the period from 1994 to 2011. \|Year\|\|Total number of crashes\|\|Year\|\|Total number of crashes\| Answer the following questions. - What is the frequency of deaths measured from 2000 through 2004? - What percentage of deaths occurred after 2006? - What is the relative frequency of deaths that occurred in 2000 or before? - What is the percentage of deaths that occurred in 2011? - What is the cumulative relative frequency for 2006? Explain what this number tells you about the data. - 190,800 (29.2%) - 260,086/653,782 or 39.8% - 75.1% of all fatal traffic crashes for the period from 1994 to 2011 happened from 1994 to 2006. “State & County QuickFacts,” U.S. Census Bureau. http://quickfacts.census.gov/qfd/download_data.html (accessed May 1, 2013). “State & County QuickFacts: Quick, easy access to facts about people, business, and geography,” U.S. Census Bureau. http://quickfacts.census.gov/qfd/index.html (accessed May 1, 2013). “Table 5: Direct hits by mainland United States Hurricanes (1851-2004),” National Hurricane Center, http://www.nhc.noaa.gov/gifs/table5.gif (accessed May 1, 2013). “Levels of Measurement,” http://infinity.cos.edu/faculty/woodbury/stats/tutorial/Data_Levels.htm (accessed May 1, 2013). Courtney Taylor, “Levels of Measurement,” about.com, http://statistics.about.com/od/HelpandTutorials/a/Levels-Of-Measurement.htm (accessed May 1, 2013). David Lane. “Levels of Measurement,” Connexions, http://cnx.org/content/m10809/latest/ (accessed May 1, 2013). Some calculations generate numbers that are artificially precise. It is not necessary to report a value to eight decimal places when the measures that generated that value were only accurate to the nearest tenth. Round off your final answer to one more decimal place than was present in the original data. This means that if you have data measured to the nearest tenth of a unit, report the final statistic to the nearest hundredth. In addition to rounding your answers, you can measure your data using the following four levels of measurement. - Nominal scale level: data that cannot be ordered nor can it be used in calculations - Ordinal scale level: data that can be ordered; the differences cannot be measured - Interval scale level: data with a definite ordering but no starting point; the differences can be measured, but there is no such thing as a ratio. - Ratio scale level: data with a starting point that can be ordered; the differences have meaning and ratios can be calculated. When organizing data, it is important to know how many times a value appears. How many statistics students study five hours or more for an exam? What percent of families on our block own two pets? Frequency, relative frequency, and cumulative relative frequency are measures that answer questions like these. Fifty part-time students were asked how many courses they were taking this term. The (incomplete) results are shown below: \|# of courses\|\|Frequency\|\|Relative frequency\|\|Cumulative relative frequency\| - Fill in the blanks in (Figure). - What percent of students take exactly two courses? - What percent of students take one or two courses? <!– <solution id=”eip-idm84865280″> 30% 90% –> Sixty adults with gum disease were asked the number of times per week they used to floss before their diagnosis. The (incomplete) results are shown in (Figure). \|# flossing per week\|\|Frequency\|\|Relative frequency\|\|Cumulative relative frequency\| - Fill in the blanks in (Figure). - What percent of adults flossed six times per week? - What percent flossed at most three times per week? # flossing per week Frequency Relative frequency Cumulative relative frequency 0 27 0.4500 0.4500 1 18 0.3000 0.7500 3 11 0.1833 0.9333 6 3 0.0500 0.9833 7 1 0.0167 1 Nineteen immigrants to the U.S were asked how many years, to the nearest year, they have lived in the U.S. The data are as follows: 257221020150702051215124510. (Figure) was produced. \|Data\|\|Frequency\|\|Relative frequency\|\|Cumulative relative frequency\| - Fix the errors in (Figure). Also, explain how someone might have arrived at the incorrect number(s). - Explain what is wrong with this statement: “47 percent of the people surveyed have lived in the U.S. for 5 years.” - Fix the statement in b to make it correct. - What fraction of the people surveyed have lived in the U.S. five or seven years? - What fraction of the people surveyed have lived in the U.S. at most 12 years? - What fraction of the people surveyed have lived in the U.S. fewer than 12 years? - What fraction of the people surveyed have lived in the U.S. from five to 20 years, inclusive? <!– <solution id=”eip-idm81790048″> The Frequencies for 15 and 20 should both be two and the Relative Frequencies should both be 2 19 . The mistake could be due to copying the data down wrong. The Cumulative Relative Frequency for five years should be 0.4737. The mistake is due to calculating the Relative Frequency instead of the Cumulative Relative Frequency. The Cumulative Relative Frequency for 15 years should be 0.8947 The 47% is the Cumulative Relative Frequency, not the Relative Frequency. 47% of the people surveyed have lived in the U.S. for five years or less. 5 19 15 19 13 19 13 19 –> How much time does it take to travel to work? (Figure) shows the mean commute time by state for workers at least 16 years old who are not working at home. Find the mean travel time, and round off the answer properly. The sum of the travel times is 1,173.1. Divide the sum by 50 to calculate the mean value: 23.462. Because each state’s travel time was measured to the nearest tenth, round this calculation to the nearest hundredth: 23.46. Forbes magazine published data on the best small firms in 2012. These were firms which had been publicly traded for at least a year, have a stock price of at least ?5 per share, and have reported annual revenue between ?5 million and ?1 billion. (Figure) shows the ages of the chief executive officers for the first 60 ranked firms. \|Age\|\|Frequency\|\|Relative frequency\|\|Cumulative relative frequency\| - What is the frequency for CEO ages between 54 and 65? - What percentage of CEOs are 65 years or older? - What is the relative frequency of ages under 50? - What is the cumulative relative frequency for CEOs younger than 55? - Which graph shows the relative frequency and which shows the cumulative relative frequency? <!– <solution id=”eip-idp30968976″> 26 (This is the count of CEOs in the 55 to 59 and 60 to 64 categories.) 12% (number of CEOs age 65 or older ÷ total number of CEOs) 14/60; 0.23; 23% 0.45 Graph A represents the cumulative relative frequency, and Graph B shows the relative frequency. –> Use the following information to answer the next two exercises:(Figure) contains data on hurricanes that have made direct hits on the U.S. Between 1851 and 2004. A hurricane is given a strength category rating based on the minimum wind speed generated by the storm. \|Category\|\|Number of direct hits\|\|Relative frequency\|\|Cumulative frequency\| \|Total = 273\| What is the relative frequency of direct hits that were category 4 hurricanes? - Not enough information to calculate What is the relative frequency of direct hits that were AT MOST a category 3 storm? <!– <solution id=”id30104819″> b –> - Cumulative Relative Frequency - The term applies to an ordered set of observations from smallest to largest. The cumulative relative frequency is the sum of the relative frequencies for all values that are less than or equal to the given value. - the number of times a value of the data occurs - Relative Frequency - the ratio of the number of times a value of the data occurs in the set of all outcomes to the number of all outcomes to the total number of outcomes
In this lesson, we will develop skills in thinking critically about articles, moving beyond what the authors have to say on a topic, to examine how and why they say it. This is a move beyond summary towards analysis. Let’s look at our sample topic for a critical comparison: Compare and contrast how Wohlsen and Prensky define digital literacy and what role education should play in achieving it. At one level, we can answer this with summary information about the content of the articles. But the challenge is not simply to repeat what the authors say about digital literacy and education, but to consider why they make the arguments they make and how they make them. To do this, we need some tools for thinking critically. Step 1 is to practice with these tools to develop interesting critical commentary on the articles. In Step 2, we will be organizing all our critical commentary into relevant categories for the critical comparison essay. Tools for Critical Response Let’s begin with a progressive set of questions that you can apply to any argument you come across. These questions are designed to help you dig more deeply into the underlying logic and goals of any point of argument. \|Critical Thinking Questions\| We can use Prensky as an example to illustrate how to apply these questions. \|Critical Thinking Questions\|\|Explanation\|\|Examples – Critical thinking about Prensky\| \|What is the point of argument?\|\|Describe a basic point of argument in the article. This could be the main argument or a smaller point within the discussion. We have defined many of these as part of our summary work. \|Here’s one point he argues: He argues that “today’s students have changed radically,” so that the education system cannot meet their needs. \|What evidence is used to support the argument?\|\|Writers can use different kinds of evidence to support their arguments and ideas. Critical reading includes assessing what kinds of evidence a writer uses to support and argument. We can look for three kinds of evidence: Reasons are used to explain why something is needed or makes sense. Examples can be used to illustrate key points. Claims to the authority of other writers can be used to support ideas. \|Let’s look at the evidence Prensky uses to support this point that today’s students have “changed radically.” Today’s students have “changed radically” because they have grown up with digital technology. Prensky notes they have “spent their entire lives surrounded by and using computers, videogames, …. And all the other toys and tools of the digital age” and provides statistics on the number of hours in front of screens. Claim to authority: Prensky cites Dr. Perry to suggest that student brains have physically changed as a result of this exposure to technology. \|What assumptions does the writer make as the basis of the argument?\|\|When making an argument a writer must begin somewhere. Any point of argument, however, depends on certain things being true. A writer must make assumptions, and hope that the reader will agree to these assumptions. When reading critically, we must consider not only the arguments being made, but also the assumptions on which those arguments are based. If the assumptions don’t make sense, the argument will have its limits. \|Prensky’s overall argument is that the older generation teachers have a responsibility to learn to teach in a suitable way for the younger generation of students. His whole article is based on a key assumption: That all younger people are fluent users of digital technology and that all older people use technology in a less fluent way. Prensky assumes that the ability to use digital technology is a result of age, rather than a result of individual opportunity in life. What do you think about this assumption? Is this true? Do you think all young people naturally have the digital literacy Prensky writes about? What other factors do you think might shape our ability to use digital technology? \|What are the consequences or implications of the arguments offered by the writer?\|\|Finally, critical thinking includes considering the consequences or implications of what a writer is arguing. If a position on a particular social debate leads to detrimental consequences for some people, for example, then it needs to be considered. \|Prensky assumes that all younger people are digital natives. We can identify several implications of this argument. First, this idea hides the fact that younger students of different social classes or in different geographical areas may have different access to digital technology. Second, his argument assumes that there is no value in holding on to ways of thinking and learning that exist before the pervasive use of digital technology. Is it possible that some of what the older generation has to say might be valuable? These points and more are discussed in Henry Jenkin’s critical response to Prensky’s article “Reconsidering Digital Immigrants”. Now it’s your turn. Practice applying the critical thinking questions to ideas from the Wohlsen article. In the exercises below, you are given a point of argument from Wohlsen. Your task is to think about the evidence, assumptions behind, and implications of that point of argument. Enter your ideas into the boxes. Use the examples in the Critical Thinking Questions (Reference) as a guide. Organizing the Key Categories Thinking critically about the two articles is a form of brainstorming, gathering together many different points about the articles that will eventually be organized into a logical essay. Before we can proceed to writing this essay, we need to think about how to organize all this material. Drawing on all our critical thinking, we can develop categories of information that allow us to group our points together in logical ways. Each reader will find different ways of doing this. Consider the possible categories of information offered here. Do you agree with them? Do they make sense based on your reading and thinking critically about the two articles? Would you add anything different? Within each of these categories, we can group our ideas about each article, focusing on arguments, evidence, assumptions and consequences.
The Mexican–American War,[a] also known as the Mexican War in the United States and in Mexico as the American intervention in Mexico,[b] was an armed conflict between the United States of America and the United Mexican States (Mexico) from 1846 to 1848. It followed in the wake of the 1845 American annexation of the independent Republic of Texas, which Mexico still considered its northeastern province and a part of its territory after its de facto secession in the 1836 Texas Revolution a decade earlier. Mexico obtained independence from the Kingdom of Spain and the Spanish Empire with the Treaty of Córdoba in 1821, and briefly experimented with monarchy, becoming a republic in 1824. It was characterized by considerable instability, leaving it ill-prepared for international conflict only two decades later, when war broke out in 1846. In the decades preceding the war, Native American raids in Mexico's sparsely settled north prompted the Mexican government to sponsor migration from the United States to the Mexican province of Texas to create a buffer. However, the newly named "Texians" revolted against the Mexican government of President/dictator Antonio López de Santa Anna, who had usurped the Mexican Constitution of 1824, in the subsequent 1836 Texas Revolution, creating a republic not recognized by Mexico, which still claimed it as part of its national territory. In 1845, the Texan Republic agreed to an offer of annexation by the U.S. Congress and became the 28th state in the Union on December 29 that year. In 1845, newly elected U.S. President James K. Polk made a proposition to the Mexican government to purchase the disputed lands between the Nueces River and the Rio Grande river further south. When that offer was rejected, President Polk moved U.S. troops commanded by Major General Zachary Taylor further south into the disputed territory. Mexican forces attacked an American Army outpost ("Thornton Affair") in the occupied territory, killing 12 U.S. soldiers and capturing 52. These same Mexican troops later laid siege to an American fort along the Rio Grande. Polk cited this attack as an invasion of U.S. territory and requested that the Congress declare war. U.S. forces quickly occupied the capital town of Santa Fe de Nuevo México along the upper Rio Grande and the Pacific coast territory province of Alta California (Upper California). They then invaded to the south into parts of central Mexico (modern-day northeastern Mexico and northwest Mexico). Meanwhile, the Pacific Squadron of the United States Navy conducted a blockade and took control of several garrisons on the Pacific coast farther south in lower Baja California Territory. The U.S. Army, under the command of Major General Winfield Scott, after several fierce battles of stiff resistance from the Mexican Army outside of the capital, Mexico City, eventually captured the city, having marched west from the port of Veracruz, where the Americans staged their first amphibious landing on the Gulf of Mexico coast. The 1848 Treaty of Guadalupe Hidalgo, forced onto the remnant Mexican government, ended the war and specified its major consequence, the Mexican Cession of the northern territories of Alta California and Santa Fe de Nuevo México to the United States. The U.S. agreed to pay $15 million compensation for the physical damage of the war. In addition, the United States assumed $3.25 million of debt already owed earlier by the Mexican government to U.S. citizens. Mexico acknowledged the loss of their province, later the Republic of Texas (and now the State of Texas), and thereafter cited and acknowledged the Rio Grande as its future northern national border with the United States. Mexico had lost over one-third of its original territory from its 1821 independence. The territorial expansion of the United States toward the Pacific coast had been the goal of Polk, the leader of the Democratic Party. At first, the war was highly controversial in the United States, with the Whig Party, anti-imperialists, and anti-slavery elements strongly opposing. Critics in the United States pointed to the heavy casualties suffered by U.S. forces compared to earlier American wars, and the conflict's high monetary cost. The war intensified the debate over slavery in the United States, contributing to bitter debates that culminated in the American Civil War (1861–1865). In Mexico, the war came in the middle of continued domestic political turmoil, which increased into chaos during the conflict. The military defeat and loss of territory was a disastrous blow, causing Mexico to enter "a period of self-examination... as its leaders sought to identify and address the reasons that had led to such a debacle." In the immediate aftermath of the war, some prominent Mexicans wrote that the war had resulted in "the state of degradation and ruin" in Mexico, further claiming, for "the true origin of the war, it is sufficient to say that the insatiable ambition of the United States, favored by our weakness, caused it." The shift in the Mexico-U.S. border left many Mexican citizens separated from their national government. For the indigenous peoples who had never accepted Spanish or Mexican rule, the change in border meant conflicts with a new outside power. The northern area of Mexico was sparsely settled and not well controlled politically by the government based in Mexico City. After independence from Spain in 1821, Mexico contended with internal struggles that sometimes verged on civil war and the northern frontier was not a high priority. In the sparsely settled interior of northern Mexico, the end of Spanish rule was marked by the end of financing for presidios and for subsidies to indigenous Americans to maintain the peace. There were conflicts between indigenous people in the northern region as well. The Comanche were particularly successful in expanding their territory in the Comanche–Mexico Wars and garnering resources. The Apache–Mexico Wars also made Mexico's north a violent place, with no effective political control. The Apache raids left thousands of people dead throughout northern Mexico. When the United States Army entered northern Mexico in 1846 they found demoralized Mexican settlers. There was little resistance to US forces from the civilian population. Hostile activity from indigenous people also made communications and trade between the interior of Mexico and provinces such as Alta California and New Mexico difficult. As a result, New Mexico was dependent on the overland Santa Fe Trail trade with the United States at the outbreak of the Mexican–American War. Mexico's military and diplomatic capabilities declined after it attained independence and left the northern half of the country vulnerable to the Comanche, Apache, and Navajo. The indigenous people, especially the Comanche, took advantage of the weakness of the Mexican state to undertake large-scale raids hundreds of miles into the country to acquire livestock for their own use and to supply an expanding market in Texas and the US. The Mexican government's policy of settlement of US citizens in its province of Tejas was aimed at expanding control into Comanche lands, the Comancheria. Instead of settlement occurring in the central and west of the province, people settled in East Texas, where there was rich farmland and which was contiguous to southern US slave states. As settlers poured in from the US, the Mexican government took steps to discourage further settlement, including its 1829 abolition of slavery. In 1836, Mexico was relatively united in refusing to recognize the independence of Texas. Mexico threatened war with the United States if it annexed the Republic of Texas. Meanwhile, U.S. President Polk's assertion of Manifest Destiny was focusing United States interest on westward expansion beyond its existing national borders. During the Spanish colonial era, the Californias (i.e., the Baja California peninsula and Alta California) were sparsely settled. After Mexico became independent, it shut down the missions and reduced its military presence. In 1842, the US minister in Mexico, Waddy Thompson Jr., suggested Mexico might be willing to cede Alta California to settle debts, saying: "As to Texas, I regard it as of very little value compared with California, the richest, the most beautiful, and the healthiest country in the world ... with the acquisition of Upper California we should have the same ascendency on the Pacific ... France and England both have had their eyes upon it." US President John Tyler's administration suggested a tripartite pact that would settle the Oregon boundary dispute and provide for the cession of the port of San Francisco from Mexico. Lord Aberdeen declined to participate but said Britain had no objection to U.S. territorial acquisition there. The British minister in Mexico, Richard Pakenham, wrote in 1841 to Lord Palmerston urging "to establish an English population in the magnificent Territory of Upper California", saying that "no part of the World offering greater natural advantages for the establishment of an English colony ... by all means desirable ... that California, once ceasing to belong to Mexico, should not fall into the hands of any power but England ... daring and adventurous speculators in the United States have already turned their thoughts in this direction." But by the time the letter reached London, Sir Robert Peel's Tory government, with its Little England policy, had come to power and rejected the proposal as expensive and a potential source of conflict. A significant number of influential Californios were in favor of annexation, either by the United States or by the United Kingdom. Pío de Jesús Pico IV, the last governor of Alta California, was in favor of British annexation. In 1800, the colonial province of Texas was sparsely populated, with only about 7,000 non-Indian settlers. The Spanish crown developed a policy of colonization to more effectively control the territory. After independence, the Mexican government implemented the policy, granting Moses Austin, a banker from Missouri, a large tract of land in Texas. Austin died before he could bring his plan of recruiting American settlers for the land to fruition, but his son, Stephen F. Austin, brought over 300 American families into Texas. This started the steady trend of migration from the United States into the Texas frontier. Austin's colony was the most successful of several colonies authorized by the Mexican government. The Mexican government intended the new settlers to act as a buffer between the Tejano residents and the Comanches, but the non-Hispanic colonists tended to settle where there was decent farmland and trade connections with American Louisiana, which the United States had acquired in the Louisiana Purchase, rather than further west where they would have been an effective buffer against the Indians. In 1829, as a result of the large influx of American immigrants, the non-Hispanic outnumbered native Spanish speakers in the Texas territory. President Vicente Guerrero, a hero of Mexican independence, moved to gain more control over Texas and its influx of southern non-Hispanic colonists and discourage further immigration by abolishing slavery in Mexico. The Mexican government also decided to reinstate the property tax and increase tariffs on shipped American goods. The settlers and many Mexican businessmen in the region rejected the demands, which led to Mexico closing Texas to additional immigration, which continued from the United States into Texas illegally. In 1834, General Antonio López de Santa Anna became the centralist dictator of Mexico, abandoning the federal system. He decided to quash the semi-independence of Texas, having succeeded in doing so in Coahuila (in 1824, Mexico had merged Texas and Coahuila into the enormous state of Coahuila y Tejas). Finally, Stephen F. Austin called Texians to arms, and they declared independence from Mexico in 1836. After Santa Anna defeated the Texians in the Battle of the Alamo, he was defeated by the Texian Army commanded by General Sam Houston and captured at the Battle of San Jacinto; he signed a treaty recognizing the independence of Texas. Texas consolidated its status as an independent republic and received official recognition from Britain, France, and the United States, which all advised Mexico not to try to reconquer the new nation. Most Texians wanted to join the United States of America, but annexation of Texas was contentious in the US Congress, where Whigs were largely opposed. In 1845 Texas agreed to the offer of annexation by the US Congress and became the 28th state on December 29, 1845. The border of Texas as an independent state was originally never settled. The Republic of Texas claimed land up to the Rio Grande based on the Treaties of Velasco, but Mexico refused to accept these as valid, claiming that the Rio Grande in the treaty was the Nueces, and referred to the Rio Grande as the Rio Bravo. The ill-fated Texan Santa Fe Expedition of 1841 attempted to realize the claim to New Mexican territory East of the Rio Grande, but its members were captured and imprisoned. Reference to the Rio Grande boundary of Texas was omitted from the US Congress's annexation resolution to help secure passage after the annexation treaty failed in the Senate. President Polk claimed the Rio Grande boundary, and when Mexico sent forces over the Rio Grande, this provoked a dispute. In July 1845, Polk sent General Zachary Taylor to Texas, and by October 3,500 Americans were on the Nueces River, ready to take by force the disputed land. Polk wanted to protect the border and also coveted for the U.S. the continent clear to the Pacific Ocean. At the same time Polk wrote to the American consul in the Mexican territory of Alta California, disclaiming American ambitions in California, but offering to support independence from Mexico or voluntary accession to the United States, and warning that the United States would oppose a British or French takeover. To end another war scare with the United Kingdom over the Oregon Country, Polk signed the Oregon Treaty dividing the territory, angering northern Democrats who felt he was prioritizing Southern expansion over Northern expansion. In the Winter of 1845–46, the federally commissioned explorer John C. Frémont and a group of armed men appeared in Alta California. After telling the Mexican governor and the American Consul Larkin he was merely buying supplies on the way to Oregon, he instead went to the populated area of California and visited Santa Cruz and the Salinas Valley, explaining he had been looking for a seaside home for his mother. Mexican authorities became alarmed and ordered him to leave. Frémont responded by building a fort on Gavilan Peak and raising the American flag. Larkin sent word that Frémont's actions were counterproductive. Frémont left California in March but returned to California and took control of the California Battalion following the outbreak of the Bear Flag Revolt in Sonoma. In November 1845, Polk sent John Slidell, a secret representative, to Mexico City with an offer to the Mexican government of $25 million for the Rio Grande border in Texas and Mexico's provinces of Alta California and Santa Fe de Nuevo México. US expansionists wanted California to thwart British ambitions in the area and to gain a port on the Pacific Ocean. Polk authorized Slidell to forgive the $3 million owed to US citizens for damages caused by the Mexican War of Independence and pay another $25 to $30 million in exchange for the two territories. Mexico was not inclined nor able to negotiate. In 1846 alone, the presidency changed hands four times, the war ministry six times, and the finance ministry sixteen times. Mexican public opinion and all political factions agreed that selling the territories to the United States would tarnish the national honor. Mexicans who opposed direct conflict with the United States, including President José Joaquín de Herrera, were viewed as traitors. Military opponents of de Herrera, supported by populist newspapers, considered Slidell's presence in Mexico City an insult. When de Herrera considered receiving Slidell to settle the problem of Texas annexation peacefully, he was accused of treason and deposed. After a more nationalistic government under General Mariano Paredes y Arrillaga came to power, it publicly reaffirmed Mexico's claim to Texas; Slidell, convinced that Mexico should be "chastised", returned to the US. The Mexican Army emerged from the war of independence (1810–1821) as a weak and divided force. Before the war with the United States, the military faced both internal and foreign challenges. The Spanish still occupied the coastal fortress of San Juan de Ulúa, and Spain did not recognize Mexico's independence, so that the new nation was at risk for invasion. In 1829, the Spanish attempted to reconquer their former colony and Antonio López de Santa Anna became a national hero defending the homeland. The army had a set of privileges (fueros), established in the colonial era, that gave it jurisdiction over many aspects of its affairs. In general, the military supported conservative positions, advocating for a strong central government and upholding privileges of the military and the Catholic Church. Some military men exercised power in local areas as caudillos and resisted central command. Liberal politicians, such as Valentín Gómez Farías, sought to rein in the military's power. The military faced insurrections and separatist movements in Tabasco, Yucatán, and Texas. The French blockaded in Veracruz in 1838 to collect debts, a conflict known to history as the Pastry War. Compounding the demands on the Mexican military, there were continuing Indian challenges to power in the northern region. On the Mexican side, only 7 of the 19 states that formed the Mexican federation sent soldiers, armament, and money for the war effort, as the young Republic had not yet developed a sense of a unifying, national identity. Mexican soldiers were not easily melded into an effective fighting force. Santa Anna said "the leaders of the army did their best to train the rough men who volunteered, but they could do little to inspire them with patriotism for the glorious country they were honored to serve." According to leading conservative politician Lucas Alamán, the "money spent on arming Mexican troops merely enabled them to fight each other and 'give the illusion' that the country possessed an army for its defense." However, an officer criticized Santa Anna's training of troops, "The cavalry was drilled only in regiments. The artillery hardly ever maneuvered and never fired a blank shot. The general in command was never present on the field of maneuvers, so that he was unable to appreciate the respective qualities of the various bodies under his command.... If any meetings of the principal commanding officers were held to discuss the operations of the campaign, it was not known, nor was it known whether any plan of campaign had been formed." At the beginning of the war, Mexican forces were divided between the permanent forces (permanentes) and the active militiamen (activos). The permanent forces consisted of 12 regiments of infantry (of two battalions each), three brigades of artillery, eight regiments of cavalry, one separate squadron and a brigade of dragoons. The militia amounted to nine infantry and six cavalry regiments. In the northern territories of Mexico, presidial companies (presidiales) protected the scattered settlements there. One of the contributing factors to loss of the war by Mexico was the inferiority of their weapons. The Mexican army was using surplus British muskets (e.g. Brown Bess) from the Napoleonic Wars period. While at the beginning of the war the majority of American soldiers were still equipped with the very similar Springfield 1816 flintlock muskets, more reliable caplock models gained large inroads within the rank and file as the conflict progressed. Some US troops carried radically modern weapons that gave them a significant advantage over their Mexican counterparts, such as the Springfield 1841 rifle of the Mississippi Rifles and the Colt Paterson revolver of the Texas Rangers. In the later stages of the war, the US Mounted Rifles were issued Colt Walker revolvers, of which the US Army had ordered 1,000 in 1846. Most significantly, throughout the war the superiority of the US artillery often carried the day. While technologically Mexican and American artillery operated on the same plane, US army training as well as the quality and reliability of their logistics gave US guns and cannoneers a significant edge. Desertion was a major problem for the Mexican army, depleting forces on the eve of battle. Most soldiers were peasants who held loyalty to their village and family, but not to the generals who had conscripted them. Often hungry and ill, under-equipped, only partially trained, and never well paid, the soldiers were held in contempt by their officers and had little reason to fight the invading US forces. Looking for their opportunity, many slipped away from camp to find their way back to their home village. Women who traveled with the men in the Mexican army where known as soldaderas. While they only carried their packs, there were recorded instances where the soldaderas would join in the battle alongside the men. These women were involved in street fighting during the defence of Mexico City and Monterey. Some women such as Dos Amandes and Maria Josefa Zozaya would be remembered as heroes. Political divisions inside Mexico were another factor in the US victory. Inside Mexico, the centralistas and republicanos vied for power, and at times these two factions inside Mexico's military fought each other rather than the invading US Army. Another faction called the monarchists, whose members wanted to install a monarch (some advocated rejoining Spain), further complicated matters. This third faction would rise to predominance in the period of the French intervention in Mexico. The ease of the American landing at Veracruz was in large part due to civil warfare in Mexico City, which made any real defense of the port city impossible. As Gen. Santa Anna said, "However shameful it may be to admit this, we have brought this disgraceful tragedy upon ourselves through our interminable in-fighting." On the U.S. side, the war was fought by regiments of regulars and various regiments, battalions, and companies of volunteers from the different states of the Union as well as Americans and some Mexicans in the California and New Mexico territories. On the West Coast, the US Navy fielded a battalion of sailors, in an attempt to recapture Los Angeles. Although the US Army and Navy were not large at the outbreak of the war, the officers were generally well trained and the numbers of enlisted men fairly large compared to Mexico's. At the beginning of the war, the US Army had eight regiments of infantry (three battalions each), four artillery regiments and three mounted regiments (two dragoons, one of mounted rifles). These regiments were supplemented by 10 new regiments (nine of infantry and one of cavalry) raised for one year of service by the act of Congress from February 11, 1847. State volunteers were raised in various sized units and for various periods of time, mostly for one year. Later some were raised for the duration of the war as it became clear it was going to last longer than a year. US soldiers' memoirs describe cases of looting and murder of Mexican civilians, mostly by State Volunteers. One officer's diary records: We reached Burrita about 5 pm, many of the Louisiana volunteers were there, a lawless drunken rabble. They had driven away the inhabitants, taken possession of their houses, and were emulating each other in making beasts of themselves. John L. O'Sullivan, a vocal proponent of Manifest Destiny, later recalled: The regulars regarded the volunteers with importance and contempt ... [The volunteers] robbed Mexicans of their cattle and corn, stole their fences for firewood, got drunk, and killed several inoffensive inhabitants of the town in the streets. Many of the volunteers were unwanted and considered poor soldiers. The expression "Just like Gaines's army" came to refer to something useless, the phrase having originated when a group of untrained and unwilling Louisiana troops were rejected and sent back by Gen. Taylor at the beginning of the war. President Polk ordered General Taylor and his forces south to the Rio Grande, entering the territory that Mexicans disputed. Mexico laid claim to all the lands as far north as the Nueces River—about 150 mi (240 km) north of the Rio Grande. The U.S. claimed that the border was the Rio Grande, citing the 1836 Treaties of Velasco. However, Mexico rejected the treaties and refused to negotiate, instead still claiming all of Texas. Taylor ignored Mexican demands to withdraw to the Nueces. He constructed a makeshift fort (later known as Fort Brown/Fort Texas) on the banks of the Rio Grande opposite the city of Matamoros, Tamaulipas. The Mexican forces under General Santa Anna immediately prepared for war. On April 25, 1846, a 2,000-man Mexican cavalry detachment attacked a 70-man U.S. patrol under the command of Captain Seth Thornton, which had been sent into the contested territory north of the Rio Grande and south of the Nueces River. In the Thornton Affair, the Mexican cavalry routed the patrol, killing 11 American soldiers. Regarding the beginning of the war, Ulysses S. Grant, who had opposed the war but served as an army lieutenant in Taylor's Army, claims in his Personal Memoirs (1885) that the main goal of the U.S. Army's advance from Nueces River to Rio Grande was to provoke the outbreak of war without attacking first, to debilitate any political opposition to the war. The presence of United States troops on the edge of the disputed territory farthest from the Mexican settlements, was not sufficient to provoke hostilities. We were sent to provoke a fight, but it was essential that Mexico should commence it. It was very doubtful whether Congress would declare war; but if Mexico should attack our troops, the Executive could announce, "Whereas, war exists by the acts of, etc.," and prosecute the contest with vigor. Once initiated there were but few public men who would have the courage to oppose it.... Mexico showing no willingness to come to the Nueces to drive the invaders from her soil, it became necessary for the "invaders" to approach to within a convenient distance to be struck. Accordingly, preparations were begun for moving the army to the Rio Grande, to a point near Matamoras (sic). It was desirable to occupy a position near the largest centre of population possible to reach, without absolutely invading territory to which we set up no claim whatever. A few days after the defeat of the U.S. troops by General Arista, the Siege of Fort Texas began on May 3, 1846. Mexican artillery at Matamoros opened fire on Fort Texas, which replied with its own guns. The bombardment continued for 160 hours and expanded as Mexican forces gradually surrounded the fort. Thirteen U.S. soldiers were injured during the bombardment, and two were killed. Among the dead was Jacob Brown, after whom the fort was later named. On May 8, Zachary Taylor and 2,400 troops arrived to relieve the fort. However, General Arista rushed north and intercepted him with a force of 3,400 at Palo Alto. The U.S. Army employed "flying artillery", their term for horse artillery, a type of mobile light artillery that was mounted on horse carriages with the entire crew riding horses into battle. It had a devastating effect on the Mexican army. In contrast to the "flying artillery" of the Americans, the Mexican cannons at the Battle of Palo Alto fired at such slow velocities that it was possible for American soldiers to dodge artillery rounds. The Mexicans replied with cavalry skirmishes and their own artillery. The U.S. flying artillery somewhat demoralized the Mexican side, and seeking terrain more to their advantage, the Mexicans retreated to the far side of a dry riverbed (resaca) during the night. It provided a natural fortification, but during the retreat, Mexican troops were scattered, making communication difficult. During the Battle of Resaca de la Palma the next day, the two sides engaged in fierce hand to hand combat. The U.S. Cavalry managed to capture the Mexican artillery, causing the Mexican side to retreat—a retreat that turned into a rout. Fighting on unfamiliar terrain, his troops fleeing in retreat, Arista found it impossible to rally his forces. Mexican casualties were heavy, and the Mexicans were forced to abandon their artillery and baggage. Fort Brown inflicted additional casualties as the withdrawing troops passed by the fort. Many Mexican soldiers drowned trying to swim across the Rio Grande. Both these engagements were fought before war was declared. In 1846, relations between the two countries had deteriorated considerably and on April 23, 1846, the president of Mexico issued a proclamation, declaring Mexico's intent to fight a "defensive war" against the encroachment of the United States. On April 25, 1846, two thousand Mexican cavalry crossed into the disputed territory and routed a small detachment of American soldiers, sparking the "Thornton Affair". Polk received word of the Thornton Affair, which, added to the Mexican government's rejection of Slidell, Polk believed, constituted a casus belli (cause for war). His message to Congress on May 11, 1846, claimed that "Mexico has passed the boundary of the United States, has invaded our territory and shed American blood upon American soil." The U.S. Congress approved the declaration of war on May 13, 1846, after a few hours of debate, with southern Democrats in strong support. Sixty-seven Whigs voted against the war on a key slavery amendment, but on the final passage only 14 Whigs voted no, including Rep. John Quincy Adams. In Mexico, although President Paredes issued a manifesto on May 23, 1846 and a declaration of a defensive war on April 23, both of which are considered by some the de facto start of the war, Mexico officially declared war by Congress on July 7, 1846. Once the U.S. declared war on Mexico, Antonio López de Santa Anna wrote to the Mexican government, saying he no longer had aspirations to the presidency but would eagerly use his military experience to fight off the foreign invasion of Mexico as he had before. President Valentín Gómez Farías, a civilian, was desperate enough to accept the offer and allowed Santa Anna to return. Meanwhile, Santa Anna had secretly been dealing with representatives of the U.S., pledging that if he were allowed back into Mexico through the U.S. naval blockades, he would work to sell all contested territory to the United States at a reasonable price. Once back in Mexico at the head of an army, Santa Anna reneged on both agreements. He declared himself president once again and unsuccessfully tried to fight off the U.S. invasion. In the United States, increasingly divided by sectional rivalry, the war was a partisan issue and an essential element in the origins of the American Civil War. Most Whigs in the North and South opposed it; most Democrats supported it. Southern Democrats, animated by a popular belief in Manifest Destiny, supported it in hope of adding slave-owning territory to the South and avoiding being outnumbered by the faster-growing North. John L. O'Sullivan, editor of the Democratic Review, coined this phrase in its context, stating that it must be "our manifest destiny to overspread the continent allotted by Providence for the free development of our yearly multiplying millions." Northern antislavery elements feared the expansion of the Southern Slave Power; Whigs generally wanted to strengthen the economy with industrialization, not expand it with more land. Among the most vocal opposing the war in the House of Representatives was John Quincy Adams of Massachusetts. Adams had first voiced concerns about expanding into Mexican territory in 1836 when he opposed Texas annexation. He continued this argument in 1846 for the same reason. War with Mexico would add new slavery territory to the nation. When the vote to go to war with Mexico came to a vote on May 13, Adams spoke a resounding "NO" in the chamber. Only 13 others followed his lead. Ex-slave Frederick Douglass opposed the war and was dismayed by the weakness of the anti-war movement. "The determination of our slave holding president, and the probability of his success in wringing from the people, men and money to carry it on, is made evident by the puny opposition arrayed against him. None seem willing to take their stand for peace at all risks." Democrats wanted more land; northern Democrats were attracted by the possibilities in the far northwest. Joshua Giddings led a group of dissenters in Washington D.C. He called the war with Mexico "an aggressive, unholy, and unjust war", and voted against supplying soldiers and weapons. He said: In the murder of Mexicans upon their own soil, or in robbing them of their country, I can take no part either now or hereafter. The guilt of these crimes must rest on others. I will not participate in them. Fellow Whig Abraham Lincoln contested Polk's causes for the war. Polk had said that Mexico had "shed American blood upon American soil". Lincoln submitted eight "Spot Resolutions", demanding that Polk state the exact spot where Thornton had been attacked and American blood shed, and clarify whether or not that location was actually American soil, or in fact had been claimed by Spain and Mexico. This war is nondescript... We charge the President with usurping the war-making power ... with seizing a country ... which had been for centuries, and was then in the possession of the Mexicans.... Let us put a check upon this lust of dominion. We had territory enough, Heaven knew. Northern abolitionists attacked the war as an attempt by slave-owners to strengthen the grip of slavery and thus ensure their continued influence in the federal government. Acting on his convictions, Henry David Thoreau was jailed for his refusal to pay taxes to support the war, and penned his famous essay Civil Disobedience. Democratic Representative David Wilmot introduced the Wilmot Proviso, which would prohibit slavery in new territory acquired from Mexico. Wilmot's proposal passed the House but not the Senate, and it spurred further hostility between the factions. Besides alleging that the actions of Mexican military forces within the disputed boundary lands north of the Rio Grande constituted an attack on American soil, the war's advocates viewed the territories of New Mexico and California as only nominally Mexican possessions with very tenuous ties to Mexico. They saw the territories as actually unsettled, ungoverned, and unprotected frontier lands, whose non-aboriginal population, where there was any at all, represented a substantial—in places even a majority—American component. Moreover, the territories were feared to be under imminent threat of acquisition by America's rival on the continent, the British. President Polk reprised these arguments in his Third Annual Message to Congress on December 7, 1847. He scrupulously detailed his administration's position on the origins of the conflict, the measures the U.S. had taken to avoid hostilities, and the justification for declaring war. He also elaborated upon the many outstanding financial claims by American citizens against Mexico and argued that, in view of the country's insolvency, the cession of some large portion of its northern territories was the only indemnity realistically available as compensation. This helped to rally congressional Democrats to his side, ensuring passage of his war measures and bolstering support for the war in the U.S. Whipping up support for the war was embraced by the press. Richard Caton Woodville's lithograph, War News From Mexico, satirizes the reactions of various segments of the American population to the war. The lithograph is generally considered unfavorable to the war's apparent pro-slavery motivations. The coverage of the war was an important development in the U.S., with journalists as well as letter-writing soldiers giving the public in the U.S. "their first-ever independent news coverage of warfare from home or abroad." During the war, inventions such as the telegraph created new means of communication that updated people with the latest news from the reporters, who were on the scene. The most important of these was George Wilkins Kendall, a Northerner who wrote for the New Orleans Picayune, and whose collected Dispatches from the Mexican War constitute an important primary source for the conflict. With more than a decade's experience reporting urban crime, the "penny press" realized the public's voracious demand for astounding war news. Moreover, Shelley Streetby demonstrates that the print revolution (1830s-1840s), which preceded the U.S.-Mexican War, made it possible for the distribution of cheap newspapers throughout the country. This was the first time in American history that accounts by journalists, instead of opinions of politicians, had great influence in shaping people's opinions about and attitudes toward a war. Along with written accounts of the war, there were war artists giving a visual dimension to the war at the time and immediately afterward. Carl Nebel's visual depictions of the war are well known. By getting constant reports from the battlefield, Americans became emotionally united as a community. News about the war always caused extraordinary popular excitement. In the Spring of 1846, news about Zachary Taylor's victory at Palo Alto brought up a large crowd that met in a cotton textile town of Lowell, Massachusetts. New York celebrated the twin victories at Veracruz and Buena Vista in May 1847. Among fireworks and illuminations, they had a "grand procession" of about 400,000 people. Generals Taylor and Scott became heroes for their people and later became presidential candidates. After the declaration of war on May 13, 1846, U.S. forces invaded Mexican territory on two main fronts. The U.S. War Department sent a U.S. Cavalry force under Stephen W. Kearny to invade western Mexico from Jefferson Barracks and Fort Leavenworth, reinforced by a Pacific fleet under John D. Sloat. This was done primarily because of concerns that Britain might also try to seize the area. Two more forces, one under John E. Wool and the other under Taylor, were ordered to occupy Mexico as far south as the city of Monterrey. This section needs additional citations for verification. (May 2017) (Learn how and when to remove this template message) United States Army General Stephen W. Kearny moved southwest from Fort Leavenworth, Kansas with about 1,700 men in his Army of the West. Kearny's orders were to secure the territories Nuevo México and Alta California. In Santa Fe, Governor Manuel Armijo wanted to avoid battle, but on August 9, Catholic priests, Diego Archuleta (the young regular-army commander), and the young militia officers Manuel Chaves and Miguel Pino forced him to muster a defense. Armijo set up a position in Apache Canyon, a narrow pass about 10 miles (16 km) southeast of the city. However, on August 14, before the American army was even in view, he decided not to fight. (An American named James Magoffin claimed he had convinced Armijo and Archuleta to follow this course; an unverified story says he bribed Armijo.) When Pino, Chaves, and some of the militiamen insisted on fighting, Armijo ordered the cannon pointed at them. The New Mexican army retreated to Santa Fe, and Armijo fled to Chihuahua. Kearny and his troops encountered no Mexican forces when they arrived on August 15. Kearny and his force entered Santa Fe and claimed the New Mexico Territory for the United States without a shot being fired. Kearny declared himself the military governor of the New Mexico Territory on August 18 and established a civilian government. American officers with a background in law drew up a temporary legal system for the territory called the Kearny Code. Kearny then took the remainder of his army west to Alta California. When he departed with his forces for California, he left Colonel Sterling Price in command of U.S. forces in New Mexico. He appointed Charles Bent as New Mexico's first territorial governor. Following Kearny's departure, dissenters in Santa Fe plotted a Christmas uprising. When the plans were discovered by the U.S. authorities, the dissenters postponed the uprising. They attracted numerous Indian allies, including Puebloan peoples, who also wanted to push the Americans from the territory. On the morning of January 19, 1847, the insurrectionists began the revolt in Don Fernando de Taos, present-day Taos, New Mexico, which later gave it the name the Taos Revolt. They were led by Pablo Montoya, a New Mexican, and Tomás Romero, a Taos pueblo Indian also known as Tomasito (Little Thomas). Romero led an Indian force to the house of Governor Charles Bent, where they broke down the door, shot Bent with arrows, and scalped him in front of his family. They moved on, leaving Bent still alive. With his wife Ignacia and children, and the wives of friends Kit Carson and Thomas Boggs, the group escaped by digging through the adobe walls of their house into the one next door. When the insurgents discovered the party, they killed Bent, but left the women and children unharmed. The next day a large armed force of approximately 500 New Mexicans and Pueblo attacked and laid siege to Simeon Turley's mill in Arroyo Hondo, several miles outside of Taos. Charles Autobees, an employee at the mill, saw the men coming. He rode to Santa Fe for help from the occupying U.S. forces. Eight to ten mountain men were left at the mill for defense. After a day-long battle, only two of the mountain men survived, John David Albert and Thomas Tate Tobin, Autobees' half brother. Both escaped separately on foot during the night. The same day New Mexican insurgents killed seven American traders who were passing through the village of Mora. At most, 15 Americans were killed in both actions on January 20. The U.S. military moved quickly to quash the revolt; Col. Price led more than 300 U.S. troops from Santa Fe to Taos, together with 65 volunteers, including a few New Mexicans, organized by Ceran St. Vrain, the business partner of the brothers William and Charles Bent. Along the way, the combined forces beat back a force of some 1,500 New Mexicans and Pueblo at Santa Cruz de la Cañada at Embudo Pass. The insurgents retreated to Taos Pueblo, where they took refuge in the thick-walled adobe church. During the ensuing battle, the U.S. breached a wall of the church and directed cannon fire into the interior, inflicting many casualties and killing about 150 rebels. They captured 400 more men after close hand-to-hand fighting. Only seven Americans died in the battle. A separate force of U.S. troops under captains Israel R. Hendley and Jesse I. Morin campaigned against the rebels in Mora. The First Battle of Mora ended in a New Mexican victory. The Americans attacked again in the Second Battle of Mora and won, which ended their operations against Mora. New Mexican rebels engaged U.S. forces three more times in the following months. The actions are known as the Battle of Red River Canyon, the Battle of Las Vegas, and the Battle of Cienega Creek. After the U.S. forces won each battle, the New Mexicans and Indians ended open warfare. Although the U.S. declared war against Mexico on May 13, 1846, it took almost three months (until early August 1846) for definitive word of Congress' declaration of war to get to California. American consul Thomas O. Larkin, stationed in Monterey, worked successfully during the events in that vicinity to avoid bloodshed between Americans and the Mexican military garrison commanded by General José Castro, the senior military officer in California. Captain John C. Frémont, leading a U.S. Army topographical expedition to survey the Great Basin, entered the Sacramento Valley in December 1845. Frémont's party was at Upper Klamath Lake, Oregon Territory, when it received word that war between Mexico and the U.S. was imminent; the party then returned to California. Mexico had issued a proclamation that unnaturalized foreigners were no longer permitted to have land in California and were subject to expulsion. With rumors swirling that General Castro was massing an army against them, American settlers in the Sacramento Valley banded together to meet the threat. On June 14, 1846, 34 American settlers seized control of the undefended Mexican government outpost of Sonoma to forestall Castro's plans. One settler created the Bear Flag and raised it over Sonoma Plaza. Within a week, 70 more volunteers joined the rebels' force, which grew to nearly 300 in early July. This event, led by William B. Ide, became known as the Bear Flag Revolt. On June 25, Frémont's party arrived to assist in an expected military confrontation. San Francisco, then called Yerba Buena, was occupied by the Bear Flaggers on July 2. On July 5 Frémont's California Battalion was formed by combining his forces with many of the rebels. Commodore John D. Sloat, commander of the U.S. Navy's Pacific Squadron, near Mazatlan, Mexico, had received orders to seize San Francisco Bay and blockade California ports when he was positive that war had begun. Sloat set sail for Monterey, reaching it on July 1. Sloat, upon hearing of the events in Sonoma and Frémont's involvement, erroneously believed Frémont to be acting on orders from Washington and ordered his forces to occupy Monterey on July 7 and raise the American flag. On Sloat's orders, Frémont brought 160 volunteers to Monterey, in addition to the California Battalion. On July 15, Sloat transferred his command of the Pacific Squadron to Commodore Robert F. Stockton, who was more militarily aggressive. He mustered the willing members of the California Battalion into military service with Frémont in command. Stockton ordered Frémont to San Diego to prepare to move northward to Los Angeles. As Frémont landed, Stockton's 360 men arrived in San Pedro. General Castro and Governor Pío Pico wrote farewells and fled separately to the Mexican state of Sonora. Stockton's army entered Los Angeles unopposed on August 13, whereupon he sent a report to the Secretary of State that "California is entirely free from Mexican dominion." Stockton, however, left a tyrannical officer in charge of Los Angeles with a small force. The Californios under the leadership of José María Flores, acting on their own and without federal help from Mexico, in the Siege of Los Angeles, forced the American garrison to retreat on September 29. They also forced small U.S. garrisons in San Diego and Santa Barbara to flee. Captain William Mervine landed 350 sailors and Marines at San Pedro on October 7. They were ambushed and repulsed at the Battle of Dominguez Rancho by Flores' forces in less than an hour. Four Americans died, with 8 severely injured. Stockton arrived with reinforcements at San Pedro, which increased the American forces there to 800. He and Mervine then set up a base of operations at San Diego. Meanwhile, U.S. Colonel Stephen W. Kearny and his force of about 100 men, who had performed a grueling march across New Mexico and the Sonoran Desert, crossed the Colorado River in late November, 1846. Stockton sent a 35-man patrol from San Diego to meet them. On December 7, 100 lancers under General Andrés Pico (brother of the governor), tipped off and lying in wait, fought Kearny's army of about 150 at the Battle of San Pasqual, where 22 of Kearny's men (one of whom later died of wounds), including three officers, were killed in 30 minutes of fighting. The wounded Kearny and his bloodied force pushed on until they had to establish a defensive position on "Mule Hill". However, General Pico kept the hill under siege for four days until a 215-man American relief force arrived. Frémont and the 428-man California Battalion arrived in San Luis Obispo on December 14 and Santa Barbara on December 27. On December 28, a 600-man American force under Kearny began a 150-mile march to Los Angeles. Flores then moved his ill-equipped 500-man force to a 50-foot-high bluff above the San Gabriel River. On January 8, 1847, the Stockton-Kearny army defeated the Californio force in the two-hour Battle of Rio San Gabriel. That same day, Frémont's force arrived at San Fernando. The next day, January 9, the Stockton-Kearny forces fought and won the Battle of La Mesa. On January 10, the U.S. Army entered Los Angeles to no resistance. On January 12, Frémont and two of Pico's officers agreed to terms for a surrender. Articles of Capitulation were signed on January 13 by Frémont, Andrés Pico and six others at a rancho at Cahuenga Pass (modern-day North Hollywood). This became known as the Treaty of Cahuenga, which marked the end of armed resistance in California. USS Independence assisted in the blockade of the Mexican Pacific coast, capturing the Mexican ship Correo and a launch on May 16, 1847. She supported the capture of Guaymas, Sonora, on October 19, 1847, and landed bluejackets and Marines to occupy Mazatlán, Sinaloa, on November 11, 1847. After upper California was secure, most of the Pacific Squadron proceeded down the California coast, capturing all major cities of the Baja California Territory and capturing or destroying nearly all Mexican vessels in the Gulf of California. Other ports, not on the peninsula, were taken as well. The objective of the Pacific Coast Campaign was to capture Mazatlán, on the Mexican mainland, which was a major supply base for Mexican forces. Numerous Mexican ships were also captured by this squadron, with the USS Cyane given credit for 18 ships captured and numerous destroyed. Entering the Gulf of California, Independence, Congress, and Cyane seized La Paz, then captured and burned the small Mexican fleet at Guaymas. Within a month, they cleared the Gulf of hostile ships, destroying or capturing 30 vessels. Later, their sailors and Marines captured the port of Mazatlán on November 11, 1847. A Mexican campaign under Manuel Pineda Muñoz to retake the various captured ports resulted in several small clashes (Battle of Mulege, Battle of La Paz, Battle of San José del Cabo) and two sieges (Siege of La Paz, Siege of San José del Cabo) in which the Pacific Squadron ships provided artillery support. U.S. garrisons remained in control of the ports. Following reinforcement, Lt. Col. Henry S. Burton marched out. His forces rescued captured Americans, captured Pineda, and, on March 31, defeated and dispersed remaining Mexican forces at the Skirmish of Todos Santos, unaware that the Treaty of Guadalupe Hidalgo had been signed in February 1848 and a truce agreed to on March 6. When the American garrisons were evacuated to Monterey following the treaty ratification, many Mexicans went with them: those who had supported the American cause and had thought Lower California would also be annexed along with Upper California. The Mexican Army's defeats at Palo Alto and Resaca de la Palma caused political turmoil in Mexico, turmoil which Antonio López de Santa Anna used to revive his political career and return from self-imposed exile in Cuba in mid-August 1846. It was President Polk's plan to bring back the exiled dictator who had defeated the Texans at the Alamo and Goliad. On 4 August 1846, "Polk negotiated a deal to not only bring Santa Anna back, but to pay him $2 million—ostensibly a bribe as an advance payment on the cession of California." Santa Anna promised the U.S. that if he was allowed to pass through the blockade, he would negotiate a peaceful conclusion to the war and sell the New Mexico and Alta California territories to the U.S. Once Santa Anna arrived in Mexico City, however, he reneged on his deal with the U.S. and offered his services to the Mexican government. Then, after being appointed commanding general, he reneged again and seized the presidency. Led by Zachary Taylor, 2,300 U.S. troops crossed the Rio Grande after some initial difficulties in obtaining river transport. His soldiers occupied the city of Matamoros, then Camargo (where the soldiery suffered the first of many problems with disease) and then proceeded south and besieged the city of Monterrey. The hard-fought Battle of Monterrey resulted in serious losses on both sides. The American light artillery was ineffective against the stone fortifications of the city. The Mexican forces were under General Pedro de Ampudia and repulsed Taylor's best infantry division at Fort Teneria. American soldiers, including many West Pointers, had never engaged in urban warfare before and they marched straight down the open streets, where they were annihilated by Mexican defenders well-hidden in Monterrey's thick adobe homes. Two days later, they changed their urban warfare tactics. Texan soldiers had fought in a Mexican city before (the Siege of Béxar in December 1835) and advised Taylor's generals that the Americans needed to "mouse hole" through the city's homes. In other words, they needed to punch holes in the side or roofs of the homes and fight hand to hand inside the structures. Mexicans called the Texas soldiers the Diabólicos Tejanos (the Devil Texans). This method proved successful. Eventually, these actions drove and trapped Ampudia's men into the city's central plaza, where howitzer shelling forced Ampudia to negotiate. Taylor agreed to allow the Mexican Army to evacuate and to an eight-week armistice in return for the surrender of the city. Under pressure from Washington, Taylor broke the armistice and occupied the city of Saltillo, southwest of Monterrey. Santa Anna blamed the loss of Monterrey and Saltillo on Ampudia and demoted him to command a small artillery battalion. On February 22, 1847, Santa Anna personally marched north to fight Taylor with 20,000 men. Taylor, with 4,600 men, had entrenched at a mountain pass called Buena Vista. Santa Anna suffered desertions on the way north and arrived with 15,000 men in a tired state. He demanded and was refused surrender of the U.S. Army; he attacked the next morning. Santa Anna flanked the U.S. positions by sending his cavalry and some of his infantry up the steep terrain that made up one side of the pass, while a division of infantry attacked frontally along the road leading to Buena Vista. Furious fighting ensued, during which the U.S. troops were nearly routed, but managed to cling to their entrenched position, thanks to the Mississippi Rifles, a volunteer regiment led by Jefferson Davis, who formed them into a defensive V formation. The Mexicans had inflicted considerable losses but Santa Anna had gotten word of upheaval in Mexico City, so he withdrew that night, leaving Taylor in control of part of Northern Mexico. Polk mistrusted Taylor, who he felt had shown incompetence in the Battle of Monterrey by agreeing to the armistice. Taylor later used the Battle of Buena Vista as the centerpiece of his successful 1848 presidential campaign. The Treaty of Bear Springs ended a large scale insurrection by the Ute, Zuni, Moquis, and Navajo tribes. After the successful conquest of New Mexico, American troops moved into modern-day northwest Mexico. On March 1, 1847, Alexander W. Doniphan occupied Chihuahua City. British consul John Potts did not want to let Doniphan search Governor Trias's mansion, and unsuccessfully asserted it was under British protection. American merchants in Chihuahua wanted the American force to stay in order to protect their business. Major William Gilpin advocated a march on Mexico City and convinced a majority of officers, but Doniphan subverted this plan. Then in late April, Taylor ordered the First Missouri Mounted Volunteers to leave Chihuahua and join him at Saltillo. The American merchants either followed or returned to Santa Fe. Along the way, the townspeople of Parras enlisted Doniphan's aid against an Indian raiding party that had taken children, horses, mules, and money. The civilian population of northern Mexico offered little resistance to the American invasion, possibly because the country had already been devastated by Comanche and Apache Indian raids. Josiah Gregg, who was with the American army in northern Mexico, said that "the whole country from New Mexico to the borders of Durango is almost entirely depopulated. The haciendas and ranchos have been mostly abandoned, and the people chiefly confined to the towns and cities." Southern Mexico had a large indigenous population and was geographically distant from the capital. Yucatán in particular had closer ties to Cuba and to the United States than it did to central Mexico. On a number of occasions in the early era of the Mexican Republic, Yucatán seceded from the federation. There were also rivalries between regional elites, with one faction based in Mérida and the other in Campeche. These issues factored into the Mexican–American War. The U.S. Navy contributed to the war by controlling the coast and clearing the way for U.S. troops and supplies, especially to Mexico's main port of Veracruz. Even before hostilities began in the disputed northern region, the U.S. Navy created a blockade. Given the shallow waters of that portion of the Gulf coast, the U.S. Navy needed ships with a shallow draft rather than large frigates. Since the Mexican Navy was almost non-existent, the U.S. Navy could operate unimpeded in Gulf waters. Commodore Matthew C. Perry led a detachment of seven vessels along the northern coast of Tabasco state. Perry arrived at the Tabasco River (now known as the Grijalva River) on October 22, 1846, and seized the town Port of Frontera along with two of their ships. Leaving a small garrison, he advanced with his troops towards the town of San Juan Bautista (Villahermosa today). Perry arrived in the city of San Juan Bautista on October 25, seizing five Mexican vessels. Colonel Juan Bautista Traconis, Tabasco Departmental commander at that time, set up barricades inside the buildings. Perry realized that the bombing of the city would be the only option to drive out the Mexican Army, and to avoid damage to the merchants of the city, withdrew its forces preparing them for the next day. On the morning of October 26, as Perry's fleet prepared to start the attack on the city, the Mexican forces began firing at the American fleet. The U.S. bombing began to yield the square, so that the fire continued until evening. Before taking the square, Perry decided to leave and return to the port of Frontera, where he established a naval blockade to prevent supplies of food and military supplies from reaching the state capital. On June 13, 1847, Commodore Perry assembled the Mosquito Fleet and began moving towards the Grijalva River, towing 47 boats that carried a landing force of 1,173. On June 15, 12 miles (19 km) below San Juan Bautista, the fleet ran through an ambush with little difficulty. Again at an "S" curve in the river known as the "Devil's Bend", Perry encountered Mexican fire from a river fortification known as the Colmena redoubt, but the fleet's heavy naval guns quickly dispersed the Mexican force. On June 16, Perry arrived at San Juan Bautista and commenced bombing the city. The attack included two ships that sailed past the fort and began shelling it from the rear. David D. Porter led 60 sailors ashore and seized the fort, raising the American flag over the works. Perry and the landing force arrived and took control of the city around 14:00. The U.S. was concerned with the extension of British power in the Caribbean, especially Spanish Cuba, as well as the strategic Yucatán peninsula. In 1847 Maya revolted against the white elites of the peninsula in a racial war known as the Caste War of Yucatan. Jefferson Davis, then a senator from Mississippi, argued in congress that the president needed no further powers to intervene in Yucatan since the war with Mexico was underway. Davis's concern was strategic and part of his vision of Manifest Destiny, considering the Gulf of Mexico "a basin of water belonging to the United States" and continuing "the cape of Yucatan and the island of Cuba must be ours" rather than under British influence. In the end, the U.S. did not intervene in Yucatán, but it had figured in congressional debates about the Mexican–American War. At one point, the government of Yucatán petitioned the U.S. for protection during the Caste War, but the U.S. did not respond. Desertion was a major problem for the Mexican Army, depleting forces on the eve of battle. Most soldiers were peasants who had a loyalty to their village and family, but not to the generals who had conscripted them. Often hungry and ill, under-equipped, only partially trained, and never well paid, the soldiers were held in contempt by their officers and had little reason to fight the Americans. Looking for their opportunity, many slipped away from camp to find their way back to their home village. The desertion rate in the U.S. Army was 8.3% (9,200 out of 111,000), compared to 12.7% during the War of 1812 and usual peacetime rates of about 14.8% per year. Many men deserted to join another U.S. unit and get a second enlistment bonus. Some deserted because of the miserable conditions in camp. It has been suggested that others used the army to get free transportation to California, where they deserted to join the gold rush; this, however, is unlikely as gold was only discovered in California on January 24, 1848, less than two weeks before the war concluded. By the time word reached the eastern U.S. that gold had been discovered, word also reached it that the war was over. Several hundred U.S. deserters went over to the Mexican side. Nearly all were recent immigrants from Europe with weak ties to the U.S.. The Mexicans issued broadsides and leaflets enticing U.S. soldiers with promises of money, land bounties, and officers' commissions. Mexican guerrillas shadowed the U.S. Army and captured men who took unauthorized leave or fell out of the ranks. The guerrillas coerced these men to join the Mexican ranks. The generous promises proved illusory for most deserters, who risked being executed if captured by U.S. forces. The most famous group of deserters from the U. S. Army, was the Saint Patrick's Battalion or (San Patricios), composed primarily several hundred immigrant soldiers, the majority Catholic Irish and German immigrants, who deserted the U.S. Army because of ill-treatment or sympathetic leanings to fellow Mexican Catholics and joined the Mexican army. The battalion also included Canadians, English, French, Italians, Poles, Scots, Spaniards, Swiss, and Mexican people, many of whom were members of the Catholic Church. Most of the battalion were killed in the Battle of Churubusco; about 100 were captured by the U.S. and roughly half of the San Patricios were tried and were hanged as deserters following their capture at Churubusco in August 1847.. The leader, Jon Riley, was merely branded since he had deserted before the war started. Rather than reinforce Taylor's army for a continued advance, President Polk sent a second army under General Winfield Scott, which was transported to the port of Veracruz by sea, to begin an invasion of the Mexican heartland. On March 9, 1847, Scott performed the first major amphibious landing in U.S. history in preparation for the Siege of Veracruz. A group of 12,000 volunteer and regular soldiers successfully offloaded supplies, weapons, and horses near the walled city using specially designed landing crafts. Included in the invading force were Robert E. Lee, George Meade, Ulysses S. Grant, James Longstreet, and Thomas "Stonewall" Jackson. The city was defended by Mexican General Juan Morales with 3,400 men. Mortars and naval guns under Commodore Matthew C. Perry were used to reduce the city walls and harass defenders. After a bombardment on March 24, 1847, the walls of Veracruz had a thirty-foot gap. The city replied the best it could with its own artillery. The effect of the extended barrage destroyed the will of the Mexican side to fight against a numerically superior force, and they surrendered the city after 12 days under siege. U.S. troops suffered 80 casualties, while the Mexican side had around 180 killed and wounded, about half of whom were civilian. During the siege, the U.S. side began to fall victim to yellow fever. Scott then marched westward on April 2, 1847, toward Mexico City with 8,500 healthy troops, while Santa Anna set up a defensive position in a canyon around the main road about 50 miles (80 km) north-west of Veracruz, near the hamlet of Cerro Gordo. Santa Anna had entrenched with 12,000 troops, and artillery that were trained on the road, where he expected Scott to appear. However, Scott had sent 2,600 mounted dragoons ahead and they reached the pass on April 12. The Mexican artillery prematurely fired on them and therefore revealed their positions, beginning the Battle of Cerro Gordo. Instead of taking the main road, Scott's troops trekked through the rough terrain to the north, setting up his artillery on the high ground and quietly flanking the Mexicans. Although by then aware of the positions of U.S. troops, Santa Anna and his troops were unprepared for the onslaught that followed. In the battle fought on April 18, the Mexican army was routed. The U.S. Army suffered 400 casualties, while the Mexicans suffered over 1,000 casualties and 3,000 were taken prisoner. In August 1847, Captain Kirby Smith, of Scott's 3rd Infantry, reflected on the resistance of the Mexican army: They can do nothing and their continued defeats should convince them of it. They have lost six great battles; we have captured six hundred and eight cannon, nearly one hundred thousand stands of arms, made twenty thousand prisoners, have the greatest portion of their country and are fast advancing on their Capital which must be ours,—yet they refuse to treat [i.e., negotiate terms]! In May, Scott pushed on to Puebla, the second largest city in Mexico. Because of the citizens' hostility to Santa Anna, the city capitulated without resistance on May 1. During the following months, Scott gathered supplies and reinforcements at Puebla and sent back units whose enlistments had expired. Scott also made strong efforts to keep his troops disciplined and treat the Mexican people under occupation justly, so as to prevent a popular rising against his army. With guerrillas harassing his line of communications back to Veracruz, Scott decided not to weaken his army to defend Puebla but, leaving only a garrison at Puebla to protect the sick and injured recovering there, advanced on Mexico City on August 7 with his remaining force. The capital was laid open in a series of battles around the right flank of the city defenses, the Battle of Contreras and Battle of Churubusco. After Churubusco, fighting halted for an armistice and peace negotiations, which broke down on September 6, 1847. With the subsequent battles of Molino del Rey and of Chapultepec, and the storming of the city gates, the capital was occupied. Scott became military governor of occupied Mexico City. His victories in this campaign made him an American national hero. The Battle of Chapultepec was an encounter between the Mexican Army and the United States on the castle of Chapultepec in Mexico City. At this time, this castle was a renowned military school in Mexico City. After the battle, which ended in an American victory, the legend of "Los Niños Héroes" was born. Although not confirmed by historians, six military cadets between the ages of 13 and 17 stayed in the school instead of evacuating. They decided to stay and fight for Mexico. These Niños Héroes (hero children) became icons in Mexico's pantheon of heroes. Rather than surrender to the U.S. Army, some military cadets leaped from the castle walls. A cadet named Juan Escutia wrapped himself in the Mexican flag and jumped to his death. In late September 1847, Santa Anna made one last attempt to defeat the Americans, by cutting them off from the coast. General Joaquín Rea began the Siege of Puebla, soon joined by Santa Anna, but they failed to take it before the approach of a relief column from Veracruz under Brig. Gen. Joseph Lane prompted Santa Anna to stop him. Puebla was relieved by Gen. Lane October 12, 1847, following his defeat of Santa Anna at the Battle of Huamantla on October 9, 1847. The battle was Santa Anna's last. Following the defeat, the new Mexican government led by Manuel de la Peña y Peña asked Santa Anna to turn over command of the army to General José Joaquín de Herrera. Following his capture and securing of the capital, General Scott sent about a quarter of his strength to secure his line of communications to Veracruz from the Light Corps of General Joaquín Rea and other Mexican guerrilla forces that had been harassing it since May. He strengthened the garrison of Puebla and by November had added a 1200-man garrison at Jalapa, established 750-man posts along the National Road, the main route between the port of Veracruz and the capital, at the pass between Mexico City and Puebla at Rio Frio, at Perote and San Juan on the road between Jalapa and Puebla, and at Puente Nacional between Jalapa and Veracruz. He had also detailed an anti guerrilla brigade under Brig. Gen. Joseph Lane to carry the war to the Light Corps and other guerrillas. He ordered that convoys would travel with at least 1,300-man escorts. Victories by General Lane over the Light Corps at Atlixco (October 18, 1847), at Izucar de Matamoros (November 23, 1847), and at Galaxara Pass (November 24, 1847) ended the threat of General Rea. Later a raid against the guerrillas of Padre Jarauta at Zacualtipan (February 25, 1848) further reduced guerrilla raids on the American line of communications. After the two governments concluded a truce to await ratification of the peace treaty, on March 6, 1848, formal hostilities ceased. However some bands continued in defiance of the Mexican government until the American evacuation in August. Some were suppressed by the Mexican Army or, like Padre Jarauta, executed. Outnumbered militarily and with many of its large cities occupied, Mexico could not defend itself; the country was also faced with many internal divisions, including the Caste War of Yucatán. The Treaty of Guadalupe Hidalgo, signed on February 2, 1848, by American diplomat Nicholas Trist and Mexican plenipotentiary representatives Luis G. Cuevas, Bernardo Couto, and Miguel Atristain, ended the war. The treaty gave the U.S. undisputed control of Texas, established the U.S.-Mexican border of the Rio Grande, and ceded to the United States the present-day states of California, Nevada, and Utah, most of New Mexico, Arizona and Colorado, and parts of Texas, Oklahoma, Kansas, and Wyoming. In return, Mexico received $15 million ($424 million today) – less than half the amount the U.S. had attempted to offer Mexico for the land before the opening of hostilities – and the U.S. agreed to assume $3.25 million ($92 million today) in debts that the Mexican government owed to U.S. citizens. The treaty was ratified by the U.S. Senate by a vote of 38 to 14 on March 10, and by Mexico through a legislative vote of 51-34 and a Senate vote of 33-4, on May 19. News that New Mexico's legislative assembly had passed an act for organization of a U.S. territorial government helped ease Mexican concern about abandoning the people of New Mexico. The acquisition was a source of controversy, especially among U.S. politicians who had opposed the war from the start. A leading antiwar U.S. newspaper, the Whig National Intelligencer, sardonically concluded that "We take nothing by conquest .... Thank God." Jefferson Davis introduced an amendment giving the U.S. most of northeastern Mexico, which failed 44–11. This amendment was supported by both senators from Texas (Sam Houston and Thomas Jefferson Rusk), Daniel S. Dickinson of New York, Stephen A. Douglas of Illinois, Edward A. Hannegan of Indiana, and one each from Alabama, Florida, Mississippi, Ohio, Missouri, and Tennessee. Most of the leaders of the Democratic party – Thomas Hart Benton, John C. Calhoun, Herschel V. Johnson, Lewis Cass, James Murray Mason of Virginia, and Ambrose Hundley Sevier – were opposed. An amendment by Whig Senator George Edmund Badger of North Carolina to exclude New Mexico and Upper California lost 35–15, with three Southern Whigs voting with the Democrats. Daniel Webster was bitter that four New England senators made deciding votes for acquiring the new territories. The acquired lands west of the Rio Grande are traditionally called the Mexican Cession in the U.S., as opposed to the Texas Annexation two years earlier, though division of New Mexico down the middle at the Rio Grande never had any basis either in control or Mexican boundaries. Mexico never recognized the independence of Texas before the war, and did not cede its claim to territory north of the Rio Grande or Gila River until this treaty. Before ratifying the treaty, the U.S. Senate made two modifications: changing the wording of Article IX (which guaranteed Mexicans living in the purchased territories the right to become U.S. citizens) and striking out Article X (which conceded the legitimacy of land grants made by the Mexican government). On May 26, 1848, when the two countries exchanged ratifications of the treaty of Guadalupe Hidalgo, they further agreed to a three-article protocol (known as the Protocol of Querétaro) to explain the amendments. The first article claimed that the original Article IX of the treaty, although replaced by Article III of the Treaty of Louisiana, would still confer the rights delineated in Article IX. The second article confirmed the legitimacy of land grants under Mexican law. The protocol was signed in the city of Querétaro by A. H. Sevier, Nathan Clifford, and Luis de la Rosa. Article XI offered a potential benefit to Mexico, in that the US pledged to suppress the Comanche and Apache raids that had ravaged northern Mexico and pay restitutions to the victims of raids it could not prevent. However, the Indian raids did not cease for several decades after the treaty, although a cholera epidemic reduced the numbers of the Comanche in 1849. Robert Letcher, U.S. Minister to Mexico in 1850, was certain "that miserable 11th article" would lead to the financial ruin of the US if it could not be released from its obligations. The US was released from all obligations of Article XI five years later by Article II of the Gadsden Purchase of 1853. Before the secession of Texas, Mexico comprised almost 1,700,000 sq mi (4,400,000 km2), but by 1849 it was just under 800,000 square miles (2,100,000 km2). Another 30,000 square miles (78,000 km2) were sold to the U.S. in the Gadsden Purchase of 1853, so the total reduction of Mexican territory was more than 55%, or 900,000 square miles (2,300,000 km2). Though the annexed territory was about the size of Western Europe, it was sparsely populated. The land contained about 14,000 non-indigenous people in Alta California and about 60,000 in Nuevo México, as well as large Indian nations, such as the Papago, Pima, Puebloan, Navajo, Apache and many others. Although some native people relocated farther south in Mexico, the great majority remained in the U.S. territory. The American settlers surging into the newly conquered Southwest were openly contemptuous of Mexican law (a civil law system based on the law of Spain) as alien and inferior and disposed of it by enacting reception statutes at the first available opportunity. However, they recognized the value of a few aspects of Mexican law and carried them over into their new legal systems. For example, most of the southwestern states adopted community property marital property systems, as well as water law. Mexicans and Indians in the annexed territories faced a loss of civil and political rights, even though the Treaty of Guadalupe Hidalgo promised American citizenship to all Mexican citizens living in the territory of the Mexican Cession. The U.S. government withheld citizenship from Indians in the southwest until the 1930s, despite the fact that they were citizens under Mexican law. In much of the United States of America, victory and the acquisition of new land brought a surge of patriotism. Victory seemed to fulfill Democrats' belief in their country's Manifest Destiny. While Whig Ralph Waldo Emerson rejected war "as a means of achieving America's destiny," he accepted that "most of the great results of history are brought about by discreditable means." Although the Whigs had opposed the war, they made Zachary Taylor their presidential candidate in the election of 1848, praising his military performance while muting their criticism of the war. Has the Mexican War terminated yet, and how? Are we beaten? Do you know of any nation about to besiege South Hadley [Massachusetts]? If so, do inform me of it, for I would be glad of a chance to escape, if we are to be stormed. I suppose [our teacher] Miss [Mary] Lyon would furnish us all with daggers and order us to fight for our lives... A month before the end of the war, Polk was criticized in a United States House of Representatives amendment to a bill praising Major General Zachary Taylor for "a war unnecessarily and unconstitutionally begun by the President of the United States." This criticism, in which Congressman Abraham Lincoln played an important role with his Spot Resolutions, followed congressional scrutiny of the war's beginnings, including factual challenges to claims made by President Polk. The vote followed party lines, with all Whigs supporting the amendment. Lincoln's attack won lukewarm support from fellow Whigs in Illinois but was harshly counter-attacked by Democrats, who rallied pro-war sentiments in Illinois; Lincoln's Spot resolutions haunted his future campaigns in the heavily Democratic state of Illinois, and were cited by enemies well into his presidency. Many of the military leaders on both sides of the American Civil War were trained at the U.S. Military Academy at West Point and had fought as junior officers in Mexico. This list includes military men fighting for the Union: Ulysses S. Grant, George B. McClellan, William T. Sherman, George Meade, William Rosecrans, and Ambrose Burnside. Military men who joined the Southern secessionists of the Confederate States of America were Robert E. Lee, Stonewall Jackson, James Longstreet, Joseph E. Johnston, Braxton Bragg, Sterling Price, and the future Confederate President Jefferson Davis. Both sides had leaders with significant experience in active combat in strategy and tactics, likely shaping ways the Civil War conflict played out. Generally, the officers of the army were indifferent whether the annexation was consummated or not; but not so all of them. For myself, I was bitterly opposed to the measure, and to this day regard the war, which resulted, as one of the most unjust ever waged by a stronger against a weaker nation. It was an instance of a republic following the bad example of European monarchies, in not considering justice in their desire to acquire additional territory. Grant also expressed the view that the war against Mexico had brought punishment on the United States in the form of the American Civil War: The Southern rebellion was largely the outgrowth of the Mexican war. Nations, like individuals, are punished for their transgressions. We got our punishment in the most sanguinary and expensive war of modern times. This view was shared by the philosopher Ralph Waldo Emerson, who towards the end of the war wrote that "The United States will conquer Mexico, but it will be as the man swallows the arsenic, which brings him down in turn. Mexico will poison us." Veterans of the war were often broken men. "As the sick and wounded from Taylor's and Scott's campaigns made their way back from Mexico to the United States, their condition shocked the folks at home. Husbands, sons, and brothers returned in broken health, some with missing limbs." As late as 1880, the "Republican Campaign Textbook" by the Republican Congressional Committee described the war as "Feculent, reeking Corruption" and "one of the darkest scenes in our history—a war forced upon our and the Mexican people by the high-handed usurpations of Pres't Polk in pursuit of territorial aggrandizement of the slave oligarchy." General Robert E. Lee, leader of the Confederate forces through the end of the American Civil War, began building his reputation as a military officer in America's war against Mexico. At the start of the Mexican–American War, Captain Lee invaded Mexico with General Wool's engineering department from the North. By early 1847, he helped take the Mexican cities of Vera Cruz, Cerro Gordo, Contreras, Churubusco, Molino del Rey, and Chapultepec. Lee was wounded in Chapultepec. By September, Mexico City surrendered and the United States was victorious. General Scott was the ranking officer in the army during the Mexican–American campaign. He described Robert E. Lee as "gallant and indefatigable," saying that Lee had displayed the "greatest feat of physical and moral courage performed by any individual in [his] knowledge during the campaign." Robert E. Lee's humility and professionalism was apparent early on in his career when gave credit to General Scott for the victories. He said that "It was his stout heart…his bold self reliance…his indomitable courage that…ressed us forward to this capital." It is important to note that although Lee is remembered for his valor during the Mexican–American War, he was only a junior officer "who had never commanded a regiment in the field". In 1861, it was General Scott who advised Abraham Lincoln to ask Lee to command the union forces. Lee declined, and later recounted "I declined the offer he made me to take command of the army that was brought into the field, stating candidly and as courteously as I could that though opposed to secession and depreciating war, I could take no part in the invasion of the southern states." (Sneiderman,118) On 9 April 1865, it was General Robert E. Lee who had surrendered to President Lincoln's Union Forces. Despite initial objections from the Whigs and abolitionists, the war nevertheless united the U.S. in a common cause and was fought almost entirely by volunteers. The army swelled from just over 6,000 to more than 115,000. The majority of 12-month volunteers in Scott's army decided that a year's fighting was enough and returned to the U.S. Anti-slavery elements fought for the exclusion of slavery from any territory absorbed by the U.S. In 1847, the House of Representatives passed the Wilmot Proviso, stipulating that none of the territory acquired should be open to slavery. The Senate avoided the issue, and a late attempt to add it to the Treaty of Guadalupe Hidalgo was defeated. The war was a decisive event for the U.S., marking a significant waypoint for the nation as a growing military power, and a milestone in the U.S. narrative of Manifest Destiny. The war did not resolve the issue of slavery in the U.S. but rather in many ways inflamed it, as potential westward expansion of the institution took an increasingly central and heated theme in national debates preceding the American Civil War. By extending the nation from coast to coast, the Mexican–American War was a next step in the huge migrations to the West of Americans, which culminated in transcontinental railroads and the Indian wars later in the same century.[original research?] The obvious impact of the war for Mexico was the loss of its northern regions and the defeat of its military. The war remains a painful historical event for Mexicans. In the immediate aftermath of the war, a group of prominent Mexicans wrote an assessment of the reasons for the war and Mexico's defeat, edited by Ramón Alcaraz and including contributions by Ignacio Ramírez, Guillermo Prieto, José María Iglesias, and Francisco Urquidi. The work was translated to English by Col. Albert Ramsey, a veteran of the Mexican–American War, and published in 1850. In Mexico City's Chapultepec Park, the Niños Héroes (Monument to the Heroic Cadets) commemorates the heroic sacrifice of six teenaged military cadets who fought to their deaths rather than surrender to American troops during the Battle of Chapultepec Castle on September 13, 1847. The monument is an important patriotic site in Mexico. On March 5, 1947, nearly one hundred years after the battle, U.S. President Harry S. Truman placed a wreath at the monument and stood for a moment of silence. Mexico has passed the boundary of the United States, has invaded our territory and shed American blood upon the American soil. She has proclaimed that hostilities have commenced, and that the two nations are now at war. \|Wikimedia Commons has media related to Mexican–American War.\|
Line of Best Fit Teacher Resources Find Line of Best Fit educational ideas and activities Showing 41 - 60 of 394 resources Students work in pairs to test the strength of spaghetti strands. They collect and graph data to determine a line of best fit. Students create a linear equation to interpret their data. Based on the data collected, students predict results with 10 strands of spaghetti. In this correlation worksheet, learners identify situations which produce positive, negative and no correlations. They draw the line of best fit. This one-page worksheet contains 5 multiple-choice problems. Eleventh graders explore coefficient of correlation for bivariate data. Through activities, 11th graders use spaghetti to demonstrate the use of scatter plots and estimating a line of best fit. After collecting information, pupils use calculators to plot ordered pairs on a coordinate plane. Classmates observe the relationship between two items. Students investigate and analyze data. For this algebra lesson, students plot data on a coordinate plane and identify the line of best fit. They plot points correctly and make predictions about their data. Students investigate different correlations. In this algebra lesson plan, students analyze graphs and identify the lines as having positive, negative or no correlation. They calculate the line of best fit using a scatter plot. Students calculate the length, width, height, perimeter, area, volume, surface area, angle measures or sums of angle measures of common geometric figures. They create an equation of a line of best fit from a set of ordered pairs or set of data points. They interpolate and extrapolate to solve problems using systems of numbers. Young scholars conduct surveys and collect data. They analyze the data through graphs and calculate the rate of change. Students write an equation that represents the line of best fit. They determine the points on a line. Young scholars participate in real world activities. Students collect and analyze data. In this statistics activity, students plot their data on a coordinate plane. They identify the line of best fit the type of correlation as positive negative or no correlation. Students graph and analyze data. In this algebra lesson plan, students relate algebra to their engineering class. They analyze a set of given points, write an equation for the line and make predictions. They find the line of best fit. For this Algebra I worksheet, 9th graders determine line of best fit given two points on a scatter plot and use a linear model to make predictions. The one page interactive worksheet contains five multiple choice questions and is self checking. Pupils collect and analyze data. In this statistics lesson, students identify the rate of unemployment using collected data and making observations. They create model to represent their data. Students, in groups, work together to determine the relationship of the distance a projector is from a screen and the size of image that results. While experimenting with the data, students identify the independent and dependent variable and write the equation of a line of best fit. They determine the best distance for the projector to illuminate the image on the entire screen. Students create a scatter plot for bivariate data and find the trend line to describe the correlation for the sports teams. In this scatter plot lesson plan, students analyze data, make predictions,and use observations about sports data using a scatter plot to find the line of best fit. Students explore a website and worksheets to complete the project. Students also write an essay and complete a quiz for assessment. Eighth graders investigate using scatter plots to illustrate the data found in sets. Then they connect the coordinate points in order to find the correct line. Students make estimations of the second variable when given the first. They work in small groups in order to prepare for an assessment. In this scatter plots and line of best fit worksheet, students create scatter plots from given sets of data. They answer questions concerning the scatter plot. Students write the equation of a line, identify the type of correlation depicted in a graph, and draw the line of best fit. This one-page worksheet contains ten problems. Students graph points on a coordinate plane. In this algebra instructional activity, students analyze the points on a coordinate plane finding the line of best fit. They compare age in years and arm span in inches. Do big bodies make big brains? Let your learners decide whether there is an association between body weight and brain weight by putting the data from different animals into a scatterplot. They can remove any outliers and then make a line of best fit to show whether the relationship is positive or negative. Fortunately for us, human brains are heavy! High schoolers investigate different types of correlation in this statistics lesson. They identify positive, negative and no correlation as it relates to their data. They then find the line of best fit for the plotted data. Start this lesson by having your class generate their own data and determine the line of best fit relating their height and shoe size. Interpret the meaning of the slope and y-intercept in the context of the problem and use the equation to estimate shoe size based on height. Discuss the accuracy of their model and introduce the concept of residuals. Follow up with a two-problem worksheet where learners can practice calculating residuals for given data sets. The first has a step-by-step guide to the process. Included on the handout are directions on how to graph residuals on a TI calculator. Your class will generate their own data relating the number of people to the time it takes to do a human wave. Once data is collected, a line of best fit is found and used to estimate how long it would take for the entire student body to produce one cycle of the wave in the school gym. How fun would it be to actually have your school do the wave and compare the actual time to the calculated estimate!
Random articlesVariance Absolute Value Equations Continued Proportion Length of an Arc Area of a Rectangle/Square Range, Quartiles, Box and Whisker Plot Area of a Cuboid To understand the area of cylinder formula that works out the surface area of a cylinder. The first thing to do is to think about how a cylinder shape comes together. A cylinder has a pipe shape middle section, which is called the lateral surface. Along with having two bases, which are both circles, one on each end. The cylinder itself has a height, and also a radius, which is the same as the radius of the two circle bases. When the curved middle lateral surface is opened up and laid out flat, the shape of the surface actually becomes a rectangle. The width of this rectangle, is the same as the distance around of both of the circles at the bases of the cylinder, their circumferences. The circumference of a circle is given by π multiplied by twice the radius. 2πr We can see that the surface area of the pipe shape lateral surface, is the same as the area when it’s laid out as a rectangle. Which is the width multiplied by the height. 2πr × h => 2πrh While the two bases of the cylinder being circles that are the same size. The area of one of the circles is given by πr². So the area of both circle bases combined is double this, 2πr². Knowing all of this, it can now be seen that the entire surface area of a cylinder is put together like so. Resulting in the full area of cylinder formula for the surface area: 2πr² + 2πrh What is the area of the following cylinder. A section of an oil pipeline is in the shape of an open cylinder. The section has the following dimensions. What is the surface area of the section? An open cylinder is a cylinder which has no bases. So it just contains the curved lateral surface. Thus the area is given only by 2πrh. Area of pipeline section = 2π × 4 × 10 = 251.33m² Most of the time, when people mention the term cylinder, they mean a right cylinder. Which is what we’ve seen so far on this page, where the two circle bases are parallel and lined up with each other. An oblique cylinder on the other hand, is a cylinder where the two circle bases are not aligned, but they area still the same size as each other. So as well as a perpendicular height, there is also a slope, or a slant height, in the cylinder shape. To work out the surface area of a cylinder in this situation, you need to use the slant-height instead of the actual height straight up from the ground. Which results in: There is also another formula that can be used to find the surface area of an oblique cylinder. The information required is the radius, the vertical height, and also the angle that the oblique cylinder is tilted at, θ. In this situation, the area of the oblique cylinder can be given by:
We are searching data for your request: Upon completion, a link will appear to access the found materials. In 1545, an unknown disease struck the Aztec Empire. Those who came down with it might become feverish, start vomiting, and develop blotches on their skin. Most horrific of all, they’d bleed from their eyes, mouth, and nose, then die within a few days. Over the next five years, the disease—then called “cocoliztli,” or “pestilence”—killed between seven and 17 million people. Scientists and historians have long wondered what the source of this mysterious epidemic was. Now, a group of researchers may have found the answer: salmonella. On January 15, 2017, the scientific journal Nature Ecology & Evolution published a study of Salmonella enterica bacteria in the teeth of cocoliztli victims. Most Americans know salmonella as a foodborne illness that you can get if you eat, for example, raw eggs or chicken. Though S. enterica was the only germ that researchers detected in the victims’ teeth, they do caution that other indetectable pathogens could have been involved, too. “We cannot say with certainty that S. enterica was the cause of the cocoliztli epidemic,” Kirsten Bos, a molecular paleopathologist at the Max Planck Institute in Germany and co-author of the recent study, told The Guardian. “We do believe that it should be considered a strong candidate.” European invaders brought many new and devastating illnesses to the Americas in the 16th and 17th centuries. It’s possible that Spanish invaders brought salmonella to the Aztecs in modern-day Mexico through domesticated animals. The study doesn’t pinpoint the source of the bacteria, leaving open the possibility that it originated in the Americas. Yet even if the Spanish didn’t bring the bacteria, they likely still played a role in how it affected the Aztec people. “We know that Europeans very much changed the landscape once they entered the new world,” Bos told NPR. “They introduced new livestock, [and] there was lots of social disruption among the indigenous population which would have increased their susceptibility to infectious disease.” What Caused the Aztec Empire to Fall? Scientists Uncover New Clues - HISTORY Laslovarga/Wikimedia Commons Tikal, an ancient Mayan city that dates from 800 B.C. to 900 A.D. Many theories have been explored to try and explain the collapse of the Maya civilization. For years, evidence trying to prove these theories had been inconclusive – until now. The Maya Empire, located in what is now present-day Guatemala, was a cultural epicenter that excelled at agriculture, pottery, writing, and mathematics. They reached their peak of power in the sixth century A.D., however, by 900 A.D. most of their great cities were abandoned. For centuries researchers have tried to discover exactly how this great civilization could have fallen apart so quickly. A new report in Science, released on August 3, has finally given quantifiable evidence confirming the most widely-believed theory to explain how the Mayan civilization met its end: drought. The key to unlocking the mystery ended up being located in Lake Chichancanab on the Yucatan Peninsula. For the report, researchers examined oxygen and hydrogen isotopes in sediment from the lake, which was close enough to the heart of Mayan civilization to provide an accurate sample of the climate. For the report, Nicholas Evans, a Cambridge University research student and co-author of the paper, measured the isotopic composition of water found in the lake’s sediment to quantify exactly how much precipitation rates fell during the end of the Mayan civilization. According to the Washington Post, analyzing sediment cores is a common practice for discovering information about the past. Scientists are able to inspect the dirt, layer by layer, and record the information found in the soil to construct an accurate timeline of the past conditions. After examining the sediments samples, Evans, along with his team of researchers, concluded that annual rainfall levels declined 41 to 54 percent in the area surrounding the lake for several long periods over roughly 400 years, according to IFLScience. The report also revealed that humidity in the area dropped by 2 to 7 percent. These two factors combined to had a devastating effect on the civilization’s agriculture production. Because these drought conditions occurred frequently over hundreds of years, the civilization must not have been able to build up food reserves enough to make up for the drop in agricultural production, eventually leading to their demise. Josh Giovo/Wikimedia Commons Ruins of a Mayan temple. Even though this paper ties up some loose ends surrounding the Mayan people, some big unanswered questions still remain, like what precisely brought on this massive and sustained drought? A previous study showed that the Mayan’s deforestation could have contributed to the dry conditions, decreasing the moisture of the area and destabilizing the soil. Evans said that the drought could have also been caused by changes to the atmospheric circulation and a decline in tropical cyclone frequency. Matthew Lachinet, a professor in geosciences at the University of Nevada at Las Vegas, who was not involved in the study, told the Washington Post that this study is impactful because it offers insights into how humans can change the climate around them. “Humans are affecting climate,” Lachinet said. “We’re making it warmer and it’s projected to become drier in Central America. What we could end up with is double-whammy of drought. If you coincide drying from natural causes with drying from human causes, then it amplified the strength of that drought.” Despite these new findings, there is still much to learn about the collapse of Mayan civilization. Origins of Tenochtitlán According to legend, the Aztec people left their home city of Aztlan nearly 1,000 years ago. Scholars do not know where Aztlan was, but according to ancient accounts one of these Aztec groups, known as the Mexica, founded Tenochtitlán in 1325. The legend continues that Huitzilopochtli, the god of war, the sun and human sacrifice, is said to have directed the Mexica to settle on the island. He “ordered his priests to look for the prickly pear cactus and build a temple in his honor. They followed the order and found the place on an island in the middle of the lake . &rdquo writes University of Madrid anthropologist Jose Luis de Rojas in his book "Tenochtitlán: Capital of the Aztec Empire" (University of Florida Press, 2012). De Rojas notes that the “early years were difficult.&rdquo People lived in huts, and the temple for Huitzilopochtli “was made of perishable material.&rdquo Also in the beginning, Tenochtitlán was under the sway of another city named Azcapotzalco, to which they had to pay tribute. Political instability at Azcapotzalco, combined with an alliance with the cities of Texcoco and Tlacopan, allowed the Tenochtitlán ruler Itzcoatl (reign 1428-1440) to break free from Azcapotzalco&rsquos control and assert the city&rsquos independence. Over the next 80 years, the territory controlled by Tenochtitlán and its allies grew, and the city became the center of a new empire. The tribute that flowed in made the inhabitants (at least the elite) wealthy. “The Mexica extracted tribute from the subjugated groups and distributed the conquered lands among the victors, and wealth began to flow to Tenochtitlán,&rdquo writes de Rojas, noting that this resulted in rapid immigration into the city. The city itself would come to boast an aqueduct that brought in potable water and a great temple dedicated to both Huitzilopochtli (the god who led the Mexica to the island) and Tlaloc, a god of rain and fertility. Changing Climate and the Maya New data suggests climate&mdashspecifically, severe drought&mdashplayed a key role in the collapse of the Maya civilization. Anthropology, Biology, Earth Science, Geography, Human Geography, Physical Geography, Social Studies, World History Maya civilization thrived thousands of years ago in present-day Central America. Anthropologists and archaeologists thought Maya culture originated in the northern reaches of what is now Guatemala about 600 BCE, and migrated north to the Yucatan Peninsula beginning around 700 CE. Throughout the film Quest for the Lost Maya, a team of anthropologists led by Dr. George Bey discovers the Maya may have been in the Yucatan as far back as 500 BCE. This new evidence indicates the Maya of the Yucatan had a very complex social structure, distinctive religious practices, and unique technological innovations that made civilization possible in the harsh jungle. Archaeologists have long puzzled over the collapse of Mayan civilization. What led to the massive depopulation of major Mayan cities in the 900s? Scientists have considered war and political factors, but this segment of Quest for the Lost Maya suggests another explanation. In a University of Florida lab, Dr. Mark Brenner evaluates sediment cores which have produced new data that suggests climate&mdashspecifically, severe drought&mdashplayed a key role in the decline of Maya civilization. This segment of Quest for the Lost Maya outlines how scientists use snail shells and sediment layers from the bottom of a lake to create a picture of climate conditions at various periods in the ancient past. Although climate was likely a major factor of the Mayan collapse, it's not the only one. Civilizations carefully balance a host of factors&mdashpolitical, environmental, military, and cultural. Troubles in one area often lead to problems in other areas. What do different bands of color in the core sediment samples represent? Brown bands represent organic material, whereas white bands represent gypsum (a type of salt). How does the gypsum found in the core sediment samples form? What does this formation indicate? The gypsum sediment layer formed as water evaporated. Salt in the water did not evaporate, and settled in layers at the bottom of the lake. This evaporation process indicates a period of drought. How did scientists determine the age of the gypsum? With what did these dates coincide? Scientists performed radio-carbon dating to find that the gypsum layers dated from the same time period as the collapse of Mayan civilization. How have snail shells helped climatologists determine aspects of the ancient environment of the Stairway site? Snail shells contain two distinct oxygen isotopes, one of which occurs much more strongly in a drought environment. Analysis of shells obtained from sediment cores at the Mayan archaeological site indicates droughts of the highest magnitude during the last 7,000 years. How many serious droughts were recorded in the sediment core, and how long did they last? What were their impacts? Climatologists determined there were a series of eight droughts lasting three to twenty years. These droughts likely forced the people living at the Stairway site to evacuate the area. Disease can drive human history Of course, the Aztecs were not the only indigenous people to suffer from the introduction of European diseases. In addition to North America’s Native American populations, the Mayan and Incan civilizations were also nearly wiped out by smallpox. And other European diseases, such as measles and mumps, also took substantial tolls – altogether reducing some indigenous populations in the new world by 90 percent or more. Recent investigations have suggested that other infectious agents, such as Salmonella – known for causing contemporary outbreaks among pet owners – may have caused additional epidemics. The ability of smallpox to incapacitate and decimate populations made it an attractive agent for biological warfare. In the 18th century, the British tried to infect Native American populations. One commander wrote, “We gave them two blankets and a handkerchief out of the smallpox hospital. I hope it will have the desired effect.” During World War II, British, American, Japanese and Soviet teams all investigated the possibility of producing a smallpox biological weapon. Mass vaccination against smallpox got going in the second half of the 1800s. Photo courtesy of Everett Historical via Shutterstock.cm Happily, worldwide vaccination efforts have been successful, and the last naturally occurring case of the disease was diagnosed in 1977. The final case occurred in 1978, when a photographer died of the disease, prompting the scientist whose research she was covering to take his own life. Many great encounters in world history, including Cortés’s clash with the Aztec empire, had less to do with weaponry, tactics and strategy than with the ravages of disease. Nations that suppose they can secure themselves strictly through investments in military spending should study history – time and time again the course of events has been definitively altered by disease outbreaks. Microbes too small to be seen by the naked eye can render ineffectual even the mightiest machinery of war. This article was originally published on The Conversation. Read the original article here. Left: A skeleton discovered at a ruined pyramid in Tlateloco in Mexico City February 10, 2009. Archaeologists have discovered a mass grave with four dozen neatly lined up human skeletons in the heart of Mexico City, revealing clues about the Spanish conquest that killed millions in battle and disease. The 49 bodies, all lying face up with their arms crossed over their chests, were discovered as investigators searched for a palace complex in the Tlatelolco area, once a major religious and political center for the Aztec elite. Photo By Daniel Aguilar/Reuters Archaeology is the study of the human past using material remains. These remains can be any objects that people created, modified, or used. Arts and Music, Geography, Human Geography, Physical Geography, Social Studies, World History This lists the logos of programs or partners of NG Education which have provided or contributed the content on this page. Leveled by Archaeology is the study of the human past using material remains. These remains can be any objects that people created, modified, or used. Portable remains are usually called artifacts. Artifacts include tools, clothing, and decorations. Non-portable remains, such as pyramids or post-holes, are called features. Archaeologists use artifacts and features to learn how people lived in specific times and places. They want to know what these people&rsquos daily lives were like, how they were governed, how they interacted with each other, and what they believed and valued. Sometimes, artifacts and features provide the only clues about an ancient community or civilization. Prehistoric civilizations did not leave behind written records, so we cannot read about them. Understanding why ancient cultures built the giant stone circles at Stonehenge, England, for instance, remains a challenge 5,000 years after the first monoliths were erected. Archaeologists studying Stonehenge do not have ancient manuscripts to tell them how cultures used the feature. They rely on the enormous stones themselves&mdashhow they are arranged and the way the site developed over time. Most cultures with writing systems leave written records that archaeologists consult and study. Some of the most valuable written records are everyday items, such as shopping lists and tax forms. Latin, the language of ancient Rome, helps archaeologists understand artifacts and features discovered in parts of the Roman Empire. The use of Latin shows how far the empire&rsquos influence extended, and the records themselves can tell archaeologists what foods were available in an area, how much they cost, and what buildings belonged to families or businesses. Many ancient civilizations had complex writing systems that archaeologists and linguists are still working to decipher. The written system of the Mayan language, for instance, remained a mystery to scholars until the 20th century. The Maya were one of the most powerful pre-Columbian civilizations in North America, and their Central American temples and manuscripts are inscribed with a collection of squared glyphs, or symbols. A series of circles and lines represents numbers. By deciphering the Mayan script, archaeologists were able to trace the ancestry of Mayan kings and chart the development of their calendar and agricultural seasons. Understanding the basics of the Mayan writing system helps archaeologists discover how Mayan culture functioned&mdashhow they were governed, how they traded with some neighbors and went to war with others, what they ate, and what gods they worshipped. As archaeologists become more fluent in Mayan writing, they are making new discoveries about the culture every day. Today, some archaeologists work with linguists and poets to preserve the once-lost Mayan language. History of Archaeology The word &ldquoarchaeology&rdquo comes from the Greek word &ldquoarkhaios,&rdquo which means &ldquoancient.&rdquo Although some archaeologists study living cultures, most archaeologists concern themselves with the distant past. People have dug up monuments and collected artifacts for thousands of years. Often, these people were not scholars, but looters and grave robbers looking to make money or build up their personal collections. For instance, grave robbers have been plundering the magnificent tombs of Egypt since the time the Pyramids were built. Grave robbing was such a common crime in ancient Egypt that many tombs have hidden chambers where the family of the deceased would place treasures. In Egypt in the mid-1800s, an Egyptian man searching for a lost goat stumbled across the tomb of Pharaoh Ramses I. (Many archaeologists doubt this story and say grave robbers, working as an organized group, routinely scouted and plundered many tombs in the area.) Ramses I ruled for a short time in the 1290s BCE. Besides the body of the pharaoh, the tomb held artifacts such as pottery, paintings, and sculpture. The man sold the mummies and artifacts from the tomb to anyone who would pay. The mummy of Ramses I wound up in a museum in Niagara Falls, Ontario, Canada, where it remained until the museum closed in 1999. The Canadian museum sold the Egyptian collection to the Michael C. Carlos Museum in Atlanta, Georgia, which confirmed the mummy&rsquos royal status through the use of CT scanners, X-rays, radiocarbon dating, computer imaging, and other techniques. Ramses I was returned to Egypt in 2003. One of the most well-known archaeological finds is the tomb of Pharaoh Tutankhamun, also known as King Tut. Unlike many other Egyptian tombs, grave robbers had never discovered King Tut. His resting place lay undisturbed for thousands of years, until it was discovered in 1922. In addition to mummies of Tutankhamun and his family, the tomb contained some 5,000 artifacts. Many early archaeologists worked in the service of invading armies. When Gen. Napoleon Bonaparte of France successfully invaded Egypt in 1798, he brought artists, archaeologists, and historians to document the conquest. Napoleon&rsquos troops took home hundreds of tons of Egyptian artifacts: columns, coffins, stone tablets, monumental statues. Today, these Egyptian antiquities take up entire floors of the Louvre Museum in Paris, France. Some archaeologists of this time were wealthy adventurers, explorers, and merchants. These amateur archaeologists often had a sincere interest in the culture and artifacts they studied. However, their work is often regarded as an example of colonialism and exploitation. The so-called Elgin Marbles are an example of this controversy. In 1801, Greece had been taken over by the Ottoman Empire. The British ambassador to the Ottoman Empire, Lord Elgin, received permission to remove half of the sculptures from the famous Acropolis of Athens, Greece. These marble sculptures were a part of buildings such as the Parthenon. Lord Elgin claimed he wanted to protect the valuable sculptures from damage caused by conflict between the Greeks and the Ottomans. The government of Greece has been lobbying for the return of the Elgin Marbles ever since. Most Greeks view the sculptures as part of their cultural heritage. Greece has cut off diplomatic relations to the United Kingdom several times, demanding the return of the sculptures, which remain in the British Museum in London. Eventually, archaeology evolved into a more systematic discipline. Scientists started using standard weights and measures and other formalized methods for recording and removing artifacts. They required detailed drawings and drafts of the entire dig site, as well as individual pieces. Archaeologists began to work with classicists, historians, and linguists to develop a unified picture of the past. In the 20th century, archaeologists began to re-assess their impact on the cultures and environments where they dig. Today, in most countries, archaeological remains become the property of the country where they were found, regardless of who finds them. Egypt, for example, is scattered with archaeological sites sponsored by American universities. These teams must obtain permission from the Egyptian government to dig at the sites, and all artifacts become the property of Egypt. Disciplines of Archaeology Archaeology is based on the scientific method. Archaeologists ask questions and develop hypotheses. They use evidence to choose a dig site, then use scientific sampling techniques to select where on the site to dig. They observe, record, categorize, and interpret what they find. Then they share their results with other scientists and the public. Underwater archaeologists study materials at the bottom of lakes, rivers, and oceans. Underwater archaeology encompasses any prehistoric and historic periods, and almost all sub-disciplines as archaeology. Artifacts and features are simply submerged. Artifacts studied by underwater archaeologists could be the remains of a shipwreck. In 1985, National Geographic Explorer-in-Residence Dr. Robert Ballard helped locate the wreck of RMS Titanic, which sank in the North Atlantic Ocean in 1912, killing about 1,500 people. Ballard and other scientists used sonar to locate the wreck, which had been lost since the ocean liner sank. By exploring Titanic using remote-controlled cameras, Ballard and his crew discovered facts about the shipwreck (such as the fact the ship broke in two large pieces as it sank) as well as hundreds of artifacts, such as furniture, lighting fixtures, and children&rsquos toys. Underwater archaeology includes more than just shipwrecks, however. Sites include hunt camps on the continental shelf of the Gulf of Mexico, and portions of the ancient city of Alexandria, Egypt, submerged due to earthquakes and sea level rise. This basic framework carries across many different disciplines, or areas of study, within archaeology. Prehistoric and Historic Archaeology There are two major disciplines of archaeology: prehistoric archaeology and historic archaeology. Within these groups are subdisciplines, based on the time period studied, the civilization studied, or the types of artifacts and features studied. Prehistoric archaeology deals with civilizations that did not develop writing. Artifacts from these societies may provide the only clues we have about their lives. Archaeologists studying the Clovis people, for instance, have only arrowheads&mdashcalled projectile points&mdash and stone tools as artifacts. The unique projectile points were first discovered in Clovis, New Mexico, in the United States, and the culture was named after the town. So-called Clovis points establish the Clovis people as one of the first inhabitants of North America. Archaeologists have dated Clovis points to about 13,000 years ago. A subdiscipline of prehistoric archaeology is paleopathology. Paleopathology is the study of disease in ancient cultures. (Paleopathology is also a subdiscipline of historical archaeology.) Paleopathologists may investigate the presence of specific diseases, what areas lacked certain diseases, and how different communities reacted to disease. By studying the history of a disease, paleopathologists may contribute to an understanding of the way modern diseases progress. Paleopathologists can also find clues about people&rsquos overall health. By studying the teeth of ancient people, for example, paleopathologists can deduce what kinds of food they ate, how often they ate, and what nutrients the foods contained. Historic archaeology incorporates written records into archaeological research. One of the most famous examples of historic archaeology is the discovery and decipherment of the Rosetta Stone. The Rosetta Stone is a large slab of marble discovered near Rashid, Egypt, by French archaeologists in 1799. It became an important tool of historic archaeology. The stone is inscribed with a decree made on behalf of Pharaoh Ptolemy V. The decree was written and carved into the stone in three different languages: hieroglyphic, demotic, and Greek. Hieroglyphics are the picture-symbols used for formal documents in ancient Egypt. Demotic is the informal script of ancient Egypt. Before the discovery of the Rosetta Stone, Egyptologists did not understand hieroglyphics or demotic. They could, however, understand Greek. Using the Greek portion of the Rosetta Stone, archaeologists and linguists were able to translate the text and decipher hieroglyphs. This knowledge has contributed vastly to our understanding of Egyptian history. Historic archaeology contributes to many disciplines, including religious studies. The Dead Sea Scrolls, for instance, are a collection of about 900 documents. The tightly rolled parchment and other writing sheets were found between 1947 and 1956 in 11 caves near Qumran, West Bank, near the Dead Sea. Among the scrolls are texts from the Hebrew Bible, written in Hebrew, Aramaic, and Greek. The Dead Sea Scrolls are the oldest versions of Biblical texts ever found, dating from between the third century BCE to the first century CE. The scrolls also contain texts, psalms, and prophecies that are not part of today&rsquos Bible. Discovery of the scrolls has increased our knowledge of the development of Judaism and Christianity. A subdiscipline of historic archaeology is industrial archaeology. Industrial archaeologists study materials that were created or used after the Industrial Revolution of the 1700s and 1800s. The Industrial Revolution was strongest in Western Europe and North America, so most industrial archaeologists study artifacts found there. One of the most important sites for industrial archaeologists is the Ironbridge Gorge in Shropshire, England. The River Severn runs through the gorge, and during the Industrial Revolution, it allowed for the transport of raw materials such as coal, limestone, and iron. In fact, the world&rsquos first iron bridge spans the Severn there. By studying artifacts and features (such as the iron bridge), industrial archaeologists are able to trace the area&rsquos economic development as it moved from agriculture to manufacturing and trade. Ethnoarchaeologists study how people use and organize objects today. They use this knowledge to understand how people used tools in the past. Archaeologists researching the ancient San culture of southern Africa, for instance, study the way modern San culture functions. Until the mid-20th century, the San, maintained a somewhat nomadic lifestyle based on hunting and gathering. Although the San culture had evolved significantly, archaeologists studying the tools of the modern San could still study the way ancient San tracked and hunted animals and gathered native plants. Environmental archaeologists help us understand the environmental conditions that influenced people in the past. Sometimes, environmental archaeology is called human paleoecology. Environmental archaeologists discovered that the expansion of the Taquara/Itararé people of the Brazilian highlands is closely linked with the expansion of the evergreen forest there. The forest grew as the climate became wetter. As the forest provided more resources to the Taquara/Itararé people (timber, as well as plants and animals that depended on the evergreen trees), they were able to expand their territory. Experimental archaeologists replicate the techniques and processes people used to create or use objects in the past. Often, re-creating an ancient workshop or home helps experimental archaeologists understand the process or method used by ancient people to create features or artifacts. One of the most famous examples of experimental archaeology is the Kon-Tiki, a large raft built by Norwegian explorer Thor Heyerdahl. In 1947, Heyerdahl sailed the Kon-Tiki from South America to Polynesia to show that ancient mariners, with the same tools and technology, could have navigated the vast Pacific Ocean. Forensic archaeologists sometimes work with geneticists to support or question DNA evidence. More often, they excavate the remains of victims of murder or genocide in areas of conflict. Forensic archaeology is important to the understanding of the &ldquoKilling Fields&rdquo of Cambodia, for instance. The Killing Fields are the sites of mass graves of thousands of victims of the Khmer Rouge regime of the 1970s. After the fall of the Khmer Rouge, forensic archaeologists studied the remains of the bodies in the Killing Fields, discovering how and when they died. The forensic archaeologists helped establish that the Khmer Rouge used starvation and overwork, as well as direct killing, to silence opponents of the regime. Archaeologists working in the field of cultural resource management help assess and preserve remains on sites where construction is scheduled to occur. Archaeologists working as cultural resource managers often collaborate with local governments to balance the infrastructure and commercial needs of a community with historic and cultural interests represented by artifacts and features found on construction sites. Where to Dig? Most archaeology involves digging. Winds and floods carry sand, dust and soil, depositing them on top of abandoned features and artifacts. These deposits build up over time, burying the remains. Sometimes catastrophes, like volcanic eruptions, speed up this burial process. In places where earth has been carved away&mdashlike in the Grand Canyon in the U.S. state of Arizona&mdashyou can actually see the layers of soil that have built up over the centuries, like layers of a cake. Cities and communities also tend to be built in layers. Rome, Italy, has been an urban center for thousands of years. The streets of downtown Rome today are several meters higher than they were during the time of Julius Caesar. Centuries of Romans have built it up&mdashmedieval home on top of ancient home, modern home on top of medieval home. Establishing a dig site in an inhabited area can be a very difficult process. Not only are the inhabitants of the area inconvenienced, archaeologists don&rsquot know what they may find. Archaeologists looking for an ancient Roman fortress, for instance, may have to first excavate a Renaissance bakery and medieval hospital. Because most artifacts lie underground, scientists have developed methods to help them figure out where they should dig. Sometimes they choose sites based on old myths and stories about where people lived or where events occurred. The ancient city of Troy, written about by Greek poet Homer as early as 1190 BCE, was thought to be a work of fiction. Homer&rsquos epic poem the Iliad was named after Troy, which the Greeks knew as Ilion. Using the Iliad as a guide, German amateur archaeologist Heinrich Schliemann discovered the ruins of the city near the town of Hisarlik, Turkey, in 1870. Schliemann&rsquos find helped provide evidence that the Trojan War may have actually taken place, and that ancient manuscripts may be based on fact. Sometimes, archaeologists use historical maps to find ancient artifacts. In 1973, for instance, archaeologists used historical maps and modern technology to locate the wreck of the USS Monitor, an &ldquoironclad&rdquo ship used by the Union during the Civil War. The Monitor sunk in a storm off the coast of Cape Hatteras, North Carolina, in 1862. After archaeologists identified the ironclad, the United States designated the area as the nation&rsquos first marine sanctuary. Before securing a site, an archaeological team surveys the area, looking for signs of remains. These might include artifacts on the ground or unusual mounds in the earth. New technology has greatly increased their ability to survey an area. For example, aerial and satellite imagery can show patterns that might not be visible from the ground. Other technologies give clues about what lies under the surface. These techniques involve radar and sonar. Radar and sonar technologies often use radio waves, electrical currents, and lasers. Archaeologists send these signals into the earth. As the signals hit something solid, they bounce back up to the surface. Scientists study the time and paths the signals take to familiarize themselves with the underground landscape. Accidental finds can also lead archaeologists to dig sites. For instance, farmers plowing their fields might come across sherds of pottery. A construction crew might discover ruins beneath a building site. Another monumental discovery was made by accident. In 1974, agricultural workers in Xian, China, were digging a well. They discovered the remains of what turned out to be an enormous mausoleum for Qin Shi Huangdi, China&rsquos first emperor. The complex includes 8,000 life-sized clay soldiers, horses, chariots, and artillery, popularly known as the Terra Cotta Warriors. The archaeological research surrounding the Terra Cotta Warriors has provided insight on the organization and leadership style of Qin Shi Huangdi and the development of Chinese culture. Once a site is chosen, archaeologists must get permission to dig from the landowner. If it is public land, they must obtain the proper permits from the local, state, or federal government. Before moving a single grain of dirt, archaeologists make maps of the area and take detailed photographs. Once they begin digging, they will destroy the original landscape, so it is important to record how things looked beforehand. The last step before digging is to divide the site into a grid to keep track of the location of each find. Then archaeologists choose sample squares from the grid to dig. This allows the archaeological team to form a complete study of the area. They also leave some plots on the grid untouched. Archaeologists like to preserve portions of their dig sites for future scientists to study&mdashscientists who may have better tools and techniques than are available today. For example, during the Great Depression in the 1930s, programs to create jobs led to many archaeological digs around the United States. Some scientists on these digs removed artifacts, such as pottery, but threw away charcoal and animal bones. These items were considered junk. Today, scientists are able to carbon-date the charcoal and analyze the bones to see what kinds of animals people were domesticating and eating at the time. It is important that archaeologists today keep some parts of each site pristine. Not all archaeology involves digging in the earth. Archaeologists and engineers work with sophisticated technology to probe the earth below without disturbing the ground. National Geographic Emerging Explorer Dr. Albert Yu-Min Lin leads an innovative archaeological project centered in Mongolia. The Valley of the Khans project is using digital imaging, aerial photography, radar, and digital surveying to locate the tomb of Genghis Khan. Using satellite technology, Lin and his team can access information about the project without disturbing the land or even going to Mongolia. The Big Dig The process of researching and securing a dig site can take years. Digging is the field work of archaeology. On occasion, archaeologists might need to move earth with bulldozers and backhoes. Usually, however, archaeologists use tools such as brushes, hand shovels, and even toothbrushes to scrape away the earth around artifacts. The most common tool that archaeologists use to dig is a flat trowel. A trowel is a hand-held shovel used for smoothing as well as digging. Archaeologists use trowels to slowly scrape away soil. For very small or delicate remains, archaeologists might also dig with dental picks, spoons, or very fine blades. Often, they will sift dirt through a fine mesh screen. Tiny remains, such as beads, can often be found this way. Archaeologists take lots of notes and photographs along each step of the process. Sometimes they include audio and video recordings. Global positioning system (GPS) units and data from geographic information systems (GIS) help them map the location of various features with a high level of precision. When archaeologists find remains, they are often broken or damaged after hundreds or even thousands of years underground. Sunlight, rain, soil, animals, bacteria, and other natural processes can cause artifacts to erode, rust, rot, break, and warp. Sometimes, however, natural processes can help preserve materials. For example, sediments from floods or volcanic eruptions can encase materials and preserve them. In one case, the chill of an Alpine glacier preserved the body of a man for more than 5,300 years! The discoverer of the so-called &ldquoIceman,&rdquo found in the Alps between Switzerland and Italy, thought he was a recent victim of murder, or one of the glacier&rsquos crevasses. Forensic archaeologists studying his body were surprised to learn that he was a murder victim&mdashthe crime just took place more than 5,000 years ago. As artifacts are uncovered, the archaeological team records every step of the process through photos, drawings, and notes. Once the artifacts have been completely removed, they are cleaned, labeled, and classified. Particularly fragile or damaged artifacts are sent to a conservator. Conservators have special training in preserving and restoring artifacts so they are not destroyed when exposed to air and light. Textiles, including clothing and bedding, are especially threatened by exposure. Textile conservators must be familiar with climate, as well as the chemical composition of the cloth and dyes, in order to preserve the artifacts. In 1961, Swedish archaeologists recovered the ship Vasa, which sank in 1628. Conservators protected the delicate oak structure of Vasa by spraying it with polyethylene glycol (PEG). The ship was sprayed with PEG for 17 years, and allowed to dry for nine. Today, Vasa sits in its own enormous museum, a hallmark of Swedish heritage. Then the artifacts are sent to a lab for analysis. This is usually the most time-consuming part of archaeology. For every day spent digging, archaeologists spend several weeks processing their finds in the lab. All of this analysis&mdashcounting, weighing, categorizing&mdashis necessary. Archaeologists use the information they find and combine it with what other scientists have discovered. They use the combined data to add to the story of humanity&rsquos past. When did people develop tools, and how did they use them? What did they use to make clothing? Did their clothing styles indicate their social ranks and roles? What did they eat? Did they live in large groups or smaller family units? Did they trade with people from other regions? Were they warlike or peaceful? What were their religious practices? Archaeologists ask all of these questions and more. The scientists write up their findings and publish them in scientific journals. Other scientists can look at the data and debate the interpretations, helping us get the most accurate story. Publication also lets the public know what scientists are learning about our history. Photograph by Richard Hewitt Stewart Sherds and Shards Many archaeologists study broken bits of pottery. These fragments are called potsherds, and sometimes just sherds. Sherds can be anything from bits of a broken water jug to a piece of a clay tablet to the components of China's "Terra Cotta Warriors." Shards are broken bits of glass, which are also important to archaeology. Shards include fragments of ancient windows, wine bottles, and jewelry. Most archaeologists study the past, but some study people who are still alive. For example, Dr. William Rathje uses his archaeological skills to dig through present-day garbage bins and landfills to learn about what Americans consume, discard, and waste. Some ancient humans may have indulged in cannibalism on a regular basis. Archaeologists discovered 800,000-year-old remains from an early human species, Homo antecessor, in a Spanish cave. Among the remains were human bones with marks on them that appear to come from stone tools used to prepare meals. The ABCs of Dating Sometimes dates are listed as BC or AD. Other times they show up as BCE or CE. What is the difference? BC stands for Before Christ, and it is used to date events that happened before the birth of Jesus, whom Christians consider the son of God. AD refers to Anno Domini, Latin for year of our Lord, and refers to all the years from Jesus birth onward. In the late 20th century, scientists realized they were basing the entire history of the world around the birth of one religious figure. Many archeologists now prefer the terms BCE (Before Common Era) and CE (Common Era). The dates are still the same, only the letters have changed. The Nahuatl words (aztecatl [asˈtekat͡ɬ] , singular) and (aztecah [asˈtekaʔ] , plural) mean "people from Aztlan," a mythical place of origin for several ethnic groups in central Mexico. The term was not used as an endonym by Aztecs themselves, but it is found in the different migration accounts of the Mexica, where it describes the different tribes who left Aztlan together. In one account of the journey from Aztlan, Huitzilopochtli, the tutelary deity of the Mexica tribe, tells his followers on the journey that "now, no longer is your name Azteca, you are now Mexitin [Mexica]". In today's usage, the term "Aztec" often refers exclusively to the Mexica people of Tenochtitlan (now the location of Mexico City), situated on an island in Lake Texcoco, who referred to themselves as Mēxihcah (Nahuatl pronunciation: [meːˈʃiʔkaʔ] , a tribal designation that included the Tlatelolco), Tenochcah (Nahuatl pronunciation: [teˈnot͡ʃkaʔ] , referring only to the Mexica of Tenochtitlan, excluding Tlatelolco) or Cōlhuah (Nahuatl pronunciation: [ˈkoːlwaʔ] , referring to their royal genealogy tying them to Culhuacan). [nb 1] [nb 2] Sometimes the term also includes the inhabitants of Tenochtitlan's two principal allied city-states, the Acolhuas of Texcoco and the Tepanecs of Tlacopan, who together with the Mexica formed the Aztec Triple Alliance that controlled what is often known as the "Aztec Empire." The usage of the term "Aztec" in describing the empire centered in Tenochtitlan, has been criticized by Robert H. Barlow who preferred the term "Culhua-Mexica", and by Pedro Carrasco who prefers the term "Tenochca empire." Carrasco writes about the term "Aztec" that "it is of no use for understanding the ethnic complexity of ancient Mexico and for identifying the dominant element in the political entity we are studying." In other contexts, Aztec may refer to all the various city states and their peoples, who shared large parts of their ethnic history and cultural traits with the Mexica, Acolhua and Tepanecs, and who often also used the Nahuatl language as a lingua franca. An example is Jerome A. Offner's Law and Politics in Aztec Texcoco. In this meaning, it is possible to talk about an "Aztec civilization" including all the particular cultural patterns common for most of the peoples inhabiting central Mexico in the late postclassic period. Such a usage may also extend the term "Aztec" to all the groups in Central Mexico that were incorporated culturally or politically into the sphere of dominance of the Aztec empire. [nb 3] When used to describe ethnic groups, the term "Aztec" refers to several Nahuatl-speaking peoples of central Mexico in the postclassic period of Mesoamerican chronology, especially the Mexica, the ethnic group that had a leading role in establishing the hegemonic empire based at Tenochtitlan. The term extends to further ethnic groups associated with the Aztec empire, such as the Acolhua, the Tepanec and others that were incorporated into the empire. Charles Gibson enumerates a number of groups in central Mexico that he includes in his study The Aztecs Under Spanish Rule (1964). These include the Culhuaque, Cuitlahuaque, Mixquica, Xochimilca, Chalca, Tepaneca, Acolhuaque, and Mexica. In older usage the term was commonly used about modern Nahuatl-speaking ethnic groups, as Nahuatl was previously referred to as the "Aztec language". In recent usage, these ethnic groups are referred to as the Nahua peoples. Linguistically, the term "Aztecan" is still used about the branch of the Uto-Aztecan languages (also sometimes called the yuto-nahuan languages) that includes the Nahuatl language and its closest relatives Pochutec and Pipil. To the Aztecs themselves the word "aztec" was not an endonym for any particular ethnic group. Rather, it was an umbrella term used to refer to several ethnic groups, not all of them Nahuatl-speaking, that claimed heritage from the mythic place of origin, Aztlan. Alexander von Humboldt originated the modern usage of "Aztec" in 1810, as a collective term applied to all the people linked by trade, custom, religion, and language to the Mexica state and the Triple Alliance. In 1843, with the publication of the work of William H. Prescott on the history of the conquest of Mexico, the term was adopted by most of the world, including 19th-century Mexican scholars who saw it as a way to distinguish present-day Mexicans from pre-conquest Mexicans. This usage has been the subject of debate in more recent years, but the term "Aztec" is still more common. Sources of knowledge Knowledge of Aztec society rests on several different sources: The many archeological remains of everything from temple pyramids to thatched huts, can be used to understand many of the aspects of what the Aztec world was like. However, archeologists often must rely on knowledge from other sources to interpret the historical context of artifacts. There are many written texts by the indigenous people and Spaniards of the early colonial period that contain invaluable information about precolonial Aztec history. These texts provide insight into the political histories of various Aztec city-states, and their ruling lineages. Such histories were produced as well in pictorial codices. Some of these manuscripts were entirely pictorial, often with glyphs. In the postconquest era many other texts were written in Latin script by either literate Aztecs or by Spanish friars who interviewed the native people about their customs and stories. An important pictorial and alphabetic text produced in the early sixteenth century was Codex Mendoza, named after the first viceroy of Mexico and perhaps commissioned by him, to inform the Spanish crown about the political and economic structure of the Aztec empire. It has information naming the polities that the Triple Alliance conquered, the types of tribute rendered to the Aztec Empire, and the class/gender structure of their society. Many written annals exist, written by local Nahua historians recording the histories of their polity. These annals used pictorial histories and were subsequently transformed into alphabetic annals in Latin script. Well-known native chroniclers and annalists are Chimalpahin of Amecameca-Chalco Fernando Alvarado Tezozomoc of Tenochtitlan Alva Ixtlilxochitl of Texcoco, Juan Bautista Pomar of Texcoco, and Diego Muñoz Camargo of Tlaxcala. There are also many accounts by Spanish conquerors who participated in Spanish invasion, such as Bernal Díaz del Castillo who wrote a full history of the conquest. Spanish friars also produced documentation in chronicles and other types of accounts. Of key importance is Toribio de Benavente Motolinia, one of the first twelve Franciscans arriving in Mexico in 1524. Another Franciscan of great importance was Fray Juan de Torquemada, author of Monarquia Indiana. Dominican Diego Durán also wrote extensively about prehispanic religion as well as a history of the Mexica. An invaluable source of information about many aspects of Aztec religious thought, political and social structure, as well as history of the Spanish conquest from the Mexica viewpoint is the Florentine Codex. Produced between 1545 and 1576 in the form of an ethnographic encyclopedia written bilingually in Spanish and Nahuatl, by Franciscan friar Bernardino de Sahagún and indigenous informants and scribes, it contains knowledge about many aspects of precolonial society from religion, calendrics, botany, zoology, trades and crafts and history. Another source of knowledge is the cultures and customs of the contemporary Nahuatl speakers who can often provide insights into what prehispanic ways of life may have been like. Scholarly study of Aztec civilization is most often based on scientific and multidisciplinary methodologies, combining archeological knowledge with ethnohistorical and ethnographic information. Central Mexico in the classic and postclassic It is a matter of debate whether the enormous city of Teotihuacan was inhabited by speakers of Nahuatl, or whether Nahuas had not yet arrived in central Mexico in the classic period. It is generally agreed that the Nahua peoples were not indigenous to the highlands of central Mexico, but that they gradually migrated into the region from somewhere in northwestern Mexico. At the fall of Teotihuacan in the 6th century CE, a number of city states rose to power in central Mexico, some of them, including Cholula and Xochicalco, probably inhabited by Nahuatl speakers. One study has suggested that Nahuas originally inhabited the Bajío area around Guanajuato which reached a population peak in the 6th century, after which the population quickly diminished during a subsequent dry period. This depopulation of the Bajío coincided with an incursion of new populations into the Valley of Mexico, which suggests that this marks the influx of Nahuatl speakers into the region. These people populated central Mexico, dislocating speakers of Oto-Manguean languages as they spread their political influence south. As the former nomadic hunter-gatherer peoples mixed with the complex civilizations of Mesoamerica, adopting religious and cultural practices, the foundation for later Aztec culture was laid. After 900 CE, during the postclassic period, a number of sites almost certainly inhabited by Nahuatl speakers became powerful. Among them the site of Tula, Hidalgo, and also city states such as Tenayuca, and Colhuacan in the valley of Mexico and Cuauhnahuac in Morelos. Mexica migration and foundation of Tenochtitlan In the ethnohistorical sources from the colonial period, the Mexica themselves describe their arrival in the Valley of Mexico. The ethnonym Aztec (Nahuatl Aztecah) means "people from Aztlan", Aztlan being a mythical place of origin toward the north. Hence the term applied to all those peoples who claimed to carry the heritage from this mythical place. The migration stories of the Mexica tribe tell how they traveled with other tribes, including the Tlaxcalteca, Tepaneca and Acolhua, but that eventually their tribal deity Huitzilopochtli told them to split from the other Aztec tribes and take on the name "Mexica". At the time of their arrival, there were many Aztec city-states in the region. The most powerful were Colhuacan to the south and Azcapotzalco to the west. The Tepanecs of Azcapotzalco soon expelled the Mexica from Chapultepec. In 1299, Colhuacan ruler Cocoxtli gave them permission to settle in the empty barrens of Tizapan, where they were eventually assimilated into Culhuacan culture. The noble lineage of Colhuacan traced its roots back to the legendary city-state of Tula, and by marrying into Colhua families, the Mexica now appropriated this heritage. After living in Colhuacan, the Mexica were again expelled and were forced to move. According to Aztec legend, in 1323, the Mexica were shown a vision of an eagle perched on a prickly pear cactus, eating a snake. The vision indicated the location where they were to build their settlement. The Mexica founded Tenochtitlan on a small swampy island in Lake Texcoco, the inland lake of the Basin of Mexico. The year of foundation is usually given as 1325. In 1376 the Mexica royal dynasty was founded when Acamapichtli, son of a Mexica father and a Colhua mother, was elected as the first Huey Tlatoani of Tenochtitlan. Early Mexica rulers In the first 50 years after the founding of the Mexica dynasty, the Mexica were a tributary of Azcapotzalco, which had become a major regional power under the ruler Tezozomoc. The Mexica supplied the Tepaneca with warriors for their successful conquest campaigns in the region and received part of the tribute from the conquered city states. In this way, the political standing and economy of Tenochtitlan gradually grew. In 1396, at Acamapichtli's death, his son Huitzilihhuitl (lit. "Hummingbird feather") became ruler married to Tezozomoc's daughter, the relation with Azcapotzalco remained close. Chimalpopoca (lit. "She smokes like a shield"), son of Huitzilihhuitl, became ruler of Tenochtitlan in 1417. In 1418, Azcapotzalco initiated a war against the Acolhua of Texcoco and killed their ruler Ixtlilxochitl. Even though Ixtlilxochitl was married to Chimalpopoca's daughter, the Mexica ruler continued to support Tezozomoc. Tezozomoc died in 1426, and his sons began a struggle for rulership of Azcapotzalco. During this struggle for power, Chimalpopoca died, probably killed by Tezozomoc's son Maxtla who saw him as a competitor. Itzcoatl, brother of Huitzilihhuitl and uncle of Chimalpopoca, was elected the next Mexica tlatoani. The Mexica were now in open war with Azcapotzalco and Itzcoatl petitioned for an alliance with Nezahualcoyotl, son of the slain Texcocan ruler Ixtlilxochitl against Maxtla. Itzcoatl also allied with Maxtla's brother Totoquihuaztli ruler of the Tepanec city of Tlacopan. The Triple Alliance of Tenochtitlan, Texcoco and Tlacopan besieged Azcapotzalco, and in 1428 they destroyed the city and sacrificed Maxtla. Through this victory Tenochtitlan became the dominant city state in the Valley of Mexico, and the alliance between the three city-states provided the basis on which the Aztec Empire was built. Itzcoatl proceeded by securing a power basis for Tenochtitlan, by conquering the city-states on the southern lake – including Culhuacan, Xochimilco, Cuitlahuac and Mizquic. These states had an economy based on highly productive chinampa agriculture, cultivating human-made extensions of rich soil in the shallow lake Xochimilco. Itzcoatl then undertook further conquests in the valley of Morelos, subjecting the city state of Cuauhnahuac (today Cuernavaca). Early rulers of the Aztec Empire Motecuzoma I Ilhuicamina In 1440, Motecuzoma I Ilhuicamina [nb 4] (lit. "he frowns like a lord, he shoots the sky" [nb 5] ) was elected tlatoani he was son of Huitzilihhuitl, brother of Chimalpopoca and had served as the war leader of his uncle Itzcoatl in the war against the Tepanecs. The accession of a new ruler in the dominant city state was often an occasion for subjected cities to rebel by refusing to pay tribute. This meant that new rulers began their rule with a coronation campaign, often against rebellious tributaries, but also sometimes demonstrating their military might by making new conquests. Motecuzoma tested the attitudes of the cities around the valley by requesting laborers for the enlargement of the Great Temple of Tenochtitlan. Only the city of Chalco refused to provide laborers, and hostilities between Chalco and Tenochtitlan would persist until the 1450s. Motecuzoma then reconquered the cities in the valley of Morelos and Guerrero, and then later undertook new conquests in the Huaxtec region of northern Veracruz, and the Mixtec region of Coixtlahuaca and large parts of Oaxaca, and later again in central and southern Veracruz with conquests at Cosamalopan, Ahuilizapan and Cuetlaxtlan. During this period the city states of Tlaxcalan, Cholula and Huexotzinco emerged as major competitors to the imperial expansion, and they supplied warriors to several of the cities conquered. Motecuzoma therefore initiated a state of low-intensity warfare against these three cities, staging minor skirmishes called "Flower Wars" (Nahuatl xochiyaoyotl) against them, perhaps as a strategy of exhaustion. Motecuzoma also consolidated the political structure of the Triple Alliance, and the internal political organization of Tenochtitlan. His brother Tlacaelel served as his main advisor (Nahuatl languages: Cihuacoatl) and he is considered the architect of major political reforms in this period, consolidating the power of the noble class (Nahuatl languages: pipiltin) and instituting a set of legal codes, and the practice of reinstating conquered rulers in their cities bound by fealty to the Mexica tlatoani. Axayacatl and Tizoc In 1469, the next ruler was Axayacatl (lit. "Water mask"), son of Itzcoatl's son Tezozomoc and Motecuzoma I's daughter Atotoztli. [nb 6] He undertook a successful coronation campaign far south of Tenochtitlan against the Zapotecs in the Isthmus of Tehuantepec. Axayacatl also conquered the independent Mexica city of Tlatelolco, located on the northern part of the island where Tenochtitlan was also located. The Tlatelolco ruler Moquihuix was married to Axayacatl's sister, and his alleged mistreatment of her was used as an excuse to incorporate Tlatelolco and its important market directly under the control of the tlatoani of Tenochtitlan. Axayacatl then conquered areas in Central Guerrero, the Puebla Valley, on the gulf coast and against the Otomi and Matlatzinca in the Toluca valley. The Toluca valley was a buffer zone against the powerful Tarascan state in Michoacan, against which Axayacatl turned next. In the major campaign against the Tarascans (Nahuatl languages: Michhuahqueh) in 1478–79 the Aztec forces were repelled by a well organized defense. Axayacatl was soundly defeated in a battle at Tlaximaloyan (today Tajimaroa), losing most of his 32,000 men and only barely escaping back to Tenochtitlan with the remnants of his army. In 1481 at Axayacatls death, his older brother Tizoc was elected ruler. Tizoc's coronation campaign against the Otomi of Metztitlan failed as he lost the major battle and only managed to secure 40 prisoners to be sacrificed for his coronation ceremony. Having shown weakness, many of the tributary towns rebelled and consequently most of Tizoc's short reign was spent attempting to quell rebellions and maintain control of areas conquered by his predecessors. Tizoc died suddenly in 1485, and it has been suggested that he was poisoned by his brother and war leader Ahuitzotl who became the next tlatoani. Tizoc is mostly known as the namesake of the Stone of Tizoc a monumental sculpture (Nahuatl temalacatl), decorated with representation of Tizoc's conquests. Final Aztec rulers and the Spanish conquest In 1517, Moctezuma received the first news of ships with strange warriors having landed on the Gulf Coast near Cempoallan and he dispatched messengers to greet them and find out what was happening, and he ordered his subjects in the area to keep him informed of any new arrivals. In 1519, he was informed of the arrival of the Spanish fleet of Hernán Cortés, who soon marched towards Tlaxcala where he formed an alliance with the traditional enemies of the Aztecs. On 8 November 1519, Moctezuma II received Cortés and his troops and Tlaxcalan allies on the causeway south of Tenochtitlan, and he invited the Spaniards to stay as his guests in Tenochtitlan. When Aztec troops destroyed a Spanish camp on the gulf coast, Cortés ordered Moctezuma to execute the commanders responsible for the attack, and Moctezuma complied. At this point, the power balance had shifted towards the Spaniards who now held Motecuzoma as a prisoner in his own palace. As this shift in power became clear to Moctezuma's subjects, the Spaniards became increasingly unwelcome in the capital city, and in June 1520, hostilities broke out, culminating in the massacre in the Great Temple, and a major uprising of the Mexica against the Spanish. During the fighting, Moctezuma was killed, either by the Spaniards who killed him as they fled the city or by the Mexica themselves who considered him a traitor. Cuitláhuac, a kinsman and adviser to Moctezuma, succeeded him as tlatoani, mounting the defense of Tenochtitlan against the Spanish invaders and their indigenous allies. He ruled only 80 days, perhaps dying in a smallpox epidemic, although early sources do not give the cause. He was succeeded by Cuauhtémoc, the last independent Mexica tlatoani, who continued the fierce defense of Tenochtitlan. The Aztecs were weakened by disease, and the Spanish enlisted tens of thousands of Indian allies, especially Tlaxcalans, for the assault on Tenochtitlan. After the siege and complete destruction of the Aztec capital, Cuahtémoc was captured on 13 August 1521, marking the beginning of Spanish hegemony in central Mexico. Spaniards held Cuauhtémoc captive until he was tortured and executed on the orders of Cortés, supposedly for treason, during an ill-fated expedition to Honduras in 1525. His death marked the end of a tumultuous era in Aztec political history. Nobles and commoners The highest class were the pīpiltin [nb 7] or nobility. The pilli status was hereditary and ascribed certain privileges to its holders, such as the right to wear particularly fine garments and consume luxury goods, as well as to own land and direct corvée labor by commoners. The most powerful nobles were called lords (Nahuatl languages: teuctin) and they owned and controlled noble estates or houses, and could serve in the highest government positions or as military leaders. Nobles made up about 5% of the population. The second class were the mācehualtin, originally peasants, but later extended to the lower working classes in general. Eduardo Noguera estimates that in later stages only 20% of the population was dedicated to agriculture and food production. The other 80% of society were warriors, artisans and traders. Eventually, most of the mācehuallis were dedicated to arts and crafts. Their works were an important source of income for the city. Macehualtin could become enslaved, (Nahuatl languages: tlacotin) for example if they had to sell themselves into the service of a noble due to debt or poverty, but enslavement was not an inherited status among the Aztecs. Some macehualtin were landless and worked directly for a lord (Nahuatl languages: mayehqueh), whereas the majority of commoners were organized into calpollis which gave them access to land and property. Commoners were able to obtain privileges similar to those of the nobles by demonstrating prowess in warfare. When a warrior took a captive he accrued the right to use certain emblems, weapons or garments, and as he took more captives his rank and prestige increased. Family and gender The Aztec family pattern was bilateral, counting relatives on the father's and mother's side of the family equally, and inheritance was also passed both to sons and daughters. This meant that women could own property just as men, and that women therefore had a good deal of economic freedom from their spouses. Nevertheless, Aztec society was highly gendered with separate gender roles for men and women. Men were expected to work outside of the house, as farmers, traders, craftsmen and warriors, whereas women were expected to take the responsibility of the domestic sphere. Women could however also work outside of the home as small-scale merchants, doctors, priests and midwives. Warfare was highly valued and a source of high prestige, but women's work was metaphorically conceived of as equivalent to warfare, and as equally important in maintaining the equilibrium of the world and pleasing the gods. This situation has led some scholars to describe Aztec gender ideology as an ideology not of a gender hierarchy, but of gender complementarity, with gender roles being separate but equal. Among the nobles, marriage alliances were often used as a political strategy with lesser nobles marrying daughters from more prestigious lineages whose status was then inherited by their children. Nobles were also often polygamous, with lords having many wives. Polygamy was not very common among the commoners and some sources describe it as being prohibited. While the Aztecs did have gender roles associated with "men" and "women" they did not live in strictly a two-gendered society. In fact, there were multiple "third gender" identities that existed throughout their society and came with their own gender roles. The term "third gender" isn't the most precise term that can be used. Rather, their native Nahuatl words such as patlache and cuiloni are more accurate since "third gender" is more of a Western concept. The names for these gender identities are deeply connected to the religious customs of the Aztecs, and as such, did play a large role in Aztec society. Altepetl and calpolli The main unit of Aztec political organization was the city state, in Nahuatl called the altepetl, meaning "water-mountain". Each altepetl was led by a ruler, a tlatoani, with authority over a group of nobles and a population of commoners. The altepetl included a capital which served as a religious center, the hub of distribution and organization of a local population which often lived spread out in minor settlements surrounding the capital. Altepetl were also the main source of ethnic identity for the inhabitants, even though Altepetl were frequently composed of groups speaking different languages. Each altepetl would see itself as standing in a political contrast to other altepetl polities, and war was waged between altepetl states. In this way Nahuatl speaking Aztecs of one Altepetl would be solidary with speakers of other languages belonging to the same altepetl, but enemies of Nahuatl speakers belonging to other competing altepetl states. In the basin of Mexico, altepetl was composed of subdivisions called calpolli, which served as the main organizational unit for commoners. In Tlaxcala and the Puebla valley, the altepetl was organized into teccalli units headed by a lord (Nahuatl languages: tecutli), who would hold sway over a territory and distribute rights to land among the commoners. A calpolli was at once a territorial unit where commoners organized labor and land use, since land was not in private property, and also often a kinship unit as a network of families that were related through intermarriage. Calpolli leaders might be or become members of the nobility, in which case they could represent their calpollis interests in the altepetl government. In the valley of Morelos, archeologist Michael E. Smith estimates that a typical altepetl had from 10,000 to 15,000 inhabitants, and covered an area between 70 and 100 square kilometers. In the Morelos valley, altepetl sizes were somewhat smaller. Smith argues that the altepetl was primarily a political unit, made up of the population with allegiance to a lord, rather than as a territorial unit. He makes this distinction because in some areas minor settlements with different altepetl allegiances were interspersed. Triple Alliance and Aztec Empire The Aztec Empire was ruled by indirect means. Like most European empires, it was ethnically very diverse, but unlike most European empires, it was more of a system of tribute than a single system of government. Ethnohistorian Ross Hassig has argued that Aztec empire is best understood as an informal or hegemonic empire because it did not exert supreme authority over the conquered lands it merely expected tributes to be paid and exerted force only to the degree it was necessary to ensure the payment of tribute. It was also a discontinuous empire because not all dominated territories were connected for example, the southern peripheral zones of Xoconochco were not in direct contact with the center. The hegemonic nature of the Aztec empire can be seen in the fact that generally local rulers were restored to their positions once their city-state was conquered, and the Aztecs did not generally interfere in local affairs as long as the tribute payments were made and the local elites participated willingly. Such compliance was secured by establishing and maintaining a network of elites, related through intermarriage and different forms of exchange. Nevertheless, the expansion of the empire was accomplished through military control of frontier zones, in strategic provinces where a much more direct approach to conquest and control was taken. Such strategic provinces were often exempt from tributary demands. The Aztecs even invested in those areas, by maintaining a permanent military presence, installing puppet-rulers, or even moving entire populations from the center to maintain a loyal base of support. In this way, the Aztec system of government distinguished between different strategies of control in the outer regions of the empire, far from the core in the Valley of Mexico. Some provinces were treated as tributary provinces, which provided the basis for economic stability for the empire, and strategic provinces, which were the basis for further expansion. Although the form of government is often referred to as an empire, in fact most areas within the empire were organized as city-states, known as altepetl in Nahuatl. These were small polities ruled by a hereditary leader (tlatoani) from a legitimate noble dynasty. The Early Aztec period was a time of growth and competition among altepetl. Even after the confederation of the Triple Alliance was formed in 1427 and began its expansion through conquest, the altepetl remained the dominant form of organization at the local level. The efficient role of the altepetl as a regional political unit was largely responsible for the success of the empire's hegemonic form of control. Agriculture and subsistence As all Mesoamerican peoples, Aztec society was organized around maize agriculture. The humid environment in the Valley of Mexico with its many lakes and swamps permitted intensive agriculture. The main crops in addition to maize were beans, squashes, chilies and amaranth. Particularly important for agricultural production in the valley was the construction of chinampas on the lake, artificial islands that allowed the conversion of the shallow waters into highly fertile gardens that could be cultivated year round. Chinampas are human-made extensions of agricultural land, created from alternating layers of mud from the bottom of the lake, and plant matter and other vegetation. These raised beds were separated by narrow canals, which allowed farmers to move between them by canoe. Chinampas were extremely fertile pieces of land, and yielded, on average, seven crops annually. On the basis of current chinampa yields, it has been estimated that one hectare (2.5 acres) of chinampa would feed 20 individuals and 9,000 hectares (22,000 acres) of chinampas could feed 180,000. The Aztecs further intensified agricultural production by constructing systems of artificial irrigation. While most of the farming occurred outside the densely populated areas, within the cities there was another method of (small-scale) farming. Each family had their own garden plot where they grew maize, fruits, herbs, medicines and other important plants. When the city of Tenochtitlan became a major urban center, water was supplied to the city through aqueducts from springs on the banks of the lake, and they organized a system that collected human waste for use as fertilizer. Through intensive agriculture the Aztecs were able to sustain a large urbanized population. The lake was also a rich source of proteins in the form of aquatic animals such as fish, amphibians, shrimp, insects and insect eggs, and water fowl. The presence of such varied sources of protein meant that there was little use for domestic animals for meat (only turkeys and dogs were kept), and scholars have calculated that there was no shortage of protein among the inhabitants of the Valley of Mexico. Crafts and trades The excess supply of food products allowed a significant portion of the Aztec population to dedicate themselves to trades other than food production. Apart from taking care of domestic food production, women weaved textiles from agave fibers and cotton. Men also engaged in craft specializations such as the production of ceramics and of obsidian and flint tools, and of luxury goods such as beadwork, featherwork and the elaboration of tools and musical instruments. Sometimes entire calpollis specialized in a single craft, and in some archeological sites large neighborhoods have been found where apparently only a single craft speciality was practiced. The Aztecs did not produce much metal work, but did have knowledge of basic smelting technology for gold, and they combined gold with precious stones such as jade and turquoise. Copper products were generally imported from the Tarascans of Michoacan. Trade and distribution Products were distributed through a network of markets some markets specialized in a single commodity (for example the dog market of Acolman) and other general markets with presence of many different goods. Markets were highly organized with a system of supervisors taking care that only authorized merchants were permitted to sell their goods, and punishing those who cheated their customers or sold substandard or counterfeit goods. A typical town would have a weekly market (every five days), while larger cities held markets every day. Cortés reported that the central market of Tlatelolco, Tenochtitlan's sister city, was visited by 60,000 people daily. Some sellers in the markets were petty vendors farmers might sell some of their produce, potters sold their vessels, and so on. Other vendors were professional merchants who traveled from market to market seeking profits. The pochteca were specialized long-distance merchants organized into exclusive guilds. They made long expeditions to all parts of Mesoamerica bringing back exotic luxury goods, and they served as the judges and supervisors of the Tlatelolco market. Although the economy of Aztec Mexico was commercialized (in its use of money, markets, and merchants), land and labor were not generally commodities for sale, though some types of land could be sold between nobles. In the commercial sector of the economy, several types of money were in regular use. Small purchases were made with cacao beans, which had to be imported from lowland areas. In Aztec marketplaces, a small rabbit was worth 30 beans, a turkey egg cost 3 beans, and a tamal cost a single bean. For larger purchases, standardized lengths of cotton cloth, called quachtli, were used. There were different grades of quachtli, ranging in value from 65 to 300 cacao beans. About 20 quachtli could support a commoner for one year in Tenochtitlan. Another form of distribution of goods was through the payment of tribute. When an altepetl was conquered, the victor imposed a yearly tribute, usually paid in the form of whichever local product was most valuable or treasured. Several pages from the Codex Mendoza list tributary towns along with the goods they supplied, which included not only luxuries such as feathers, adorned suits, and greenstone beads, but more practical goods such as cloth, firewood, and food. Tribute was usually paid twice or four times a year at differing times. Archaeological excavations in the Aztec-ruled provinces show that incorporation into the empire had both costs and benefits for provincial peoples. On the positive side, the empire promoted commerce and trade, and exotic goods from obsidian to bronze managed to reach the houses of both commoners and nobles. Trade partners also included the enemy Purépecha (also known as Tarascans), a source of bronze tools and jewelry. On the negative side, imperial tribute imposed a burden on commoner households, who had to increase their work to pay their share of tribute. Nobles, on the other hand, often made out well under imperial rule because of the indirect nature of imperial organization. The empire had to rely on local kings and nobles and offered them privileges for their help in maintaining order and keeping the tribute flowing. Aztec society combined a relatively simple agrarian rural tradition with the development of a truly urbanized society with a complex system of institutions, specializations and hierarchies. The urban tradition in Mesoamerica was developed during the classic period with major urban centers such as Teotihuacan with a population well above 100,000, and at the time of the rise of the Aztec, the urban tradition was ingrained in Mesoamerican society, with urban centers serving major religious, political and economic functions for the entire population. The capital city of the Aztec empire was Tenochtitlan, now the site of modern-day Mexico City. Built on a series of islets in Lake Texcoco, the city plan was based on a symmetrical layout that was divided into four city sections called campan (directions). Tenochtitlan was built according to a fixed plan and centered on the ritual precinct, where the Great Pyramid of Tenochtitlan rose 50 m (164.04 ft) above the city. Houses were made of wood and loam, roofs were made of reed, although pyramids, temples and palaces were generally made of stone. The city was interlaced with canals, which were useful for transportation. Anthropologist Eduardo Noguera estimated the population at 200,000 based on the house count and merging the population of Tlatelolco (once an independent city, but later became a suburb of Tenochtitlan). If one includes the surrounding islets and shores surrounding Lake Texcoco, estimates range from 300,000 to 700,000 inhabitants. Michael E. Smith gives a somewhat smaller figure of 212,500 inhabitants of Tenochtitlan based on an area of 1,350 hectares (3,300 acres) and a population density of 157 inhabitants per hectare. The second largest city in the valley of Mexico in the Aztec period was Texcoco with some 25,000 inhabitants dispersed over 450 hectares (1,100 acres). The center of Tenochtitlan was the sacred precinct, a walled-off square area which housed the Great Temple, temples for other deities, the ballcourt, the calmecac (a school for nobles), a skull rack tzompantli, displaying the skulls of sacrificial victims, houses of the warrior orders and a merchants palace. Around the sacred precinct were the royal palaces built by the tlatoanis. The Great Temple The centerpiece of Tenochtitlan was the Templo Mayor, the Great Temple, a large stepped pyramid with a double staircase leading up to two twin shrines – one dedicated to Tlaloc, the other to Huitzilopochtli. This was where most of the human sacrifices were carried out during the ritual festivals and the bodies of sacrificial victims were thrown down the stairs. The temple was enlarged in several stages, and most of the Aztec rulers made a point of adding a further stage, each with a new dedication and inauguration. The temple has been excavated in the center of Mexico City and the rich dedicatory offerings are displayed in the Museum of the Templo Mayor. Archaeologist Eduardo Matos Moctezuma, in his essay Symbolism of the Templo Mayor, posits that the orientation of the temple is indicative of the totality of the vision the Mexica had of the universe (cosmovision). He states that the "principal center, or navel, where the horizontal and vertical planes intersect, that is, the point from which the heavenly or upper plane and the plane of the Underworld begin and the four directions of the universe originate, is the Templo Mayor of Tenochtitlan." Matos Moctezuma supports his supposition by claiming that the temple acts as an embodiment of a living myth where "all sacred power is concentrated and where all the levels intersect." Other major city-states Other major Aztec cities were some of the previous city state centers around the lake including Tenayuca, Azcapotzalco, Texcoco, Colhuacan, Tlacopan, Chapultepec, Coyoacan, Xochimilco, and Chalco. In the Puebla valley, Cholula was the largest city with the largest pyramid temple in Mesoamerica, while the confederacy of Tlaxcala consisted of four smaller cities. In Morelos, Cuahnahuac was a major city of the Nahuatl speaking Tlahuica tribe, and Tollocan in the Toluca valley was the capital of the Matlatzinca tribe which included Nahuatl speakers as well as speakers of Otomi and the language today called Matlatzinca. Most Aztec cities had a similar layout with a central plaza with a major pyramid with two staircases and a double temple oriented towards the west. Aztec religion was organized around the practice of calendar rituals dedicated to a pantheon of different deities. Similar to other Mesoamerican religious systems, it has generally been understood as a polytheist agriculturalist religion with elements of animism. Central in the religious practice was the offering of sacrifices to the deities, as a way of thanking or paying for the continuation of the cycle of life. The main deities worshipped by the Aztecs were Tlaloc, a rain and storm deity, Huitzilopochtli a solar and martial deity and the tutelary deity of the Mexica tribe, Quetzalcoatl, a wind, sky and star deity and cultural hero, Tezcatlipoca, a deity of the night, magic, prophecy and fate. The Great Temple in Tenochtitlan had two shrines on its top, one dedicated to Tlaloc, the other to Huitzilopochtli. Quetzalcoatl and Tezcatlipoca each had separate temples within the religious precinct close to the Great Temple, and the high priests of the Great Temple were named "Quetzalcoatl Tlamacazqueh". Other major deities were Tlaltecutli or Coatlicue a female earth deity, the deity couple Tonacatecuhtli and Tonacacihuatl were associated with life and sustenance, Mictlantecutli and Mictlancihuatl, a male/female couple of deities of the underworld and death, Chalchiutlicue, a female deity of lakes and springs, Xipe Totec, a deity of fertility and the natural cycle, Huehueteotl or Xiuhtecuhtli a fire god, Tlazolteotl a female deity tied to childbirth and sexuality, and a Xochipilli and Xochiquetzal gods of song, dance and games. In some regions, particularly Tlaxcala, Mixcoatl or Camaxtli was the main tribal deity. A few sources mention a deity Ometeotl who may have been a god of the duality between life and death, male and female and who may have incorporated Tonacatecuhtli and Tonacacihuatl. Apart from the major deities there were dozens of minor deities each associated with an element or concept, and as the Aztec empire grew so did their pantheon because they adopted and incorporated the local deities of conquered people into their own. Additionally the major gods had many alternative manifestations or aspects, creating small families of gods with related aspects. Mythology and worldview Aztec mythology is known from a number of sources written down in the colonial period. One set of myths, called Legend of the Suns, describe the creation of four successive suns, or periods, each ruled by a different deity and inhabited by a different group of beings. Each period ends in a cataclysmic destruction that sets the stage for the next period to begin. In this process, the deities Tezcatlipoca and Quetzalcoatl appear as adversaries, each destroying the creations of the other. The current Sun, the fifth, was created when a minor deity sacrificed himself on a bonfire and turned into the sun, but the sun only begins to move once the other deities sacrifice themselves and offers it their life force. In another myth of how the earth was created, Tezcatlipoca and Quetzalcoatl appear as allies, defeating a giant crocodile Cipactli and requiring her to become the earth, allowing humans to carve into her flesh and plant their seeds, on the condition that in return they will offer blood to her. And in the story of the creation of humanity, Quetzalcoatl travels with his twin Xolotl to the underworld and brings back bones which are then ground like corn on a metate by the goddess Cihuacoatl, the resulting dough is given human form and comes to life when Quetzalcoatl imbues it with his own blood. Huitzilopochtli is the deity tied to the Mexica tribe and he figures in the story of the origin and migrations of the tribe. On their journey, Huitzilopochtli, in the form of a deity bundle carried by the Mexica priest, continuously spurs the tribe on by pushing them into conflict with their neighbors whenever they are settled in a place. In another myth, Huitzilopochtli defeats and dismembers his sister the lunar deity Coyolxauhqui and her four hundred brothers at the hill of Coatepetl. The southern side of the Great Temple, also called Coatepetl, was a representation of this myth and at the foot of the stairs lay a large stone monolith carved with a representation of the dismembered goddess. Aztec religious life was organized around the calendars. As most Mesoamerican people, the Aztecs used two calendars simultaneously: a ritual calendar of 260 days called the tonalpohualli and a solar calendar of 365 days called the xiuhpohualli. Each day had a name and number in both calendars, and the combination of two dates were unique within a period of 52 years. The tonalpohualli was mostly used for divinatory purposes and it consisted of 20 day signs and number coefficients of 1–13 that cycled in a fixed order. The xiuhpohualli was made up of 18 "months" of 20 days, and with a remainder of 5 "void" days at the end of a cycle before the new xiuhpohualli cycle began. Each 20-day month was named after the specific ritual festival that began the month, many of which contained a relation to the agricultural cycle. Whether, and how, the Aztec calendar corrected for leap year is a matter of discussion among specialists. The monthly rituals involved the entire population as rituals were performed in each household, in the calpolli temples and in the main sacred precinct. Many festivals involved different forms of dancing, as well as the reenactment of mythical narratives by deity impersonators and the offering of sacrifice, in the form of food, animals and human victims. Every 52 years, the two calendars reached their shared starting point and a new calendar cycle began. This calendar event was celebrated with a ritual known as Xiuhmolpilli or the New Fire Ceremony. In this ceremony, old pottery was broken in all homes and all fires in the Aztec realm were put out. Then a new fire was drilled over the breast of a sacrificial victim and runners brought the new fire to the different calpolli communities where fire was redistributed to each home. The night without fire was associated with the fear that star demons, tzitzimime, might descend and devour the earth – ending the fifth period of the sun. Human sacrifice and cannibalism To the Aztecs, death was instrumental in the perpetuation of creation, and gods and humans alike had the responsibility of sacrificing themselves in order to allow life to continue. As described in the myth of creation above, humans were understood to be responsible for the sun's continued revival, as well as for paying the earth for its continued fertility. Blood sacrifice in various forms was conducted. Both humans and animals were sacrificed, depending on the god to be placated and the ceremony being conducted, and priests of some gods were sometimes required to provide their own blood through self-mutilation. It is known that some rituals included acts of cannibalism, with the captor and his family consuming part of the flesh of their sacrificed captives, but it is not known how widespread this practice was. While human sacrifice was practiced throughout Mesoamerica, the Aztecs, according to their own accounts, brought this practice to an unprecedented level. For example, for the reconsecration of the Great Pyramid of Tenochtitlan in 1487, the Aztecs reported that they sacrificed 80,400 prisoners over the course of four days, reportedly by Ahuitzotl, the Great Speaker himself. This number, however, is not universally accepted and may have been exaggerated. The scale of Aztec human sacrifice has provoked many scholars to consider what may have been the driving factor behind this aspect of Aztec religion. In the 1970s, Michael Harner and Marvin Harris argued that the motivation behind human sacrifice among the Aztecs was actually the cannibalization of the sacrificial victims, depicted for example in Codex Magliabechiano. Harner claimed that very high population pressure and an emphasis on maize agriculture, without domesticated herbivores, led to a deficiency of essential amino acids among the Aztecs. While there is universal agreement that the Aztecs practiced sacrifice, there is a lack of scholarly consensus as to whether cannibalism was widespread. Harris, author of Cannibals and Kings (1977), has propagated the claim, originally proposed by Harner, that the flesh of the victims was a part of an aristocratic diet as a reward, since the Aztec diet was lacking in proteins. These claims have been refuted by Bernard Ortíz Montellano who, in his studies of Aztec health, diet, and medicine, demonstrates that while the Aztec diet was low in animal proteins, it was rich in vegetable proteins. Ortiz also points to the preponderance of human sacrifice during periods of food abundance following harvests compared to periods of food scarcity, the insignificant quantity of human protein available from sacrifices and the fact that aristocrats already had easy access to animal protein. Today many scholars point to ideological explanations of the practice, noting how the public spectacle of sacrificing warriors from conquered states was a major display of political power, supporting the claim of the ruling classes to divine authority. It also served as an important deterrent against rebellion by subjugated polities against the Aztec state, and such deterrents were crucial in order for the loosely organized empire to cohere. The Aztec greatly appreciated the toltecayotl (arts and fine craftsmanship) of the Toltec, who predated the Aztec in central Mexico. The Aztec considered Toltec productions to represent the finest state of culture. The fine arts included writing and painting, singing and composing poetry, carving sculptures and producing mosaic, making fine ceramics, producing complex featherwork, and working metals, including copper and gold. Artisans of the fine arts were referred to collectively as tolteca (Toltec). Urban standard details Mexico-Tenochtitlan remnants in Templo Mayor Museum (Mexico City) The Mask of Xiuhtecuhtli 1400–1521 cedrela wood, turquoise, pine resin, mother-of-pearl, conch shell, cinnabar height: 16.8 cm, width: 15.2 cm British Museum (London) The Mask of Tezcatlipoca 1400–1521 turquoise, pyrite, pine, lignite, human bone, deer skin, conch shell and agave height: 19 cm, width: 13.9 cm, length: 12.2 cm British Museum Double-headed serpent 1450–1521 cedro wood (Cedrela odorata), turquoise, shell, traces of gilding & 2 resins are used as adhesive (pine resin and Bursera resin) height: 20.3 cm, width: 43.3 cm, depth: 5.9 cm British Museum Page 12 of the Codex Borbonicus, (in the big square): Tezcatlipoca (night and fate) and Quetzalcoatl (feathered serpent) before 1500 bast fiber paper height: 38 cm, length of the full manuscript: 142 cm Bibliothèque de l'Assemblée nationale (Paris) Aztec calendar stone 1502–1521 basalt diameter: 358 cm thick: 98 cm discovered on 17 December 1790 during repairs on the Mexico City Cathedral National Museum of Anthropology (Mexico City) Tlāloc effigy vessel 1440–1469 painted earthenware height: 35 cm Templo Mayor Museum (Mexico City) Kneeling female figure 15th–early 16th century painted stone overall: 54.61 x 26.67 cm Metropolitan Museum of Art (New York City) Frog-shaped necklace ornaments 15th–early 16th century gold height: 2.1 cm Metropolitan Museum of Art (New York City) Writing and iconography The Aztecs did not have a fully developed writing system like the Maya, however like the Maya and Zapotec, they did use a writing system that combined logographic signs with phonetic syllable signs. Logograms would, for example, be the use of an image of a mountain to signify the word tepetl, "mountain", whereas a phonetic syllable sign would be the use of an image of a tooth tlantli to signify the syllable tla in words unrelated to teeth. The combination of these principles allowed the Aztecs to represent the sounds of names of persons and places. Narratives tended to be represented through sequences of images, using various iconographic conventions such as footprints to show paths, temples on fire to show conquest events, etc. Epigrapher Alfonso Lacadena has demonstrated that the different syllable signs used by the Aztecs almost enabled the representation of all the most frequent syllables of the Nahuatl language (with some notable exceptions), but some scholars have argued that such a high degree of phoneticity was only achieved after the conquest when the Aztecs had been introduced to the principles of phonetic writing by the Spanish. Other scholars, notably Gordon Whittaker, have argued that the syllabic and phonetic aspects of Aztec writing were considerably less systematic and more creative than Lacadena's proposal suggests, arguing that Aztec writing never coalesced into a strictly syllabic system such as the Maya writing, but rather used a wide range of different types of phonetic signs. The image to right demonstrates the use of phonetic signs for writing place names in the colonial Aztec Codex Mendoza. The uppermost place is "Mapachtepec", meaning literally "On the Hill of the Raccoon ", but the glyph includes the phonetic signs "MA" (hand) and "PACH" (moss) over a mountain "TEPETL" spelling the word "mapach" ("raccoon") phonetically instead of logographically. The other two place names, Mazatlan ("Place of Many Deer") and Huitztlan ("Place of many thorns"), use the phonetic element "TLAN" represented by a tooth (tlantli) combined with a deer head to spell "MAZA" (mazatl = deer) and a thorn (huitztli) to spell "HUITZ". Music, song and poetry Song and poetry were highly regarded there were presentations and poetry contests at most of the Aztec festivals. There were also dramatic presentations that included players, musicians and acrobats. There were several different genres of cuicatl (song): Yaocuicatl was devoted to war and the god(s) of war, Teocuicatl to the gods and creation myths and to adoration of said figures, xochicuicatl to flowers (a symbol of poetry itself and indicative of the highly metaphorical nature of a poetry that often utilized duality to convey multiple layers of meaning). "Prose" was tlahtolli, also with its different categories and divisions. A key aspect of Aztec poetics was the use of parallelism, using a structure of embedded couplets to express different perspectives on the same element. Some such couplets were diphrasisms, conventional metaphors whereby an abstract concept was expressed metaphorically by using two more concrete concepts. For example, the Nahuatl expression for "poetry" was in xochitl in cuicatl a dual term meaning "the flower, the song". A remarkable amount of this poetry survives, having been collected during the era of the conquest. In some cases poetry is attributed to individual authors, such as Nezahualcoyotl, tlatoani of Texcoco, and Cuacuauhtzin, Lord of Tepechpan, but whether these attributions reflect actual authorship is a matter of opinion. Important collection of such poems are Romances de los señores de la Nueva España, collected (Tezcoco 1582), probably by Juan Bautista de Pomar, [nb 8] and the Cantares Mexicanos. The Aztecs produced ceramics of different types. Common are orange wares, which are orange or buff burnished ceramics with no slip. Red wares are ceramics with a reddish slip. And polychrome ware are ceramics with a white or orange slip, with painted designs in orange, red, brown, and/or black. Very common is "black on orange" ware which is orange ware decorated with painted designs in black. Aztec black on orange ceramics are chronologically classified into four phases: Aztec I and II corresponding to ca, 1100–1350 (early Aztec period), Aztec III ca. (1350–1520), and the last phase Aztec IV was the early colonial period. Aztec I is characterized by floral designs and day- name glyphs Aztec II is characterized by a stylized grass design above calligraphic designs such as s-curves or loops Aztec III is characterized by very simple line designs Aztec IV continues some pre-Columbian designs but adds European influenced floral designs. There were local variations on each of these styles, and archeologists continue to refine the ceramic sequence. Typical vessels for everyday use were clay griddles for cooking (comalli), bowls and plates for eating (caxitl), pots for cooking (comitl), molcajetes or mortar-type vessels with slashed bases for grinding chilli (molcaxitl), and different kinds of braziers, tripod dishes and biconical goblets. Vessels were fired in simple updraft kilns or even in open firing in pit kilns at low temperatures. Polychrome ceramics were imported from the Cholula region (also known as Mixteca-Puebla style), and these wares were highly prized as a luxury ware, whereas the local black on orange styles were also for everyday use. Aztec painted art was produced on animal skin (mostly deer), on cotton lienzos and on amate paper made from bark (e.g. from Trema micrantha or Ficus aurea), it was also produced on ceramics and carved in wood and stone. The surface of the material was often first treated with gesso to make the images stand out more clearly. The art of painting and writing was known in Nahuatl by the metaphor in tlilli, in tlapalli - meaning "the black ink, the red pigment". There are few extant Aztec painted books. Of these none are conclusively confirmed to have been created before the conquest, but several codices must have been painted either right before the conquest or very soon after - before traditions for producing them were much disturbed. Even if some codices may have been produced after the conquest, there is good reason to think that they may have been copied from pre-Columbian originals by scribes. The Codex Borbonicus is considered by some to be the only extant Aztec codex produced before the conquest - it is a calendric codex describing the day and month counts indicating the patron deities of the different time periods. Others consider it to have stylistic traits suggesting a post-conquest production. Some codices were produces post-conquest, sometimes commissioned by the colonial government, for example Codex Mendoza, were painted by Aztec tlacuilos (codex creators), but under the control of Spanish authorities, who also sometimes commissioned codices describing pre-colonial religious practices, for example Codex Ríos. After the conquest, codices with calendric or religious information were sought out and systematically destroyed by the church - whereas other types of painted books, particularly historical narratives and tribute lists continued to be produced. Although depicting Aztec deities and describing religious practices also shared by the Aztecs of the Valley of Mexico, the codices produced in Southern Puebla near Cholula, are sometimes not considered to be Aztec codices, because they were produced outside of the Aztec "heartland". Karl Anton Nowotny, nevertheless considered that the Codex Borgia, painted in the area around Cholula and using a Mixtec style, was the "most significant work of art among the extant manuscripts". The first Aztec murals were from Teotihuacan. Most of our current Aztec murals were found in Templo Mayor. The Aztec capitol was decorated with elaborate murals. In Aztec murals humans are represented like they are represented in the codices. One mural discovered in Tlateloco depicts an old man and an old woman. This may represent the gods Cipactonal and Oxomico. Sculptures were carved in stone and wood, but few wood carvings have survived. Aztec stone sculptures exist in many sizes from small figurines and masks to large monuments, and are characterized by a high quality of craftsmanship. Many sculptures were carved in highly realistic styles, for example realistic sculpture of animals such as rattlesnakes, dogs, jaguars, frogs, turtle and monkeys. In Aztec artwork a number of monumental stone sculptures have been preserved, such sculptures usually functioned as adornments for religious architecture. Particularly famous monumental rock sculpture includes the so-called Aztec "Sunstone" or Calendarstone discovered in 1790 also discovered in 1790 excavations of the Zócalo was the 2.7 meter tall Coatlicue statue made of andesite, representing a serpentine chthonic goddess with a skirt made of rattlesnakes. The Coyolxauhqui Stone representing the dismembered goddess Coyolxauhqui, found in 1978, was at the foot of the staircase leading up to the Great Temple in Tenochtitlan. Two important types of sculpture are unique to the Aztecs, and related to the context of ritual sacrifice: the cuauhxicalli or "eagle vessel", large stone bowls often shaped like eagles or jaguars used as a receptacle for extracted human hearts the temalacatl, a monumental carved stone disk to which war captives were tied and sacrificed in a form of gladiatorial combat. The most well known examples of this type of sculpture are the Stone of Tizoc and the Stone of Motecuzoma I, both carved with images of warfare and conquest by specific Aztec rulers. Many smaller stone sculptures depicting deities also exist. The style used in religious sculpture was rigid stances likely meant to create a powerful experience in the onlooker. Although Aztec stone sculptures are now displayed in museums as unadorned rock, they were originally painted in vivid polychrome color, sometimes covered first with a base coat of plaster. Early Spanish conquistador accounts also describe stone sculptures as having been decorated with precious stones and metal, inserted into the plaster. An especially prized art form among the Aztecs was featherwork - the creation of intricate and colorful mosaics of feathers, and their use in garments as well as decoration on weaponry, war banners, and warrior suits. The class of highly skilled and honored craftsmen who created feather objects was called the amanteca, named after the Amantla neighborhood in Tenochtitlan where they lived and worked. They did not pay tribute nor were required to perform public service. The Florentine Codex gives information about how feather works were created. The amanteca had two ways of creating their works. One was to secure the feathers in place using agave cord for three-dimensional objects such as fly whisks, fans, bracelets, headgear and other objects. The second and more difficult was a mosaic type technique, which the Spanish also called "feather painting." These were done principally on feather shields and cloaks for idols.Feather mosaics were arrangements of minute fragments of feathers from a wide variety of birds, generally worked on a paper base, made from cotton and paste, then itself backed with amate paper, but bases of other types of paper and directly on amate were done as well. These works were done in layers with "common" feathers, dyed feathers and precious feathers. First a model was made with lower quality feathers and the precious feathers found only on the top layer. The adhesive for the feathers in the Mesoamerican period was made from orchid bulbs. Feathers from local and faraway sources were used, especially in the Aztec Empire. The feathers were obtained from wild birds as well as from domesticated turkeys and ducks, with the finest quetzal feathers coming from Chiapas, Guatemala and Honduras. These feathers were obtained through trade and tribute. Due to the difficulty of conserving feathers, fewer than ten pieces of original Aztec featherwork exist today. Mexico City was built on the ruins of Tenochtitlan, gradually replacing and covering the lake, the island and the architecture of Aztec Tenochtitlan. After the fall of Tenochtitlan, Aztec warriors were enlisted as auxiliary troops alongside the Spanish Tlaxcalteca allies, and Aztec forces participated in all of the subsequent campaigns of conquest in northern and southern Mesoamerica. This meant that aspects of Aztec culture and the Nahuatl language continued to expand during the early colonial period as Aztec auxiliary forces made permanent settlements in many of the areas that were put under the Spanish crown. The Aztec ruling dynasty continued to govern the indigenous polity of San Juan Tenochtitlan, a division of the Spanish capital of Mexico City, but the subsequent indigenous rulers were mostly puppets installed by the Spanish. One was Andrés de Tapia Motelchiuh, who was appointed by the Spanish. Other former Aztec city states likewise were established as colonial indigenous towns, governed by a local indigenous gobernador. This office was often initially held by the hereditary indigenous ruling line, with the gobernador being the tlatoani, but the two positions in many Nahua towns became separated over time. Indigenous governors were in charge of the colonial political organization of the Indians. In particular they enabled the continued functioning of the tribute and obligatory labor of commoner Indians to benefit the Spanish holders of encomiendas. Encomiendas were private grants of labor and tribute from particular indigenous communities to particular Spaniards, replacing the Aztec overlords with Spanish. In the early colonial period some indigenous governors became quite rich and influential and were able to maintain positions of power comparable to that of Spanish encomenderos. After the arrival of the Europeans in Mexico and the conquest, indigenous populations declined significantly. This was largely the result of the epidemics of viruses brought to the continent against which the natives had no immunity. In 1520–1521, an outbreak of smallpox swept through the population of Tenochtitlan and was decisive in the fall of the city further significant epidemics struck in 1545 and 1576. There has been no general consensus about the population size of Mexico at the time of European arrival. Early estimates gave very small population figures for the Valley of Mexico, in 1942 Kubler estimated a figure 200,000. In 1963 Borah and Cook used pre-Conquest tribute lists to calculate the number of tributaries in central Mexico, estimating over 18–30 million . Their very high figure has been highly criticized for relying on unwarranted assumptions. Archeologist William Sanders based an estimate on archeological evidence of dwellings, arriving at an estimate of 1–1.2 million inhabitants in the Valley of Mexico. Whitmore used a computer simulation model based on colonial censuses to arrive at an estimate of 1.5 million for the Basin in 1519, and an estimate of 16 million for all of Mexico. Depending on the estimations of the population in 1519 the scale of the decline in the 16th century, range from around 50% to around 90% – with Sanders's and Whitmore's estimates being around 90%. Social and political continuity and change Although the Aztec empire fell, some of its highest elites continued to hold elite status in the colonial era. The principal heirs of Moctezuma II and their descendants retained high status. His son Pedro Moctezuma produced a son, who married into Spanish aristocracy and a further generation saw the creation of the title, Count of Moctezuma. From 1696 to 1701, the Viceroy of Mexico was held the title of count of Moctezuma. In 1766, the holder of the title became a Grandee of Spain. In 1865, (during the Second Mexican Empire) the title, which was held by Antonio María Moctezuma-Marcilla de Teruel y Navarro, 14th Count of Moctezuma de Tultengo, was elevated to that of a Duke, thus becoming Duke of Moctezuma, with de Tultengo again added in 1992 by Juan Carlos I. Two of Moctezuma's daughters, Doña Isabel Moctezuma and her younger sister, Doña Leonor Moctezuma, were granted extensive encomiendas in perpetuity by Hernán Cortes. Doña Leonor Moctezuma married in succession two Spaniards, and left her encomiendas to her daughter by her second husband. The different Nahua peoples, just as other Mesoamerican indigenous peoples in colonial New Spain, were able to maintain many aspects of their social and political structure under the colonial rule. The basic division the Spanish made was between the indigenous populations, organized under the Republica de indios, which was separate from the Hispanic sphere, the República de españoles. The República de españoles included not just Europeans, but also Africans and mixed-race castas. The Spanish recognized the indigenous elites as nobles in the Spanish colonial system, maintaining the status distinction of the pre-conquest era, and used these noblemen as intermediaries between the Spanish colonial government and their communities. This was contingent on their conversion to Christianity and continuing loyalty to the Spanish crown. Colonial Nahua polities had considerable autonomy to regulate their local affairs. The Spanish rulers did not entirely understand the indigenous political organization, but they recognized the importance of the existing system and their elite rulers. They reshaped the political system utilizing altepetl or city-states as the basic unit of governance. In the colonial era, altepetl were renamed cabeceras or "head towns" (although they often retained the term altepetl in local-level, Nahuatl-language documentation), with outlying settlements governed by the cabeceras named sujetos, subject communities. In cabeceras, the Spanish created Iberian-style town councils, or cabildos, which usually continued to function as the elite ruling group had in the pre-conquest era. Population decline due to epidemic disease resulted in many population shifts in settlement patterns, and the formation of new population centers. These were often forced resettlements under the Spanish policy of congregación. Indigenous populations living in sparsely populated areas were resettled to form new communities, making it easier for them to brought within range of evangelization efforts, and easier for the colonial state to exploit their labor. Today the legacy of the Aztecs lives on in Mexico in many forms. Archeological sites are excavated and opened to the public and their artifacts are prominently displayed in museums. Place names and loanwords from the Aztec language Nahuatl permeate the Mexican landscape and vocabulary, and Aztec symbols and mythology have been promoted by the Mexican government and integrated into contemporary Mexican nationalism as emblems of the country. During the 19th century, the image of the Aztecs as uncivilized barbarians was replaced with romanticized visions of the Aztecs as original sons of the soil, with a highly developed culture rivaling the ancient European civilizations. When Mexico became independent from Spain, a romanticized version of the Aztecs became a source of images that could be used to ground the new nation as a unique blend of European and American. The Aztecs and Mexico's national identity Aztec culture and history has been central to the formation of a Mexican national identity after Mexican independence in 1821. In 17th and 18th century Europe, the Aztecs were generally described as barbaric, gruesome and culturally inferior. Even before Mexico achieved its independence, American-born Spaniards (criollos) drew on Aztec history to ground their own search for symbols of local pride, separate from that of Spain. Intellectuals utilized Aztec writings, such as those collected by Fernando de Alva Ixtlilxochitl, and writings of Hernando Alvarado Tezozomoc, and Chimalpahin to understand Mexico's indigenous past in texts by indigenous writers. This search became the basis for what historian D.A. Brading calls "creole patriotism." Seventeenth-century cleric and scientist, Carlos de Sigüenza y Góngora acquired the manuscript collection of Texcocan nobleman Alva Ixtlilxochitl. Creole Jesuit Francisco Javier Clavijero published La Historia Antigua de México (1780–81) in his Italian exile following the expulsion of the Jesuits in 1767, in which he traces the history of the Aztecs from their migration to the last Aztec ruler, Cuauhtemoc. He wrote it expressly to defend Mexico's indigenous past against the slanders of contemporary writers, such as Pauw, Buffon, Raynal, and William Robertson. Archeological excavations in 1790 in the capital's main square uncovered two massive stone sculptures, buried immediately after the fall of Tenochtitlan in the conquest. Unearthed were the famous calendar stone, as well as a statue of Coatlicue. Antonio de León y Gama’s 1792 Descripción histórico y cronológico de las dos piedras examines the two stone monoliths. A decade later, German scientist Alexander von Humboldt spent a year in Mexico, during his four-year expedition to Spanish America. One of his early publications from that period was Views of the Cordilleras and Monuments of the Indigenous Peoples of the Americas. Humboldt was important in disseminating images of the Aztecs to scientists and general readers in the Western world. In the realm of religion, late colonial paintings of the Virgin of Guadalupe have examples of her depicted floating above the iconic nopal cactus of the Aztecs. Juan Diego, the Nahua to whom the apparition was said to appear, links the dark Virgin to Mexico's Aztec past. When New Spain achieved independence in 1821 and became a monarchy, the First Mexican Empire, its flag had the traditional Aztec eagle on a nopal cactus. The eagle had a crown, symbolizing the new Mexican monarchy. When Mexico became a republic after the overthrow of the first monarch Agustín de Iturbide in 1822, the flag was revised showing the eagle with no crown. In the 1860s, when the French established the Second Mexican Empire under Maximilian of Habsburg, the Mexican flag retained the emblematic eagle and cactus, with elaborate symbols of monarchy. After the defeat of the French and their Mexican collaborators, the Mexican Republic was re-established, and the flag returned to its republican simplicity. This emblem has also been adopted as Mexico's national Coat of Arms, and is emblazoned on official buildings, seals, and signs. Tensions within post-independence Mexico pitted those rejecting the ancient civilizations of Mexico as source of national pride, the Hispanistas, mostly politically conservative Mexican elites, and those who saw them as a source of pride, the Indigenistas, who were mostly liberal Mexican elites. Although the flag of the Mexican Republic had the symbol of the Aztecs as its central element, conservative elites were generally hostile to the current indigenous populations of Mexico or crediting them with a glorious prehispanic history. Under Mexican president Antonio López de Santa Anna, pro-indigenist Mexican intellectuals did not find a wide audience. With Santa Anna's overthrow in 1854, Mexican liberals and scholars interested in the indigenous past became more active. Liberals were more favorably inclined to the indigenous populations and their history, but considered a pressing matter being the "Indian Problem." Liberals’ commitment to equality before the law meant that for upwardly mobile indigenous, such as Zapotec Benito Juárez, who rose in the ranks of the liberals to become Mexico's first president of indigenous origins, and Nahua intellectual and politician Ignacio Altamirano, a disciple of Ignacio Ramírez, a defender of the rights of the indigenous, liberalism presented a way forward in that era. For investigations of Mexico's indigenous past, however, the role of moderate liberal José Fernando Ramírez is important, serving as director of the National Museum and doing research utilizing codices, while staying out of the fierce conflicts between liberals and conservatives that led to a decade of civil war. Mexican scholars who pursued research on the Aztecs in the late nineteenth century were Francisco Pimentel, Antonio García Cubas, Manuel Orozco y Berra, Joaquín García Icazbalceta, and Francisco del Paso y Troncoso contributing significantly to the nineteenth-century development of Mexican scholarship on the Aztecs. The late nineteenth century in Mexico was a period in which Aztec civilization became a point of national pride. The era was dominated by liberal military hero, Porfirio Díaz, a mestizo from Oaxaca who was president of Mexico from 1876 to 1911. His policies opening Mexico to foreign investors and modernizing the country under a firm hand controlling unrest, "Order and Progress," undermined Mexico's indigenous populations and their communities. However, for investigations of Mexico's ancient civilizations, his was a benevolent regime, with funds supporting archeological research and for protecting monuments. "Scholars found it more profitable to confine their attention to Indians who had been dead for a number of centuries." His benevolence saw the placement of a monument to Cuauhtemoc in a major traffic roundabout (glorieta) of the wide Paseo de la Reforma, which he inaugurated in 1887. In world's fairs of the late nineteenth century, Mexico's pavilions included a major focus on its indigenous past, especially the Aztecs. Mexican scholars such as Alfredo Chavero helped shape the cultural image of Mexico at these exhibitions. The Mexican Revolution (1910–1920) and significant participation of indigenous people in the struggle in many regions, ignited a broad government-sponsored political and cultural movement of indigenismo, with symbols of Mexico's Aztec past becoming ubiquitous, most especially in Mexican muralism of Diego Rivera. In their works, Mexican authors such as Octavio Paz and Agustin Fuentes have analyzed the use Aztec symbols by the modern Mexican state, critiquing the way it adopts and adapts indigenous culture to political ends, yet they have also in their works made use of the symbolic idiom themselves. Paz for example critiqued the architectural layout of the National Museum of Anthropology, which constructs a view of Mexican history as culminating with the Aztecs, as an expression of a nationalist appropriation of Aztec culture. Aztec history and international scholarship Scholars in Europe and the United States increasingly wanted investigations into Mexico's ancient civilizations, starting in the nineteenth century. Humboldt had been extremely important bringing ancient Mexico into broader scholarly discussions of ancient civilizations. French Americanist Charles Étienne Brasseur de Bourbourg (1814–1874) asserted that "science in our own time has at last effectively studied and rehabilitated America and the Americans from the [previous] viewpoint of history and archeology. It was Humboldt. who woke us from our sleep." Frenchman Jean-Frédéric Waldeck published Voyage pittoresque et archéologique dans la province d'Yucatan pendant les années 1834 et 1836 in 1838. Although not directly connected with the Aztecs, it contributed to the increased interest in ancient Mexican studies in Europe. English aristocrat Lord Kingsborough spent considerable energy in their pursuit of understanding of ancient Mexico. Kingsborough answered Humboldt's call for the publication of all known Mexican codices, publishing nine volumes of Antiquities of Mexico (1831–1846) that were richly illustrated, bankrupting him. He was not directly interested in the Aztecs, but rather in proving that Mexico had been colonized by Jews. [ citation needed ] However, his publication of these valuable primary sources gave others access to them. [ citation needed ] In the United States in the early nineteenth century, interest in ancient Mexico propelled John Lloyd Stephens to travel to Mexico and then publish well-illustrated accounts in the early 1840s. But the research of a half-blind Bostonian, William Hickling Prescott, into the Spanish conquest of Mexico resulted in his highly popular and deeply researched The Conquest of Mexico (1843). Although not formally trained as a historian, Prescott drew on the obvious Spanish sources, but also Ixtlilxochitl and Sahagún's history of the conquest. His resulting work was a mixture of pro- and anti-Aztec attitudes. It was not only a bestseller in English, it also influenced Mexican intellectuals, including the leading conservative politician, Lucas Alamán. Alamán pushed back against his characterization of the Aztecs. In the assessment of Benjamin Keen, Prescott's history "has survived attacks from every quarter, and still dominates the conceptions of the laymen, if not the specialist, concerning Aztec civilization." In the later nineteenth century, businessman and historian Hubert Howe Bancroft oversaw a huge project, employing writers and researchers, to write the history the "Native Races" of North America, including Mexico, California, and Central America. One entire work was devoted to ancient Mexico, half of which concerned the Aztecs. It was a work of synthesis drawing on Ixtlilxochitl and Brasseur de Bourbourg, among others. When the International Congress of Americanists was formed in Nancy, France in 1875, Mexican scholars became active participants, and Mexico City has hosted the biennial multidisciplinary meeting six times, starting in 1895. Mexico's ancient civilizations have continued to be the focus of major scholarly investigations by Mexican and international scholars. Language and placenames The Nahuatl language is today spoken by 1.5 million people, mostly in mountainous areas in the states of central Mexico. Mexican Spanish today incorporates hundreds of loans from Nahuatl, and many of these words have passed into general Spanish use, and further into other world languages. In Mexico, Aztec place names are ubiquitous, particularly in central Mexico where the Aztec empire was centered, but also in other regions where many towns, cities and regions were established under their Nahuatl names, as Aztec auxiliary troops accompanied the Spanish colonizers on the early expeditions that mapped New Spain. In this way even towns, that were not originally Nahuatl speaking came to be known by their Nahuatl names. In Mexico City there are commemorations of Aztec rulers, including on the Mexico City Metro, line 1, with stations named for Moctezuma II and Cuauhtemoc. Mexican cuisine continues to be based on staple elements of Mesoamerican cooking and, particularly, of Aztec cuisine: corn, chili, beans, squash, tomato, avocado. Many of these staple products continue to be known by their Nahuatl names, carrying in this way ties to the Aztec people who introduced these foods to the Spaniards and to the world. Through spread of ancient Mesoamerican food elements, particularly plants, Nahuatl loan words (chocolate, tomato, chili, avocado, tamale, taco, pupusa, chipotle, pozole, atole) have been borrowed through Spanish into other languages around the world. Through the spread and popularity of Mexican cuisine, the culinary legacy of the Aztecs can be said to have a global reach. Today Aztec images and Nahuatl words are often used to lend an air of authenticity or exoticism in the marketing of Mexican cuisine. In popular culture The idea of the Aztecs has captivated the imaginations of Europeans since the first encounters, and has provided many iconic symbols to Western popular culture. In his book The Aztec Image in Western Thought, Benjamin Keen argued that Western thinkers have usually viewed Aztec culture through a filter of their own cultural interests. The Aztecs and figures from Aztec mythology feature in Western culture. The name of Quetzalcoatl, a feathered serpent god, has been used for a genus of pterosaurs, Quetzalcoatlus, a large flying reptile with a wingspan of as much as 11 metres (36 ft). Quetzalcoatl has appeared as a character in many books, films and video games. D.H. Lawrence gave the name Quetzalcoatl to an early draft of his novel The Plumed Serpent, but his publisher, Alfred A. Knopf, insisted on a change of title. American author Gary Jennings wrote two acclaimed historical novels set in Aztec-period Mexico, Aztec (1980) and Aztec Autumn (1997). The novels were so popular that four more novels in the Aztec series were written after his death. Aztec society has also been depicted in cinema. The Mexican feature film The Other Conquest (Spanish: La Otra Conquista) from 2000 was directed by Salvador Carrasco, and illustrated the colonial aftermath of the 1520s Spanish Conquest of Mexico. It adopted the perspective of an Aztec scribe, Topiltzin, who survived the attack on the temple of Tenochtitlan. The 1989 film Retorno a Aztlán by Juan Mora Catlett is a work of historical fiction set during the rule of Motecuzoma I, filmed in Nahuatl and with the alternative Nahuatl title Necuepaliztli in Aztlan. In Mexican exploitation B movies of the 1970s, a recurring figure was the "Aztec mummy" as well as Aztec ghosts and sorcerers. This article was kindly written specially for us (well, we helped a little with the Aztecs bit. ) by Katherine Ashenburg, prize-winning non-fiction author, lecturer and journalist. Her latest book, &lsquoThe Dirt on Clean&rsquo, is a social history of Western cleanliness, which &lsquoholds a welcome mirror up to our intimate selves. &rsquo Many things about Aztec civilization amazed the Spanish Conquistadores, including their intensive, highly productive agricultural system of chinampas or &lsquofloating gardens&rsquo (Picture 1), and the size and sophistication of their great city Tenochtitlan (Picture 2). At a time in Europe when street cleaning was almost non-existent and people emptied their overflowing chamber pots into the streets as a matter of course, the Aztecs employed a thousand public service cleaners to sweep and water their streets daily, built public toilets in every neighbourhood, and transported human waste in canoes for use as fertilizer. \|Pic 2: The city of Tenochtitlan - painting by Luis Covarrubias, National Museum of Anthropology, Mexico City (Click on image to enlarge)\| While London was still drawing its drinking water from the polluted River Thames as late as 1854, the Aztecs supplied their capital city with fresh water from the nearby hill of Chapultepec by means of two aqueducts, the first built by Netzahualcóyotl between 1466 and 1478, the second some 20 years later by the ruler Ahuitzotl. The symbolic importance of water to the Aztecs is clear from their (metaphorical) word for &lsquocity&rsquo - altepetl which means literally &lsquowater-mountain&rsquo in Náhuatl. The aqueducts were described by Hernán Cortés in 1520: Along one of the causeways to this great city run two aqueducts made of mortar. Each one is two paces wide and some six feet deep, and along one of them a stream of very good fresh water, as wide as a man&rsquos body, flows into the heart of the city and from this they all drink. The other, which is empty, is used when they wish to clean the first channel. Where the aqueducts cross the bridges, the water passes along some channels which are as wide as an ox and so they serve the whole city. \|Pic 3: Stylized image of Aztec daily life: detail of mural by Regina Raúll &lsquoPaisaje Mexica&rsquo, 1964, National Museum of Anthropology, Mexico City (Click on image to enlarge)\| But probably nothing seemed more bizarre to the Spaniards than the Aztec attitude to personal hygiene. In a word, they valued cleanliness. The conquistador Andres de Tapia reported, in a tone of wonder, that Montezuma bathed twice a day. He did, but there was nothing extraordinary about that for an Aztec, since everybody, according to the Jesuit historian Francisco Javier Clavijero, &lsquobathed often, and many of them every day&rsquo in the rivers, lakes or pools. \|Pic 4: Copalxocotl (&lsquosoap-tree&rsquo) (Left) Xiuhamolli (soap plant) (Middle & Right) - L & M: Badianus Manuscript (pls 104 & 11), R: Florentine Codex Book 11 (Click on image to enlarge)\| They lacked true soap but made up for it with the fruit of the copalxocotl , called the &lsquosoap-tree&rsquo by the Spanish, and the sticky root of the xiuhamolli or soap-plant [Saponaria Americana] both gave a lather rich enough to wash body and clothes. The encyclopedic Florentine Codex, written with Aztec informants shortly after the Conquest, includes a small illustration and description of the amolli soap plant (see Picture 4): It is long and narrow like reeds. It has a shoot its flower is white. It is a cleanser. The large, the thick [roots] remove one&rsquos hair, make one bald the small, the slender ones are cleansers, a soap. They wash, they cleanse, they remove the filth. \|Pic 5: Washing hair Florentine Codex, Book 2 (Click on image to enlarge)\| Their documents also make frequent mention of deodorants, breath fresheners and dentifrices. (Spaniards of the time cleaned their teeth with urine.) As well as bathing in lakes and rivers, the Aztecs cleaned themselves &ndash often daily &ndash in low sauna-like hot-houses. An external fire heated one of the walls to red-hot, and the bather threw water on the baking wall, creating steam. As in a traditional Russian steam bath, the bathers could speed up perspiration by thrashing themselves with twigs and grasses. Almost every building had such a bath-house or temazcalli , used for medical treatments and ritual purifications as well as ordinary grooming (Picture 6). \|Pic 6: Aztec &lsquotemazcalli&rsquo bathhouse Codex Tudela folio 62r (Click on image to enlarge)\| As Jacques Soustelle has written: &lsquoA love of cleanliness seems to have been general throughout the population&rsquo: the Florentine Codex hints at the importance placed on personal hygiene in documenting the instructions given by an Aztec father to his daughter:- [In the morning] wash your face, wash your hands, clean your mouth. Listen to me, child: never make up your face nor paint it never put red on your mouth to look beautiful. Make-up and paint are things that light women use - shameless creatures. If you want your husband to love you, dress well, wash yourself and wash your clothes. \|Pic 7: Dortmund - a town in the centre of Europe in the Middle Ages\| Into this hygienically enlightened place thundered the Spaniards. The 16th century was one of the dirtiest periods in European history, and on top of that, the Spaniards had their own unique distrust of cleanliness. Europe in general had gone from a culture where people enjoyed a regular trip to the town or neighbourhood bath-house to a culture that shunned water as dangerous. \|Pic 8: The Black Death - illustration from the Toggenburg Bible, 1411 (Click on image to enlarge)\| The catalyst was the Black Death of 1347, a plague that would ultimately kill at least one out of every three Europeans. When Philippe VI of France asked the medical faculty of the University of Paris to pronounce on this terrifying occurrence in 1348, they wrote that hot baths, which created openings in the skin, allowed disease to enter the body. Bath-houses all over Europe were closed and for four or five hundred years people avoided water as much as possible. For those who wanted to think of themselves as clean, a fresh linen shirt for a man and a fresh chemise for a woman was considered safer and even more effective than water. Louis XIV of France only bathed twice in a long, athletic life but he was regarded as unusually &lsquoclean&rsquo because he changed his linen shirt twice a day. \|Pic 9: &lsquoBed bugs and head lice&rsquo - from Hortus Sanitatis, Strassburg, 1499 (Click on image to enlarge)\| The 16th-century Spaniards inherited that pan-European fear of water, but they had an additional, peculiarly Spanish aversion to cleanliness. Like every other part of the Roman empire, they had had their own well-patronized bath-houses. But when the Visigoths conquered Spain in the 5th century, they scorned hot baths as effeminate and weakening, and they demolished the bath-houses. By the time the Moors invaded the country in 711, the Spanish had lost the old, bath-loving link. At that point, they saw the Moors&rsquo well-washed ways as part of their heretical convictions, and their own dirtiness as a Christian virtue. (Some early Christians had regarded cleanliness as a dangerous luxury, along with good food, wine and sexual enjoyments, and tried to abstain from it Spain continued in this austere tradition longer than most.) \|Pic 10: Part of the recently restored Moorish Baths dating from 1333-1374, now in the Gibraltar Museum\| Arab Spain sparkled with water, whether in fountains, pools or hundreds of bath-houses. Christians in the north of Spain, not under Arab rule, continued to revel in their squalor, washing &lsquoneither their bodies nor their clothes which they only remove when they fall into pieces,&rsquo according to a contemporary observer. The more their Arab conquerors washed, the more suspicious, decadent and un-Christian the practice seemed to the Spaniards, and their dislike endured long after the Arabs had left. \|Pic 11: Diego Rivera&rsquos critical view of the role of the Spanish church in Colonial Mexico - part of his mural of Mexican history, National Palace, Mexico City (Click on image to enlarge)\| Richard Ford, a 19th-century English traveller who knew Spain well, spoke for many when he connected a centuries-old Spanish distaste for washing with the Moorish occupation. He wrote:- The mendicant Spanish monks, according to their practice of setting up a directly antagonistic principle [to the Arabs], considered physical dirt as the test of moral purity and true faith and by dining and sleeping from year&rsquos end to year&rsquos end in the same unchanged woolen frock, arrived at the height of their ambition, according to their view of the odor of sanctity, the olor de santidad. This was a euphemism for &lsquofoul smell,&rsquo but it came to represent Christian godliness, and many of the saints are pictured sitting in their own excrement. \|Pic 12: Cardinal Cisneros the ruins of the Moorish Baths at Ronda (Click on image to enlarge)\| Cardinal Jiménez de Cisneros, himself a Franciscan - wrote Ford - persuaded King Ferdinand and Queen Isabella to close and abolish the Moorish baths after their conquest of Granada. They forbade not only the Christians but the Moors from using anything but holy water. Fire, not water, became the grand element of inquisitorial purification. \|Pic 13: Traditional Moorish baths (Click on image to enlarge)\| Sure enough, one of the first things the Spaniards did during the Reconquest was to destroy the Moorish baths (just as the Visigoths had destroyed the Roman ones). Even after that, suspicions remained: Moors who converted to Christianity were forbidden to bathe. During the Inquisition, one of the worst things that could be said about Jews as well as Moors was that they were &lsquoknown to bathe.&rsquo As Richard Ford noted, these attitudes were still current in the 19th century. He tells the story of the Spanish Duke of Frias, who visited an English lady for a fortnight and &lsquonever once troubled his basins and jugs [on his washstand in his bedroom] he simply rubbed his face occasionally with the white of an egg.&rsquo This, Ford assures us, was the only ablution used by Spanish ladies in the time of Philip IV, and apparently it was good enough for the Duke. \|Pic 14: The meeting of Spanish and Aztecs outside Tenochtitlan - a folding screen mural by Roberto Cueva del Río (Click on image to enlarge)\| Imagine, then, the redolence of the conquistadores, after weeks of close confinement in a ship, on arrival in a hot country. To make the contrast between the Spaniards and Aztecs even more stark, the Aztecs, being originally Asian, had many fewer merocrine glands than Westerners, and those are the glands that produce sweat. Asians will tell you that even a very clean Westerner smells strong to an Asian nose, so the fragrance of the unwashed conquistadores must have been . impressive if not downright disgusting to the Aztecs. Small wonder that they responded by fumigating the Spaniards with incense as they approached. The Spaniards took it as an honour, but for the Aztecs it was a practical necessity. Sources/further reading (Aztecs) &bull The Badianus Manuscript (Codex Barberini, Latin 241) (original in Vatican Library): An Aztec Herbal of 1552 - intro, trans & annotations by Emily Walcott Emmart, John Hopkins Press, Baltimore, 1940 &bull The Florentine Codex , Book 11 - Earthly Things - trans by Charles E. Dibble and Arthur J.O. Anderson, University of Utah, Part XII, 1963 &bull Aztec Medicine, Health and Nutrition by Bernard R. Ortiz de Montellano, Rutgers University Press, 1990 &bull An Aztec Herbal: The Classic Codex of 1552 - trans & commentary by William Gates, Dover Publications, 1939/2000 &bull Daily Life of the Aztecs by Jacques Soustelle, Stanford University Press, 1961 (English trans) &bull Handbook to Life in the Aztec World by Manuel Aguilar-Moreno, Facts on File, 2006 Sources/further reading (Europe) &bull Katherine Ashenbug, Clean: An Unsanitised History, Profile Books, 2008 &bull John A. Crow, Spain: The Root and the Flower (Harper and Row, 1963) &bull Erna Paris, The End of Days: A Story of Tolerance, Tyranny, and the expulsion of the Jews from Spain (Lester, 1995). &bull Pics 1, 3 & 14: Photos by Ian Mursell/Mexicolore &bull Pics 2 & 11: Photos by Sean Sprague/Mexicolore &bull Badianus Manuscript images scanned from our own copy of the 1940 facsimile edition (see above) &bull Florentine Codex (original in the Biblioteca Medicea Laurenziana, Florence): images scanned from our own copy of the Club Internacional del Libro 3-volume facsimile edition, Madrid, 1994 &bull Codex Tudela image scanned from our copy of the Testimonio Compañía Editorial facsimile edition, Madrid, 2002 &bull Pic 7: from Medieval Life and People (Clip Art) - Dover Publications, New York, 2007 &bull Pic 8: from Wikipedia/Black Death &bull Pics 9 & 13: courtesy Wellcome Library, London &bull Pic 10: from the Gibraltar Museum website &bull Pic 12 (left): from Wikipedia/Cardinal Cisneros &bull Pic 12 (right): photo courtesy Barry Liimakka Migration into the continents Edit The specifics of Paleo-Indian migration to and throughout the Americas, including the exact dates and routes traveled, are subject to ongoing research and discussion. The traditional theory has been that these early migrants moved into the Beringia land bridge between eastern Siberia and present-day Alaska around 40,000 – 17,000 years ago, when sea levels were significantly lowered due to the Quaternary glaciation. These people are believed to have followed herds of now-extinct Pleistocene megafauna along ice-free corridors that stretched between the Laurentide and Cordilleran ice sheets. Another route proposed is that, either on foot or using primitive boats, they migrated down the Pacific Northwest coast to South America. Evidence of the latter would since have been covered by a sea level rise of a hundred meters following the last ice age. Archaeologists contend that the Paleo-Indian migration out of Beringia (eastern Alaska), ranges from 40,000 to around 16,500 years ago. This time range is a hot source of debate. The few agreements achieved to date are the origin from Central Asia, with widespread habitation of the Americas during the end of the last glacial period, or more specifically what is known as the late glacial maximum, around 16,000 – 13,000 years before present. The American Journal of Human Genetics released an article in 2007 stating "Here we show, by using 86 complete mitochondrial genomes, that all Indigenous American haplogroups, including Haplogroup X (mtDNA), were part of a single founding population." Amerindian groups in the Bering Strait region exhibit perhaps the strongest DNA or mitochondrial DNA relations to Siberian peoples. The genetic diversity of Amerindian indigenous groups increase with distance from the assumed entry point into the Americas. Certain genetic diversity patterns from West to East suggest, particularly in South America, that migration proceeded first down the west coast, and then proceeded eastward. Geneticists have variously estimated that peoples of Asia and the Americas were part of the same population from 42,000 to 21,000 years ago. New studies shed light on the founding population of indigenous Americans, suggesting that their ancestry traced to both east Asian and western Eurasians who migrated to North America directly from Siberia. A 2013 study in the journal Nature reported that DNA found in the 24,000-year-old remains of a young boy in Mal’ta Siberia suggest that up to one-third of the indigenous Americans may have ancestry that can be traced back to western Eurasians, who may have "had a more north-easterly distribution 24,000 years ago than commonly thought" Professor Kelly Graf said that "Our findings are significant at two levels. First, it shows that Upper Paleolithic Siberians came from a cosmopolitan population of early modern humans that spread out of Africa to Europe and Central and South Asia. Second, Paleoindian skeletons with phenotypic traits atypical of modern-day Native Americans can be explained as having a direct historical connection to Upper Paleolithic Siberia." A route through Beringia is seen as more likely than the Solutrean hypothesis. On October 3, 2014, the Oregon cave where the oldest DNA evidence of human habitation in North America was found was added to the National Register of Historic Places. The DNA, radiocarbon dated to 14,300 years ago, was found in fossilized human coprolites uncovered in the Paisley Five Mile Point Caves in south central Oregon. Lithic stage (before 8000 BCE) Edit The Lithic stage or Paleo-Indian period, is the earliest classification term referring to the first stage of human habitation in the Americas, covering the Late Pleistocene epoch. The time period derives its name from the appearance of "Lithic flaked" stone tools. Stone tools, particularly projectile points and scrapers, are the primary evidence of the earliest well known human activity in the Americas. Lithic reduction stone tools are used by archaeologists and anthropologists to classify cultural periods. Archaic stage (8000 BCE – 1000 BCE) Edit Several thousand years after the first migrations, the first complex civilizations arose as hunter-gatherers settled into semi-agricultural communities. Identifiable sedentary settlements began to emerge in the so-called Middle Archaic period around 6000 BCE. Particular archaeological cultures can be identified and easily classified throughout the Archaic period. In the late Archaic, on the north-central coastal region of Peru, a complex civilization arose which has been termed the Norte Chico civilization, also known as Caral-Supe. It is the oldest known civilization in the Americas and one of the five sites where civilization originated independently and indigenously in the ancient world, flourishing between the 30th and 18th centuries BC. It pre-dated the Mesoamerican Olmec civilization by nearly two millennia. It was contemporaneous with the Egypt following the unification of its kingdom under Narmer and the emergence of the first Egyptian hieroglyphics. Monumental architecture, including earthwork platform mounds and sunken plazas have been identified as part of the civilization. Archaeological evidence points to the use of textile technology and the worship of common god symbols. Government, possibly in the form of theocracy, is assumed to have been required to manage the region. However, numerous questions remain about its organization. In archaeological nomenclature, the culture was pre-ceramic culture of the pre-Columbian Late Archaic period. It appears to have lacked ceramics and art. Ongoing scholarly debate persists over the extent to which the flourishing of Norte Chico resulted from its abundant maritime food resources, and the relationship that these resources would suggest between coastal and inland sites. The role of seafood in the Norte Chico diet has been a subject of scholarly debate. In 1973, examining the Aspero region of Norte Chico, Michael E. Moseley contended that a maritime subsistence (seafood) economy had been the basis of society and its early flourishing. This theory, later termed "maritime foundation of Andean Civilization" was at odds with the general scholarly consensus that civilization arose as a result of intensive grain-based agriculture, as had been the case in the emergence of civilizations in northeast Africa (Egypt) and southwest Asia (Mesopotamia). While earlier research pointed to edible domestic plants such as squash, beans, lucuma, guava, pacay, and camote at Caral, publications by Haas and colleagues have added avocado, achira, and maize (Zea Mays) to the list of foods consumed in the region. In 2013, Haas and colleagues reported that maize was a primary component of the diet throughout the period of 3000 to 1800 BC. Cotton was another widespread crop in Norte Chico, essential to the production of fishing nets and textiles. Jonathan Haas noted a mutual dependency, whereby "The prehistoric residents of the Norte Chico needed the fish resources for their protein and the fishermen needed the cotton to make the nets to catch the fish." In the 2005 book 1491: New Revelations of the Americas Before Columbus, journalist Charles C. Mann surveyed the literature at the time, reporting a date "sometime before 3200 BC, and possibly before 3500 BC" as the beginning date for the formation of Norte Chico. He notes that the earliest date securely associated with a city is 3500 BC, at Huaricanga in the (inland) Fortaleza area. The Norte Chico civilization began to decline around 1800 BC as more powerful centers appeared to the south and north along its coast, and to the east within the Andes Mountains. Mesoamerica, the Woodland Period, and Mississippian culture (2000 BCE – 500 CE) Edit After the decline of the Norte Chico civilization, several large, centralized civilizations developed in the Western Hemisphere: Chavin, Nazca, Moche, Huari, Quitus, Cañaris, Chimu, Pachacamac, Tiahuanaco, Aymara and Inca in the Central Andes (Ecuador, Peru and Bolivia) Muisca in Colombia Taínos in Dominican Republic (Hispaniola, Española) and part of Caribbean and the Olmecs, Maya, Toltecs, Mixtecs, Zapotecs, Aztecs and Purepecha in southern North America (Mexico, Guatemala). The Olmec civilization was the first Mesoamerican civilization, beginning around 1600–1400 BC and ending around 400 BC. Mesoamerica is considered one of the six sites around the globe in which civilization developed independently and indigenously. This civilization is considered the mother culture of the Mesoamerican civilizations. The Mesoamerican calendar, numeral system, writing, and much of the Mesoamerican pantheon seem to have begun with the Olmec. Some elements of agriculture seem to have been practiced in Mesoamerica quite early. The domestication of maize is thought to have begun around 7,500 to 12,000 years ago. The earliest record of lowland maize cultivation dates to around 5100 BC. Agriculture continued to be mixed with a hunting-gathering-fishing lifestyle until quite late compared to other regions, but by 2700 BC, Mesoamericans were relying on maize, and living mostly in villages. Temple mounds and classes started to appear. By 1300/ 1200 BC, small centres coalesced into the Olmec civilization, which seems to have been a set of city-states, united in religious and commercial concerns. The Olmec cities had ceremonial complexes with earth/clay pyramids, palaces, stone monuments, aqueducts and walled plazas. The first of these centers was at San Lorenzo (until 900 bc). La Venta was the last great Olmec centre. Olmec artisans sculpted jade and clay figurines of Jaguars and humans. Their iconic giant heads – believed to be of Olmec rulers – stood in every major city. The Olmec civilization ended in 400 BC, with the defacing and destruction of San Lorenzo and La Venta, two of the major cities. It nevertheless spawned many other states, most notably the Mayan civilization, whose first cities began appearing around 700–600 BC. Olmec influences continued to appear in many later Mesoamerican civilizations. Cities of the Aztecs, Mayas, and Incas were as large and organized as the largest in the Old World, with an estimated population of 200,000 to 350,000 in Tenochtitlan, the capital of the Aztec Empire. The market established in the city was said to have been the largest ever seen by the conquistadors when they arrived. The capital of the Cahokians, Cahokia, located near modern East St. Louis, Illinois, may have reached a population of over 20,000. At its peak, between the 12th and 13th centuries, Cahokia may have been the most populous city in North America. Monk's Mound, the major ceremonial center of Cahokia, remains the largest earthen construction of the prehistoric New World. These civilizations developed agriculture as well, breeding maize (corn) from having ears 2–5 cm in length to perhaps 10–15 cm in length. Potatoes, tomatoes, beans (greens), pumpkins, avocados, and chocolate are now the most popular of the pre-Columbian agricultural products. The civilizations did not develop extensive livestock as there were few suitable species, although alpacas and llamas were domesticated for use as beasts of burden and sources of wool and meat in the Andes. By the 15th century, maize was being farmed in the Mississippi River Valley after introduction from Mexico. The course of further agricultural development was greatly altered by the arrival of Europeans. Classic stage (800 BCE – 1533 CE) Edit Cahokia was a major regional chiefdom, with trade and tributary chiefdoms located in a range of areas from bordering the Great Lakes to the Gulf of Mexico. The Iroquois League of Nations or "People of the Long House", based in present-day upstate and western New York, had a confederacy model from the mid-15th century. It has been suggested that their culture contributed to political thinking during the development of the later United States government. Their system of affiliation was a kind of federation, different from the strong, centralized European monarchies. Leadership was restricted to a group of 50 sachem chiefs, each representing one clan within a tribe the Oneida and Mohawk people had nine seats each the Onondagas held fourteen the Cayuga had ten seats and the Seneca had eight. Representation was not based on population numbers, as the Seneca tribe greatly outnumbered the others. When a sachem chief died, his successor was chosen by the senior woman of his tribe in consultation with other female members of the clan property and hereditary leadership were passed matrilineally. Decisions were not made through voting but through consensus decision making, with each sachem chief holding theoretical veto power. The Onondaga were the "firekeepers", responsible for raising topics to be discussed. They occupied one side of a three-sided fire (the Mohawk and Seneca sat on one side of the fire, the Oneida and Cayuga sat on the third side.) Elizabeth Tooker, an anthropologist, has said that it was unlikely the US founding fathers were inspired by the confederacy, as it bears little resemblance to the system of governance adopted in the United States. For example, it is based on inherited rather than elected leadership, selected by female members of the tribes, consensus decision-making regardless of population size of the tribes, and a single group capable of bringing matters before the legislative body. Long-distance trading did not prevent warfare and displacement among the indigenous peoples, and their oral histories tell of numerous migrations to the historic territories where Europeans encountered them. The Iroquois invaded and attacked tribes in the Ohio River area of present-day Kentucky and claimed the hunting grounds. Historians have placed these events as occurring as early as the 13th century, or in the 17th century Beaver Wars. Through warfare, the Iroquois drove several tribes to migrate west to what became known as their historically traditional lands west of the Mississippi River. Tribes originating in the Ohio Valley who moved west included the Osage, Kaw, Ponca and Omaha people. By the mid-17th century, they had resettled in their historical lands in present-day Kansas, Nebraska, Arkansas and Oklahoma. The Osage warred with Caddo-speaking Native Americans, displacing them in turn by the mid-18th century and dominating their new historical territories. Alcohol in the Ancient World This lecture and discussion-based course provides an introduction to the production and consumption of beer, wine, and other fermented beverages across the ancient world. We will explore the full range of available source material – written evidence, physical remains, artistic representations, ethnographic accounts, and experimental archaeology – to develop an account of alcohol as a uniquely potent form of material culture that was embedded within complex webs of social, political, economic, and ritual activity.
\|Part of the Politics series\| \|Basic forms of government\| \|Part of a series on\| Democracy (Greek: δημοκρατία dēmokratía, literally "rule of the people"), in modern usage, is a system of government in which the citizens exercise power directly or elect representatives from among themselves to form a governing body, such as a parliament. Democracy is sometimes referred to as "rule of the majority". Democracy is a system of processing conflicts in which outcomes depend on what participants do, but no single force controls what occurs and its outcomes. The uncertainty of outcomes is inherent in democracy, which makes all forces struggle repeatedly for the realization of their interests, being the devolution of power from a group of people to a set of rules. Western democracy, as distinct from that which existed in pre-modern societies, is generally considered to have originated in city states such as Classical Athens and the Roman Republic, where various schemes and degrees of enfranchisement of the free male population were observed before the form disappeared in the West at the beginning of late antiquity. The English word dates to the 16th century, from the older Middle French and Middle Latin equivalents. According to political scientist Larry Diamond, democracy consists of four key elements: (a) A political system for choosing and replacing the government through free and fair elections; (b) The active participation of the people, as citizens, in politics and civic life; (c) Protection of the human rights of all citizens, and (d) A rule of law, in which the laws and procedures apply equally to all citizens. The term appeared in the 5th century BC, to denote the political systems then existing in Greek city-states, notably Athens, to mean "rule of the people", in contrast to aristocracy (ἀριστοκρατία, aristokratía), meaning "rule of an elite". While theoretically these definitions are in opposition, in practice the distinction has been blurred historically, the political system of Classical Athens, for example, granted democratic citizenship to free men and excluded slaves and women from political participation. In 1906, Finland became the first government to herald a more inclusive democracy at the national level; in virtually all democratic governments throughout ancient and modern history, democratic citizenship consisted of an elite class until full enfranchisement was won for all adult citizens in most modern democracies through the suffrage movements of the 19th and 20th centuries. Democracy contrasts with forms of government where power is either held by an individual, as in an absolute monarchy, or where power is held by a small number of individuals, as in an oligarchy. Nevertheless, these oppositions, inherited from Greek philosophy, are now ambiguous because contemporary governments have mixed democratic, oligarchic, and monarchic elements. Karl Popper defined democracy in contrast to dictatorship or tyranny, thus focusing on opportunities for the people to control their leaders and to oust them without the need for a revolution. - 1 Characteristics - 2 History - 3 Measurement of democracy - 4 Types of governmental democracies - 4.1 Basic forms - 4.2 Variants - 4.2.1 Constitutional monarchy - 4.2.2 Republic - 4.2.3 Liberal democracy - 4.2.4 Socialist - 4.2.5 Anarchist - 4.2.6 Sortition - 4.2.7 Consociational - 4.2.8 Consensus democracy - 4.2.9 Supranational - 4.2.10 Inclusive - 4.2.11 Participatory politics - 4.2.12 Cosmopolitan - 4.2.13 Creative democracy - 4.2.14 Guided democracy - 5 Non-governmental democracy - 6 Theory - 7 Criticism - 8 Development - 9 See also - 10 References - 11 Further reading - 12 External links No consensus exists on how to define democracy, but legal equality, political freedom and rule of law have been identified as important characteristics. These principles are reflected in all eligible citizens being equal before the law and having equal access to legislative processes, for example, in a representative democracy, every vote has equal weight, no unreasonable restrictions can apply to anyone seeking to become a representative,[according to whom?] and the freedom of its eligible citizens is secured by legitimised rights and liberties which are typically protected by a constitution. Other uses of "democracy" include that of direct democracy. One theory holds that democracy requires three fundamental principles: (1) upward control, i.e. sovereignty residing at the lowest levels of authority, (2) political equality, and (3) social norms by which individuals and institutions only consider acceptable acts that reflect the first two principles of upward control and political equality. The term "democracy" is sometimes used as shorthand for liberal democracy, which is a variant of representative democracy that may include elements such as political pluralism; equality before the law; the right to petition elected officials for redress of grievances; due process; civil liberties; human rights; and elements of civil society outside the government. Roger Scruton argues that democracy alone cannot provide personal and political freedom unless the institutions of civil society are also present. In some countries, notably in the United Kingdom which originated the Westminster system, the dominant principle is that of parliamentary sovereignty, while maintaining judicial independence. In the United States, separation of powers is often cited as a central attribute; in India, parliamentary sovereignty is subject to the Constitution of India which includes judicial review. Though the term "democracy" is typically used in the context of a political state, the principles also are applicable to private organisations. Majority rule is often listed as a characteristic of democracy. Hence, democracy allows for political minorities to be oppressed by the "tyranny of the majority" in the absence of legal protections of individual or group rights. An essential part of an "ideal" representative democracy is competitive elections that are substantively and procedurally "fair," i.e., just and equitable. In some countries, freedom of political expression, freedom of speech, freedom of the press, and internet democracy are considered important to ensure that voters are well informed, enabling them to vote according to their own interests. It has also been suggested that a basic feature of democracy is the capacity of all voters to participate freely and fully in the life of their society, with its emphasis on notions of social contract and the collective will of all the voters, democracy can also be characterised as a form of political collectivism because it is defined as a form of government in which all eligible citizens have an equal say in lawmaking. While representative democracy is sometimes equated with the republican form of government, the term "republic" classically has encompassed both democracies and aristocracies. Many democracies are constitutional monarchies, such as the United Kingdom. The term "democracy" first appeared in ancient Greek political and philosophical thought in the city-state of Athens during classical antiquity. The word comes from demos, "common people" and kratos, strength. Led by Cleisthenes, Athenians established what is generally held as the first democracy in 508–507 BC. Cleisthenes is referred to as "the father of Athenian democracy." Athenian democracy took the form of a direct democracy, and it had two distinguishing features: the random selection of ordinary citizens to fill the few existing government administrative and judicial offices, and a legislative assembly consisting of all Athenian citizens. All eligible citizens were allowed to speak and vote in the assembly, which set the laws of the city state. However, Athenian citizenship excluded women, slaves, foreigners (μέτοικοι / métoikoi), non-landowners, and men under 20 years of age.[contradictory] The exclusion of large parts of the population from the citizen body is closely related to the ancient understanding of citizenship; in most of antiquity the benefit of citizenship was tied to the obligation to fight war campaigns. Athenian democracy was not only direct in the sense that decisions were made by the assembled people, but also the most direct in the sense that the people through the assembly, boule and courts of law controlled the entire political process and a large proportion of citizens were involved constantly in the public business. Even though the rights of the individual were not secured by the Athenian constitution in the modern sense (the ancient Greeks had no word for "rights"), the Athenians enjoyed their liberties not in opposition to the government but by living in a city that was not subject to another power and by not being subjects themselves to the rule of another person. Range voting appeared in Sparta as early as 700 BC. The Apella was an assembly of the people, held once a month, in which every male citizen of at least 30 years of age could participate; in the Apella, Spartans elected leaders and cast votes by range voting and shouting. Aristotle called this "childish", as compared with the stone voting ballots used by the Athenians. Sparta adopted it because of its simplicity, and to prevent any bias voting, buying, or cheating that was predominant in the early democratic elections. Even though the Roman Republic contributed significantly to many aspects of democracy, only a minority of Romans were citizens with votes in elections for representatives, the votes of the powerful were given more weight through a system of gerrymandering, so most high officials, including members of the Senate, came from a few wealthy and noble families. In addition, the Roman Republic was the first government in the western world to have a Republic as a nation-state, although it didn't have much of a democracy, the Romans invented the concept of classics and many works from Ancient Greece were preserved. Additionally, the Roman model of governance inspired many political thinkers over the centuries, and today's modern representative democracies imitate more the Roman than the Greek models because it was a state in which supreme power was held by the people and their elected representatives, and which had an elected or nominated leader. Other cultures, such as the Iroquois Nation in the Americas between around 1450 and 1600 AD also developed a form of democratic society before they came in contact with the Europeans, this indicates that forms of democracy may have been invented in other societies around the world. During the Middle Ages, there were various systems involving elections or assemblies, although often only involving a small part of the population, these included: - the Frostating, Gulating, Eidsivating and Borgarting in Norway, - the Althing in Iceland, - the Løgting in the Faeroe Islands, - Scandinavian Things, - the election of Uthman in the Rashidun Caliphate, - the South Indian Kingdom of the Chola in the state of Tamil Nadu in the Indian Subcontinent had an electoral system at 920 A.D., about 1100 years ago, - Carantania, old Slavic/Slovenian principality, the Ducal Inauguration from 7th to 15th century, - the upper-caste election of the Gopala in the Bengal region of the Indian Subcontinent, - the Holy Roman Empire's Hoftag and Imperial Diets (mostly Nobles and Clergy), - Frisia in the 10th–15th Century (Weight of vote based on landownership) - the Polish–Lithuanian Commonwealth (10% of population), - certain medieval Italian city-states such as Venice, Genoa, Florence, Pisa, Lucca, Amalfi, Siena and San Marino - the Cortes of León, - the tuatha system in early medieval Ireland, - the Veche in Novgorod and Pskov Republics of medieval Russia, - The States in Tirol and Switzerland, - the autonomous merchant city of Sakai in the 16th century in Japan, - Volta-Nigeric societies such as Igbo. - the Mekhk-Khel system of the Nakh peoples of the North Caucasus, by which representatives to the Council of Elders for each teip (clan) were popularly elected by that teip's members. - The 10th Sikh Guru Gobind Singh ji (Nanak X) established the world's first Sikh democratic republic state ending the aristocracy on day of 1st Vasakh 1699 and Gurbani as sole constitution of this Sikh republic on the Indian subcontinent. Most regions in medieval Europe were ruled by clergy or feudal lords. The Kouroukan Fouga divided the Mali Empire into ruling clans (lineages) that were represented at a great assembly called the Gbara. However, the charter made Mali more similar to a constitutional monarchy than a democratic republic. A little closer to modern democracy were the Cossack republics of Ukraine in the 16th and 17th centuries: Cossack Hetmanate and Zaporizhian Sich, the highest post – the Hetman – was elected by the representatives from the country's districts. The Parliament of England had its roots in the restrictions on the power of kings written into Magna Carta (1215), which explicitly protected certain rights of the King's subjects and implicitly supported what became the English writ of habeas corpus, safeguarding individual freedom against unlawful imprisonment with right to appeal. The first representative national assembly in England was Simon de Montfort's Parliament in 1265, the emergence of petitioning is some of the earliest evidence of parliament being used as a forum to address the general grievances of ordinary people. However, the power to call parliament remained at the pleasure of the monarch. Early modern period In 17th century England, there was renewed interest in Magna Carta. The Parliament of England passed the Petition of Right in 1628 which established certain liberties for subjects, the English Civil War (1642–1651) was fought between the King and an oligarchic but elected Parliament, during which the idea of a political party took form with groups debating rights to political representation during the Putney Debates of 1647. Subsequently, the Protectorate (1653-59) and the English Restoration (1660) restored more autocratic rule although Parliament passed the Habeas Corpus Act in 1679, which strengthened the convention that forbade detention lacking sufficient cause or evidence. After the Glorious Revolution of 1688, the Bill of Rights was enacted in 1689, which codified certain rights and liberties, and is still in effect, the Bill set out the requirement for regular elections, rules for freedom of speech in Parliament and limited the power of the monarch, ensuring that, unlike much of Europe at the time, royal absolutism would not prevail. In North America, representative government began in Jamestown, Virginia, with the election of the House of Burgesses (forerunner of the Virginia General Assembly) in 1619. English Puritans who migrated from 1620 established colonies in New England whose local governance was democratic and which contributed to the democratic development of the United States; although these local assemblies had some small amounts of devolved power, the ultimate authority was held by the Crown and the English Parliament. The Puritans (Pilgrim Fathers), Baptists, and Quakers who founded these colonies applied the democratic organisation of their congregations also to the administration of their communities in worldly matters. 18th and 19th centuries The first Parliament of Great Britain was established in 1707, after the merger of the Kingdom of England and the Kingdom of Scotland under the Acts of Union. Although the monarch increasingly became a figurehead, only a small minority actually had a voice; Parliament was elected by only a few percent of the population (less than 3% as late as 1780). During the Age of Liberty in Sweden (1718–1772), civil rights were expanded and power shifted from the monarch to parliament, the taxed peasantry was represented in parliament, although with little influence, but commoners without taxed property had no suffrage. The creation of the short-lived Corsican Republic in 1755 marked the first nation in modern history to adopt a democratic constitution (all men and women above age of 25 could vote). This Corsican Constitution was the first based on Enlightenment principles and included female suffrage, something that was not granted in most other democracies until the 20th century. In the American colonial period before 1776, and for some time after, often only adult white male property owners could vote; enslaved Africans, most free black people and most women were not extended the franchise. On the American frontier, democracy became a way of life, with more widespread social, economic and political equality, although not described as a democracy by the founding fathers, they shared a determination to root the American experiment in the principles of natural freedom and equality. The American Revolution led to the adoption of the United States Constitution in 1787, the oldest surviving, still active, governmental codified constitution, the Constitution provided for an elected government and protected civil rights and liberties for some, but did not end slavery nor extend voting rights in the United States beyond white male property owners (about 6% of the population). The Bill of Rights in 1791 set limits on government power to protect personal freedoms but had little impact on judgements by the courts for the first 130 years after ratification. In 1789, Revolutionary France adopted the Declaration of the Rights of Man and of the Citizen and, although short-lived, the National Convention was elected by all men in 1792. However, in the early 19th century, little of democracy – as theory, practice, or even as word – remained in the North Atlantic world. During this period, slavery remained a social and economic institution in places around the world, this was particularly the case in the United States, and especially in the last fifteen slave states that kept slavery legal in the American South until the Civil War. A variety of organisations were established advocating the movement of black people from the United States to locations where they would enjoy greater freedom and equality. The United Kingdom's Slave Trade Act 1807 banned the trade across the British Empire, which was enforced internationally by the Royal Navy under treaties Britain negotiated with other nations. As the voting franchise in the U.K. was increased, it also was made more uniform in a series of reforms beginning with the Reform Act 1832. In 1833, the United Kingdom passed the Slavery Abolition Act which took effect across the British Empire. Universal male suffrage was established in France in March 1848 in the wake of the French Revolution of 1848. In 1848, several revolutions broke out in Europe as rulers were confronted with popular demands for liberal constitutions and more democratic government. In the 1860 United States Census, the slave population in the United States had grown to four million, and in Reconstruction after the Civil War (late 1860s), the newly freed slaves became citizens with a nominal right to vote for men. Full enfranchisement of citizens was not secured until after the Civil Rights Movement gained passage by the United States Congress of the Voting Rights Act of 1965. 20th and 21st centuries 20th-century transitions to liberal democracy have come in successive "waves of democracy", variously resulting from wars, revolutions, decolonisation, and religious and economic circumstances. Global waves of "democratic regression" reversing democratization, have also occurred in the 1920s and 30s, in the 1960s and 1970s, and in the 2010s. In the 1920s democracy flourished and women's suffrage advanced, but the Great Depression brought disenchantment and most of the countries of Europe, Latin America, and Asia turned to strong-man rule or dictatorships. Fascism and dictatorships flourished in Nazi Germany, Italy, Spain and Portugal, as well as non-democratic governments in the Baltics, the Balkans, Brazil, Cuba, China, and Japan, among others. World War II brought a definitive reversal of this trend in western Europe. The democratisation of the American, British, and French sectors of occupied Germany (disputed), Austria, Italy, and the occupied Japan served as a model for the later theory of government change. However, most of Eastern Europe, including the Soviet sector of Germany fell into the non-democratic Soviet bloc. The war was followed by decolonisation, and again most of the new independent states had nominally democratic constitutions. India emerged as the world's largest democracy and continues to be so. Countries that were once part of the British Empire often adopted the British Westminster system. By 1960, the vast majority of country-states were nominally democracies, although most of the world's populations lived in nations that experienced sham elections, and other forms of subterfuge (particularly in "Communist" nations and the former colonies.) A subsequent wave of democratisation brought substantial gains toward true liberal democracy for many nations. Spain, Portugal (1974), and several of the military dictatorships in South America returned to civilian rule in the late 1970s and early 1980s (Argentina in 1983, Bolivia, Uruguay in 1984, Brazil in 1985, and Chile in the early 1990s). This was followed by nations in East and South Asia by the mid-to-late 1980s. Economic malaise in the 1980s, along with resentment of Soviet oppression, contributed to the collapse of the Soviet Union, the associated end of the Cold War, and the democratisation and liberalisation of the former Eastern bloc countries. The most successful of the new democracies were those geographically and culturally closest to western Europe, and they are now members or candidate members of the European Union. The liberal trend spread to some nations in Africa in the 1990s, most prominently in South Africa, some recent examples of attempts of liberalisation include the Indonesian Revolution of 1998, the Bulldozer Revolution in Yugoslavia, the Rose Revolution in Georgia, the Orange Revolution in Ukraine, the Cedar Revolution in Lebanon, the Tulip Revolution in Kyrgyzstan, and the Jasmine Revolution in Tunisia. According to Freedom House, in 2007 there were 123 electoral democracies (up from 40 in 1972). According to World Forum on Democracy, electoral democracies now represent 120 of the 192 existing countries and constitute 58.2 percent of the world's population. At the same time liberal democracies i.e. countries Freedom House regards as free and respectful of basic human rights and the rule of law are 85 in number and represent 38 percent of the global population. According to Freedom House, starting in 2005, there have been eleven consecutive years in which declines in political rights and civil liberties throughout the world have outnumbered improvements, as populist and nationalist political forces have gained ground everywhere from Poland (under the Law and Justice Party) to the Philippines (under Rodrigo Duterte). Measurement of democracy Several freedom indices are published by several organisations according to their own various definitions of the term: - Freedom in the World published each year since 1972 by the U.S.-based Freedom House ranks countries by political rights and civil liberties that are derived in large measure from the Universal Declaration of Human Rights. Countries are assessed as free, partly free, or unfree. - Worldwide Press Freedom Index is published each year since 2002 (except that 2011 was combined with 2012) by France-based Reporters Without Borders. Countries are assessed as having a good situation, a satisfactory situation, noticeable problems, a difficult situation, or a very serious situation. - The Index of Freedom in the World is an index measuring classical civil liberties published by Canada's Fraser Institute, Germany's Liberales Institute, and the U.S. Cato Institute. It is not currently included in the table below. - The CIRI Human Rights Data Project measures a range of human, civil, women's and workers rights. It is now hosted by the University of Connecticut, it was created in 1994. In its 2011 report, the U.S. was ranked 38th in overall human rights. - The Democracy Index, published by the U.K.-based Economist Intelligence Unit, is an assessment of countries' democracy. Countries are rated to be either Full Democracies, Flawed Democracies, Hybrid Regimes, or Authoritarian regimes. Full democracies, flawed democracies, and hybrid regimes are considered to be democracies, and the authoritarian nations are considered to be dictatorial, the index is based on 60 indicators grouped in five different categories. - The U.S.-based Polity data series is a widely used data series in political science research. It contains coded annual information on regime authority characteristics and transitions for all independent states with greater than 500,000 total population and covers the years 1800–2006. Polity's conclusions about a state's level of democracy are based on an evaluation of that state's elections for competitiveness, openness and level of participation. Data from this series is not currently included in the table below, the Polity work is sponsored by the Political Instability Task Force (PITF) which is funded by the U.S. Central Intelligence Agency. However, the views expressed in the reports are the authors' alone and do not represent the views of the US Government. - MaxRange, a dataset defining level of democracy and institutional structure(regime-type) on a 100-graded scale where every value represents a unique regime type. Values are sorted from 1–100 based on level of democracy and political accountability. MaxRange defines the value corresponding to all states and every month from 1789 to 2015 and updating. MaxRange is created and developed by Max Range, and is now associated with the university of Halmstad, Sweden. Types of governmental democracies Democracy has taken a number of forms, both in theory and practice, some varieties of democracy provide better representation and more freedom for their citizens than others. However, if any democracy is not structured so as to prohibit the government from excluding the people from the legislative process, or any branch of government from altering the separation of powers in its own favour, then a branch of the system can accumulate too much power and destroy the democracy. The following kinds of democracy are not exclusive of one another: many specify details of aspects that are independent of one another and can co-exist in a single system. Several variants of democracy exist, but there are two basic forms, both of which concern how the whole body of all eligible citizens executes its will. One form of democracy is direct democracy, in which all eligible citizens have active participation in the political decision making, for example voting on policy initiatives directly; in most modern democracies, the whole body of eligible citizens remain the sovereign power but political power is exercised indirectly through elected representatives; this is called a representative democracy. Direct democracy is a political system where the citizens participate in the decision-making personally, contrary to relying on intermediaries or representatives, the use of a lot system, a characteristic of Athenian democracy, is unique to direct democracies. In this system, important governmental and administrative tasks are performed by citizens picked from a lottery. A direct democracy gives the voting population the power to: - Change constitutional laws, - Put forth initiatives, referendums and suggestions for laws, - Give binding orders to elective officials, such as revoking them before the end of their elected term, or initiating a lawsuit for breaking a campaign promise. Within modern-day representative governments, certain electoral tools like referendums, citizens' initiatives and recall elections are referred to as forms of direct democracy. Direct democracy as a government system currently exists in the Swiss cantons of Appenzell Innerrhoden and Glarus, and kurdish cantons of Rojava. Representative democracy involves the election of government officials by the people being represented. If the head of state is also democratically elected then it is called a democratic republic, the most common mechanisms involve election of the candidate with a majority or a plurality of the votes. Most western countries have representative systems. Representatives may be elected or become diplomatic representatives by a particular district (or constituency), or represent the entire electorate through proportional systems, with some using a combination of the two, some representative democracies also incorporate elements of direct democracy, such as referendums. A characteristic of representative democracy is that while the representatives are elected by the people to act in the people's interest, they retain the freedom to exercise their own judgement as how best to do so, such reasons have driven criticism upon representative democracy, pointing out the contradictions of representation mechanisms with democracy Parliamentary democracy is a representative democracy where government is appointed by, or can be dismissed by, representatives as opposed to a "presidential rule" wherein the president is both head of state and the head of government and is elected by the voters. Under a parliamentary democracy, government is exercised by delegation to an executive ministry and subject to ongoing review, checks and balances by the legislative parliament elected by the people. Parliamentary systems have the right to dismiss a Prime Minister at any point in time that they feel he or she is not doing their job to the expectations of the legislature, this is done through a Vote of No Confidence where the legislature decides whether or not to remove the Prime Minister from office by a majority support for his or her dismissal. In some countries, the Prime Minister can also call an election whenever he or she so chooses, and typically the Prime Minister will hold an election when he or she knows that they are in good favour with the public as to get re-elected; in other parliamentary democracies extra elections are virtually never held, a minority government being preferred until the next ordinary elections. An important feature of the parliamentary democracy is the concept of the "loyal opposition", the essence of the concept is that the second largest political party (or coalition) opposes the governing party (or coalition), while still remaining loyal to the state and its democratic principles. Presidential Democracy is a system where the public elects the president through free and fair elections, the president serves as both the head of state and head of government controlling most of the executive powers. The president serves for a specific term and cannot exceed that amount of time. Elections typically have a fixed date and aren't easily changed, the president has direct control over the cabinet, specifically appointing the cabinet members. The president cannot be easily removed from office by the legislature, but he or she cannot remove members of the legislative branch any more easily, this provides some measure of separation of powers. In consequence however, the president and the legislature may end up in the control of separate parties, allowing one to block the other and thereby interfere with the orderly operation of the state, this may be the reason why presidential democracy is not very common outside the Americas, Africa, and Central and Southeast Asia. A semi-presidential system is a system of democracy in which the government includes both a prime minister and a president, the particular powers held by the prime minister and president vary by country. Hybrid or semi-direct Some modern democracies that are predominantly representative in nature also heavily rely upon forms of political action that are directly democratic, these democracies, which combine elements of representative democracy and direct democracy, are termed hybrid democracies, semi-direct democracies or participatory democracies. Examples include Switzerland and some U.S. states, where frequent use is made of referendums and initiatives. The Swiss confederation is a semi-direct democracy, at the federal level, citizens can propose changes to the constitution (federal popular initiative) or ask for a referendum to be held on any law voted by the parliament. Between January 1995 and June 2005, Swiss citizens voted 31 times, to answer 103 questions (during the same period, French citizens participated in only two referendums), although in the past 120 years less than 250 initiatives have been put to referendum. The populace has been conservative, approving only about 10% of the initiatives put before them; in addition, they have often opted for a version of the initiative rewritten by government. In the United States, no mechanisms of direct democracy exists at the federal level, but over half of the states and many localities provide for citizen-sponsored ballot initiatives (also called "ballot measures", "ballot questions" or "propositions"), and the vast majority of states allow for referendums. Examples include the extensive use of referendums in the US state of California, which is a state that has more than 20 million voters. In New England, Town meetings are often used, especially in rural areas, to manage local government, this creates a hybrid form of government, with a local direct democracy and a state government which is representative. For example, most Vermont towns hold annual town meetings in March in which town officers are elected, budgets for the town and schools are voted on, and citizens have the opportunity to speak and be heard on political matters. Many countries such as the United Kingdom, Spain, the Netherlands, Belgium, Scandinavian countries, Thailand, Japan and Bhutan turned powerful monarchs into constitutional monarchs with limited or, often gradually, merely symbolic roles. For example, in the predecessor states to the United Kingdom, constitutional monarchy began to emerge and has continued uninterrupted since the Glorious Revolution of 1688 and passage of the Bill of Rights 1689. In other countries, the monarchy was abolished along with the aristocratic system (as in France, China, Russia, Germany, Austria, Hungary, Italy, Greece and Egypt). An elected president, with or without significant powers, became the head of state in these countries. Elite upper houses of legislatures, which often had lifetime or hereditary tenure, were common in many nations, over time, these either had their powers limited (as with the British House of Lords) or else became elective and remained powerful (as with the Australian Senate). The term republic has many different meanings, but today often refers to a representative democracy with an elected head of state, such as a president, serving for a limited term, in contrast to states with a hereditary monarch as a head of state, even if these states also are representative democracies with an elected or appointed head of government such as a prime minister. The Founding Fathers of the United States rarely praised and often criticised democracy, which in their time tended to specifically mean direct democracy, often without the protection of a constitution enshrining basic rights; James Madison argued, especially in The Federalist No. 10, that what distinguished a democracy from a republic was that the former became weaker as it got larger and suffered more violently from the effects of faction, whereas a republic could get stronger as it got larger and combats faction by its very structure. What was critical to American values, John Adams insisted, was that the government be "bound by fixed laws, which the people have a voice in making, and a right to defend." As Benjamin Franklin was exiting after writing the U.S. constitution, a woman asked him "Well, Doctor, what have we got—a republic or a monarchy?". He replied "A republic—if you can keep it." A liberal democracy is a representative democracy in which the ability of the elected representatives to exercise decision-making power is subject to the rule of law, and moderated by a constitution or laws that emphasise the protection of the rights and freedoms of individuals, and which places constraints on the leaders and on the extent to which the will of the majority can be exercised against the rights of minorities (see civil liberties). In a liberal democracy, it is possible for some large-scale decisions to emerge from the many individual decisions that citizens are free to make; in other words, citizens can "vote with their feet" or "vote with their dollars", resulting in significant informal government-by-the-masses that exercises many "powers" associated with formal government elsewhere. Socialist thought has several different views on democracy. Social democracy, democratic socialism, and the dictatorship of the proletariat (usually exercised through Soviet democracy) are some examples. Many democratic socialists and social democrats believe in a form of participatory, industrial, economic and/or workplace democracy combined with a representative democracy. Within Marxist orthodoxy there is a hostility to what is commonly called "liberal democracy", which they simply refer to as parliamentary democracy because of its often centralised nature, because of their desire to eliminate the political elitism they see in capitalism, Marxists, Leninists and Trotskyists believe in direct democracy implemented through a system of communes (which are sometimes called soviets). This system ultimately manifests itself as council democracy and begins with workplace democracy. (See Democracy in Marxism.) Democracy cannot consist solely of elections that are nearly always fictitious and managed by rich landowners and professional politicians. Anarchists are split in this domain, depending on whether they believe that a majority-rule is tyrannic or not. The only form of democracy considered acceptable to many anarchists is direct democracy. Pierre-Joseph Proudhon argued that the only acceptable form of direct democracy is one in which it is recognised that majority decisions are not binding on the minority, even when unanimous. However, anarcho-communist Murray Bookchin criticised individualist anarchists for opposing democracy, and says "majority rule" is consistent with anarchism. Some anarcho-communists oppose the majoritarian nature of direct democracy, feeling that it can impede individual liberty and opt in favour of a non-majoritarian form of consensus democracy, similar to Proudhon's position on direct democracy. Henry David Thoreau, who did not self-identify as an anarchist but argued for "a better government" and is cited as an inspiration by some anarchists, argued that people should not be in the position of ruling others or being ruled when there is no consent. Anarcho-capitalists, voluntaryists and other right-anarchists oppose institutional democracy as they consider it in conflict with widely held moral values and ethical principles and their conception of individual rights. The a priori Rothbardian argument is that the state is a coercive institution which necessarily violates the non-aggression principle (NAP). Some right-anarchists also criticise democracy on a posteriori consequentialist grounds, in terms of inefficiency or disability in bringing about maximisation of individual liberty, they maintain the people who participate in democratic institutions are foremost driven by economic self-interest. Sometimes called "democracy without elections", sortition chooses decision makers via a random process, the intention is that those chosen will be representative of the opinions and interests of the people at large, and be more fair and impartial than an elected official. The technique was in widespread use in Athenian Democracy and Renaissance Florence and is still used in modern jury selection. A consociational democracy allows for simultaneous majority votes in two or more ethno-religious constituencies, and policies are enacted only if they gain majority support from both or all of them. A consensus democracy, in contrast, would not be dichotomous. Instead, decisions would be based on a multi-option approach, and policies would be enacted if they gained sufficient support, either in a purely verbal agreement, or via a consensus vote—a multi-option preference vote. If the threshold of support were at a sufficiently high level, minorities would be as it were protected automatically. Furthermore, any voting would be ethno-colour blind. Qualified majority voting is designed by the Treaty of Rome to be the principal method of reaching decisions in the European Council of Ministers. This system allocates votes to member states in part according to their population, but heavily weighted in favour of the smaller states, this might be seen as a form of representative democracy, but representatives to the Council might be appointed rather than directly elected. \|Part of the Politics series on\| Inclusive democracy is a political theory and political project that aims for direct democracy in all fields of social life: political democracy in the form of face-to-face assemblies which are confederated, economic democracy in a stateless, moneyless and marketless economy, democracy in the social realm, i.e. self-management in places of work and education, and ecological democracy which aims to reintegrate society and nature. The theoretical project of inclusive democracy emerged from the work of political philosopher Takis Fotopoulos in "Towards An Inclusive Democracy" and was further developed in the journal Democracy & Nature and its successor The International Journal of Inclusive Democracy. The basic unit of decision making in an inclusive democracy is the demotic assembly, i.e. the assembly of demos, the citizen body in a given geographical area which may encompass a town and the surrounding villages, or even neighbourhoods of large cities. An inclusive democracy today can only take the form of a confederal democracy that is based on a network of administrative councils whose members or delegates are elected from popular face-to-face democratic assemblies in the various demoi. Thus, their role is purely administrative and practical, not one of policy-making like that of representatives in representative democracy. The citizen body is advised by experts but it is the citizen body which functions as the ultimate decision-taker . Authority can be delegated to a segment of the citizen body to carry out specific duties, for example to serve as members of popular courts, or of regional and confederal councils, such delegation is made, in principle, by lot, on a rotation basis, and is always recallable by the citizen body. Delegates to regional and confederal bodies should have specific mandates. A Parpolity or Participatory Polity is a theoretical form of democracy that is ruled by a Nested Council structure, the guiding philosophy is that people should have decision making power in proportion to how much they are affected by the decision. Local councils of 25–50 people are completely autonomous on issues that affect only them, and these councils send delegates to higher level councils who are again autonomous regarding issues that affect only the population affected by that council. A council court of randomly chosen citizens serves as a check on the tyranny of the majority, and rules on which body gets to vote on which issue. Delegates may vote differently from how their sending council might wish, but are mandated to communicate the wishes of their sending council. Delegates are recallable at any time. Referendums are possible at any time via votes of most lower-level councils, however, not everything is a referendum as this is most likely a waste of time. A parpolity is meant to work in tandem with a participatory economy. Cosmopolitan democracy, also known as Global democracy or World Federalism, is a political system in which democracy is implemented on a global scale, either directly or through representatives. An important justification for this kind of system is that the decisions made in national or regional democracies often affect people outside the constituency who, by definition, cannot vote. By contrast, in a cosmopolitan democracy, the people who are affected by decisions also have a say in them. According to its supporters, any attempt to solve global problems is undemocratic without some form of cosmopolitan democracy, the general principle of cosmopolitan democracy is to expand some or all of the values and norms of democracy, including the rule of law; the non-violent resolution of conflicts; and equality among citizens, beyond the limits of the state. To be fully implemented, this would require reforming existing international organisations, e.g. the United Nations, as well as the creation of new institutions such as a World Parliament, which ideally would enhance public control over, and accountability in, international politics. Cosmopolitan Democracy has been promoted, among others, by physicist Albert Einstein, writer Kurt Vonnegut, columnist George Monbiot, and professors David Held and Daniele Archibugi. The creation of the International Criminal Court in 2003 was seen as a major step forward by many supporters of this type of cosmopolitan democracy. Creative Democracy is advocated by American philosopher John Dewey, the main idea about Creative Democracy is that democracy encourages individual capacity building and the interaction among the society. Dewey argues that democracy is a way of life in his work of "Creative Democracy: The Task Before Us" and an experience built on faith in human nature, faith in human beings, and faith in working with others. Democracy, in Dewey's view, is a moral ideal requiring actual effort and work by people; it is not an institutional concept that exists outside of ourselves. "The task of democracy", Dewey concludes, "is forever that of creation of a freer and more humane experience in which all share and to which all contribute". Guided democracy is a form of democracy which incorporates regular popular elections, but which often carefully "guides" the choices offered to the electorate in a manner which may reduce the ability of the electorate to truly determine the type of government exercised over them, such democracies typically have only one central authority which is often not subject to meaningful public review by any other governmental authority. Russian-style democracy has often been referred to as a "Guided democracy." Russian politicians have referred to their government as having only one center of power/ authority, as opposed to most other forms of democracy which usually attempt to incorporate two or more naturally competing sources of authority within the same government. Aside from the public sphere, similar democratic principles and mechanisms of voting and representation have been used to govern other kinds of groups. Many non-governmental organisations decide policy and leadership by voting. Most trade unions and cooperatives are governed by democratic elections. Corporations are controlled by shareholders on the principle of one share, one vote. An analogous system, that fuses elements of democracy with sharia law, has been termed islamocracy. Aristotle contrasted rule by the many (democracy/polity), with rule by the few (oligarchy/aristocracy), and with rule by a single person (tyranny or today autocracy/absolute monarchy). He also thought that there was a good and a bad variant of each system (he considered democracy to be the degenerate counterpart to polity). For Aristotle the underlying principle of democracy is freedom, since only in a democracy the citizens can have a share in freedom; in essence, he argues that this is what every democracy should make its aim. There are two main aspects of freedom: being ruled and ruling in turn, since everyone is equal according to number, not merit, and to be able to live as one pleases. But one factor of liberty is to govern and be governed in turn; for the popular principle of justice is to have equality according to number, not worth, ... And one is for a man to live as he likes; for they say that this is the function of liberty, inasmuch as to live not as one likes is the life of a man that is a slave. Early Republican theory A common view among early and renaissance Republican theorists was that democracy could only survive in small political communities. Heeding the lessons of the Roman Republic's shift to monarchism as it grew larger, these Republican theorists held that the expansion of territory and population inevitably led to tyranny. Democracy was therefore highly fragile and rare historically, as it could only survive in small political units, which due to their size were vulnerable to conquest by larger political units. Montesquieu famously said, "if a republic is small, it is destroyed by an outside force; if it is large, it is destroyed by an internal vice." Rousseau asserted, "It is, therefore the natural property of small states to be governed as a republic, of middling ones to be subject to a monarch, and of large empires to be swayed by a despotic prince." The theory of aggregative democracy claims that the aim of the democratic processes is to solicit citizens' preferences and aggregate them together to determine what social policies society should adopt. Therefore, proponents of this view hold that democratic participation should primarily focus on voting, where the policy with the most votes gets implemented. Different variants of aggregative democracy exist. Under minimalism, democracy is a system of government in which citizens have given teams of political leaders the right to rule in periodic elections. According to this minimalist conception, citizens cannot and should not "rule" because, for example, on most issues, most of the time, they have no clear views or their views are not well-founded. Joseph Schumpeter articulated this view most famously in his book Capitalism, Socialism, and Democracy. Contemporary proponents of minimalism include William H. Riker, Adam Przeworski, Richard Posner. According to the theory of direct democracy, on the other hand, citizens should vote directly, not through their representatives, on legislative proposals. Proponents of direct democracy offer varied reasons to support this view. Political activity can be valuable in itself, it socialises and educates citizens, and popular participation can check powerful elites. Most importantly, citizens do not really rule themselves unless they directly decide laws and policies. Governments will tend to produce laws and policies that are close to the views of the median voter—with half to their left and the other half to their right, this is not actually a desirable outcome as it represents the action of self-interested and somewhat unaccountable political elites competing for votes. Anthony Downs suggests that ideological political parties are necessary to act as a mediating broker between individual and governments. Downs laid out this view in his 1957 book An Economic Theory of Democracy. Robert A. Dahl argues that the fundamental democratic principle is that, when it comes to binding collective decisions, each person in a political community is entitled to have his/her interests be given equal consideration (not necessarily that all people are equally satisfied by the collective decision). He uses the term polyarchy to refer to societies in which there exists a certain set of institutions and procedures which are perceived as leading to such democracy. First and foremost among these institutions is the regular occurrence of free and open elections which are used to select representatives who then manage all or most of the public policy of the society. However, these polyarchic procedures may not create a full democracy if, for example, poverty prevents political participation. Similarly, Ronald Dworkin argues that "democracy is a substantive, not a merely procedural, ideal." Deliberative democracy is based on the notion that democracy is government by deliberation. Unlike aggregative democracy, deliberative democracy holds that, for a democratic decision to be legitimate, it must be preceded by authentic deliberation, not merely the aggregation of preferences that occurs in voting. Authentic deliberation is deliberation among decision-makers that is free from distortions of unequal political power, such as power a decision-maker obtained through economic wealth or the support of interest groups. If the decision-makers cannot reach consensus after authentically deliberating on a proposal, then they vote on the proposal using a form of majority rule. Many theorists is discussing the conception of Debliberative Democracy, considering specially the thought of Jürgen Habermas. Radical democracy is based on the idea that there are hierarchical and oppressive power relations that exist in society. Democracy's role is to make visible and challenge those relations by allowing for difference, dissent and antagonisms in decision making processes. Some economists have criticized the efficiency of democracy, citing the premise of the irrational voter, or a voter who makes decisions without all of the facts or necessary information in order to make a truly informed decision. Another argument is that democracy slows down processes because of the amount of input and participation needed in order to go forward with a decision. A common example often quoted to substantiate this point is the high economic development achieved by China (a non-democratic country) as compared to India (a democratic country). According to economists, the lack of democratic participation in countries like China allows for unfettered economic growth. Popular rule as a façade The 20th-century Italian thinkers Vilfredo Pareto and Gaetano Mosca (independently) argued that democracy was illusory, and served only to mask the reality of elite rule. Indeed, they argued that elite oligarchy is the unbendable law of human nature, due largely to the apathy and division of the masses (as opposed to the drive, initiative and unity of the elites), and that democratic institutions would do no more than shift the exercise of power from oppression to manipulation, as Louis Brandeis once professed, "We may have democracy, or we may have wealth concentrated in the hands of a few, but we can't have both." Between 1946 and 2000 Soviet Union/Russia and USA have intervened in at least 117 elections. Plato's The Republic presents a critical view of democracy through the narration of Socrates: "Democracy, which is a charming form of government, full of variety and disorder, and dispensing a sort of equality to equals and unequaled alike." In his work, Plato lists 5 forms of government from best to worst. Assuming that the Republic was intended to be a serious critique of the political thought in Athens, Plato argues that only Kallipolis, an aristocracy led by the unwilling philosopher-kings (the wisest men), is a just form of government. James Madison critiqued direct democracy (which he referred to simply as "democracy") in Federalist No. 10, arguing that representative democracy—which he described using the term "republic"—is a preferable form of government, saying: "... democracies have ever been spectacles of turbulence and contention; have ever been found incompatible with personal security or the rights of property; and have in general been as short in their lives as they have been violent in their deaths." Madison offered that republics were superior to democracies because republics safeguarded against tyranny of the majority, stating in Federalist No. 10: "the same advantage which a republic has over a democracy, in controlling the effects of faction, is enjoyed by a large over a small republic". More recently, democracy is criticised for not offering enough political stability, as governments are frequently elected on and off there tends to be frequent changes in the policies of democratic countries both domestically and internationally. Even if a political party maintains power, vociferous, headline grabbing protests and harsh criticism from the popular media are often enough to force sudden, unexpected political change. Frequent policy changes with regard to business and immigration are likely to deter investment and so hinder economic growth, for this reason, many people have put forward the idea that democracy is undesirable for a developing country in which economic growth and the reduction of poverty are top priorities. This opportunist alliance not only has the handicap of having to cater to too many ideologically opposing factions, but it is usually short lived since any perceived or actual imbalance in the treatment of coalition partners, or changes to leadership in the coalition partners themselves, can very easily result in the coalition partner withdrawing its support from the government. Biased media has been accused of causing political instability, resulting in the obstruction of democracy, rather than its promotion. In representative democracies, it may not benefit incumbents to conduct fair elections. A study showed that incumbents who rig elections stay in office 2.5 times as long as those who permit fair elections. Democracies in countries with high per capita income have been found to be less prone to violence, but in countries with low incomes the tendency is the reverse. Election misconduct is more likely in countries with low per capita incomes, small populations, rich in natural resources, and a lack of institutional checks and balances. Sub-Saharan countries, as well as Afghanistan, all tend to fall into that category. Governments that have frequent elections tend to have significantly more stable economic policies than those governments who have infrequent elections. However, this trend does not apply to governments where fraudulent elections are common. Democracy in modern times has almost always faced opposition from the previously existing government, and many times it has faced opposition from social elites, the implementation of a democratic government within a non-democratic state is typically brought about by democratic revolution. Post-Enlightenment ideologies such as fascism, nazism, and neo-fundamentalism oppose democracy on different grounds, generally citing that the concept of democracy as a constant process is flawed and detrimental to a preferable course of development. Several philosophers and researchers have outlined historical and social factors seen as supporting the evolution of democracy. Cultural factors like Protestantism influenced the development of democracy, rule of law, human rights and political liberty (the faithful elected priests, religious freedom and tolerance has been practiced). Other commentators have mentioned the influence of wealth (e.g. S. M. Lipset, 1959); in a related theory, Ronald Inglehart suggests that improved living-standards can convince people that they can take their basic survival for granted, leading to increased emphasis on self-expression values, which is highly correlated to democracy. Carroll Quigley concludes that the characteristics of weapons are the main predictor of democracy: Democracy tends to emerge only when the best weapons available are easy for individuals to buy and use. By the 1800s, guns were the best personal weapons available, and in America, almost everyone could afford to buy a gun, and could learn how to use it fairly easily. Governments couldn't do any better: it became the age of mass armies of citizen soldiers with guns Similarly, Periclean Greece was an age of the citizen soldier and democracy. Recent theories stress the relevance of education and of human capital – and within them of cognitive ability to increasing tolerance, rationality, political literacy and participation. Two effects of education and cognitive ability are distinguished: a cognitive effect (competence to make rational choices, better information-processing) and an ethical effect (support of democratic values, freedom, human rights etc.), which itself depends on intelligence. Evidence that is consistent with conventional theories of why democracy emerges and is sustained has been hard to come by. Recent statistical analyses have challenged modernisation theory by demonstrating that there is no reliable evidence for the claim that democracy is more likely to emerge when countries become wealthier, more educated, or less unequal. Neither is there convincing evidence that increased reliance on oil revenues prevents democratisation, despite a vast theoretical literature on "the Resource Curse" that asserts that oil revenues sever the link between citizen taxation and government accountability, seen as the key to representative democracy, the lack of evidence for these conventional theories of democratisation have led researchers to search for the "deep" determinants of contemporary political institutions, be they geographical or demographic. More inclusive institutions lead to democracy because as people gain more power, they are able to demand more from the elites, who in turn have to concede more things to keep their position, this virtuous circle, may end up in democracy. An example of this is the disease environment. Places with different mortality rates had different populations and productivity levels around the world, for example, in Africa, the Tsetse fly which is harmful to humans and livestock reduced the ability of the Africans to plow the land. This made Africa less settled, as a consequence, political power was less concentrated. This also affected the colonial institutions that where set in place by the European countries in Africa. If the colonial settlers could live or not in a place made them develop different institutions which led to different economic and social paths, this also affected the distribution of power and the collective actions people could take. As a result, some African countries ended up having democracies and others autocracies. Another example of geographical determinants for democracy is having access to coastal areas and rivers, this natural endowment has a positive relation with economic development thanks to the benefits of trade. Trade brought economic development, which in turn, broaden the power. If the ruler wanted to increase his revenues, he had to protect property rights to create incentives for people to invest, as more people had more power, more concessions had to be made by the ruler and in many places this process lead to democracy. These determinants defined the structur of the society moving the balance of political power. In the 21st century, democracy has become such a popular method of reaching decisions that its application beyond politics to other areas such as entertainment, food and fashion, consumerism, urban planning, education, art, literature, science and theology has been criticised as "the reigning dogma of our time", the argument suggests that applying a populist or market-driven approach to art and literature (for example), means that innovative creative work goes unpublished or unproduced. In education, the argument is that essential but more difficult studies are not undertaken. Science, as a truth-based discipline, is particularly corrupted by the idea that the correct conclusion can be arrived at by popular vote. However, more recently, theorists have also advanced the concept epistemic democracy to assert that democracy actually does a good job tracking the truth. Robert Michels asserts that although democracy can never be fully realised, democracy may be developed automatically in the act of striving for democracy: "The peasant in the fable, when on his death-bed, tells his sons that a treasure is buried in the field, after the old man's death the sons dig everywhere in order to discover the treasure. They do not find it, but their indefatigable labor improves the soil and secures for them a comparative well-being. The treasure in the fable may well symbolise democracy." Dr. Harald Wydra, in his book Communism and The Emergence of Democracy (2007), maintains that the development of democracy should not be viewed as a purely procedural or as a static concept but rather as an ongoing "process of meaning formation". Drawing on Claude Lefort's idea of the empty place of power, that "power emanates from the people [...] but is the power of nobody", he remarks that democracy is reverence to a symbolic mythical authority as in reality, there is no such thing as the people or demos. Democratic political figures are not supreme rulers but rather temporary guardians of an empty place. Any claim to substance such as the collective good, the public interest or the will of the nation is subject to the competitive struggle and times of for[clarification needed] gaining the authority of office and government. The essence of the democratic system is an empty place, void of real people which can only be temporarily filled and never be appropriated, the seat of power is there, but remains open to constant change. As such, what "democracy" is or what is "democratic" progresses throughout history as a continual and potentially never ending process of social construction. In 2010 a study by a German military think-tank analyzed how peak oil might change the global economy, the study raises fears for the survival of democracy itself. It suggests that parts of the population could perceive the upheaval triggered by peak oil as a general systemic crisis, this would create "room for ideological and extremist alternatives to existing forms of government". - Link to the map above - Oxford English Dictionary: Democracy. - "Democracy – Definition of Democracy by Merriam-Webster". - Przeworski, Adam (1991). Democracy and the Market. 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Cambridge University Press. ISBN 978-0-521-80066-2 - Benhabib, Seyla. (1996). Democracy and Difference: Contesting the Boundaries of the Political. Princeton University Press. ISBN 978-0-691-04478-1 - Blattberg, Charles. (2000). From Pluralist to Patriotic Politics: Putting Practice First, Oxford University Press, ISBN 978-0-19-829688-1. - Birch, Anthony H. (1993). The Concepts and Theories of Modern Democracy. London: Routledge. ISBN 978-0-415-41463-0 - Bittar, Eduardo C. B. (2016). "Democracy, Justice and Human Rights: Studies of Critical Theory and Social Philosophy of Law". Saarbrücken: LAP, 2016. ISBN 978-3-659-86065-2 - Castiglione, Dario. (2005). "Republicanism and its Legacy." European Journal of Political Theory. pp 453–65. - Copp, David, Jean Hampton, & John E. Roemer. (1993). The Idea of Democracy. Cambridge University Press. ISBN 978-0-521-43254-2 - Caputo, Nicholas. (2005). America's Bible of Democracy: Returning to the Constitution. SterlingHouse Publisher, Inc. ISBN 978-1-58501-092-9 - Dahl, Robert A. (1991). Democracy and its Critics. Yale University Press. ISBN 978-0-300-04938-1 - Dahl, Robert A. (2000). On Democracy. Yale University Press. ISBN 978-0-300-08455-9 - Dahl, Robert A. Ian Shapiro & Jose Antonio Cheibub. (2003). The Democracy Sourcebook. MIT Press. ISBN 978-0-262-54147-3 - Dahl, Robert A. (1963). A Preface to Democratic Theory. University of Chicago Press. ISBN 978-0-226-13426-0 - Davenport, Christian. (2007). State Repression and the Domestic Democratic Peace. Cambridge University Press. ISBN 978-0-521-86490-9 - Diamond, Larry & Marc Plattner. (1996). The Global Resurgence of Democracy. Johns Hopkins University Press. ISBN 978-0-8018-5304-3 - Diamond, Larry & Richard Gunther. (2001). Political Parties and Democracy. JHU Press. ISBN 978-0-8018-6863-4 - Diamond, Larry & Leonardo Morlino. (2005). Assessing the Quality of Democracy. JHU Press. ISBN 978-0-8018-8287-6 - Diamond, Larry, Marc F. Plattner & Philip J. Costopoulos. (2005). World Religions and Democracy. JHU Press. ISBN 978-0-8018-8080-3 - Diamond, Larry, Marc F. Plattner & Daniel Brumberg. (2003). Islam and Democracy in the Middle East. JHU Press. ISBN 978-0-8018-7847-3 - Elster, Jon. (1998). Deliberative Democracy. Cambridge University Press. ISBN 978-0-521-59696-1 - Emerson, Peter (2007) "Designing an All-Inclusive Democracy." Springer. ISBN 978-3-540-33163-6 - Emerson, Peter (2012) "Defining Democracy." Springer. ISBN 978-3-642-20903-1 - Everdell, William R. (2003) The End of Kings: A History of Republics and Republicans. Chicago: University of Chicago Press. ISBN 0-226-22482-1. - Gabardi, Wayne. (2001). Contemporary Models of Democracy. Polity. - Gutmann, Amy, and Dennis Thompson. (1996). Democracy and Disagreement. Princeton University Press. ISBN 978-0-674-19766-4 - Gutmann, Amy, and Dennis Thompson. (2002). Why Deliberative Democracy? Princeton University Press. ISBN 978-0-691-12019-5 - Haldane, Robert Burdone (1918). The future of democracy. London: Headley Bros. Publishers Ltd. - Halperin, M. H., Siegle, J. T. & Weinstein, M. M. (2005). The Democracy Advantage: How Democracies Promote Prosperity and Peace. Routledge. ISBN 978-0-415-95052-7 - Hansen, Mogens Herman. (1991). The Athenian Democracy in the Age of Demosthenes. Oxford: Blackwell. ISBN 978-0-631-18017-3 - Held, David. (2006). Models of Democracy. Stanford University Press. ISBN 978-0-8047-5472-9 - Inglehart, Ronald. (1997). Modernisation and Postmodernisation. Cultural, Economic, and Political Change in 43 Societies. Princeton University Press. ISBN 978-0-691-01180-6 - Isakhan, Ben and Stockwell, Stephen (co-editors). (2011) The Secret History of Democracy. Palgrave MacMillan. ISBN 978-0-230-24421-4 - Jarvie, I. C.; Milford, K. (2006). Karl Popper: Life and time, and values in a world of facts Volume 1 of Karl Popper: A Centenary Assessment, Karl Milford. Ashgate Publishing, Ltd. ISBN 978-0-7546-5375-2. - Khan, L. Ali. (2003). A Theory of Universal Democracy: Beyond the End of History. Martinus Nijhoff Publishers. ISBN 978-90-411-2003-8 - Köchler, Hans. (1987). The Crisis of Representative Democracy. Peter Lang. ISBN 978-3-8204-8843-2 - Lijphart, Arend. (1999). Patterns of Democracy: Government Forms and Performance in Thirty-Six Countries. Yale University Press. ISBN 978-0-300-07893-0 - Lipset, Seymour Martin. (1959). "Some Social Requisites of Democracy: Economic Development and Political Legitimacy". American Political Science Review. 53 (1): 69–105. doi:10.2307/1951731. JSTOR 1951731. - Macpherson, C. B. (1977). The Life and Times of Liberal Democracy. Oxford University Press. ISBN 978-0-19-289106-8 - Morgan, Edmund. (1989). Inventing the People: The Rise of Popular Sovereignty in England and America. Norton. ISBN 978-0-393-30623-1 - Mosley, Ivo (2003). Democracy, Fascism, and the New World Order. Imprint Academic. ISBN 0 907845 649. - Mosley, Ivo (2013). In The Name Of The People. Imprint Academic. ISBN 9781845402624. - Ober, J.; Hedrick, C. W. (1996). Dēmokratia: a conversation on democracies, ancient and modern. Princeton University Press. ISBN 0-691-01108-7. - Plattner, Marc F. & Aleksander Smolar. (2000). Globalisation, Power, and Democracy. JHU Press. ISBN 978-0-8018-6568-8 - Plattner, Marc F. & João Carlos Espada. (2000). The Democratic Invention. Johns Hopkins University Press. ISBN 978-0-8018-6419-3 - Putnam, Robert. (2001). Making Democracy Work. Princeton University Press. ISBN 978-5-551-09103-5 - Raaflaub, Kurt A.; Ober, Josiah; Wallace, Robert W (2007). Origins of Democracy in Ancient Greece. University of California Press. ISBN 978-0-520-24562-4. - Riker, William H.. (1962). The Theory of Political Coalitions. Yale University Press. - Sen, Amartya K. (1999). "Democracy as a Universal Value". Journal of Democracy. 10 (3): 3–17. doi:10.1353/jod.1999.0055. - Tannsjo, Torbjorn. (2008). Global Democracy: The Case for a World Government. Edinburgh University Press. ISBN 978-0-7486-3499-6. Argues that not only is world government necessary if we want to deal successfully with global problems it is also, pace Kant and Rawls, desirable in its own right. - Thompson, Dennis (1970). The Democratic Citizen: Social Science and Democratic Theory in the 20th Century. Cambridge University Press. ISBN 978-0-521-13173-5 - Vinje, Victor Condorcet (2014). The Versatile Farmers of the North; The Struggle of Norwegian Yeomen for Economic Reforms and Political Power, 1750–1814. Nisus Publications. https://www.amazon.com/dp/B00HU4KHI4/ref=cm_sw_r_cp_dp_T1_u0ypzb4AM7QD3 - Volk, Kyle G. (2014). Moral Minorities and the Making of American Democracy. New York: Oxford University Press. - Weingast, Barry. (1997). "The Political Foundations of the Rule of Law and Democracy". American Political Science Review. 91 (2): 245–263. doi:10.2307/2952354. JSTOR 2952354. - Weatherford, Jack. (1990). Indian Givers: How the Indians Transformed the World. New York: Fawcett Columbine. ISBN 978-0-449-90496-1 - Whitehead, Laurence. (2002). Emerging Market Democracies: East Asia and Latin America. JHU Press. ISBN 978-0-8018-7219-8 - Willard, Charles Arthur. (1996). Liberalism and the Problem of Knowledge: A New Rhetoric for Modern Democracy. University of Chicago Press. ISBN 978-0-226-89845-2 - Wood, E. M. (1995). Democracy Against Capitalism: Renewing historical materialism. Cambridge University Press. ISBN 978-0-521-47682-9 - Wood, Gordon S. (1991). The Radicalism of the American Revolution. Vintage Books. ISBN 978-0-679-73688-2 examines democratic dimensions of republicanism \|Wikimedia Commons has media related to Democracy.\| \|Wikiquote has quotations related to: Democracy\| \|Look up democracy in Wiktionary, the free dictionary.\| \|Library resources about - Democracy at the Stanford Encyclopedia of Philosophy - Dictionary of the History of Ideas: Democracy - The Economist Intelligence Unit's index of democracy - Alexis de Tocqueville, Democracy in America Full hypertext with critical essays on America in 1831–32 from American Studies at the University of Virginia - Data visualizations of data on democratisation and list of data sources on political regimes on 'Our World in Data', by Max Roser. - MaxRange Classifying political regime type and democracy level to all states and months 1789–2015
\|Feature Article - May 2008\| \|by Do-While Jones\| Isochrons are graphs of the amounts of various minerals found in rocks. These graphs supposedly tell how old the rock is. This month we will look at how the method is supposed to work, and see why it doesn’t. The isochron method is considered by some to be the most accurate rock dating method (when it confirms evolutionary prejudice ). Most people, however, don’t know how the method actually works. They just accept the results on face value. Here’s a little tutorial about how ages are calculated using isochrons. Rocks are made up of minerals. Minerals are specific chemical combinations of atoms. For example, table salt is a mineral called sodium chloride. The chemical formula is NaCl, which means it is made of one sodium (a.k.a. Natrium) atom, and one Chlorine atom. Some atoms come in different varieties, called isotopes. You may have heard of uranium 235 and uranium 238. These are two variations of uranium which have slightly different weights. The numbers are measures of how much they weigh. An atomic mass spectrometer is a machine that takes powdered rock and divides it into isotopes. It can tell you how much gold, or iron, or silver, or whatever is in a rock. The idea of “how much” can be expressed two different ways. If we are out prospecting and find a rock that we think might have gold in it, we can take a sample to an assayer to find out “how much” there is. The answer might be 0.1 gram. That is an absolute amount. But, is that a lot of gold? It depends upon how heavy the sample is that we gave to the assayer. If the rock only weighs 0.15 grams, then the rock is 2/3 gold. But if the rock is 3,000 pounds, then 0.1 gram is practically nothing. The second notion of “how much” is based on percentage. Percentage is independent of sample size, so it is often more useful. Atomic mass spectrometers tend to give results as ratios of one isotope to another. This is effectively a percentage. Dividing the amounts of other isotopes by a common isotope effectively normalizes the sample, making the size of the sample irrelevant. Remember that isotopes are differently weighted variations of atoms (elements). Sometimes the weight matters, and sometimes it doesn’t. When it matters, we talk about the ratios of isotopes. When it doesn’t matter, we talk about the ratios of elements. So, with that background, let’s look at some actual data. The data we are going to look at is data from moon rocks brought back by the Apollo 11 astronauts. There are four reasons for using this particular data. First, this isn’t data published by “crackpot creationists.” It is data that was published by “real” scientists. Second, it isn’t data about some insignificant rocks that was only published in an obscure geology journal that nobody ever heard of, and therefore can’t be easily verified. Third, every geologist in the world wanted to analyze these rocks, so NASA carefully screened all the requests and let only the most qualified scientists take the measurements. Every precaution was taken to avoid contamination. The results were carefully peer-reviewed and presented at the Apollo 11 Lunar Science Conference, and the complete proceedings (335 pages) were published in the January 30, 1970, issue of Science (the most prestigious scientific publication in the United States). Fourth, we are going to write more about the findings of the Apollo 11 Lunar Science Conference next month, so we are laying some groundwork here. Here is the raw data, expressed in tabular and plotted form, and some of the official explanation of the data from the Lunar Conference. The Rb-Sr [rubidium-strontium] isotopic data for the lunar samples are shown in Table 1. The total range observed in the 87Sr/86Sr ratio is 0.8 percent. From these data, we have attempted to determine the solidification ages of the lunar rocks. The data have been grouped in different ways on the basis of assumptions regarding their genesis and internal relationships and checked for the requirements of isochronism, that is, a uniform initial 87Sr/86Sr ratio and chemical closure for the same time. If these assumptions are satisfied, we should obtain a linear relationship between the present values of 87Sr/86Sr and 87Rb/86Sr ratios. From the best-fit lines corresponding to various groupings, both the initial 87Sr/86Sr ratio and the age can be obtained. The initial 87Sr/86Sr values, the slopes of the best-fit lines, and the ages thus obtained for various groups of lunar rocks are shown in Table 2. Although there is no a priori reason to group the data, this was deliberately done to search for any differences between the initial Sr-isotopic compositions and ages of the various types of rocks. All the lunar samples studied here can fit a linear relationship on the Sr-evolution diagram (Fig. 1) with an age of 4.43 ± 0.13 x 109 years and an initial 87Sr/86Sr ratio [(87Sr/86Sr)I] of 0.69784 ± 0.00012 (Table 2). 1 Table 1 tells how much of various elements and isotopes were found in the moon rocks. The eight moon rocks of interest are listed in the first eight lines of Table 1. The moon rocks were numbered 10045, 10044, 10058, etc. They were classified as Type A, Type B, etc. in another article. Those classifications are irrelevant for our discussion. In the various columns of Table 1 they listed the number of micrograms of each element per gram of rock. The first column tells how much potassium (K) there was in each sample. The second column tells the amount of rubidium (Rb). The third and fourth columns tell the amount of strontium (Sr) and barium (Ba). The next three columns are simply ratios of data from the first four columns. The next two columns are isotope ratios. The final column is a measure of uncertainty. Figure 1 is their plot of isotope ratios. They found the slope of that line, and inferred an age (4.43 billion years) from the slope of the line. Before we consider their assumptions and the conclusions they drew from their graph, let’s look at something they did not plot. On the X (horizontal) axis we have plotted the amount of rubidium in each moon rock sample. The black diamonds show, on the Y (vertical) axis how much strontium is in that sample. The pink squares show how much barium is in that rock. Notice that the pink squares tend to fall on a line that goes from the lower left corner to the upper right corner, but the black diamonds don’t. The pink squares show that there is a correlation between rubidium and barium in these moon rocks. If the astronauts had brought back a moon rock with 2 units of rubidium, it is a pretty good bet that it would have about 150 units of barium. If they had brought back a moon rock with 5 units of rubidium, there probably would have been about 250 units of barium. Knowing how much rubidium is in the rock helps us guess how much barium there is likely to be. The black squares show there is no correlation between rubidium and strontium. Knowing the amount of rubidium in the rock doesn’t tell us anything about how much strontium is in it. Now, let’s plot that graph again, and include the data about potassium. The potassium data points are shown as orange triangles. Notice that we had to change the scale on the vertical axis because there is much more potassium than strontium or barium. Suppose you used a ruler to draw a straight line through the orange triangles (potassium) and another line drawn through the pink squares (barium). The slope of a line drawn through the potassium data points is much steeper than the slope of the line drawn through the barium data points. But some of the orange triangles would be farther away from their line than the pink squares are from their line. The amount of difference between the data points and the best line you could draw through them is a measure of how well the data is correlated. The slope of the best line you could draw through the data points is a measure of how strong the correlation is. So, there is a better correlation of rubidium and barium, but there is a stronger correlation between rubidium and potassium. There isn’t any correlation to speak of between rubidium and strontium. One reason for showing you these graphs is to explain the concept of correlation. A more important reason is to make the distinction between the facts shown on the graph and speculative inferences drawn from those facts. It is a fact that the more rubidium there is in a moon rock (taken from the Sea of Tranquillity), the more potassium there is. But we can’t say for sure why there is more potassium. We don’t know what process made the elements in the moon rocks; but whatever the process was, it put more potassium in the rocks whenever it put more rubidium in the rocks. The existence of the correlation between potassium and rubidium is factual, but speculation about why there is a correlation is nothing more than speculation. We can’t emphasize this too much. The data shows there is a relationship between the amount of rubidium and the amount of potassium in a moon rock, but it doesn’t tell us anything at all about why that relationship exists. Now, with that background, let’s look at rubidium-strontium data that was graphed in Figure 1. The amount of rubidium 87 isotope is plotted on the horizontal axis. The amount of strontium 87 isotope is plotted on the vertical axis. They drew a sloping line through the data points using the “least squares” method. This is the standard way to do “linear regression.” In other words, there is a well-known, widely accepted mathematical way to define the “best” straight-line fit to a set of data points. The “best” line is the one in which the sum of the squares of all the differences between the data points and the line is the smallest. The data points are properly plotted and the line showing the correlation between the data points is correctly drawn. But there is something you might not have noticed about the graph. The Y axis doesn’t start at 0. It starts at 0.6970. The top of the graph is 0.7050. The amount of rubidium ranges from 2 to 10, but the amount of strontium is never much different from 0.7. So, there isn’t a very strong correlation. The line would be essentially flat at 0.7 if the vertical axis were scaled 0 to 1. In the graphs we plotted, knowing the amount of rubidium helped us greatly guess how much barium and potassium is in the rock. Knowing the amount of rubidium doesn’t really tell us much about the amount of all the isotopes of strontium. In particular, the amount of the strontium 87 isotope is always about 0.7 regardless of how much rubidium 87 there is. The second significant thing is that some of the error bars don’t touch the best-fit line. The error bars are those short line segments going up and down from the actual data points. They represent the amount of uncertainty in the data due to experimental error. It would be more compelling if the best-fit line went through all of the error bars; but the fact that it doesn’t isn’t a deal-breaker. But what does this all have to do with the age of the moon rocks? It all depends upon an assumption about why the line is sloped (slight as that slope might be). How did the line acquire that slope? Rubidium 87 decays into strontium 87 very, very slowly. If we were to analyze those very same rocks billions of years from now, the amounts of rubidium 87 would be slightly less, and the amounts of strontium 87 would be slightly higher. Therefore, billions of years from now, the slope of that line will be just a little bit steeper. The data have been grouped in different ways on the basis of assumptions regarding their genesis and internal relationships and checked for the requirements of isochronism, that is, a uniform initial 87Sr/86Sr ratio and chemical closure for the same time. 2 In other words, the assumption is that when the moon rocks solidified (“chemical closure”), the amount of strontium 87 (the “uniform initial 87Sr/86Sr ratio”) was 0.69784 ± 0.00012 regardless of how much rubidium 87 there was in the rock. In other words, they assume the line was perfectly flat when the rock solidified. They assume that the slope of the line was produced by 4.43 billion years of decay (they actually used the word “evolution”) of rubidium into strontium. There is no valid basis for that assumption. We know that rubidium does not decay (or even evolve ) into barium or potassium. Since the slopes of the rubidium-barium and rubidium-potassium lines are not the result of radioactive decay, why should one assume that the slope of the rubidium-strontium line is? The data tells us that some moon rocks have more rubidium in them than other moon rocks do. The data tells us that some moon rocks have more potassium in them than other moon rocks do. The data doesn’t tell us why some rocks are richer in these minerals than other ones are. It just tells us that they are. The data also tells us that the rocks that are richer in rubidium are richer in potassium. The data doesn’t tell us why that is true—it simply tells us that it is true. It certainly doesn’t tell us that rubidium decayed into potassium or barium. The data tells us that the rocks that are richer in rubidium 87 are richer in strontium 87. It doesn’t tell us why. There is no way to know how much rubidium 87 and strontium 87 were in the rocks to begin with. Therefore, there is no way to tell how much (if any) of the strontium 87 came from the decay of rubidium 87. The isochron dating method rests entirely on the unsubstantiated assumption that the amount of strontium 87 was entirely independent of the amount of rubidium 87 when the moon rocks solidified. We know that the amount of potassium wasn’t independent of the amount of rubidium when the moon rocks solidified. We know that the amount of barium wasn’t independent of the amount of rubidium when the moon rocks solidified. Why should we assume that the strontium 87 was independent? What makes strontium 87 special? If the isochron method is so reliable and accurate, shouldn’t it give consistent results? Shouldn’t the other “reliable” methods of dating rocks give the same ages? It seems like they should. So, let’s look at the other dates given at the Apollo 11 Lunar Conference for these same moon rocks. But let’s do that next month. \|Quick links to\| \|Science Against Evolution \|Back issues of of the Month Science, 30 January 1970, “Rubidium-Strontium and Elemental and Isotopic Abundances of Some Trace Elements in Lunar Samples”, pages 476-479, https://www.science.org/doi/10.1126/science.167.3918.476
A Fallacy is the failure to apply logic to a line of reasoning that renders an argument invalid. The ability to recognize a variety of different forms of fallacy can be useful when analyzing arguments made by others and help avoid making logical errors when forming one’s own beliefs. The structure of a logical argument should follow a certain basic structure. They begin with one or more premises, which act as the arguments starting point and then by applying principles of logic come to a valid conclusion. If A = B and B = C then we can conclude A=C. It is the failure to apply logic rigorously that leads to fallacious arguments. Fallacies are divided into formal and informal groups. A formal fallacy has a flaw in the logical structure of the argument which renders the argument invalid, whilst an informal fallacy has a logical form, but is false due to the characteristics of its premises, or its justification structure. There are dozens of different forms of fallacy some of the most common include:- Ad hominem - where the character of the individual making the opposing argument is attacked, rather than the argument itself. e.g “He’s old, fat and bald. There’s no way he would make a good President.” False dilemma - where the argument proposes only a limited number of possible choices, when a variety of other options may be available. e.g “All people who commit murder should be executed, otherwise once they are released from prison they will murder again.” Post hoc ergo propter hoc - asserting that because event B followed event A, event A caused event B. “My team won after I wore my new shirt, therefore my new shirt is a lucky shirt.” Straw man - where an argument takes the form of a deliberately weak or inaccurate description of the counter-argument rendering it easy to “burn down”. e.g “All modern artists do is slap a bit of paint randomly on the canvas without any skill or understanding, if that is art then my three-year old must be genius.” An appeal to Authority - where an attempt to bolster an argument is made by using well known figure. e.g “We should not go to war with that country because Bono doesn’t want us to.” False Accusations of Fallaciousness Matters are further complicated by arguing parties incorrectly claiming that an assertion is false due to a fallacy. For example, if one party was to declare “Albert Einstein has claimed that time and space are relative qualities of the Universe.”, another party might responded by saying that this is an ‘’’argument from authority’’’. However, Albert Einstein’s claims are based on highly detailed mathematical models that identify him as an expert in this field of inquiry, rather than a casual observer. Equally, if somebody was to make the ad hominem attack “That guy can’t play for the Lakers, he’s only 3 feet tall!”, it would be a valid point as the characteristics of the individual do have a bearing on his ability to play basketball. Whilst it is possible to overcome these issues by clarifying ones point e.g "Einstein's equations demonstrate that time and space are relative qualities of the Universe" or "He's only 3 feet tall which will make it much harder for him to score" - the necessity to validate each and every aspect of every premise would ultimately mean every argument would have to infinitely regress into explaining all aspects of the entire Universe. So certain commonsense, shared assumptions do need to be made in order to communicate an idea. However it remains important to consider the possibility that under certain circumstances the structure of an argument may take the form of a recognized fallacy, but under closer examination may be perfectly valid.

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