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Ableism – Prejudiced thoughts and discriminatory actions based on differences in physical, mental, and/or emotional ability; usually that of able-bodied / minded persons against people with illness, disabilities, or less developed skills / talents.
Accessibility – The extent to which a facility is readily approachable and usable by individuals with disabilities, particularly such areas as the personnel office, worksite and public areas.
Acculturation – refers to the processes by which families, communities and societies react to inter-cultural contact while retaining characteristics of own culture. As a result a new, composite culture emerges, in which some existing cultural features are combined, some are lost, and new features appear. The earliest recorded western discussion of acculturation appears to be that of Plato in 348 BC. More than 100 different taxonomies of acculturation have been formulated since then. See also adaptation, assimilation, enculturation, syncretism and transculturation.
Acculturation Difficulty – A problem stemming from an inability to appropriately adapt to a different culture or environment. The problem is not based on any coexisting mental disorder.
Achieved Status – Social status and prestige of an individual acquired as a result of individual accomplishments (cf. ascribed status).
Achievement Gap (n.) – A term used to describe a persistent trend in the U.S. educational system in which white students achieve greater academic success than students of color. This term can also refer to the gap between girls’ and boys’ academic achievement.
Actor-Observer Effect – The tendency for actors to weigh any situation more heavily when explaining their behavior, while observers weigh the actor’s dispositions more heavily when explaining the same behavior.
Adaptation – is a process of reconciliation and of coming to terms with a changed socio-cultural environment by making “adjustments” in one’s cultural identity. It is also a stage of intercultural sensitivity, which may allow the person to function in a bicultural capacity. In this stage, a person is able to take the perspective of another culture and operate successfully within that culture. The person should know enough about his or her own culture and a second culture to allow a mental shift into the value scheme of the other culture, and an evaluation of behavior based on its norms, rather than the norms of the individual’s culture of origin. This is referred to as “cognitive adaptation.” The more advanced form of adaptation is “behavioral adaptation,” in which the person can produce behaviors appropriate to the norms of the second culture. Adaptation may also refer to patterns of behavior which enable a culture to cope with its surroundings.
Adaptation Level – Individual standards of comparison for evaluating properties of physical and social environment such as crowding and noise.
Adultism – Prejudiced thoughts and discriminatory actions against young people, in favor of older person(s).
Advocacy View – of applied anthropology is the belief that as anthropologists have acquired expertise on human problems and social change, and because they study, understand, and respect cultural values, they should be responsible for making policies affecting people.
Advocate – Someone who speaks up for her/himself and members of his/her identity group; e.g., a woman who lobbies for equal pay for women.
Aesthetics – Appreciation of the qualities discernible in superior works of art; the mind and emotions in relation to a sense of beauty.
Affinal Kin – Persons related by marriage. Direct affinity is the relationship between the husband and his wife’s relations by blood or between the wife and the husband’s relations by blood. Collateral affinity is the relationship between the husband and the relations of his wife’s relations.
Affinals – Relatives by marriage, whether of lineals (e.g., son’s wife) or collaterals (e.g., sister’s husband).
Affinity Group (n) – Also known as employee networks, or employee-resource groups, affinity groups are groups of people who share a common interest. These entities can support organizational and business objectives by serving as liaisons between a company and the community.
Affirmative Action – “Affirmative action” refers to positive steps taken to increase the representation of minorities (racial, ethnic minorities and women in general) in areas of employment, education, and business from which they have been historically excluded.
African American (n) – Of or related to African Americans. The U.S. Census Bureau defines black or African American as “people having origins in any of the black racial groups of Africa. It includes people who indicated their race or races as ‘black, African American, or Negro’ or wrote in entries such as ‘African American,’ ‘Afro American,’ ‘Nigerian,’ or ‘Haitian.’ According to Census 2000, African Americans make up approximately 12.3% of the total U.S. population, and 12.9% including persons of mixed race.
Age Discrimination – is discrimination against a person or group on the basis of age. Age discrimination usually comes in one of two forms: discrimination against youth, and discrimination against the elderly.
Age set – Group uniting all men or women born during a certain historical time span.
Ageism – Prejudiced thoughts and discriminatory actions based on differences in age; usually that of younger persons against older.
Agent – The perpetrator or perpetuator of oppression and/or discrimination; usually a member of the dominant, non-target identity group.
Aggregate – Any collection of individuals who do not interact with one another.
Alaska Natives (n.) – Aboriginal peoples of Alaska, including American Indians, Eskimo, and Aluet peoples. Eskimo people, also called Inuit, are racially distinct from American Indians and are more closely related to peoples of East Asia.
Alien (n.) – The United States Bureau of Citizenship and Immigration Services define an alien as “any person not a citizen or national of the United States.” However, many people take offense at the use of this term because it places emphasis on difference. Preferable terms might be “immigrant” or “refugee,” and for those who have entered the United States illegally, “undocumented workers” as opposed to “illegal aliens.”
Ally – A person of one social identity group who stands up in support of members of another group; typically member of dominant group standing beside member(s) of targeted group; e.g., a male arguing for equal pay for women.
Alternative Medicine -Any form of medicine or healthcare practices which are not within the jurisdiction of the official health care delivery system nor legally sanctioned.
Altruism – A voluntary form of behavior motivated by a desire to improve another person’s welfare rather than the expectation of reward for oneself.
Ambient Environment – Changeable aspects of an individual’s immediate surroundings, e.g., light, sounds, air quality, humidity, temperature etc.
Ambient Stressors – Factors in the environment that contribute to the experience of stress.
Ambilineal – Principle of descent that does not automatically exclude the children of either sons or daughters.
Amerasian (n.) – A term that refers to individuals born in Asian countries whose biological father is a U.S. citizen. The Amerasian Act of 1982 granted permission to certain Amerasian individuals to immigrate to the United States. Those who qualified had to have been born in Cambodia, Korea, Laos, Thailand, or Vietnam after December 31, 1950, and fathered by a U.S. citizen. Family members such as children, spouses or parents, and guardians of the individual were also granted entry. Amerasian is not synonymous to Asian American or Eurasian.
American (n., adj.) – Of or related to the Americas (North, Central, and South America). This term is commonly misused as a synonym for U.S. citizens and residents, as well as their values, beliefs, and behaviors.
American Indian (n., adj.) – Of or related to American Indians. The U.S. Census Bureau defines “American Indians” as “people having origins in any of the original peoples of North and South America (including Central America), and who maintain tribal affiliation or community attachment. According to Census 2000, American Indians and Alaska Natives are approximately 0.9 percent of the total U.S. population, and 1.5% including persons of more than one race. Native American is generally considered the more politically correct alternative to American Indian.
American Indian Movement (AIM) (n.) – AIM was founded in 1968 to act as proponent for Native American rights.
Americanization– Philosophy of immigrant acculturation in which immigrants expected to assimilate to the existing American culture even if this required loss of their original culture.
Americans with Disabilities Act (ADA) (n.) – On July 26, 1990, President George H. W. Bush signed into law the most sweeping legislation in the history of disability rights, the Americans with Disabilities Act (ADA), prohibiting discrimination against, and mandating equal opportunity for, persons with disabilities, in “state and local government services, public accommodations, commercial facilities, and transportation.” The ADA defines a person with a disability as someone with a physical or mental impairment that substantially limits a major life activity, who has a record of such an impairment.
Anchor – A reference point for making judgments. In social judgement theory, anchor is the point corresponding to the centre of the latitude of acceptance.
Androgynous – Someone who reflects an appearance that is both masculine and feminine, or who appears to be neither or both a boy and a girl.
Anglo or Anglo-Saxon (adj.) – Of or related to the descendants of Germanic peoples (Angles, . Saxons, and Jutes) who reigned in Britain until the Norman conquest in 1066.
Animism – is the belief that souls inhabit all or most objects. Animism attributes personalized souls to animals, vegetables, and minerals in a manner that the material object is also governed by the qualities which compose its particular soul. Animistic religions generally do not accept a sharp distinction between spirit and matter.
Anthropocentricity – The belief that humans are the most important elements in the universe and reality can be approached exclusively in terms of human values and experience.
Anthropology – The study of the human species and its immediate ancestors. Anthropology is the comparative study of past and contemporary cultures, focusing on the ways of life, and customs of all peoples of the world. Main sub-disciplines are physical anthropology, archaeology, linguistic anthropology, ethnology (which is also called social or cultural anthropology) and theoretical anthropology, and applied anthropology.
Anticonformity – Any behavior, which is directly antithetical to or contradicts group norms. Also called counterconformity.
Anti-Semitism – The fear or hatred of Jews, Judaism, and related symbols.
Apartheid – was a system of racial segregation used in South Africa from 1948 to the early 1990s. Though first used in 1917 by Jan Smuts, the future Prime Minister of South Africa, apartheid was simply an extension of the segregationist policies of previous white governments in South Africa. The term originates in Afrikaans or Dutch, where it means “separateness“. Races, classified by law into White, Black, Indian, and Coloured groups, were separated, each with their own homelands and institutions. This prevented non-white people from having a vote or influence on the governance. Education, medical care and other public services available to non-white people were vastly inferior and non-whites were not allowed to run businesses or professional practices in those areas designated as ‘White South Africa’.
Applied Anthropology – The application of anthropological data, perspectives, theory, and methods to identify, assess, and solve contemporary social problems.
Appreciative Inquiry (n.) – Appreciative Inquiry is a way of thinking, seeing and acting for powerful, purposeful change. It operates on the assumptions that whatever one wants… already exists. Appreciative Inquiry generates images that affirm the forces that give life and energy.
Aquatic Ape Theory – This hypothesis or theory suggests that the ancestors of humans went through periods of living in aquatic settings and this was responsible for the development of many of the characteristics of Homo genus that are not seen in other primates. This hypothesis has been criticized as well as supported in mainstream paleoanthropology.
Arab (n., adj.) – Of or relating to the cultures or people that have ethnic roots in the following
Arabic- speaking lands – Algeria, Bahrain, Egypt, Iraq, Jordan, Kuwait, Lebanon, Libya, Morocco, Oman, Palestine, Qatar, Saudi Arabia, Sudan, Syria, Tunisia, the United Arab Emirates, and Yemen. “Arab” is not synonymous with “Muslim.” Arabs practice many religions, including Islam, Christianity, Judaism, and others.
Arbitration – Third-party assistance to two or more groups for reaching an agreement, where the third party or arbitror has the power to force everyone to accept a particular solution.
Archaeological Anthropology (Prehistoric Archaeology) – The study of human behavior and cultural patterns and processes through the material remains and artifacts of that culture.
Archaeomagnetic Dating – A method of dating artifacts from the past. Sometimes also called paleomagnetic dating. It is based on the fact that changes in the earth’s magnetic field over time can be recorded as remnant magnetism in materials such as baked clay structure (ovens, kilns, and hearths used much earlier).
Archetype – the original pattern or model from which all things of the same kind are copied or on which they are based; a prototype. Also (in Jungian psychology) a collectively inherited unconscious idea, pattern of thought, image, etc., universally present in individual psyches.
Archival Research – Any study of data in records being studied, which were not collected specifically for the study itself.
Arousal – A state of physiological or psychological excitation.
Arousal/Cost-reward Model – A model of helping, which predicts that people will help if they are aware of a need for help, experience physiological arousal, label that arousal as a response to the victim, and decide that cost and reward favor intervention on their part.
Arranged Marriage – Any marriage in which the selection of a spouse is outside the control of the bride and groom. Usually parents or their representatives select brides or grooms by trying to match compatibility rather than relying on romantic attraction.
Ascribed Status – Social status which is the result of inheritance (cf. achieved status).
Asexual – Having no evident sex or sex organs. In usage, may refer to a person who is not sexually active, or not sexually attracted to other people.
Asian American – Of or related to Asian Americans. The U.S. Census Bureau defines “Asian” as “people having origins in any of the original peoples of Asia or the Indian subcontinent. It includes people who indicated their race or races as ‘Asian,’ ‘Indian,’ ‘Chinese,’ ‘Filipino,’ ‘Korean,’ ‘Japanese,’ ‘Vietnamese,’ or ‘Other Asian.’ Asian Americans are approximately 3.6 percent of the total U.S. population, and 4.2% including persons of mixed race.
Assimilation – is a process of consistent integration whereby members of an ethno-cultural group, typically immigrants, or other minority groups, are “absorbed” into an established larger community. If a child assimilates into a new culture, he/she gives up his/her cultural values and beliefs and adopts the new cultural values in their place. Originates from a Piagetian (Swiss Developmental Psychologist JEAN PIAGET, 1896-1980) term describing a person’s ability to comprehend and integrate new experiences.
Assimilation Effects – Shifts in judgments towards an anchor point in social judgment theory.
Assortative Mating – Nonrandom coupling of individuals based on resemblance of one or more characteristics.
Asylum (n.) – Protection sought in another country for fear of persecution in an individual’s
Attachment Theory – A theory of the formation and characterization of relationships based on the progress and outcome of an individual’s experiences as an infant in relation to the primary caregiver.
Attitude – Evaluation of people, objects, or issues about which an individual has some knowledge.
Attitudes – Internal dispositions involving affect or evaluation of people, objects, behaviors.
Attribution Theory – Attribution theory is a social psychology theory developed by Fritz Heider, Harold Kelley, Edward E. Jones, and Lee Ross. The theory is concerned with the ways in which people explain (or attribute) the behavior of others or themselves (self-attribution) with something else. It explores how individuals “attribute” causes to events and how this cognitive perception affects their usefulness in an organization.
Augmentation Principle – In Kelley’s attribution theory, the idea that the existence of difficulties in performing a behavior results in a stronger conclusion that the actor is the cause of the event.
Autokinetic Effect – A stationary light, when viewed in an otherwise completely dark room, would appear to be moving.
Availability Heuristic – The tendency to be biased by events readily accessible in our memory.
Baak Gwai – A derogatory term meaning “White devil” or “white ghost” used by the Chinese in Mainland China and Hong Kong to refer to Caucasians.
Baby Boomers (n.) – Term used to describe the generation born during the two decades following World War II, from the 1940’s through the ‘60’s, when the United States experienced a significant rise in birth rates.
Balance Theory – A theory of attitude change based on the principle of consistency among elements in a relationship. Psychologist Fritz Heider, proposer of this model suggested that unbalanced states create tension, so people try to reduce tension by changing some attitude.
Banana – Derogatory term for an East Asian person who is “yellow on the outside, white on the inside” used by other Asian Americans to indicate someone who has lost touch with their cultural identity and have over-assimilated in white, American culture.
Band -Basic unit of social organization among foragers. A band includes fewer than 100 people; it often splits up seasonally.
Bargaining – The process by which two or more parties attempt to settle what each shall give and take in their mutual transactions.
Barrio (n.) – The Spanish word for “neighborhood” that can also refer to a predominately Latino/Hispanic area of a neighborhood, city or town. In some contexts, “barrio” may refer to the inner-city or street culture.
Behavioral Cue – A stimulus, either consciously or unconsciously perceived, that elicits or signals a type of behavior. In other words it is a stimulus that provides information about what to do in a particular situation.
Behaviorism – A theoretical perspective, also called learning perspective, made famous by Ivan Pavlov, John B. Watson, B.F.Skinner, Edward Lee Thorndike, in which behavior is explained by external stimuli and learning processes.
Belief in a Just World – The tendency of people to want to believe that the world is “just” so that when they witness an otherwise inexplicable injustice they will rationalize it by searching for things that the victim might have done to deserve it. Also called the just-world theory, just-world fallacy, just-world effect, or just-world hypothesis, Famous proponent is Melvin Lerner.
Belief System – is the way in which a culture collectively constructs a model or framework for how it thinks about something. A religion is a particular kind of belief system. Other examples of general forms of belief systems are ideologies, paradigms and world-views also known by the German word Weltanschauung. In addition to governing almost all aspects of human activity, belief systems have a significant impact on what a culture deems worthy of passing down to following generations as its cultural heritage. This also influences how cultures view the cultural heritage of other cultures. Many people today recognize that there is no one correct belief system or way of thinking. This is known as relativism or conceptual relativism. This contrasts with objectivism and essentialism, both of which posit a reality that is independent of the way in which people conceptualize. A plurality of belief systems is a hallmark of postmodernism.
Bias – Prejudice; an inclination or preference, especially one that interferes with impartial judgment.
Bicultural– A degree of acculturation in which an individual is at an intermediate level of acculturation between two cultures. ( usually the old and new cultures)
Biculturalism – The simultaneous identification with two cultures when an individual feels equally at home in both cultures and feels emotional attachment with both cultures. The term started appearing in the 1950s.
Biethnic – Of two ethnic groups: belonging or relating to two different ethnic groups. Usually used in reference to a person. For example: if a person’s father is French and mother English, she is biethnic though not biracial. See also biracial.
Big Man – In anthropology the most influential man in a tribe of horticulturalists and pastoralists; a person with power in a community. The big man usually occupies no formal office and has no coercive authority but creates his reputation through skills, wisdom, entrepreneurship and generosity to others. His wealth or his position may not pass to his heirs.
Bigendered/Dual Gendered (v) – A person who possesses and expresses a distinctly masculine persona and a distinctly feminine persona. Is comfortable in and enjoys presenting in both gender roles.
Bigotry (n.) – Intolerance of cultures, religions, races, ethnicities, or political beliefs that differ from one’s own.
Bilateral Kinship Calculation – is a system in which kinship ties are calculated equally through both sexes: mother and father, sister and brother, daughter and son, and so on.
Bilingual (adj.) – Of or related to proficiency in two distinct languages.
Bilingual Education – teaching a second language by relying heavily on the native language of the speaker. The background theory claims that a strong sense of one’s one culture and language is necessary to acquire another language and culture.
Biological Anthropology – is the study of human biological variation in time and space; includes evolution, genetics, growth and development, and primatology.
Biological Determinists – are those who argue that human behavior and social organization are biologically determined and not learnt.
Biphobia – The fear or hatred of homosexuality (and other non-heterosexual identities), and persons perceived to be bisexual.
Biracial – A person of two races. Usually, used to refer to people whose parents come from two different races, e.g., father is Chinese and mother English.
Bisexual (adj.) – attracted to members of either the male or female sex.
Black (n., adj.) – Of or related to persons having ethnic origins in the African continent; persons belonging to the African Diaspora. Some individuals have adopted the term to represent all people around the world who are not of white European descent, although this usage is not common. “Black” is often used interchangeably with “African American” in the United States.
Blaming The Victim – Process by which people enhance their belief in a just world by believing that people get what they deserve.
Bobo (n.) – Bourgeois bohemian is a recent term used to refer to the upper-middle and upper class sector of “Generation X” (children of the baby-boomers). Bobos are characterized as a highly educated, politically active, environmentally responsible, art friendly, well-traveled, and technology savvy group that has merged the pre-1950’s concepts of “bourgeois” with a new 1990’s “bohemian.”
Bottom-up Development – Economic and social changes brought about by activities of individuals and social groups in society rather than by the state and its agents.
Bourgeoisie – describes a social class of people who are in the upper or merchant class, whose status or power comes from employment, education, and wealth rather than from aristocratic origin. They are the owners of the means of production (factories, mines, large farms, and other sources of subsistence).
Bride Price -is the payment made by a man to the family from whom he takes a daughter in marriage.
Brown (n., adj.) – A term most often used to refer to people of Latino/Hispanic descent, or of the Latin American Diaspora (Mexico, Central and South America, Puerto Rico, the Dominican Republic, Cuba, as well as Latinos/Hispanics in the United States and Canada). Some individuals may use the word to refer to all people of color.
Bush Doctrine – The Bush Doctrine describes various foreign policy principles of United States president George W. Bush. According to this doctrine, the United States had the right to aggressively protect itself from countries that harbor or give aid to terrorist groups, which was used to justify the 2001 invasion of Afghanistan and Iraq. Further, it contains the controversial policy of preventive war, which held that the United States should depose foreign regimes that represented a potential or perceived threat to the security of the United States, even if that threat was not immediate; a policy of spreading democracy around the world, especially in the Middle East, as a strategy for combating terrorism; and a willingness to pursue U.S. military interests in a unilateral way even without the sanction of allies or international bodies.
Bystander Effect – The finding that a person is less likely to offer help when in the presence of witnesses than when alone. The bystander effect was first demonstrated in the laboratory by John Darley and Bibb Latane in 1968
Capital – Wealth or resources invested in business, with the intent of producing a profit for the owner of the capital.
Capitalism – Economic or socio-economic system in which production and distribution are designed to accumulate capital and create profit. A characteristic feature of the system is the separation of those who own the means of production and those who work for them. The Communist Manifesto by Karl Marx and Friedrich Engels first used the term Kapitalist in 1848. The first use of the word capitalism is by novelist William Thackeray in 1854.
Capitalist World Economy- The single world system, committed to production for sale, with the object of maximizing profits rather than supplying domestic needs. The term was launched by the US historical social scientist, Immanuel Wallerstein.
Caste System – A hereditary system of stratification. Hierarchical social status is ascribed at birth and often dictated by religion or other social norms. Today, it is most commonly associated with the Indian caste system and the Varna in Hinduism.
Categorization – The natural cognitive process of grouping and labeling people, things, etc. based on their similarities. Categorization becomes problematic when the groupings become oversimplified and rigid (e.g. stereotypes).
Catharsis – is a Greek word meaning “purification” or “cleansing“. Nowadays used to mean intense emotional release associated with talking about the underlying causes of a problem. In mystical traditions, catharsis is a process leading to the transcending of psychological, as well as spiritual, traumas and negativities. Used in modern psychotherapy, particularly Freudian psychoanalysis, to describe the act of expressing deep emotions often associated with events in the individual’s past which have never before been adequately expressed.
Caucasian (n., adj.) – Of or related to the Caucasus region, a geographic area between the Black and Caspian seas; a former racial classification that included indigenous persons of Europe, northern Africa, western Asia, and India, characterized by light to brown skin and straight to wavy or curly hair. In the U.S., “Caucasian” is often used interchangeably with “white.”
Charlie – Non-derogatory slang term used by American troops during the Vietnam War as a shorthand term for Vietnamese guerrillas. Shortened from “Victor Charlie”, the phonetic alphabet for Viet Cong, or VC. It was also a mildly derogatory term used by African Americans, in the 1960s and 1970s, for a white person (from James Baldwin’s novel, Blues For Mr. Charlie).
Chicano Movement (n.) – Mexican American individuals and organizations across the country united for the common purpose of increasing educational opportunities, workers rights for farm laborers, land allocation, and resources to Mexican American communities.
Chicano/a (n.) – A term adopted by some Mexican Americans to demonstrate pride in their heritage, born out of the national Chicano Movement that was politically aligned with the Civil Rights Movement to end racial oppression and social inequalities of Mexican Americans. Chicano pertains to the particular experience of Mexican-descended individuals living in the United States. Not all Mexican Americans identify as Chicano.
Chiefdom – Kin-based form of sociopolitical organization between the tribe and the state. It comes with differential access to resources and a permanent political structure. The relations among villages as well as among individuals are unequal, with smaller villages under the authority of leaders in larger villages; it has a two-level settlement hierarchy.
Civil Rights Movement (n.) – The Civil Rights Movement (n.) – The Civil Rights Movement is known as the events that took place between 1955 and 1965 when minority groups across the US sought their rights.
Clan – Form of unilineal descent group based on stipulated descent. A clan is a group of people united by kinship and descent, which is defined by perceived descent from a common ancestor. As kinship based bonds can be merely symbolical in nature some clans share a “stipulated” common ancestor.
Clash of Civilizations – is a hotly debated theory publicized by Samuel P. Huntington with his 1996 book The Clash of Civilizations and the Remaking of World Order. He argues that the world has cultural fault lines similar to the physical ones that cause earthquakes and that people’s cultural/religious identity will be the primary agent of conflict in the post-Cold War world. Bernard Lewis first used the term in an article in the September 1990 issue of The Atlantic Monthly called “The Roots of Muslim Rage.”
Classism – Prejudiced thoughts and discriminatory actions based on difference in socio-economic status, income, class; usually by upper classes against lower.
Coalition – A collection of different people or groups, working toward a common goal.
Codification – The capture and expression of a complex concept in a simple symbol, sign or prop; for example, symbolizing “community” (equity, connection, unity) with a circle.
Collateral Household – is a type of expanded family household including siblings and their spouses and children.
Collectivism – Individualism/Collectivism is one of the Hofstede dimensions in intercultural communication studies. “Collectivism pertains to societies in which people from birth onwards are integrated into strong, cohesive in-groups, which throughout people’s lifetime continue to protect them in exchange for unquestioning loyalty.” (Hofstede, G. (1991).
Collusion – Willing participation in the discrimination against and/or oppression of one’s own group (e.g., a woman who enforces dominant body ideals through her comments and actions).
Colonialism – The political, social, economic, and cultural domination of a territory and its people by a foreign power for an extended time.
Color Blind – the belief in treating everyone “equally” by treating everyone the same; based in the presumption that differences are by definition bad or problematic, and therefore best ignored (i.e., “ I don’t see race, gender, etc.”).
Communism – A political theory of Karl Marx and Friedrich Engels. Communism is characterized by the common ownership of the means of production contra private ownership in capitalism. The Soviet Union was the first communist state and lasted from 1917 to 1991.
Complementary Medicine -Traditional or alternative health beliefs or practices which are brought into a healing practice to enhance the dominant healthcare modality.
Complex Societies – are usually nation states; large and populous, with social stratification and ccentralized forms of governments.
Consanguineal Kin – A blood relative. An individual related by common descent from the same individual. In most societies of the world, kinship can be traced both by common descent and through marriage, although a distinction is usually made between the two categories. The degree of consanguinity between any two people can be calculated as the percentage of genes they share through common descent.
Conspicuous Consumption – the excessive display of material items for the purpose of impressing others. People who make money very quickly or the noveau riche are often portrayed as doing this with unrefined taste. The term was first used by the American economist Thorstein Veblen, in The Theory of the Leisure Class (1899).
Contact Hypothesis – The original scientific motivation for integration of education and the armed forces, this theory posits that bringing peoples of different backgrounds together (on a college campus, for example) will lead to improved relations among them. Additional research has shown this to be true only under certain conditions including – sanction by authority, common goals, and equal status contact (both numerically and psychologically). (Allport, 1957)
Contact Zone – The space in which transculturation takes place – where two different cultures meet and inform each other, often in highly asymmetrical ways.
Core Values – Basic, or central values that integrate a culture and help distinguish it from others.
Corporate Culture -The fundamental philosophy of an organization is determined by its corporate culture. The behavior and actions of individuals within a corporation illustrate the existing culture of that organization.
Cosmology – Ideas and beliefs about the universe as an ordered system, its origin and the place of humans in the universe through which, people in that culture understand the makeup and the workings of all things.
Counterculture – is a sociological term used to describe a cultural or social group whose values and norms are at odds with those of the social mainstream. The term became popular during the youth rebellion and unrest in the USA and Western Europe in the 1960s as a reaction against the conservative social norms of the 1950s. The Russian term Counterculture has a different meaning and is used to define a cultural movement that promotes acting outside the usual conventions of Russian culture – using explicit language, graphical description of sex, violence and illicit activities. Counterculture in an Asian context as launched by Dr. Sebastian Kappen, an Indian Theologian very influential in the third world, means an approach for navigating between the two opposing cultural phenomena in modern Asian countries: (1) invasion by western capitalist culture and (2) the emergence of revivalist movements in reaction. Identification with the first requires losing own identity and with the second results in living in a world of obsolete myths and phantoms of the dead past. Thus discovering one’s own cultural roots in a creative and yet critical fashion while being open to the positive facets of the other. (Adapted from http://www.wikipedia.org)
Cross Cousins – Children of a brother and a sister.
Cross Cultural – Interaction between individuals from different cultures. The term cross-cultural is generally used to describe comparative studies of cultures. Inter cultural is also used for the same meaning. Whereas multiculturalism deals with cultural diversity within a particular nation or social group, cross culturalism is concerned with exchange beyond the boundaries of the nation or cultural group.
Cross Cultural Awareness – develops from cross-cultural knowledge as the learner understands and appreciates the deeper functioning of a culture. This may also be followed by changes in the learner’s own behavior and attitudes and a greater flexibility and openness becomes visible.
Cross Cultural Communication – (also referred to as Intercultural Communication) is a field of study that looks at how people from differing cultural backgrounds try to communicate. As a science, Cross-cultural communication tries to bring together such seemingly unrelated disciplines as communication, information theory, learning theories and cultural anthropology. The aim is to produce increased understanding and some guidelines, which would help people from different cultures to better, communicate with each other.
Cross Cultural Communication Skills – refers to the ability to recognize cultural differences and similarities when dealing with someone from another culture and also the ability to recognize features of own behavior, which are affected by culture.
Cross Cultural Competence – is the final stage of cross-cultural learning and signals the individual’s ability to work effectively across cultures. Cross cultural competency necessitates more than knowledge, awareness and sensitivity because it requires the digestion, integration and transformation of all the skills and information acquired through them and applied to create cultural synergy within the workplace or elsewhere. This should be the aim of all those dealing with multicultural clients, customers or colleagues.
Cross Cultural Knowledge – refers to a surface level familiarization with cultural characteristics, values, beliefs and behaviors. It is vital to basic cross-cultural understanding and without it cross-cultural competence cannot develop.
Cross Cultural Sensitivity – refers to an individual’s ability to read into situations, contexts and behaviors that are culturally rooted and consequently the individual is able to react to them suitably. A suitable response necessitates that the individual no longer carries his/her own culturally predetermined interpretations of the situation or behavior (i.e. good/bad, right/wrong).
Cross Cultural Trainer – Those who train people to become familiar with other cultural norms and to improve their interactions with cultures to which these norms belong.
Cross Culture Counseling – generally refer to any counseling relationship in which two or more of the participants are ethnically different.
Cultivation Continuum – A term used in cultural anthropology. It is a continuum based on the comparative study of nonindustrial cultivating societies in which labor intensity increases and fallowing decreases.
Cultural Alienation – is the process of devaluing or abandoning one’s own culture or cultural background in favor of another.
Cultural Anthropology – The study of contemporary and recent historical cultures among humans all over the world. The focus is on social organization, culture change, economic and political systems and religion. Cultural anthropologists argue that culture is “human nature,” and that all people have a capacity to classify experiences, encode classifications symbolically and teach such abstractions to others. They believe that humans acquire culture through learning and people living in different places or different circumstances may develop different cultures because it is through culture that people can adapt to their environment in non-genetic ways. Cultural anthropology is also referred to as social or socio-cultural anthropology. Key theorists: Franz Boas, Emile Durkheim, Clifford Geertz, Marvin Harris, Claude Levi-Strauss, Karl Marx.
Cultural Boundaries – Cultural Boundaries can be defined as those invisible lines, which divide territories, cultures, traditions, practices, and worldviews. Typically they are not aligned with the physical boundaries of political entities such as nation states.
Cultural Competency -The ability to respond respectfully and effectively to people of all cultures, classes, ethnic background and religions in a manner that recognizes and values cultural differences and similarities.
Cultural Components -Attributes that vary from culture to culture, including religion, language, architecture, cuisine, technology, music, dance, sports, medicine, dress, gender roles, laws, education, government, agriculture, economy, grooming, values, work ethic, etiquette, courtship, recreation, and gestures.
Cultural Construct – the idea that the characteristics people attribute to social categories such as gender, illness, death, status of women, and status of men is culturally defined.
Cultural Convergence – is an idea that increased communication among the peoples of the world via the Internet will lead to the differences among national cultures becoming smaller over time, eventually resulting in the formation of a single global culture. One outcome of this process is that unique national identities will disappear, replaced by a single transnational identity. Henry Jenkins, a professor at the Massachusetts Institute of Technology, USA coined the term in 1998.
Cultural Cringe – refers to an internalized inferiority complex of an entire culture. This leads people of that culture to dismiss their own culture as inferior to the cultures of other countries. In 1950 the Melbourne critic A.A.Philips coined the term Cultural cringe to show how Australians widely assumed that anything produced by local artists, dramatists, actors, musicians and writers was inferior to the works of the British and European counterparts. The term cultural cringe is very close to “cultural alienation” or the process of devaluing or abandoning one’s own culture or cultural background in favor of another.
Cultural Determinists – are those who relate behavior and social organization to cultural or environmental factors. The focus is on variation rather than on universals and stresses learning and the role of culture in human adaptation.
Cultural Diffusion – The spreading of a cultural trait (e.g., material object, idea, or behavior pattern) from one society to another.
Cultural Dissonance -Elements of discord or lack of agreement within a culture.
Cultural Diversity – Differences in race, ethnicity, language, nationality or religion. Cultural diversity refers to the variety or multiformity of human social structures, belief systems, and strategies for adapting to situations in different parts of the world.
Cultural Evolution – Theories that have developed since the mid-19th century, which attempt to explain processes and patterns of cultural change. Often such theories have presented such change as “progress,” from “earlier” forms (“primitive”, “less developed,” “less advanced” etc.) to “later” forms (“more developed,” “more advanced“). These schemes usually have reflected the ethnocentrism of the theorists, as they frequently put their own societies at the pinnacle of “progress.”
Cultural Identity – is the identity of a group or culture or of an individual as her/his belonging to a group or culture affects her/his view of herself/himself. People who feel they belong to the same culture share a common set of norms.
Cultural Imperialism – is the rapid spread or advance of one culture at the expense of others, or its imposition on other cultures, which it modifies, replaces, or destroys-usually due to economic or political reasons.
Cultural landscape-The natural landscape as modified by human activities and bearing the imprint of a culture group or society including buildings, shrines, signage, sports and recreational facilities, economic and agricultural structures, transportation systems, etc.
Cultural Materialism – Is a theoretical approach in Cultural Anthropology that explores and examines culture as a reflection or product of material conditions in a society. Cultural materialism is a variation on basic materialist approaches to understanding culture. The Anthropologist Marvin Harris is a famous representative.
Cultural Norms – are behavior patterns that are typical of specific groups, which have distinct identities, based on culture, language, ethnicity or race separating them from other groups. Such behaviors are learned early in life from parents, teachers, peers and other human interaction. Norms are the unwritten rules that govern individual behavior. Norms assume importance especially when broken or when an individual finds him/herself in a foreign environment dealing with an unfamiliar culture where the norms are different.
Cultural Relativism – The position that the values, beliefs and customs of cultures differ and deserve recognition and acceptance. This principle was established by the German anthropologist Franz Boas (1858-1942) in the first few decades of the 20th century. Cultural relativism as a movement was in part a response to Western ethnocentrism. Between World War I and World War II, “Cultural relativism” was the central tool for American anthropologists in their refusal of Western claims to universality.
Cultural Resource Management (CRM) – is the branch of applied archaeology which aims to preserve archeological sites threatened by prospective dams, highways, and other projects.
Cultural Rights – is the idea that certain rights are vested not in individuals but in larger identifiable groups, such as religious and ethnic minorities and indigenous societies. Cultural rights include a group’s ability to preserve its culture, to raise its children in the ways of its ancestors, to continue practicing its language, and not to be deprived of its economic base by the nation-state or large political entity in which it is located.
Cultural Safety -A concept that originated with the Maori of New Zealand, that focuses on culturally –appropriate health care services, as well as improving healthcare access, inequalities in health, unequal power relations, and the social, political, and historical context of care
Cultural Sensitivity – is a necessary component of cultural competence, meaning that we make an effort to be aware of the potential and actual cultural factors that affect our interactions with others.
Cultural Traits -Distinguishing features of a culture such as language, dress, religion, values, and an emphasis on family; these traits are shared throughout that culture. -is the identity of a group or culture, or of an individual as her/his belonging to a group or culture affects her/his view of her/him. People who feel they belong to the same culture share a common set of norms.
Cultural Universal – General cultural traits and features found in all societies of the world. Some examples are organization of family life; roles of males, females, children and elders; division of labor; religious beliefs and practices; birth and death rituals; stories of creation and myths for explaining the unknown; “rights” and “wrongs” of behavior etc.
Cultural Universalism – Cultural Universalism is the assertion that there exist values, which transcend cultural and national differences. Universalism claims that more “primitive” cultures will eventually evolve to have the same system of law and rights as Western cultures. Cultural relativists on the other hand hold an opposite viewpoint, that a traditional culture is unchangeable. In universalism, an individual is a social unit, possessing inalienable rights, and driven by the pursuit of self-interest. In the cultural relativist model, a community is the basic social unit where concepts such as individualism, freedom of choice, and equality are absent.
Cultural values – The individual’s desirable or preferred way of acting or knowing something that is sustained over time and that governs actions
Culturally Competent Healthcare -Healthcare practice which recognizes the importance of cultural beliefs and practices in restoration and maintenance of health, and thus adapts, modifies and reorients perceptions and practices within a bio-medical setting in response to the cultural background of the patient.
Culture – The shared values, norms, traditions, customs, arts, history, folklore and institutions of a group of people. “Integrated pattern of human knowledge, belief, and behavior that is both a result of and integral to the human capacity for learning and transmitting knowledge to succeeding generations.” The etymological root of the word is from the Latin ‘colere‘ which means to cultivate, from which is derived ‘cultus‘, that which is cultivated or fashioned. In comparison of words such as “Kultur” and “Zivilisation” in German, “culture” and civilization” in English, and “culture” and “civilization” in French the concepts reveal very different perspectives. The meaning of these concepts is however, converging across languages as a result of international contacts, cultural exchanges and other information processes.
Culture of Poverty (n.) – The concept that the conditions of poverty (e.g., unemployment, out-of-wedlock births, teen pregnancies, welfare dependency, etc.) creates within individuals and groups a socially pathological state of mind that perpetuates these same conditions and eventually increases the number of dependents on the state. A culture of poverty assumes that there is a social, pathological or cultural deficiency inherent to members of certain groups that make them prone to being poor which may make the phrase offensive.
Culture Shock – A state of distress and tension with possible physical symptoms after a person relocates to an unfamiliar cultural environment. This term was used by social scientists in the 1950s to describe, the difficulties of a person moving from the country to a big city but now the meaning has changed to mean relocating to a different culture or country. One of the first recorded uses of the term was in 1954 by the anthropologist Dr. Kalervo Oberg who was born to Finnish parents in British Columbia, Canada. While giving a talk to the Women’s Club of Rio de Janeiro, August 3, 1954, he identified four stages of culture shock-the honeymoon of being a newcomer and guest, the hostility and aggressiveness of coming to grips with different way of life, working through feelings of superiority and gaining ability to operate in the culture by learning the language and finally acceptance of another way of living and worldview. (Source: American Anthropologist June, 1974 Vol.76 (2): 357-359.
Daily Indignity (n.) – Refers to the experiences of individuals and groups brought about by behaviors of members of the majority or dominant culture who may willingly or inadvertently assert their unearned privilege or power in a manner that offends discriminates against, or subjugates another individual.
Daughter Languages – are languages developing out of the same parent language; for example, French and Spanish are daughter languages of Latin or Bengali and Hindi are daughter languages of Sanskrit.
Debriefing – Open discussion at the end of a study or experiment when the researcher reveals the complete procedure and background to the subject and explains the reasons for any possible deceptions that may have taken place and were necessary for the success.
Deindividuation – A state of relative anonymity in which a member of a group does not feel identifiable or singled out.
Demand Characteristics – Explicit and implicit perceptual cues, which communicate what behavior is expected in any particular situation.
Demarginalization – The process which facilitates a marginal or stigmatized space becoming ‘normalized‘ so that its population is incorporated into the mainstream.
Denotation – The explicit meaning of a word or expression.
Dependant Variable – A measure of a participant’s responses in a research situation. In a scientifically controlled experiment, changes in the dependant variable are presumed to be caused by the independent variable.
Deportation (n.) – Forced removal of an individual who is not a citizen of the United States when that individual has been found to violate immigration law.
Descent Group – is a permanent social unit whose members claim common ancestry. Usually this is fundamental to tribal society.
Development Anthropology – is the branch of applied anthropology that focuses on social issues and the cultural dimension of economic development. Development here refers to the social action by institutions, private business, state, independent volunteers, who are aiming to modify the economic, technical, political or/and social life of a given place, mostly in developing nations.
Dialogue – “Communication that creates and recreates multiple understandings” (Wink, 1997); it is bidirectional, not zero-sum and may or may not end in agreement; it can be emotional and uncomfortable, but is safe, respectful and has greater understanding as its goal.
Diaspora – The term was originally used by the ancient Greeks to mean citizens of a large city who migrated to a conquered land with the purpose of colonization to assimilate the territory into the empire. Later the word was used to refer specifically to the populations of Jews exiled from Judea in 586 BC and from Jerusalem in 70 AD by the Romans. Now the term is used to refer to other population dispersals, voluntary and non-voluntary. The modern term evokes a sense of exile and homelessness.
Differential Access – refers to unequal access to resources, which is the basic attribute of different social structures from chiefdoms and states.
Diffuse – Diffuse/Specific is one of the value dimensions proposed by Trompenaars & Hampden-Turner (1997). It shows “how far we choose to get involved“. In a very diffuse culture, a large part of the life is regarded as “private”, where other persons without explicit consent have no access.
Diffusion – is the borrowing of cultural traits between societies, either directly or through intermediaries.
Diglossia – is the existence in a given society of two (often closely-related) languages, one of high prestige, which is generally used by the government and in formal texts, and one of low prestige, which is usually the spoken vernacular tongue. The high-prestige language tends to be the more formalized. For example in Pakistan, there is a diglossia between the extremely Persianised Urdu (used by the literary elite and the Government officials) and an Urdu that is very similar to Hindi spoken by common people.
Dimensions of Diversity – Dimensions of diversity in humans includes, but is not limited to: culture, gender, age, ethnicity, nationality, geography, lifestyle, education, income, health, physical appearance, pigmentation, language, personality, beliefs, faith, dreams, interests, aspirations, skills, professions, perceptions, and experiences.
Discounting – In Kelley’s attribution theory, the tendency to reduce the importance of any one cause when other, plausible causes are present.
Discrimination – Treatment or consideration based on class or category defined by prejudicial attitudes and beliefs rather than individual merit. The denial of equal treatment, civil liberties and opportunities to education, accommodation, health care, employment and access. In many countries discrimination by law consists of making unjust distinctions based on:
Distinctiveness – In Kelley’s attribution theory, the extent to which the actor’s behavior differs in relation to different targets.
Distributive Justice – A proposition of social exchange theory in which one’s rewards should be in proportion to one’s investments.
Diversity – The concept of diversity means understanding that each individual is unique, and recognizing individual differences along the dimensions of race, ethnicity, gender, sexual orientation, socio-economic status, age, physical abilities, religious beliefs, political beliefs, or other ideologies. Primary dimensions are those that cannot be changed e.g., age, ethnicity, gender, physical abilities/qualities, race and sexual orientation. Secondary dimensions of diversity are those that can be changed, e.g., educational background, geographic location, income, marital status, parental status, religious beliefs, and work role/experiences. Diversity or diversity management includes, therefore, knowing how to relate to those qualities and conditions that are different from our own and outside the groups to which we belong.
Diversity Council (n.) – An internal organizational structure whose purpose is to support and direct an organization’s diversity initiative. A diversity council can be made up of individuals who represent a cross section of the community or organization involved and is committed to the initiative. Also, instrumental in building support for a diversity initiative and implementing it successfully.
Diversity Initiative – Sets of policy, definitions, action-plans and steps to map out, support and protect diversity in different dimensions such as age, gender ethnicity etc in any organization, society or area.
Domestic Partner – either member of unmarried, cohabiting, and same-sex couples that seeks benefits usually available only to spouses.
Dominant Culture -There is usually one “dominant” culture in each area that forms the basis for defining that culture. This is determined by power and control in cultural institutions (church, government, education, mass media, monetary systems, and economics). Often, those in the dominant culture do not see the privilege that accrues to them by being dominant “norm” and do not identify themselves as being the dominant culture. Rather, they believe that their cultural norm.
Door-in-the-face Effect – A technique for eliciting compliance by making a very large initial request, which the recipient is sure to turn down, followed by a smaller request.
Dowry – A marital exchange in which the wife’s family provides substantial gifts of money, goods or property to the husband’s family. The opposite direction, property given to the bride by the groom, is called dower.
Drag Queen/King (n) – A man or woman dressed as the opposite gender, usually for the purpose of performance or entertainment. Many times overdone or outrageous and may present a “stereotyped image.”
Egalitarianism – Affirming, promoting, or characterized by belief in equal political, economic, social, and civil rights for all people. One of the seven fundamental value dimensions of Shalom Schwartz measuring how other people are recognized as moral equals.
Embeddedness – One of the seven fundamental value dimensions of Shalom Schwartz describing people as part of a collective.
Emic Perspective (Emic View) – A term used by ethnographers or cultural anthropologists to refer to the insider’s or native’s view of his or her world, it is an attempt at understanding a culture from “inside,” from within its own frame of reference, from experiencing it as a participant (see also etic perspective).
Emotionalistic Disease Theories – Theories that assume that illness is caused by intense emotional experiences (e.g., the experience of Susto, which is a folk illness, specifically a “fright sickness” with strong psychological overtones among some Latin American populations). There are two other theories about the causes of illnesses – Personalistic disease theories blame illness on agents such as sorcerers, witches, ghosts, or ancestral spirits. Naturalistic disease theories explain illness in impersonal terms (e.g., Western biomedicine).
Enculturation – is the process whereby an established culture teaches an individual its accepted norms and values, by establishing a context of boundaries and correctness that dictates what is and is not permissible within that society’s framework. Enculturation is learned through communication by way of speech, words, action and gestures. The six components of culture learnt are: technological, economic, political, interactive, ideological and world-view. It is also called socialization. (Conrad Phillip Kottack, Cultural Anthropology)
Endogamy – is the practice of marrying within one’s own social group. Cultures that practice endogamy require marriage between specified social groups, classes, or ethnicities. Strictly endogamous communities like the Jews, the Parsees of India and the Yazidi of Iraq claim that endogamy helps minorities to survive over a long time in societies with other practices and beliefs. The opposite practice is exogamy.
Environmental Racism (n.) – The concept that members of certain groups are deliberately located in less-desirable geographic areas or that undesirable businesses, activities are deliberately located in range of or within neighborhoods of certain groups, particularly racial minorities and the urban poor.
Equal Employment Opportunity (EEO) (n.) – Title VII of the Civil Rights Act of 1964 (Title VII) prohibits employment discrimination based on an individual’s race, color, religion, sex, or national origin.
Equity (n.) – Fairness and justice, especially pertaining to rights and protection under the law.
Equity, Increased – is a reduction in absolute poverty and a fairer or more even distribution of wealth in a particular society or nation state.
ESL (n.) – (E)nglish as a (S)econd (L)anguage. A term used to describe language learning programs in the U.S. for individuals for whom English is not their first or native language.
Essentialism (n.) – The practice of categorizing an entire group based on assumptions about what constitutes the “essence” of that group (e.g., assuming that women are better nurturers due to something that is innate in their being). Essentialism prevents individuals from remaining open to individual differences within groups.
Ethnic Competence – The capacity to function effectively in more than one culture, requiring the ability to appreciate and understand features of other ethnic groups and further to interact with people of ethnic groups other than one’s own.
Ethnic Group – Group characterized by cultural similarities (shared among members of that group) and differences (between that group and others). Members of an ethnic group share beliefs, values, habits, customs, norms, a common language, religion, history, geography, kinship, and/or race.
Ethnic Minority Counseling– refers to any counseling situation in which the client is a member of an ethnic minority group.
Ethnic Slur – Is a term used to insult someone on the basis of ethnicity, race or nationality. Some derogatory examples are Flip (Western derogatory term used for Filipinos), Ginzo in US (for Italian Americans), Gweilo (“Foreign devil” or “white ghost”, term used by the Chinese to refer to Westerners), Paki (UK for a South Asian) etc.
Ethnicity – Belonging to a common group with shared heritage, often linked by race, nationality and language.
Ethnocentrism – Belief in the superiority of one’s own ethnic group. Seeing the world through the lenses of one’s own people or culture so that own culture always looks best and becomes the pattern everyone else should fit into.
Ethnography – A research methodology associated with anthropology and sociology that systematically tries to describe the culture of a group of people by trying to understand the natives’/insiders’ view of their own world (an emic view of the world).
Ethnology – Cross-cultural comparison or the comparative study of ethnographic data, of society and of culture
Ethnomusicology – is the comparative study of the music’s of different places of the world and of music as a central aspect of culture and society.
Ethnosemantics – is the study of meaning attached to specific terms used by members of a group. Ethnosemantics concentrates on the meaning of categories of reality and folk taxonomies to the people who use them. (Source: Cultural Anthropology. A.R.N.Srivastava. Prentice-Hall)
Etic – is the research strategy used by ethnographers that emphasizes the observer’s rather than the natives’ explanations, categories, and criteria of significance. Etic is the phase in the study of a particular culture, after having experienced it and participated in it first-hand, of “stepping back” and evaluating the experience into explanatory terms in one’s own culture (see emic perspective).
Eurocentrism (n.) – The practice of using Europe and European culture as a frame of reference or standard criteria from which to view the world. Eurocentrism favors European cultural norms and excludes the realities and experiences of other cultural groups.
Exogamy – is the custom of marrying outside a specific group to which one belongs. Some experts hold that the custom of exogamy originated from a scarcity of women, which forced men to seek wives from other groups, e.g., marriage by capture. Another viewpoint ascribes the origin of exogamy to totemism, and claim that a religious respect for the blood of a totemic clan, led to exogamy. The opposite of exogamy is endogamy.
Expatriate – Someone who has left his or her home country to live and work in another country. When we go to another country to live, we become expatriates or expats for short.
Experimental Research – A research methodology used to establish cause-and-effect relationships between the independent and dependent variables by means of manipulation of variables, control and randomization. A true experiment involves the random allocation of participants to experimental and control groups, manipulation of the independent variable, and the introduction of a control group for comparison purposes. Participants are assessed before and after the manipulation of the independent variable in order to assess its effect on the dependent variable (the outcome).
Extended Family – The relatives of an individual, both by blood and by marriage, other than its immediate family, such as aunts, uncles, grandparents and cousins, who live in close proximity and often under one roof. Extended families are very common in collectivistic cultures. This is the opposite of the nuclear family.
F to M/FTM/F2M – Female to male. Abbreviation used to specify the direction of sex or gender role change, usually used by those who identify as transsexual.
Family of Orientation – Nuclear family in which one is born and grows up.
Fascism – A term used particularly to describe the nationalistic and totalitarian regimes of Benito Mussolini (Italy, 1922-45) and Adolf Hitler (Germany, 1933-45). Fascism is characterized by totalitarian attempts to impose state control over almost all aspects of life: political, social, cultural, and economic. The fascist state also regulates and controls the means of production and takes all investment decisions. The word “fascism” comes from the fasces (rods bundled around an axe), which was the ancient Roman symbol of the authority of judges.
Faux Pas – (French word meaning false step) is a violation of accepted and unwritten, social norms. What is considered good manners in one culture can be considered a faux pas in another. For example, in Western societies it is usually considered a friendly gesture to bring a bottle of wine when invited to someone’s house for dinner. French hosts may consider this insulting as it implies that the hosts are unable to serve their own good wine.
Feminism (n.) – Theory and practice that advocates for educational and occupational equity between men and women and undermines traditional cultural practices that support the subjugation of women by men and the devaluation of women’s contributions to society.
Feminist Anthropology- Approaches to the study of culture that emphasizes the need to understand the gendered nature of human societies, and the gendered nature of social/cultural inquiry.
Feminity – Masculinity/Feminity is one of the Hofstede dimensions. Hofstede defines this dimension as follows: “femininity pertains to societies in which social agenda roles overlap (i.e., men and women are supposed be modest, tender, and concerned with the quality of life).” (Hofstede, 1991, p. 83)
Feudalism – Hierarchical social and political system common in Europe during the medieval period. The majority of the population was engaged in subsistence agriculture while simultaneously having an obligation to fulfill certain duties for the landholder. At the same time the landholder owed various obligations called fealty to his overlord.
First Nation – The indigenous population of Canada, excepting the Inuit or Métis people. The term came into common usage in the 1980s to refer mostly to Canada’s aboriginal people, most of who live around Ontario and British Columbia.
First Nations People – Individuals who identify as those who were the first people to live on the Western Hemisphere continent. People also identified as Native Americans.
Flip – Is a Western derogatory term used for Filipinos.
FOB (n.) – A derogatory term used to refer to recent immigrants to the U.S., meaning “fresh off the boat.”
Folk – means ‘Of the people’, originally coined for European peasants. It refers to the art, music, and lore of ordinary people, as contrasted with the “high” art or “classic” art of the European elites.
Functional Explanation – The study of social institutions by behavioral scientists on the premise that social customs can be explained by considering their function or role in society. Term originally used by A.R.Radcliffe-Brown (1933).
Functionalism – In the social sciences, specifically sociology and sociocultural anthropology, functionalism (also called functional analysis) attempts to focus on the ways in which social institutions fill social needs, especially social stability. Functionalism treats society as a living organism or a complex machine, the parts of which can only be understood as they function in the whole. Aspects of a culture or society are studied in the context of how they function in the larger processes of society; they may also be considered in relation to the key “needs” they serve in a given society (e.g. needs for subsistence, social law and order, etc.)
Fundamental Attribution Error – A common cognitive action in which one attributes his/her own success and positive actions to his/her own innate characteristics (“I’m a good person”) and failure to external influences (“I lost it in the sun”), while attributing others success to external influences (“he had help, was lucky”) and failure to others’ innate characteristics (‘they’re bad people”). This operates on the group levels as well, with the in-group giving itself favorable attributions, while giving the out-group unfavorable attributions, as way of maintaining a feeling of superiority. A “double standard.”
Gay (n., adj.) – A homosexual. This term was said to originate in Paris during the 1930’s and referred to the male homosexual underground community. The term was reclaimed during the
Gay Bashing (v.) – Term used to describe forms of harassment and hate crimes directed towards homosexuals, such as verbal and physical threats and assault and vandalism.
Gay Liberation Movement (n.) – The Gay Liberation Movement is generally understood to have begun at the start of the 1969 Stonewall riots in Greenwich Village of New York City. The catalyst for the riots was a police raid of a gay bar on Christopher Street, near the Stonewall Inn. The patrons decided to fight back and were quickly joined by others who supported “Gay Power.” Word and wake of the riot rippled through the gay, lesbian, bisexual, and transgender (GLBT) community and some individuals came together to form the Gay Liberation Front (GLF), which was politically aligned with gay rights and the anti-imperialist struggle overseas.
Gender – The socially constructed concepts of masculinity and femininity; the ‘appropriate’ qualities accompanying biological sex.
Gender (n.) – Sexual classification based on the social construction of the categories of “men” and “women.” Gender differs from one’s biological sex (male or female) in that one can assume a gender that is different from one’s biological sex.
Gender Bending (v) – Dressing or behaving in such a way as to question the traditional feminine or masculine qualities assigned to articles of clothing, jewelry, or mannerisms.
Gender Discrimination – Gender discrimination is any action that allows or denies opportunities, privileges or rewards to a person on the basis of their gender alone. The term ‘glass ceiling’ describes the process by which women are barred from promotion by means of an invisible barrier. In the United States, the Glass Ceiling Commission has stated that women represent 1.1% of inside directors (those drawn from top management of the company) on the boards of Fortune 500 companies.
Gender Identity (n.) – A term used to describe “a person’s internal sense of being male or female.”
Gender Roles – Norms that delineate the permissible behaviors of individuals of a given sex.
Gender Stereotypes – are oversimplified but strongly held ideas about the characteristics, roles and behavior models of males and females.
Gender Stratification – Unequal distribution of rewards (socially valued resources, power, prestige, and personal freedom) between men and women, depending on their different positions in a social hierarchy.
Gendered – Having a denotative or connotative association with being either (traditionally) masculine or feminine.
Genealogical Method – Procedures by which ethnographers discover and record connections of kinship, descent, and marriage in societies by using diagrams and symbols.
General Anthropology – The field of anthropology as a whole, consisting of cultural, archaeological, biological, and linguistic anthropology.
Generalized Reciprocity – is the principle that characterizes exchanges between closely related individuals. As social distance increases, reciprocity becomes balanced and finally negative.
Genetic Marker – Is a known DNA sequence of the human DNA. Genetic markers can be used to study the relationship between an inherited disease and its likely genetic cause.
Genitor – Biological father of a child.
Gentrification – The process by which middle- and upper class incomers displace established working-class communities. Gentrification may be small-scale and incremental (i.e. started by individuals) or be associated with major redevelopment and regeneration schemes by governments or public bodies e.g. Docklands and Notting Hill in London.
Ghetto (n., adj.) – Term used to represent the social and physical isolation of urban blacks, or communities of color in general, as well as the dire conditions these communities endure- densely populated slums, economic hardship, and racial discrimination in the central city.
Ginzo – Is a US derogatory term to refer to Italian Americans.
Glass Ceiling (n.) – Term used to describe the “unseen” barrier that prevents women and people of color from being hired or promoted beyond a certain level of responsibility, prestige, or seniority in the workplace.
Global Culture – One world culture. The earth’s inhabitants will lose their individual cultural diversity and one culture will remain for all the people.
Global Village – A term coined by Marshall McLuhan in the 1960s that refers to a world in which communication technology links people from remote parts of the world.
Globalization – A disputed term relating to transformation in the relationship between space, economy and society. The International Monetary Fund defines globalization as “the growing economic interdependence of countries worldwide through increasing volume and variety of cross-border transactions in goods and services, free international capital flows, and more rapid and widespread diffusion of technology“. Meanwhile, The International Forum on Globalization defines it as “the present worldwide drive toward a globalized economic system dominated by supranational corporate trade and banking institutions that are not accountable to democratic processes or national governments.”
Green Card (n.) – Official documentation obtained by immigrants from the United States government that grants legal permission to work within the country.
Green Revolution – Agricultural development based on chemical fertilizers, pesticides, 20th-century cultivation techniques, and new crop varieties.
Gringo (n., adj.) – A derogatory term used in Latin American countries to refer to a foreigner, particularly one of (North) American or English descent.
Gweilo – A derogatory term meaning “Foreign devil” or “white ghost” used by the Chinese in South of Mainland China and Hong Kong to refer to Westerners.
Hapa – a Hawaiian language term used to describe a person of mixed Asian or Pacific Islander racial or ethnic heritage.
Harassment (n.) – Unwelcome, intimidating, or hostile behavior.
Harmony – One of the seven fundamental value dimensions of Shalom Schwartz measuring the fitting in harmoniously with the environment.
Hate Crime – Hate crime legislation often defines a hate crime as a crime motivated by the actual or perceived race, color, religion, national origin, ethnicity, gender, disability, or sexual orientation of any person.
Hazing (v.) – Verbal and physical testing, often of newcomers into a society or group, that may range from practical joking to tests of physical and mental endurance. This behavior is common among some U.S. fraternities and sororities.
Health-Care Systems – Beliefs, customs, knowledge and specialists concerned with ensuring health and preventing and curing illness; a cultural universal.
Hegemony – Term derived from the work of the Italian writer and political theorist Antonio Gramsci (1891-1937), which refers to the ability of a dominant group to exert or maintain control through a combination of overt and subtle mechanisms.
Helping Behavior – Prosocial behavior that benefits others more than the person. Different from prosocial cooperation, in which mutual benefit is gained.
Hermaphrodite (n) – An individual having the reproductive organs and many of the secondary sex characteristics of both sexes. (Not a preferred term. See – Intersex)
Heterosexism – The presumption that everyone is, and should be, heterosexual.
Heterosexual (adj.) – Attracted to members of other or the opposite sex.
Heuristics – Rules of thumb or shortcuts for making judgments for which we have insufficient or unverified information.
Hidden Transcript – A term used by James Scott to describe the coded critique of power by the oppressed that goes on offstage and in private, where the power holders can’t see it.
Hierarchy – One of the seven fundamental value dimensions of Shalom Schwartz measuring the unequal distribution of power in a culture.
High Context and Low Context Cultures – According to E.T. Hall (1981), all communication (verbal as well as nonverbal) is contextually bound. What we do or do not pay attention to is largely dictated by cultural contexting. In low-context cultures, the majority of the information is explicitly communicated in the verbal message. In high-context cultures the information is embedded in the context. High- and low-context cultures also differ in their definition of social and power hierarchies, relationships, work ethics, business practices, time management. Low-context cultures tend to emphasize the individual while high-context cultures places more importance on the collective.
Hispanic (n., adj.) – The U.S. Census Bureau defines Hispanics as “those people who classified themselves in one of the specific Spanish, Hispanic, or Latino categories listed on the Census 2000 questionnaire (Mexican, Mexican American, Chicano, Puerto Rican, or Cuban.
Historical Linguistics – also called diachronic linguistics, is the study of how and why languages change.
Holistic – Emphasizing the importance of the whole and the interdependence of its parts. Interested in the whole of the human condition: past, present, and future; biology, society, language, and culture.
Holocultural Analysis – A paradigm of research for testing hypotheses “by means of correlations found in a worldwide, comparative study whose units of study are entire societies or cultures, and whose sampling universe is either (a) all known cultures… or (b) all known primitive tribes” (Naroll, Michik, & Naroll, 1976).
Homeworkers – People who do paid work from their own homes.
Homophobia – The fear or hatred of homosexuality (and other non-heterosexual identities), and persons perceived to be gay or lesbian.
Homosexual – (adj.) attracted to members of the same sex. (Not a preferred term. See – Gay, Lesbian)
Horticulture – The science or art of cultivating fruits, vegetables, flowers, or ornamental plants. In behavioral sciences, nonindustrial system of plant cultivation in which plots lie fallow for varying lengths of time.
Human Rights – Human rights refers to the basic rights and freedoms to which all humans irrespective of countries, cultures, politics, languages, skin color and religions are entitled. Examples of human rights are the right to life and liberty, freedom of expression, and equality before the law, the right to participate in culture, the right to work, the right to hold religious beliefs without persecution, and to not be enslaved, or imprisoned without charge and the right to education.
Hybridity – Refers to groups as a mixture of local and non-local influences; their character and cultural attributes are a product of contact with the world beyond a local place. The term originates from agriculture and has for a long time been strongly related to pejorative concepts of racism and racial purity from western colonial history.
Hyperdescent – is the practice of determining the lineage of a child of mixed race ancestry by assigning the child the race of his more socially dominant parent (opposite of Hypodescent).
Hypodescent – A social rule that automatically places the children of a union or mating between members of different socioeconomic groups in the less-privileged group. In its most extreme form in the United States, hypodescent came to be known as the “one drop rule,” meaning that if a person had one drop of black blood, he was considered black. The opposite of hypodescent is hyperdescent.
Hypothesis – Tentative description of a relationship between variables or that such a relationship exists. In research some scientific method is used to test (in order to prove or disprove) a hypothesis.
Identity Group (n.) – A particular group, culture, or community with which an individual identifies or shares a sense of belonging.
Ideology (n.) – The way in which a given society “talks and thinks about itself.” Ideology can also be thought of as a shared belief system in which the knowledge shared is considered unquestionable “common sense,” knowledge that seems “obvious and natural” regardless of societal reality.
Illegal Alien (n.) – The official term used by the United States Federal Government to refer to citizens of foreign countries whose entry into the United States is prohibited by law, or those who reside in the United States without evidence of legal documentation where permission for entrance has been granted.
Imaginary Geographies – The ideas and representations that divide the world into spaces and areas with specific meanings and associations. These can exist on different scales e.g. the imaginaries that divide the world into a developed core and less developed peripheries or the imagined divide between the deprived inner city and the affluent suburbs. (Sibley)
Immigrant (n.) – A person who voluntarily and/or legally re-locates to a country different from that in which he or she was born. Ex – An Irishman who migrates to the United States is an emigrant of Ireland and an immigrant to the U.S.
Imperialism – A policy of extending the rule of a nation or empire over foreign nations or of taking and holding foreign colonies by forceful conquest.
Incest – Forbidden sexual relations with a close relative. The incest taboo is one of the most common of all taboos as almost all societies have some form of incest avoidance.
Inclusive Language (n.) – Words or phrases that include both women and men if applicable.
Inclusive language does not assume or connote the absence of women. Ex – Use of word “police officers instead of “policemen” or “humankind” instead of “mankind.”
Independent Invention – Appearance of the same cultural trait or pattern in separate cultures as a result of comparable needs and circumstances.
Indigenized – Adapted or modified to fit the local culture.
Indigenous Peoples – Those peoples native to a particular territory that was later colonized, particularly by Europeans. Other terms for indigenous peoples include aborigines, native peoples, first peoples, Fourth World, first nations and autochthonous (this last term having a derivation from Greek, meaning “sprung from the earth”). The UN Permanent Forum on Indigenous Issues estimates range from 300 million to 350 million as of the start of the 21st century or just fewer than 6% of the total world population. This includes at least 5000 distinct peoples in over 72 countries.
Individualism – Individualism/Collectivism is one of the Hofstede dimensions in intercultural communication studies. He defines this dimension as: “individualism pertains to societies in which the ties between individuals are loose: everyone is expected to look after himself or herself and his or her immediate family.” (Hofstede, 1991, p.51)
Industrial Revolution – The process of historical transformation (in Europe, after 1750) of-“traditional” into “modern” societies through industrialization of the economy by applying new discoveries in science, production methods and distribution of labor.
In-group Bias (favoritism) – the tendency for groups to “favor” themselves by rewarding group members economically, socially, psychologically, and emotionally in order to uplift one group over another.
Institutional Racism– Involves the social policies, laws, and regulations whose purpose is to maintain the economic or social advantage of the ethnic group in power.
Integration – The bringing of people of different racial or ethnic groups into unrestricted and equal association, as in society or an organization; desegregation. An individual integrates when s/he becomes a part of the existing society.
Intercultural – Intercultural describes contact between people of different cultures including different groups within a nation or people of different national origins. Intercultural is sometimes used as a synonym for cross cultural. However, cross cultural generally refers to contact between persons of different nations. Multicultural refers to contact between persons of the same nation. Intercultural can be used as a more inclusive term that refers to both cross cultural and multicultural contact.
Intergroup Conflict – Tension and conflict which exists between social groups. And which may be enacted by individual members of these groups.
International Culture – Cultural traditions that extend beyond the boundaries of nation states.
Interpretive Approach in Cultural Anthropology – Regards culture as “texts,” to be read and translated for their “thick” meaning. Clifford Geertz is an example of those who represents this approach.
Intersex – 1. A person who is biologically intermediate between male and female. 2. A person with both ovarian and testicular tissue. 3. A person with two ovaries or two testes, but ambiguous genitals.
Intervention Philosophy – Guiding principle of colonialism, conquest, missionization, or development; an ideological justification for outsiders to guide native peoples in specific directions. It was the ideological justification for foreign powers to guide native peoples in specific directions, usually of benefit to the intruders.
Inuit (n. or adj.) – Eskimo people who are distinct form American Indians and are more closely related to peoples of East Asia.
IPR – Intellectual Property Rights is a legal concept that includes copyrights, trademarks, patents, and related rights, whereby the holder of one these abstract “properties” has certain exclusive rights to the creative work, commercial symbol, or invention which is covered by it. Intellectual property rights, consisting of each society’s cultural core beliefs and principles is also claimed as a group right, a cultural right, allowing indigenous groups to control who may know and use their collective knowledge and its applications.
Islamophobia – Fear and dread of Islam, which has been increasing particularly since September 11th 2001. The Runnymede Trust in 1997 identified ‘closed‘ and ‘open‘ views of Islam. Closed views see Islam as static and unchanging, as primitive, sexist, aggressive, and threatening. Closed views of Islam see hostility towards Muslims as ‘normal’ and are used to justify discrimination because no common values with other religions are admitted. Central to closed views, or ‘Islamophobia’, and propagated by the Western media, is the assumption that all Muslims support all actions taken in the name of Islam. Terrorists are called ‘Islamic Fundamentalists’ although Muslims see them as breaking Islamic law and they suffer from being associated with terrorists and murderers. Open views see Islam as a diverse and progressive faith with internal differences, debates and developments. Recognizing shared values with other faiths and cultures Islam is perceived to be equally worthy of respect. Criticisms by the West are considered and differences and disagreements do not diminish efforts to combat discrimination while care is taken that critical views of Islam are not unfair and inaccurate.
-Ism – A social phenomenon and psychological state where prejudice is accompanied by the power to systemically enact it.
Ivory tower view – of applied anthropology; the belief that anthropologists should avoid practical matters and concentrate on research, publication, and teaching.
Jati – A local subcastes in Hindu India.
Jet Lag – A temporary disruption of bodily rhythms caused by high-speed travel across several time zones typically in a jet aircraft. Typical symptoms are fatigue, insomnia. The world has 24 time zones, one for each hour in the day. A part of the brain called the hypothalamus acts as a kind of alarm clock to activate various body functions such as hunger, thirst, and sleep. It also regulates body temperature, blood pressure, and the level of hormones and glucose in the bloodstream. Thus, when the eye of an air traveler perceives dawn or dusk many hours earlier or later than usual, the hypothalamus may trigger activities that the rest of the body is not ready for, and jet lag occurs.
Joint Family Household – Is a complex family unit formed through polygyny or polyandry or through the decision of married siblings to live together with or without their parents.
Jook Sing – A Chinese term used to refer to “American Born Chinese” of either U.S. or Canadian birth. Meaning “hollow bamboo” in Cantonese, it suggests that the target of the remark may be Chinese on the outside, but lacks the cultural beliefs and values that would make them “truly” Chinese.
Kelley’s Attribution Theory – Kelley’s view of the attribution theory assumes that the attributions we make are, mostly, accurate and logical. There are three main aspects of his view: 1) Consistency: “Is the behavior consistent across most people in the given situation?” 2) Distinctiveness: “Does the behavior vary across different situations?” and 3) Consensus: “Do most people engage in this behavior in this situation?”
Kike or Kyke – Derogatory term in the U.S. for a Jew. From kikel, in Yiddish for “circle”. Probably came from the practice that early immigrant Jews signed legal documents with an “O” (rather than an “X”)
Kinesics – The study of non-linguistic bodily movements, such as gestures, stances and facial expressions as a systematic mode of communication.
Kinship Calculation – The system by which people in a particular society reckon kin relationships.
KKK (n.) – The Ku Klux Klan was an organization originally founded in Pulaski, Tennessee in 1866 that functioned as a “secret society organized in the South after the Civil War to reassert white supremacy by means of terrorism.”
Language – is the primary means of communication for humans. It may be spoken or written and features productivity and displacement and is culturally transmitted.
Law – A legal code, including trial and enforcement. Examples are Code of Hammurabi (also known as Codex Hammurabi) which is one of the earliest and best preserved law codes from ancient Babylon created ca. 1760 BC, The Code Napoléon in France was established under Napoléon I and entered into force on March 21, 1804.
Lesbian – A woman who is attracted to other women. (adj.) describing such women.
Leveling Mechanisms – is a social or economic practice that operates to reduce differences in wealth and thus to bring standouts in line with community norms.
Levirate – Custom by which a widow marries the brother of her deceased husband.
LGBTA – Acronym encompassing the diverse groups of lesbian, gay, bisexual, transgendered populations and allies and/or lesbian, gay, bisexual, and transgender alliances/associations.
LGBTIQQ – Lesbian, Gay, Bisexual, Transgender, Intersex, Queer, and Questioning.
Life Expectancy – is the length of time that a person can, on the average, expect to live.
Life History – provides a personal cultural portrait of existence or change in a culture.
Liminality – The critically important marginal or in-between phase of a rite of passage.
Lineage – Unilineal descent group based on demonstrated descent.
Linguistic Anthropology – The descriptive, comparative, and historical study of language and of linguistic similarities and differences in time, space, and society.
Linguistic Isolation (n.) – May be used to describe the experience of feeling confused or alienated when one is unfamiliar with the language spoken by those around them.
Linguistic Profiling (v.) – The practice of making assumptions or value judgments about an individual based on the way he or she speaks and/or the language he or she uses, and then discriminating against that individual because of these factors.
M to F/MTF/M2F – Male to Female. Abbreviation used to specify the direction of sex or gender role change, usually used by those who identify as transsexual.
Machismo – The word machismo-and its derivatives machista and macho, comes from the Spanish word macho, meaning “male” or “manly” and refers to a prominently exhibited or excessive masculinity. Machistas firmly believe in the superiority of men over women and that women were created to stay home and be mothers and wives. In many cultures, from Latin America to Korea and to countries of the Muslim world, machismo is acceptable and even expected male behavior.
Magic – Use of supernatural techniques to accomplish specific aims. Common in many societies. Example: Folk magic, Witchcraft or Voodoo.
Mainstream (n., adj.) – Refers to the dominant cultural norms of a given society. In the United
Mana – Sacred impersonal force in Melanesian and Polynesian religions.
Marginalization (n.) – The placement of minority groups and cultures outside mainstream society. All that varies from the norm of the mainstream is devalued and at times perceived as deviant and regressive.
Marginalized – Excluded, ignored, or relegated to the outer edge of a group/society/community.
Market Principle – Profit-oriented principle of exchange that dominates in states, particularly industrial states. Goods and services are bought and sold, and values are determined by supply and demand.
Market-Based States – Modern states e.g. UK, where the market is the dominant means by which land, labor, capital and goods are exchanged and has a major influence over social and political organization.
Masculinity – One of the Hofstede dimensions. Hofstede defines this dimension as follows: “masculinity pertains to societies in which social roles are clearly distinct (i.e., men are supposed to be assertive, tough and focused on material success whereas women are supposed to be more modest, tender and concerned with the quality of life).” (Hofstede, 1991, p. 83)
Mater – Socially recognized mother of a child.
Materialism – Understands culture to be the product of the material conditions of a given society. Religion, law, and even art forms, reflect the power relationships of a given society as they are generated by the material order of that society. Karl Marx and later anthropologist following Marx’s analysis are representatives.
Matriarchy – A society ruled by women. There is consensus among modern anthropologists and sociologists that a strictly matriarchal society never existed, but there are examples of matrifocal societies. There exist many matriarchal animal societies including bees, elephants, and killer whales. The word matriarchy is coined as the opposite of Patriarchy.
Matrifocal – Mother-centered society. It often refers to a household with no resident husband-father.
Matrilineage – Line of descent as traced through women on the maternal side of a family. In some cultures, membership of a specific group is inherited matrilineally. For example one is a Jew if one’s mother (rather than one’s father) is a Jew. The Nairs of Kerala, India are also matrilineal.
Matrilineal Descent – Unilineal descent rule in which people join the mother’s group automatically at birth and stay members throughout life.
Matrilocality – Customary residence with the wife’s relatives after marriage, so that children grow up in their mother’s community. The Nair community in Kerala in South India and the Mosuo of Yunnan and Sichuan in southwestern China are contemporary examples.
Means (or factors) of Production – Land, labor, technology, and capital-major productive resources.
Medical Anthropology – Field of study where anthropologists are concerned with the sociocultural context and implications of disease and illness.
Melting Pot-The idea that a nation in which all nationalities and ethnicities blend into one unique culture.
Meme – is a theoretical concept introduced by Richard Dawkins, in his book The Selfish Gene in 1976. Meme is derived from a shortening of the Greek “mimeme” (something imitated) and shortened so that it sounds similar to “gene“. Meme refers to any unit of cultural information, such as a cultural practice, idea or concept, which one mind transmits (verbally or by demonstration) to another mind. Examples of cultural memes are thoughts, ideas, theories, opinions, beliefs, moods, poetry, habits, dance, tunes, catch-phrases, fashions, and ways of building arches. Memes propagate themselves in the meme pool by leaping from brain to brain via a process broadly called imitation very similarly how genes propagate themselves in the gene pool by leading from body to body via sperm or eggs. A list of memetic concepts can be found here.
Meritocracy – A system of government based on rule by ability or merit rather than by wealth, race or other determinants of social position. Nowadays this term refers to openly competitive societies like the USA where large inequalities of income and wealth accrued by merit rather than birth is accepted. In contrast egalitarian societies like the Scandinavian countries aim to reduce such disparities of wealth.
Mestizo – A term used to refer to people of partly Native American descent. From Spanish.
Minority Group – A group that occupies a subordinate position in a society. Minorities may be separated by physical or cultural traits disapproved of by the dominant group and as a result often experience discrimination. Minorities may not always be defined along social, ethnic, religious or sexual lines but could be broad based e.g. non-citizens or foreigners.
Miscegenation (n.) – The mixing of races.
Mode of Production – Way of organizing production. It is a set of social relations through which labor is deployed to wrest energy from nature by means of tools, skills, and knowledge.
Model Minority – Refers to a minority ethnic, racial, or religious group whose members achieve a higher degree of success than the population average. This success is typically measured in income, education, and related factors such as low crime rate and high family stability.
Monochronic – E.T.Hall introduced the concept of Polychronic/Monochronic cultures. According to him, in monochronic cultures, people try to sequence actions on the “one thing at a time” principle. Interpersonal relations are subordinate to time schedules and deadlines.
Monoethnic – Belonging to the same ethnic group.
Monotheism – Worship of an eternal, omniscient, omnipotent, and omnipresent supreme being. Judaism and Islam are examples.
More Developed Countries (MDCs) – Countries with significant competitive advantages in today’s globalizing economy. They have well-developed, increasingly knowledge-based and strongly interconnected manufacturing and service sectors that provide a significant proportion of employment and contribute to significant national and individual wealth. In these countries indices such as literacy levels, incomes and quality of life are high and these countries exercise considerable political influence at the global scale. Examples are the UK, the US, Germany and France.
Morphology – The study of form. It is used in linguistics (the study of morphemes and word construction).
Mulato – A term used for people of partly African descent. Originates from Spanish.
Multicultural – relating to or containing several cultural or ethnic groups within a society (nation).
Multicultural Counseling– may be used interchangeably with cross-cultural counseling. (counseling that takes place between or among individuals from different cultural backgrounds.
Multiculturalism – A belief or policy that endorses the principle of cultural diversity of different cultural and ethnic groups so that they retain distinctive cultural identities. The United States is understood as a “mosaic” of various and diverse cultures, as opposed to the single monolithic culture that results from the “melting pot” or assimilation model. Pluralism tends to focus on differences within the whole, while multiculturalism emphasizes the individual groups that make up the whole. The term multiculturalism is also used to refer to strategies and measures intended to promote diversity. According to Wikipedia, the word was first used in 1957 to describe Switzerland, but came into common currency in Canada in the late 1960s.
Multiethnic – An individual that comes from more than one ethnicity. An individual whose parents are born from more than one ethnicity.
Multiplicity – The quality of having multiple, simultaneous social identities (e.g., being male and Buddhist and working class).
Multiracial – The terms multiracial and mixed-race describe people whose parents are not the same race. Multiracial is more commonly used to describe a society or group of people from more than one racial or ethnic group. Mulato (for people of partly African descent) and mestizo (people of partly Native American descent) in Spanish and métis in Candian French (for people of mixed white and original inhabitants of Canada descent) are also used in English.
Myth -Story told in one’s culture to explain things like the creation of the world, and the behavior of its inhabitants.
Naming – “When we articulate a thought that traditionally has not been discussed”.
Nation – Earlier a synonym for “ethnic group,” designating a single culture sharing a language, religion, history, territory, ancestry, and kinship. Now usually a synonym for state or nation-state.
National Culture – Cultural experiences, beliefs, learned behavior patterns, and values shared by citizens of the same nation.
National Origin – The political state from which an individual hails; may or may not be the same as that the person’s current location or citizenship.
Nationalities – Ethnic groups that have, once had, or wish to have or regain, autonomous political status (their own country).
Nation-State – A symbolic system of institutions claiming sovereignty over a bounded territory. The Oxford English Dictionary defines “nation-state“: a sovereign state of which most of the citizens or subjects are united also by factors which define a nation, such as language or common descent. Japan and Iceland could be two examples of near ideal nation-states.
Natural Selection – Originally formulated by Charles Darwin and Alfred Russell Wallace. Refers to the process by which nature selects the forms most fit to survive and reproduce in a given environment such as the tropics.
Naturalistic Disease Theories – One of the theories of diseases used in anthropology that explain illness in impersonal systemic terms. It includes scientific medicine.
Naturalization (v.) – The U.S. Bureau of Citizenship and Immigration Services define naturalization as “the conferring, by any means, of citizenship upon a person after birth.
Négritude – Black association and identity. It is an idea developed by dark-skinned intellectuals in Francophone (French-speaking) West Africa and the Caribbean.
Negro – Negro usually refers to people of Black African ancestry. Originates from Spanish negro meaning black. The term negro is considered offensive nowadays. Modern synonyms in common use: “Black“, “Dark-skinned“, “African“, “African American” in the US.
Neoconservatism – Neoconservatism is a political philosophy that emerged in the United States. The term neoconservative was originally used as a criticism against liberals who had “moved to the right“. Michael Harrington, a democratic socialist, coined the usage of neoconservative in a 1973 Dissent magazine article concerning welfare policy.
Neolocality – Postmarital residence pattern in which a couple establishes a new place of residence rather than living with or near either set of parents.
New Economic Geography – An economic geography that recognizes the importance of culture as an influence on economic processes and outcomes. This draws attention to the culturalization of the economy in contrast to the economization of culture.
New International Division of Labour (NIDL) – The global shift of economic activity that occurs when the process of production is no longer centered primarily around national economies.
New Racism– a subtle form of racism that facilitates discrimination in liberal, democratic societies.
Newly Agriculturizing Countries (NACs) – Some low-middle income countries which have specialized in the export of high-value foods e.g. Brazil, Mexico, China, Argentina and Kenya.
Newly Industrialized Countries (NICs) – Countries where there has been a relatively recent and significant shift away from primary activities such as agriculture towards manufacturing production e.g. South Korea and Mexico. In some cases the proportion of manufacturing production is similar to that of the more developed countries like UK or the US.
Nigga – Term used in African American vernacular English to refer to a person of Black African ancestry living in the US. The use of the term by persons not of African descent is still widely viewed as unacceptable and hostile even if there is no intention to slander.
Nigger – Extremely offensive term to refer to people of Black African ancestry in the USA.
Nigrew – In the U.S. it is a derogatory term for a Jew of African-American descent (shortened version of Nigger and Jew.)
Nomadism, Pastoral – Movement throughout the year by the whole pastoral group (men, women, and children) with their animals: More generally it means such constant movement in pursuit of strategic resources.
Norms – Prescriptions for appropriate behavior held by members of a social group.
Nuclear Family – is a household consisting of two heterosexual parents and their children as distinct from the extended family. Nuclear families are typical in societies where people must be relatively mobile e.g., hunter-gatherers and industrial societies.
Nuyorican (n.) – Of or related to a person born in New York City of Puerto Rican ancestry.
Obedience – A form of compliance in which behavior happens in response to a direct order.
Observational Learning – A type of learning, in which an individual acquires new behaviors simply by observing the behaviors of others.
One-World Culture – A belief that the future will bring development of a single homogeneous world culture through advances and links created by modern communication, transportation and trade.
Open Class System – Stratification system that facilitates social mobility, with individual achievement and personal merit determining social rank.
Open Plan Office – A system of office design where work spaces occupy large areas undivided by walls. However, plants, movable partitions or furniture may separate areas.
Oppression – Results from the use of institutional power and privilege where one person or group benefits at the expense of another. Oppression is the use of power and the effects of domination.
Orishas (n.) – The various gods and goddesses of Caribbean and Latin American religion of
Osenbei (Senbei) – Derogatory term in the US and the UK used to refer to a half Asian, half Caucasian person. It means “rice cracker” in Japanese. Its use derives from the US slang “cracker” for a white person, and “rice” to refer to an Asian.
Ought Self – Duties, obligations, responsibilities – facets of the self concept which should exist.
Out Group – A group of which a person is not a member but is aware of the group.
Overinnovation – Characteristic of projects that require major changes in the daily lives of the natives in the target community, especially ones that interfere with customary subsistence pursuits.
Pacific Islander (n.) – The term “Pacific Islander” refers to persons whose origins are of the following nations – Polynesian, Melanesia, Micronesia, or any of the Pacific Islands.
Paddy (n.) – A derogatory term for persons of Irish descent.
Paleoethnobotany (Archaeobotany) – is the recovery and identification of plant remains from archaeological contexts, important in the reconstruction of past environments and economies.
Pansexual – A term referring to the potential for sexual attractions or romantic love toward people of all gender identities and biological sexes. The concept of pansexuality deliberately rejects the gender binary, and derives its origin from the transgender movement.
Paradigm – is the set of fundamental assumptions that influence how people think and how they perceive the world.
Paradigmatic view – is an approach to science, developed by Thomas Kuhn, which holds that science develops from a set of assumptions (paradigm) and that revolutionary science ends with the acceptance of a new paradigm which ushers in a period of normal science.
Parallel Cousins – Children of two brothers or two sisters.
Participant Observation – Technique for cross-cultural adjustment. This entails keeping a detailed record of your observations, interactions and interviews while living in a culture that is not your own. Participant observation is also a fundamental method of research used in cultural anthropology. A researcher lives within a given culture for an extended period of time, to take part in its daily life in all its richness and diversity. The anthropologist in this approach tries to experience a culture “from within,” as a person native to that culture is presumed to.
Participative competence – The ability to interact on equal terms in multicultural environments so that knowledge is shared and the learning experience is professionally enhancing for all involved. Even when using a second language, people with high participative competence are able to contribute equitably to the common task under discussion and can also share knowledge, communicate experience, and stimulate group learning to benefit all parties. (Adapted from source: Holden, Nigel 2001, Cross-Cultural Management: A Knowledge Management Perspective) Financial Times Management
Particularism – One of the value dimensions as proposed by Trompenaars & Hampden-Turner (1997). It reflects the preference for rules over relationships (or vice versa). Particularist societies tend to be more flexible with rules, and acknowledge the unique circumstances around a particular rule.
Particularity – Distinctive or unique culture trait, pattern, or integration.
Pastoral Nomadism – A form of social organization that is based on livestock husbandry for largely subsistence purposes. Pastoral nomads are characterized by a high level of mobility which allows them continually to search for new pastures in order to maintain their herds of animals. First known nomadic pastoral society developed in the period from 6200 – 6000 BC in the Middle East.
Pastoralists – People who use a food-producing strategy of adaptation based on care of herds of domesticated animals.
Pater – Socially recognized father of a child though not necessarily the genitor or biological father.
Patriarchy – Political system ruled by men in which women have inferior social and political status, including basic human rights.
Patrilineage – Line of descent as traced through men on the paternal side of a family each of whom is related to the common ancestor through males. Synonym is agnation and opposite is matrilineage.
Patrilineal – An interrelated constellation of patrilineality, patrilocality, warfare, and male supremacy.
Patrilineal Descent – Unilineal descent rule in which people join the father’s group automatically at birth and stay members throughout life.
Patrilocality – Customary residence with the husband’s relatives after marriage, so that children grow up in their father’s community.
Peasant – Small-scale agriculturalist living with rent fund obligations.
Peer Pressure – the influences that people of the same rank, age or group have on each other. Under peer pressure a group norm of attitudes and/or behaviors may override individual moral inhibitions, sexual personal habits or individual attitudes or behavioral patterns.
Peer-Polity Interaction – is the full range of exchanges taking place, including imitation, emulation, competition, warfare, and the exchange of material goods and information between autonomous (self-governing) sociopolitical units, generally within the same geographic region.
Peers Pressure -the influences that people of the same rank, age or group have on each other. Under peer pressure a group norm of attitudes and/or behaviors may override individual moral inhibitions, sexual personal habits or individual attitudes or behavioral patterns.
People of Color – A collective term for men and women of Asian, African, Latin and Native American backgrounds; as opposed to the collective “White” for those of European ancestry.
Periphery – is the weakest structural position in the world system.
Personal Identity – Our identities as individuals-including our personal characteristics, history, personality, name, and other characteristics that make us unique and different from other individuals.
Personal Space – Humans desire to have a pocket of space around them and into which they tend to resent others intruding. Personal space is highly variable. Those who live in a densely populated environment tend to have smaller personal space requirements. Thus a resident of a city in India or China may have a smaller personal space than someone who lives in Northern Lapland. See also Proxemics.
Personalistic Disease theories – One of the theories in Anthropology that attributes illness to sorcerers, witches, ghosts, or ancestral spirits.
Phenotype – An organism’s evident traits, its “manifest biology“. The term is used in anatomy and physiology.
Phoneme – Significant sound contrast in a language that serves to distinguish meaning, as in minimal pairs.
Phonemics – The study of the sound contrasts (phonemes) of a particular language.
Phonetics – The study of speech sounds in general; what people actually say in various languages.
Phonology – The study of sounds used in speech.
Phylogenetic tree – is a graphic representation of evolutionary relationships among animal species.
Plural Society – A society that combines ethnic contrasts and economic interdependence of the ethnic groups.
Polack (n.) – Derogatory term for persons of Polish descent.
Polyamory – The practice of having multiple open, honest love relationships.
Polyandry – A variety of plural marriage in which a woman has more than one husband. Tibet is the most well-documented cultural domain within which polyandry is practiced, though it has recently been outlawed.
Polychronic – The concept of Polychronic/Monochronic cultures was introduced by E.T. Hall. He suggested that in Polychronic cultures, multiple tasks are handled at the same time, and time is subordinate to interpersonal relations.
Polytheism – Belief in several deities who control aspects of nature. The ancient Greeks believed that their gods were independent deities who weren’t aspects of a great deity.
Positive Eugenics – is a method of increasing the frequency of desirable traits by encouraging reproduction by individuals with these traits. Negative eugenics is aimed at lowering fertility among the genetically disadvantaged by means of abortions, sterilization, and other methods of family planning
Positivism – refers to the theoretical position that explanations must be empirically verifiable, that there are universal laws in the structure and transformation of human institutions, and that theories which incorporate individualistic elements, such as minds, are not verifiable.
Postcolonial – Refers to interactions between European nations and the societies they colonized (mainly after 1800). “Postcolonial” may be used to signify a position against imperialism and Eurocentrism
Postmodern – Describes the blurring and breakdown of established canons (rules, standards), categories, distinctions, and boundaries.
Postmodernity – Refers to the condition of a world in flux, with people on the move, in which established groups, boundaries, identities, contrasts, and standards are breaking down.
Post-Partum Sex Taboo – is the prohibition of a woman from having sexual intercourse for a specified period of time following the birth of a child.
Power Distance – One of the Hofstede dimensions of national cultures. “The extent to which the less powerful members of institutions and organizations within a country expect and accept that power is distributed unequally” (Hofstede, 1991 p.27)
Power Geometry – The notion of Power Geometry is a product of globalization and refers to the ways that different groups of individuals interact at different scales, linking local development to national, international, and global processes.
Prejudice – Over-generalized, oversimplified or exaggerated beliefs associated with a category or group of people. These beliefs are not easily changed, even in the fact of contrary evidence. Example: A French woman is in an elevator alone. She grabs her purse tight when an African young man enters. Prejudice can also be devaluing (looking down on) a group because of its assumed behavior, values, capabilities, attitudes, or other attributes.
Prestige – Esteem, respect, or approval for acts, deeds, or qualities considered exemplary.
Privilege – a right, license, or exemption from duty or liability granted as a special benefit, advantage, or favor.
Pro-choice (adj.) – Of or related to the belief that it is a woman’s right to choose whether or not
Progeny Price – A gift from the husband and his kin to the wife and her kin before, at, or after marriage. It legitimizes children born to the woman as members of the husband’s descent group.
Pro-Life (adj.) – Of or related to the belief in an un-born child’s right to life. Pro-life advocates
Protestant Work Ethic – a bible based value system that stresses the moral value of work, self-discipline, and individual responsibility as the means to improving one’s economic well-being. Also known as the Puritan work ethic, the term was first coined by Max Weber, a German Economist and Sociologist in 1904. Many Europeans and Americans consider it as one of the cornerstones of national prosperity.
Protoculture – is the simplest or beginning aspects of culture as seen in some nonhuman primates.
Proto-language – refers to a language ancestral to several daughter languages. Example: Latin or Sankrit.
Proxemics – is the study of human “perception and use of space” (Hall 1959). Proxemics tries to identify the distance and the way the space around persons are “organised“. In some cultures, people are comfortable with being very close, or even touching each other as a normal sign of friendship. In other cultures, touching and sitting/standing very close can cause considerable discomfort.
Public Transcript – A term used by James Scott to refer to the open, public interactions between dominators and oppressed. It points to the outer shell of power relations and is the opposite of ‘Private Transcript’.
Purdah – is the Muslim or Hindu practice of keeping women hidden from men outside their own family; or, a curtain, veil, or the like used for such a purpose.
Pygmalion Effect – A labeling phenomenon in which teachers’ expectations affect students’ classroom performances.
Quaker (n.) – A member of the Society of Friends, a Christian sect founded by George Fox in the 1600s. Quakers historically have been outspoken critics of slavery and violence.
Qualitative Research – Qualitative research involves the gathering of data through methods that involve observing forms of behavior e.g. conversations, non-verbal communication, rituals, displays of emotion, which cannot easily be expressed in terms of quantities or numbers.
Quantitative Research – Quantitative research is the systematic scientific investigation of quantitative or measurable properties and phenomena and interrelationships. Quantitative research aims to develop and employ hypotheses, theories and models, which can be verified scientifically.
Queer – An umbrella term that can refer to anyone who transgresses society’s view of gender or sexuality. The definitional indeterminacy of the word Queer, its elasticity, is one of its constituent characteristics – “A zone of possibilities.”
Queer (n., adj.) – Term used to refer to people or culture of the gay, lesbian, bisexual, and transgender (GLBT) community. A term once perceived as derogatory is now embraced by some members of the GLBT community.
Questioning – A term used to refer to an individual who is uncertain of her/his sexual orientation or identity.
Questionnaire – Survey research technique in which the researcher suplies written questions to the subject, who gives written answers to the questions asked.
Quota (n.) – A number or percentage particularly of people designated as a targeted minimum for a particular group or organization. A term often used in reference to admission to colleges and universities and organizational hiring practices.
Racism – Theories, attitudes and practices that display dislike or antagonism towards people seen as belonging to a particular ethnic groups. Social or political significance is attached to culturally constructed ideas of difference.
Rainbow Flag – The Rainbow Freedom Flag was designed in 1978 by Gilbert Baker to designate the great diversity of the LGBTIQ community. It has been recognized by the International Flag Makers Association as the official flag of the LGBTIQ civil rights movement.
Random Sample – A sample in which all members of the population have an equal statistical chance of being included.
Ranked Society – A society in which there is an unequal division of status and power between its members, where such divisions are based primarily on such factors as family and inherited social position. This is in contrast with egalitarian society, which aims to minimise such unequal divisions.
Reciprocity – One of the three principles of exchange. It governs exchange between social equals and is a major exchange mode in band and tribal societies. Since virtually all humans live in some kind of society and have at least a few possessions, reciprocity is common to every culture. Reciprocity is the basis of most non-market economies.
Re-fencing (exception-making) – A cognitive process for protecting stereotypes by explaining any evidence/example to the contrary as an isolated exception.
Regional Inversion – is a process of radical change when the established order of territorial influence changes. Through regional inversion, previously backward regions become predominant in a national context. Lagging areas that emerge through this process eventually overshadow the influence of predominant regions.
Relativism -A willingness to consider other persons’ or groups’ theories and values as equally reasonable as one’s own.
Religion – A system of beliefs, usually spiritual in nature, and often in terms of a formal, organized denomination.
Religious Discrimination – Religious discrimination is treating someone differently because of what they do or don’t believe. Religious discrimination is closely related to racism, but there are differences in how it is expressed and how it is treated in law. An example of religious discrimination by the state is non-Muslims being discriminated against in some Islamic states. In many countries legislation specifically prohibits employers from discriminating against individuals because of their religion in relation to hiring, firing and other terms and conditions of employment. Today, many western states forbid discrimination based on religion, though this is not always enforced. For example, since the terrorist attacks of September 11, 2001 in the United States of America, research conducted by the Level Playing Field Institute and the Center for Survey Research and Analysis at the University of Connecticut revealed that Muslims were rated very low relative to other racial, ethnic, and religious groups in terms of their fit in the American workplace. Adapted from source: http://en.wikipedia.org
Rescue Archaeology – A term applied to the emergency salvage of sites in immediate danger of destruction by major land modification projects such as reservoir construction.
Reverse Discrimination (n.) – A term used by opponents to affirmative action who believe that these policies are causing members of traditionally dominant groups to be discriminated against.
Revitalization Movements – Movements that occur in times of change, in which religious leaders emerge and undertake to alter or revitalize a society.
Rites of Passage – Culturally defined activities (rituals) that mark a person’s transition from one stage of life to another. These aim to help participants move into new social roles, positions or statuses. Puberty, wedding, childbirth are examples.
Ritual – Behavior that is formal, stylized, repetitive, and stereotyped. A ritual is performed earnestly as a social act. Rituals are held at set times and places and have liturgical orders.
Rust Belt – A region of the North-Eastern USA roughly between Chicago and New York City that suffered substantial industrial decline, especially after the Second World War.
Safe Space – Refers to an environment in which everyone feels comfortable in expressing themselves and participating fully, without fear of attack, ridicule or denial of experience.
Saliency – The quality of a group identity of which an individual is more conscious and which plays a larger role in that individual’s day-to-day life; for example, a man’s awareness of his “maleness” in an elevator with only women.
Same Gender Loving – a term coined by activist Cleo Manago as a description for homosexuals, particularly in the African American community. SGL is an alternative to Eurocentric homosexual identities e.g. gay and lesbian.
Sample – A smaller study group chosen to represent a larger population.
Sapir – Sapir–Whorf hypothesis (SWH) (also known as the “linguistic relativity hypothesis“) is a theory that different languages produce different ways of thinking. It postulates a systematic relationship between the grammatical categories of the language a person speaks and how that person both understands the world and behaves in it.
Scapegoating – The directing of hostility towards less powerful groups when the actual source of frustration or anger cannot be attacked or is unavailable.
Schema – An organized pattern of knowledge, acquired from past experience, humans use to interpret current experience.
Schizoid view-of Applied Anthropology – is the belief that anthropologists should help carry out, but not make or criticize, policy, and that personal value judgments should be kept strictly separate from scientific investigation in applied anthropology.
Script – A conceptual representation of a stereotyped sequence of events.
Segmentary Lineage Organization – Political organization based on descent, usually patrilineal, with multiple descent segments that form at different genealogical levels and function in different contexts. A segmentary lineage society is characterized by the organization of the society into segments; what is often referred to as a tribal society.
Selective Exposure – Seeking information to support one’s attitudes and beliefs and intentionally avoiding information that is incosistent with one’s attitude.
Self-affirmation – A phenomenon in which an individual responds to a threat to self-esteem by enhancing some facet of the self-concept.
Self-awareness – A psychological state in which individuals focus their attention on and evaluate different aspects of their self-concepts. These can vary from physical experiences to differences between “Ideal” self and “Real” self.
Self-categorization – The process of an individual spontaneously including herself or himself as a member of a group.
Self-concept – The entirety of an individual’s thoughts and feelings with reference to the self as an object.
Self-consciousness – An inclination to focus on one’s self. Private self-consciousness relates to self-awareness, while public self-consciousness handles other people’s view of the self.
Self-disclosure – How an individual reveals information about the self; self-revelation.
Self-esteem – The evaluation of oneself in either positive or negative terms.
Self-fulfilling prophecy – When a perceiver’s belief about an observed person can actually elicit desired behavior from the observed person. Also called expectancy confirmation sequence.
Self-handicapping strategy – Any action or choice of performance setting that increases the opportunity to avoid blame for failure and to get credit for success.
Self-monitoring – The use by an individual of cues from other people’s self-presentations to control his or her own self-presentation. Impression management in social relations require well-developed self-presentation skills acquired through high self-monitoring.
Self-perception theory – Proposes that we learn about our emotions, attitudes and other internal states by observing our own behavior.
Self-schema – Cognitive generalizations about own self. These guide and organize the processing of self-related information.
Self-serving attitude bias – A tendency to infer causes for events in order to confirm the individual’s self-concept, usually by claiming greater personal responsibility for beneficial outcomes than negative outcomes.
Semantic differential technique – A method of measuring attitude in which test subjects rate a concept on a series of bipolar scales of adjectives.
Semiperiphery – Structural position in the world system intermediate between core and periphery.
Semitic (adj.) – Of or related to the language and culture of Semites. Semitic languages are characterized as Afro-Asiatic languages that include Arabic, Hebrew, Amharic, and Aramaic.
Sex – biological classification of male or female (based on genetic or physiological features); as opposed to gender.
Sexism – Discrimination or prejudice against some people because of their gender.
Sexual Dimorphism – Marked differences in male and female biology, besides the contrasts in breasts and genitals, and temperament.
Sexual Harassment (n) – The Equal Employment Opportunity Commission defines sexual harassment as “a form of sex discrimination that violates Title VII of the Civil Rights Act of 1964.
Sexual Orientation – A person’s habitual sexual attraction to, and activities with: persons of the opposite sex, heterosexuality; the same sex, homosexuality; or both sexes, bisexuality.
Sexual Orientation Discrimination – Sexual orientation discrimination is discrimination against individuals, couples or groups based on sexual orientation or perceived sexual orientation. Usually, this means the discrimination of a person who has a same-sex sexual orientation, whether or not they identify as gay, lesbian or bisexual. Acceptability of sexual orientation varies greatly from society to society. The Republic of South Africa is the first nation on earth to integrate freedom from discrimination based on sexual orientation into its constitution.
Shaman – A religious practitioner who mediates between ordinary people and supernatural beings and forces. A Shaman travels between worlds in a state of trance. Once in the spirit world, the shaman would commune with the spirits for assistance in healing, hunting or weather management.
Shantytown – Neighborhoods where poor migrants to cities live. Also called slum, favela, township.
Shared Stress Effect – People who are together in a stressful environment tend to feel mutual attraction.
Silencing – The conscious or unconscious processes by which the voice or participation of particular social identities is exclude or inhibited.
Simulation – A research method that tries to imitate crucial aspects some real-world situation in order to understand the underlying mechanism of that situation.
Slavery – is the most extreme, coercive, abusive, and inhumane form of legalized inequality where people are treated as things or someone’s property.
Social Comparison Theory – Proposes that we use other people for comparing in order to evaluate our own attitudes and abilities.
Social Distance – The degree of physical, social or psychological closeness or intimacy to members of a group like ethnic, racial or religious groups.
Social Drift Theory – The theory that people move into the social class that is commensurate with their personal abilities and behavior.
Social Exchange Theory – A theoretical model within the learning perspective, in which interpersonal relationships are considered in terms of rewards gained and costs for the participants.
Social Exclusion – The various ways in which people are excluded from the accepted norms within a society. Exclusion can be economic, social, religious or political.
Social Facilitation – The condition when the presence of others improves an individual’s performance.
Social Identity – It involves the ways in which one characterizes oneself, the affinities one has with other people, the ways one has learned to behave in stereotyped social settings, the things one values in oneself and in the world, and the norms that one recognizes or accepts governing everyday behavior.
Social Identity Development – The stages or phases that a person’s group identity follows as it matures or develops.
Social Impact Theory – A theory of social influence which includes the immediacy, number and strength of influence agents.
Social Inhibition – Happens when the presence of other people causes a decline in a person’s performance. Also called Social Impairment.
Social Judgement Theory – A theory of attitude change which emphasizes the individual’s perception and judgement of a persuasive communication. Central concepts in this theory are anchors, assimilation and contrast effects, and latitudes of acceptance, rejection and noncommitment.
Social Justice – A broad term for action intended to create genuine equality, fairness and respect among peoples.
Social Learning Theory – A theory that proposes that social behavior develops as a result of observing others and of being reinforced for certain behaviors.
Social Loafing – A decrease in individual effort when people work in groups compared to them working alone.
Social Network – The people with whom an individual is in actual contact.
Social Oppression – “Exist when one social group, whether knowingly or unconsciously, exploits another group for its own benefit” (Hardiman and Jackson, 1997)
Social Problem– A condition affecting a significant number of people, in ways considered undesirable, about which it is felt that something can be done, through collective, social action.
Social Race – A group assumed to have a biological basis but actually perceived and defined in a social context, by a particular culture rather than by scientific criteria. The term “social race” has been used in the past as well as in today’s American societies. Terms as “Negro”, “white”, “Indian”, or “mulatto” do not have any genetic meanings in most of the American societies – in one society they may be classifications based on real or imaginary physical characteristics, in another they may refer more to criteria of social status such as education, wealth, language and custom, or in yet another society they may indicate near or distant ancestry.
Social Register – A way of expressing that a message is addressed to a particular individual. For example, a higher-pitched simplified speech is used for communicating with a baby.
Social Responsibility Norm – Dictates how people should help other people who need help or are dependant.
Social Self-Esteem – The degree of positive-negative evaluation an individual holds about his/her particular situation in regards to his/her social identities.
Social Self-View – An individual’s perception of to which social identity groups he/she belongs.
Social Support – Help and resourced provided by others for coping.
Social Theory – A belief about how variables in the social environment go together.
Socialization – A process of behaviors accepted by society.
Sociobiology – Identifies biological and genetic bases for social behavior in humans and other animals.
Sociofugal Space – Settings created to discourage conversation among people by making eye contact difficult. e.g. sside by side seating in waiting rooms.
Sociolinguistics – is the study of relationships between social and linguistic variation or the study of language (performance) in its social context.
Sociopetal Space – Setting that encourage interpersonal interaction through increased eye contact. e.g. cafés, cocktail lounges.
Sororate – Custom by which a widower marries the sister of the deceased wife.
Spanglish – A colloquial and contested mixture of Spanish and English words, phrases and grammar.
Spotlighting – The practice of inequitably calling attention to particular social groups in language, while leaving others as the invisible, de facto norm. For example – “black male suspect”(versus “male suspect,” presumed white); “WNBA” (as opposed to “NBA,” presumed male).
Status Characteristics Theory – A theory of group processes proposing that differences in evaluations and beliefs about types of individuals become the basis for inequalities in social interaction.
Status Markers – Physical symbols to indicate a person’s rank or relative standing in an organization or a group or society. e.g. the size and position of one’s office.
Stereotypes – Stereotypes (or “characterizations“) are generalizations or assumptions that people make about the characteristics of all members of a group, based on an inaccurate image about what people in that group are like. For example, Americans are generally friendly, generous, and tolerant, but also arrogant, impatient, and domineering. Asians are humble, shrewd and alert, but reserved. Stereotyping is common and causes most of the problems in cross-cultural conflicts.
Stigma – A term describing the condition of possessing an identity which has been branded ‘spoiled’ or discredited identity by others. Examples of negative social stigmas are physical or mental handicaps and disorders, as well as homosexuality or affiliation with a specific nationality, religion or ethnicity.
Stimulus – Any internal or external event that produces a change in a person’s behavior.
Stimulus Discrimination – The distinguishing between similar stimuli.
Stimulus Generalization – A process in which a person, after having learnt a response to one stimulus, produces the same response when exposed to some other similar stimulus, even though having never before being exposed to that stimulus.
Strategic Human Resource Management – Strategic human resource management can be defined as the linking of human resources with strategic goals and objectives in order to improve business performance and develop organizational culture that foster innovation, flexibility and competitive advantage.
Stratification – Characteristic of a system with socioeconomic strata, sharp social divisions based on unequal access to wealth and power.
Stratified Society – A society where there is an unequal division of material wealth between its members.
Strength – Power, status or resources associated with a social influence agent in social impact theory.
Stress – An imbalance between environmental demands and an organism’s response capabilities. Also the human body’s response to excessive change.
Structuralism – There has been a number of forms of “structuralism” in the history of anthropology. Structural-functionalism approaches the basic structures of a given society as serving key functions in meeting basic human needs. Another form of structuralism, developed by Claude Levi-Strauss, argues that social/cultural structures are actually rooted in the fundamental structure of the human brain, which generates basic building-blocks of social/cultural systems. In this approach, culture is studied for its deeper meaning to be discovered in the careful structural analysis of meaning in myth and ritual.
Sub-Culture – A part or subdivision of a dominant culture or an enclave within it with a distinct integrated network of behavior, beliefs and attitudes. The subculture may be distinctive because of the race, ethnicity, social class, gender or age of its members.
Sun Belt – Used for the major growth areas of the southern and western parts of the USA during recent years in contrast to the contracting and declining industrial base of the north-east (rust belt). The term has also been used in other parts of the developed world to describe dynamic regions, e.g. the M4 corridor in England.
Superego – In psychoanalytic theory, the part of personality oriented toward morally proper actions; the conscience. The superego includes a person’s ideal self-image.
Superordinate Goal – A significant goal that can be achieved only through cooperation among different individuals and groups.
Symbolic Racism – A blend of negative affect and traditional moral values embodied in e.g., the Protestant ethic; underlying attitudes that support racist positions.
Syncretism – Blending traits from two different cultures to form a new trait. Also called fusion. This occurs when a subordinate group moulds elements of a dominant culture to fit its own traditions.
Syntax – The arrangement and order of words in phrases and sentences.
System of Oppression – Conscious and unconscious, non-random, and organized harassment, discrimination , exploitation, discrimination, prejudice and other forms of unequal treatment that impact different groups.
Taboo – is a strong social prohibition with grave consequences about certain areas of human activity or social custom. The term originally came from the Tongan language. The first recorded usage in English was by Captain James Cook in 1777. Some examples of taboo are dietary restrictions such as halal or kosher, restrictions on sexual activities such as incest, bestiality or animal-human sex, necrophilia or sex with the dead etc.
Terrorism (n.) – The use or threat to use, unlawful acts of force or violence to intimidate or coerce another person, group, or government, often for ideological, religious, or political reasons. The U.S. Department of State defines terrorism as “premeditated, politically motivated violence perpetrated against noncombatant targets by sub-national groups or clandestine agents, usually intended to influence an audience.”
Theory – An explanatory framework, containing a series of statements, that helps us understand why (something exists or functions in a certain manner). Theories suggest patterns, connections, and relationships that may be confirmed by new research.
Third World – A very vague term used to describe those regions of the world in which levels of development, applying such measures as GDP, are significantly below those of the economically more advanced regions. The term is increasingly seen as an inadequate description of the prevailing world situation since it fails to describe a significant amount of internal differentiation and development.
Tokenism (n.) – The policy of making only a perfunctory effort or symbolic gesture toward the accomplishment of a goal, such as racial integration; the practice of hiring or appointing a token number of people from underrepresented groups in order to deflect criticism or comply with affirmative action rules.
Tolerance (n) – Acceptance and open-mindedness to different practices, attitudes, and cultures; does not necessarily mean agreement with the differences.
Traditional Medicine-Medicine and healthcare practices which originated in a particular culture, and have been practiced by an ethnic or cultural group centuries in the country of origin or of emigration
Trait – Describes regularities in behavior, especially with reference to an individual’s personality.
Transactionalism – Transactionalism perspective sees an individual and an environment as integral aspects of a unitary system of change.
Transculturation – is a term coined by Fernando Ortiz in the 1940s to describe the phenomenon of merging and converging of different cultures. It argues that the natural tendency of people is to resolve conflicts over time, rather than aggravating them. Global communication and transportation technology nowadays replaces the ancient tendency of cultures drifting or remaining apart by bringing cultures more into interaction. The term “Ethnoconvergence” is sometimes used in cases where tranculturation affects ethnic issues.
Transgender – Appearing as, wishing to be considered as, or having undergone surgery to become a member of the opposite sex. Transgendered people can include transsexuals, cross-dressers, drag kings/queens, masculine women, feminine men, and those who defy what society tells them is appropriate for their gender.
Transhumance – One of two variants of pastoralism. A part of the population moves seasonally with the herds while the other part remains in home villages.
Transnationalism – Is the system of multiple ties and interactions linking people or organizations across the borders of nation-states and identified, for example, by flows of capital, images, information and people.
Transphobia – The fear or hatred of homosexuality (and other non-heterosexual identities), and persons perceived to be transgender and/or transexual.
Transracial Adoption (n.) – The adoption of a child of a race different than that of the parent or guardian.
Transsexual – One who identifies as a gender other that of their biological sex.
Tribe – A type of social formation usually considered to arise from the development of agriculture. Tribes tend to have a higher population density than bands and are also characterized by common descent or ancestry.
Tropics – World area of geographic belt extending about 23 degrees north and south of the equator, between the Tropic of Cancer (north) and the Tropic of Capricorn (south).
Two Spirit – A Native American term for individuals who identify both as male and female. In western culture these individuals are identified as lesbian, gay, bi-sexual or transgendered.
Uncertainty Avoidance – is one of the Hofstede dimensions, which he defines as “the extent to which the members of a culture feel threatened by uncertain or unknown situations.” (Hofstede, 1991)
Uncertainty of Approval – Measures how much any member of a group is concerned about getting acceptance from other group members.
Underdifferentiation – In developmental anthropology it refers to planning fallacy of viewing less-developed countries as an undifferentiated group. Ignoring cultural diversity and adopting a uniform approach (often ethnocentric) for very different types of project beneficiaries. In Linguistics it is the representation of two or more phonemes, syllables, or morphemes with a single symbol.
Undocumented Workers (n.) – A term used to describe the populations of laborers in the
Unearned Privilege (n) – Privileges accorded to some individuals because they possess or demonstrate certain characteristics associated with the dominant culture in society, such as being heterosexual, white, or male. These privileges are deeply ingrained into U.S. culture.
Unilineal Descent – Matrilineal or patrilineal descent.
Unilineal Evolution – also referred to as classical social evolution) is a 19th century social theory which claims a pattern of cultural progress through a sequence of evolutionary stages. It was the basic premise of the early cultural evolutionists but is considered obsolete.
Universal – Something that exists in every culture.
Universalism – One of the Trompenaars & Hampden-Turner (1997) dimensions describing the preference for rules over relationships (or vice versa). In a Universalist culture, a rule cannot be broken and is a “hard fact“, no matter what the relationship with the person is. People in universalistic cultures share the belief that general rules, codes, values and standards take precedence over particular needs and claims of friends and relations.
Unobtrusive Measures – A measurement that can be made without the person being aware of being studied. This is done to reduce the problem of evaluation apprehension, when the person being evaluated is concerned about performing suitably.
Unstructured Interview – is an ethnographic data-gathering technique usually used in the early stages of fieldwork in which interviewees are asked to respond to broad, open-ended questions.
Urbanization – The process by which increasing number of people come to live in cities.
Urbanized society – A society in which the majority of people live in cities in contrast to rural society.
Urban-overload hypothesis – Assumes that city dwellers react to excessive stimulation by avoiding interpersonal involvement.
Validity – The extent to which a measure represents accurately what it is supposed to represent.
Variables – Attributes (e.g., sex, age, height, weight) that differ from one person or case to the next.
Vertical Mobility – Upward or downward change in a person’s social status.
Veteran Status – Whether or not an individual has served in a nation’s armed forces (or other uniformed service).
Visual dominance behavior – Is the tendency of high-status positions to look more fixedly at lower-status people when speaking than when listening.
Vividness – The intensity or emotional interest of a stimulus.
WASP (n.) – The acronym translates to (W)hite (A)nglo (S)axon (P)rotestant, a term used in the United States to refer to the demographic of people who are of this ancestry. Often refers to white English-speaking persons of European descent in England or North America, not of Hispanic or French origin.
Wealth – All a person’s material assets, including income, land, and other types of property. It is the basis of economic and often social status.
Welfare (n.) – Economic assistance provided by the government to persons in need.
Weltanschaung – A worldview is a term from the German word Weltanschauung. Welt is the German word for “world”, and Anschauung is the German word for “view” or “outlook.” Usually it refers to the framework of ideas and beliefs through which an individual interprets the world in order to function. A “cosmology” is a “worldview” on a grand scale, reflecting not only the workings of one’s “world” but its relation to the rest of the entire cosmos.
Westernization – The acculturative influence of Western expansion on native cultures.
Wetback – Derogatory US term used to describe Mexican illegal immigrants, who allegedly entered the country by swimming the Rio Grande.
White Nigger / Wigger / Whigger / Wigga – Derogatory term used in 19th-century United States to describe the Irish. Nowadays used mainly to demean any White person as being
White Trash or to describe white youth that imitate urban black youth by means of clothing style, mannerisms, and slang speech.
White Privilege– refers to the many subtle but pervasive ways in which European Americans experience advantages and entitlements, often without being aware of it, that are not available to ethnic minorities.
Work space – Work station or area in an office or factory where a single individual regularly works.
Working class – Also called proletariat. Those who must sell their labor to survive. It is the antithesis of the bourgeoisie in Marx’s class analysis.
Working self-concept – The specific aspects of an individual’s identity that are activated by the role the individual is playing at any particular time.
World system – A term coined by the historian Immanuel Wallerstein to designate an economic unit, articulated by trade networks extending far beyond the boundaries of individual political units (nation states), and linking them together in a larger functioning unit.
Worldview – Is the English translation of the German word Weltanschaung. Also called World View.
Xenophile – is a person attracted to everything that is foreign, especially to foreign peoples, manners, or cultures.
Xenophobe -is a person who is fearful or contemptuous of anything foreign, especially of strangers or foreign peoples or cultures.
Xenophobia -The belief that people and things from other countries are dangerous and always have ulterior motives. Xenophobia is an irrational fear or hatred of anything foreign or unfamiliar.
Yang -Yin and Yang are two opposing and complementing aspects of phenomena in Chinese philosophy. Yin qualities are hot, fire, restless, hard, dry, excitement, non-substantial, rapidity, and correspond to the day.
YAVIS– Acronym for Young, Attractive, Verbal, Intelligent, and Successful; people with these characteristics are most likely to be selected by counselors to receive help.
Yellow (n.) – A term used to refer to people of the Asian Diaspora. Although the use of this word finds its roots as derogatory slang birthed in the era of exploration and colonialism, it has recently become more prevalent in academia and among Asian communities in the U.S. who use the word to embrace their ethnic origins and express pride in their identity.
Yin -Yin and Yang are two opposing and complementing aspects of phenomena in Chinese philosophy. Yin qualities are characterized as soft, substantial, water, cold, conserving, tranquil, gentle, and corresponds to the night.
Yuppie (n.) – “yuppie” is commonly used to refer to an 1980’s and early 1990’s term for financially secure, upper-middle class young people in their 20’s and early 30’s. It translates to
“(y)oung (u)pwardly –mobile (p)rofessionals” of the baby-boomer generation.
Zooarchaeology – The study of faunal remains found in archaeological sites and their cultural significance.
Zoomorphic – “Animal-like“. refers to art-work or decorated objects with an animal motif or appearance.
WereVerse Universe Baby! |
Standard C library provides qsort() that can be used for sorting an array. As the name suggests, the function uses QuickSort algorithm to sort the given array. Following is prototype of qsort()
The key point about qsort() is comparator function comparator. The comparator function takes two arguments and contains logic to decide their relative order in sorted output. The idea is to provide flexibility so that qsort() can be used for any type (including user defined types) and can be used to obtain any desired order (increasing, decreasing or any other).
The comparator function takes two pointers as arguments (both type-casted to const void*) and defines the order of the elements by returning (in a stable and transitive manner
int comparator(const void* p1, const void* p2); Return value meaning <0 The element pointed by p1 goes before the element pointed by p2 0 The element pointed by p1 is equivalent to the element pointed by p2 >0 The element pointed by p1 goes after the element pointed by p2 Source: http://www.cplusplus.com/reference/cstdlib/qsort/
For example, let there be an array of students where following is type of student.
Lets say we need to sort the students based on marks in ascending order. The comparator function will look like:br>
See following posts for more sample uses of qsort().
Given a sequence of words, print all anagrams together
Box Stacking Problem
Closest Pair of Points
Following is an interesting problem that can be easily solved with the help of qsort() and comparator function.
Given an array of integers, sort it in such a way that the odd numbers appear first and the even numbers appear later. The odd numbers should be sorted in descending order and the even numbers should be sorted in ascending order.
The simple approach is to first modify the input array such that the even and odd numbers are segregated followed by applying some sorting algorithm on both parts(odd and even) separately.
However, there exists an interesting approach with a little modification in comparator function of Quick Sort. The idea is to write a comparator function that takes two addresses p and q as arguments. Let l and r be the number pointed by p and q. The function uses following logic:
1) If both (l and r) are odd, put the greater of two first.
2) If both (l and r) are even, put the smaller of two first.
3) If one of them is even and other is odd, put the odd number first.
Following is C implementation of the above approach.
Output array is 9 7 5 3 1 2 4 6 8
Given an array of integers, sort it in alternate fashion. Alternate fashion means that the elements at even indices are sorted separately and elements at odd indices are sorted separately.
This article is compiled by Aashish Barnwal. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. |
Mercury is the closest planet to our Sun, the smallest of the eight planets, and one of the most extreme worlds in our Solar Systems. Named for the Roman messenger of the Gods, the planet is one of a handful that can be viewed without the aid of telescopes. As such, it has played an active role in the mythological and astrological systems of many cultures.
In spite of that, Mercury is one of the least understood planets in our Solar System. Much like Venus, its orbit between Earth and the Sun means that it can be seen at both morning and evening (but never in the middle of the night). And like Venus and the Moon, it also goes through phases, a characteristic which originally confounded astronomers, but eventually helped them to realize the true nature of the Solar System.
Size, Mass and Orbit:
With a mean radius of 3.3022×1023 kg and a mass of 3.3022×1023 kg, Mercury is the smallest planet in our Solar System – equivalent to 0.38 Earths. And while it is smaller than the largest natural satellites in our system – such as Ganymede and Titan – it is more massive. In fact, Mercury’s density (at of 5.427 g/cm3) is the second highest in the Solar System, only slightly less than Earth’s density of 5.515 g/cm3.
Mercury has the most eccentric orbit of any planet in the Solar System. At 0.205, its distance from the Sun ranges from 46,000,000 to 70,000,000 km (29,000,000 – 43,000,000 mi), and it takes 87.969 Earth days to complete an orbit. Mercury also has the lowest axial tilt of any planet in the Solar System – approximately 0.027 degrees compared to Jupiter’s 3.1 degrees which has the second smallest axial tilt of all the planets.
But with an average orbital speed of 47.362 km/s, Mercury takes 115.88 days to complete a single rotation. Between its slow rate of rotation and its orbit, a single day on Mercury lasts 176 Earth days. Another consequence of this slow rotation is Mercury’s spin-orbit resonance, which is 3:2. This means that the planet makes three completes rotations for every two orbits it makes around the Sun.
Composition and Surface Features:
As one of the four terrestrial planets of the Solar System, Mercury is composed of approximately 70% metallic and 30% silicate material. Based on its density and size, a number of inferences can be made about its internal structure. For example, geologists estimate that Mercury’s core occupies about 42% of its volume, compared to Earth’s 17%.
The interior is believed to be composed of a molten iron which is surrounded by a 500 – 700 km mantle of silicate material. At the outermost layer is Mercury’s crust, which is believed to be 100 – 300 km thick. The surface is also marked by numerous narrow ridges that extend up to hundreds of kilometers in length. It is believed that these were formed as Mercury’s core and mantle cooled and contracted at a time when the crust had already solidified.
Mercury’s core has a higher iron content than that of any other major planet in the Solar System, and several theories have been proposed to explain this. The most widely accepted theory is that Mercury was once a larger planet which was then struck by a planetesimals measuring several thousand km in diameter. This impact could have then stripped away much of the original crust and mantle, leaving behind the core as a major component.
Another theory is that Mercury may have formed from the solar nebula before the Sun’s energy output had stabilized. It would have originally been twice its present mass, but as the protosun contracted, Mercury would have been subjected to temperatures of 2,500 – 3,500 K, or even as high as 10,000 K. This process would have vaporized much of Mercury’s surface rock, leaving behind on oversized iron core.
A third hypothesis proposes that the solar nebula caused drag on the particles from which Mercury was accreting, which meant that lighter particles were lost and not gathered by Mercury. However, further analysis is needed before any of these theories can be confirmed or ruled out.
At a glance, Mercury looks similar to the Earth’s moon. It has a dry landscape pockmarked by asteroid impact craters and ancient lava flows. Combined with extensive plains, these indicate that the planet has been geologically inactive for billions of years. However, unlike the Moon and Mars, which have significant stretches of similar geology, Mercury’s surface appears much more jumbled. Other common features include dorsa (aka. “wrinkle-ridges, Moon-like highlands, montes (mountains), planitiae (plains), rupes (escarpments) and valles (valleys).
Names for these features come from a variety of sources. Craters are named for artists, musicians, painters, and authors; ridges are named for scientists; depressions are named for works of architecture; mountains are named for the word “hot” in different languages; planes are named for Mercury in various languages; escarpments are named for ships of scientific expeditions and valleys are named after radio telescope facilities.
During and following its formation 4.6 billion years ago, Mercury was heavily bombarded by comets and asteroids, and perhaps again during the Late Heavy Bombardment period. During this period of intense crater formation, the planet received impacts over its entire surface, thanks in part to the lack of any atmosphere to slow impactors down. During this time the planet was volcanically active, and release magma would have produced smooth plains.
Craters on Mercury range in diameter from small bowl-shaped cavities to multi-ringed impact basins hundreds of kilometers across. The largest known crater is Caloris Basin, with a diameter of 1,550 km. The impact that created it was so powerful that it caused lava eruptions and left a concentric ring over 2 km tall surrounding the impact crater. Overall, about 15 impact basins have been identified on the imaged part of Mercury.
Atmosphere and Temperature:
Mercury is too hot and too small to retain an atmosphere. However, it does a tenuous and variable exosphere that is made up of hydrogen, helium, oxygen, sodium, calcium, potassium and water vapor, with a combined pressure level of about 10?14 bar (one-quadrillionth of Earth’s atmospheric pressure). It is believed this exosphere was formed from particles captured from the Sun, volcanic outgassing and debris kicked into orbit by micrometeorite impacts.
Because it lacks a viable atmosphere, Mercury has no way to retain the heat from the Sun. Because of this, and its high eccentricity, the planet experiences considerable variations in temperature. Whereas the side that faces the Sun can reach temperatures of up to 700 K (427° C), while the side in shadow dips down to 100 K (-173° C).
Despite these highs in temperature, the existence of water ice has been confirmed on Mercury’s surface. The floors of deep craters at the poles are never exposed to direct sunlight, and temperatures there remain below the average. These icy regions are believed to contain about 1014–1015 kg of frozen water, and may be covered by a layer of regolith that inhibits sublimation. The origin of the ice on Mercury is not yet known, but the two most likely sources are from outgassing of water from the planet’s interior or deposition by impacts of comets.
Much like the other planets that are visible to the naked eye, Mercury has a long history of being observed by human astronomers. The earliest recorded observations of Mercury are believed to be in the Mul.Apin, a Babylonian compendium of Babylonian astronomy and astrology.
The observations, which were most likely made during the 14th century BCE, refer to the planet as “the jumping planet”. Other Babylonian records, which refer to the planet as “Nabu” (after the messenger to the gods in Babylonian mythology) date back to the first millennium BCE.
To the ancient Greeks, Mercury was known as variously as “Stilbon” (a name which means “the gleaming”), Hermaon, and Hermes. As with the Babylonians, this latter name came from the messenger of the Greek pantheon as well. The Romans continued this tradition, naming the planet Mercurius after the swiftfooted messenger of the gods, which they equated with the Greek Hermes. The reason for this has to do with Mercury being the fastest-moving planet across the sky.
In his book Planetary Hypotheses, Greco-Egyptian astronomer Ptolemy wrote about the possibility of planetary transits across the face of the Sun. For Mercury, he suggested that no transits had been observed either because the planet was either too small to see or because the transits are too infrequent.
To the ancient Chinese, Mercury was known as Chen Xing (“the Hour Star), and was associated with the direction of north and the element of water – based on the Five Elements. Similarly, modern Chinese, Korean, Japanese and Vietnamese cultures refer to the planet literally as the “water star”. In, Hindu mythology, the name Budha was used for Mercury, the god that was thought to preside over Wednesday.
The same is true of the Germanic tribes, who associated the god Odin (or Woden) with the planet Mercury and Wednesday. The Maya may have represented Mercury as an owl – or possibly four owls, two for the morning aspect and two for the evening – that served as a messenger to the underworld.
In medieval Islamic astronomy, the Andalusian astronomer Abu Ishaq Ibrahim al-Zarqali in the 11th century described Mercury’s geocentric orbit as being oval, although this insight did not influence his astronomical theory or his astronomical calculations. In the 12th century, Ibn Bajjah observed “two planets as black spots on the face of the Sun”, which was later suggested as the transit of Mercury and/or Venus.
In India, the Kerala school astronomer Nilakantha Somayaji in the 15th century developed a partially heliocentric planetary model in which Mercury orbits the Sun, which in turn orbits Earth, similar to the Tychonic system later proposed by Tycho Brahe in the 16th century.
The first observations using a telescope took place in the early 17th century by Galileo Galilei. Although he had observed phases when looking at Venus, his telescope was not powerful enough to see Mercury going through similar phases. In 1631, Pierre Gassendi made the first telescopic observations of the transit of a planet across the Sun when he saw a transit of Mercury predicted by Johannes Kepler.
In 1639, Giovanni Zupi used a telescope to discover that the planet had orbital phases similar to Venus and the Moon. These observations demonstrated conclusively that Mercury orbited around the Sun, which helped to definitively prove that the Copernican Heliocentric model of the universe was correct.
The first spacecraft to reach Mercury was NASA’s Mariner 10, which flew past the planet in 1974. It was only able to photograph about half of the planet over the course of a few flybys. And then 2004 NASA launched its latest MESSENGER spacecraft mission to Mercury. At the time of writing, the spacecraft had completed several flybys of the planet, is scheduled to go into orbit in 2011, where it will be able to study the planet in great detail.
Even though you can see Mercury without a telescope, it’s hard to find it because it’s lost within the glare of the Sun most of the time. When Mercury is visible, you’ll be able to see it to the west just after sunset, or to the east just before sunrise.
Here are some articles on Mercury that we hope you find interesting, illuminating, and fun to read:
Location and Movement of Mercury
- Rotation of Mercury
- Orbit of Mercury
- How Long is a Day on Mercury
- How Long is a Year on Mercury?
- Mercury Retrograde
- Mercury Revolution
- Length of Day on Mercury
- Length of Year on Mercury
- Transit of Mercury
- How Long Does it Take Mercury to Orbit the Sun?
Structure of Mercury
- Mercury Diagram
- Interior of Mercury
- Composition of Mercury
- Formation of Mercury
- What is Mercury Made Of?
- What Type of Planet is Mercury?
- Does Mercury Have Rings?
- How Many Moons Does Mercury Have?
Conditions on Mercury
- Surface of Mercury
- Temperature of Mercury
- Color of Mercury
- How Hot is Mercury?
- Life on Mercury
- Atmosphere of Mercury
- Weather on Mercury
- Is There Ice on Mercury?
- Water on Mercury
- Geology of Mercury
- Mercury Magnetic Field
- Climate of Mercury
History of Mercury
- How Old is Mercury?
- Discovery of Planet Mercury?
- Have Humans Visited Mercury?
- Exploration of Mercury
- Who Discovered Mercury?
- Missions to Mercury
- How Did Mercury Get its Name?
- Symbol for Mercury
Other Mercury Articles
- Interesting Facts About Mercury
- Closest Planet to Mercury
- How Long Does it Take to Get to Mercury?
- Is Mercury the Hottest Planet?
- Pictures of Mercury
- Mercury Wallpaper
- Mercury Compared to Earth
- Characteristics of Mercury |
The invention of printing also fostered the scientific revival by making it easy to spread knowledge abroad in every land. The pioneers of Renaissance science were Italians, but students in France, England, Germany, and other countries soon took up the work of enlightenment.
The names of some Renaissance scientists stand as landmarks in the history of thought. The first place must be given to Copernicus, the founder of modern astronomy. He was a Pole, but lived many years in Italy. Patient study and calculation led him to the conclusion that the earth turns upon its own axis, and, together with the planets, revolves around the sun. The book in which he announced this conclusion did not appear until the very end of his life. A copy of it reached him on his deathbed.
THE COPERNICAN THEORY
Medieval astronomers had generally accepted the Ptolemaic system. Some students before Copernicus had indeed suggested that the earth and planets might rotate about a central sun, but he first gave reasons for such a belief. The new theory met much opposition, not only in the universities, which clung to the time-honored Ptolemaic system, but also among theologians, who thought that it contradicted many statements in the Bible. Moreover, people could not easily reconcile themselves to the idea that the earth, instead of being the center of the universe, is only one member of the solar system, that it is, in fact, only a mere speck of cosmic dust.
An Italian scientist, Galileo, made one of the first telescopes--it was about as powerful as an opera glass--and turned it on the heavenly bodies with wonderful results. He found the sun moving unmistakably on its axis, Venus showing phases according to her position in relation to the sun, Jupiter accompanied by revolving moons, or satellites, and the Milky Way composed of a multitude of separate stars. Galileo rightly believed that these discoveries confirmed the theory of Copernicus.
Another man of genius, the German Kepler, worked out the mathematical laws which govern the movements of the planets. He made it clear that the planets revolve around sun in elliptical instead of circular orbits. Kepler's investigations afterwards led to the discovery of the principle of gravitation.
VESALIUS, 1514-1564 AND HARVEY, 1578-1657
Two other scientists did epochal work in a field far removed from astronomy. Vesalius, a Fleming, who studied in Italian medical schools, gave to the world the first careful description of the human body based on actual dissection. He was thus the founder of human anatomy. Harvey, an Englishman, after observing living animals, announced the discovery of the circulation of the blood. He thereby founded human physiology.
THE SCIENTIFIC METHOD
Copernicus, Galileo, Kepler, Vesalius, Harvey, and their fellow workers built up the scientific method. In the Middle Ages students had mostly been satisfied to accept what Aristotle and other philosophers had said, without trying to prove their statements. Kepler, for instance, was the first to disprove the Aristotelian idea that, as all perfect motion is circular, therefore the heavenly bodies must move in circular orbits. Similarly, the world had to wait many centuries before Harvey showed Aristotle's error in supposing that the blood arose in the liver, went thence to the heart, and by the veins was conducted over the body. The new scientific method rested on observation and experiment. Students learned at length to take nothing for granted, to set aside all authority, and to go straight to nature for their facts. As Lord Bacon, one of Shakespeare's contemporaries and a severe critic of the old scholasticism, declared, "All depends on keeping the eye steadily fixed upon the facts of nature, and so receiving their images simply as they are, for God forbid that we should give out a dream of our own imagination for a pattern of the world." Modern science, to which we owe so much, is a product of the Renaissance. |
In the previous part of Lesson 2, the use of kinematic equations to solve projectile problems was introduced and demonstrated. These equations were used to solve problems involving the launching of projectiles in a horizontal direction from an elevated position. In this section of Lesson 2, the use of kinematic equations to solve non-horizontally launched projectiles will be demonstrated. A non-horizontally launched projectile is a projectile that begins its motion with an initial velocity that is both horizontal and vertical. To treat such problems, the same principles that were discussed earlier in Lesson 2 will have to be combined with the kinematic equations for projectile motion. You may recall from earlier that there are two sets of kinematic equations - a set of equations for the horizontal components of motion and a similar set for the vertical components of motion. For the horizontal components of motion, the equations are
x = vix•t + 0.5*ax*t2
vfx = vix + ax•t
vfx2 = vix2 + 2*ax•x
||x = horiz. displacement
||ax = horiz. acceleration
||t = time
||vfx = final horiz. velocity
||vix = initial horiz. velocity
Of these three equations, the top equation is the most commonly used. The other two equations are seldom (if ever) used. An application of projectile concepts to each of these equations would also lead one to conclude that any term with ax in it would cancel out of the equation since ax = 0 m/s/s.
For the vertical components of motion, the three equations are
y = viy•t + 0.5*ay*t2
vfy = viy + ay•t
vfy2 = viy2 + 2*ay•y
||y = vert. displacement
||ay = vert. acceleration
||t = time
||vfy = final vert. velocity
||viy = initial vert. velocity
In each of the above equations, the vertical acceleration of a projectile is known to be -9.8 m/s/s (the acceleration of gravity).
As discussed earlier in Lesson 2, the vix and viy values in each of the above sets of kinematic equations can be determined by the use of trigonometric functions. The initial x-velocity (vix) can be found using the equation vix = vi•cosine(Theta) where Theta is the angle that the velocity vector makes with the horizontal. The initial y-velocity (viy) can be found using the equation viy = vi•sine(Theta) where Theta is the angle that the velocity vector makes with the horizontal. The topic of components of the velocity vector was discussed earlier in Lesson 2.
To illustrate the usefulness of the above equations in making predictions about the motion of a projectile, consider their use in the solution of the following problem.
A football is kicked with an initial velocity of 25 m/s at an angle of 45-degrees with the horizontal. Determine the time of flight, the horizontal displacement, and the peak height of the football.
The solution of any non-horizontally launched projectile problem (in which vi and Theta are given) should begin by first resolving the initial velocity into horizontal and vertical components using the trigonometric functions discussed above. Thus,
vix = vi•cos(Theta)
vix = 25 m/s•cos(45 deg)
vix = 17.7 m/s
viy = vi•sin(Theta)
viy = 25 m/s•sin(45 deg)
viy = 17.7 m/s
In this case, it happens that the vix and the viy values are the same as will always be the case when the angle is 45-degrees.
The solution continues by declaring the values of the known information in terms of the symbols of the kinematic equations - x, y, vix, viy, ax, ay, and t. In this case, the following information is either explicitly given or implied in the problem statement:
x = ???
vix = 17.7 m/s
vfx = 17.7 m/s
ax = 0 m/s/s
y = ???
viy = 17.7 m/s
vfy = -17.7 m/s
ay = -9.8 m/s/s
As indicated in the table, the final x-velocity (vfx) is the same as the initial x-velocity (vix). This is due to the fact that the horizontal velocity of a projectile is constant; there is no horizontal acceleration. The table also indicates that the final y-velocity (vfy) has the same magnitude and the opposite direction as the initial y-velocity (viy). This is due to the symmetrical nature of a projectile's trajectory.
The unknown quantities are the horizontal displacement, the time of flight, and the height of the football at its peak. The solution of the problem now requires the selection of an appropriate strategy for using the kinematic equations and the known information to solve for the unknown quantities. There are a variety of possible strategies for solving the problem. An organized listing of known quantities in two columns of a table provides clues for the selection of a useful strategy.
From the vertical information in the table above and the second equation listed among the vertical kinematic equations (vfy = viy + ay*t), it becomes obvious that the time of flight of the projectile can be determined. By substitution of known values, the equation takes the form of
-17.7 m/s = 17.7 m/s + (-9.8 m/s/s)•t
The physics problem now takes the form of an algebra problem. By subtracting 17.7 m/s from each side of the equation, the equation becomes
-35.4 m/s = (-9.8 m/s/s)•t
If both sides of the equation are divided by -9.8 m/s/s, the equation becomes
3.61 s = t
(rounded from 3.6077 s)
The total time of flight of the football is 3.61 seconds.
With the time determined, information in the table and the horizontal kinematic equations can be used to determine the horizontal displacement (x) of the projectile. The first equation (x = vix•t + 0.5•ax•t2) listed among the horizontal kinematic equations is suitable for determining x. With the equation selected, the physics problem once more becomes transformed into an algebra problem. By substitution of known values, the equation takes the form of
x = (17.7 m/s)•(3.6077 s) + 0.5•(0 m/s/s)•(3.6077 s)2
Since the second term on the right side of the equation reduces to 0, the equation can then be simplified to
x = (17.7 m/s)•(3.6077 s)
x = 63.8 m
The horizontal displacement of the projectile is 63.8 m.
Finally, the problem statement asks for the height of the projectile at is peak. This is the same as asking, "what is the vertical displacement (y) of the projectile when it is halfway through its trajectory?" In other words, find y when t = 1.80 seconds (one-half of the total time). To determine the peak height of the projectile (y with t = 1.80 sec), the first equation (y = viy•t +0.5•ay•t2) listed among the vertical kinematic equations can be used. By substitution of known values into this equation, it takes the form of
y = (17.7 m/s)•(1.80 s) + 0.5*(-10 m/s/s)•(1.80 s)2
Using a calculator, this equation can be simplified to
y = 31.9 m + (-15.9 m)
y = 15.9 m
The solution to the problem statement yields the following answers: the time of flight of the football is 3.61 s, the horizontal displacement of the football is 63.8 m, and the peak height of the football 15.9 m.
(Note that in all calculations performed above, unrounded numbers were used. The numbers reported in the preliminary steps and in the final answer were the rounded form of the actual unrounded values.)
A Typical Problem-Solving Approach
The following procedure summarizes the above problem-solving approach.
- Use the given values of the initial velocity (the magnitude and the angle) to determine the horizontal and vertical components of the velocity (vix and viy).
- Carefully read the problem and list known and unknown information in terms of the symbols of the kinematic equations. For convenience sake, make a table with horizontal information on one side and vertical information on the other side.
- Identify the unknown quantity that the problem requests you to solve for.
- Select either a horizontal or vertical equation to solve for the time of flight of the projectile. For non-horizontally launched projectiles, the second equation listed among the vertical equations (vfy = viy + ay*t) is usually the most useful equation.
- With the time determined, use a horizontal equation (usually x = vix*t + 0.5*ax*t2 ) to determine the horizontal displacement of the projectile.
- Finally, the peak height of the projectile can be found using a time value that is one-half the total time of flight. The most useful equation for this is usually y = viy*t +0.5*ay*t2 .
One caution is in order: the sole reliance upon 4- and 5-step procedures to solve physics problems is always a dangerous approach. Physics problems are usually just that - problems! And problems can often be simplified by the use of short procedures as the one above. However, not all problems can be solved with the above procedure. While steps 1, 2 and 3 above are critical to your success in solving non-horizontally launched projectile problems, there will always be a problem that doesn't "fit the mold." Problem solving is not like cooking; it is not a mere matter of following a recipe. Rather, problem solving requires careful reading, a firm grasp of conceptual physics, critical thought and analysis, and lots of disciplined practice. Never divorce conceptual understanding and critical thinking from your approach to solving problems.
Your Turn to Try It!
Use the Range of an Angle-Launched Projectile widget to practice a projectile problem (or two) (or three). Using the given launch velocity and launch angle, determine the expected horizontal displacement (dx). After completing your calculation, use the Submit button to check your answer.
Check Your Understanding
A long jumper leaves the ground with an initial velocity of 12 m/s at an angle of 28-degrees above the horizontal. Determine the time of flight, the horizontal distance, and the peak height of the long-jumper.
We Would Like to Suggest ...
Sometimes it isn't enough to just read about it. You have to interact with it! And that's exactly what you do when you use one of The Physics Classroom's Interactives. We would like to suggest that you combine the reading of this page with the use of our Projectile Motion Simulator
. You can find it in the Physics Interactives section of our website. The simulator allows one to explore projectile motion concepts in an interactive manner. Change a height, change an angle, change a speed, and launch the projectile. |
A comet’s nucleus is in the center of its coma. A comet’s nucleus is like a snowball made of ice. As the comet nears the Sun, the ice starts to melt off, along with particles of dust. These particles and gases make a cloud around the nucleus, called a coma.
A comet’s nucleus, or heart, is the solid chunk of something in the center of its fuzzy coma. As it approaches the Sun, some of its surface boils off and creates a long tail.
But what IS inside a comet’s nucleus?
Marshmallows? Chewy caramel? Nuts?
What Scientists Have Learned
Comets are part of the solar system. They orbit the Sun, just as planets do, except a comet usually has a very elongated orbit. Part of its orbit is very, very far from the Sun and part is quite close to the Sun.
A comet’s nucleus is like a dirty snowball made of ice. As the comet gets closer to the Sun, some of the ice starts to melt and boil off, along with particles of dust. These particles and gases make a cloud around the nucleus, called a coma. The coma is lit by the Sun. The sunlight also pushes this material into the beautiful brightly lit tail of the comet.
Scientists have now had a look inside a comet’s nucleus.
On July 4, 2005, NASA’s Deep Impact spacecraft’s “smart impactor” scooped out . . . well, more like blasted out a crater in the nucleus of Comet Tempel 1. What did they find? Was it dark and crusty like the surface, or soft and squishy like a marshmallow, or full of holes like Swiss cheese, or full of big rocks like nutty nougat?
Comet Tempel 1
Here’s some of what they have found out so far from looking at Deep Impact’s encounter with Tempel 1:
The comet’s nucleus is spongy, with lots of holes inside. No one knows yet whether there are a few large holes or many smaller ones. So what?
If there are a few large holes, it might mean that the comet was formed from large, dirty ice boulders. If there are many smaller holes, it might mean the comet was formed from many more dirty ice snowballs.
Parts of the surface are very fragile and weak. So what?
It may be that the comet’s ice was the “glue” that held the comet dust and rocks together. Then, as the comet came closer to the Sun, the surface ice evaporated, leaving little or no “glue.” The rocky and dusty structures would then be fragile and crumbly.
The surface of the nucleus is covered with fine dust, like baby powder. What is this dust and where did it come from?
Originally, the comet’s surface ice probably contained a lot of fine dust. When the orbit of the comet brings it close to the Sun, the ice evaporates into space, leaving some of the fine dust sitting on the surface. The dust is fine like talcum powder because comets are too small to have enough gravity to squeeze the dust together into larger particles.
The surface is very black. What is this black stuff?
The very black material on the surface is carbon-based material similar to the greasy black goo that burns onto your barbecue grill. The comet originally formed from ices (mostly water ice), silicate dust (like powdered beach sand), and this type of black space gunk.
Some parts of the nucleus are smooth and young, while other areas are cratered and old. What happened?
The old-looking part of the surface has been battered for thousands of years by small, rocky asteroids or other comets. So why are some areas smooth? It is possible that as the comet has approached the Sun over the years, the ices on the surface have vaporized, and taken some of the embedded dust particles with it. Then, some of the dust particles could have settled back down on the surface, filling in some of the craters. Or, maybe the smooth surface areas that are covered with dust and dirty ice are disappearing as the comet repeadedly gets close to the Sun. After a long time, the smooth icy regions may have retreated, revealing the older cratered surface below.
The nucleus seems to have formed from overlapping layers of different materials. Why?
The layers must have formed as the comet grew. As it got bigger, gravitational forces drew in ices, dust, and the black “space gunk” we talked about earlier from the comet’s neighborhood.
There is ice beneath the surface, both water ice just below the surface and carbon dioxide ice (also known as “dry ice”) farther down. Why different kinds of ice at different depths?
Most of the ice in our solar system, including the ice in comets, is water ice. In Comet Tempel 1, almost all the ice is water ice, but some is carbon dioxide ice—or “dry ice.” Carbon dioxide ice vaporizes faster than water ice. (That is why you might use “dry ice” to make “smoke” for a model volcano or “fog” for a stage play.) As the comet gets close to the Sun, the carbon dioxide ice will vaporize before the water ice. So, after thousands of years, even though the two kinds of ice were initially mixed together near the surface, only the water ice remains. The carbon dioxide ice a meter or so beneath the surface is more protected from the Sun’s heat, so may survive, with water ice above it.
Tempel 1 contains materials from the outer, middle, and inner parts of the solar system. Why?
We are not sure. Comets probably formed in the outer solar system. The inner solar system type of dust particles found in them could have traveled to the outer solar system where the comets formed. Or, not as likely, these dust particles could have arrived from other solar systems. Water and carbon dioxide ices are both found in the outer solar system, so comets could pick up both ices while forming.
Of course, not every comet may be just like Tempel 1.
Deep Impact blasted lots of material from beneath the surface into the comet’s coma. Remember, the coma is the cloud of dust and gas that boils off the nucleus as the comet’s orbit takes it closer and closer to the Sun.
The coma contains material from near the surface of the nucleus. This material is what the Sun heats up most and what boils off first. Scientists saw what was in the coma right after the impact, and compared that with what was there before the impact. This way, they could get an idea what was added from the material blasted out of the hole in the nucleus.
But, whether before or after the blast, how do the scientists know what the coma is made of? After all, the comet and its coma are millions of miles away!
Here’s how: They observe the coma through a telescope equipped with a spectrometer.
A spectrometer creates something like a rainbow. Like droplets of water may do after a rain, a spectrometer breaks light apart into its different wavelengths, or “colors.” Depending on what gases (such as those in air) the light has passed through, the “rainbow” will look different. That is because each gas absorbs one or more particular colors of the light that passes through it. |
Civil Rights Act of 1875
No issue concerned black Representatives more than the civil rights bill of 1875. The Civil Rights Act of 1866, which guaranteed citizens the right to enter into contracts and to purchase, sell, or lease property, had been a first step. And the series of Ku Klux Klan Acts, which had incrementally outlawed discrimination in voter registration in local and congressional elections and empowered circuit judges to appoint election supervisors, had advanced the cause of civil rights a bit further. But neither effort fully satisfied ardent reformers, such as Senator Charles Sumner. On May 13, 1870, Sumner introduced sweeping legislation that promised to fully enforce and expand upon the Thirteenth, Fourteenth, and Fifteenth Amendments. The centerpiece of his original bill outlawed racial discrimination in juries, schools, transportation, and public accommodations. But with Illinois Senator Lyman Trumbull, chairman of the powerful Judiciary Committee, opposed to the measure, Sumner’s bill remained trapped in committee.96
On December 2, 1873, the Opening Day of the 43rd Congress, Sumner dutifully submitted his civil rights bill.97 Two weeks later on December 18—bolstered by the GOP’s 111-Member majority—House Judiciary Committee Chairman Benjamin Butler of Massachusetts submitted his own civil rights bill, which echoed much of Sumner’s language.98 A Democrat who supported the doctrine of states’ rights, Butler changed his party allegiances and his attitude toward African Americans while serving as a brigadier general in the Union Army during the Civil War. Recalling the deaths of black Union soldiers on the battlefield, Butler declared, “May my right hand forget its cunning and my tongue cleave to the roof of my mouth if I ever fail to defend the rights of these men who have given their blood for me and my country. . . . God helping me, I will keep that oath.”99
Opponents lined up to denounce Butler’s bill when it came to the House Floor the following January. Democratic Representative Milton Durham of Kentucky accused the measure of trying to start “a war of the races, [in which] the black race in this country will be exterminated.”100 Other Democrats stood up one by one, claiming that the civil rights bill attempted to enforce rights beyond the scope of the Constitution; that it usurped the power of the states to regulate public schools; and that it forced Southerners to develop what they believed to be unattainable—an equitable multiracial society. Amendments aimed at killing the civil rights bill flooded in at such an alarming rate that Butler pulled the bill from the floor and sent it back to his committee.
In the Senate, Sumner’s death on March 11, 1874, breathed new life into his legislative agenda. On his deathbed, Sumner allegedly repeated at least three times to Representative George Hoar: “You must take care of the civil rights bill—my bill, the civil rights bill—don’t let it fail!”101 Primarily out of respect for their deceased colleague, Senators passed the bill—29 to 16—two months later.102 The legislation was referred to the House Judiciary Committee on June 18, leaving the chamber to consider both Sumner’s and Butler’s legislation.103
Widespread Republican losses in the 1874 midterm elections further endangered the civil rights bill. Sixty-two House Republican incumbents failed to win re-election; 43 hailed from northern or western states. The large GOP majority in the House during the 43rd Congress gave way to a 79-Member Democratic advantage in the 44th Congress.104 A financial panic in 1873 followed by the onset of a depression, combined with multiple charges of corruption in Republican President Ulysses S. Grant’s administration, were primarily blamed for the loss.105
There was also a sense on Capitol Hill that the public had grown disinterested in civil rights legislation. A top House Republican, James Garfield of Ohio—where GOP electoral losses were especially devastating—observed “a general apathy among the people concerning the war and the negro.”106James Sener, a scalawag from Virginia, blamed prolonged congressional debate on the civil rights bill for his electoral loss. Sener noted that although he continually opposed the bill during the first session of the 43rd Congress, his constituents feared that “under the whip and spur of party pressure” that Sener might “yield my honest convictions to the will of the majority.”107 Among those who lost their elections that year was Benjamin Butler; Democrat Charles P. Thompson defeated him by six percent of the vote.108 On the other hand, the electoral loss also rallied Republican Representatives, who returned to the lame duck session in 1875 determined not to leave office without passing some form of civil rights legislation.
Democrats, however, believed their election win gave them a mandate to scuttle the civil rights bill. They continually halted business by submitting multiple motions to adjourn every time Butler attempted to place the legislation on the House Calendar for debate. A top GOP lieutenant, John Cessna of Pennsylvania, attempted to circumvent Democrats by drastically changing House Rules, disposing of all dilatory motions (those put forward strictly to stall consideration of legislation) for the remainder of the term. The change failed to achieve the two-thirds majority needed to alter House Rules after 15 Republicans defected. But over strong Democratic objections, Cessna worked with Speaker Blaine to broker a compromise, restricting the use of dilatory motions and opening an opportunity to debate civil rights legislation.109
African Americans in Congress Lead the Debate
During the precarious lead-up to the 1874 elections, as white Republicans in the House avoided commenting on the civil rights bill, African-American Representatives took the lead in debate. Facing some of the former Confederacy’s great orators, the seven black Members serving in the House at the time made some of their most famous and impassioned speeches in support of the civil rights bill. That the House had seven black Representatives (a record number) was, in itself, an argument in favor of the bill. As one scholar notes, “their presence demonstrated that equality in politics could work [and] . . . signaled the drastic change that had overtaken the country’s political order.”110
The climax of the first session of the 43rd Congress starred the talented and charismatic black South Carolina Representative Robert Elliott. The rules of debate governing the civil rights bill limited each Member to 20 minutes. Late in the day on January 5, 1874, however, former Confederate vice president Alexander Stephens of Georgia requested a full hour to make his argument. Ebenezer Hoar of Massachusetts—George Hoar’s brother and one of the bill’s champions—initially objected to giving the former rebel leader additional time to make his argument against the bill. African-American Representative Josiah Walls joined in the objection. But after what must have been a quick strategic discussion on the Republican side of the chamber, both Hoar and Walls agreed to withdraw their objections on the condition that Elliott would receive an hour to speak as well.111
At 63 and suffering from frequent headaches, Stephens stood feebly in the back of the chamber. Dressed in all black and leaning precariously on a stack of Congressional Record volumes―which held his written speech close to his face—the Georgian delivered his argument in what was described as a loud, shrill monotone. Though the Democratic side of the chamber filled to hear Stephens speak, the Republicans nearly abandoned the House Chamber, leaving only 20 or so of their Members present.112 Stephens outlined arguments that served as the rallying cry for the bill’s opponents: that the legislation was unconstitutional because it overreached into private lives and businesses; that racial segregation was the natural order of the South; and that, if left in their own social, political, and economic spheres, both white and black Southerners would prosper independently. African Americans “have no desire for anything partaking of the character of social rights,” the Georgian argued, “and if the people, colored and white, in several Southern States, shall be left to themselves to work out their own destiny under the present system, subject alone to the controlling law of justice . . . without external interference of any sort, it will, in my judgment, be infinitely better for both races.”113 When Stephens finished after 4:00 pm, Republicans requested that the House adjourn so that Elliott could lead off the debate the next day.114
Whether intentional or not, delaying Elliott’s response proved a brilliant strategic move. After word spread overnight that Elliott would deliver his rebuttal the next day, Members crowded the House Floor and African-American visitors packed the public galleries to hear Elliott speak. Reporters sat in the press gallery, pens poised. There was an immediate, visible contrast between Elliott and Stephens. Stephens was old and frail, but Elliott was only 31, tall and square-shouldered, and he strode confidently into the chamber. Though he later admitted to feeling nervous, Elliott spoke with rhetorical flourish, and rarely referred to his notes. Standing straight and gesturing enthusiastically, he converted his reportedly quick temper into a passionate response. Elliott subtly poked fun of Stephens’ stature and personal history, at one point referring to the Georgian’s arguments as “impotent.” “Sir, the gentleman from Georgia has learned much since 1861,” Elliott declared, “but he is still a laggard.” Elliott dismissed Stephens’ extensive constitutional argument, claiming he would not take such a legal lesson from someone who had so recently sought “the break up of the Union of these States and to blot the American Republic from the galaxy of nations.” Elliott argued that African Americans were entitled to the protections of the Fourteenth Amendment and the Constitution in all spheres of life. He concluded by listing the contributions made by African Americans to the United States and praised the impressive way in which freedmen and women had integrated themselves so newly into the political process. “The passage of this bill will determine the civil status, not only of the negro, but of any other class of citizens who may feel themselves discriminated against,” Elliott said. “It will form the cap-stone of that temple of liberty. . . . [W]e are at last politically free. The last vestiture only is needed—civil rights.”115
Elliott ended his speech to an eruption of wild applause. Democrats—who had sat at their desks on the House Floor and feigned inattention—found themselves staring at Elliott during his delivery. Members on the Republican side (and reportedly some Democrats) lined up to shake Elliott’s hand afterward; he was later greeted at his Washington, DC, boardinghouse with a large crowd and a brass band.116 Journalists pounced on the symbolism of the exchange between Elliott and Stephens: a man described as “blacker than boot polish,” had verbally skewered one of the former Confederacy’s stalwart politicians. The South Carolinian “has demonstrated the real force of the new order of things,” a reporter from the Chicago Tribune declared.117
Elliott was hardly alone among his African-American colleagues in deftly defending the bill. As southern Democrats denied that southern railroads, hotels, theaters, and restaurants discriminated against black customers, African-American Representatives provided vivid anecdotes of personal experiences with racism and segregation in public accommodations as evidence of the need for a civil rights bill. Joseph Rainey claimed he was unable to procure first-class tickets on some railway lines and pointed out that he could not eat in the first-class dining room on a boat from Washington to Norfolk. Forced to wait for a table in the servants’ dining room, Rainey had shouted, “I’d starve first”; from then on he brought his own meals while traveling. Rainey drilled this injustice into the heads of his colleagues: “Do you think it is right that when I go forth from this capital as an honored member of Congress that I should be subjected to the insults from the lowest fellow in the street if he should happen to feel so inclined?”118
When traveling from his district to the nation’s capital, John Lynch noted, “I am treated, not as an American citizen, but as a brute. Forced to occupy a filthy smoking car both night and day, with drunkards, gamblers, and criminals; and for what? Not that I am unable or unwilling to pay my way; not that I am obnoxious in my personal appearance or disrespectful in my conduct; but simply because I happen to be of a darker complexion.”119
James Rapier noted the irony of the second-class treatment he received while traveling even though he had a privileged role as a United States Representative. “Just think that the law recognizes my right upon this floor as a law-maker, but that there is no law to secure me an accommodation whatever while traveling here to discharge my duties as a Representative. . . . Is not this most anomalous and ridiculous?” Rapier reminded his colleagues that, “Every day my life and property are exposed, are left to the mercy of others, and will be so long as every hotel-keeper, railroad conductor, and steamboat captain can refuse me with impunity.”120
Opponents of the bill argued that regulating discrimination in public accommodations was beyond the scope of the Constitution. The Reconstruction Amendments, which already guaranteed the basic political rights afforded to all male citizens, extended the federal government’s power to its limit. “The colored people are now in substantial enjoyment of their full rights and privileges granted by the recent amendments to the Constitution,” argued Democrat John Storm of Pennsylvania. “This bill is thrust upon us now for no other purpose than exciting bad feelings.” Virginian Thomas Whitehead added “now the colored man is a citizen. He can vote. He can hold office. . . . He can hold property. He can do in my state just what any other man can do. . . . Now, what is the object of this bill?”121
While the Constitution could provide political equality before the law, Southerners argued that it could not enforce social equality. John Harris declared that the racial division was “a natural prejudice that God himself placed in the hearts of southern children,” absurdly adding that a Representative of any race could be “thrust from a particular railroad car when his high position was not known.”122 Representative Whitehead went even farther and argued that “the Almighty has given [African Americans] what he cannot get rid of—a black skin! . . . You have not the power to make him white and he will never be satisfied short of that.”123James Blount of Georgia tried to blame the victims of discrimination and claimed that African Americans in the South did not care for equal access to theaters, hotels, and streetcars. “These people are poor,” he said, “and these things they care nothing about. . . . They are especially often involved in criminal charges. . . . [Judicial rights] are the rights of most practical value to them.”124
The greatest fear of southern Democrats was treating African Americans as equals in everyday society. “There are in the Southern States two races, as distinct in their social feelings and prejudices as in color,” declared Representative Blount. “The sooner they are recognized by our rulers the better for both races and the country.”125 Democrat Charles Eldredge of Wisconsin blamed the violence and unrest in the South on the “unnatural relation in which two races have been placed to each other,” adding, “it is a result . . . which may always be expected when it is attempted to subject men of culture . . . to the domination and rule of brute force.”126
Despite their idealism, most Radical Republicans also believed African Americans belonged to a separate social sphere. But that did not mean the federal government should deny them equal opportunity. “We do not propose to legislate to establish any equality,” Benjamin Butler said. What Butler intended to do, instead, was establish a level playing field: “Not all men are equal, but every man has the right to be the equal of every other man if he can. . . . And all constitutions, all laws, all enactments, all prejudices, all caste, all custom, all contravention of that right is unjust, impolitic, and unchristian.”127
The African-American Members during this era were pragmatists when addressing the issue of using legislation to compel social and racial equality. Richard Cain noted that “no laws enacted by legislators can compel social equality.”128 James Rapier claimed that the civil rights bill “does not and cannot contemplate any such idea as social equality; nor is there any man upon this floor so silly as to believe that there can be any law enacted or enforced that would compel one man to recognize the other as his equal socially.” But he also rejected segregation as a caste system that prevented social mobility, calling such a method “an anti-republican principle in our free country.”129 John Lynch pointed out the hypocrisy of the argument that social equality divided on matters of race: “I have never believed for a moment that social equality could be brought about even between persons of the same race. . . . But those who contend that the passage of this bill will have a tendency to bring about social equality between the races virtually and substantially admit that there are no social distinctions among white people, whatsoever.”130
As white Southerners made dire predictions about the deleterious effects of the civil rights bill on white southern culture, Richard Cain responded with his characteristic wit: “I think [that if] so harmless a measure as the civil-rights bill, guaranteeing to every man of the African race equal rights with other men, would bring death to the South, then certainly that noble march of Sherman to the sea would have fixed them long ago.”131
“No Compromise to Offer on this Subject”: The Education Clause
The sticking point on the final version of the 1875 civil rights bill became the section providing federal funding for and the desegregation of public education in the South. Traditionally, states and local municipalities controlled public schools. But throughout the former Confederacy, local prejudice led to uneven educational opportunities where schools were deeply segregated. Both Southern Democrats and moderate Republicans feared that angry white parents would pull their children out of mixed-race schools, effectively ending public education in the South. “The great evil this bill has in store for the black man is found in the destruction of the common schools of the South,” declared Roger Mills, a white Democrat from East Texas. “When the common schools are broken up in all the Southern States . . . what is to become of the children of the colored people? Are they to grow up on ignorance and vice?”132 Democrat Milton Durham of Kentucky argued that his white constituents paid the bulk of the taxes and that many took advantage of public schools. “Should this bill pass,” Durham warned, “and the children of freedmen demand admission into these schools, I believe the system in Kentucky will be so injured as to become worthless.”133 Moderate Republicans were wary of the education clause as well. Though Barbour Lewis of Tennessee supported the civil rights bill, noting that “the colored people deserve this measure,” he argued that integrated schools were unacceptable “because people of their own choice . . . simply as a matter of taste, have maintained separate schools.”134
To move the bill out of the Judiciary Committee in the face of such broad opposition, Butler amended the education clause by inserting language that called for “separate, but equal” public schools.135 By the time the bill came to a vote on February 4, 1875, three versions existed, each differing only on the education provisions: the amended House bill, calling for “separate, but equal” public schools; the Senate bill, which included the legislation’s original intent to desegregate and federally fund common schools; and an amended version offered by Republican Representative Stephen Kellogg of Connecticut, stripping the bill of all references to public education.
Black Members vigorously defended the education clause, preferring almost unanimously the Senate version of the bill.136 John Lynch contended that increased federal funding for education was the most harmless provision of the bill: “All share its benefits alike,” he said.137 Richard Cain sharply admonished his southern colleagues: “Examine the laws of the South, and you will find that it was a penal offense for anyone to educate the colored people there. . . . You robbed us for two hundred years. During all that time we toiled for you. We have raised your cotton, your rice, your corn. . . . And yet you upbraid us for being ignorant; call us a horde of barbarians!”138Alonzo Ransier had great faith that access to equal educational rights and opportunities would allow talented black men to earn good standing in their communities and would in turn curb discrimination. “Let the doors of the public school house be thrown open to us alike,” he declared, “if you mean to give these people equal rights at all, or to protect them in the exercise of the rights and privileges attaching to all freemen and citizens of our country.”139
By the time the civil rights bill came to a vote, the measure had been gravely wounded. The bill’s last days were filled with desperate pleas from its supporters. “Spare us our liberties; give us peace; give us a chance to live; . . . place no obstruction in our way; give us an equal chance,” Richard Cain pleaded. “We ask no more of the American people.”140 James Rapier despaired, “I have no compromise to offer on this subject. . . . After all, this question resolves itself into this: either I am a man or I am not a man.”141
Minutes before the final measure came to a vote in the House, Members passed Kellogg’s amendment eliminating all references to public education, 128 to 48. A motion replacing the House version with the Senate bill failed soon afterward, 148 to 114. The battered civil rights bill finally passed 162 to 99. The measure provided no mechanism to regulate public schools but stipulated equal access to public transportation and accommodations regardless of race. It also prohibited the exclusion of African Americans from jury service. Black Members received the final version of the bill with mixed reactions. Despite its diluted form Richard Cain, John Lynch, Joseph Rainey, and James Rapier voted in its favor. But Alonzo Ransier and Josiah Walls were so disappointed by the elimination of the education clause, they declined to vote.142 The legislation passed the Senate on February 27. On March 1, President Ulysses S. Grant signed it into law.143 The fact that Republicans, who within days would be relegated to minority status, managed to steer such a bill through the chamber at the conclusion of a lame duck session represented a considerable legislative victory. But in their desperation to pass the measure, Republicans had left the Civil Rights Act of 1875 in such a weakened state that it did little to impede the creation of an insidious system of segregation in the South. Moreover, the limited protection it did afford would soon be stripped by the courts.
96For a concise summary of congressional civil rights legislation in the 19th and 20th centuries, see Donald Bacon et al., The Encyclopedia of the United States Congress, vol. 1 (New York: Simon and Schuster, 1995): 354–363. Office of the Historian, U.S. House of Representatives, “Constitutional Amendments and Major Civil Rights Acts of Congress Referenced in Black Americans in Congress.”
97Congressional Record, Senate, 43rd Cong., 1st sess. (2 December 1873): 2.
98"For protecting all citizens in their civil rights," H.R. 796, 43rd Cong. (1873); Congressional Record, House, 43rd Cong., 1st sess. (18 December 1873): 318.
99Congressional Record, House, 43rd Cong., 1st sess. (7 January 1874): 458.
100Congressional Record, House, 43rd Cong., 1st sess. (6 January 1874): 406.
101Edward L. Pierce, Memoir and Letters of Charles Sumner, vol. 4 (New York: Arno Press, 1969): 598.
102Congressional Record, Senate, 43rd Cong., 1st sess. (22 May 1874): 4176.
103Congressional Record, House, 43rd Cong., 1st sess. (18 June 1874): 5162–5163.
104Office of the Historian, U.S. House of Representatives, “Party Divisions.”
105Steven W. Stathis, Landmark Legislation, 1774–2002: Major U.S. Acts and Treaties (Washington, DC: Congressional Quarterly Press, 2003): 111.
106Quoted in Foner, Reconstruction: 555.
107Congressional Record, House, 43rd Cong., 1st sess. (4 February 1875): 978.
108Dubin et al., U.S. Congressional Elections, 1788–1997: 231.
109Asher C. Hinds, Hinds’ Precedents of the House of Representatives, vol. 4 (Washington, DC: Government Printing Office, 1907): 353–354; Foner, Reconstruction: 555; Wilson, The Reconstruction Desegregation Debate: 38. Republicans lost some support in the final vote on the civil rights bill because of the rule change. In a speech denouncing the bill, William Phelps of New Jersey noted, “In order to pass this bill we have altered the rules of procedure under which for fifty years this House has transacted its business.” See Congressional Record, House, 43rd Cong., 2nd sess. (4 February 1875): 1001. Debate was often very contentious, with Butler facing the brunt of the attacks. On February 3, 1875, Butler found himself squaring off in the center aisle of the House Chamber with William McLean of Texas when the latter accused Butler of denigrating the South. McLean hurled a personal insult at Butler, in violation of House Rules, and later retracted his comment. See Congressional Record, House, 43rd Cong., 2nd sess. (3 February 1875): 940–941, 943. The following day, John Brown of Kentucky declared, “If I wished to describe all that was pusillanimous in war, inhuman in peace, forbidden in morals, and infamous in politics, I should call it ‘Butlerism.’ ” Brown was censured for his remarks. See Congressional Record, House, 43rd Cong., 2nd sess. (4 February 1875): 985–992. An attempt to strike Butler’s words from the Congressional Record failed just before the civil rights bill passed. See Congressional Record, House, 43rd Cong., 2nd sess. (4 February 1875): 1008. Though they overwhelmingly favored censuring Brown, black Members remained silent during the more heated bickering on the House Floor.
110Wilson, The Reconstruction Desegregation Debate: 25.
111Congressional Record, House, 43rd Cong., 1st sess. (5 January 1874): 378.
112Philip Dray, Capitol Men: The Epic Story of Reconstruction Through the Lives of the First Black Congressmen (Boston, MA: Houghton Mifflin, 2008): 169–170; Wilson, The Reconstruction Desegregation Debate: 29–30.
113Congressional Record, House, 43rd Cong., 1st sess. (5 January 1874): 381.
114Ibid., 386. The House Journal indicates that the House adjourned at 4:40 PM on January 5. See House Journal, 43rd Cong., 1st sess. (5 January 1874): 186.
115Congressional Record, House, 43rd Cong., 1st sess. (6 January 1874): 409–410.
116Dray, Capitol Men: 175–177.
117“Congressman Elliott’s Speech,” 8 January 1874, Chicago Daily Tribune: 4; “Congress,” 7 January 1874, New York Times: 1.
118Christopher, Black Americans in Congress: 32–33.
119Congressional Record, House, 43rd Cong., 2nd sess. (3 February 1875): 945.
120Congressional Record, House, 43rd Cong., 1st sess. (9 June 1874): 4782–4785.
121Congressional Record, House, 43rd Cong., 2nd sess. (3 February 1875): 951–953.
122Congressional Record, House, 43rd Cong., 1st sess. (5 January 1874): 377.
123Congressional Record, House, 43rd Cong., 2nd sess. (3 February 1875): 953.
124Congressional Record, House, 43rd Cong., 2nd sess. (4 February 1875): 978. For further discussion of the constitutional arguments made during the debates on the civil rights bill, see Wilson, The Reconstruction Desegregation Debate: 151–181.
125Congressional Record, House, 43rd Cong., 1st sess. (6 January 1874): 411.
126Congressional Record, House, 43rd Cong., 2nd sess. (4 February 1875): 983.
127Congressional Record, House, 43rd Cong., 1st sess. (7 January 1874): 455–456.
128Congressional Record, House, 43rd Cong., 1st sess. (10 January 1874): 565.
129Congressional Record, House, 43rd Cong., 1st sess. (9 June 1874): 4785.
130Congressional Record, House, 43rd Cong., 2nd sess. (3 February 1875): 944.
131Congressional Record, House, 43rd Cong., 1st sess. (24 January 1874): 901–903. For more on the equality debate in the civil rights bill, see Wilson, The Reconstruction Desegregation Debate: 77–120.
132Congressional Record, House, 43rd Cong., 1st sess. (5 January 1874): 385.
133Congressional Record, House, 43rd Cong., 1st sess. (6 January 1874): 406.
134Congressional Record, House, 43rd Cong., 2nd sess. (4 February 1875): 998–999.
135Wilson, The Reconstruction Desegregation Debate: 37.
136Most African-American Members preferred the Senate version of the civil rights bill. See, for example, Congressional Record, House, 43rd Cong., 2nd sess. (4 February 1875): 1001. Richard Cain expressed lukewarm support for Kellogg’s version, probably because of his firm rejection of the compromise “separate, but equal” legislation. See Congressional Record, House, 43rd Cong., 2nd sess. (4 February 1875): 982.
137Congressional Record, House, 43rd Cong., 2nd sess. (3 February 1875): 943–947.
138Congressional Record, House, 43rd Cong., 1st sess. (24 January 1874): 901–903.
139Congressional Record, House, 43rd Cong., 1st sess. (7 February 1874): 1314.
140Congressional Record, House, 43rd Cong., 2nd sess. (4 February 1875): 982.
143Congressional Record, Senate, 43rd Cong., 2nd sess. (27 February 1875): 1870; Congressional Record, House, 43rd Cong., 2nd sess. (1 March 1875): 2013. |
Garbage collection (GC) in Solid-State Drives (SSDs) is a crucial process for managing data storage and maintaining drive efficiency. Unlike traditional Hard Disk Drives (HDDs), SSDs use flash memory, which requires empty blocks for writing new data. Garbage collection helps by clearing out invalid data and making room for new information. This process is vital for preserving SSD performance and lifespan.
The importance of understanding garbage collection lies in its direct impact on SSD performance. Efficient garbage collection ensures faster data writing speeds and reduces the risk of performance degradation over time. However, it can also pose challenges, including potential slowdowns during the GC process and increased wear on the SSD due to repetitive write and erase cycles.
Fundamentals of SSD Operation
How Solid-State Drives (SSDs) Work:
Solid-state drives revolutionized data storage with their flash memory technology. Unlike traditional HDDs that use spinning disks to read/write data, SSDs store data on interconnected flash memory chips. These chips, typically NAND-based, allow for faster data access and reduced latency compared to mechanical HDDs. SSDs have no moving parts, which contributes to their durability, shock resistance, and overall faster performance.
SSD Structure and Key Operating Principles:
An SSD consists of several key components: a controller, NAND flash memory chips, and a cache. The controller is the brain of the SSD, managing data storage and retrieval, error correction, and garbage collection. NAND flash memory chips are where data is stored. These chips are organized into pages (for data writing) and blocks (for erasing data). The cache acts as a temporary storage area for quick data access.
Data in an SSD is written in pages but can only be erased at the block level. This difference leads to a phenomenon known as write amplification, where the actual amount of data written is more than the data the user intended to write. This occurs because, to modify data, the SSD must first copy data from the block to the cache, modify it, and then write it back, often to a new block.
Garbage Collection in SSDs
Definition and Process:
Garbage collection in SSDs refers to the process of reorganizing and consolidating data to free up space. This process is necessary because SSDs can only write data to empty pages within a block. Once a block is filled, to write new data, the SSD must find a block with enough empty pages, transfer the valid data from the full block to this new block, and then erase the old block entirely, making it available for new data.
This process is critical because, in SSDs, deleting or modifying data doesn’t immediately free up space. Instead, it marks the data as invalid. Over time, these invalid data accumulate, reducing the number of free pages available for new data. Garbage collection thus cleans up these invalid data, maintaining the SSD’s performance and lifespan.
Necessity in SSDs:
Garbage collection is a fundamental aspect of SSD management due to the nature of NAND flash memory. It’s essential for:
Ensuring consistent performance: Without GC, the write performance of SSDs would deteriorate over time as free pages become scarce.
Prolonging lifespan: By efficiently managing the write and erase cycles, GC helps reduce the wear and tear of the memory cells, thereby extending the SSD’s lifespan.
Garbage collection runs in the background and is managed by the SSD’s firmware. The efficiency of this process varies based on the algorithm used and can significantly impact the overall performance of the SSD. Different SSD manufacturers implement various garbage collection algorithms, each with its trade-offs in terms of performance, durability, and data integrity.
Impact of Garbage Collection on SSD Performance
Influence on Read and Write Speeds:
Garbage collection in SSDs directly affects the drive’s read and write speeds. When the SSD needs to write new data, it may first need to perform garbage collection to free up space, which can temporarily slow down write operations. This impact is particularly noticeable in SSDs that are nearly full or have gone through extensive write operations without enough idle time for garbage collection.
Moreover, during the garbage collection process, the SSD’s controller is busy relocating existing data and erasing blocks, which can lead to increased response times and slower read speeds. The impact on read speeds is generally less pronounced than on write speeds but can still affect overall system performance, especially in high-demand scenarios.
Issues of Wear and Longevity:
Each block in an SSD has a limited number of write-erase cycles before it becomes unreliable. Garbage collection can exacerbate wear and tear because it often involves additional write-erase cycles. This phenomenon, known as write amplification, occurs when the data moved and rewritten during garbage collection exceeds the amount of data actually written by the user.
Write amplification not only reduces the overall performance of the SSD but also impacts its longevity. SSDs mitigate this issue through wear leveling, a process that distributes write and erase cycles evenly across the memory cells to prevent premature wear in any particular area. However, efficient garbage collection algorithms are crucial for minimizing write amplification and extending the SSD’s lifespan.
Overall Performance Considerations:
The performance impact of garbage collection is a balance between maintaining adequate space for new data and managing the wear on the SSD. Manufacturers optimize this balance through firmware updates and sophisticated garbage-collection algorithms. The overall effect of garbage collection on performance can vary based on the SSD’s design, the efficiency of its garbage collection algorithm, and the user’s data usage patterns.
Optimization Technologies for Garbage Collection in SSDs
Overview of Optimization Technologies:
Manufacturers employ various technologies to optimize garbage collection in SSDs, aiming to minimize its impact on performance and extend the drive’s lifespan. These technologies are designed to efficiently manage data storage and retrieval, reduce write amplification, and ensure consistent performance over time.
Examples of Manufacturer-Specific Solutions:
Over-Provisioning: This involves reserving a portion of the SSD’s storage capacity that is not accessible to the user. This extra space allows for more efficient garbage collection and wear leveling, reducing write amplification and prolonging the SSD’s lifespan.
Advanced Garbage Collection Algorithms: Manufacturers develop sophisticated algorithms that intelligently decide when and how to execute garbage collection. These algorithms aim to perform garbage collection during idle periods, thereby minimizing the impact on active tasks.
TRIM Command: The TRIM command, supported by modern operating systems, informs the SSD about blocks of data that are no longer in use. This preemptive communication allows the SSD to manage garbage collection more effectively, freeing up blocks without waiting for them to be overwritten.
Methods to Mitigate Negative Impact:
Background Garbage Collection: This method involves running garbage collection in the background when the drive is idle or under light use. By doing this, the impact on performance during peak usage is reduced.
Dynamic Wear-Leveling: Dynamic wear-leveling distributes data evenly across the memory cells, ensuring that all cells are used uniformly. This helps in reducing the wear on any particular cell, extending the overall life of the SSD.
Improved Data Compression: By compressing data before storage, SSDs can reduce the amount of physical space required for data, effectively decreasing the need for frequent garbage collection cycles.
In conclusion, the optimization of garbage collection in SSDs is a critical aspect of drive design and firmware development. By employing a combination of hardware and software strategies, manufacturers can significantly reduce the performance drawbacks of garbage collection, ensuring that SSDs deliver fast, reliable storage solutions. |
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A histogram is a graph that shows the frequency, or the number of times, something happens within a specific interval. A histogram is similar to a bar chart; however, the area represented by the histogram is used to graph the number of times a group of numbers appears. You may want to use a histogram to display continuous data such as time, measurements, and temperature. However, a problem with histograms is that it is difficult to compare two sets of data and exact data cannot be read. Knowing how to draw a histogram can by very useful for students to represent statistical findings of a project as well as for business professionals.
Method 1 of 3:Drawing by Hand
1Using a ruler, draw out the basic axes. These are the vertical and horizontal lines that form basic outline of the histogram. If you have trouble making the right angle where the axes meet, go ahead and cheat: use a corner of a sheet of paper!
2Measure out the groups. In a histogram, the data is visualized in groups. These groups are evenly distributed, so you'll need to make set marks along your lower axis.
- For example: 0-4 apples, 5-9 apples, 10-14 apples, etc at 1", 2", and 3" along the axis.
3Measure out the vertical axis. The vertical axis in a histogram is always for frequency. What measure of time is necessary, though, is up to your data of course (but the numbers will still need to be equally spaced). Just be sure to leave extra room at the top to make your chart easier to read.
- If the upper limit of your histogram is 54, for example, you should make the highest number on the axis 60.
- If the frequency doesn't start until a fairly high number, you can cut out many of the numbers below it. For example, if the first frequency is 32, you can start the chart at 25 or 30.
4Draw the bars. Draw the horizontal top line for each interval or group lightly, at the level that data was measured. Then, draw in the bars centered over the data point they represent. Make sure the bars are even and the same width as each other. Generally, histogram bars are supposed to touch, but if you have no results for a particular group, then don't worry about it.
5Add some color. Add different colors to the histogram rectangles with colored pencils, markers, or crayons to help differentiate among the intervals.Advertisement
Method 2 of 3:Using Excel
1Fill out your data. In an open Excel document, fill the second column with the "bins", or data groups that you want (20/30/40, 0/5/10/15, etc) with one group per cell. Fill the first column with the frequency of results for that group (called the grade), or the levels that you want the bars for that group to be at.
2Do a data analysis. Click Tools → Data Analysis. This is not always a standard feature in Excel so you may need to install it using the Add-ins option.
3Select histogram. Select the histogram option in the Data Analysis menu and then click OK.
4Adjust your input and bin ranges. You will need to use the menu to select which column is which.
5Select chart output. Select the chart output button and then press OK.
6Done! Enjoy your chart. Don't forget to save it.Advertisement
Method 3 of 3:Using an Online Program
1Go to a website which generates histograms. We recommend using this one.
2Choose a preset format. There is a drop down menu at the top of the chart that gives you a few basic sample charts that you can fill with your own data. Alternatively, you can build one completely from scratch.
3Name the chart. You will see a box labeled "Title" towards the middle of the page. You should title your chart there.
4Enter your data in the box at the bottom. You will see a large box below the title bar, towards the bottom of the page. Enter each data point that you have, with one data point per line (so...5, 5, 5, 10, 10, 15, 15, 20, 20, 25, etc).
5Click Update Data. Click the Update Data button above the data box.
6Adjust the frequency. The chart should automatically adjust to your data, but you can also manually set the interval size and the maximums and minimums for the axes.
7Print or save your chart. Use the print screen function on your keyboard to take a picture of the completed graph. Paste and crop the image in MS Paint or whatever basic image software came with your computer. Save the image and print it if you want to.Advertisement
QuestionHow do I know how high to put my bars?Community AnswerThe bars go as high as the values you have. So, if you're representing people's favorite colors and 5 people like blue, the bar representing blue has to be 5 units high of whatever scale you're using.
QuestionDo you always have to use a piece of graph paper, or is using a piece of plain paper okay as well?Community AnswerA piece of plain paper is also okay but the measurements should be accurate. A graph paper will be more detailed and specific.
- Don't forget to label the y-axis and x-axis to ensure that the information is correct.
- When tallying the numbers into interval sets, it may be helpful to cross out the numbers in the data so you do not count a number twice.
- When drawing a histogram, be sure to use the ruler in making all the lines so that they are straight and neat.
Things You'll Need
- Graph paper
- Colored pencils, markers, or crayons
About This Article
To draw a histogram, start by using a ruler to draw your X and Y axes. Then, divide your range of values into “bins,” or data groups, and place them evenly along the horizontal X axis so that all the bars touch. The Y axis in a histogram always refers to frequency, so put your highest frequency toward the top of the Y axis, then space out the lower frequencies evenly along the Y axis. For each “bin,” draw a line where the frequency is measured, then draw and color in a vertical bar centered on the “bin.” To learn how to use Excel to make a histogram, keep reading! |
Almost all known neutron stars are also known as pulsars, because they emit pulsed beams of radio waves or X rays that sweep past Earth like lighthouse beams. But on most occasions, these beams miss Earth, making the neutron star effectively invisible at radio or X-ray wavelengths. But according to some theoretical predictions, a pulsar's gamma-ray beam should be wider than a radio or X-ray beam, making it more likely that its beam would illuminate Earth. The key is to have a gamma-ray satellite sensitive enough to detect these beams, and measure their pulsations.
During the 1990s, NASA's Compton Gamma-Ray Observatory discovered dozens of mysterious gamma-ray-emitting objects in the plane of our Milky Way Galaxy. But Compton lacked the spatial and time resolution to pin down the nature of these sources. Astronomers suspected that some or most of them are neutron stars, but scientists knew that a good fraction of them might be background galaxies or some other type of object.
In just a week of observing during its July commissioning phase, Fermi's primary instrument, the Large Area Telescope (LAT), has resolved any lingering uncertainty about one of these unidentified sources: a bright gamma-ray-emitting object at the center of a supernova remnant known as CTA 1, located about 4,600 light-years from Earth. With the LAT's vastly improved sensitivity and timing capability, it not only detected the source easily, it found that it is pulsing with a frequency of 0.317 second. In other words, the object rotates on its axis 3.17 times per second. Based on this result, and its energy pattern, the object must be a pulsar."This is the first pulsar discovered only through gamma-ray pulses. This is an exciting result because it means that a lot of pulsars are hidden," says Fermi science team member Alice Harding (NASA/Goddard Space Flight Center), coauthor of a paper on the discovery that appears in the October 16th issue of Science Express. Harding points out that deep observations of CTA 1 at radio and X-ray wavelengths have yet to reveal any hint of pulsations.
"Fermi is doing exactly what we expected it to do: find all these pulsars in gamma-rays that we don't see in the radio," adds radio astronomer Michael Kramer (University of Manchester, UK), who is not on the discovery team.
Harding predicts that many of the unidentified Compton sources will turn out to be pulsars, and that Fermi will see many new sources that will also be pulsars. Studies of these neutron stars will provide clues that will help astronomers piece together the life cycle of neutron stars, and how pulsars emit their beamed radiation.
Kramer points out another important implication. Neutron stars are born in supernova explosions, but many remnants of these explosions lack neutron stars. "It's great that we will start to populate these previously 'empty' supernova remnants with neutron stars that are now at least detectable at other parts of the spectrum," he says.
The discovery also demonstrates that the $690 million Fermi observatory, formerly known as GLAST, is living up to its billing. The spacecraft and its instruments are performing as expected, and it's 5-year mission of scanning the gamma-ray sky at depths never before possible is just getting started. Says Harding, "This is just the first of many exciting things to come." |
BACKGROUND IMAGE: iSTOCK/GETTY IMAGES
Deep learning is a type of machine learning (ML) and artificial intelligence (AI) that imitates the way humans gain certain types of knowledge. Deep learning is an important element of data science, which includes statistics and predictive modeling. It is extremely beneficial to data scientists who are tasked with collecting, analyzing and interpreting large amounts of data; deep learning makes this process faster and easier.
At its simplest, deep learning can be thought of as a way to automate predictive analytics. While traditional machine learning algorithms are linear, deep learning algorithms are stacked in a hierarchy of increasing complexity and abstraction.
To understand deep learning, imagine a toddler whose first word is dog. The toddler learns what a dog is -- and is not -- by pointing to objects and saying the word dog. The parent says, "Yes, that is a dog," or, "No, that is not a dog." As the toddler continues to point to objects, he becomes more aware of the features that all dogs possess. What the toddler does, without knowing it, is clarify a complex abstraction -- the concept of dog -- by building a hierarchy in which each level of abstraction is created with knowledge that was gained from the preceding layer of the hierarchy.
How deep learning works
Computer programs that use deep learning go through much the same process as the toddler learning to identify the dog. Each algorithm in the hierarchy applies a nonlinear transformation to its input and uses what it learns to create a statistical model as output. Iterations continue until the output has reached an acceptable level of accuracy. The number of processing layers through which data must pass is what inspired the label deep.
In traditional machine learning, the learning process is supervised, and the programmer has to be extremely specific when telling the computer what types of things it should be looking for to decide if an image contains a dog or does not contain a dog. This is a laborious process called feature extraction, and the computer's success rate depends entirely upon the programmer's ability to accurately define a feature set for "dog." The advantage of deep learning is the program builds the feature set by itself without supervision. Unsupervised learning is not only faster, but it is usually more accurate.
Initially, the computer program might be provided with training data -- a set of images for which a human has labeled each image "dog" or "not dog" with meta tags. The program uses the information it receives from the training data to create a feature set for "dog" and build a predictive model. In this case, the model the computer first creates might predict that anything in an image that has four legs and a tail should be labeled "dog." Of course, the program is not aware of the labels "four legs" or "tail." It will simply look for patterns of pixels in the digital data. With each iteration, the predictive model becomes more complex and more accurate.
Unlike the toddler, who will take weeks or even months to understand the concept of "dog," a computer program that uses deep learning algorithms can be shown a training set and sort through millions of images, accurately identifying which images have dogs in them within a few minutes.
To achieve an acceptable level of accuracy, deep learning programs require access to immense amounts of training data and processing power, neither of which were easily available to programmers until the era of big data and cloud computing. Because deep learning programming can create complex statistical models directly from its own iterative output, it is able to create accurate predictive models from large quantities of unlabeled, unstructured data. This is important as the internet of things (IoT) continues to become more pervasive, because most of the data humans and machines create is unstructured and is not labeled.
What are deep learning neural networks?
A type of advanced machine learning algorithm, known as artificial neural networks, underpins most deep learning models. As a result, deep learning may sometimes be referred to as deep neural learning or deep neural networking.
Neural networks come in several different forms, including recurrent neural networks, convolutional neural networks, artificial neural networks and feedforward neural networks -- and each has benefits for specific use cases. However, they all function in somewhat similar ways, by feeding data in and letting the model figure out for itself whether it has made the right interpretation or decision about a given data element.
Neural networks involve a trial-and-error process, so they need massive amounts of data on which to train. It's no coincidence neural networks became popular only after most enterprises embraced big data analytics and accumulated large stores of data. Because the model's first few iterations involve somewhat-educated guesses on the contents of an image or parts of speech, the data used during the training stage must be labeled so the model can see if its guess was accurate. This means, though many enterprises that use big data have large amounts of data, unstructured data is less helpful. Unstructured data can only be analyzed by a deep learning model once it has been trained and reaches an acceptable level of accuracy, but deep learning models can't train on unstructured data.
Deep learning methods
Various different methods can be used to create strong deep learning models. These techniques include learning rate decay, transfer learning, training from scratch and dropout.
Learning rate decay. The learning rate is a hyperparameter -- a factor that defines the system or sets conditions for its operation prior to the learning process -- that controls how much change the model experiences in response to the estimated error every time the model weights are altered. Learning rates that are too high may result in unstable training processes or the learning of a suboptimal set of weights. Learning rates that are too small may produce a lengthy training process that has the potential to get stuck.
The learning rate decay method -- also called learning rate annealing or adaptive learning rates -- is the process of adapting the learning rate to increase performance and reduce training time. The easiest and most common adaptations of learning rate during training include techniques to reduce the learning rate over time.
Transfer learning. This process involves perfecting a previously trained model; it requires an interface to the internals of a preexisting network. First, users feed the existing network new data containing previously unknown classifications. Once adjustments are made to the network, new tasks can be performed with more specific categorizing abilities. This method has the advantage of requiring much less data than others, thus reducing computation time to minutes or hours.
Training from scratch. This method requires a developer to collect a large labeled data set and configure a network architecture that can learn the features and model. This technique is especially useful for new applications, as well as applications with a large number of output categories. However, overall, it is a less common approach, as it requires inordinate amounts of data, causing training to take days or weeks.
Dropout. This method attempts to solve the problem of overfitting in networks with large amounts of parameters by randomly dropping units and their connections from the neural network during training. It has been proven that the dropout method can improve the performance of neural networks on supervised learning tasks in areas such as speech recognition, document classification and computational biology.
Examples of deep learning applications
Because deep learning models process information in ways similar to the human brain, they can be applied to many tasks people do. Deep learning is currently used in most common image recognition tools, natural language processing and speech recognition software. These tools are starting to appear in applications as diverse as self-driving cars and language translation services.
What is deep learning used for?
Use cases today for deep learning include all types of big data analytics applications, especially those focused on natural language processing, language translation, medical diagnosis, stock market trading signals, network security and image recognition.
Specific fields in which deep learning is currently being used include the following:
- Customer experience. Deep learning models are already being used for chatbots. And, as it continues to mature, deep learning is expected to be implemented in various businesses to improve the customer experiences and increase customer satisfaction.
- Text generation. Machines are being taught the grammar and style of a piece of text and are then using this model to automatically create a completely new text matching the proper spelling, grammar and style of the original text.
- Aerospace and military. Deep learning is being used to detect objects from satellites that identify areas of interest, as well as safe or unsafe zones for troops.
- Industrial automation. Deep learning is improving worker safety in environments like factories and warehouses by providing services that automatically detect when a worker or object is getting too close to a machine.
- Adding color. Color can be added to black and white photos and videos using deep learning models. In the past, this was an extremely time-consuming, manual process.
- Medical research. Cancer researchers have started implementing deep learning into their practice as a way to automatically detect cancer cells.
- Computer vision. Deep learning has greatly enhanced computer vision, providing computers with extreme accuracy for object detection and image classification, restoration and segmentation.
Limitations and challenges
The biggest limitation of deep learning models is they learn through observations. This means they only know what was in the data on which they trained. If a user has a small amount of data or it comes from one specific source that is not necessarily representative of the broader functional area, the models will not learn in a way that is generalizable.
The issue of biases is also a major problem for deep learning models. If a model trains on data that contains biases, the model will reproduce those biases in its predictions. This has been a vexing problem for deep learning programmers, because models learn to differentiate based on subtle variations in data elements. Often, the factors it determines are important are not made explicitly clear to the programmer. This means, for example, a facial recognition model might make determinations about people's characteristics based on things like race or gender without the programmer being aware.
The learning rate can also become a major challenge to deep learning models. If the rate is too high, then the model will converge too quickly, producing a less-than-optimal solution. If the rate is too low, then the process may get stuck, and it will be even harder to reach a solution.
The hardware requirements for deep learning models can also create limitations. Multicore high-performing graphics processing units (GPUs) and other similar processing units are required to ensure improved efficiency and decreased time consumption. However, these units are expensive and use large amounts of energy. Other hardware requirements include random access memory (RAM) and a hard drive or RAM-based solid-state drive (SSD).
Other limitations and challenges include the following:
- Deep learning requires large amounts of data. Furthermore, the more powerful and accurate models will need more parameters, which, in turn, requires more data.
- Once trained, deep learning models become inflexible and cannot handle multitasking. They can deliver efficient and accurate solutions, but only to one specific problem. Even solving a similar problem would require retraining the system.
- Any application that requires reasoning -- such as programming or applying the scientific method -- long-term planning and algorithmic-like data manipulation is completely beyond what current deep learning techniques can do, even with large data.
Deep learning vs. machine learning
Deep learning is a subset of machine learning that differentiates itself through the way it solves problems. Machine learning requires a domain expert to identify most applied features. On the other hand, deep learning learns features incrementally, thus eliminating the need for domain expertise. This makes deep learning algorithms take much longer to train than machine learning algorithms, which only need a few seconds to a few hours. However, the reverse is true during testing. Deep learning algorithms take much less time to run tests than machine learning algorithms, whose test time increases along with the size of the data.
Furthermore, machine learning does not require the same costly, high-end machines and high-performing GPUs that deep learning does.
In the end, many data scientists choose traditional machine learning over deep learning due to its superior interpretability, or the ability to make sense of the solutions. Machine learning algorithms are also preferred when the data is small.
Instances where deep learning becomes preferable include situations where there is a large amount of data, a lack of domain understanding for feature introspection or complex problems, such as speech recognition and natural language processing.
Deep learning can trace its roots back to 1943 when Warren McCulloch and Walter Pitts created a computational model for neural networks using mathematics and algorithms. However, it was not until the mid-2000s that the term deep learning started to appear. It gained popularity following the publication of a paper by Geoffrey Hinton and Ruslan Salakhutdinov that showed how a neural network with many layers could be trained one layer at a time.
In 2012, Google made a huge impression on deep learning when its algorithm revealed the ability to recognize cats. Two years later, in 2014, Google bought DeepMind, an artificial intelligence startup from the U.K. Two years after that, in 2016, Google DeepMind's algorithm, AlphaGo, mastered the complicated board game Go, beating professional player Lee Sedol at a tournament in Seoul.
Recently, deep learning models have generated the majority of advances in the field of artificial intelligence. Deep reinforcement learning has emerged as a way to integrate AI with complex applications, such as robotics, video games and self-driving cars. The primary difference between deep learning and reinforcement learning is, while deep learning learns from a training set and then applies what is learned to a new data set, deep reinforcement learning learns dynamically by adjusting actions using continuous feedback in order to optimize the reward.
A reinforcement learning agent has the ability to provide fast and strong control of generative adversarial networks (GANs). The Adversarial Threshold Neural Computer (ATNC) combines deep reinforcement learning with GANs in order to design small organic molecules with a specific, desired set of pharmacological properties.
GANs are also being used to generate artificial training data for machine learning tasks, which can be used in situations with imbalanced data sets or when data contains sensitive information.
Here is a very simple illustration of how a deep learning program works. This video by the LuLu Art Group shows the output of a deep learning program after its initial training with raw motion capture data. This is what the program predicts the abstract concept of "dance" looks like.
With each iteration, the program's predictive model became more complex and more accurate. |
A rotation is a circular movement of an object around a center (or point) of rotation. The geometric plane along which the rotation occurs is called the rotation plane, and the imaginary line extending from the center and perpendicular to the rotation plane is called the rotation axis ( AK-seez). A three-dimensional object can always be rotated about an infinite number of rotation axes.
If the rotation axis passes internally through the body's own center of mass, then the body is said to be autorotating or spinning, and the surface intersection of the axis can be called a pole. A rotation around a completely external axis, e.g. the planet Earth around the Sun, is called revolving or orbiting, typically when it is produced by gravity, and the ends of the rotation axis can be called the orbital poles.
Mathematically, a rotation is a rigid body movement which, unlike a translation, keeps a point fixed. This definition applies to rotations within both two and three dimensions (in a plane and in space, respectively.)
All rigid body movements are rotations, translations, or combinations of the two.
A rotation is simply a progressive radial orientation to a common point. That common point lies within the axis of that motion. The axis is 90 degrees perpendicular to the plane of the motion. If the axis of the rotation lies external of the body in question then the body is said to orbit. There is no fundamental difference between a "rotation" and an "orbit" and or "spin". The key distinction is simply where the axis of the rotation lies, either within or outside of a body in question. This distinction can be demonstrated for both "rigid" and "non rigid" bodies.
If a rotation around a point or axis is followed by a second rotation around the same point/axis, a third rotation results. The reverse (inverse) of a rotation is also a rotation. Thus, the rotations around a point/axis form a group. However, a rotation around a point or axis and a rotation around a different point/axis may result in something other than a rotation, e.g. a translation.
Rotations around the x, y and z axes are called principal rotations. Rotation around any axis can be performed by taking a rotation around the x axis, followed by a rotation around the y axis, and followed by a rotation around the z axis. That is to say, any spatial rotation can be decomposed into a combination of principal rotations.
In astronomy, rotation is a commonly observed phenomenon. Stars, planets and similar bodies all spin around on their axes. The rotation rate of planets in the solar system was first measured by tracking visual features. Stellar rotation is measured through Doppler shift or by tracking active surface features.
This rotation induces a centrifugal acceleration in the reference frame of the Earth which slightly counteracts the effect of gravity the closer one is to the equator. One effect is that an object weighs slightly less at the equator. Another is that the Earth is slightly deformed into an oblate spheroid.
Another consequence of the rotation of a planet is the phenomenon of precession. Like a gyroscope, the overall effect is a slight "wobble" in the movement of the axis of a planet. Currently the tilt of the Earth's axis to its orbital plane (obliquity of the ecliptic) is 23.44 degrees, but this angle changes slowly (over thousands of years). (See also Precession of the equinoxes and Pole star.)
While revolution is often used as a synonym for rotation, in many fields, particularly astronomy and related fields, revolution, often referred to as orbital revolution for clarity, is used when one body moves around another while rotation is used to mean the movement around an axis. Moons revolve around their planet, planets revolve about their star (such as the Earth around the Sun); and stars slowly revolve about their galaxial center. The motion of the components of galaxies is complex, but it usually includes a rotation component.
Most planets in our solar system, including Earth, spin in the same direction as they orbit the Sun. The exceptions are Venus and Uranus. Uranus rotates nearly on its side relative to its orbit. Current speculation is that Uranus started off with a typical prograde orientation and was knocked on its side by a large impact early in its history. Venus may be thought of as rotating slowly backward (or being "upside down"). The dwarf planet Pluto (formerly considered a planet) is anomalous in this and other ways.
The speed of rotation is given by the angular frequency (rad/s) or frequency (turns per time), or period (seconds, days, etc.). The time-rate of change of angular frequency is angular acceleration (rad/s²), caused by torque. The ratio of the two (how heavy is it to start, stop, or otherwise change rotation) is given by the moment of inertia.
The physics of the rotation around a fixed axis is mathematically described with the axis-angle representation of rotations. According to the right-hand rule, the direction away from the observer is associated with clockwise rotation and the direction towards the observer with counterclockwise rotation, like a screw.
In modern physical cosmology, the cosmological principle is the notion that the distribution of matter in the universe is homogeneous and isotropic when viewed on a large enough scale, since the forces are expected to act uniformly throughout the universe and have no preferred direction, and should, therefore, produce no observable irregularities in the large scale structuring over the course of evolution of the matter field that was initially laid down by the Big Bang.
In particular, for a system which behaves the same regardless of how it is oriented in space, its Lagrangian is rotationally invariant. According to Noether's theorem, if the action (the integral over time of its Lagrangian) of a physical system is invariant under rotation, then angular momentum is conserved.
Euler rotations provide an alternative description of a rotation. It is a composition of three rotations defined as the movement obtained by changing one of the Euler angles while leaving the other two constant. Euler rotations are never expressed in terms of the external frame, or in terms of the co-moving rotated body frame, but in a mixture. They constitute a mixed axes of rotation system, where the first angle moves the line of nodes around the external axis z, the second rotates around the line of nodes and the third one is an intrinsic rotation around an axis fixed in the body that moves.
In flight dynamics, the principal rotations described with Euler angles above are known as pitch, roll and yaw. The term rotation is also used in aviation to refer to the upward pitch (nose moves up) of an aircraft, particularly when starting the climb after takeoff.
Principal rotations have the advantage of modelling a number of physical systems such as gimbals, and joysticks, so are easily visualised, and are a very compact way of storing a rotation. But they are difficult to use in calculations as even simple operations like combining rotations are expensive to do, and suffer from a form of gimbal lock where the angles cannot be uniquely calculated for certain rotations.
Many amusement rides provide rotation. A Ferris wheel has a horizontal central axis, and parallel axes for each gondola, where the rotation is opposite, by gravity or mechanically. As a result, at any time the orientation of the gondola is upright (not rotated), just translated. The tip of the translation vector describes a circle. A carousel provides rotation about a vertical axis. Many rides provide a combination of rotations about several axes. In Chair-O-Planes the rotation about the vertical axis is provided mechanically, while the rotation about the horizontal axis is due to the centripetal force. In roller coaster inversions the rotation about the horizontal axis is one or more full cycles, where inertia keeps people in their seats.
Rotation of a ball or other object, usually called spin, plays a role in many sports, including topspin and backspin in tennis, English, follow and draw in billiards and pool, curve balls in baseball, spin bowling in cricket, flying disc sports, etc. Table tennis paddles are manufactured with different surface characteristics to allow the player to impart a greater or lesser amount of spin to the ball.
Rotation of a player one or more times around a vertical axis may be called spin in figure skating, twirling (of the baton or the performer) in baton twirling, or 360, 540, 720, etc. in snowboarding, etc. Rotation of a player or performer one or more times around a horizontal axis may be called a flip, roll, somersault, heli, etc. in gymnastics, waterskiing, or many other sports, or a one-and-a-half, two-and-a-half, gainer (starting facing away from the water), etc. in diving, etc. A combination of vertical and horizontal rotation (back flip with 360°) is called a möbius in waterskiing freestyle jumping.
Rotation of a player around a vertical axis, generally between 180 and 360 degrees, may be called a spin move and is used as a deceptive or avoidance maneuver, or in an attempt to play, pass, or receive a ball or puck, etc., or to afford a player a view of the goal or other players. It is often seen in hockey, basketball, football of various codes, tennis, etc.
The end result of any sequence of rotations of any object in 3D about a fixed point is always equivalent to a rotation about an axis. However, an object may physically rotate in 3D about a fixed point on more than one axis simultaneously, in which case there is no single fixed axis of rotation - just the fixed point. However, these two descriptions can be reconciled - such a physical motion can always be re-described in terms of a single axis of rotation, provided the orientation of that axis relative to the object is allowed to change moment by moment.
2 dimensional rotations, unlike the 3 dimensional ones, possess no axis of rotation. This is equivalent, for linear transformations, with saying that there is no direction in the place which is kept unchanged by a 2 dimensional rotation, except, of course, the identity.
The question of the existence of such a direction is the question of existence of an eigenvector for the matrix A representing the rotation. Every 2D rotation around the origin through an angle in counterclockwise direction can be quite simply represented by the following matrix:
as its eigenvalues. Therefore, there is no real eigenvalue whenever , meaning that no real vector in the plane is kept unchanged by A.
Knowing that the trace is an invariant, the rotation angle for a proper orthogonal 3x3 rotation matrix is found by
Using the principal arc-cosine, this formula gives a rotation angle satisfying . The corresponding rotation axis must be defined to point in a direction that limits the rotation angle to not exceed 180 degrees. (This can always be done because any rotation of more than 180 degrees about an axis can always be written as a rotation having if the axis is replaced with .)
Every proper rotation in 3D space has an axis of rotation, which is defined such that any vector that is aligned with the rotation axis will not be affected by rotation. Accordingly, , and the rotation axis therefore corresponds to an eigenvector of the rotation matrix associated with an eigenvalue of 1. As long as the rotation angle is nonzero (i.e., the rotation is not the identity tensor), there is one and only one such direction. Because A has only real components, there is at least one real eigenvalue, and the remaining two eigenvalues must be complex conjugates of each other (see Eigenvalues and eigenvectors#Eigenvalues and the characteristic polynomial). Knowing that 1 is an eigenvalue, it follows that the remaining two eigenvalues are complex conjugates of each other, but this does not imply that they are complex--they could be real with double multiplicity. In the degenerate case of a rotation angle , the remaining two eigenvalues are both equal to -1. In the degenerate case of a zero rotation angle, the rotation matrix is the identity, and all three eigenvalues are 1 (which is the only case for which the rotation axis is arbitrary).
A spectral analysis is not required to find the rotation axis. If denotes the unit eigenvector aligned with the rotation axis, and if denotes the rotation angle, then it can be shown that . Consequently, the expense of an eigenvalue analysis can be avoided by simply normalizing this vector if it has a nonzero magnitude. On the other hand, if this vector has a zero magnitude, it means that . In other words, this vector will be zero if and only if the rotation angle is 0 or 180 degrees, and the rotation axis may be assigned in this case by normalizing any column of that has a nonzero magnitude.
This discussion applies to a proper rotation, and hence . Any improper orthogonal 3x3 matrix may be written as , in which is proper orthogonal. That is, any improper orthogonal 3x3 matrix may be decomposed as a proper rotation (from which an axis of rotation can be found as described above) followed by an inversion (multiplication by -1). It follows that the rotation axis of is also the eigenvector of corresponding to an eigenvalue of -1.
As much as every tridimensional rotation has a rotation axis, also every tridimensional rotation has a plane, which is perpendicular to the rotation axis, and which is left invariant by the rotation. The rotation, restricted to this plane, is an ordinary 2D rotation.
The proof proceeds similarly to the above discussion. First, suppose that all eigenvalues of the 3D rotation matrix A are real. This means that there is an orthogonal basis, made by the corresponding eigenvectors (which are necessarily orthogonal), over which the effect of the rotation matrix is just stretching it. If we write A in this basis, it is diagonal; but a diagonal orthogonal matrix is made of just +1's and -1's in the diagonal entries. Therefore, we don't have a proper rotation, but either the identity or the result of a sequence of reflections.
It follows, then, that a proper rotation has some complex eigenvalue. Let v be the corresponding eigenvector. Then, as we showed in the previous topic, is also an eigenvector, and and are such that their scalar product vanishes:
because, since is real, it equals its complex conjugate , and and are both representations of the same scalar product between and .
This means and are orthogonal vectors. Also, they are both real vectors by construction. These vectors span the same subspace as and , which is an invariant subspace under the application of A. Therefore, they span an invariant plane.
This plane is orthogonal to the invariant axis, which corresponds to the remaining eigenvector of A, with eigenvalue 1, because of the orthogonality of the eigenvectors of A. |
This animation tracks several gamma rays through space and time, from their emission in the jet of a distant blazar to their arrival in Fermi's Large Area Telescope (LAT). During their journey, the number of randomly moving ultraviolet and optical photons (blue) increases as more and more stars are born in the universe. Eventually, one of the gamma rays encounters a photon of starlight and the gamma ray transforms into an electron and a positron. The remaining gamma-ray photons arrive at Fermi, interact with tungsten plates in the LAT, and produce the electrons and positrons whose paths through the detector allows astronomers to backtrack the gamma rays to their source. Credit: NASA's Goddard Space Flight Center/Cruz deWilde.
Astronomers using data from NASA's Fermi Gamma-ray Space Telescope have made the most accurate measurement of starlight in the universe and used it to establish the total amount of light from all of the stars that have ever shone, accomplishing a primary mission goal. "The optical and ultraviolet light from stars continues to travel throughout the universe even after the stars cease to shine, and this creates a fossil radiation field we can explore using gamma rays from distant sources," said lead scientist Marco Ajello, a postdoctoral researcher at the Kavli Institute for Particle Astrophysics and Cosmology at Stanford University in California and the Space Sciences Laboratory at the University of California at Berkeley. Gamma rays are the most energetic form of light. Since Fermi's launch in 2008, its Large Area Telescope (LAT) observes the entire sky in high-energy gamma rays every three hours, creating the most detailed map of the universe ever known at these energies.The total sum of starlight in the cosmos is known to astronomers as the extragalactic background light (EBL). To gamma rays, the EBL functions as a kind of cosmic fog. Ajello and his team investigated the EBL by studying gamma rays from 150 blazars, or galaxies powered by black holes, that were strongly detected at energies greater than 3 billion electron volts (GeV), or more than a billion times the energy of visible light. "With more than a thousand detected so far, blazars are the most common sources detected by Fermi, but gamma rays at these energies are few and far between, which is why it took four years of data to make this analysis," said team member Justin Finke, an astrophysicist at the Naval Research Laboratory in Washington.As matter falls toward a galaxy's supermassive black hole, some of it is accelerated outward at almost the speed of light in jets pointed in opposite directions. When one of the jets happens to be aimed in the direction of Earth, the galaxy appears especially bright and is classified as a blazar. Gamma rays produced in blazar jets travel across billions of light-years to Earth. During their journey, the gamma rays pass through an increasing fog of visible and ultraviolet light emitted by stars that formed throughout the history of the universe. Occasionally, a gamma ray collides with starlight and transforms into a pair of particles -- an electron and its antimatter counterpart, a positron. Once this occurs, the gamma ray light is lost. In effect, the process dampens the gamma ray signal in much the same way as fog dims a distant lighthouse. From studies of nearby blazars, scientists have determined how many gamma rays should be emitted at different energies. More distant blazars show fewer gamma rays at higher energies -- especially above 25 GeV -- thanks to absorption by the cosmic fog. The farthest blazars are missing most of their higher-energy gamma rays.The researchers then determined the average gamma-ray attenuation across three distance ranges between 9.6 billion years ago and today. From this measurement, the scientists were able to estimate the fog's thickness. To account for the observations, the average stellar density in the cosmos is about 1.4 stars per 100 billion cubic light-years, which means the average distance between stars in the universe is about 4,150 light-years."The Fermi result opens up the exciting possibility of constraining the earliest period of cosmic star formation, thus setting the stage for NASA's James Webb Space Telescope," said Volker Bromm, an astronomer at the University of Texas, Austin, who commented on the findings. "In simple terms, Fermi is providing us with a shadow image of the first stars, whereas Webb will directly detect them." Measuring the extragalactic background light was one of the primary mission goals for Fermi. "We're very excited about the prospect of extending this measurement even farther," said Julie McEnery, the mission's project scientist at NASA's Goddard Space Flight Center in Greenbelt, Md.
NASA'S Fermi Measures Cosmic 'Fog' Produced by Ancient Starlight. Explores the Early Universe http://WWW.GOODNEWS.WS
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In its current form, architecture is still a product of the Industrial Age, as is the idea that underpins it, namely that every change is an improvement. No profession is so imbued with the soap powder advertising optimism of ‘now better than ever’. But buildings also belong to the category of products on which financial capitalism thrived. Just as the millions of unpaid Facebook users ensure that Mark Zuckerberg is on his way to becoming the richest man in the universe, so all the (in this case paid) parties who make buildings, starting with architects, ensure that those who own the buildings become wealthier from it. At least, that’s how things worked until the recession. Because construction alone will not make you seriously rich.
- Hans Ibelings, SHIFTS
Nanne de Ru of Powerhouse Company and Hans Ibelings explore the themes of the exhibition in a far-reaching discussion with leading UK based practioners, at the forefront of conversations around global change and new economies, including worldwide urban development perspectives from Christopher Choa (AECOM) and fresh research on alternative economies and their implications for architecture, from Alice Fung (00:/, Hub Westminster). The conversation will be chaired by Peter Buchanan, author of the Architecture Review's recent 12 part series of essays exploring the future of architecture, The Big Rethink.
Are we now seeing the formal end of the Industrial Revolution, the tipping point from which the East takes the reins from the West? What have de-regulation and the changing role of credit done to the world’s built environment? Through exploration of these vital questions, the evening will also launch a new publication resulting from Ibelings and Powerhouse's research.
Hans Ibelings (b. Rotterdam, 1963) is an architectural historian and critic. From 1989 to 2000 he was a curator at the Netherlands Architecture Institute; from 2004 to 2012 he was editor-in-chief of A10; in 2005 and 2006 he was a visiting professor at the EPFL (Lausanne). Ibelings is the author of several books including Supermodernism: Architecture in the age of globalization and European architecture since 1890. Since 2012 he is editor of The Architecture Observer, which employs a variety of old and new media in the pursuit of architectural criticism.
Nanne de Ru (1976, the Netherlands) received the Master of Excellence in Architecture from the Berlage Institute, Postgraduate Laboratory of Architecture, Rotterdam (2002), a Bachelor of Architectural engineering from the Hogeschool van Amsterdam in (1998) and won the Vitae Bouwaward for best Dutch Architectural Engineering graduation project (1999). From 1998 to 1999 de Ru worked as a project leader at One Architecture in Amsterdam. During the years 2002-2004 de Ru worked at Rem Koolhaas' think tank AMO in Rotterdam as a lead researcher and designer on numerous large scale regional planning projects including Ruhrgebiet (a study for a new identity for the Ruhrvalley in Germany); Eurocore (a study into new forms of urbanity in Europe); Beijing Olympic conference center competition; Beijing preservation strategies; and The Image of Europe – a joint commission of the Dutch presidency and the European Commission. In 2005 he co-founded Powerhouse Company, an office for architecture, urbanism and research, with branches in Rotterdam and Copenhagen. Powerhouse Company employs 15 people and is working throughout Europe and Asia on design and research projects. Nanne de Ru teaches regularly at the Academy of Architecture in Rotterdam and has been guest professorships at various institutions including Aarhus University (DK), TU Delft (NL), Design Academy Eindhoven (NL) and AHO Oslo School of Architecture (NO). Nanne de Ru is member of the research board of the Berlage Institute.
Christopher Choa is a Principal with AECOM, the international land development and infrastructure consultancy. He focuses on urban regeneration, sustainable strategies for new development, and enhancing regional competitiveness. A prize-winning architect and native New Yorker, he is based in London and leads the firm’s urban development studio. Christopher served as co-chair of New York New Visions - the design coalition for the rebuilding of Lower Manhattan. Some of his ongoing or completed projects include the planning of Cairo Airport City, the regeneration of Sao Paolo’s Nova Luz district, the Saadiyat Island Masterplan in Abu Dhabi, the masterplan of Shanghai's North Bund, and the Zeitinburnu Seaport in Istanbul. A graduate of both Harvard and Yale, he has been a visiting critic at the Harvard School of Design, Columbia University, and UCL/Bartlett. His work, citations, and professional columns have been published in a wide range of journals, including World Architecture, Architectural Review, The Shanghai Daily, The Wall Street Journal, and The New York Times.
Alice Fung trained as an architect and is co-founder of 00:/, a strategic development and design practice, and of Hub Westminster, an incubator for 1000 startups. She has experience in the strategic development of place design projects that focus on delivering social institutions and places. Alice's recent roles include project architect of Hub Kings Cross and the development and operational delivery of Hub Westminster. Her previous experiences include an institutional development strategy for Somerset House, affordable housing schemes, innovative workspace environments and urban regeneration projects. Alice was the lead designer on the Compendium for the Civic Economy, a collection of 25 civic enterprises showcasing more sustainable routes to a different economy in our cities, towns and neighbourhoods, commissioned by CABE and NESTA. She is a Future 100 Award winner for entrepreneurial flair and innovation in progressing a responsible business venture. Alice is a fellow of the RSA, has tutored at the University of Bath and served as a member of the RIBA Validation Panel visiting architecture schools in the UK.
Peter Buchanan is a writer, critic, consultant and curator. He was born in Malawi, schooled in Zimbabwe and graduated B.Arch from the University of Cape Town in 1968. Peter worked as an architect and urban designer/planner in various parts of Africa, Europe and the Middle East before joining the Architect’s Journal and The Architectural Review in 1979, becoming Deputy Editor of the latter in 1982. As a freelance since 1992, he has curated the travelling exhibitions Renzo Piano Building Workshop: Selected Projects and Ten Shades of Green for The Architectural League of New York, written books and served as a consultant on urban design projects and publications. He has published copiously in journals from many countries, and lectured and taught summer schools and master classes in a similarly wide range of places and universities. His many books include the five volumes of Renzo Piano Building Workshop: Complete Works (Phaidon Press) and Ten Shades of Green (WW Norton).# vimeo.com/43281796 Uploaded 1,428 Plays 11 Likes 0 Comments
Speakers: Jonathan Grudin and Umer Farooq
Title: Where to Go After Grad School: A Discussion about Jobs and Careers
Both of us have academic and industry research laboratory experience. We also both worked in industry product development groups after getting our PhDs, Jonathan as a software engineer at Wang Laboratories in the 1980s and Umer as a user experience researcher in the Server & Tools Division at Microsoft where he is now. The viability of academic and research lab paths is quite evident, although students often have questions about their relative merits and drawbacks, and we will spend some time on this facet. Less clear to many students today are the possibilities for staying active in research while working in non-research jobs, as we did. This does not preclude an eventual return to research; in fact, it can be a less stressful and a more impactful and successful path in the long run, if undertaken thoughtfully by someone with appropriate interests and skills. It is also possible that changes in the field make this especially attractive at this time.
We will describe some merits and drawbacks of academic, industry research, and industry development paths, illustrated with brief biographical sketches of graduates from the 80s, 90s, and 00s (not only our own). We’ll also leave time for discussion.
Bio: Jonathan Grudin
After getting a PhD in cognitive psychology with Don Norman, Jonathan did a postdoc in a government research lab, then spent three years as a software engineer. He subsequently drifted back into research, eventually becoming Professor of Information and Computer Science at UC Irvine. He is now a Principal Researcher at Microsoft Research and Affiliate Professor at the Information School. He was Editor in Chief of ACM Transactions on Computer-Human Interaction, is co-chairing iConference 2011 with Harry Bruce (and a superlative committee doing most of the work), and is co-program chair for CSCW 2012. Both conferences will be in Seattle.
Bio: Umer Farooq
With a background in computer science, Umer finished his PhD in information sciences and technology with John M. Carroll from Penn State. During his graduate work, Umer did summer stints at IBM T.J. Watson Researcher Center and SRI International. He is now a User Experience Researcher at Microsoft. For the products Umer works on, his end users are highly technical developers, which presents a unique user experience dilemma: Do developers really care about usability, given that they are so tech savvy? While shipping Visual Studio 2010, Umer actively worked with product teams to convey that developers are in fact human and they too prefer a usable product.# vimeo.com/16296017 Uploaded 341 Plays 3 Likes 0 Comments
The AstraZeneca Research Centre was established in Australia in 2000. This is a rare inside look at what happens behind the scenes of a research laboratory, told by the clinical researchers themselves.# vimeo.com/9541289 Uploaded 75 Plays 1 Like 1 Comment
During a week in august 2011, 100 designers from all over the world, curators, experts and students have been working together on the theme of water : how to preserve it, how to transport it, how to purify it or package it... selected teams run for the "Art_science" prize in Boston, where the film was shown. The workshop took place at Le laboratoire in Paris, an Art & Science foundation in the network of "Art science labs" founded and animated by researcher David Edwards.# vimeo.com/48125297 Uploaded
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Given the economic and social importance of cotton as a raw material, it is not surprising that cotton has played an important role in history in both the ancient and modern worlds. Cotton fabric has been used since ancient times and the development of cotton agriculture was an important step in the advance of civilization among ancient civilizations. It did not play a major role in European history until the technical developments which led to the industrial revolution, a critical development in the making of the modern world and the rise of the West. Cotton also played a central role in the economic development of the United States, leading to both the expansion of slavery and financing the industrialization of the United States.
Cotton fabric has been used since ancient times and the development of cotton agriculture was an important step in the advance of civilization among ancient civilizations. The original habitat of cotton is unknown. It is a plant that occurred naturally in both the Old World and rhe New World. One source reports that cotton was grown in the Indus Valley of modern India and Pakistan as early as 3,000 BC, but was almost ceratinly grown much earlier. Litle information is available, largely because of the great river valley civilizations, the least is known about the Indus Valley people. Another source suggests that cotton was domesticated about 1500 BC in three different locations: the Indus Valley, Ethiopia, and Peru. [Yafa] It seems likely that the Indus River and Ethiopian developments were related. The domestication of cotton in Peru would have had to have been an independent development. Cotton was also cultivated in ancient China and Egypt.
Cotton was virtually unknown in Medieval Euroope until the Crusades of the 11th, 12th, and 13th centuries. The exposure of the Crusaders to luxuruy goods like silk and cotton, fueled European demand. Trade route to India, howevrer, were controlled by the Arabs and this cotton was enormously expensive in Europe. The Poruguese and Spanish voyages of discovery in the 15th century were primarily organized to establish direct trade contacts with the East.
Cotton did not prove to be an immediate success, especially in norther Europe. Here climate was a factor. Another problem with cotton was that it was difficult to dye. Cotton gabric would very quily fade with washing. The Indians had figured out how to do this. It involved anamilzing the fabric, soaking it in solutions such as urine. [Yafa] As trade expanded with India, brightly colored Indian cotton fabric became enormously popular in Europe. European fashions except for the very rich had been rather drab until about 1700. This began to change as Indian cottons began to enter the European markets in quantities. The English acquired the technology for dyeing. The next step to compete with the fabric from India was how to produce it more cheaply. There was no way of under-cutting the Indians with cheaper labor. Thus the only option was to develop new more efficent mechanical process. This lead directly to the most significant development of modern times--the Industrial Revolution. And cotton was at the center of it.
Cotton was grown in pre-colonial America, although I am unsure to waht extent it was actually cultured. Cotton was one of the plants brought to America by the orgiginal English settlers that founded the Jamestown colony in 1607. Cotton was grown in tbe southern states. It was not, however, the mainstay of southern agriculture. Th problm was the seeds. They wre vefy time consuming to remove. This greatly increased the cost of produving it, maning there was little profit in doing so. This only changed when Eli Whitney inventd the cotton gin (1793). One reason that slavery did not blow up the Constitutional Convention was that slavery was seen to be a dying institution and southerners would giv it up because of its inherent inefficency. Whiney's cotton gin changed this. Cotton production soon became an immensly profitable crop. Thisas in part because the cotton gin reduced producion coasts. And because at the same time, the Industrial Recolution had begin in Britain, creating aremendous demand for raw cotton.
Cotton also played a major role in the Industrial Revolution that has so changed modern life. No development in modern history has affected individuals more than the Industrial Revolution and the manufacture of textiles played a key role. Historians debate just where and when the Industrail Revolution began. We would set it at about the mid-18th century in the English Midlands. The first industry affected was the textile or clothing industry--one reason that the study of the clothing industry is so important. It was at this time that workers instead of weaving piece work at home, began to work in factories. Here cotton manufacture became especially important and it was the first industry to be fully mechanized. [Ashworth, pp. 7-8.] Several inventions at this time were
responsible, including the spinning jenny, flying shuttle, and a water-powered loom. This was soon followed by the key invention of our time which served as a catalyst for industrial expansion--the steam engine. John Newcomen and James Watt developed the steam engine. The spread of the Industrail Revolution to the Continent generally followed the ame pattern as in Britain with the mechanization and inroduction of the factory system first in cotton mills. [Ashworth, p. 12.]
Cotton is today the most widely used natural fiber in the manufacture of clothing. It has a number of qualities making it ideal for making textiles and clothing. It is a natural vegetable fiber--the most important textile raw material. This was not the case in the 18th century. The reason the shift to cotton occurred was technical advances in first manufactuing textiles and second in the production of raw cotton. Cotton played a major role in the Industrial Revolution that has so changed modern life. The first industrial machines designed for mass production were developed to manufacture cotton textiles. This created a demand for raw cotton. American slavery was declining in importance in the late 18th century. Many even in the South thought that it would eventually disappear as was happening in the North. The Industrial Revolution, however, led to Ely Whitney's cotton gin. Suddenly there was way of supplying the European demand for cotton. The resulting efficiences changed the economies of cotton cultivation. New plantations were founded on King Cotton as Southern planters moved west into Alabama and Mississpi and eventually Texas. Huge profits could be made in cotton. But it was a labor-intensive crop. This meant that large plantations and slave labor were the most effecient production system. A very subsrantial proprtion of American slaves were employed in the production of this single crop. Cotton became the orimary American export commodity, in effect financing America's early industrial development. The revitalization of the South's slave-based economy began a process that was to lead inexorably to Civil War. Cotton today continues to be the most important natural textile, still widely used in the production of clothing.
After the invention of the cotton gin in 1793 by Eli Whitney, cotton production rapidly increased and became a leading factor in the drive west. New states were founded in the southeastern United States, all with economies based on the cultivation of cotton on large plantations using slave labor. This domination of the southern economy became known as "King Cotton". The United States rapidly became the principal source of cotton in the 19th century. The export of cotton rapidly became the principal Americam export commodity. These export earnings provided the financing for the American industrial revolution, which primarily occurred in the Northern states. It can be argued that it was the toil of unpaid slaves in the American South that financed the beginning steps toward the industrialization of the United States. The manufacture of cottons goods was one of the principal early American industries. [Ashworth, p. 25.] High tariffs incouraged the purchase of American-produced goods. Southerns objected to these tariffs, preferring to produce cheaper and often hifger-quality foreign goods.
The production of cotton textiles had been transformed by the Industrial Revolution--especially in England. Until the outbreak of the American Civil War (1861), cotton mills in Lancashire were obtaining 85 percent of their raw cotton from the United States. The Federal naval strategy in the War was to blockade the South and deprive its agricultural economy of needed manufactured imports and proceedes from exports sales of cotton. This blockade by October 1861 had begun to affect Lancashire mills. The mills exhaused their stocks of cotton and workers had to be discahrged or put on part time. The Federal blockadecby 1862 was extremely effective and little American cotton reached England. There was extreme distress and hunger among the English mill workers. Nearly 0.5 million people in Lancashire received relief to prevent starvation. Cotton prices skyrocketed from 7 pence per pound in 1861 to 31 pence in 1864. As the Federal firces began to seize cotton growing areas of the Condereracy in 1863, some American cotton began to reach England, but it was not until the end of the War in 1865 that shipments began to reach normal levels. The Federal blockade generated support for the Confederacy, primarily among mill workers and artistocratic elements that still resented the American Revolution and Republican Government. Among the mill workers themselves forced to endure great suffering, hatred for slavery was so wide spread that there was no great public outcry for Britain to support the Confederacy, a step that would have had enormously political consequences for America, Britain, and the entire world. Britain with the Royal Navy certainly could have broken the Federal blockade.
Sharecropping is an agricultural system which developed in the Southern states during the Civil War. It was a farm tenancy system in which families worked a farm or section of land in return for a share of the crop rather than wages. Sharecropping replaced the plantation system destroyed by the Civil War. The victorious Federal authorities which occupied the South did not seize plantations, but empancipation meant that the owners no longer had a captive labor force. The former planters, even those activly engged in rebellion, for the most part still had their land, but no slaves or money to pay wages. The former slaves on the other hand did not have jobs or land and because they had been denied education, had few options. Sharecropping developed because the former slaves and planters needed each other. The principal crop continued to be cotton. And the planters under the sharecropping system contnued to a large degree to control the lives of the blacks working their land. While the system at first developed to obtain black labor, eventually poor whites also entered the sharecropping system. The system varied, but in many cases all the cropper brouht to the arrangement was his labor. The planter provided the land, but also commonly animals, equipment, seeds and other items. The land owners also commonly advanced credits for the family's living expences until the crop was harvested. The system was open to considerable abuse because the cropers were uneducated, commonly iliterate. Akmost all slaves in the Deep South following the Civil War would have been illiterate. It was illegal to teach slaves to read. By the 20th century black and white cropers would have had some minimal education, but iliteracy was still high. The land owner marketed the crop and kept all accounts. He charged interests on cash advances, often quite high interest. He also commonly operated a store where the cropers had to make their purchases. The normal arrangement was that the the croper got half the proceeds from the harvest. The landowner then deducted cash advances which because of high interest and dishonest accounting commonly left the croper very little. The system continued into the Depression of the 1930s. School portraits from the rural South during the late 19th and early 20th century will often include cropers children. Many did not go very far in school. (The Southern states commonly had very weak compulsory school attendance laws.) The children commonly were barefoot. During the 20th century many wore overalls. After World War II, migrtion to the North, farm mechanization, education, other employment options, and the Civil Rights movement brought the system to an end.
The Unkited States continues to be a major world cotton producer. The two most important producers are India and China. Harrvests vary and in some years India is the leading producer ' India is the major producer, with harvests about twice that of the United States--5.7 million tons (2015-16). Cotton has been grown in India for millenia, first noted along with the Inus Valley civilization. The climate in northern India is particularly favorable for cotton. China harvested somewhat less, 4.8 million tons. China has some 7,500 textile companies, which produce US $73 billion of cotton textiles annually. Cotton cultivation requires moderate rainfall which causes substantial annual fluctuations. And to protect the crop, there is a huge usage of pesticides and fertilizers with few environmental restrictions. The other major producers re the United States (2.8 million tons), Pakistan (1.5 million tons), and Brazil (1.3 million tons). The Soviet Union was a major producer, but did enormous enviromntal damage in Central Asia. Uzbeckistan and Turkmenistan continue to be important producers. Turkey is the most important producer in the Middle East. Egypt was once very important. The most important Africn producer is Burkina. Australia is the only important producer in Oceania.
Ashworth, William. A Short Histiory of the International Economy Since 1850 (Longman Paperback: London, 1977), 318p.
Yafa, Stephen. Big Cotton.
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The immune system protects the body against infection and disease. It is a complex and integrated system of cells, tissues, and organs that have specialized roles in defending against foreign substances and pathogenic microorganisms, including bacteria, viruses, and fungi. The immune system also functions to guard against the development of cancer. For these actions, the immune system must recognize foreign invaders as well as abnormal cells and distinguish them from self (1). However, the immune system is a double-edged sword in that host tissues can be damaged in the process of combating and destroying invading pathogens. A key component of the immediate immune response is inflammation, which can cause damage to host tissues, although the damage is usually not significant (2). Inflammation is discussed in a separate article; this article focuses on nutrition and immunity.
Cells of the immune system originate in the bone marrow and circulate to peripheral tissues through the blood and lymph. Organs of the immune system include the thymus, spleen, and lymph nodes (3). T-lymphocytes develop in the thymus, which is located in the chest directly above the heart. The spleen, which is located in the upper abdomen, functions to coordinate secretion of antibodies into the blood and also removes old and damaged red blood cells from the circulation (4). Lymph nodes serve as local sentinel stations in tissues throughout the body, trapping antigens and infectious agents and promoting organized immune cell activation.
The immune system is broadly divided into two major components: innate immunity and adaptive immunity. Innate immunity involves immediate, nonspecific responses to foreign invaders, while adaptive immunity requires more time to develop its complex, specific responses (1).
Innate immunity is the first line of defense against foreign substances and pathogenic microorganisms. It is an immediate, nonspecific defense that does not involve immunologic memory of pathogens. Because of the lack of specificity, the actions of the innate immune system can result in damage to the body’s tissues (5). A lack of immunologic memory means that the same response is mounted regardless of how often a specific antigen is encountered (6).
The innate immune system is comprised of various anatomical barriers to infection, including physical barriers (e.g., the skin), chemical barriers (e.g., acidity of stomach secretions), and biological barriers (e.g., normal microflora of the gastrointestinal tract) (1). In addition to anatomical barriers, the innate immune system is comprised of soluble factors and phagocytic cells that form the first line of defense against pathogens. Soluble factors include the complement system, acute phase reactant proteins, and messenger proteins called cytokines (6). The complement system, a biochemical network of more than 30 proteins in plasma and on cellular surfaces, is a key component of innate immunity. The complement system elicits responses that kill invading pathogens by direct lysis (cell rupture) or by promoting phagocytosis. Complement proteins also regulate inflammatory responses, which are an important part of innate immunity (7-9). Acute phase reactant proteins are a class of plasma proteins that are important in inflammation. Cytokines secreted by immune cells in the early stages of inflammation stimulate the synthesis of acute phase reactant proteins in the liver (10). Cytokines are chemical messengers that have important roles in regulating the immune response; some cytokines directly fight pathogens. For example, interferons have antiviral activity (6). These soluble factors are important in recruiting phagocytic cells to local areas of infection. Monocytes, macrophages, and neutrophils are key immune cells that engulf and digest invading microorganisms in the process called phagocytosis. These cells express pattern recognition receptors that identify pathogen-associated molecular patterns (PAMPs) that are unique to pathogenic microorganisms but conserved across several families of pathogens (see figure). For more information about the innate immune response, see the article on Inflammation.
Adaptive immunity (also called acquired immunity), a second line of defense against pathogens, takes several days or weeks to fully develop. However, adaptive immunity is much more complex than innate immunity because it involves antigen-specific responses and immunologic “memory.” Exposure to a specific antigen on an invading pathogen stimulates production of immune cells that target the pathogen for destruction (1). Immunologic “memory” means that immune responses upon a second exposure to the same pathogen are faster and stronger because antigens are “remembered.” Primary mediators of the adaptive immune response are B lymphocytes (B cells) and T lymphocytes (T cells). B cells produce antibodies, which are specialized proteins that recognize and bind to foreign proteins or pathogens in order to neutralize them or mark them for destruction by macrophages. The response mediated by antibodies is called humoral immunity. In contrast, cell-mediated immunity is carried out by T cells, lymphocytes that develop in the thymus. Different subgroups of T cells have different roles in adaptive immunity. For instance, cytotoxic T cells (killer T cells) directly attack and kill infected cells, while helper T cells enhance the responses and thus aid in the function of other lymphocytes (5, 6). Regulatory T cells, sometimes called suppressor T cells, suppress immune responses (12). In addition to its vital role in innate immunity, the complement system modulates adaptive immune responses and is one example of the interplay between the innate and adaptive immune systems (7, 13). Components of both innate and adaptive immunity interact and work together to protect the body from infection and disease.
Nutritional status can modulate the actions of the immune system; therefore, the sciences of nutrition and immunology are tightly linked. In fact, malnutrition is the most common cause of immunodeficiency in the world (14), and chronic malnutrition is a major risk factor for global morbidity and mortality (15). More than 800 million people are estimated to be undernourished, most in the developing world (16), but undernutrition is also a problem in industrialized nations, especially in hospitalized individuals and the elderly (17). Poor overall nutrition can lead to inadequate intake of energy and macronutrients, as well as deficiencies in certain micronutrients that are required for proper immune function. Such nutrient deficiencies can result in immunosuppression and dysregulation of immune responses. In particular, deficiencies in certain nutrients can impair phagocytic function in innate immunity and adversely affect several aspects of adaptive immunity, including cytokine production as well as antibody- and cell-mediated immunities (18, 19). Overnutrition, a form of malnutrition where nutrients, specifically macronutrients, are provided in excess of dietary requirements, also negatively impacts immune system functions (see Overnutrition and Obesity below).
Impaired immune responses induced by malnutrition can increase one’s susceptibility to infection and illness. Infection and illness can, in turn, exacerbate states of malnutrition, for example, by reducing nutrient intake through diminished appetite, impairing nutrient absorption, increasing nutrient losses, or altering the body’s metabolism such that nutrient requirements are increased (19). Thus, states of malnutrition and infection can aggravate each other and lead to a vicious cycle (14).
Protein-energy malnutrition (PEM; also sometimes called protein-calorie malnutrition) is a common nutritional problem that principally affects young children and the elderly (20). Clinical conditions of severe PEM are termed marasmus, kwashiorkor, or a hybrid of these two syndromes. Marasmus is a wasting disorder that is characterized by depletion of fat stores and muscle wasting. It results from a deficiency in both protein and calories (i.e., all nutrients). Individuals afflicted with marasmus appear emaciated and are grossly underweight and do not present with edema (21). In contrast, a hallmark of kwashiorkor is the presence of edema. Kwashiorkor is primarily caused by a deficiency in dietary protein, while overall caloric intake may be normal (21, 22). Both forms are more common in developing nations, but certain types of PEM are also present in various subgroups in industrialized nations, such as the elderly and individuals who are hospitalized (17). In the developed world, PEM more commonly occurs secondary to a chronic disease that interferes with nutrient metabolism, such as inflammatory bowel disease, chronic renal failure, or cancer (22).
Regardless of the specific cause, PEM significantly increases susceptibility to infection by adversely affecting aspects of both innate immunity and adaptive immunity (15). With respect to innate immunity, PEM has been associated with reduced production of certain cytokines and several complement proteins, as well as impaired phagocyte function (20, 23, 24). Such malnutrition disorders can also compromise the integrity of mucosal barriers, increasing vulnerability to infections of the respiratory, gastrointestinal, and urinary tracts (21). With respect to adaptive immunity, PEM primarily affects cell-mediated aspects instead of components of humoral immunity. In particular, PEM leads to atrophy of the thymus, the organ that produces T cells, which reduces the number of circulating T cells and decreases the effectiveness of the memory response to antigens (21, 24). PEM also compromises functions of other lymphoid tissues, including the spleen and lymph nodes (20). While humoral immunity is affected to a lesser extent, antibody affinity and response is generally decreased in PEM (24). It is important to note that PEM usually occurs in combination with deficiencies in essential micronutrients, especially vitamin A, vitamin B6, folate, vitamin E, zinc, iron, copper, and selenium (21).
Experimental studies have shown that several types of dietary lipids (fatty acids) can modulate the immune response (25). Fatty acids that have this role include the long-chain polyunsaturated fatty acids (PUFAs) of the omega-3 and omega-6 classes. PUFAs are fatty acids with more than one double bond between carbons. In all omega-3 fatty acids, the first double bond is located between the third and fourth carbon atom counting from the methyl end of the fatty acid (n-3). Similarly, the first double bond in all omega-6 fatty acids is located between the sixth and seventh carbon atom from the methyl end of the fatty acid (n-6) (26). Humans lack the ability to place a double bond at the n-3 or n-6 positions of a fatty acid; therefore, fatty acids of both classes are considered essential nutrients and must be derived from the diet (26). More information is available in the article on Essential fatty acids. Alpha-linolenic acid (ALA) is a nutritionally essential n-3 fatty acid, and linoleic acid (LA) is a nutritionally essential n-6 fatty acid; dietary intake recommendations for essential fatty acids are for ALA and LA. Other fatty acids in the n-3 and n-6 classes can be endogenously synthesized from ALA or LA (see the figure in a separate article on essential fatty acids). For instance the long-chain n-6 PUFA, arachidonic acid, can be synthesized from LA, and the long-chain n-3 PUFAs, eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA), can be synthesized from ALA (26). However, synthesis of EPA and, especially, DHA may be insufficient under certain conditions, such as during pregnancy and lactation (27, 28). EPA and DHA, like other PUFAs, modulate cellular function, including immune and inflammatory responses (29).
Long-chain PUFAs are incorporated into membrane phospholipids of immune cells, where they modulate cell signaling of immune and inflammatory responses, such as phagocytosis and T-cell signaling. They also modulate the production of eicosanoids and other lipid mediators (29, 30). Eicosanoids are 20-carbon PUFA derivatives that play key roles in inflammatory and immune responses. During an inflammatory response, long-chain PUFAs (e.g., arachidonic acid [AA] of the n-6 series and EPA of the n-3 series) in immune cell membranes can be metabolized by enzymes to form eicosanoids (e.g., prostaglandins, leukotrienes, and thromboxanes), which have varying effects on inflammation (29). Eicosanoids derived from AA can also regulate B- and T-cell functions. Resolvins are lipid mediators derived from EPA and DHA that appear to have anti-inflammatory properties (30). To a certain extent, the relative production of these lipid mediators can be altered by dietary and supplemental intake of lipids. In those who consume a typical Western diet, the amount of AA in immune cell membranes is much greater than the amount of EPA, which results in the formation of more eicosanoids derived from AA than EPA. However, increasing n-3 fatty acid intake dose-dependently increases the EPA content of immune cell membranes. The resulting effect would be increased production of eicosanoids derived from EPA and decreased production of eicosanoids derived from AA, leading to an overall anti-inflammatory effect (30, 31). While eicosanoids derived from EPA are less biologically active than AA-derived eicosanoids (32), supplementation with EPA and other n-3 PUFAs may nevertheless have utility in treating various inflammatory diseases. This is a currently active area of investigation; see the article on Essential fatty acids. While n-3 PUFA supplementation may benefit individuals with inflammatory or autoimmune diseases, high n-3 PUFA intakes could possibly impair host-defense mechanisms and increase vulnerability to infectious disease (for more information, see the article on Essential fatty acids) (25, 33).
In addition to PUFAs, isomers of LA called conjugated linoleic acid (CLA) have been shown to modulate immune function, mainly in animal and in vitro studies (34). CLA is found naturally in meat and milk of ruminant animals, but it is also available as a dietary supplement that contains two isomers, cis-9,trans-11 CLA and trans-10,cis-12 CLA. One study in 28 men and women found that CLA supplementation (3 g/day of a 50:50 mixture of the two main CLA isomers) was associated with an increase in plasma levels of IgA and IgM (35), two classes of antibodies. CLA supplementation was also associated with a decrease in levels of two pro-inflammatory cytokines and an increase in levels of an anti-inflammatory cytokine (35). Similar effects on the immune response have been observed in some animal studies (36, 37); however, a few other human studies have not found beneficial effects of CLA on various measures of immune status and function (38-40). More research is needed to understand the effects of CLA on the human immune response.
Further, lipids in general have a number of other roles in immunity besides being the precursors of eicosanoids and similar immune mediators. For instance, lipids are metabolized by immune cells to generate energy and are also important structural and functional components of cell membranes. Moreover, lipids can regulate gene expression through stimulation of membrane receptors or through modification of transcription factor activity. Further, lipids can covalently modify proteins, thereby affecting their function (30).
Deficiencies in select micronutrients (vitamins and nutritionally-essential minerals) can adversely affect aspects of both innate and adaptive immunity, increasing vulnerability to infection and disease. Micronutrient inadequacies are quite common in the general U.S. population, but especially in the poor, the elderly, and those who are obese (see Overnutrition and Obesity below) (41, 42). According to data from the U.S. National Health and Nutrition Examination Survey (NHANES), 93% of the U.S. population do not meet the estimated average requirement (EAR) for vitamin E, 56% for magnesium, 44% for vitamin A, 31% for vitamin C, 14% for vitamin B6, and 12% for zinc (43). Moreover, vitamin D deficiency is a major problem in the U.S. and elsewhere; it has been estimated that 1 billion people in the world have either vitamin D deficiency or insufficiency (44). Because micronutrients play crucial roles in the development and expression of immune responses, selected micronutrient deficiencies can cause immunosuppression and thus increased susceptibility to infection and disease. The roles of several micronutrients in immune function are addressed below.
Vitamin A and its metabolites play critical roles in both innate and adaptive immunity. In innate immunity, the skin and mucosal cells of the eye and respiratory, gastrointestinal, and genitourinary tracts function as a barrier against infections. Vitamin A helps to maintain the structural and functional integrity of these mucosal cells. Vitamin A is also important to the normal function of several types of immune cells important in the innate response, including natural killer (NK) cells, macrophages, and neutrophils. Moreover, vitamin A is needed for proper function of cells that mediate adaptive immunity, such as T and B cells; thus, vitamin A is necessary for the generation of antibody responses to specific antigens (45).
Most of the immune effects of vitamin A are carried out by vitamin A derivatives, namely isomers of retinoic acid. Isomers of retinoic acid are steroid hormones that bind to retinoid receptors that belong to two different classes: retinoic acid receptors (RARs) and retinoid X receptors (RXRs). In the classical pathway, RAR must first heterodimerize with RXR and then bind to small sequences of DNA called retinoic acid response elements (RAREs) to initiate a cascade of molecular interactions that modulate the transcription of specific genes (46). More than 500 genes are directly or indirectly regulated by retinoic acid (47). Several of these genes control cellular proliferation and differentiation; thus, vitamin A has obvious importance in immunity.
Vitamin A deficiency is a major public health problem worldwide, especially in developing nations, where availability of foods containing preformed vitamin A is limited (for information on sources of vitamin A, see the separate article on Vitamin A). Experimental studies in animal models, along with epidemiological studies, have shown that vitamin A deficiency leads to immunodeficiency and increases the risk of infectious diseases (45). In fact, deficiency in this micronutrient is a leading cause of morbidity and mortality among infants, children, and women in developing nations. Vitamin A-deficient individuals are vulnerable to certain infections, such as measles, malaria, and diarrheal diseases (45). Subclinical vitamin A deficiency might increase risk of infection as well (48). Infections can, in turn, lead to vitamin A deficiency in a number of different ways, for example, by reducing food intake, impairing vitamin absorption, increasing vitamin excretion, interfering with vitamin utilization, or increasing metabolic requirements of vitamin A (49).
Many of the specific effects of vitamin A deficiency on the immune system have been elucidated using animal models. Vitamin A deficiency impairs components of innate immunity. As mentioned above, vitamin A is essential in maintaining the mucosal barriers of the innate immune system. Thus, vitamin A deficiency compromises the integrity of this first line of defense, thereby increasing susceptibility to some types of infection, such as eye, respiratory, gastrointestinal, and genitourinary infections (50-56). Vitamin A deficiency results in reductions in both the number and killing activity of NK cells, as well as the function of neutrophils and other cells that phagocytose pathogens like macrophages. Specific measures of functional activity affected appear to include chemotaxis, phagocytosis, and immune cell ability to generate oxidants that kill invading pathogens (45). In addition, cytokine signaling may be altered in vitamin A deficiency, which would affect inflammatory responses of innate immunity.
Additionally, vitamin A deficiency impairs various aspects of adaptive immunity, including humoral and cell-mediated immunity. In particular, vitamin A deficiency negatively affects the growth and differentiation of B cells, which are dependent on retinol and its metabolites (57, 58). Vitamin A deficiency also affects B cell function; for example, animal experiments have shown that vitamin A deficiency impairs antibody responses (59-61). With respect to cell-mediated immunity, retinol is important in the activation of T cells (62), and vitamin A deficiency may affect cell-mediated immunity by decreasing the number or distribution of T cells, altering cytokine production, or by decreasing the expression of cell-surface receptors that mediate T-cell signaling (45).
Vitamin A supplementation enhances immunity and has been shown to reduce the infection-related morbidity and mortality associated with vitamin A deficiency. A meta-analysis of 12 controlled trials found that vitamin A supplementation in children decreased the risk of all-cause mortality by 30%; this analysis also found that vitamin A supplementation in hospitalized children with measles was associated with a 61% reduced risk of mortality (63). Vitamin A supplementation has been shown to decrease the severity of diarrheal diseases in several studies (64) and has also been shown to decrease the severity, but not the incidence, of other infections, such as measles, malaria, and HIV (45). Moreover, vitamin A supplementation can improve or reverse many of the abovementioned, untoward effects on immune function, such as lowered antibody production and an exacerbated inflammatory response (65). However, vitamin A supplementation is not beneficial in those with lower respiratory infections, such as pneumonia, and supplementation may actually aggravate the condition (45, 66, 67). Because of potential adverse effects, vitamin A supplements should be reserved for undernourished populations and those with evidence of vitamin A deficiency (64). For information on vitamin A toxicity, see the separate article on Vitamin A.
Like vitamin A, the active form of vitamin D, 1,25-dihydroxyvitamin D3, functions as a steroid hormone to regulate expression of target genes. Many of the biological effects of 1,25-dihydroxyvitamin D3 are mediated through a nuclear transcription factor known as the vitamin D receptor (VDR) (68). Upon entering the nucleus of a cell, 1,25-dihydroxyvitamin D3 associates with the VDR and promotes its association with the retinoid X receptor (RXR). In the presence of 1,25-dihydroxyvitamin D3, the VDR/RXR complex binds small sequences of DNA known as vitamin D response elements (VDREs) and initiates a cascade of molecular interactions that modulate the transcription of specific genes. More than 200 genes in tissues throughout the body are known to be regulated either directly or indirectly by 1,25-dihydroxyvitamin D3 (44).
In addition to its effects on mineral homeostasis and bone metabolism, 1,25-dihydroxyvitamin D3 is now recognized to be a potent modulator of the immune system. The VDR is expressed in several types of immune cells, including monocytes, macrophages, dendritic cells, and activated T cells (69-72). Macrophages also produce the 25-hydroxyvitamin D3-1-hydroxylase enzyme, allowing for local conversion of vitamin D to its active form (73). Studies have demonstrated that 1,25-dihydroxyvitamin D3 modulates both innate and adaptive immune responses.
Antimicrobial peptides (AMPs) and proteins are critical components of the innate immune system because they directly kill pathogens, especially bacteria, and thereby enhance immunity (74). AMPs also modulate immune functions through cell-signaling effects (75). The active form of vitamin D regulates an important antimicrobial protein called cathelicidin (76-78). Vitamin D has also been shown to stimulate other components of innate immunity, including immune cell proliferation and cytokine production (79). Through these roles, vitamin D helps protect against infections caused by pathogens.
Vitamin D has mainly inhibitory effects on adaptive immunity. In particular, 1,25-dihydroxyvitamin D3 suppresses antibody production by B cells and also inhibits proliferation of T cells in vitro (80-82). Moreover, 1,25-dihydroxyvitamin D3 has been shown to modulate the functional phenotype of helper T cells as well as dendritic cells (75). T cells that express the cell-surface protein CD4 are divided into two subsets depending on the particular cytokines that they produce: T helper (Th)1 cells are primarily involved in activating macrophages and inflammatory responses and Th2 cells are primarily involved in stimulating antibody production by B cells (12). Some studies have shown that 1,25-dihydroxyvitamin D3 inhibits the development and function of Th1 cells (83, 84) but enhances the development and function of Th2 cells (85, 86) and regulatory T cells (87, 88). Because these latter cell types are important regulators in autoimmune disease and graft rejections, vitamin D is suggested to have utility in preventing and treating such conditions (89). Studies employing various animal models of autoimmune diseases and transplantation have reported beneficial effects of 1,25-dihydroxyvitamin D3 (reviewed in 84).
Indeed, vitamin D deficiency has been implicated in the development of certain autoimmune diseases, such as insulin-dependent diabetes mellitus (IDDM; type 1 diabetes mellitus), multiple sclerosis (MS), and rheumatoid arthritis (RA). Autoimmune diseases occur when the body mounts an immune response against its own tissues instead of a foreign pathogen. The targets of the inappropriate immune response are the insulin-producing beta-cells of the pancreas in IDDM, the myelin-producing cells of the central nervous system in MS, and the collagen-producing cells of the joints in RA (90). Some epidemiological studies have found the prevalence of various autoimmune conditions increases as latitude increases (91). This suggests that lower exposure to ultraviolet-B radiation (the type of radiation needed to induce vitamin D synthesis in skin) and the associated decrease in endogenous vitamin D synthesis may play a role in the pathology of autoimmune diseases. Additionally, results of several case-control and prospective cohort studies have associated higher vitamin D intake or serum levels with decreased incidence, progression, or symptoms of IDDM (92), MS (93-96), and RA (97). For more information, see the separate article on Vitamin D. It is not yet known whether vitamin D supplementation will reduce the risk of certain autoimmune disorders. Interestingly, a recent systematic review and meta-analysis of observational studies found that vitamin D supplementation during early childhood was associated with a 29% lower risk of developing IDDM (98). More research is needed to determine the role of vitamin D in various autoimmune conditions.
Vitamin C is a highly effective antioxidant that protects the body’s cells against reactive oxygen species (ROS) that are generated by immune cells to kill pathogens. Primarily through this role, the vitamin affects several components of innate and adaptive immunity. Vitamin C has been shown to stimulate both the production (99-103) and function (104, 105) of leukocytes (white blood cells), especially neutrophils, lymphocytes, and phagocytes. Specific measures of functions stimulated by vitamin C include cellular motility (104), chemotaxis (104, 105), and phagocytosis (105). Neutrophils, which attack foreign bacteria and viruses, seem to be the primary cell type stimulated by vitamin C, but lymphocytes and other phagocytes are also affected (106). Additionally, several studies have shown that supplemental vitamin C increases serum levels of antibodies (107, 108) and C1q complement proteins (109-111) in guinea pigs, which—like humans—cannot synthesize vitamin C and hence depend on dietary vitamin C. However, some studies have reported no beneficial changes in leukocyte production or function with vitamin C treatment (112-115). Vitamin C may also protect the integrity of immune cells. Neutrophils, mononuclear phagocytes, and lymphocytes accumulate vitamin C to high concentrations, which can protect these cell types from oxidative damage (103, 116, 117). In response to invading microorganisms, phagocytic leukocytes release non-specific toxins, such as superoxide radicals, hypochlorous acid (“bleach”), and peroxynitrite; these ROS kill pathogens and, in the process, can damage the leukocytes themselves (118). Vitamin C, through its antioxidant functions, has been shown to protect leukocytes from such effects of autooxidation (119). Phagocytic leukocytes also produce and release cytokines, including interferons, which have antiviral activity (120). Vitamin C has been shown to increase interferon levels in vitro (121). Further, vitamin C regenerates the antioxidant vitamin E from its oxidized form (122).
It is widely thought by the general public that vitamin C boosts the function of the immune system, and accordingly, may protect against viral infections and perhaps other diseases. While some studies suggest the biological plausibility of vitamin C as an immune enhancer, human studies published to date are conflicting. Controlled clinical trials of appropriate statistical power would be necessary to determine if supplemental vitamin C boosts the immune system. For a review of vitamin C and the common cold, see the separate article on Vitamin C.
Vitamin E is a lipid-soluble antioxidant that protects the integrity of cell membranes from damage caused by free radicals (123). In particular, the alpha-tocopherol form of vitamin E protects against peroxidation of polyunsaturated fatty acids, which can potentially cause cellular damage and subsequently lead to improper immune responses (124). Several studies in animal models as well as humans indicate that vitamin E deficiency impairs both humoral and cell-mediated aspects of adaptive immunity, including B and T cell function (reviewed in 124). Moreover, vitamin E supplementation in excess of current intake recommendations has been shown to enhance immunity and decrease susceptibility to certain infections, especially in elderly individuals.
Aging is associated with immune senescence (125). For example, T-cell function declines with increasing age, evidenced by decreased T-cell proliferation and decreased T-cell production of the cytokine, interleukin-2 (126). Studies in mice have found that vitamin E ameliorates these two age-related, immune effects (127, 128). Similar effects have been observed in some human studies (129). A few clinical trials of alpha-tocopherol supplementation in elderly subjects have demonstrated improvements in immunity. For example, elderly adults given 200 mg/day of synthetic alpha-tocopherol (equivalent to 100 mg of RRR-alpha-tocopherol or 150 IU of RRR-tocopherol; RRR-alpha-tocopherol is also referred to as "natural" or d-alpha-tocopherol) for several months displayed increased formation of antibodies in response to hepatitis B vaccine and tetanus vaccine (130). However, it is not known if such enhancements in the immune response of older adults actually translate to increased resistance to infections like the flu (influenza virus) (131). A randomized, placebo-controlled trial in elderly nursing home residents reported that daily supplementation with 200 IU of synthetic alpha-tocopherol (equivalent to 90 mg of RRR-alpha-tocopherol) for one year significantly lowered the risk of contracting upper respiratory tract infections, especially the common cold, but had no effect on lower respiratory tract (lung) infections (132). Yet, other trials have not reported an overall beneficial effect of vitamin E supplements on respiratory tract infections in older adults (133-136). More research is needed to determine whether supplemental vitamin E may protect the elderly against the common cold or other infections.
Vitamin B6 is required in the endogenous synthesis and metabolism of amino acids—the building blocks of proteins like cytokines and antibodies. Animal and human studies have demonstrated that vitamin B6 deficiency impairs aspects adaptive immunity, including both humoral and cell-mediated immunity. Specifically, deficiency in this micronutrient has been shown to affect lymphocyte proliferation, differentiation, and maturation as well as cytokine and antibody production (137-139). Correcting the vitamin deficiency restores the affected immune functions (139).
The B vitamin, folate, is required as a coenzyme to mediate the transfer of one-carbon units. Folate coenzymes act as acceptors and donors of one-carbon units in a variety of reactions critical to the endogenous synthesis and metabolism of nucleic acids (DNA and RNA) and amino acids (140, 141). Thus, folate has obvious importance in immunity. Folate deficiency results in impaired immune responses, primarily affecting cell-mediated immunity. However, antibody responses of humoral immunity may also be impaired in folate deficiency (142).
In humans, vitamin B12 functions as a coenzyme for two enzymatic reactions. One of the vitamin B12-dependent enzymes is involved in the synthesis of the amino acid, methionine, from homocysteine. Methionine in turn is required for the synthesis of S-adenosylmethionine, a methyl group donor used in many biological methylation reactions, including the methylation of a number of sites within DNA and RNA. The other vitamin B12-dependent enzyme, L-methylmalonyl-CoA mutase, converts L-methylmalonyl-CoA to succinyl-CoA, a compound that is important in the production of energy from fats and proteins as well as in the synthesis of hemoglobin, the oxygen carrying pigment in red blood cells (143). Patients with diagnosed vitamin B12 deficiency have been reported to have suppressed natural killer cell activity and decreased numbers of circulating lymphocytes (144, 145). One study found that these immunomodulatory effects were corrected by treating the vitamin deficiency (144).
Zinc is critical for normal development and function of cells that mediate both innate and adaptive immunity (146). The cellular functions of zinc can be divided into three categories: 1) catalytic, 2) structural, and 3) regulatory (see Function in the separate article on zinc) (147). Because zinc is not stored in the body, regular dietary intake of the mineral is important in maintaining the integrity of the immune system. Thus, inadequate intake can lead to zinc deficiency and compromised immune responses (148). With respect to innate immunity, zinc deficiency impairs the complement system, cytotoxicity of natural killer cells, phagocytic activity of neutrophils and macrophages, and immune cell ability to generate oxidants that kill invading pathogens (149-151). Zinc deficiency also compromises adaptive immune function, including lymphocyte number and function (152). Even marginal zinc deficiency, which is more common than severe zinc deficiency, can suppress aspects of immunity (148). Zinc-deficient individuals are known to experience increased susceptibility to a variety of infectious agents (see the separate article on Zinc).
Adequate selenium intake is essential for the host to mount a proper immune response because it is required for the function of several selenium-dependent enzymes known as selenoproteins (see the separate article on Selenium). For example, the glutathione peroxidases (GPx) are selenoproteins that function as important redox regulators and cellular antioxidants, which reduce potentially damaging reactive oxygen species, such as hydrogen peroxide and lipid hydroperoxides, to harmless products like water and alcohols by coupling their reduction with the oxidation of glutathione (see the diagram in the article on selenium) (153). These roles have implications for immune function and cancer prevention.
Selenium deficiency impairs aspects of innate as well as adaptive immunity (154, 155), adversely affecting both humoral immunity (i.e., antibody production) and cell-mediated immunity (156). Selenium deficiency appears to enhance the virulence or progression of some viral infections (see separate article on Selenium). Moreover, selenium supplementation in individuals who are not overtly selenium deficient appears to stimulate the immune response. In two small studies, healthy (157, 158) and immunosuppressed individuals (159) supplemented with 200 micrograms (mcg)/day of selenium as sodium selenite for eight weeks showed an enhanced immune cell response to foreign antigens compared with those taking a placebo. A considerable amount of basic research also indicates that selenium plays a role in regulating the expression of cytokines that orchestrate the immune response (160).
Iron is an essential component of hundreds of proteins and enzymes that are involved in oxygen transport and storage, electron transport and energy generation, antioxidant and beneficial pro-oxidant functions, and DNA synthesis (see Function in the article on iron) (161-163). Iron is required by the host in order to mount effective immune responses to invading pathogens, and iron deficiency impairs immune responses (164). Sufficient iron is critical to several immune functions, including the differentiation and proliferation of T lymphocytes and generation of reactive oxygen species (ROS) that kill pathogens. However, iron is also required by most infectious agents for replication and survival. During an acute inflammatory response, serum iron levels decrease while levels of ferritin (the iron storage protein) increase, suggesting that sequestering iron from pathogens is an important host response to infection (162, 165). Moreover, conditions of iron overload (e.g., hereditary hemochromatosis) can have detrimental consequences to immune function, such as impairments in phagocytic function, cytokine production, complement system activation, and T and B lymphocyte function (164). Further, data from the first National Health and Nutrition Examination Survey (NHANES), a U.S. national survey, indicate that elevated iron levels may be a risk factor for cancer and death, especially in men (167). For men and women combined, there were significant trends for increasing risk of cancer and mortality with increasing transferrin saturation, with risks being higher in those with transferrin saturation >40% compared to ≤30% (167).
Despite the critical functions of iron in the immune system, the nature of the relationship between iron deficiency and susceptibility to infection, especially with respect to malaria, remains controversial. High-dose iron supplementation of children residing in the tropics has been associated with increased risk of clinical malaria and other infections, such as pneumonia. Studies in cell cultures and animals suggest that the survival of infectious agents that spend part of their life cycle within host cells, such as plasmodia (malaria) and mycobacteria (tuberculosis), may be enhanced by iron therapy. Controlled clinical studies are needed to determine the appropriate use of iron supplementation in regions where malaria is common, as well as in the presence of infectious diseases, such as HIV, tuberculosis, and typhoid (168).
Copper is a critical functional component of a number of essential enzymes known as cuproenzymes (see the separate article on Copper). The mineral plays an important role in the development and maintenance of immune system function, but the exact mechanism of its action is not yet known. Copper deficiency results in neutropenia, an abnormally low number of neutrophils (169), which may increase one’s susceptibility to infection. Adverse effects of insufficient copper on immune function appear most pronounced in infants. Infants with Menkes disease, a genetic disorder that results in severe copper deficiency, suffer from frequent and severe infections (170, 171). In a study of 11 malnourished infants with evidence of copper deficiency, the ability of certain white blood cells to engulf pathogens increased significantly after one month of copper supplementation (172).
Immune effects have also been observed in adults with low intake of dietary copper. In one study, 11 men on a low-copper diet (0.66 mg copper/day for 24 days and 0.38 mg/day for another 40 days) showed a reduced proliferation response when white blood cells, called mononuclear cells, were isolated from blood and presented with an immune challenge in cell culture (173). While it is known that severe copper deficiency has adverse effects on immune function, the effects of marginal copper deficiency in humans are not yet clear (174). However, long-term high intakes of copper can result in adverse effects on immune function (175).
Probiotics are usually defined as live microorganisms that, when administered in sufficient amounts, benefit the overall health of the host (176). Common examples belong to the Lactobacilli and Bifidobacteria species; these probiotics are consumed in yogurt and other fermented foods. Ingested probiotics that survive digestion can transiently inhabit the lower part of the gastrointestinal tract (177). Here, they can modulate immune functions by interacting with various receptors on intestinal epithelial cells and other gut-associated immune cells, including dendritic cells and M-cells (178). Immune modulation requires regular consumption because probiotics have not been shown to permanently alter intestinal microflora (179). Probiotics have been shown to benefit both innate and adaptive immune responses of the host (180). For example, probiotics can strengthen the gut epithelial barrier—an important innate defense—through a number of ways, such as by inhibiting apoptosis and promoting the survival of intestinal epithelial cells (181). Probiotics can also stimulate the production of antibodies and T lymphocytes, which are critical in the adaptive immune response (180). Several immune effects of probiotics are mediated through altering cell-signaling cascades that modify cytokine and other protein expression (181). However, probiotics exert diverse effects on the immune system that are dependent not only on the specific strain but also on the dose, route, and frequency of delivery (182). Probiotics may have utility in the prevention of inflammatory bowel disorders, diarrheal diseases, allergic diseases, gastrointestinal and other types of infections, and certain cancers. However, more clinical research is needed in order to elucidate the health effects of probiotics (180).
Overnutrition is a form of malnutrition where nutrients are supplied in excess of the body’s needs. Overnutrition can create an imbalance between energy intake and energy expenditure and lead to excessive energy storage, resulting in obesity (15). Obesity is a major public health problem worldwide, especially in industrialized nations. Obese individuals are at increased risk of morbidity from a number of chronic diseases, including hypertension and cardiovascular diseases, type 2 diabetes, liver and gallbladder disease, osteoarthritis, sleep apnea, and certain cancers (183). Obesity has also been linked to increased risk of mortality (184).
Overnutrition and obesity have been shown to alter immunocompetence. Obesity is associated with macrophage infiltration of adipose tissue; macrophage accumulation in adipose tissue is directly proportional to the degree of obesity (185). Studies in mouse models of genetic and high-fat diet-induced obesity have documented a marked up-regulation in expression of inflammation and macrophage-specific genes in white adipose tissue (186). In fact, obesity is characterized by chronic, low-grade inflammation, and inflammation is thought to be an important contributor in the pathogenesis of insulin resistance—a condition that is strongly linked to obesity. Adipose tissue secretes fatty acids and other molecules, including various hormones and cytokines (called adipocytokines or adipokines), that trigger inflammatory processes (185). Leptin is one such hormone and adipokine that plays a key role in the regulation of food intake, body weight, and energy homeostasis (187, 188). Leptin is secreted from adipose tissue and circulates in direct proportion to the amount of fat stores. Normally, higher levels of circulating leptin suppress appetite and thereby lead to a reduction in food intake (189). Leptin has a number of other functions as well, such as modulation of inflammatory responses and aspects of humoral and cell-mediated responses of the adaptive immune system (187, 190). Specific effects of leptin, elucidated in animal and in vitro studies, include the promotion of phagocytic function of immune cells; stimulation of pro-inflammatory cytokine production; and regulation of neutrophil, natural killer (NK) cell, and dendritic cell functions (reviewed in 190). Leptin also affects aspects of cell-mediated immunity; for example, leptin promotes T helper (Th)1 immune responses and thus may have implications in the development of autoimmune disease (191). Th1 cells are primarily involved in activating macrophages and inflammatory responses (12). Obese individuals have been reported to have higher plasma leptin concentrations compared to lean individuals. However, in the obese, the elevated leptin signal is not associated with the normal responses of reduced food intake and increased energy expenditure, suggesting obesity is associated with a state of leptin resistance. Leptin resistance has been documented in mouse models of obesity, but more research is needed to better understand leptin resistance in human obesity (189).
Obese individuals may exhibit increased susceptibility to various infections. Some epidemiological studies have shown that obese patients have a higher incidence of postoperative and other nosocomial infections compared with patients of normal weight (192, 193; reviewed in 194). Obesity has been linked to poor wound healing and increased occurrence of skin infections (195-197). A higher body mass index (BMI) may also be associated with increased susceptibility to respiratory, gastrointestinal, liver, and biliary infections (reviewed in 194). In obesity, the increased vulnerability, severity, or complications of certain infections may be related to a number of factors, such as select micronutrient deficiencies. For example, one study in obese children and adolescents associated impairments in cell-mediated immunity with deficiencies in zinc and iron (198). Deficiencies or inadequacies of other micronutrients, including the B vitamins and vitamins A, C, D, and E, have also been associated with obesity (41). Overall, immune responses appear to be compromised in obesity, but more research is needed to clarify the relationship between obesity and infection-related morbidity and mortality.
Written in August 2010 by:
Victoria J. Drake, Ph.D.
Linus Pauling Institute
Oregon State University
Reviewed in August 2010 by:
Adrian F. Gombart, Ph.D.
Department of Biochemistry and Biophysics
Principal Investigator, Linus Pauling Institute
Oregon State University
Reviewed in August 2010 by:
Malcolm B. Lowry, Ph.D.
Department of Microbiology
Oregon State University
This article was underwritten, in part, by a grant from
Bayer Consumer Care AG, Basel, Switzerland.
Last updated 9/2/10 Copyright 2010-2014 Linus Pauling Institute
The Linus Pauling Institute Micronutrient Information Center provides scientific information on the health aspects of dietary factors and supplements, foods, and beverages for the general public. The information is made available with the understanding that the author and publisher are not providing medical, psychological, or nutritional counseling services on this site. The information should not be used in place of a consultation with a competent health care or nutrition professional.
The information on dietary factors and supplements, foods, and beverages contained on this Web site does not cover all possible uses, actions, precautions, side effects, and interactions. It is not intended as nutritional or medical advice for individual problems. Liability for individual actions or omissions based upon the contents of this site is expressly disclaimed.
Thank you for signing up for the LPI Research Newsletter; this newsletter is available at: http://lpi.oregonstate.edu/nswltrmain.html |
Series of chemical reactions in the cell by which amino acids, lined up in the order specified by the corresponding gene, are connected to form a molecular chain, the polypeptide, which will then adopt the three-dimensional shape characteristic of a protein (known as protein folding).
Before a protein can be made, the corresponding gene (encoded in DNA) needs to be transcribed into RNA (see transcription). The resulting messenger RNA (mRNA) may be edited before its translation into an amino acid sequence. Protein biosynthesis as such occurs on the ribosome, a highly complex particle of RNA and proteins found in all organisms. There are separate mechanisms for the beginning (initiation), continuation (elongation), and termination of protein synthesis, each requiring specific sets of protein factors – the initiation, elongation, and release factors respectively. The ensemble of the ribosome with all associated factors and RNAs is called the translational apparatus.
A set of 20 standard amino acids is used in the synthesis of virtually all proteins. Additional amino acids, such as selenocysteine, can be incorporated with the help of special mechanisms.
Amino acids can only take part in protein synthesis if they are attached to a specific transfer RNA, or tRNA, by a specific set of enzymes, the tRNA synthetases. The tRNA is at the heart of the translation of the three-letter code of the nucleic acids DNA and RNA into the amino acid sequence of a protein, as specified by the genetic code. It has an L-shaped structure binding the amino acid at one arm and recognizing the corresponding three-letter codon with the other.
The ribosome has three binding sites for tRNAs. Each tRNA charged with an amino acid first comes into the A (acceptor site), while the tRNA bound to the last amino acid that has been added to the chain is located in the P (peptidyl) site. The third site is the E (exit) site.
In the course of the elongation cycle, the ribosome transfers the growing polypeptide chain from the P-bound tRNA onto the new amino acid in the A site, thus creating a new polypeptide bond. This is the only catalytic activity of the ribosome. Then, the now empty tRNA in the P site moves on to the E site, and the tRNA carrying the extended chain moves into the P site, so the cycle can be repeated.
The growing polypeptide chain is threaded through a tunnel in the ribosome before it emerges.
In bacteria and Archaea, transcription, translation, and protein folding can occur in a production-line style, such that a messenger RNA still being synthesized can already be translated, and a polypeptide chain emerging from the ribosome can already undergo folding and interact with molecular chaperones assisting their folding and assembly.
In eukaryotes, however, transcription is located in the nucleus, yet protein synthesis occurs in the cytoplasm and on the membranes of the endoplasmatic reticulum. Thus, messenger RNA needs to be exported from the nucleus and there is a time lag between transcription and translation.
All proteins and some shorter peptides are produced on ribosomes as described here. However, some short peptides are produced by multi-enzyme complexes that are completely independent of the ribosome.
RNA and protein synthesis
Proteins are formed by a directed condensation of a sequence of 20 amino acids. The information for the sequence of amino acids in a protein is...
a relatively small RNA that transfers a particular amino acid to a growing polypeptide chain at the ribosomal site of protein synthesis during trans
The process of decoding a strand of mRNA, thereby producing a protein based on the code. This process requires ribosomes (which are composed of rRNA |
The density (more precisely, the volumetric mass density; also known as specific mass), of a substance is its mass per unit volume. The symbol most often used for density is ρ (the lower case Greek letter rho), although the Latin letter D can also be used. Mathematically, density is defined as mass divided by volume:
where ρ is the density, m is the mass, and V is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume, although this is scientifically inaccurate – this quantity is more specifically called specific weight.
For a pure substance the density has the same numerical value as its mass concentration. Different materials usually have different densities, and density may be relevant to buoyancy, purity and packaging. Osmium and iridium are the densest known elements at standard conditions for temperature and pressure but certain chemical compounds may be denser.
To simplify comparisons of density across different systems of units, it is sometimes replaced by the dimensionless quantity "relative density" or "specific gravity", i.e. the ratio of the density of the material to that of a standard material, usually water. Thus a relative density less than one means that the substance floats in water.
The density of a material varies with temperature and pressure. This variation is typically small for solids and liquids but much greater for gases. Increasing the pressure on an object decreases the volume of the object and thus increases its density. Increasing the temperature of a substance (with a few exceptions) decreases its density by increasing its volume. In most materials, heating the bottom of a fluid results in convection of the heat from the bottom to the top, due to the decrease in the density of the heated fluid. This causes it to rise relative to more dense unheated material.
The reciprocal of the density of a substance is occasionally called its specific volume, a term sometimes used in thermodynamics. Density is an intensive property in that increasing the amount of a substance does not increase its density; rather it increases its mass.
In a well-known but probably apocryphal tale, Archimedes was given the task of determining whether King Hiero's goldsmith was embezzling gold during the manufacture of a golden wreath dedicated to the gods and replacing it with another, cheaper alloy. Archimedes knew that the irregularly shaped wreath could be crushed into a cube whose volume could be calculated easily and compared with the mass; but the king did not approve of this. Baffled, Archimedes is said to have taken an immersion bath and observed from the rise of the water upon entering that he could calculate the volume of the gold wreath through the displacement of the water. Upon this discovery, he leapt from his bath and ran naked through the streets shouting, "Eureka! Eureka!" (Εύρηκα! Greek "I have found it"). As a result, the term "eureka" entered common parlance and is used today to indicate a moment of enlightenment.
The story first appeared in written form in Vitruvius' books of architecture, two centuries after it supposedly took place. Some scholars have doubted the accuracy of this tale, saying among other things that the method would have required precise measurements that would have been difficult to make at the time.
From the equation for density (ρ = m/V), mass density has units of mass divided by volume. As there are many units of mass and volume covering many different magnitudes there are a large number of units for mass density in use. The SI unit of kilogram per cubic metre (kg/m3) and the cgs unit of gram per cubic centimetre (g/cm3) are probably the most commonly used units for density. One g/cm3 is equal to one thousand kg/m3. One cubic centimetre (abbreviation cc) is equal to one millilitre. In industry, other larger or smaller units of mass and or volume are often more practical and US customary units may be used. See below for a list of some of the most common units of density.
Measurement of density
A number of techniques as well as standards exist for the measurement of density of materials. Such techniques include the use of a hydrometer (a buoyancy method for liquids), Hydrostatic balance (a buoyancy method for liquids and solids), immersed body method (a buoyancy method for liquids), pycnometer (liquids and solids), air comparison pycnometer (solids), oscillating densitometer (liquids), as well as pour and tap (solids). However, each individual method or technique measures different types of density (e.g. bulk density, skeletal density, etc.), and therefore it is necessary to have an understanding of the type of density being measured as well as the type of material in question.
The density at all points of a homogeneous object equals its total mass divided by its total volume. The mass is normally measured with a scale or balance; the volume may be measured directly (from the geometry of the object) or by the displacement of a fluid. To determine the density of a liquid or a gas, a hydrometer, a dasymeter or a Coriolis flow meter may be used, respectively. Similarly, hydrostatic weighing uses the displacement of water due to a submerged object to determine the density of the object.
If the body is not homogeneous, then its density varies between different regions of the object. In that case the density around any given location is determined by calculating the density of a small volume around that location. In the limit of an infinitesimal volume the density of an inhomogeneous object at a point becomes: , where is an elementary volume at position . The mass of the body then can be expressed as
In practice, bulk materials such as sugar, sand, or snow contain voids. Many materials exist in nature as flakes, pellets, or granules.
Voids are regions which contain something other than the considered material. Commonly the void is air, but it could also be vacuum, liquid, solid, or a different gas or gaseous mixture.
The bulk volume of a material—inclusive of the void fraction—is often obtained by a simple measurement (e.g. with a calibrated measuring cup) or geometrically from known dimensions.
Mass divided by bulk volume determines bulk density. This is not the same thing as volumetric mass density.
To determine volumetric mass density, one must first discount the volume of the void fraction. Sometimes this can be determined by geometrical reasoning. For the close-packing of equal spheres the non-void fraction can be at most about 74%. It can also be determined empirically. Some bulk materials, however, such as sand, have a variable void fraction which depends on how the material is agitated or poured. It might be loose or compact, with more or less air space depending on handling.
In practice, the void fraction is not necessarily air, or even gaseous. In the case of sand, it could be water, which can be advantageous for measurement as the void fraction for sand saturated in water—once any air bubbles are thoroughly driven out—is potentially more consistent than dry sand measured with an air void.
In the case of non-compact materials, one must also take care in determining the mass of the material sample. If the material is under pressure (commonly ambient air pressure at the earth's surface) the determination of mass from a measured sample weight might need to account for buoyancy effects due to the density of the void constituent, depending on how the measurement was conducted. In the case of dry sand, sand is so much denser than air that the buoyancy effect is commonly neglected (less than one part in one thousand).
Mass change upon displacing one void material with another while maintaining constant volume can be used to estimate the void fraction, if the difference in density of the two voids materials is reliably known.
Changes of density
In general, density can be changed by changing either the pressure or the temperature. Increasing the pressure always increases the density of a material. Increasing the temperature generally decreases the density, but there are notable exceptions to this generalization. For example, the density of water increases between its melting point at 0 °C and 4 °C; similar behavior is observed in silicon at low temperatures.
The effect of pressure and temperature on the densities of liquids and solids is small. The compressibility for a typical liquid or solid is 10−6 bar−1 (1 bar = 0.1 MPa) and a typical thermal expansivity is 10−5 K−1. This roughly translates into needing around ten thousand times atmospheric pressure to reduce the volume of a substance by one percent. (Although the pressures needed may be around a thousand times smaller for sandy soil and some clays.) A one percent expansion of volume typically requires a temperature increase on the order of thousands of degrees Celsius.
In contrast, the density of gases is strongly affected by pressure. The density of an ideal gas is
where M is the molar mass, P is the pressure, R is the universal gas constant, and T is the absolute temperature. This means that the density of an ideal gas can be doubled by doubling the pressure, or by halving the absolute temperature.
In the case of volumic thermal expansion at constant pressure and small intervals of temperature the temperature dependence of density is :
where is the density at a reference temperature, is the thermal expansion coefficient of the material at temperatures close to .
Density of solutions
The density of a solution is the sum of mass (massic) concentrations of the components of that solution.
Mass (massic) concentration of each given component ρi in a solution sums to density of the solution.
Expressed as a function of the densities of pure components of the mixture and their volume participation, it allows the determination of excess molar volumes:
provided that there is no interaction between the components.
Knowing the relation between excess volumes and activity coefficients of the components, one can determine the activity coefficients.
- Selected chemical elements are listed here. For the densities of all chemical elements, see List of chemical elements
|Material||ρ (kg/m3)[note 1]||Notes|
|Metallic microlattice||0.9||[note 2]|
|Air||1.2||At sea level|
|Tungsten hexafluoride||12.4||One of the heaviest known gases at standard conditions|
|Liquid hydrogen||70||At approx. −255 °C|
|Ice||916.7||At temperature < 0 °C|
|Water (fresh)||1,000||At 4 °C, the temperature of its maximum density|
|Liquid oxygen||1,141||At approx. −219 °C|
|Plastics||1,175||Approx.; for polypropylene and PETE/PVC|
|Diiodomethane||3,325||Liquid at room temperature|
|Interstellar medium||1×10−19||Assuming 90% H, 10% He; variable T|
|The Earth||5,515||Mean density.|
|Earth's inner core||13,000||Approx., as listed in Earth.|
|The core of the Sun||33,000–160,000||Approx.|
|Super-massive black hole||9×105||Density of a 4.5-million-solar-mass black hole|
Event horizon radius is 13.5 million km.
|White dwarf star||2.1×109||Approx.|
|Atomic nuclei||2.3×1017||Does not depend strongly on size of nucleus|
|Stellar-mass black hole||1×1018||Density of a 4-solar-mass black hole|
Event horizon radius is 12 km.
|Temp. (°C)[note 1]||Density (kg/m3)|
|T (°C)||ρ (kg/m3)|
Molar volumes of liquid and solid phase of elements
The SI unit for density is:
- kilogram per cubic metre (kg/m3)
The litre and metric tons are not part of the SI, but are acceptable for use with it, leading to the following units:
- kilogram per litre (kg/L)
- gram per millilitre (g/mL)
- metric ton per cubic metre (t/m3)
Densities using the following metric units all have exactly the same numerical value, one thousandth of the value in (kg/m3). Liquid water has a density of about 1 kg/dm3, making any of these SI units numerically convenient to use as most solids and liquids have densities between 0.1 and 20 kg/dm3.
- kilogram per cubic decimetre (kg/dm3)
- gram per cubic centimetre (g/cm3)
- 1 g/cm3 = 1000 kg/m3
- megagram (metric ton) per cubic metre (Mg/m3)
In US customary units density can be stated in:
- Avoirdupois ounce per cubic inch (1 g/cm3 ≈ 0.578036672 oz/cu in)
- Avoirdupois ounce per fluid ounce (1 g/cm3 ≈ 1.04317556 oz/US fl oz = 1.04317556 lb/US fl pint)
- Avoirdupois pound per cubic inch (1 g/cm3 ≈ 0.036127292 lb/cu in)
- pound per cubic foot (1 g/cm3 ≈ 62.427961 lb/cu ft)
- pound per cubic yard (1 g/cm3 ≈ 1685.5549 lb/cu yd)
- pound per US liquid gallon (1 g/cm3 ≈ 8.34540445 lb/US gal)
- pound per US bushel (1 g/cm3 ≈ 77.6888513 lb/bu)
- slug per cubic foot
Imperial units differing from the above (as the Imperial gallon and bushel differ from the US units) in practice are rarely used, though found in older documents. The Imperial gallon was based on the concept that an Imperial fluid ounce of water would have a mass of one Avoirdupois ounce, and indeed 1 g/cm3 ≈ 1.00224129 ounces per Imperial fluid ounce = 10.0224129 pounds per Imperial gallon. The density of precious metals could conceivably be based on Troy ounces and pounds, a possible cause of confusion.
- List of elements by density
- Air density
- Area density
- Bulk density
- Charge density
- Density prediction by the Girolami method
- Energy density
- Lighter than air
- Linear density
- Number density
- Orthobaric density
- Paper density
- Specific weight
- Spice (oceanography)
- Standard temperature and pressure
- The National Aeronautic and Atmospheric Administration's Glenn Research Center. "Gas Density Glenn research Center". grc.nasa.gov. Archived from the original on April 14, 2013. Retrieved April 9, 2013.
- "Density definition in Oil Gas Glossary". Oilgasglossary.com. Archived from the original on August 5, 2010. Retrieved September 14, 2010.
- Archimedes, A Gold Thief and Buoyancy Archived August 27, 2007, at the Wayback Machine – by Larry "Harris" Taylor, Ph.D.
- Vitruvius on Architecture, Book IX, paragraphs 9–12, translated into English and in the original Latin.
- "EXHIBIT: The First Eureka Moment". Science. 305 (5688): 1219e. 2004. doi:10.1126/science.305.5688.1219e.
- Fact or Fiction?: Archimedes Coined the Term "Eureka!" in the Bath, Scientific American, December 2006.
- "OECD Test Guideline 109 on measurement of density".
- New carbon nanotube struructure aerographite is lightest material champ Archived October 17, 2013, at the Wayback Machine. Phys.org (July 13, 2012). Retrieved on July 14, 2012.
- Aerographit: Leichtestes Material der Welt entwickelt – SPIEGEL ONLINE Archived October 17, 2013, at the Wayback Machine. Spiegel.de (July 11, 2012). Retrieved on July 14, 2012.
- "Re: which is more bouyant [sic] styrofoam or cork". Madsci.org. Archived from the original on February 14, 2011. Retrieved September 14, 2010.
- Raymond Serway; John Jewett (2005), Principles of Physics: A Calculus-Based Text, Cengage Learning, p. 467, ISBN 0-534-49143-X, archived from the original on May 17, 2016
- "Wood Densities". www.engineeringtoolbox.com. Archived from the original on October 20, 2012. Retrieved October 15, 2012.
- "Density of Wood". www.simetric.co.uk. Archived from the original on October 26, 2012. Retrieved October 15, 2012.
- CRC Press Handbook of tables for Applied Engineering Science, 2nd Edition, 1976, Table 1-59
- glycerol composition at Archived February 28, 2013, at the Wayback Machine. Physics.nist.gov. Retrieved on July 14, 2012.
- Hugh D. Young; Roger A. Freedman. University Physics with Modern Physics Archived April 30, 2016, at the Wayback Machine. Addison-Wesley; 2012. ISBN 978-0-321-69686-1. p. 374.
- Density of the Earth, wolframalpha.com, archived from the original on October 17, 2013
- Density of Earth's core, wolframalpha.com, archived from the original on October 17, 2013
- Density of the Sun's core, wolframalpha.com, archived from the original on October 17, 2013
- Extreme Stars: White Dwarfs & Neutron Stars Archived September 25, 2007, at the Wayback Machine, Jennifer Johnson, lecture notes, Astronomy 162, Ohio State University. Accessed: May 3, 2007.
- Nuclear Size and Density Archived July 6, 2009, at the Wayback Machine, HyperPhysics, Georgia State University. Accessed: June 26, 2009.
- Encyclopædia Britannica. 8 (11th ed.). 1911. .
. The New Student's Reference Work. 1914.
- Video: Density Experiment with Oil and Alcohol
- Video: Density Experiment with Whiskey and Water
- Glass Density Calculation – Calculation of the density of glass at room temperature and of glass melts at 1000 – 1400°C
- List of Elements of the Periodic Table – Sorted by Density
- Calculation of saturated liquid densities for some components
- Field density test
- On-line calculator for densities and partial molar volumes of aqueous solutions of some common electrolytes and their mixtures, at temperatures up to 323.15 K.
- Water – Density and specific weight
- Temperature dependence of the density of water – Conversions of density units
- A delicious density experiment
- Water density calculator Water density for a given salinity and temperature.
- Liquid density calculator Select a liquid from the list and calculate density as a function of temperature.
- Gas density calculator Calculate density of a gas for as a function of temperature and pressure.
- Densities of various materials.
- Determination of Density of Solid, instructions for performing classroom experiment.
- density prediction
- density prediction |
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A java applet that simulates the sampling distribution of the mean. It allows students to explore the effect of sample size.
Independent Samples t-Test: Chips Ahoy® vs. Supermarket Brand part of CAUSE Teaching Methods:Testing Conjectures:Examples
In this hands-on activity, students count the number of chips in cookies in order to carry out an independent samples t-test to compare Chips Ahoy® cookies and a supermarket brand. It can involve discussion of randomness and independence of samples, comparing two parameters with null and alternative hypotheses, and the practical issues of counting chips in a cookie. |
Soil erosion is the denudation of the upper layer of soil. It is a form of soil degradation. This natural process is caused by the dynamic activity of erosive agents, that is, water, ice (glaciers), snow, air (wind), plants, and animals (including humans). In accordance with these agents, erosion is sometimes divided into water erosion, glacial erosion, snow erosion, wind (aeolean) erosion, zoogenic erosion and anthropogenic erosion such as tillage erosion. Soil erosion may be a slow process that continues relatively unnoticed, or it may occur at an alarming rate causing a serious loss of topsoil. The loss of soil from farmland may be reflected in reduced crop production potential, lower surface water quality and damaged drainage networks. Soil erosion could also cause sinkholes.
Human activities have increased by 10–50 times the rate at which erosion is occurring world-wide. Excessive (or accelerated) erosion causes both "on-site" and "off-site" problems. On-site impacts include decreases in agricultural productivity and (on natural landscapes) ecological collapse, both because of loss of the nutrient-rich upper soil layers. In some cases, the eventual end result is desertification. Off-site effects include sedimentation of waterways and eutrophication of water bodies, as well as sediment-related damage to roads and houses. Water and wind erosion are the two primary causes of land degradation; combined, they are responsible for about 84% of the global extent of degraded land, making excessive erosion one of the most significant environmental problems worldwide.
Intensive agriculture, deforestation, roads, acid rains, anthropogenic climate change and urban sprawl are amongst the most significant human activities in regard to their effect on stimulating erosion. However, there are many prevention and remediation practices that can curtail or limit erosion of vulnerable soils.
Rainfall, and the surface runoff which may result from rainfall, produces four main types of soil erosion: splash erosion, sheet erosion, rill erosion, and gully erosion. Splash erosion is generally seen as the first and least severe stage in the soil erosion process, which is followed by sheet erosion, then rill erosion and finally gully erosion (the most severe of the four).
In splash erosion, the impact of a falling raindrop creates a small crater in the soil, ejecting soil particles. The distance these soil particles travel can be as much as 0.6 m (two feet) vertically and 1.5 m (five feet) horizontally on level ground.
If the soil is saturated, or if the rainfall rate is greater than the rate at which water can infiltrate into the soil, surface runoff occurs. If the runoff has sufficient flow energy, it will transport loosened soil particles (sediment) down the slope. Sheet erosion is the transport of loosened soil particles by overland flow.
Rill erosion refers to the development of small, ephemeral concentrated flow paths which function as both sediment source and sediment delivery systems for erosion on hillslopes. Generally, where water erosion rates on disturbed upland areas are greatest, rills are active. Flow depths in rills are typically of the order of a few centimeters (about an inch) or less and along-channel slopes may be quite steep. This means that rills exhibit hydraulic physics very different from water flowing through the deeper wider channels of streams and rivers.
Gully erosion occurs when runoff water accumulates and rapidly flows in narrow channels during or immediately after heavy rains or melting snow, removing soil to a considerable depth. Another cause of gully erosion is grazing, which often results in ground compaction. Because the soil is exposed, it loses the ability to absorb excess water, and erosion can develop in susceptible areas.
Further information on water's erosive ability: Hydraulic action
Valley or stream erosion occurs with continued water flow along a linear feature. The erosion is both downward, deepening the valley, and headward, extending the valley into the hillside, creating head cuts and steep banks. In the earliest stage of stream erosion, the erosive activity is dominantly vertical, the valleys have a typical V cross-section and the stream gradient is relatively steep. When some base level is reached, the erosive activity switches to lateral erosion, which widens the valley floor and creates a narrow floodplain. The stream gradient becomes nearly flat, and lateral deposition of sediments becomes important as the stream meanders across the valley floor. In all stages of stream erosion, by far the most erosion occurs during times of flood, when more and faster-moving water is available to carry a larger sediment load. In such processes, it is not the water alone that erodes: suspended abrasive particles, pebbles and boulders can also act erosively as they traverse a surface, in a process known as traction.
Bank erosion is the wearing away of the banks of a stream or river. This is distinguished from changes on the bed of the watercourse, which is referred to as scour. Erosion and changes in the form of river banks may be measured by inserting metal rods into the bank and marking the position of the bank surface along the rods at different times.
Thermal erosion is the result of melting and weakening permafrost due to moving water. It can occur both along rivers and at the coast. Rapid river channel migration observed in the Lena River of Siberia is due to thermal erosion, as these portions of the banks are composed of permafrost-cemented non-cohesive materials. Much of this erosion occurs as the weakened banks fail in large slumps. Thermal erosion also affects the Arctic coast, where wave action and near-shore temperatures combine to undercut permafrost bluffs along the shoreline and cause them to fail. Annual erosion rates along a 100-kilometre (62-mile) segment of the Beaufort Sea shoreline averaged 5.6 metres (18 feet) per year from 1955 to 2002.
At extremely high flows, kolks, or vortices are formed by large volumes of rapidly rushing water. Kolks cause extreme local erosion, plucking bedrock and creating pothole-type geographical features called Rock-cut basins. Examples can be seen in the flood regions result from glacial Lake Missoula, which created the channeled scablands in the Columbia Basin region of eastern Washington.
Main article: Aeolian processes
Wind erosion is a major geomorphological force, especially in arid and semi-arid regions. It is also a major source of land degradation, evaporation, desertification, harmful airborne dust, and crop damage—especially after being increased far above natural rates by human activities such as deforestation, urbanization, and agriculture.
Wind erosion is of two primary varieties: deflation, where the wind picks up and carries away loose particles; and abrasion, where surfaces are worn down as they are struck by airborne particles carried by wind. Deflation is divided into three categories: (1) surface creep, where larger, heavier particles slide or roll along the ground; (2) saltation, where particles are lifted a short height into the air, and bounce and saltate across the surface of the soil; and (3) suspension, where very small and light particles are lifted into the air by the wind, and are often carried for long distances. Saltation is responsible for the majority (50–70%) of wind erosion, followed by suspension (30–40%), and then surface creep (5–25%). Silty soils tend to be the most affected by wind erosion; silt particles are relatively easily detached and carried away.
Wind erosion is much more severe in arid areas and during times of drought. For example, in the Great Plains, it is estimated that soil loss due to wind erosion can be as much as 6100 times greater in drought years than in wet years.
Mass movement is the downward and outward movement of rock and sediments on a sloped surface, mainly due to the force of gravity.
Mass movement is an important part of the erosional process, and is often the first stage in the breakdown and transport of weathered materials in mountainous areas. It moves material from higher elevations to lower elevations where other eroding agents such as streams and glaciers can then pick up the material and move it to even lower elevations. Mass-movement processes are always occurring continuously on all slopes; some mass-movement processes act very slowly; others occur very suddenly, often with disastrous results. Any perceptible down-slope movement of rock or sediment is often referred to in general terms as a landslide. However, landslides can be classified in a much more detailed way that reflects the mechanisms responsible for the movement and the velocity at which the movement occurs. One of the visible topographical manifestations of a very slow form of such activity is a scree slope.
Slumping happens on steep hillsides, occurring along distinct fracture zones, often within materials like clay that, once released, may move quite rapidly downhill. They will often show a spoon-shaped isostatic depression, in which the material has begun to slide downhill. In some cases, the slump is caused by water beneath the slope weakening it. In many cases it is simply the result of poor engineering along highways where it is a regular occurrence.
Surface creep is the slow movement of soil and rock debris by gravity which is usually not perceptible except through extended observation. However, the term can also describe the rolling of dislodged soil particles 0.5 to 1.0 mm (0.02 to 0.04 in) in diameter by wind along the soil surface.
Tillage erosion is a form of soil erosion occurring in cultivated fields due to the movement of soil by tillage. There is growing evidence that tillage erosion is a major soil erosion process in agricultural lands, surpassing water and wind erosion in many fields all around the world, especially on sloping and hilly lands A signature spatial pattern of soil erosion shown in many water erosion handbooks and pamphlets, the eroded hilltops, is actually caused by tillage erosion as water erosion mainly causes soil losses in the midslope and lowerslope segments of a slope, not the hilltops. Tillage erosion results in soil degradation, which can lead to significant reduction in crop yield and, therefore, economic losses for the farm.
The amount and intensity of precipitation is the main climatic factor governing soil erosion by water. The relationship is particularly strong if heavy rainfall occurs at times when, or in locations where, the soil's surface is not well protected by vegetation. This might be during periods when agricultural activities leave the soil bare, or in semi-arid regions where vegetation is naturally sparse. Wind erosion requires strong winds, particularly during times of drought when vegetation is sparse and soil is dry (and so is more erodible). Other climatic factors such as average temperature and temperature range may also affect erosion, via their effects on vegetation and soil properties. In general, given similar vegetation and ecosystems, areas with more precipitation (especially high-intensity rainfall), more wind, or more storms are expected to have more erosion.
In some areas of the world (e.g. the mid-western USA), rainfall intensity is the primary determinant of erosivity, with higher intensity rainfall generally resulting in more soil erosion by water. The size and velocity of rain drops is also an important factor. Larger and higher-velocity rain drops have greater kinetic energy, and thus their impact will displace soil particles by larger distances than smaller, slower-moving rain drops.
In other regions of the world (e.g. western Europe), runoff and erosion result from relatively low intensities of stratiform rainfall falling onto previously saturated soil. In such situations, rainfall amount rather than intensity is the main factor determining the severity of soil erosion by water.
The composition, moisture, and compaction of soil are all major factors in determining the erosivity of rainfall. Sediments containing more clay tend to be more resistant to erosion than those with sand or silt, because the clay helps bind soil particles together. Soil containing high levels of organic materials are often more resistant to erosion, because the organic materials coagulate soil colloids and create a stronger, more stable soil structure. The amount of water present in the soil before the precipitation also plays an important role, because it sets limits on the amount of water that can be absorbed by the soil (and hence prevented from flowing on the surface as erosive runoff). Wet, saturated soils will not be able to absorb as much rainwater, leading to higher levels of surface runoff and thus higher erosivity for a given volume of rainfall. Soil compaction also affects the permeability of the soil to water, and hence the amount of water that flows away as runoff. More compacted soils will have a larger amount of surface runoff than less compacted soils.
See also: Vegetation and slope stability
Vegetation acts as an interface between the atmosphere and the soil. It increases the permeability of the soil to rainwater, thus decreasing runoff. It shelters the soil from winds, which results in decreased wind erosion, as well as advantageous changes in microclimate. The roots of the plants bind the soil together, and interweave with other roots, forming a more solid mass that is less susceptible to both water and wind erosion. The removal of vegetation increases the rate of surface erosion.
The topography of the land determines the velocity at which surface runoff will flow, which in turn determines the erosivity of the runoff. Longer, steeper slopes (especially those without adequate vegetative cover) are more susceptible to very high rates of erosion during heavy rains than shorter, less steep slopes. Steeper terrain is also more prone to mudslides, landslides, and other forms of gravitational erosion processes.
Unsustainable agricultural practices increase rates of erosion by one to two orders of magnitude over the natural rate and far exceed replacement by soil production. The tillage of agricultural lands, which breaks up soil into finer particles, is one of the primary factors. The problem has been exacerbated in modern times, due to mechanized agricultural equipment that allows for deep plowing, which severely increases the amount of soil that is available for transport by water erosion. Others include mono-cropping, farming on steep slopes, pesticide and chemical fertilizer usage (which kill organisms that bind soil together), row-cropping, and the use of surface irrigation. A complex overall situation with respect to defining nutrient losses from soils, could arise as a result of the size selective nature of soil erosion events. Loss of total phosphorus, for instance, in the finer eroded fraction is greater relative to the whole soil. Extrapolating this evidence to predict subsequent behaviour within receiving aquatic systems, the reason is that this more easily transported material may support a lower solution P concentration compared to coarser sized fractions. Tillage also increases wind erosion rates, by dehydrating the soil and breaking it up into smaller particles that can be picked up by the wind. Exacerbating this is the fact that most of the trees are generally removed from agricultural fields, allowing winds to have long, open runs to travel over at higher speeds. Heavy grazing reduces vegetative cover and causes severe soil compaction, both of which increase erosion rates.
In an undisturbed forest, the mineral soil is protected by a layer of leaf litter and an humus that cover the forest floor. These two layers form a protective mat over the soil that absorbs the impact of rain drops. They are porous and highly permeable to rainfall, and allow rainwater to slow percolate into the soil below, instead of flowing over the surface as runoff. The roots of the trees and plants hold together soil particles, preventing them from being washed away. The vegetative cover acts to reduce the velocity of the raindrops that strike the foliage and stems before hitting the ground, reducing their kinetic energy. However it is the forest floor, more than the canopy, that prevents surface erosion. The terminal velocity of rain drops is reached in about 8 metres (26 feet). Because forest canopies are usually higher than this, rain drops can often regain terminal velocity even after striking the canopy. However, the intact forest floor, with its layers of leaf litter and organic matter, is still able to absorb the impact of the rainfall.
Deforestation causes increased erosion rates due to exposure of mineral soil by removing the humus and litter layers from the soil surface, removing the vegetative cover that binds soil together, and causing heavy soil compaction from logging equipment. Once trees have been removed by fire or logging, infiltration rates become high and erosion low to the degree the forest floor remains intact. Severe fires can lead to significant further erosion if followed by heavy rainfall.
Globally one of the largest contributors to erosive soil loss in the year 2006 is the slash and burn treatment of tropical forests. In a number of regions of the earth, entire sectors of a country have been rendered unproductive. For example, on the Madagascar high central plateau, comprising approximately ten percent of that country's land area, virtually the entire landscape is sterile of vegetation, with gully erosive furrows typically in excess of 50 metres (160 ft) deep and 1 kilometre (0.6 miles) wide. Shifting cultivation is a farming system which sometimes incorporates the slash and burn method in some regions of the world. This degrades the soil and causes the soil to become less and less fertile.
Human Impact has major effects on erosion processes—first by denuding the land of vegetative cover, altering drainage patterns, and compacting the soil during construction; and next by covering the land in an impermeable layer of asphalt or concrete that increases the amount of surface runoff and increases surface wind speeds. Much of the sediment carried in runoff from urban areas (especially roads) is highly contaminated with fuel, oil, and other chemicals. This increased runoff, in addition to eroding and degrading the land that it flows over, also causes major disruption to surrounding watersheds by altering the volume and rate of water that flows through them, and filling them with chemically polluted sedimentation. The increased flow of water through local waterways also causes a large increase in the rate of bank erosion.
Main article: Land degradation
The warmer atmospheric temperatures observed over the past decades are expected to lead to a more vigorous hydrological cycle, including more extreme rainfall events. The rise in sea levels that has occurred as a result of climate change has also greatly increased coastal erosion rates.
Studies on soil erosion suggest that increased rainfall amounts and intensities will lead to greater rates of soil erosion. Thus, if rainfall amounts and intensities increase in many parts of the world as expected, erosion will also increase, unless amelioration measures are taken. Soil erosion rates are expected to change in response to changes in climate for a variety of reasons. The most direct is the change in the erosive power of rainfall. Other reasons include: a) changes in plant canopy caused by shifts in plant biomass production associated with moisture regime; b) changes in litter cover on the ground caused by changes in both plant residue decomposition rates driven by temperature and moisture dependent soil microbial activity as well as plant biomass production rates; c) changes in soil moisture due to shifting precipitation regimes and evapo-transpiration rates, which changes infiltration and runoff ratios; d) soil erodibility changes due to decrease in soil organic matter concentrations in soils that lead to a soil structure that is more susceptible to erosion and increased runoff due to increased soil surface sealing and crusting; e) a shift of winter precipitation from non-erosive snow to erosive rainfall due to increasing winter temperatures; f) melting of permafrost, which induces an erodible soil state from a previously non-erodible one; and g) shifts in land use made necessary to accommodate new climatic regimes.
Studies by Pruski and Nearing indicated that, other factors such as land use unconsidered, it is reasonable to expect approximately a 1.7% change in soil erosion for each 1% change in total precipitation under climate change. In recent studies, there are predicted increases of rainfall erosivity by 17% in the United States, by 18% in Europe, and globally 30 to 66%
Due to the severity of its ecological effects, and the scale on which it is occurring, erosion constitutes one of the most significant global environmental problems we face today.
Water and wind erosion are now the two primary causes of land degradation; combined, they are responsible for 84% of degraded acreage.
Each year, about 75 billion tons of soil is eroded from the land—a rate that is about 13–40 times as fast as the natural rate of erosion. Approximately 40% of the world's agricultural land is seriously degraded. According to the United Nations, an area of fertile soil the size of Ukraine is lost every year because of drought, deforestation and climate change. In Africa, if current trends of soil degradation continue, the continent might be able to feed just 25% of its population by 2025, according to UNU's Ghana-based Institute for Natural Resources in Africa.
Recent modeling developments have quantified rainfall erosivity at global scale using high temporal resolution (<30 min) and high fidelity rainfall recordings. The results is an extensive global data collection effort produced the Global Rainfall Erosivity Database (GloREDa) which includes rainfall erosivity for 3,625 stations and covers 63 countries. This first ever Global Rainfall Erosivity Database was used to develop a global erosivity map at 30 arc-seconds(~1 km) based on sophisticated geostatistical process. According to a new study published in Nature Communications, almost 36 billion tons of soil is lost every year due to water, and deforestation and other changes in land use make the problem worse. The study investigates global soil erosion dynamics by means of high-resolution spatially distributed modelling (ca. 250 × 250 m cell size). The geo-statistical approach allows, for the first time, the thorough incorporation into a global soil erosion model of land use and changes in land use, the extent, types, spatial distribution of global croplands and the effects of different regional cropping systems.
The loss of soil fertility due to erosion is further problematic because the response is often to apply chemical fertilizers, which leads to further water and soil pollution, rather than to allow the land to regenerate.
Soil erosion (especially from agricultural activity) is considered to be the leading global cause of diffuse water pollution, due to the effects of the excess sediments flowing into the world's waterways. The sediments themselves act as pollutants, as well as being carriers for other pollutants, such as attached pesticide molecules or heavy metals.
The effect of increased sediments loads on aquatic ecosystems can be catastrophic. Silt can smother the spawning beds of fish, by filling in the space between gravel on the stream bed. It also reduces their food supply, and causes major respiratory issues for them as sediment enters their gills. The biodiversity of aquatic plant and algal life is reduced, and invertebrates are also unable to survive and reproduce. While the sedimentation event itself might be relatively short-lived, the ecological disruption caused by the mass die off often persists long into the future.
One of the most serious and long-running water erosion problems worldwide is in the People's Republic of China, on the middle reaches of the Yellow River and the upper reaches of the Yangtze River. From the Yellow River, over 1.6 billion tons of sediment flows into the ocean each year. The sediment originates primarily from water erosion in the Loess Plateau region of the northwest.
Soil particles picked up during wind erosion of soil are a major source of air pollution, in the form of airborne particulates—"dust". These airborne soil particles are often contaminated with toxic chemicals such as pesticides or petroleum fuels, posing ecological and public health hazards when they later land, or are inhaled/ingested.
Dust from erosion acts to suppress rainfall and changes the sky color from blue to white, which leads to an increase in red sunsets. Dust events have been linked to a decline in the health of coral reefs across the Caribbean and Florida, primarily since the 1970s. Similar dust plumes originate in the Gobi desert, which combined with pollutants, spread large distances downwind, or eastward, into North America.
See also: Erosion prediction
Monitoring and modeling of erosion processes can help people better understand the causes of soil erosion, make predictions of erosion under a range of possible conditions, and plan the implementation of preventative and restorative strategies for erosion. However, the complexity of erosion processes and the number of scientific disciplines that must be considered to understand and model them (e.g. climatology, hydrology, geology, soil science, agriculture, chemistry, physics, etc.) makes accurate modelling challenging. Erosion models are also non-linear, which makes them difficult to work with numerically, and makes it difficult or impossible to scale up to making predictions about large areas from data collected by sampling smaller plots.
The most commonly used model for predicting soil loss from water erosion is the Universal Soil Loss Equation (USLE). This was developed in the 1960s and 1970s. It estimates the average annual soil loss A on a plot-sized area as:
where R is the rainfall erosivity factor, K is the soil erodibility factor, L and S are topographic factors representing length and slope, C is the cover and management factor and P is the support practices factor.
Despite the USLE's plot-scale spatial basis, the model has often been used to estimate soil erosion on much larger areas, such as watersheds, continents, and globally. One major problem is that the USLE cannot simulate gully erosion, and so erosion from gullies is ignored in any USLE-based assessment of erosion. Yet erosion from gullies can be a substantial proportion (10–80%) of total erosion on cultivated and grazed land.
During the 50 years since the introduction of the USLE, many other soil erosion models have been developed. But because of the complexity of soil erosion and its constituent processes, all erosion models can only roughly approximate actual erosion rates when validated i.e. when model predictions are compared with real-world measurements of erosion. Thus new soil erosion models continue to be developed. Some of these remain USLE-based, e.g. the G2 model. Other soil erosion models have largely (e.g. the Water Erosion Prediction Project model) or wholly (e.g. RHEM, the Rangeland Hydrology and Erosion Model ) abandoned usage of USLE elements. Global studies continue to be based on the USLE
The most effective known method for erosion prevention is to increase vegetative cover on the land, which helps prevent both wind and water erosion. Terracing is an extremely effective means of erosion control, which has been practiced for thousands of years by people all over the world. Windbreaks (also called shelterbelts) are rows of trees and shrubs that are planted along the edges of agricultural fields, to shield the fields against winds. In addition to significantly reducing wind erosion, windbreaks provide many other benefits such as improved microclimates for crops (which are sheltered from the dehydrating and otherwise damaging effects of wind), habitat for beneficial bird species, carbon sequestration, and aesthetic improvements to the agricultural landscape. Traditional planting methods, such as mixed-cropping (instead of monocropping) and crop rotation have also been shown to significantly reduce erosion rates. Crop residues play a role in the mitigation of erosion, because they reduce the impact of raindrops breaking up the soil particles. There is a higher potential for erosion when producing potatoes than when growing cereals, or oilseed crops. Forages have a fibrous root system, which helps combat erosion by anchoring the plants to the top layer of the soil, and covering the entirety of the field, as it is a non-row crop. In tropical coastal systems, properties of mangroves have been examined as a potential means to reduce soil erosion. Their complex root structures are known to help reduce wave damage from storms and flood impacts while binding and building soils. These roots can slow down water flow, leading to the deposition of sediments and reduced erosion rates. However, in order to maintain sediment balance, adequate mangrove forest width needs to be present.
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2.1 Introduction: There are some physical quantities, which are completely described by a single number with a unit, for example; mass of a body. On the other hand, there are other quantities that need a direction specified along with the magnitude for a complete description.
The quantities which are described only via magnitudes are called Scalar quantities. For example if we say that we drive 10 miles, we are talking about the total distance traveled. Here we are talking about magnitude only (distance) i.e. a Scalar quantity.
Those quantities which are fully described by magnitude as well as direction are known as Vector quantities. For example, traveling with a velocity of 20 miles per hour due south is not the same as traveling with a velocity of 40 miles per hour due east. These quantities are Vectors and it is important to distinguish them from scalars (physical quantities described by a single number). Examples of vector quantities are forces, velocity or the position of a robot etc.
Variables that are vectors will be indicated with a boldface variable, although it is common to see vectors denoted with small arrows above the variable.
A unit vector is a vector that has a magnitude of one. A vector representing a unit vector is also boldface, and it will have a carat (^) above it to indicate the unit nature of the variable. The unit vector x, when written with a carat, is read as "x-hat" as the carat looks like a hat on the variable.
The zero vector, or null vector, is a vector with a magnitude of zero. It is written as 0.
Vectors are parallel if they have the same direction. Both components of one vector must be in the same ratio to the corresponding components of the parallel vector.
Two vectors that are parallel to each other are called ``collinear'', as they can be drawn onto the same line.
2.1.5 Anti-parallel vectors: When two vectors V1 and V2 are in opposite directions, their magnitudes being same or not, we say that they are anti-parallel. If they have the same magnitude, the relation between the two vectors is
V1 = −V2 or
V2 = −V1
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The term ‘deep-sky objects’ is used by astronomers to refer to galaxies, nebulae or star clusters, which, as the name suggests, lie well beyond the limits of our solar system.
Galaxies were originally classed as nebulae, until they were shown, by Edwin Hubble in the early 1920s (see Hubble’s Law), to be enormous collections of stars, at distances far beyond the limits of our own galaxy.
It is now estimated that the observable universe contains at least 100 billion galaxies.
Quasars are extremely luminous and highly-redshifted galaxies, visible at the furthest limits of the observable universe, the brightest of which appear as faint, star-like points of light through the largest amateur telescopes.
Charles Messier was the first to catalogue the positions of around 100 of the brightest nebulae and star clusters, in 1771. However, he did so to distinguish them from comets, for which he was hunting, in collaboration with his assistant Pierre Méchain. There are now 110 objects in the Messier Catalogue, which are assigned numbers from M1 – the Crab Nebula – to M110 – a dwarf elliptical galaxy, also known as ‘The Edward Young Star’.
The New General Catalogue (NGC), charted the positions of around 1,000 deep-sky objects, when it was first published by John Louis Emil Dreyer, in 1888. However, through subsequent editions, the NGC now contains 7,840 objects. |
In mathematics, a square root of a number a is a number y such that y2 = a, or, in other words, a number y whose square (the result of multiplying the number by itself, or y × y) is a. For example, 4 is a square root of 16 because 42 = 16.
Every non-negative real number a has a unique non-negative square root, called the principal square root, which is denoted by, where √ is called the radical sign or radix. For example, the principal square root of 9 is 3, denoted, because 32 = 3 × 3 = 9 and 3 is non-negative. The term whose root is being considered is known as the radicand. The radicand is the number or expression underneath the radical sign, in this example 9.
Every positive number a has two square roots:, which is positive, and, which is negative. Together, these two roots are denoted (see ± shorthand). Although the principal square root of a positive number is only one of its two square roots, the designation "the square root" is often used to refer to the principal square root. For positive a, the principal square root can also be written in exponent notation, as a1/2.
Square roots of negative numbers can be discussed within the framework of complex numbers. More generally, square roots can be considered in any context in which a notion of "squaring" of some mathematical objects is defined (including algebras of matrices, endomorphism rings, etc.)
Square roots of positive whole numbers that are not perfect squares are always irrational numbers: numbers not expressible as a ratio of two integers (that is to say they cannot be written exactly as m/n, where m and n are integers). This is the theorem Euclid X, 9 almost certainly due to Theaetetus dating back to circa 380 BC. The particular case is assumed to date back earlier to the Pythagoreans and is traditionally attributed to Hippasus. It is exactly the length of the diagonal of a square with side length 1.
Read more about Square Root: Properties, Computation, Square Roots of Negative and Complex Numbers, Square Roots of Matrices and Operators, Uniqueness of Square Roots in General Rings, Geometric Construction of The Square Root, History
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Famous quotes containing the words root and/or square:
“But a cultivated man becomes ashamed of his property, out of new respect for his nature. Especially he hates what he has if he see that it is accidental,came to him by inheritance, or gift, or crime; then he feels that it is not having; it does not belong to him, has no root in him and merely lies there because no revolution or no robber takes it away.”
—Ralph Waldo Emerson (18031882)
“The square dance fiddlers first concern is to carry a tune, but he must carry it loud enough to be heard over the noise of stamping feet, the cries of the caller, and the shouts of the dancers. When he fiddles, he fiddles all over; feet, hands, knees, head, and eyes are all busy.”
—State of Oklahoma, U.S. public relief program (1935-1943) |
"Confirmation Bias" is a pervasive danger to hypothesis creation and testing.
The information that we sense and perceive is filtered through our beliefs and experiences (Elstein, 1999). For example, how people perceive and act on information is often based on heuristics (simple rules) instead of strong reasoning (Tversky and Kahneman, 1974). Heuristics are one example of "cognitive biases," or tendencies for people to think and act in consistently distorted ways (Hicks and Kluemper, 2011). Therefore, cognitive biases can affect scientific, clinical, and political decision making.
One cognitive bias that is particularly relevant to science is "confirmation bias" (Nickerson, 1998).
DEFINITION: Confirmation bias is seeking or interpreting evidence in ways that confirmexisting beliefs, expectations, or hypotheses.
Confirmation bias reflects the tendency for people to resist changes to their preconceptions by selectively focusing on information consistent with previous beliefs and expectations while ignoring information that conflicts with their preconceptions (Stanovich et al., 2013). For example, the pre-conception that the world is flat can make it difficult for children to conceptualize a spherical world. Children try to interpret new information (e.g. the world is round) to support their preconception of a flat earth, and think of the world as a pancake shape instead of a sphere (Vosniadou and Brewer, 1989). Therefore, confirmation bias can prevent or hinder learning.
Confirmation bias is sometimes confused with skepticism (being critical of evidence). Skepticism is an important part of scientific reasoning. For example, the author Carl Sagan famously wrote: "Extraordinary claims require extraordinary evidence." However, whereas skepticism is being critical of ALL evidence, confirmation bias is being selectively critical of evidence that doesn't match preconceptions or expectations (Taber and Lodge, 2006). Therefore, confirmation bias actually hinders skepticism by limiting critical thinking to pre-determined areas.
Confirmation bias affects many aspects of science. For example, when making basic measurements, researchers may double-check measurements that conflict with the expectations of the researchers, but may not double-check measurements consistent with expectations. Therefore, errors that make measurements more consistent with expectations are less likely to be caught than errors that make measurements less consistent with expectations. Confirmation bias therefore affects premises used for both deductive and inductive reasoning.
Confirmation bias can also affect deductive and inductive arguments in other ways. Confirmation bias can influence the questions and hypotheses that individuals (or even entire communities) develop. Questions that challenge existing beliefs or expectations may simply not be asked in favor of questions structured to support existing ideas. For example, science reflects prevailing social and cultural assumptions. When racial prejudices were common and more widely accepted, many researchers sought scientific evidence to confirm prevailing biases (Gould, 1996). Objective data, internally-consistent biological models, and quantitative research has ultimately led to the rejection of most race-based hypotheses. However, some social "scientists" and others continue to use confirmation bias (among other fallacies) to promote prejudiced viewpoints (Hernstein and Murray, 1994).
Confirmation bias is a particular concern for inductive reasoning. Inductive reasoning often draws from large bodies of information, presenting the possibility for "cherry picking" information to support pre-determined conclusions. For example, opponents of efforts to reduce climate change cherry-pick data to make misleading arguments. Representatives of the extractive industries have used a single year (1998) that was abnormally warm to argue that global temperatures are not rising, despite data from more than a century that clearly show increases in global temperature (Temple, 2013). Therefore, confirmation bias can lead to un-reasonable judgments, particularly for individual inductive arguments.
Encouraging and increasing diversity in science can mitigate some of the problems associated with cognitive biases.
Science is an evolutionary process that requires extensive communication among individuals and communities of scientists. Scientific discoveries typically "emerge" from interactions among many scientists (Hill, 1933). Although scientists often pride themselves on individuality, scientific progress is more than the sum of contributions by individual scientists. Instead, scientific progress depends on the composition of the entire scientific community.
A diverse scientific community helps to mitigate Confirmation Bias and facilitates scientific progress. A diverse scientific community is more likely to result in many viable alternative hypotheses for any particular problem. Scientists can be attached to particular hypotheses so long as the scientific community is diverse, and there are other groups of scientists in the scientific community attached to other hypotheses. Even if each group explicitly champions a particular hypothesis, over time the hypothesis most consistent with data will prevail. Therefore, all forms of diversity (of scientific perspective, gender, race/ethnicity, background, etc.) strengthen scientific inquiry.
If the overall scientific community is diverse, then individual scientists may not need to be completely objective when they interpret data (objective data collection remains critical for science, however). Inductive reasoning can help scientists evaluate which hypotheses are most consistent with objectively-collected knowledge given a diversity of alternative hypotheses.
Cognitive biases like Confirmation Bias can affect scientific judgment. Individual scientists can reduce the impact of cognitive biases by understanding what cognitive biases are, and how biases can affect reasoning. Diversity within scientific communities can reduce the impacts of cognitive biases by increasing the number and range of alternative hypotheses. |
1948 Arab–Israeli War
The 1948 Arab–Israeli War or the First Arab–Israeli War was fought between the State of Israel and a military coalition of Arab states, forming the second stage of the 1948 Palestine war.
There had been tension and conflict between the Arabs and the Jews, and between each of them and the British forces, ever since the 1917 Balfour Declaration and the 1920 creation of the British Mandate of Palestine. British policies dissatisfied both Arabs and Jews. The Arabs' opposition developed into the 1936–1939 Arab revolt in Palestine, while the Jewish resistance developed into the Jewish insurgency in Palestine (1944–1947). In 1947 these ongoing tensions erupted into civil war, following the 29 November 1947 adoption of the United Nations Partition Plan for Palestine which planned to divide Palestine into three areas: an Arab state, a Jewish state and the Special International Regime for the cities of Jerusalem and Bethlehem.
On 15 May 1948 the ongoing civil war transformed into an inter-state conflict between Israel and the Arab states, following the Israeli Declaration of Independence the previous day. A combined invasion by Egypt, Jordan and Syria, together with expeditionary forces from Iraq, entered Palestine – Jordan having declared privately to Yishuv emissaries on 2 May it would abide by a decision not to attack the Jewish state. The invading forces took control of the Arab areas and immediately attacked Israeli forces and several Jewish settlements. The 10 months of fighting, interrupted by several truce periods, took place mostly on the former territory of the British Mandate and for a short time also in the Sinai Peninsula and southern Lebanon.
As a result of the war the State of Israel retained the area that the UN General Assembly Resolution 181 had recommended for the proposed Jewish state as well as almost 60% of the area of Arab state proposed by the 1948 Partition Plan, including the Jaffa, Lydda and Ramle area, Galilee, some parts of the Negev, a wide strip along the Tel-Aviv-Jerusalem road, West Jerusalem, and some territories in the West Bank. Transjordan took control of the remainder of the former British mandate, which it annexed, and the Egyptian military took control of the Gaza Strip. At the Jericho Conference on 1 December 1948, 2,000 Palestinian delegates called for unification of Palestine and Transjordan as a step toward full Arab unity." No state was created for the Palestinian Arabs.
The conflict triggered significant demographic change throughout the Middle East. Around 700,000 Palestinian Arabs fled or were expelled from their homes in the area that became Israel and they became Palestinian refugees in what they refer to as Al-Nakba ("the catastrophe"). In the three years following the war, about 700,000 Jews immigrated to Israel with many of them having been expelled from their previous countries of residence in the Middle East.
Following World War II, the surrounding Arab nations were emerging from mandatory rule. Transjordan, under the Hashemite ruler Abdullah I, gained independence from Britain in 1946 and was called Jordan in 1949, but it remained under heavy British influence. Egypt gained nominal independence in 1922, but Britain continued to exert a strong influence on the country until the Anglo-Egyptian Treaty of 1936 which limited Britain’s presence to a garrison of troops on the Suez Canal until 1945. Lebanon became an independent state in 1943, but French troops would not withdraw until 1946, the same year that Syria won its independence from France.
In 1945, at British prompting, Egypt, Iraq, Lebanon, Saudi Arabia, Syria, Transjordan, and Yemen formed the Arab League to coordinate policy between the Arab states. Iraq and Transjordan coordinated policies closely, signing a mutual defence treaty, while Egypt, Syria, and Saudi Arabia feared that Transjordan would annex part or all of Palestine, and use it as a steppingstone to attack or undermine Syria, Lebanon, and the Hijaz.
On 29 November 1947, the United Nations General Assembly adopted a resolution recommending the adoption and implementation of a plan to partition the British Mandate of Palestine into two states, one Arab and one Jewish, and the City of Jerusalem.
The General Assembly resolution on Partition was greeted with overwhelming joy in Jewish communities and widespread outrage in the Arab world. In Palestine, violence erupted almost immediately, feeding into a spiral of reprisals and counter-reprisals. The British refrained from intervening as tensions boiled over into a low-level conflict that quickly escalated into a full-scale civil war.
From January onwards, operations became increasingly militarized, with the intervention of a number of Arab Liberation Army regiments inside Palestine, each active in a variety of distinct sectors around the different coastal towns. They consolidated their presence in Galilee and Samaria. Abd al-Qadir al-Husayni came from Egypt with several hundred men of the Army of the Holy War. Having recruited a few thousand volunteers, al-Husayni organized the blockade of the 100,000 Jewish residents of Jerusalem. To counter this, the Yishuv authorities tried to supply the city with convoys of up to 100 armoured vehicles, but the operation became more and more impractical as the number of casualties in the relief convoys surged. By March, Al-Hussayni's tactic had paid off. Almost all of Haganah's armoured vehicles had been destroyed, the blockade was in full operation, and hundreds of Haganah members who had tried to bring supplies into the city were killed. The situation for those who dwelt in the Jewish settlements in the highly isolated Negev and North of Galilee was even more critical.
While the Jewish population had received strict orders requiring them to hold their ground everywhere at all costs, the Arab population was more affected by the general conditions of insecurity to which the country was exposed. Up to 100,000 Arabs, from the urban upper and middle classes in Haifa, Jaffa and Jerusalem, or Jewish-dominated areas, evacuated abroad or to Arab centres eastwards.
This situation caused the US to withdraw their support for the Partition plan, thus encouraging the Arab League to believe that the Palestinian Arabs, reinforced by the Arab Liberation Army, could put an end to the plan for partition. The British, on the other hand, decided on 7 February 1948, to support the annexation of the Arab part of Palestine by Transjordan.
Although a certain level of doubt took hold among Yishuv supporters, their apparent defeats were due more to their wait-and-see policy than to weakness. David Ben-Gurion reorganized Haganah and made conscription obligatory. Every Jewish man and woman in the country had to receive military training. Thanks to funds raised by Golda Meir from sympathisers in the United States, and Stalin's decision to support the Zionist cause, the Jewish representatives of Palestine were able to sign very important armament contracts in the East. Other Haganah agents recuperated stockpiles from the Second World War, which helped improve the army's equipment and logistics. Operation Balak allowed arms and other equipment to be transported for the first time by the end of March.
Ben-Gurion invested Yigael Yadin with the responsibility to come up with a plan of offense whose timing was related to the foreseeable evacuation of British forces. This strategy, called Plan Dalet, was readied by March and implemented towards the end of April. A separate plan, Operation Nachshon, was devised to lift the siege of Jerusalem. 1500 men from Haganah's Givati brigade and Palmach's Harel brigade conducted sorties to free up the route to the city between 5 and 20 April. Both sides acted offensively in defiance of the Partition Plan, which foresaw Jerusalem as a corpus separatum, under neither Jewish nor Arab jurisdiction. The Arabs did not accept the Plan, while the Jews were determined to oppose the internationalization of the city, and secure it as part of the Jewish state. The operation was successful, and enough foodstuffs to last two months were trucked into to Jerusalem for distribution to the Jewish population. The success of the operation was assisted by the death of al-Hasayni in combat. During this time, and independently of Haganah or the framework of Plan Dalet, irregular fighters from Irgun and Lehi formations massacred a substantial number of Arabs at Deir Yassin, an event that, though publicly deplored and criticized by the principal Jewish authorities, had a deep impact on the morale of the Arab population and contributed to generate the exode of the Arab population.
At the same time, the first large-scale operation of the Arab Liberation Army ended in a debacle, having been roundly defeated at Mishmar HaEmek, coinciding with the loss of their Druze allies through defection.
Within the framework of the establishment of Jewish territorial continuity foreseen by Plan Dalet, the forces of Haganah, Palmach and Irgun intended to conquer mixed zones. The Palestinian Arab society was shaken. Tiberias, Haifa, Safed, Beisan, Jaffa and Acre fell, resulting in the flight of more than 250,000 Palestinian Arabs.
The British had, at that time, essentially withdrawn their troops. The situation pushed the leaders of the neighbouring Arab states to intervene, but their preparation was not finalized, and they could not assemble sufficient forces to turn the tide of the war. The majority of Palestinian Arab hopes lay with the Arab Legion of Transjordan's monarch, King Abdullah I, but he had no intention of creating a Palestinian Arab-run state, since he hoped to annexe as much of the territory of the British Mandate for Palestine as he could. He was playing a double-game, being just as much in contact with the Jewish authorities as with the Arab League.
In preparation for the offensive, Haganah successfully launched Operations Yiftah and Ben-'Ami to secure the Jewish settlements of Galilee, and Operation Kilshon, which created a united front around Jerusalem. The inconclusive meeting between Golda Meir and Abdullah I, followed by the Kfar Etzion massacre on 13 May by the Arab Legion led to predictions that the battle for Jerusalem would be merciless.
On 14 May 1948, David Ben-Gurion declared the establishment of the State of Israel and the 1948 Palestine war entered its second phase with the intervention of the Arab state armies and the beginning of the 1948 Arab–Israeli War.
By September 1947 the Haganah had "10,489 rifles, 702 light machine-guns, 2,666 submachine guns, 186 medium machine-guns, 672 two-inch mortars and 92 three-inch (76 mm) mortars".
- Importing arms
In 1946, Ben-Gurion decided that the Yishuv would probably have to defend itself against both the Palestinian Arabs and neighbouring Arab states and accordingly began a "massive, covert arms acquisition campaign in the West", and acquired many more during the first few months of hostilities.
The Yishuv managed to clandestinely amass arms and military equipment abroad for transfer to Palestine once the British blockade was lifted. In the United States, Yishuv agents purchased three Boeing B-17 Flying Fortress bombers, one of which bombed Cairo in July 1948, some Curtiss C-46 Commando transport planes, and dozens of half-tracks, which were repainted and defined as "agricultural equipment". In Western Europe, Haganah agents amassed fifty 65mm French mountain guns, twelve 120mm mortars, ten H-35 light tanks, and a large number of half-tracks. By mid-May or thereabouts the Yishuv had purchased from Czechoslovakia 25 Avia S-199 fighters (an inferior version of the Messerschmitt Bf-109), 200 heavy machine guns, 5,021 light machine guns, 24,500 rifles, and 52 million rounds of ammunition, enough to equip all units, but short of heavy arms. The airborne arms smuggling missions from Czechoslovakia were codenamed Operation Balak.
The airborne smuggling missions were carried out by mostly American aviators – Jews and non-Jews – led by ex-U.S. Air Transport Command flight engineer Al Schwimmer.
Schwimmer’s operation also included recruiting and training fighter pilots such as Lou Lenart, commander of the first Israeli air assault against the Arabs.
- Arms production
The Yishuv also had "a relatively advanced arms producing capacity", that between October 1947 and July 1948" produced 3 million 9 mm bullets, 150,000 Mills grenades, 16,000 submachine guns (Sten Guns) and 210 three-inch (76 mm) mortars", along with a few "Davidka" mortars, which had been indigenously designed and produced. They were inaccurate but had a spectacularly loud explosion that demoralized the enemy. A large amount of the munitions used by the Israelis came from the Ayalon Institute, a clandestine bullet factory underneath kibbutz Ayalon, which produced about 2.5 million bullets for Sten guns. The munitions produced by the Ayalon Institute were said to have been the only supply that was not in shortage during the war. Locally produced explosives were also plentiful. After Israel's independence, these clandestine arms manufacturing operations no longer had to be concealed, and were moved above ground. All of the Haganah's weapons-manufacturing was centralized and later became Israel Military Industries.
In November 1947, the Haganah was an underground paramilitary force that had existed as a highly organized, national force, since the Arab riots of 1920–21, and throughout the riots of 1929, Great Uprising of 1936–39, and World War 2. It had a mobile force, the HISH, which had 2,000 full-time fighters (men and women) and 10,000 reservists (all aged between 18 and 25) and an elite unit, the Palmach composed of 2,100 fighters and 1,000 reservists. The reservists trained three or four days a month and went back to civilian life the rest of the time. These mobile forces could rely on a garrison force, the HIM (Heil Mishmar, lit. Guard Corps), composed of people aged over 25. The Yishuv's total strength was around 35,000 with 15,000 to 18,000 fighters and a garrison force of roughly 20,000.
There were also several thousand men and women who had served in the British Army in World War II who did not serve in any of the underground militias but would provide valuable military experience during the war. Walid Khalidi says the Yishuv had the additional forces of the Jewish Settlement Police, numbering some 12,000, the Gadna Youth Battalions, and the armed settlers. Few of the units had been trained by December 1947. On 5 December 1947, conscription was instituted for all men and women aged between 17 and 25 and by the end of March, 21,000 had been conscripted. On 30 March, the call-up was extended to men and single women aged between 26 and 35. Five days later, a General Mobilization order was issued for all men under 40.
The Irgun, whose activities were considered by MI5 to be terrorism, was monitored by the British.
By March 1948, the Yishuv had a numerical superiority, with 35,780 mobilised and deployed fighters for the Haganah, 3,000 of Stern and Irgun, and a few thousand armed settlers.
- Arab forces
The effective number of Arab combatants is listed at 12,000 by some historians while others calculate a total Arab strength of approximately 23,500 troops, and with this being more of less or roughly equal to that of the Yishuv. However, as Israel mobilized most of its most able citizens during the war while the Arab troops were only a small percentage of its far greater population, the strength of the Yishuv grew steadily and dramatically during the war.
According to Benny Morris, by the end of 1947, the Palestinians "had a healthy and demoralising respect for the Yishuv's military power" and if it came to battle the Palestinians expected to lose.
Yishuv's aims evolved during the war. Mobilization for a total war was organized. Initially, the aim was "simple and modest": to survive the assaults of the Palestinian Arabs and the Arab states. "The Zionist leaders deeply, genuinely, feared a Middle Eastern reenactment of the Holocaust, which had just ended; the Arabs' public rhetoric reinforced these fears". As the war progressed, the aim of expanding the Jewish state beyond the UN partition borders appeared: first to incorporate clusters of isolated Jewish settlements and later to add more territories to the state and give it defensible borders. A third and further aim that emerged among the political and military leaders after four or five months was to "reduce the size of Israel's prospective large and hostile Arab minority, seen as a potential powerful fifth column, by belligerency and expulsion".
Plan Dalet, or Plan D, (Hebrew: תוכנית ד', Tokhnit dalet) was a plan worked out by the Haganah, a Jewish paramilitary group and the forerunner of the Israel Defense Forces, in autumn 1947 to spring 1948, which was sent to Haganah units in early March 1948. According to the academic Ilan Pappe, its purpose was to conquer as much of Palestine and to expel as many Palestinians as possible, though according to Benny Morris there was no such intent. In his book The Ethnic Cleansing of Palestine, Pappé asserts that Plan Dalet was a "blueprint for ethnic cleansing" with the aim of reducing both rural and urban areas of Palestine. According to Gelber, the plan specified that in case of resistance, the population of conquered villages was to be expelled outside the borders of the Jewish state. If no resistance was met, the residents could stay put, under military rule. According to Morris, Plan D called for occupying the areas within the U.N sponsored Jewish state, several concentrations of Jewish population outside those areas (West Jerusalem and Western Galilee), and areas along the roads where the invading Arab armies were expected to attack.
The intent of Plan Dalet is subject to much controversy, with historians on the one extreme asserting that it was entirely defensive, and historians on the other extreme asserting that the plan aimed at maximum conquest and expulsion of the Palestinians.
The Yishuv perceived the peril of an Arab invasion as threatening its very existence. Having no real knowledge of the Arabs' true military capabilities, the Jews took Arab propaganda literally, preparing for the worst and reacting accordingly."
The Arab League as a whole
The Arab League had unanimously rejected the UN partition plan and were bitterly opposed to the establishment of a Jewish state.
The Arab League before partition affirmed the right to the independence of Palestine, while blocking the creation of a Palestinian government. Towards the end of 1947, the League established a military committee commanded by the retired Iraqi general Isma'il Safwat whose mission was to analyse the chance of victory of the Palestinians against the Jews. His conclusions were that they had no chance of victory and that an invasion of the Arab regular armies was mandatory. The political committee nevertheless rejected these conclusions and decided to support an armed opposition to the Partition Plan excluding the participation of their regular armed forces.
In April with the Palestinian defeat, the refugees coming from Palestine and the pressure of their public opinion, the Arab leaders decided to invade Palestine.
The Arab League gave reasons for its invasion in Palestine in the cablegram:
- the Arab states find themselves compelled to intervene in order restore law and order and to check further bloodshed
- the Mandate over Palestine has come to an end, leaving no legally constituted authority
- the only solution of the Palestine problem is the establishment of a unitary Palestinian state.
British diplomat Alec Kirkbride wrote in his 1976 memoirs about a conversation with the Arab League's Secretary-General Azzam Pasha a week before the armies marched: "...when I asked him for his estimate of the size of the Jewish forces, [he] waved his hands and said: 'It does not matter how many there are. We will sweep them into the sea.'" Approximately six months previously, according to an interview in an 11 October 1947 article of Akhbar al-Yom, Azzam said: "I personally wish that the Jews do not drive us to this war, as this will be a war of extermination and a momentous massacre which will be spoken of like the Mongolian massacres and the Crusades".
According to Yoav Gelber, the Arab countries were "drawn into the war by the collapse of the Palestinian Arabs and the Arab Liberation Army [and] the Arab governments' primary goal was preventing the Palestinian Arabs' total ruin and the flooding of their own countries by more refugees. According to their own perception, had the invasion not taken place, there was no Arab force in Palestine capable of checking the Haganah's offensive". Anyway, the Yishuv perceived the peril of an Arab invasion as threatening its very existence. Having no real knowledge of the Arabs' true military capabilities, the Jews took Arab propaganda literally, preparing for the worst and reacting accordingly."
King Abdullah I of Jordan
King Abdullah was the commander of the Arab Legion, the strongest Arab army involved in the war. However, the Egyptian army was the most powerful and threatening army. The Arab Legion had about 10,000 soldiers, trained and commanded by British officers.
In 1946–47, Abdullah said that he had no intention to "resist or impede the partition of Palestine and creation of a Jewish state." Ideally, Abdullah would have liked to annex all of Palestine, but he was prepared to compromise. He supported the partition, intending that the West Bank area of the British Mandate allocated for the Arab state be annexed to Jordan. Abdullah had secret meetings with the Jewish Agency (at which the future Israeli Prime Minister Golda Meir was among the delegates) that reached an agreement of Jewish non-interference with Jordanian annexation of the West Bank (although Abdullah failed in his goal of acquiring an outlet to the Mediterranean Sea through the Negev desert) and of Jordanian agreement not to attack the area of the Jewish state contained in the United Nations partition resolution (in which Jerusalem was given neither to the Arab nor the Jewish state, but was to be an internationally administered area). In order to keep their support to his plan of annexation of the Arab State, Abdullah promised to the British he would not attack the Jewish State.
The neighbouring Arab states pressured Abdullah into joining them in an "all-Arab military invasion" against the newly created State of Israel, that he used to restore his prestige in the Arab world, which had grown suspicious of his relatively good relationship with Western and Jewish leaders. Jordan's undertakings not to cross partition lines were not taken at face value. While repeating assurances that Jordan would only take areas allocated to a future Arab State, on the eve of war Tawfik Abu al-Huda told the British that were other Arab armies to advance against Israel, Jordan would follow suit. On 23 May Abdullah told the French consul in Amman that he "was determined to fight Zionism and prevent the establishment of an Israeli state on the border of his kingdom".
Abdullah's role in this war became substantial. He saw himself as the "supreme commander of the Arab forces" and "persuaded the Arab League to appoint him" to this position. Through his leadership, the Arabs fought the 1948 war to meet Abdullah's political goals.
The other Arab states
King Farouk of Egypt was anxious to prevent Abdullah from being seen as the main champion of the Arab world in Palestine, which he feared might damage his own leadership aspirations of the Arab world. In addition, Farouk wished to annex all of southern Palestine to Egypt. According to Gamal Abdel Nasser the Egyptian army first communique described the Palestine operations as a merely punitive expedition against the Zionist "gangs", using a term frequent in Haganah reports of Palestinian fighters.
Nuri as-Said, the strongman of Iraq, had ambitions for bringing the entire Fertile Crescent under Iraqi leadership. Both Syria and Lebanon wished to take certain areas of northern Palestine.
One result of the ambitions of the various Arab leaders was a distrust of all the Palestinian leaders who wished to set up a Palestinian state, and a mutual distrust of each other. Co-operation was to be very poor during the war between the various Palestinian factions and the Arab armies.
Arab Higher Committee of Amin al-Husayni
Following rumours that King Abdullah was re-opening the bilateral negotiations with Israel that he had previously conducted in secret with the Jewish Agency, the Arab League, led by Egypt, decided to set up the All-Palestine Government in Gaza on 8 September under the nominal leadership of the Mufti. Abdullah regarded the attempt to revive al-Husayni's Holy War Army as a challenge to his authority and all armed bodies operating in the areas controlled by the Arab Legion were disbanded. Glubb Pasha carried out the order ruthlessly and efficiently.
Initial line-up of forces
Though the state of Israel faced the formidable armies of neighbouring Arab counties, yet due to previous battles by the middle of May the Palestinians themselves hardly existed as a military force. The British Intelligence and Arab League military reached similar conclusions.
The British Foreign Ministry and C.I.A believed that the Arab States would finally win in case of war. Martin Van Creveld says that in terms of manpower, the sides were fairly evenly matched.
In May, Egyptian generals told their government that the invasion will be "A parade without any risks" and Tel Aviv "in two weeks". Egypt, Iraq, and Syria all possessed air forces, Egypt and Syria had tanks, and all had some modern artillery. Initially, the Haganah had no heavy machine guns, artillery, armoured vehicles, anti-tank or anti-aircraft weapons, nor military aircraft or tanks. The four Arab armies that invaded on 15 May were far stronger than the Haganah formations they initially encountered.
On 12 May, three days before the invasion, David Ben-Gurion was told by his chief military advisers (who over-estimated the size of the Arab armies and the numbers and efficiency of the troops who would be committed – much as the Arab generals tended to exaggerate Jewish fighters' strength) that Israel's chances of winning a war against the Arab states were only about even.
Jewish forces at the invasion: Sources disagree about the amount of arms at the Yishuv's disposal at the end of the Mandate. According to Karsh before the arrival of arms shipments from Czechoslovakia as part of Operation Balak, there was roughly one weapon for every three fighters, and even the Palmach could arm only two out of every three of its active members. According to Collins and LaPierre, by April 1948, the Haganah had managed to accumulate only about 20,000 rifles and Sten guns for the 35,000 soldiers who existed on paper. According to Walid Khalidi "the arms at the disposal of these forces were plentiful". France authorized Air France to transport cargo to Tel Aviv on 13 May.
Yishuv forces were organised in 9 brigades, and their numbers grew following Israeli independence, eventually expanding to 12 brigades. Although both sides increased their manpower over the first few months of the war, the Israeli forces grew steadily as a result of the progressive mobilization of Israeli society and the influx of an average of 10,300 immigrants each month. By the end of 1948, the Israel Defense Forces had 88,033 soldiers, including 60,000 combat soldiers.
|Golani||Moshe Mann||4,500||Dekel, Hiram|
|Alexandroni||Dan Even||5,200||Latrun, Hametz|
|Kiryati||Michael Ben-Gal||1,400||Dani, Hametz|
|Givati||Shimon Avidan||5,000||Hametz, Barak, Pleshet|
|Etzioni||David Shaltiel||Battle of Jerusalem, Shfifon, Yevusi, Battle of Ramat Rachel|
|7th Armoured||Shlomo Shamir||Battles of Latrun|
|8th Armoured||Yitzhak Sadeh||Danny, Yoav, Horev|
|Oded||Avraham Yoffe||Yoav, Hiram|
|Harel||Yitzhak Rabin||1,400||Nachshon, Danny|
|Yiftach||Yigal Allon||4,500 inc. some Golani||Yiftah, Danny, Yoav, Battles of Latrun|
After the invasion: France allowed aircraft carrying arms from Czechoslovakia to land on French territory in transit to Israel, and permitted two arms shipments to ‘Nicaragua’, which were actually intended for Israel.
Czechoslovakia supplied vast quantities of arms to Israel during the war, including thousands of vz. 24 rifles and MG 34 and ZB 37 machine guns, and millions of rounds of ammunition. Czechoslovakia supplied fighter aircraft, including at first ten Avia S-199 fighter planes.
The Haganah readied twelve cargo ships throughout European ports to transfer the accumulated equipment, which would set sail as soon as the British blockade was lifted with the expiration of the Mandate.
Following Israeli independence, the Israelis managed to build three Sherman tanks from scrap-heap material found in abandoned British ordnance depots.
The Haganah also managed to obtain stocks of British weapons due to the logistical complexity of the British withdrawal, and the corruption of a number of officials.
After the first truce: By July 1948, the Israelis had established an air force, a navy, and a tank battalion.
On June 29, 1948, the day before the last British troops left Haifa, two British soldiers sympathetic to the Israelis stole two Cromwell tanks from an arms depot in the Haifa port area, smashing them through the unguarded gates, and joined the IDF with the tanks. These two tanks would form the basis of the Israeli Armored Corps.
After the second truce: Czechoslovakia supplied Supermarine Spitfire fighter planes, which were smuggled to Israel via an abandoned Luftwaffe runway in Yugoslavia, with the agreement of the Yugoslav government. The airborne arms smuggling missions from Czechoslovakia were codenamed Operation Balak.
At the invasion: In addition to the local irregular Palestinians militia groups, the five Arab states that joined the war were Egypt, Jordan (Transjordan), Syria, Lebanon and Iraq sending expeditionary forces of their regular armies. Additional contingents came from Saudi Arabia and Yemen. On the eve of the war, the available number of Arab troops likely to be committed to war was between 23,500 and 26,500 (10,000 Egyptians, 4,500 Jordanians, 3,000 Iraqis, 3,000–6,000 Syrians, 2,000 ALA volunteers, 1,000 Lebanese, and several hundred Saudis), in addition to the irregular Palestinians already present. Prior to the war, Arab forces had been trained by British and French instructors. This was particularly true of Jordan's Arab Legion under command of Lt Gen Sir John Glubb.
Syria bought a quantity of small arms for the Arab Liberation Army from Czechoslovakia, but the shipment never arrived due to Hagana force intervention.
- Arab states
Jordan's Arab Legion was considered the most effective Arab force. Armed, trained and commanded by British officers, this 8,000–12,000 strong force was organised in four infantry/mechanised regiments supported by some 40 artillery pieces and 75 armoured cars. Until January 1948, it was reinforced by the 3,000-strong Transjordan Frontier Force. As many as 48 British officers served in the Arab Legion. Glubb Pasha, the commander of the Legion, organized his forces into four brigades as follows:
|Military Division||Commander||Rank||Military Zone of operations|
|First Brigade, includes: 1st and 3rd regiments||Desmond Goldie||Colonel||Nablus Military Zone|
|Second Brigade, includes: Fifth and Sixth Regiments||Sam Sidney Arthur Cooke||Brigadier||Support force|
|Third Brigade, includes: Second and Fourth Regiments||Teel Ashton||Colonel||Ramallah Military Zone|
|Fourth Brigade||Ahmad Sudqi al-Jundi||Colonel||Support: Ramallah, Hebron, and Ramla|
The Arab Legion joined the war in May 1948, but fought only in the area that King Abdullah wanted to secure for Jordan: the West Bank, including East Jerusalem.
France prevented a large sale of arms by a Swiss company to Ethiopia, brokered by the U.K foreign office, which was actually destined for Egypt and Jordan, denied a British request at the end of April to permit the landing of a squadron of British aircraft on their way to Transjordan, and applied diplomatic pressure on Belgium to suspend arms sales to the Arab states.
The Jordanian forces were probably the best trained of all combatants. Other combatant forces lacked the ability to make strategic decisions and tactical maneuvers, as evidenced by positioning the fourth regiment at Latrun, which was abandoned by ALA combatants before the arrival of the Jordanian forces and the importance of which was not fully understood by the Haganah general-staff. In the later stages of the war, Latrun proved to be of extreme importance, and a decisive factor in Jerusalem's fate.
In 1948, Iraq's army had 21,000 men in 12 brigades and the Iraqi Air Force had 100 planes, mostly British. Initially the Iraqis committed around 3,000 men to the war effort, including four infantry brigades, one armoured battalion and support personnel. These forces were to operate under Jordanian guidance The first Iraqi forces to be deployed reached Jordan in April 1948 under the command of Gen. Nur ad-Din Mahmud.
In 1948, Egypt's army was able to put a maximum of around 40,000 men into the field, 80% of its military-age male population being unfit for military service and its embryonic logistics system being limited in its ability to support ground forces deployed beyond its borders. Initially, an expeditionary force of 10,000 men was sent to Palestine under the command of Maj. Gen. Ahmed Ali al-Mwawi. This force consisted of five infantry battalions, one armoured battalion equipped with British Light Tank Mk VI and Matilda tanks, one battalion of sixteen 25-pounder guns, a battalion of eight 6-pounder guns and one medium-machine-gun battalion with supporting troops.
The Egyptian Air Force had over 30 Spitfires, 4 Hawker Hurricanes and 20 C47s modified into crude bombers.
Syria had 12,000 soldiers at the beginning of the 1948 War, grouped into three infantry brigades and an armoured force of approximately battalion size. The Syrian Air Force had fifty planes, the 10 newest of which were World War II–generation models.
France suspended arms sales to Syria, notwithstanding signed contracts.
Lebanon's army was the smallest of the Arab armies, consisting of only 3,500 soldiers. According to Gelber, in June 1947, Ben-Gurion "arrived at an agreement with the Maronite religious leadership in Lebanon that cost a few thousand pounds and kept Lebanon's army out of the War of Independence and the military Arab coalition." According to Rogan and Shlaim, a token force of 1,000 was committed to the invasion. It crossed into the northern Galilee and was repulsed by Israeli forces. Israel then invaded and occupied southern Lebanon until the end of the war.
Arab forces after the first truce: By the time of the second truce, the Egyptians had 20,000 men in the field in thirteen battalions equipped with 135 tanks and 90 artillery pieces.
During the first truce, the Iraqis increased their force to about 10,000. Ultimately, the Iraqi expeditionary force numbered around 18,000 men.
Saudi Arabia sent hundreds of volunteers to join the Arab forces. In February 1948, around 800 tribesmen had gathered near Aqaba so as to invade the Negev, but crossed to Egypt after Saudi rival King Abdallah officially denied them permission to pass through Jordanian territory. The Saudi troops were attached to the Egyptian command throughout the war, and estimates of their total strength ranged up to 1,200. By July 1948, the Saudis comprised three brigades within the Egyptian expeditionary force, and were stationed as guards between Gaza city and Rafah. This area came under heavy aerial bombardment during Operation Yoav in October, and faced a land assault beginning in late December which culminated in the Battle of Rafah in early January of the new year. With the subsequent armistice of 24 February 1949 and evacuation of almost 4,000 Arab soldiers and civilians from Gaza, the Saudi contingent withdrew through Arish and returned to Saudi Arabia.
During the first truce, Sudan sent six companies of regular troops to fight alongside the Egyptians. Yemen also committed a small expeditionary force to the war effort, and contingents from Morocco joined the Arab armies as well.
Course of the war
At the last moment, several Arab leaders, to avert catastrophe – secretly appealed to the British to hold on in Palestine for at least another year.
First phase: 15 May – 11 June 1948
On 14 May 1948, David Ben-Gurion declared the establishment of a Jewish state in Eretz-Israel to be known as the State of Israel, a few hours before the termination of the Mandate at midnight. On 15 May 1948, Iraq and the neighboring Arab states, Egypt, Jordan (Transjordan) and Syria, invaded what had just ceased to be the territory of the British Mandate, and immediately attacked Jewish settlements. What was now Israel had already, from 1 April down to 14 May, conducted 8 of its 13 full-scale military operations outside of the area allotted to a Jewish state by partition, and the operational commander Yigal Allon later stated that had it not been for the Arab invasion, Haganah's forces would have reached 'the natural borders of western Israel.' Although the Arab invasion was denounced by the United States, the Soviet Union, and UN secretary-general Trygve Lie, it found support from Taiwan and other UN member states.
The initial Arab plans called for Syrian and Lebanese forces to invade from north while Jordanian and Iraqi forces were to invade from east in order to meet at Nazareth and then to push forward together to Haifa. In the south, the Egyptians were to advance and take Tel Aviv. At the Arab League meeting in Damascus on 11–13 May, Abdullah rejected the plan, which served Syrian interests, using the fact his allies were afraid to go to war without his army. He proposed that the Iraqis attack the Jezreel valley and the Arab Legion enter Ramallah and Nablus and link with the Egyptian army at Hebron, which was more in compliance with his political objective to occupy the territory allocated to the Arab State by the partition plan and promises not to invade the territory allocated to the Jewish State by the partition plan. In addition, Lebanon decided not to take part in the war at the last minute due to the still influential Christians' opposition and to Jewish bribes.
Intelligence provided by the French consulate in Jerusalem on 12 May 1948 on the Arab armies' invading forces and their revised plan to invade the new state contributed to Israel’s success in withstanding the Arab invasion.
The first mission of the Jewish forces was to hold on against the Arab armies and stop them, although the Arabs had enjoyed major advantages (the initiative, vastly superior firepower). As the British stopped blocking the incoming Jewish immigrants and arms supply, the Israeli forces grew steadily with large numbers of immigrants and weapons, that allowed the Haganah to transform itself from a paramilitary force into a real army. Initially, the fighting was handled mainly by the Haganah, along with the smaller Jewish militant groups Irgun and Lehi. On 26 May 1948, Israel established the Israel Defense Forces (IDF), incorporating these forces into one military under a central command.
Southern front – Negev
The Egyptian force, the largest among the Arab armies, invaded from the south.
On 15 May 1948, the Egyptians attacked two settlements: Nirim, using artillery, armoured cars carrying cannons, and Bren carriers; and Kfar Darom using artillery, tanks and aircraft. The Egyptians attacks met fierce resistance from the few and lightly armed defenders of both settlements, and failed. On 19 May the Egyptians attacked Yad Mordechai, where an inferior force of 100 Israelis armed with nothing more than rifles, a medium machinegun and a PIAT anti-tank weapon, held up a column of 2,500 Egyptians, well-supported by armor, artillery and air units, for five days. The Egyptians took heavy losses, while the losses sustained by the defenders were comparatively light.
One of the Egyptian force two main columns made its way northwards along the shoreline, through what is today the Gaza Strip and the other column advanced eastwards toward Beersheba. To secure their flanks, the Egyptians attacked and laid siege to a number of kibbutzim in the Negev, among those Kfar Darom, Nirim, Yad Mordechai, and Negba. The Israeli defenders held out fiercely for days against vastly superior forces, and managed to buy valuable time for the IDF's Givati Brigade to prepare to stop the Egyptian drive on Tel Aviv.
On 28 May the Egyptians renewed their northern advance, and stopped at a destroyed bridge north to Isdud. The Givati Brigade reported this advance but no fighters were sent to confront the Egyptians. Had the Egyptians wished to continue their advance northward, towards Tel Aviv, there would have been no Israeli force to block them.
From 29 May to 3 June, Israeli forces stopped the Egyptian drive north in Operation Pleshet. In the first combat mission performed by Israel's fledgling air force, four Avia S-199s attacked an Egyptian armored column of 500 vehicles on its way to Isdud. The Israeli planes dropped 70 kilogram bombs and strafed the column, although their machine guns jammed quickly. Two of the planes crashed, killing a pilot. The attack caused the Egyptians to scatter, and they had lost the initiative by the time they had regrouped. Following the air attack, Israeli forces constantly bombarded Egyptian forces in Isdud with Napoleonchik cannons, and IDF patrols engaged in small-scale harassment of Egyptian lines. Following another air attack, the Givati Brigade launched a counterattack. Although the counterattack was repulsed, the Egyptian offensive was halted as Egypt changed its strategy from offensive to defensive, and the initiative shifted to Israel.
On 6 June, in the Battle of Nitzanim, Egyptian forces attacked the kibbutz of Nitzanim, located between Majdal (now Ashkelon) and Isdud, and the Israeli defenders surrendered after resisting for five days.
Battles of Latrun
The heaviest fighting occurred in Jerusalem and on the Jerusalem – Tel Aviv road, between Jordan's Arab Legion and Israeli forces. As part of the redeployment to deal with the Egyptian advance, the Israelis abandoned the Latrun fortress overlooking the main highway to Jerusalem, which the Arab Legion immediately seized. The Arab Legion also occupied the Latrun Monastery. From these positions, the Jordanians were able to cut off supplies to Israeli fighters and civilians in Jerusalem.
The Israelis attempted to take the Latrun fortress in a series of battles lasting from 24 May to 18 July. The Arab Legion held Latrun and managed to repulse the attacks. During the attempts to take Latrun, Israeli forces suffered some 586 casualties, among them Mickey Marcus, Israel's first general, who was killed by friendly fire. The Arab Legion also took losses, losing 90 dead and some 200 wounded up to 29 May.
Building the Burma Road
A bulldozer tows a truck on the "Burma road", June 1948
The besieged Israeli Jerusalem was only saved via the opening of the so-called "Burma Road", a makeshift bypass road built by Israeli forces that allowed Israeli supply convoys to pass into Jerusalem. Parts of the area where the road was built were cleared of Jordanian snipers in May and the road was completed on 14 June. Supplies had already begun passing through before the road was completed, with the first convoy passing through on the night of 1–2 June. The Jordanians spotted the activity and attempted to shell the road, but were ineffective, as it could not be seen. However, Jordanian sharpshooters killed several road workers, and an attack on 9 June left eight Israelis dead. On 18 July, elements of the Harel Brigade took about 10 villages to the south of Latrun to enlarge and secure the area of the Burma Road.
The Arab Legion was able to repel an Israeli attack on Latrun. The Jordanians launched two counterattacks, temporarily taking Beit Susin before being forced back, and capturing Gezer after a fierce battle, which was retaken by two Palmach squads the same evening.
Jordanian artillery shelling Jerusalem in 1948
Arab Legion soldier standing in ruins of the most sacred Synagogue, the "Hurva", Old City.
Jewish residents of Jerusalem Old City fleeing during the Jordanian offensive
Battle for Jerusalem
The Jordanians in Latrun cut off supplies to western Jerusalem. Though some supplies, mostly munitions, were airdropped into the city, the shortage of food, water, fuel and medicine was acute. The Israeli forces were seriously short of food, water and ammunition.
King Abdullah ordered Glubb Pasha, the commander of the Arab Legion, to enter Jerusalem on 17 May. The Arab Legion fired 10,000 artillery and mortar shells a day, and also attacked West Jerusalem with sniper fire.
Heavy house-to-house fighting occurred between 19 and 28 May, with the Arab Legion eventually succeeding in pushing Israeli forces from the Arab neighborhoods of Jerusalem as well as the Jewish Quarter of the Old City. The 1,500 Jewish inhabitants of the Old City's Jewish Quarter were expelled, and several hundred were detained. The Jews had to be escorted out by the Arab Legion to protect them against Palestinian Arab mobs that intended to massacre them. On 22 May, Arab forces attacked kibbutz Ramat Rachel south of Jerusalem. After a fierce battle in which 31 Jordanians and 13 Israelis were killed, the defenders of Ramat Rachel withdrew, only to partially retake the kibbutz the following day. Fighting continued until 26 May, until the entire kibbutz was recaptured. Radar Hill was also taken from the Arab Legion, and held until 26 May, when the Jordanians retook it in a battle that left 19 Israelis and 2 Jordanians dead. A total of 23 attempts by the Harel Brigade to capture Radar Hill in the war failed.
The same day, Thomas C. Wasson, the US Consul-General in Jerusalem and a member of the UN Truce Commission was shot dead in West Jerusalem. It was disputed whether Wasson was killed by the Arabs or Israelis.
An Iraqi force consisting of two infantry and one armoured brigade crossed the Jordan River from northern Jordan, attacking the Israeli settlement of Gesher with little success. Following this defeat, Iraqi forces moved into the strategic triangle bounded by the Arab towns Nablus, Jenin and Tulkarm. On 25 May, they were making their way towards Netanya, when they were stopped. On 29 May, an Israeli attack against the Iraqis led to three days of heavy fighting over Jenin, but Iraqi forces managed to hold their positions. After these battles, the Iraqi forces became stationary and their involvement in the war effectively ended.
Iraqi forces failed in their attacks on Israeli settlements with the most notable battle taking place at Gesher, and instead took defensive positions around Jenin, Nablus, and Tulkarm, from where they could put pressure on the Israeli center. On 25 May, Iraqi forces advanced from Tulkarm, taking Geulim and reaching Kfar Yona and Ein Vered on the Tulkarm-Netanya road. The Alexandroni Brigade then stopped the Iraqi advance and retook Geulim. On 1 June, the Carmeli and Golani Brigades captured Jenin from Iraqi forces. They were pushed out by an Iraqi counterattack, and lost 34 dead and 100 wounded.
Northern front – Lake of Galilee
On 14 May Syria invaded Palestine with the 1st Infantry Brigade supported by a battalion of armoured cars, a company of French R 35 and R 37 tanks, an artillery battalion and other units. The Syrian president, Shukri al-Quwwatli instructed his troops in the front, "to destroy the Zionists". "The situation was very grave. There aren’t enough rifles. There are no heavy weapons," Ben-Gurion told the Israeli Cabinet. On 15 May, the Syrian forces turned to the eastern and southern Sea of Galilee shores, and attacked Samakh the neighboring Tegart fort and the settlements of Sha'ar HaGolan, Ein Gev, but they were bogged down by resistance. Later, they attacked Samakh using tanks and aircraft, and on 18 May they succeeded in conquering Samakh and occupied the abandoned Sha'ar HaGolan.
On 21 May, the Syrian army was stopped at kibbutz Degania Alef in the north, where local militia reinforced by elements of the Carmeli Brigade halted Syrian armored forces with Molotov cocktails, hand grenades and a single PIAT. One tank that was disabled by Molotov cocktails and hand grenades still remains at the kibbutz. The remaining Syrian forces were driven off the next day by four Napoleonchik mountain guns – Israel's first use of artillery during the war. Following the Syrian forces' defeat at the Deganias a few days later, they abandoned the Samakh village. The Syrians were forced to besiege the kibbutz rather than advance. One author claims that the main reason for the Syrian defeat was the Syrian soldiers' low regard for the Israelis who they believed would not stand and fight against the Arab army.
On 6 June, nearly two brigades of the Arab Liberation Army and the Lebanese Army took Al-Malkiyya and Qadas in what became the only intervention of the Lebanese army during the war.
On 6 June, Syrian forces attacked Mishmar HaYarden, but they were repulsed. On 10 June, the Syrians overran Mishmar HaYarden and advanced to the main road, where they were stopped by units of the Oded Brigade. Subsequently, the Syrians reverted to a defensive posture, conducting only a few minor attacks on small, exposed Israeli settlements.
In the continuity of the civil war between Jewish and Arab forces that had begun in 1947, battles between Israeli forces and Palestinian Arab militias took place, particularly in the Lydda, al-Ramla, Jerusalem, and Haifa areas. On 23 May, the Alexandroni Brigade captured Tantura, south of Haifa, from Arab forces. On 2 June, Holy War Army commander Hasan Salama was killed in a battle with Haganah at Ras al-Ein.
All Jewish aviation assets were placed under the control of the Sherut Avir (Air Service, known as the SA) in November 1947 and flying operations began in the following month from a small civil airport on the outskirts of Tel Aviv called Sde Dov, with the first ground support operation (in an RWD-13) taking place on 17 December. The Galilee Squadron was formed at Yavne'el in March 1948, and the Negev Squadron was formed at Nir-Am in April. By 10 May, when the SA suffered its first combat loss, there were three flying units, an air staff, maintenance facilities and logistics support. At the outbreak of the war on 15 May, the SA became the Israeli Air Force. With its fleet of light planes it was no match for Arab forces during the first few weeks of the war with their T-6s, Spitfires, C-47s, and Avro Ansons.
On 15 May, with the beginning of the war, four Royal Egyptian Air Force (REAF) Spitfires attacked Tel Aviv, bombing Sde Dov Airfield, where the bulk of Sherut Avir's aircraft were concentrated, as well as the Reading Power Station. Several aircraft were destroyed, some others were damaged, and five Israelis were killed. Throughout the following hours, additional waves of Egyptian aircraft bombed and strafed targets around Tel Aviv, although these raids had little effect. One Spitfire was shot down by anti-aircraft fire, and its pilot was taken prisoner. Throughout the next six days, the REAF would continue to attack Tel Aviv, causing civilian casualties. On 18 May, Egyptian warplanes attacked the Tel Aviv Central Bus Station, killing 42 people and wounding 100. In addition to their attacks on Tel Aviv, the Egyptians also bombed rural settlements and airfields, though few casualties were caused in these raids.
At the outset of the war, the REAF was able to attack Israel with near impunity, due to the lack of Israeli fighter aircraft to intercept them, and met only ground fire.
As more effective air defenses were transferred to Tel Aviv, the Egyptians began taking significant aircraft losses. As a result of these losses, as well as the loss of five Spitfires downed by the British when the Egyptians mistakenly attacked RAF Ramat David, the Egyptian air attacks became less frequent. By the end of May 1948, almost the entire REAF Spitfire squadron based in El Arish had been lost, including many of its best pilots.
Although lacking fighter or bomber aircraft, in the first few days of the war, Israel's embryonic air force still attacked Arab targets, with light aircraft being utilized as makeshift bombers, striking Arab encampments and columns. The raids were mostly carried out at night to avoid interception by Arab fighter aircraft. These attacks usually had little effect, except on morale.
The balance of air power soon began to swing in favor of the Israeli Air Force following the arrival of 25 Avia S-199s from Czechoslovakia, the first of which arrived in Israel on 20 May. Ironically, Israel was using the Avia S-199, an inferior derivative of the Bf-109 designed in Nazi Germany to counter British-designed Spitfires flown by Egypt. Throughout the rest of the war, Israel would acquire more Avia fighters, as well as 62 Spitfires from Czechoslovakia. On 28 May 1948, Sherut Avir became the Israeli Air Force.
Many of the pilots who fought for the Israeli Air Force were foreign volunteers or mercenaries, including many World War II veterans.
On 3 June, Israel scored its first victory in aerial combat when Israeli pilot Modi Alon shot down a pair of Egyptian DC-3s that had just bombed Tel Aviv. Although Tel Aviv would see additional raids by fighter aircraft, there would be no more raids by bombers for the rest of the war. From then on, the Israeli Air Force began engaging the Arab air forces in air-to-air combat. The first dogfight took place on June 8, when an Israeli fighter plane flown by Gideon Lichtman shot down an Egyptian Spitfire. By the fall of 1948, the IAF had achieved air superiority and had superior firepower and more knowledgeable personnel, many of whom had seen action in World War II. Israeli planes then began intercepting and engaging Arab aircraft on bombing missions.
Following Israeli air attacks on Egyptian and Iraqi columns, the Egyptians repeatedly bombed Ekron Airfield, where IAF fighters were based. During a 30 May raid, bombs aimed for Ekron hit central Rehovot, killing 7 civilians and wounding 30. In response to this, and probably to the Jordanian victories at Latrun, Israel began bombing targets in Arab cities. On the night of 31 May/1 June, the first Israeli raid on an Arab capital took place when three IAF planes flew to Amman and dropped several dozen 55 and 110-pound bombs, hitting the King's Palace and an adjacent British airfield. Some 12 people were killed and 30 wounded. During the attack, an RAF hangar was damaged, as were some British aircraft. The British threatened that in the event of another such attack, they would shoot down the attacking aircraft and bomb Israeli airfields, and as a result, Israeli aircraft did not attack Amman again for the rest of the war. Israel also bombed Arish, Gaza, Damascus, and Cairo. Israeli Boeing B-17 Flying Fortress bombers coming to Israel from Czechoslovakia bombed Egypt on their way to Israel. According to Alan Dershowitz, Israeli planes focused on bombing military targets in these attacks, though Benny Morris wrote that an 11 June air raid on Damascus was indiscriminate.
At the outset of the war, the Israeli Navy consisted of three former Aliyah Bet ships that had been seized by the British and impounded in Haifa harbor, where they were tied up at the breakwater. Work on establishing a navy had begun shortly before Israeli independence, and the three ships were selected due to them having a military background – one, the INS Eilat, was an ex-US Coast Guard icebreaker, and the other two, the INS Haganah and INS Wedgwood, had been Royal Canadian Navy corvettes. The ships were put into minimum running condition by contractors dressed as stevedores and port personnel, who were able to work in the engine rooms and below deck. The work had to be clandestine to avoid arousing British suspicion. On 21 May 1948, the three ships set sail for Tel Aviv, and were made to look like ships that had been purchased by foreign owners for commercial use. In Tel Aviv, the ships were fitted with small field guns dating to the late 19th century and anti-aircraft guns. After the British left Haifa port on 30 June, Haifa became the main base of the Israeli Navy. In October 1948, a submarine chaser was purchased from the United States. The warships were manned by former merchant seamen, former crewmembers of Aliyah Bet ships, Israelis who had served in the Royal Navy during World War II, and foreign volunteers. The newly refurbished and crewed warships served on coastal patrol duties and bombarded Egyptian coastal installations in and around the Gaza area all the way to Port Said.
End of the first phase
Throughout the following days, the Arabs were only able to make limited gains due to fierce Israeli resistance, and were quickly driven off their new holdings by Israeli counterattacks.
As the war progressed, the IDF managed to field more troops than the Arab forces. In July 1948, the IDF had 63,000 troops; by early spring 1949, they had 115,000. The Arab armies had an estimated 40,000 troops in July 1948, rising to 55,000 in October 1948, and slightly more by the spring of 1949.
First truce: 11 June – 8 July 1948
The UN declared a truce on 29 May, which came into effect on 11 June and lasted 28 days. The truce was designed to last 28 days and an arms embargo was declared with the intention that neither side would make any gains from the truce. Neither side respected the truce; both found ways around the restrictions placed on them. Both the Israelis and the Arabs used this time to improve their positions, a direct violation of the terms of the ceasefire.
At the time of the truce, the British view was that "the Jews are too weak in armament to achieve spectacular success". As the truce commenced, a British officer stationed in Haifa stated that the four-week-long truce "would certainly be exploited by the Jews to continue military training and reorganization while the Arabs would waste [them] feuding over the future divisions of the spoils". During the truce, the Israelis sought to bolster their forces by massive import of arms. The IDF was able to acquire weapons from Czechoslovakia as well as improve training of forces and reorganization of the army during this time. Yitzhak Rabin, an IDF commander at the time of the war and later Israel's fifth Prime Minister, stated "[w]ithout the arms from Czechoslovakia... it is very doubtful whether we would have been able to conduct the war".
The Israeli army increased its manpower from approximately 30,000–35,000 men to almost 65,000 during the truce due to mobilization and the constant immigration into Israel. It was also able to increase its arms supply to more than 25,000 rifles, 5,000 machine guns, and fifty million bullets. As well as violating the arms and personnel embargo, they also sent fresh units to the front lines, much as their Arab enemies did.
During the truce, Irgun attempted to bring in a private arms shipment aboard a ship called "Altalena". When they refused to hand the arms to the Israeli government, Ben-Gurion ordered that the arms be confiscated by force if necessary. After meeting with armed resistance, the army was ordered by Ben-Gurion to sink the ship. Several Irgun members and IDF soldiers were killed in the fighting.
UN mediator Bernadotte
The ceasefire was overseen by UN mediator Folke Bernadotte and a team of UN Observers made up of army officers from Belgium, United States, Sweden and France. Bernadotte was voted in by the General Assembly to "assure the safety of the holy places, to safeguard the well being of the population, and to promote 'a peaceful adjustment of the future situation of Palestine'".
Folke Bernadotte reported:
During the period of the truce, three violations occurred ... of such a serious nature:
- the attempt by ...the Irgun Zvai Leumi to bring war materials and immigrants, including men of military age, into Palestine aboard the ship "Altalena" on 21 June...
- Another truce violation occurred through the refusal of Egyptian forces to permit the passage of relief convoys to Jewish settlements in the Negeb...
- The third violation of the truce arose as a result of the failure of the Transjordan and Iraqi forces to permit the flow of water to Jerusalem.
After the truce was in place, Bernadotte began to address the issue of achieving a political settlement. The main obstacles in his opinion were "the Arab world's continued rejection of the existence of a Jewish state, whatever its borders; Israel's new 'philosophy', based on its increasing military strength, of ignoring the partition boundaries and conquering what additional territory it could; and the emerging Palestinian Arab refugee problem".
Taking all the issues into account, Bernadotte presented a new partition plan. He proposed there be a Palestinian Arab state alongside Israel and that a "Union" "be established between the two sovereign states of Israel and Jordan (which now included the West Bank); that the Negev, or part of it, be included in the Arab state and that Western Galilee, or part of it, be included in Israel; that the whole of Jerusalem be part of the Arab state, with the Jewish areas enjoying municipal autonomy and that Lydda Airport and Haifa be 'free ports' – presumably free of Israeli or Arab sovereignty". Israel rejected the proposal, in particular the aspect of losing control of Jerusalem, but they did agree to extend the truce for another month. The Arabs rejected both the extension of the truce and the proposal.
Second phase: 8–18 July 1948
On 8 July, the day before the expiration of the truce, Egyptian forces under General Muhammad Naguib renewed the war by attacking Negba. The following day, Israeli forces launched a simultaneous offensive on all three fronts. The fighting continued for ten days until the UN Security Council issued the Second Truce on 18 July. During the fighting, the Israelis were able to open a lifeline to a number of besieged kibbutzim.
During those 10 days, the fighting was dominated by large-scale Israeli offensives and a defensive posture from the Arab side.
In the south, the IDF carried out several offensives, including Operation An-Far and Operation Death to the Invader. The task of the 11th Brigades's 1st Battalian on the southern flank was to capture villages, and its operation ran smoothly, with but little resistance from local irregulars. According to Amnon Neumann, a Palmach veteran of the Southern front, hardly any Arab villages in the south fought back, due to the miserable poverty of their means and lack of weapons, and suffered expulsion. What slight resistance was offered was quelled by an artillery barrage, followed by the storming of the village, whose residents were expelled and houses destroyed.
On 12 July, the Egyptians launched an offensive action, and again attacked Negba, which they had previously failed to capture, using three infantry battalions, an armored battalion, and an artillery regiment. In the battle that followed, the Egyptians were repulsed, suffering 200–300 casualties, while the Israelis lost 5 dead and 16 wounded.
After failing to take Negba, the Egyptians turned their attention to more isolated settlements and positions. On 14 July, an Egyptian attack on Gal On was driven off by a minefield and by resistance from Gal On's residents.
The Egyptians then assaulted the lightly defended village of Be'erot Yitzhak. The Egyptians managed to penetrate the village perimeter, but the defenders concentrated in an inner position in the village and fought off the Egyptian advance until IDF reinforcements arrived and drove out the attackers. The Egyptians suffered an estimated 200 casualties, while the Israelis had 17 dead and 15 wounded. The battle was one of Egypt's last offensive actions during the war, and the Egyptians did not attack any Israeli villages following this battle.
Lydda and al-Ramla
On 10 July, Glubb Pasha ordered the defending Arab Legion troops to "make arrangements...for a phony war". Israeli Operation Danny was the most important Israeli offensive, aimed at securing and enlarging the corridor between Jerusalem and Tel Aviv by capturing the roadside cities Lod (Lydda) and Ramle. In a second planned stage of the operation the fortified positions of Latrun – overlooking the Tel Aviv-Jerusalem highway – and the city of Ramallah were also to be captured. Hadita, near Latrun, was captured by the Israelis at a cost of 9 dead.
The objectives of Operation Danny were to capture territory east of Tel Aviv and then to push inland and relieve the Jewish population and forces in Jerusalem. Lydda had become an important military center in the region, lending support to Arab military activities elsewhere, and Ramle was one of the main obstacles blocking Jewish transportation. Lydda was defended by a local militia of around 1,000 residents, with an Arab Legion contingent of 125–300.
The IDF forces gathered to attack the city numbered around 8,000. It was the first operation where several brigades were involved. The city was attacked from the north via Majdal al-Sadiq and al-Muzayri'a, and from the east via Khulda, al-Qubab, Jimzu and Daniyal. Bombers were also used for the first time in the conflict to bombard the city. The IDF captured the city on 11 July.
Up to 450 Arabs and 9–10 Israeli soldiers were killed. The next day, Ramle fell. The civilian populations of Lydda and Ramle fled or were expelled to the Arab front lines, and following resistance in Lydda, the population there was expelled without provision of transport vehicles; some of the evictees died on the long walk under the hot July sun.
On 15–16 July, an attack on Latrun took place but did not manage to occupy the fort. A desperate second attempt occurred on 18 July by units from the Yiftach Brigade equipped with armored vehicles, including two Cromwell tanks, but that attack also failed. Despite the second truce, which began on 18 July, the Israeli efforts to conquer Latrun continued until 20 July.
Operation Kedem aim was to secure the Old City of Jerusalem, but fewer resources were allocated. The operation failed. Originally the operation was to begin on 8 July, immediately after the first truce, by Irgun and Lehi forces. However, it was delayed by David Shaltiel, possibly because he did not trust their ability after their failure to capture Deir Yassin without Haganah assistance.
Irgun forces commanded by Yehuda Lapidot were to break through at the New Gate, Lehi was to break through the wall stretching from the New Gate to the Jaffa Gate, and the Beit Horon Battalion was to strike from Mount Zion.
The battle was planned to begin on the Shabbat, at 20:00 on 16 July, two days before the second ceasefire of the war. The plan went wrong from the beginning and was postponed first to 23:00 and then to midnight. It was not until 02:30 that the battle actually began. The Irgun managed to break through at the New Gate, but the other forces failed in their missions. At 05:45 on 17 July, Shaltiel ordered a retreat and to cease hostilities.
On 14 July 1948, Irgun occupied the Arab village of Malha after a fierce battle. Several hours later, the Arabs launched a counterattack, but Israeli reinforcements arrived, and the village was retaken at a cost of 17 dead.
The second plan was Operation Dekel, which was aimed at capturing the Lower Galilee including Nazareth. Nazareth was captured on 16 July, and by the time the second truce took effect at 19:00 18 July, the whole Lower Galilee from Haifa Bay to the Sea of Galilee was captured by Israel.
Operation Brosh was launched in a failed attempt to dislodge Syrian forces from the Eastern Galilee and the Benot Yaakov Bridge. During the operation, 200 Syrians and 100 Israelis were killed. The Israeli Air Force also bombed Damascus for the first time.
Second truce: 18 July – 15 October 1948
At 19:00 on 18 July, the second truce of the conflict went into effect after intense diplomatic efforts by the UN.
On 16 September, Count Folke Bernadotte proposed a new partition for Palestine in which the Negev would be divided between Jordan and Egypt, and Jordan would annex Lydda and Ramla. There would be a Jewish state in the whole of Galilee, with the frontier running from Faluja northeast towards Ramla and Lydda. Jerusalem would be internationalized, with municipal autonomy for the city's Jewish and Arab inhabitants, the Port of Haifa would be a free port, and Lydda Airport would be a free airport. All Palestinian refugees would be granted the right of return, and those who chose not to return would be compensated for lost property. The UN would control and regulate Jewish immigration.
The plan was once again rejected by both sides. On the next day, 17 September, Bernadotte was assassinated in Jerusalem by the militant Zionist group Lehi. A four-man team ambushed Bernadotte's motorcade in Jerusalem, killing him and a French UN observer sitting next to him. Lehi saw Bernadotte as a British and Arab puppet, and thus a serious threat to the emerging State of Israel, and feared that the provisional Israeli government would accept the plan, which it considered disastrous. Unbeknownst to Lehi, the government had already decided to reject it and resume combat in a month. Bernadotte's deputy, American Ralph Bunche, replaced him.
On 22 September 1948, the Provisional State Council of Israel passed the Area of Jurisdiction and Powers Ordnance, 5708–1948. The law officially added to Israel's size by annexing all land it had captured since the war began. It also declared that from then on, any part of Palestine captured by the Israeli army would automatically become part of Israel.
Little triangle pocket
The Arab villagers of the area known as the "Little Triangle" south of Haifa, repeatedly fired at Israeli traffic along the main road from Tel Aviv to Haifa and were supplied by the Iraqis from northern Samaria. The sniping at traffic continued during the Second Truce. The poorly planned assaults on 18 June and 8 July had failed to dislodge Arab militia from their superior positions. The Israelis launched Operation Shoter on 24 July in order to gain control of the main road to Haifa and to destroy all the enemy in the area. Israeli assaults on 24 and 25 July were beaten back by stiff resistance. The Israelis then broke the Arab defenses with an infantry and armour assault backed by heavy artillery shelling and aerial bombing. Three Arab villages surrendered, and most of the inhabitants fled before and during the attack. The Israeli soldiers and aircraft struck at one of the Arab retreat routes, killing 60 Arab soldiers.. Most of the inhabitants fled before and during the attack, reaching northern Samaria; hundreds were forcibly expelled during the following days. At least a hundred militiamen and civilians were killed.
The Arabs claimed that the Israelis had massacred Arab civilians, but the Israelis rejected the claims. A United Nations investigation found no evidence of a massacre. Following the operation, the Tel Aviv-Haifa road was open to Israeli military and civilian traffic, and Arab roadblocks along the route were removed. Traffic along the Haifa-Hadera coastal railway was also restored.
Third phase: 15 October 1948 – 10 March 1949
Israel launched a series of military operations to drive out the Arab armies and secure the northern and southern borders of Israel.
Northern front – Galilee
On 22 October, the third truce went into effect. Irregular Arab forces refused to recognize the truce, and continued to harass Israeli forces and settlements in the north. On the same day that the truce came into effect, the Arab Liberation Army violated the truce by attacking Manara, capturing the strongpoint of Sheikh Abed, repulsing counterattacks by local Israeli units, and ambushed Israeli forces attempting to relieve Manara. The IDF's Carmeli Brigade lost 33 dead and 40 wounded. Manara and Misgav Am were totally cut off, and Israel's protests at the UN failed to change the situation.
On 24 October, the IDF launched Operation Hiram and captured the entire upper Galilee area, driving the ALA and Lebanese Army back to Lebanon, and ambushing and destroying an entire Syrian battalion. The Israeli force of four infantry brigades was commanded by Moshe Carmel. The entire operation lasted just 60 hours, during which numerous villages were captured, often after locals or Arab forces put up resistance. Arab losses were estimated at 400 dead and 550 taken prisoner, with low Israeli casualties.
Some prisoners were reportedly executed by the Israeli forces. An estimated 50,000 Palestinian refugees fled into Lebanon, some of them fleeing ahead of the advancing forces, and some expelled from villages which had resisted, while the Arab inhabitants of those villages which had remained at peace were allowed to remain and became Israeli citizens. The villagers of Iqrit and Birim were persuaded to leave their homes by Israeli authorities, who promised them that they would be allowed to return. Israel eventually decided not to allow them to return, and offered them financial compensation, which they refused to accept.
At the end of the month, the IDF had captured the whole of Galilee, driven all Lebanese forces out of Israel, and had advanced 5 miles (8.0 km) into Lebanon to the Litani River, occupying thirteen Lebanese villages. In the village of Hula, two Israeli officers killed between 35 and 58 prisoners as retaliation for the Haifa Oil Refinery massacre. Both officers were later put on trial for their actions.
Israel launched a series of military operations to drive out the Arab armies and secure the borders of Israel. However, invading the West Bank might have brought into the borders of the expanding State of Israel a massive Arab population it could not absorb. The Negev desert was an empty space for expansion, so the main war effort shifted to Negev from early October. Israel decided to destroy or at least drive out the Egyptian expeditionary force since the Egyptian front lines were too vulnerable as permanent borders.
On 15 October, the IDF launched Operation Yoav in the northern Negev. Its goal was to drive a wedge between the Egyptian forces along the coast and the Beersheba-Hebron-Jerusalem road and ultimately to conquer the whole Negev. This was a special concern on the Israeli part because of a British diplomatic campaign to have the entire Negev handed over to Egypt and Jordan, and which thus made Ben-Gurion anxious to have Israeli forces in control of the Negev as soon as possible.
Operation Yoav was headed by the Southern Front commander Yigal Allon. Committed to Yoav were three infantry and one armoured brigades, who were given the task of breaking through the Egyptian lines. The Egyptian positions were badly weakened by the lack of a defense in depth, which meant that once the IDF had broken through the Egyptian lines, there was little to stop them. The operation was a huge success, shattering the Egyptian ranks and forcing the Egyptian Army from the northern Negev, Beersheba and Ashdod.
In the so-called "Faluja Pocket", an encircled Egyptian force was able to hold out for four months until the 1949 Armistice Agreements, when the village was peacefully transferred to Israel and the Egyptian troops left. Four warships of the Israeli Navy provided support by bombarding Egyptian shore installations in the Ashkelon area, and preventing the Egyptian Navy from evacuating retreating Egyptian troops by sea.
On 19 October, Operation Ha-Har commenced in the Jerusalem Corridor, while a naval battle also took place near Majdal (now Ashkelon), with three Israeli corvettes facing an Egyptian corvette with air support. An Israeli sailor was killed and four wounded, and two of the ships were damaged. One Egyptian plane was shot down, but the corvette escaped. Israeli naval vessels also shelled Majdal on 17 October, and Gaza on 21 October, with air support from the Israeli Air Force. The same day, the IDF captured Beersheba, and took 120 Egyptian soldiers prisoner. On 22 October, Israeli naval commandos using explosive boats sank the Egyptian flagship Emir Farouk, and damaged an Egyptian minesweeper.
On 9 November 1948, the IDF launched Operation Shmone to capture the Tegart fort in the village of Iraq Suwaydan. The fort's Egyptian defenders had previously repulsed eight attempts to take it, including two during Operation Yoav. Israeli forces bombarded the fort before an assault with artillery and airstrikes by B-17 bombers. After breaching the outlying fences without resistance, the Israelis blew a hole in the fort's outer wall, prompting the 180 Egyptian soldiers manning the fort to surrender without a fight. The defeat prompted the Egyptians to evacuate several nearby positions, including hills the IDF had failed to take by force. Meanwhile, IDF forces took Iraq Suwaydan itself after a fierce battle, losing 6 dead and 14 wounded.
From 5 to 7 December, the IDF conducted Operation Assaf to take control of the Western Negev. The main assaults were spearheaded by mechanized forces, while Golani Brigade infantry covered the rear. An Egyptian counterattack was repulsed. The Egyptians planned another counterattack, but it failed after Israeli aerial reconnaissance revealed Egyptian preparations, and the Israelis launched a preemptive strike. About 100 Egyptians were killed, and 5 tanks were destroyed, with the Israelis losing 5 killed and 30 wounded.
On 22 December, the IDF launched Operation Horev (also called Operation Ayin). The goal of the operation was to drive all remaining Egyptian forces from the Negev, destroying the Egyptian threat on Israel's southern communities and forcing the Egyptians into a ceasefire. During five days of fighting, the Israelis secured the Western Negev, expelling all Egyptian forces from the area.
Israeli forces subsequently launched raids into the Nitzana area, and entered the Sinai Peninsula on 28 December. The IDF captured Umm Katef and Abu Ageila, and advanced north towards Al Arish, with the goal of encircling the entire Egyptian expeditionary force. Israeli forces pulled out of the Sinai on 2 January 1949 following joint British-American pressure and a British threat of military action. IDF forces regrouped at the border with the Gaza Strip. Israeli forces attacked Rafah the following day, and after several days of fighting, Egyptian forces in the Gaza Strip were surrounded. The Egyptians agreed to negotiate a ceasefire on 7 January, and the IDF subsequently pulled out of Gaza. According to Morris, "the inequitable and unfair rules of engagement: the Arabs could launch offensives with impunity, but international interventions always hampered and restrained Israel’s counterattacks."
On 28 December, the Alexandroni Brigade failed to take the Falluja Pocket, but managed to seize Iraq el-Manshiyeh and temporarily hold it. The Egyptians counterattacked, but were mistaken for a friendly force and allowed to advance, trapping a large number of men. The Israelis lost 87 soldiers.
On 5 March, Operation Uvda was launched following nearly a month of reconnaissance, with the goal of securing the Southern Negev from Jordan. The IDF entered and secured the territory, but did not meet significant resistance along the way, as the area was already designated to be part of the Jewish state in the UN Partition Plan, and the operation meant to establish Israeli sovereignty over the territory rather than actually conquer it. The Golani, Negev, and Alexandroni brigades participated in the operation, together with some smaller units and with naval support.
On 10 March, Israeli forces secured the Southern Negev, reaching the southern tip of Palestine: Umm Rashrash on the Red Sea (where Eilat was built later) and taking it without a battle. Israeli soldiers raised a hand-made Israeli flag ("The Ink Flag") at 16:00 on 10 March, claiming Umm Rashrash for Israel. The raising of the Ink Flag is considered to be the end of the war.
Anglo-Israeli air clashes
As the fighting progressed and Israel mounted an incursion into the Sinai, the Royal Air Force began conducting almost daily reconnaissance missions over Israel and the Sinai. RAF reconnaissance aircraft took off from Egyptian airbases and sometimes flew alongside Royal Egyptian Air Force planes. High-flying British aircraft frequently flew over Haifa and Ramat David Airbase, and became known to the Israelis as the "shuftykeit."
On 20 November 1948, an unarmed RAF photo-reconnaissance De Havilland Mosquito of No. 13 Squadron RAF was shot down by an Israeli Air Force P-51 Mustang flown by American volunteer Wayne Peake as it flew over the Galilee towards Hatzor Airbase. Peake opened fire with his cannons, causing a fire to break out in the port engine. The aircraft turned to sea and lowered its altitude, then exploded and crashed off Ashdod. Both of the crew were killed.
Just before noon on 7 January 1949, four Spitfire FR18s from No. 208 Squadron RAF on a reconnaissance mission in the Deir al-Balah area flew over an Israeli convoy that had been attacked by five Egyptian Spitfires fifteen minutes earlier. The pilots had spotted smoking vehicles and were drawn to the scene out of curiosity. Two planes dived to below 500 feet altitude to take pictures of the convoy, while the remaining two covered them from 1,500 feet.
Israeli soldiers on the ground, alerted by the sound of the approaching Spitfires and fearing another Egyptian air attack, opened fire with machine guns. One Spitfire was shot down by a tank-mounted machine gun, while the other was lightly damaged and rapidly pulled up. The remaining three Spitfires were then attacked by patrolling IAF Spitfires flown by Slick Goodlin and John McElroy, volunteers from the United States and Canada respectively. All three Spitfires were shot down, and one pilot was killed.
Two pilots were captured by Israeli soldiers and taken to Tel Aviv for interrogation, and were later released. Another was rescued by Bedouins and handed over to the Egyptian Army, which turned him over to the RAF. Later that day, four RAF Spitfires from the same squadron escorted by seven Hawker Tempests from No. 213 Squadron RAF and eight from No. 6 Squadron RAF went searching for the lost planes, and were attacked by four IAF Spitfires. The Israeli formation was led by Ezer Weizman. The remaining three were manned by Weizman's wingman Alex Jacobs and American volunteers Bill Schroeder and Caesar Dangott. The Tempests found they could not jettison their external fuel tanks, and some had non-operational guns. Schroeder shot down a British Tempest, killing pilot David Tattersfield, and Weizman severely damaged a British plane flown by Douglas Liquorish. Weizman's plane and two other British aircraft also suffered light damage during the engagement. The battle ended after the British wiggled their wings to be more clearly identified, and the Israelis eventually realized the danger of their situation and disengaged, returning to Hatzor Airbase.
Israeli Prime Minister David Ben-Gurion personally ordered the wrecks of the RAF fighters that had been shot down to be dragged into Israeli territory. Israeli troops subsequently visited the crash sites, removed various parts, and buried the other aircraft. However, the Israelis did not manage to conceal the wrecks in time to prevent British reconnaissance planes from photographing them. An RAF salvage team was deployed to recover the wrecks, entering Israeli territory during their search. Two were discovered inside Egypt, while Tattersfield's Tempest was found north of Nirim, four miles inside Israel. Interviews with local Arabs confirmed that the Israelis had visited the crash sites to remove and bury the wrecks. Tattersfield was initially buried near the wreckage, but his body was later removed and reburied at the British War Cemetery in Ramla.
In response, the RAF readied all Tempests and Spitfires to attack any IAF aircraft they encountered and bomb IAF airfields. British troops in the Middle East were placed on high alert with all leave cancelled, and British citizens were advised to leave Israel. The Royal Navy was also placed on high alert. At Hatzor Airbase, the general consensus among the pilots, most of whom had flown with or alongside the RAF during World War II, was that the RAF would not allow the loss of five aircraft and two pilots to go without retaliation, and would probably attack the base at dawn the next day. That night, in anticipation of an impending British attack, some pilots decided not to offer any resistance and left the base, while others prepared their Spitfires and were strapped into the cockpits at dawn, preparing to repel a retaliatory airstrike. However, despite pressure from the squadrons involved in the incidents, British commanders refused to authorize any retaliatory strikes.
The day following the incident, British pilots were issued a directive to regard any Israeli aircraft infiltrating Egyptian or Jordanian airspace as hostile and to shoot them down, but were also ordered to avoid activity close to Israel's borders. Later in January 1949, the British managed to prevent the delivery of aviation spirit and other essential fuels to Israel in retaliation for the incident. The British Foreign Office presented the Israeli government with a demand for compensation over the loss of personnel and equipment.
UN Resolution 194
In December 1948, the UN General Assembly passed Resolution 194. It called to establish a UN Conciliation Commission to facilitate peace between Israel and Arab states. However, many of the resolution's articles were not fulfilled, since these were opposed by Israel, rejected by the Arab states, or were overshadowed by war as the 1948 conflict continued.
Largely leftover World War II era weapons were used by both sides. Egypt had some British equipment; the Syrian army had some French. German, Czechoslovak and British equipment was used by Israel.
1949 Armistice Agreements
In 1949, Israel signed separate armistices with Egypt on 24 February, Lebanon on 23 March, Jordan on 3 April, and Syria on 20 July. The Armistice Demarcation Lines, as set by the agreements, saw the territory under Israeli control encompassing approximately three-quarters of the prior British administered Mandate as it stood after Transjordan's independence in 1946. Israel occupied territories of about one-third more than was allocated to the Jewish State under the UN partition proposal. After the armistices, Israel had control over 78% of the territory comprising former Mandatory Palestine or some 8,000 square miles (21,000 km2), including the entire Galilee and Jezreel Valley in the north, whole Negev in south, West Jerusalem and the coastal plain in the center.
The armistice lines were known afterwards as the "Green Line". The Gaza Strip and the West Bank (including East Jerusalem) were occupied by Egypt and Jordan respectively. The United Nations Truce Supervision Organization and Mixed Armistice Commissions were set up to monitor ceasefires, supervise the armistice agreements, to prevent isolated incidents from escalating, and assist other UN peacekeeping operations in the region.
Just before the signing of the Israel-Jordan armistice agreement, general Yigal Allon proposed to conquer the West Bank up to the Jordan River as the natural, defensible border of the state. Ben-Gurion refused, although he was aware that the IDF was militarily strong enough to carry out the conquest. He feared the reaction of Western powers and wanted to maintain good relations with the United States and not to provoke the British. More, the results of the war were already satisfactory and Israeli leaders had to build a nation.
Israel lost 6,373 of its people, about 1% of its population at the time, in the war. About 4,000 were soldiers and the rest were civilians. Around 2,000 were Holocaust survivors.
The exact number of Arab casualties is unknown. One estimate places the Arab death toll at 7,000, including 3,000 Palestinians, 2,000 Egyptians, 1,000 Jordanians, and 1,000 Syrians. In 1958, Palestinian historian Aref al-Aref calculated that the Arab armies' combined losses amounted to 3,700, with Egypt losing 961 regular and 200 irregular soldiers and Jordan losing 362 regulars and 200 irregulars. According to Henry Laurens, the Palestinians suffered double the Jewish losses, with 13,000 dead, 1,953 of whom are known to have died in combat situations. Of the remainder, 4,004 remain nameless but the place, tally and date of their death is known, and a further 7,043, for whom only the place of death is known, not their identities nor the date of their death. According to Laurens, the largest part of Palestinian casualties consisted of non-combatants and corresponds to the successful operations of the Israelis.
During the 1947–1948 Civil War in Mandatory Palestine and the 1948 Arab–Israeli War that followed, around 750,000 Palestinian Arabs fled or were expelled from their homes, out of approximately 1,200,000 Arabs living in former British Mandate of Palestine. In 1951, the UN Conciliation Commission for Palestine estimated that the number of Palestinian refugees displaced from Israel was 711,000.
This number did not include displaced Palestinians inside Israeli-held territory. More than 400 Arab villages, and about ten Jewish villages and neighborhoods, were depopulated during the Arab-Israeli conflict, most of them during 1948. According to estimate based on earlier census, the total Muslim population in Palestine was 1,143,336 in 1947. The causes of the 1948 Palestinian exodus are a controversial topic among historians. After the war, around 156,000 Arabs remained in Israel and became Israeli citizens.
Displaced Palestinian Arabs, known as Palestinian refugees, were settled in Palestinian refugee camps throughout the Arab world. The United Nations established UNRWA as a relief and human development agency tasked with providing humanitarian assistance to Palestinian refugees. Arab nations refused to absorb Palestinian refugees, instead keeping them in refugee camps while insisting that they be allowed to return.
Refugee status was also passed on to their descendants, who were also largely denied citizenship in Arab states, except in Jordan. The Arab League instructed its members to deny Palestinians citizenship "to avoid dissolution of their identity and protect their right of return to their homeland." More than 1.4 million Palestinians still live in 58 recognized refugee camps, while more than 5 million Palestinians live outside Israel and the Palestinian territories.
The Palestinian refugee problem and debate about the Palestinian right of return are also major issues of the Arab-Israeli conflict. Palestinians and their supporters have staged annual demonstrations and commemorations on 15 May of each year, which is known to them as "Nakba Day". The popularity and number of participants in these annual Nakba demonstrations has varied over time. During the Second Intifada after the failure of the Camp David 2000 Summit, the attendance at the demonstrations against Israel increased.
|Jewish exodus from|
Arab and Muslim
During the 1948 War, around 10,000 Jews were forced to evacuate their homes from Arab dominated parts of former Mandatory Palestine. But in the three years from May 1948 to the end of 1951, 700,000 Jews settled in Israel, mainly along the borders and in former Arab lands, doubling the Jewish population there. Of these, upwards of 300,000 arrived from Asian and North African nations. Among them, the largest group (over 100,000) was from Iraq. The remaining came mostly from Europe, including 136,000 from the 250,000 displaced Jews of World War II living in refugee camps and urban centers in Germany, Austria, and Italy, and more than 270,000 coming from Eastern Europe, mainly Romania and Poland (over 100,000 each). On the establishment of the state, a top priority was given to a policy for the "ingathering of exiles", and the Mossad LeAliyah Bet gave key assistance to the Jewish Agency to organize immigrants from Europe and the Middle East, and arrange for their transport to Israel. For Ben-Gurion, a fundamental defect of the State was that 'it lacked Jews'.
Jewish immigrants from Arab and Muslim countries left for numerous reasons. The war's outcome had exacerbated Arab hostilities to local Jewish communities. News of the victory aroused messianic expectations in Libya and Yemen; Zionism had taken root in many countries; active incentives for making aliyah formed a key part of Israeli policy; and better economic prospects and security were to be expected from a Jewish state. Some Arab governments, Egypt, for example, held their Jewish communities hostage at times. Persecution, political instability, and news of a number of violent pogroms also played a role. Some 800,000–1,000,000 Jews eventually left the Arab world over the next three decades as a result of these various factors. Approximately 680,000 of them immigrated to Israel; the rest mostly settled in Europe (mainly France) or the Americas.
Israel initially relied on Jewish Agency-run tent camps known as immigrant camps to accommodate displaced Jews from Europe and Muslim nations. In the 1950s, these were transformed into transition camps ("Ma'abarot"), where living conditions were improved and tents were replaced with tin dwellings. Unlike the situation in the immigrant camps, when the Jewish Agency provided for immigrants, residents of the transition camps were required to provide for themselves. These camps began to decline in 1952, with the last one closing in 1963. The camps were largely transformed into permanent settlements known as development towns, while others were absorbed as neighborhoods of the towns they were attached to, and the residents were given permanent housing in these towns and neighborhoods.
Most development towns eventually grew into cities. Some Jewish immigrants were also given the vacant homes of Palestinian refugees. There were also attempts to settle Jewish refugees from Arab and Muslim countries in moshavim (cooperative farming villages), though these efforts were only partially successful, as they had historically been craftsmen and merchants in their home countries, and did not traditionally engage in farm work.
After the war, Israeli and Palestinian historiographies differed on the interpretation of the events of 1948: in the West the majority view was of a tiny group of vastly outnumbered and ill-equipped Jews fighting off the massed strength of the invading Arab armies; it was also widely believed that the Palestinian Arabs left their homes on the instruction of their leaders.
From 1980, with the opening of the Israeli and British archives, some Israeli historians have developed a different account of the period. In particular, the role played by Abdullah I of Jordan, the British government, the Arab aims during the war, the balance of force and the events related to the Palestinian exodus have been nuanced or given new interpretations. Some of them are still hotly debated among historians and commentators of the conflict today.
In popular culture
A 2015 PBS documentary, A Wing and a Prayer, depicts the Al Schwimmer-led airborne smuggling missions to arm Israel.
The film Cast a Giant Shadow, tells the story of an American colonel who was instrumental in the Israeli victory.
- 1948 Palestinian exodus
- Jewish exodus from Arab and Muslim countries
- List of battles and operations in the 1948 Palestine war
- List of villages depopulated during the Arab–Israeli conflict
- List of modern conflicts in the Middle East
- Arms shipments from Czechoslovakia to Israel 1947–49
- ↑ This includes the entire military personnel count – both combat units and logistical units.
- ↑ At maximum, not half of the forces of the Israelis but these numbers include only the combat units sent to the former mandate-territory of Palestine, not the entire military strength.</ref>Casualties and losses
6,373 killed (about 4,000 fighters and 2,400 civilians)
3,000–13,000 killed (both fighters and civilians)<ref>Morris 2008, pp. 404–06.
- ↑ Anita Shapira, L'imaginaire d'Israël : histoire d'une culture politique (2005), Latroun : la mémoire de la bataille, Chap. III. 1 l'événement pp. 91–96
- ↑ Benny Morris (2008), p. 419.
- 1 2 3 4 Oren 2003, p. 5.
- ↑ Morris (2008), p. 260.
- ↑ Gelber, pp. 55, 200, 239
- ↑ Morris, 2008, p. 332.
- 1 2 Gelber (2006), p. 12.
- ↑ Pollack, 2004; Sadeh, 1997
- 1 2 Politics and society in modern Israel: myths and realities. Google Books. 2000. ISBN 9780765605146. Retrieved 28 March 2011.
- 1 2 Laurens 2007 p. 194
- ↑ David Tal,War in Palestine, 1948: Israeli and Arab Strategy and Diplomacy, p. 153.
- ↑ Benny Morris (2008), p. 401.
- 1 2 3 4 5 6 7 Morris,2008, pp. 236, 237, 247, 253, 254
- ↑ Zeev Maoz, Defending the Holy Land, University of Michigan Press, 2009 p. 4: 'A combined invasion of a Jordanian and Egyptian army started . . . The Syrian and the Lebanese armies engaged in a token effort but did not stage a major attack on the Jewish state.'
- ↑ Rogan and Shlaim 2007 p. 99.
- ↑ Cragg 1997 pp. 57, 116.
- ↑ Benvenisti, Meron (1996), City of Stone: The Hidden History of Jerusalem, University of California Press, ISBN 0-520-20521-9. p. 27
- ↑ – Benny Morris, 2004. The Birth of the Palestinian Refugee Problem Revisited, pp. 602–604. Cambridge University Press; ISBN 978-0-521-00967-6. "It is impossible to arrive at a definite persuasive estimate. My predilection would be to opt for the loose contemporary British formula, that of 'between 600,000 and 760,000' refugees; but, if pressed, 700,000 is probably a fair estimate";
– Memo US Department of State, 4 May 1949, FRUS, 1949, p. 973.: "One of the most important problems which must be clared up before a lasting peace can be established in Palestine is the question of the more than 700,000 Arab refugees who during the Palestine conflict fled from their homes in what is now Israeli occupied territory and are at present living as refugees in Arab Palestine and the neighbouring Arab states.";
– Memorandum on the Palestine Refugee Problem, 4 May 1949, FRUS, 1949, p. 984.: "Approximately 700,000 refugees from the Palestine hostilities, now located principally in Arab Palestine, Transjordan, Lebanon and Syria, will require repatriation to Israel or resettlement in the Arab states."
- 1 2 Morris, 2001, pp. 259–60.
- ↑ Morris, 2008, pp. 66–69
- ↑ UNITED NATIONS: General Assembly: A/RES/181(II): 29 November 1947: Resolution 181 (II). Future government of Palestine.
- ↑ Greg Cashman, Leonard C. Robinson, An Introduction to the Causes of War: Patterns of Interstate Conflict from World War 1 to Iraq, Rowman & Littlefield 2007 p. 165.
- ↑ Benjamin Grob-Fitzgibbon,Imperial Endgame: Britain's Dirty Wars and the End of Empire, Palgrave/Macmillan 2011 p. 57
- ↑ Ilan Pappé (2000), p. 111
- ↑ Morris 2008, p. 76
- ↑ Efraïm Karsh (2002), p. 30
- ↑ Benny Morris (2003), p. 101
- ↑ Yoav Gelber (2006), pp. 51–56
- ↑ Dominique Lapierre et Larry Collins (1971), chap. 7, pp. 131–53
- ↑ Benny Morris (2003), p. 163
- ↑ Dominique Lapierre et Larry Collins (1971), p. 163
- ↑ Benny Morris (2003), p. 67
- ↑ Henry Laurens (2005), p. 83
- ↑ David Tal, War in Palestine, 1948: Israeli and Arab Strategy and Diplomacy, Routledge 2004 p. 89.
- ↑ Benny Morris (2008). 1948: a history of the first Arab-Israeli war. Yale University Press. p. 116. Retrieved 13 July 2013.
At the time, Ben-Gurion and the HGS believed that they had initiated a one-shot affair, albeit with the implication of a change of tactics and strategy on the Jerusalem front. In fact, they had set in motion a strategic transformation of Haganah policy. Nahshon heralded a shift from the defensive to the offensive and marked the beginning of the implementation of tochnit dalet (Plan D) – without Ben-Gurion or the HGS ever taking an in principle decision to embark on its implementation.
- ↑ David Tal, pp. 89–90.
- ↑ Dominique Lapierre et Larry Collins (1971), pp. 369–81
- ↑ Benny Morris (2003), pp. 242–43
- ↑ Benny Morris (2003), p. 242
- ↑ Henry Laurens (2005), pp. 85–86
- ↑ Benny Morris (2003), pp. 248–52
- ↑ Benny Morris (2003), pp. 252–54
- 1 2 3 4 5 6 Morris, 2003, p. 16.
- ↑ Martin Van Creveld, Sword and the Olive: A Critical History of the Israeli Defense Force, Public Affairs (1998) 2002 p. 78
- ↑ "A Wing and a Prayer". American Public Television.
- ↑ A Wing and a Prayer, retrieved 2015-12-11
- ↑ How a fake kibbutz was built to hide a bullet factory – Haaretz
- ↑ Gelber, p. 73; Karsh 2002, p. 25.
- 1 2 3 Karsh 2002, p. 25
- 1 2 W. Khalidi, 'Plan Dalet: Master Plan for the Conquest of Palestine', J. Palestine Studies 18(1), pp. 4–33, 1988 (reprint of a 1961 article)
- ↑ Joseph, Dov. "The Faithful City – The Siege of Jerusalem, 1948." Simon and Suchuster, 1960. Congress # 60 10976. pp. 23, 38.
- ↑ Levin, Harry. "Jerusalem Embattled – A Diary of the City under Siege." Cassels, 1997. ISBN 9780304337651. pp. 32, 117. Pay £P2 per month. c.f. would buy 2lb of meat in Jerusalem, April 1948. p. 91.
- ↑ "Mi5 Files of Jewish Interest "the activities of Irgun, the Jewish organisation involved or implicated in numerous acts of terrorism in the closing years of the British mandate in Palestine"". Nationalarchives.gov.uk. Retrieved 2014-06-29.
- ↑ Benny Morris (2004), p. 16
- ↑ Gelber (2006), p. 73
- ↑ D. Kurzman, "Genesis 1948", 1970, p. 282.
- ↑ Henry Laurens, La Question de Palestine, vol.3, Fayard 2007 p. 70
- ↑ Bregman, Ahron (2010). Israel's Wars : A History Since 1947 (3rd ed.). London: Taylor & Francis. pp. 23, 24. ISBN 0415424380. Retrieved 19 April 2015.
- 1 2 Morris, 2008, pp. 397–98.
- ↑ Moshe Naor,Social Mobilization in the Arab/Israeli War of 1948: On the Israeli Home Front, Routledge 2013 p. 15.
- ↑ Pappe, Ilan. The Ethnic Cleansing of Palestine.
- ↑ Pappé, 2006, pp.xii, 86–126
- ↑ Gelber 2006 p. 306
- ↑ Morris 2008 p. 119
- 1 2 3 Yoav Gelber, 2006, p. 137.
- 1 2 Gelber (2006), p. 11
- ↑ Henry Laurens, La Question de Palestine, Fayard, 2007 p. 32.
- 1 2 Gelber (2006), p. 11.
- ↑ "PDF copy of Cablegram from the Secretary-General of the League of Arab States to the Secretary-General of the United Nations: S/745: 15 May 1948: Retrieved 6 June 2012". Un.org. 2002-09-09. Retrieved 2014-06-29.
- ↑ Morris 2008 p. 187; quoting p. 24 of Kirkbride's memoirs
- ↑ "Azzam's Genocidal Threat". The Middle East Quarterly. Fall 2011. Retrieved 6 January 2012.
- ↑ Rogan and Shlaim 2007 p. 110.
- ↑ Morris, 2008, p. 310
- 1 2 Sela, 2002, p. 14.
- 1 2 3 4 5 6 7 Karsh 2002, p. 26
- ↑ Karsh 2002, p. 51
- ↑ Morris (2008), pp. 190–92
- ↑ Avi Shlaim (1988). The Politics of Partition: King Abdullah, the Zionists and Palestine 1921–1951. Columbia University Press. ISBN 978-0-231-07365-3.
- ↑ Tal,War in Palestine, 1948: Israeli and Arab Strategy and Diplomacy, p. 154.
- ↑ Zamir, 2010, p. 34
- ↑ Tripp, 2001, p. 137.
- ↑ Gamal Abdel Nasser. "Nasser's memoirs of the first palestine war" (PDF). Walid Khalidi (trans.). Journal of Palestine studies, Vol. 2 no. 2 (Win. 73): 3–32. p. 9.
why did the first communique described the Palestine operations as a merely punitive expedition against the Zionist "gangs"
- ↑ Morris, 2004 pp. 76, 82, 104, 126, 130, 202, 253
- ↑ Shlaim, 2001, p. 97.
- ↑ Shlaim, 2001, p. 99.
- ↑ Benny Morris (2003), p. 189.
- ↑ Martin Van Creveld,Sword and the Olive: A Critical History of the Israeli Defense Force,, Public Affairs (1998) 2002 p. 75
- ↑ Morris (2003), pp. 32–33.
- ↑ Morris (2008), p. 81.
- ↑ Benny (2008), p. 174.
- ↑ Martin Van Creveld,Sword and the Olive: A Critical History of the Israeli Defense Force,, Public Affairs (1998) 2002 p. 78
- ↑ Morris 2008 p. 185
- 1 2 Morris, 2003, p. 35.
- ↑ Morris, 2008, p. 401
- ↑ Collins and LaPierre, 1973 p. 355
- 1 2 3 4 Zamir, Meir (January 2010). "'Bid' for Altalena: France's Covert Action in the 1948 War in Palestine". Middle Eastern Studies. Routledge. 46 (1): 22. doi:10.1080/00263200903432258.
a) the suspension of arms sales to Syria, notwithstanding signed contracts; b) prevention of a large sale of arms by a Swiss company to Ethiopia, which was actually destined for Egypt and Jordan; c) diplomatic pressure on Belgium to suspend arms sales to the Arab states; d) denial of a British request at the end of April to permit the landing of a squadron of British aircraft on their way to Transjordan; e) authorization of Air France to transport cargo to Tel Aviv on 13 May; f) allowing aircraft [carrying arms from Czechoslovakia] to land on French territory in transit to Israel; g) discreet French diplomatic support for Israel in the UN; h) two arms shipments to ‘Nicaragua’, which were actually intended for Israel.
- ↑ Bregman, Ahron (2002). Israel's Wars: A History since 1947. Routledge. p. 24. ISBN 9780415287166.
- ↑ Morgan, Michael L.:The Philosopher as Witness: Fackenheim and Responses to the Holocaust, p. 182
- ↑ Ben Gurion, David War Diaries, 1947–1949. Arabic edition translated by Samir Jabbour. Institute of Palestine Studies, Beirut, 1994. p. 303.
- ↑ Morris, 2008: pp. 176–77
- 1 2 3 "Wars of the World: Israeli War of Independence 1948–1949". Onwar.com. Retrieved 2014-06-29.
- ↑ Laffin, John: The Israeli Army in the Middle East Wars 1948–73, p. 8
- ↑ Laurens, vol. 3 p. 69.
- ↑ Yaakov, Yifa (2014-02-02). "British deserter who stole tanks for Haganah dies". Timesofisrael.com. Retrieved 2014-06-29.
- ↑ Gelber (2006), p. 50.
- ↑ Karsh 2002, pp. 26–27
- 1 2 Karsh 2002, p. 27
- ↑ "TRANS-JORDAN: Chess Player & Friend". Time. 16 February 1948. Retrieved 20 April 2010.
- ↑ Ma'an Abu Nawar, The Jordanian-Israeli war, 1948–1951: a history of the Hashemite Kingdom of Jordan, p. 393.
- ↑ Benny Morris, Victimes : histoire revisitée du conflit arabo-sioniste, 2003, pp. 241, 247–55.
- ↑ Pollack 2004, p. ?.
- ↑ D. Kurzman, 'Genesis 1948', 1972, p. 382.
- ↑ I. Pappe, "The ethnic cleansing of Palestine", 2006, p. 129.
- 1 2 Pollack, 2002, pp. 149–55.
- ↑ Yoav Gelber, 2006, "Sharon's Inheritance" Archived 5 June 2013 at the Wayback Machine.
- ↑ Rogan and Shlaim 2001, p. 8.
- ↑ Pollack, 2002, pp. 15–27.
- ↑ D. Kurzman, "Genesis 1948", 1972, p. 556.
- ↑ Charles Tripp (2002). A History of Iraq. Cambridge University Press. p. 73. ISBN 978-0-521-52900-6.
.= Iraq had dispatched 3,000 troops to the front in May and in the months that followed a further 15,000 troops were sent, making them the largest single Arab force in Palestine (also – The War for Palestine: Rewriting the History of 1948, edited by Eugene L. Rogan, Avi Shlaim, chapter at pp. 125–49)
- ↑ Pollack, 2002, p. 150.
- ↑ Gelber, p. 55
- ↑ Morris, 2008, pp. 322 and 326.
- ↑ Uthman Hasan Salih. DAWR AL-MAMLAKA AL-'ARABIYYA AL-SA'UDIYYA FI HARB FILASTIN 1367H/1948 (The role of Saudi Arabia in the Palestine war of 1948), Revue d'Histoire Maghrébine [Tunisia] 1986 13(43–44): 201–21. ISSN 0330-8987.
- ↑ Morris, 2008, p. 205; cites British diplomatic communications.
- ↑ Gelber, p. 200
- ↑ Gelber, p. 203
- ↑ Gelber, p. 239
- ↑ Morris, 2008, p. 269.
- ↑ Morris, 2008, p. 205.
- ↑ Benny Morris (1 October 2008). 1948: A History of the First Arab-Israeli War. Yale University Press. p. 185. ISBN 978-0-300-14524-3. Retrieved 14 July 2013.
King Abdullah had always acknowledged Arab (as distinct from Jordanian) weakness, and his son, Prince Talal, openly predicted defeat. at the last moment, several leaders, including King Ibn Sagud and Azzam Pasha – to avert catastrophe – secretly appealed to the British to soldier on in Palestine for at least another year. Egypt's foreign minister, Khashaba, had already done so. He 'wished they would remain, and suggested that it was their duty to do so.'
- ↑ "Communication dated 11 May 1948 from J. Fletcher-Cooke of the United Kingdom delegation to the United Nations Commission on Palestine to Dr. Ralph J. Bunche, Principal Secretary to the Commission: Retrieved 15 December 2013". Unispal.un.org. 12 May 1948. Archived from the original on 12 December 2013. Retrieved 2014-06-29.
- ↑ Yoav Gelber, Palestine 1948, 2006 – Chap. 8 "The Arab Regular Armies' Invasion of Palestine".
- ↑ Yoav Gelber (1 January 2006). Palestine 1948: War, Escape and the Emergence of the Palestinian Refugee Problem. Sussex Academic Press. p. 138. ISBN 978-1-84519-075-0. Retrieved 14 July 2013.
A war between Israel and the Arab States broke out immediately, and the Arab armies invaded Palestine.
- ↑ Sean F. McMahon,The Discourse of Palestinian-Israeli Relations: Persistent Analytics and Practices, Routledge 2010 p. 37: "If it wasn't for the Arab invasion there would have been no stop to the expansion of the forces of Haganah who could have, with the same drive, reached the natural borders of western Israel". Walid Khalidi, "Plan Dalet: Master Plan for the Conquest of Palestine," Journal of Palestine Studies, Vol. 18, No. 1, Special Issue: Palestine 1948, (Autumn,1988), pp. 4–33, p. 19.
- ↑ Tucker, Spencer C. (2008). The Encyclopedia of the Arab-Israeli Conflict: A Political, Social, and Military History. ABC-CLIO. p. 528. ISBN 9781851098415.
- 1 2 Yoav Gelber (2006), p. 130.
- ↑ Zamir, Meir (January 2010). "'Bid' for Altalena: France's Covert Action in the 1948 War in Palestine". Middle Eastern Studies. Routledge. 46 (1): 21, 32. doi:10.1080/00263200903432258.
Intelligence provided by the French consulate in Jerusalem on 12 May 1948 on the Arab armies’ revised plan to invade the new state was crucial in Israel’s success in withstanding the Arab invasion
- ↑ Morris, 2008, p. 263
- ↑ Karsh 2002, p. 57
- 1 2 3 Karsh 2002, p. 56
- ↑ Wallach et al. (Volume 2, 1978), p. 29
- ↑ Tal, 2004, p. 179
- ↑ Morris, 2008, p. 239
- ↑ tal 2004 p. 182
- ↑ "1948: The War of Independence". Jewishvirtuallibrary.org. Retrieved 26 June 2010.
- ↑ Karsh 2002, pp. 61–62
- ↑ Karsh 2002, p. 61
- 1 2 3 4 5 6 7 Karsh 2002, p. 62
- ↑ War in Palestine, 1948: Israeli and Arab Strategy and Diplomacy. David Tal.
- ↑ Morris, 2008, pp. 229–30
- ↑ Benny Morris (1 October 2008). 1948: A History of the First Arab-Israeli War. Yale University Press. p. 218. ISBN 978-0-300-14524-3. Retrieved 14 July 2013.
On 26–27 May, the Legionnaires took the Hurvat Israel (or "Hurva") Synagogue, the quarter’s largest and most sacred building, and then, without reason, blew it up. 'This affair will rankle for generations in the heart of world Jewry,' predicted one Foreign Office official. The destruction of the synagogue shook Jewish morale.
- ↑ (Benny (2008), "1948: The First Arab-Israeli War", Yale University Press, New Haven, ISBN 978-0-300-12696-9).Mordechai Weingarten
- 1 2 3 4 5 Karsh 2002, p. 60
- ↑ The Palestine Post: State of Israel is Born (1948)
- 1 2 3 4 Pollack 2002, pp. 448–57
- ↑ Morris, 2008, pp. 253–54
- 1 2 Tal, 2004, pp. 251
- ↑ Dupuy, Trevor N. (2002). Elusive Victory: The Arab–Israeli Wars, 1947–1974. Military Book Club. p. 49. ISBN 0965442802.
- ↑ Khalidi, Walid (1992). All That Remains: The Palestinian Villages Occupied and Depopulated by Israel in 1948. Institute for Palestine Studies. p. 480. ISBN 9780887282249.
- ↑ "Virtual Aviation Museum – RWD 13". Luftfahrtmuseum.com. Retrieved 2014-06-29.
- ↑ Hayles, John (19 September 1999). "Israel Air Force Aircraft Types". John Hayles, aeroflight.co.uk. Archived from the original on 22 February 2007.
- ↑ Morris (2008), p. 261
- ↑ Morris, 2008, p. 235
- ↑ Morris, 2001, pp. 217–18.
- ↑ Morris, 2008, p. 262.
- ↑ Aloni, 2001, pp. 7–11.
- ↑ Gershoni, pp. 46–47
- 1 2 3 4 5 6 7 8 9 10 Karsh 2002, p. 64
- 1 2 3 4 5 6 7 8 Morris, 2008, pp. 269–71
- ↑ Bregman, 2002, p. 24 citing Ben Gurion's diary of the war
- ↑ Ahron Bregman; Jihan El-Tahri (1999). The Fifty Years War: Israel and the Arabs. BBC Books.
- ↑ "The First Truce". Retrieved 22 February 2009.
- ↑ Security Council, S/1025, 5 October 1948, REPORT BY THE UNITED NATIONS, MEDIATOR ON THE OBSERVATION OF THE TRUCE IN, PALESTINE DURING THE PERIOD FROM 11 JUNE, TO 9 JULY 1948, During the period of the truce, three violations occurred ... of such a serious nature... the "Altalena" incident, the Negeb convoys, and the question of the water supply to Jerusalem....
- the attempt by ...the Irgun Zvai Leumi to bring war materials and immigrants, including men of military age, into Palestine aboard the ship "Altalena" on 21 June...
- Another truce violation occurred through the refusal of Egyptian forces to permit the passage of relief convoys to Jewish settlements in the Negeb...
- The third violation of the truce arose as a result of the failure of the Transjordan and Iraqi forces to permit the flow of water to Jerusalem.
- ↑ Alfred A. Knopf. A History of Israel from the Rise of Zionism to Our Time. New York. 1976. p. 330. ISBN 978-0-394-48564-5.
- ↑ Morris, 2008.
- ↑ Gideon Levy and Alex Levac, 'Drafting the blueprint for Palestinian refugees' right of return,' at Haaretz 4 October 2013: 'In all the Arab villages in the south almost nobody fought. The villagers were so poor, so miserable, that they didn't even have weapons ... The flight of these residents began when we started to clean up the routes used by those accompanying the convoys. Then we began to expel them, and in the end they fled on their own.'
- ↑ David Tal, War in Palestine, 1948: Israeli and Arab Strategy and Diplomacy, Routledge 2004 p. 307.
- ↑ Herzog and Gazit, 2005, p. 86
- ↑ Lorch, Netanel (1998). History of the War of Independence
- ↑ 1948: A History of the First Arab-Israeli War, by Benny Morris. Books.google.co.uk. 2008-10-01. Retrieved 2014-06-29.
- ↑ Kadish, Alon, and Sela, Avraham. (2005) "Myths and historiography of the 1948 Palestine War revisited: the case of Lydda," The Middle East Journal, 22 September 2005; and Khalidi, Walid. (1998) Introduction to Munayyer, Spiro. The fall of Lydda. Journal of Palestine Studies, Vol. 27, No. 4, pp. 80–98.
- ↑ Benny Morris (1987). The Birth of the Palestinian Refugee Problem, 1947–1949. Cambridge University Press. pp. 203–11. ISBN 978-0-521-33889-9.
- ↑ Map of the Attacks.
- ↑ Karsh 2002, p. 76
- ↑ A. Ilan, Bernadotte in Palestine, 1948 (Macmillan, 1989) p. 194
- ↑ J. Bowyer Bell, Assassination in International Politics, International Studies Quarterly, vol. 16, March 1972, pp. 59–82.
- ↑ Haberman, Clyde (22 February 1995). "Terrorism Can Be Just Another Point of View". New York Times. Retrieved 28 December 2008.
Mr. Shamir, nearly 80, still speaks elliptically about the Bernadotte assassination. Years later, when Ben-Gurion moved to a kibbutz in the Negev desert, Sdeh Bokker, one of his closest friends there was Yehoshua Cohen, who had been one of the assassins.Review of Kati Marton's biography.
- ↑ Cowell, Alan (2 November 1991). "THE MIDDLE EAST TALKS: REPORTER'S NOTEBOOK; Syria Offers Old Photo To Fill an Empty Chair". The New York Times. Retrieved 28 December 2008.
In recent years, several members of the group known by the British as the Stern Gang have acknowledged responsibility for the killing. Mr. Shamir, who was a member of the Stern Gang, has declined to discuss the killing, and one of his spokesman has said he had no role in it.
- ↑ "Area of Jurisdiction and Powers Ordinance (1948)". Israellawresourcecenter.org. Retrieved 18 January 2013.
- 1 2 3 Benny Morris (2008). 1948: a history of the first Arab-Israeli war. Yale University Press. p. 116. Retrieved 13 July 2013.
'the Little Triangle': Ijzim, Ein Ghazal, and Jaba. The villages repeatedly fired at Israeli traffic along the coast road and were supplied by the Iraqis from northern Samaria. … Sniping at traffic continued after the start of the Second Truce, …on 24 July Israel launched mivtza shoter (Operation Policeman). The aim was 'to gain control' of the coast road between Zikhron Yaakov and Haifa 'and to destroy all the enemy in the area.'… By 26 July it was over. Most of the inhabitants fled before and during the attack, reaching northern Samaria; hundreds of others were forcibly expelled during the following days. At least a hundred militiamen and civilians were killed.
- ↑ Shapira, Anita. Yigal Allon; Native Son; A Biography Translated by Evelyn Abel, University of Pennsylvania Press ISBN 978-0-8122-4028-3 p. 247
- ↑ Gelber, 2006, p. 33
- 1 2 3 4 5 6 7 8 9 10 11 12 Karsh 2002, p. 68
- ↑ Hussein, Hussein Abu (2003). Access Denied: Palestinian Land Rights in Israel. Zed Books. p. 85. ISBN 1842771221.
- ↑ "Operation Hiram". Zionism-israel.com. Retrieved 2014-06-29.
- ↑ Shlomo Ben-Ami (Shlomo Ben-Ami (2006), pp. 41–42)
- ↑ Benny Morris (2008). 1948: a history of the first Arab-Israeli war. Yale University Press. p. 320. Retrieved 13 July 2013.
If the front lines of 14 October were to turn into permanent borders, Israel would be truncated and extremely vulnerable. Moreover, the no-peace, no-war situation was untenable. As David Ben-Gurion put it to his ministers on 26 September, "A protracted truce will break us. The Egyptian expeditionary force had to be destroyed or, at the least, driven from Palestine
- ↑ Morris 2008, p. 404
- ↑ Khalidi, Walid (1992). All That Remains: The Palestinian Villages Occupied and Depopulated by Israel in 1948. Institute for Palestine Studies. p. 108. ISBN 9780887282249.
- ↑ Weissenstein, Rudi; Dvir, Ori (2008). Rudi Weissenstein: Israel Early Photographs. Modan Publishing House. p. 32. ISBN 9789657141106.
- ↑ Dan, Uri (1988). To the Promised Land: The Birth of Israel. Doubleday Religious Publishing Group. p. 267. ISBN 9780385245975.
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- ↑ Aloni, 2001, p. 18.
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- ↑ Cohen, Michael Joseph: Truman and Israel (1990)
- ↑ Adrian, p. 7
- ↑ Adrian, p. 59
- ↑ Weapons and Vehicles of the Arab-Israeli Wars
- ↑ L. Carl Brown (2013), p. 126.
- ↑ "Legal Status in Palestine". Lawcenter.birzeit.edu. Retrieved 2014-06-29.
- ↑ Tobin, Maurine and Robert (2002). How Long O Lord?: Christian, Jewish, and Muslim Voices from the Ground and visions for the future in Israel–Palestine. Cowley Publications. ISBN 9781561012145.
- ↑ Anita Shapira (25 November 2014). Ben-Gurion: Father of Modern Israel. Yale University Press. pp. 173–. ISBN 978-0-300-18273-6.
(Ben Gurion) He also did not flinch from provoking the United Nations by breaking the truce agreement. But the limit of his fearlessness was a clash with a Western power. Vainly, the right and Mapam accused him of defeatism. He did not flinch from confronting them but chose to maintain good relations with the United States, which he perceived as a potential ally of the new state, and also not to provoke the British lion, even though its fangs had been drawn. At the end of the war, when Yigal Allon, who represented the younger generation of commanders that had grown up in the war, demanded the conquest of the West Bank up to the Jordan River as the natural, defensible border of the state, Ben-Gurion refused. He recognized that the IDF was militarily strong enough to carry out the conquest, but he believed that the young state should not bite off more than it had already chewed. There was a limit to what the world was prepared to accept. Furthermore, the armistice borders – which later became known as the Green Line – were better than those he had dreamed of at the beginning of the war. In Ben-Gurion's opinion, in terms of territory Israel was satisfied. It was time to send the troops home and start work on building the new nation.
- ↑ Benny Morris (2009). One state, two states: resolving the Israel/Palestine conflict. Yale University Press. p. 79.
in March 1949, just before the signing of the Israel-Jordan armistice agreement, when IDF general Yigal Allon proposed conquering the West Bank, Ben-Gurion turned him down flat. Like most Israelis, Ben-Gurion had given up the dream
- ↑ Zaki Shalom (2002). David Ben-Gurion, the State of Israel and the Arab World, 1949-1956. Sussex Academic Press. pp. 174–. ISBN 978-1-902210-21-6.
The clearest expression of this 'activist' approach is found in a "personal, top secret" letter sent by Yigal Allon to BG shortly after ... We cannot imagine a border more stable than the Jordan River, which runs the entire length of the country
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In order to highlight the plight of the refugees and to put pressure on Israel to admit responsibility for them, Arab countries (except Jordan) have denied citizenship rights to the Palestinians in their midst; in so doing, they claimed they were serving the interests of the Palestinians and supporting their right of return.
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One of the important reaction mechanisms in organic chemistry is the radical reaction. Radicals are highly reactive intermediates, and new bonds can be formed by using radical reactions.
Radical reactions are a different reaction mechanism from the general organic synthetic reactions with acids and bases. It is difficult for many people to understand a radical reaction because we learn something new with different properties.
However, the conditions under which radical reactions occur are fixed. Also, there are certain substances, such as halogens and peracids, that can produce radicals. What’s more, the types of radical reactions are common. Therefore, if you learn when radical reactions occur, you will be able to understand radical reactions.
In this section, we will explain the basics of radical reactions and check how radical reactions proceed to obtain the products.
Table of Contents
- 1 The Difference Between Heterolysis (Ion) and Homolysis (Radical)
- 2 Understanding the Types of Radical Reactions
- 3 Radical Chain Reaction: Initiation and Propagation Step
- 4 Reacts with Alkyl Chains to Create New Bonds
- 5 Synthetic Reactions with Highly Reactive Unpaired Electrons
The Difference Between Heterolysis (Ion) and Homolysis (Radical)
In general, synthetic reactions in organic chemistry focus on the movement of ions. The relationship between an acid and a base causes the movement of electrons, which causes a synthetic reaction to occur.
When electrons move, two electrons are transferred in most cases. This transfer of electrons is called heterolysis. Heterolysis results in the formation of ions.
By forming ions, the compound will take on a positive or negative charge. This is the relationship between acids and bases, and heterolysis is involved in most synthetic reactions.
In radical reactions, on the other hand, a phenomenon is called homolysis. When a bond is broken, two electrons do not move to form an ion. Radicals are created when the bond cleaves so that the electrons move one by one to each atom.
In radical reactions, homolysis is always the first step. Just as acids and bases carry out most synthetic reactions, radical reactions start with radical formation. Therefore, if homolysis does not occur, a radical reaction cannot occur.
Radicals Are Highly Reactive and Give Different Compounds
Among the intermediates of organic compounds, radicals are known to be highly reactive. Because they have one electron instead of two, they can easily react chemically with other compounds.
Also, compared to the ions produced by heterolysis, the radicals produced by homolysis can yield different products. For example, in the addition reaction of hydrogen bromide, the acid/base reaction products and the radical reaction are different as follows.
Different reaction conditions will result in different compounds. Radical reactions are important in organic chemistry because they give a different product than reactions with ions.
So why are the products different as described above? In the addition reaction of hydrogen bromide to an alkene, a carbocation is formed, and the synthetic reaction proceeds.
On the other hand, when hydrogen bromide is reacted with the same alkene, radical products can be synthesized in the presence of oxygen or peroxide. Radical reactions mainly use peracids. The peracids create radicals by causing homolysis, which results in radical products.
-Conditions for Obtaining Radicals
When are radicals produced? In most cases, radicals are formed at high temperatures above 200°C by homolysis. Radicals are created when high energy is applied.
However, there are cases where radicals can be produced even if the temperature is a little higher than room temperature. In compounds with weak bonds, radicals are created when the bonds are broken. As mentioned above, we mainly use peracids in radical reactions, and peracids are known to easily produce radicals.
Hydrogen peroxide is one of the most famous peracids. Among these peracids, benzoyl peroxide (BPO) is frequently used as a radical initiator. This is because the bond between oxygen is weak, and radicals are easily generated.
Halogens such as chlorine (Cl2) and bromine (Br2) are also frequently given as examples of radical reactions. When halogens are exposed to heat or light (ultraviolet/UV), the bonds are cleaved, and radicals are formed.
Halogens are also known to bond weakly with each other. Therefore, when halogens such as chlorine and bromine are present, radicals are created.
Understanding the Types of Radical Reactions
What are the different types of radical reactions? We have already discussed homolysis. In all radical reactions, homolysis occurs first. Homolysis is the reason why radical reactions proceed.
There is also the reverse of homolysis. When radicals react with each other and form a bond, it is called radical coupling. The following reaction is radical coupling.
Among the radical reactions, homolysis and radical coupling are easy to understand. However, there are three other types of radical reactions that must be learned. These are the following radical reactions.
- Radical hydrogen abstraction
- Radical addition to a double bond
- Alkene formation in β-cleavage
Learning about these reaction mechanisms will help you to understand how radical reactions occur.
Radical Atom Abstraction Causes Hydrogen Atom Abstraction
One reaction that is characteristic of radicals is the withdrawal of hydrogen atoms. In short, in the presence of radicals, hydrogen atoms are pulled out, and new radicals are formed.
This reaction is known as radical atom abstraction. The most important type of atom abstraction is the hydrogen atom abstraction. For this reason, radical atom abstraction is also called hydrogen atom abstraction.
Why are there two different names for it? Because not only hydrogen but also halogen atoms such as chlorine and bromine can be pulled out. In other words, radical atom abstraction is not limited to hydrogen atom abstraction.
However, if no halogen is present, only hydrogen atom abstraction will occur. Therefore, hydrogen atom abstraction is the most important in radical atom abstraction.
Radical Addition Reaction to Double Bond Is Important
When there is a double bond in a molecule, radicals react with alkenes to cause an addition reaction. The following two points are important in the radical addition reaction to a double bond.
- Reacting with the end of the double bond to create a bond.
- A new radical is created on the opposite side of the added site.
A polysubstituted alkane is synthesized in a normal addition reaction to an alkene, as mentioned in the hydrogen bromide example earlier. On the other hand, in the radical reaction, the radical reacts with the terminal part of the alkene to form a new bond.
After the addition reaction, a new radical is formed on the opposite side. For example, it is as follows.
Why do radicals attack the terminal carbon atom? This is because the stability of the radical intermediate is involved.
In general addition reactions, the stability of the carbocation is involved. In the same way, radical intermediates have an order of stability. They are as follows.
When new radicals are formed on the other side after a radical reaction, they tend to be more stable if they are tertiary or secondary radicals. Although radicals are highly reactive intermediates, they have an order of stability. Therefore, in the radical addition reaction to the double bond, there is regioselectivity.
In the case of the compound mentioned earlier, the intermediate formed after the radical reaction is a tertiary radical. In this way, we can predict the compound to be synthesized.
β-Cleavage Creates a New Double Bond
In radical reactions, a new double bond may be created. This is called beta cleavage (β-cleavage). We have just described the radical addition reaction to a double bond. The opposite reaction is the formation of an alkene by β-cleavage.
When an atom, such as a halogen that causes a radical reaction is bonded to the beta position of a carbon atom, radical cleavage can occur. In this case, a radical is transferred to the halogen while creating a double bond. The reaction mechanism is as follows.
In radical reactions, double bonds can be created by β-cleavage. In this reaction, the radical is transferred to a chlorine atom.
Radical Chain Reaction: Initiation and Propagation Step
There are several types of radical reactions. Importantly, these radical reactions can occur in a chain. In other words, the production of radicals through homolysis leads to a number of radical reactions.
There are always the following stages in a radical reaction.
- Initiation step
- Propagation step
- Termination step
We will explain how the chain reaction works in the following simple radical reaction.
-A Radical Reaction Begins in the Initiation Step
When chlorine molecules are used in a radical reaction, they are exposed to heat or light (ultraviolet: UV). Then, radicals are generated. All radical reactions have an initiation step due to homolysis.
-Obtain Products in the Propagation Step
After the radicals are formed, the radicals attack other molecules, which leads to further reactions. In this reaction, the chlorine radical produces a radical in methane by hydrogen atom abstraction. It is as follows.
After producing a methyl radical, the radical next attacks the chlorine. This attack yields the desired compound, chloromethane.
It is important to note that radicals are still being generated even after the target compound is obtained. The radicals generated in this reaction cause radical atom abstraction again, producing methyl radicals. This is called a chain reaction because the reaction occurs one after another.
In this reaction, hydrogen is pulled out by radicals. On the other hand, when an alkene is reacted, for example, an addition reaction to a double bond occurs. The product will differ depending on the type of reagent used in the reaction.
Termination Step Creates Bonds and Stops the Reaction
So, does the chain reaction continue forever? Of course not. Although the chain reaction occurs due to homolysis, the reaction stops at some stage. This is called the termination step.
Radicals cause hydrogen abstraction, addition to double bonds, and beta cleavage. However, radicals often react with each other to form new bonds. Specifically, the reverse reaction of homolysis occurs. The following reactions are examples of this.
When these reactions occur, the radicals disappear. There is no new homolysis, and the reaction is completed with the creation of new bonds. Radicals make bonds with each other, and the chain reaction is stopped by the termination step.
Strictly speaking, the reaction with oxygen in the air and water is also a radical termination reaction. However, let’s not consider the reaction with air or water and think of the termination step as a radical reaction between compounds.
-A Certain Amount of Radical Reaction Initiator Is Needed
Since the reaction proceeds by a chain reaction, the desired product can be obtained even with a small amount of an initiator such as benzoyl peroxide (BPO).
However, if the amount of initiator is too small, the reaction will not proceed. This is because some of the generated radicals can form new bonds with each other and stop the reaction, as described above. Therefore, the best amount of initiators is not too much or too little.
Reacts with Alkyl Chains to Create New Bonds
How can we use these radical reactions in organic chemistry? Synthetic reactions using radical reactions are frequently used to create new bonds.
For example, by reacting an alkane with a halogen (Cl2 or Br2), we can synthesize a compound with an added halogen.
New carbon bonds can also be created by reacting a compound with a double bond. There are several ways to make carbon chains in organic chemistry. One of them is the radical reaction. For example, new carbon chains can be made by the following synthetic reactions.
Radical reactions are useful when you want to make new bonds. Radical reactions can be used to add halogens to carbon chains or to create carbon chains.
-Polymers Are Obtained Through Polymerization Reactions
In addition, because the reaction proceeds through a chain reaction, some compounds often undergo a polymerization reaction to yield polymers. Polymers are produced by the formation of carbon chains one after another.
For reference, in compounds that generate radicals by heat or light (UV), radical terminators such as antioxidants are often added. This is because, without the terminator, molecules would cause radical reactions to occur and polymerize to form polymers.
Regioselectivity and Radical Stability
In addition, when using radical reactions, we must consider regioselectivity. It is important to understand which part of the alkyl chain reacts with the radical and what kind of product is obtained.
We have already discussed regioselectivity. The stability of the radical intermediate greatly influences regioselectivity. Again, the order of radical stability is as follows.
- Tertiary radicals > Secondary radicals > Primary radicals
Therefore, when radicals are formed, the formation of radicals with more substituents is given priority. For example, the following is an example.
Checking the radical intermediates, the more stable secondary radicals are preferentially produced in this case. Therefore, there is one main compound.
Stability of Allyl and Benzyl Compounds
Allyl and benzyl compounds also exist, depending on the compound. If these compounds have radicals, the structural formula is as follows.
The intermediates of allyl and benzyl radicals are highly stable. Of course, because they are radicals, they are highly reactive. However, allyl and benzyl radicals are known to be more stable than tertiary radicals. The stability of radicals is as follows.
- Benzyl radicals > Allyl radicals > Tertiary radicals > Tertiary radicals > Secondary radicals > Primary radicals
The reason for this order is that we can write the following resonance structures for allyl radicals and benzyl radicals.
When you understand these, you will be able to understand how the reaction proceeds according to the regioselectivity. For example, in the following reaction, we can consider two types of reactions.
However, there is only one reaction that actually occurs. In the intermediate, you can draw an allyl radical or a secondary radical.
In radicals, the benzyl radicals are more stable. Therefore, the product is 3-bromocyclohexene. Of the compounds shown in the figure above, the upper compound (3-bromocyclohexene) can be obtained selectively. This is the regioselectivity in the radical reaction.
Synthetic Reactions with Highly Reactive Unpaired Electrons
Many people are not familiar with radical reactions because they are not common chemical reactions. Radicals are unstable intermediates with unpaired electrons, and they cause chain reactions.
However, radical reactions are useful for creating new bonds. Nucleophilic substitution, addition, and cleavage reactions are known to be caused by the relationship between acids and bases. Radical reactions are used to obtain compounds that cannot be synthesized by these chemical reactions.
In radicals, the reaction is started by the presence of an initiator that causes homolysis, such as a halogen or peracids. In addition, there are fixed reactions that occur, such as radical atom abstraction and addition to double bonds. Radical intermediates have an order of stability and also regioselectivity.
Once you know these properties, you will be able to understand what kind of compounds can be obtained by radical reactions. |
Welcome to the exciting world of proofs in mathematics! Proofs are among the most powerful tools mathematicians use to establish the truth. They are the reasons why mathematics is often described as the most exact of all sciences. Let us explore how this concept fits into our daily lives and learning.
While the concept of proof can be introduced as early as grade 3, it becomes more formal and significant around grades 6 to 9. Students start engaging with simple proofs at these levels, particularly in geometry and number theory. As students get older and their mathematical skills develop, the complexity and importance of proofs also increase.
Proof exists across all domains of mathematics. However, they are most commonly found in Geometry, Algebra, and Number Theory at the school level. Students will encounter proofs in Calculus, Abstract Algebra, and Real Analysis as they move on to more advanced topics.
Applicable Common Core Standards
The concept of proving satisfies various Common Core Standards, especially in Geometry and Expressions & Equations. For example:
CCSS.MATH.CONTENT.HSG.CO.C.9: Prove theorems about lines and angles.
CCSS.MATH.CONTENT.HSG.SRT.B.5: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Definition of the Topic
Proof is a logical argument that uses rules and definitions to show that a mathematical statement is true. It consists of a series of statements, each following logically from the previous ones. A proof concludes with the statement being proved, ensuring that the conclusion is a logical consequence of the given information.
Theorem: A mathematical statement that we can prove to be true.
Axiom or Postulate: A statement assumed to be true without proof.
Proof: A logical argument showing that a theorem is true.
Proposition: A proved and accepted statement, but less central than a theorem.
Lemma: A minor result whose main purpose is to help prove a theorem.
Corollary: A result which follows directly from a theorem that has already been proven.
Discussion with Illustrative Examples
What is proof? A mathematical concept can be found true by supporting proof or a series of logical proofs. It is a logical argument that stabilizes the truth of a statement.
One of the standard proof formats is the two-column proof. It consists of two columns, wherein the first column contains numbered logical arguments called statements. The second column has the justification that supports the statements in column one, called reasons.
Two-Column Proof Format
In proving, we use geometric concepts and properties to solve problems. Here are a few fundamental ideas and congruence-related properties.
Line segments that are the same length are congruent to each other. From the figure above, both line segments CJ and YD measure 6 inches. Therefore, we can conclude that line segment CJ ≅ line segment YD.
Two angles that have the exact measurement are congruent to each other. Angles JYH and TKV both measure 45॰. Therefore, we can conclude that ∠JYH ≅ ∠TKV.
If two triangles are the same size and shape, they are congruent. From the figure above, triangles SKY and HCV have the same sides and equal angle measurements. Therefore, triangles SKY and HCV are congruent with each other.
Properties of Congruence
Shapes, line segments, and angles are always congruent to themselves.
Symmetric Property of Congruence
If a shape is congruent to a second shape, then the second shape is also congruent to the first shape.”
Transitive Property of Congruence
If an object is congruent to a second object and the second object is congruent to a third one, then the first object is congruent to the third object.
SAS (Side-Angle-Side) Postulate
If one triangle’s two sides and included angle correspond to another triangle’s two sides and included angle, the two triangles are congruent.
ASA (Angle-Side-Angle) Postulate
The two triangles are congruent if one triangle’s two angles and included side correspond to the other triangle’s corresponding two angles and included side.
SSS (Side-Side-Side) Theorem
The two triangles are congruent if the three sides of one triangle correspond to the three sides of the other triangle.
Corresponding Parts of Congruent Triangles are Congruent
If two triangles are congruent, the six pairs of their corresponding parts are congruent.
AAS (Angle-Angle-Side) Theorem
If the corresponding two angles and the non-included side of one triangle match those of the other’s corresponding two angles and the non-included side, the two triangles are congruent.
Steps in Writing an Indirect Proof
Step 1: Know the statement to be proved. Assume that the statement is false by negating it or making it’s opposite a true statement.
Step 2: State logical proofs until a contradiction (two statements cannot be both true) is made.
Step 3: The assumption (negating the desired conclusion) has been proven false by contradiction. Therefore, the original conclusion must be true.
You can write an indirect proof in this format:
Case 1: Write the assumption (Suppose… We assume that…).
Case 2: State the logical reasons.
Case 3: Write the conclusion.
Examples with Solution
Given: J is not the midpoint of YH.
Prove: YJ ≇ JH
We assume that YJ ≅ JH.
Then YJ and JH are congruent by the Definition of Midpoint (Midpoint bisects a line segment into two congruent parts).
This contradicts the given information that J is not the midpoint of YH. Therefore, the assumption that YJ ≅ JH must be false, and the original conclusion, YJ ≇ JH, must be true.
Prove that a triangle’s total angles equal 180 degrees.
Draw a line that passes through the other vertex of the triangle while remaining parallel to the triangle’s base.
By the definition of alternate angles, ∠3 = ∠4 and ∠2 = ∠5. So, ∠4 + ∠5 = ∠2 + ∠3.
Adding ∠1 on both sides, ∠1 + ∠4 + ∠5 = ∠1 + ∠2 + ∠3
The adjacent angles along the line sum up to 180 degrees (a straight line).
The triangle’s angles correspond to these angles.
As a result, a triangle’s angles add up to 180 degrees.
Consider the Pythagorean theorem, a fundamental theorem in geometry. According to this theorem, the square of the side (hypotenuse) opposite the right angle equals the sum or total of the squares of the other two sides. Show that the equation is a² + b² = c².
To prove this theorem, we often use a geometrical proof where we draw squares on each side of the right triangle and show that the two smaller squares’ combined area is equal to the area of the larger square.
Can you tell us which pair of woods are congruent to each other?
Y ≅ J
C ≅ S
H ≅ T
Real-life Application with Solution
The understanding of proof is not just limited to mathematics but also extends to everyday life. For instance, a detective might need to prove that a particular person committed a crime.
Suppose we have three clues:
The criminal has a red car.
The criminal has a pet parrot.
The criminal lives in a blue house.
Let us say we have three suspects, and based on the clues, we have the following information:
Suspect A has a red car and a blue house but has a pet dog.
Suspect B has a green car, a pet parrot, and a blue house.
Suspect C has a red car, a pet parrot, and a blue house.
We apply the logical process similar to a mathematical proof:
We first observe that Suspect A cannot be the criminal because even though he has a red car and a blue house, he doesn’t have a pet parrot.
Similarly, Suspect B can’t be the criminal because his car is not red, even though he has a pet parrot and a blue house.
Therefore, by the process of elimination, we deduce that Suspect C must be the criminal because he satisfies all the given conditions.
This is an application of how proof works in real-life situations.
Now, let’s practice a bit! Try solving these problems:
1. If you know that a number is even, prove that its square will also be even.
2. Prove that the sum of two odd numbers is always even.
3. Prove that the diagonals of a rectangle are equal.
1. A number is an even number if it is divisible by 2.
If we have 2n as an even number, squaring it shall give us (2n)(2n) = 4n2 = 2(2n2). Therefore, the obtained number is divisible by 2.
2. Let us say that 2m and 2n are even numbers because they can be divided by 2, then 2m + 1 and 2n +1 are odd numbers. If we add the odd numbers ( 2m + 1 ) + ( 2n + 1) equals 2m + 2n + 2. The sum can be written as 2 (m + n + 1 ). Since it has 2 as its factor, two odd integers add up to an even number.
3. Say we have a rectangle ABCD, then AC and BD are diagonals.
In ∆ABC and ∆BCD, ∠ABC and ∠BCD are angles of rectangles which are both 90°.
BC is a common side.
AB = CD since opposite sides of a parallelogram are equal.
By Side-Angle-Side (SAS) Congruency, ∆ABC ≅ ∆BCD.
By corresponding parts of congruent triangles, AC = DC.
Hence, the diagonals are equal.
Frequently Asked Questions (FAQs)
What is mathematical proof?
Mathematical proof is a logical argument that uses rules and definitions to show a mathematical statement is true.
Why are proofs important in mathematics?
Proofs are important because they ensure that mathematical theorems are universally and undeniably true, given that the axioms and definitions they are based on are true.
Can a mathematical proof be wrong?
A proof could be incorrect if it contains a logical fallacy, a mistake in the reasoning, or if it is based on false axioms or definitions. However, it is considered universally true once a proof has been established and verified.
How do theorems and proofs differ from one another?
A proof is a process or logical argument showing a theorem
is true, while a theorem is a mathematical statement or assertion that has been proven true.
Are proofs necessary in all areas of mathematics?
Proofs are a fundamental part of all areas of mathematics. While some areas, like geometry, may use more visual proofs, every branch of mathematics relies on proofs to establish the truth of mathematical statements. |
Hooke's law is a principle of physics that states that the force needed to extend or compress a spring by some distance is proportional to that distance. That is: where is a constant factor characteristic of the spring, its stiffness. The law is named after 17th century British physicist Robert Hooke. He first stated the law in 1660 as a Latin anagram. He published the solution of his anagram in 1678 as: ut tensio, sic vis ("as the extension, so the force" or "the extension is proportional to the force").
Hooke's equation in fact holds (to some extent) in many other situations where an elastic body is deformed, such as wind blowing on a tall building, a musician plucking a string of a guitar, or the filling of a party balloon. An elastic body or material for which this equation can be assumed is said to be linear-elastic or Hookean.
Hooke's law is only a first order linear approximation to the real response of springs and other elastic bodies to applied forces. It must eventually fail once the forces exceed some limit, since no material can be compressed beyond a certain minimum size, or stretched beyond a maximum size, without some permanent deformation or change of state. In fact, many materials will noticeably deviate from Hooke's law well before those elastic limits are reached.
On the other hand, Hooke's law is an accurate approximation for most solid bodies, as long as the forces and deformations are small enough. For this reason, Hooke's law is extensively used in all branches of science and engineering, and is the foundation of many disciplines such as seismology, molecular mechanics and acoustics. It is also the fundamental principle behind the spring scale, the manometer, and the balance wheel of the mechanical clock.
The modern theory of elasticity generalizes Hooke's law to say that the strain (deformation) of an elastic object or material is proportional to the stress applied to it. However, since general stresses and strains may have multiple independent components, the "proportionality factor" may no longer be just a single real number, but rather a linear map (a tensor) that can be represented by a matrix of real numbers.
In this general form, Hooke's law and Newton's laws of static equilibrium make it possible to deduce the relation between strain and stress for complex objects in terms of intrinsic properties of the materials it is made of. For example, one can deduce that a homogeneous rod with uniform cross section will behave like a simple spring when stretched, with a stiffness directly proportional to its cross-section area and inversely proportional to its length.
- 1 Formal definition
- 2 Analogous laws
- 3 Units of measurement
- 4 General application to elastic materials
- 5 Derived formulas
- 6 Linear elasticity theory for continuous media
- 7 Thermodynamic basis
- 8 See also
- 9 Notes
- 10 References
- 11 External links
For linear springs
Consider a simple helical spring that has one end attached to some fixed object, while the free end is being pulled by a force whose magnitude is . Suppose that the spring has reached a state of equilibrium, where its length is not changing anymore. Let be the amount by which the free end of the spring was displaced from its "relaxed" position (when it is not being stretched). Hooke's law states that
where is a positive real number, characteristic of the spring. Moreover, the same formula holds when the spring is compressed, with and both negative in that case. According to this formula, the graph of the applied force as a function of the displacement will be a straight line passing through the origin, whose slope is .
Hooke's law for a spring is often stated under the convention that is the restoring (reaction) force exerted by the spring on whatever is pulling its free end. In that case the equation becomes
since the direction of the restoring force is opposite to that of the displacement.
General "scalar" springs
Hooke's spring law usually applies to any elastic object, of arbitrary complexity, as long as both the deformation and the stress can be expressed by a single number that can be both positive and negative.
For example, when a block of rubber attached to two parallel plates is deformed by shearing, rather than stretching or compression, the shearing force and the sideways displacement of the plates obey Hooke's law (for small enough deformations).
Hooke's law also applies when a straight steel bar or concrete beam, supported at both ends, is bent by a weight placed at some intermediate point. The displacement in this case is the deviation of the beam, measured in the transversal direction, relative to its unloaded shape.
The law also applies when a stretched steel wire is twisted by pulling on a lever attached to one end. In this case the stress can be taken as the force applied to the lever, and as the distance traveled by it along its circular path. Or, equivalently, one can let be the torque applied by the lever to the end of the wire, and be the angle by which that end turns. In either case is proportional to (although the constant is different in each case.)
In the case of a helical spring that is stretched or compressed along its axis, the applied (or restoring) force and the resulting elongation or compression have the same direction (which is the direction of said axis). Therefore, if and are defined as vectors, Hooke's equation still holds, and says that the force vector is the elongation vector multiplied by a fixed scalar.
General tensor form
Some elastic bodies will deform in one direction when subjected to a force with a different direction. One example is a horizontal wood beam with non-square rectangular cross section that is bent by a transverse load that is neither vertical nor horizontal. In such cases, the magnitude of the displacement will be proportional to the magnitude of the force , as long as the direction of the latter remains the same (and its value is not too large); so the scalar version of Hooke's law will hold. However, the force and displacement vectors will not be scalar multiples of each other, since they have different directions. Moreover, the ratio between their magnitudes will depend of the direction of the vector .
Yet, in such cases there is often a fixed linear relation between the force and deformation vectors, as long as they are small enough. Namely, there is a function from vectors to vectors, such that , and for any real numbers and any displacement vectors . Such a function is called a (second-order) tensor.
With respect to an arbitrary Cartesian coordinate system, the force and displacement vectors can be represented by 1×3 matrices of real numbers. Then the tensor connecting them can be represented by a 3×3 matrix of real coefficients, that, when multiplied by the displacement vector, gives the force vector:
for equal to 1,2, and 3. Therefore, Hooke's law can be said to hold also when and are vectors with variable directions, except that the stiffness of the object is a tensor , rather than a single real number .
Hooke's law for continuous media
The stresses and strains of the material inside a continuous elastic material (such as a block of rubber, the wall of a boiler, or a steel bar) are connected by a linear relationship that is mathematically similar to Hooke's spring law, and is often referred to by that name.
However, the strain state in a solid medium around some point cannot be described by a single vector. The same parcel of material, no matter how small, can be compressed, stretched, and sheared at the same time, along different directions. Likewise, the stresses in that parcel can be at once pushing, pulling, and shearing.
In order to capture this complexity, the relevant state of the medium around a point must be represented by two second-order tensors, the strain tensor (in lieu of the displacement ) and the stress tensor (replacing the restoring force ).The analogous of Hooke's spring law for continuous media is then
where the tensor , called the compliance tensor, represents the inverse of said linear map.
In a Cartesian coordinate system, the stress and strain tensors can be represented by 3×3 matrices
Being a linear mapping between the nine numbers and the nine numbers , the stiffness tensor is represented by a matrix of 3×3×3×3 = 81 real numbers . Hooke's law then says that
where and are 1, 2, or 3.
All three tensors generally vary from point to point inside the medium, and may vary with time as well. The strain tensor merely specifies the displacement of the medium particles in the neighborhood of the point, while the stress tensor specifies the forces that neighboring parcels of the medium are exerting on each other. Therefore, they are independent of the composition and physical state of the material. The stiffness tensor , on the other hand, is a property of the material, and often depends on physical state variables such as temperature, pressure, and microstructure.
Due to the inherent symmetries of , , and , only 21 elastic coefficients of the latter are independent. For isotropic media (which have the same physical properties in any direction), can be reduced to only two independent numbers, the bulk modulus and the shear modulus , that quantify the material's resistance to changes in volume and to shearing deformations, respectively.
Since Hooke's law is a simple proportionality between two quantities, its formulas and consequences are mathematically similar to those of many other physical laws, such as those describing the motion of fluids, or the polarization of a dielectric by an electric field.
In particular, the tensor equation relating elastic stresses to strains is entirely similar to the equation relating the viscous stress tensor and the strain rate tensor in flows of viscous fluids; although the former pertains to static stresses (related to amount of deformation) while the latter pertains to dynamical stresses (related to the rate of deformation).
Units of measurement
In SI units, displacements are measured in metres (m), and forces in newtons (N or kg·m/s2). Therefore the spring constant , and each element of the tensor , is measured in newtons per metre (N/m), or kilograms per second squared (kg/s2).
For continuous media, each element of the stress tensor is a force divided by an area; it is therefore measured in units of pressure, namely pascals (Pa, or N/m2, or kg/m/s2. The elements of the strain tensor are dimensionless (displacements divided by distances). Therefore the entries of are also expressed in units of pressure.
General application to elastic materials
Objects that quickly regain their original shape after being deformed by a force, with the molecules or atoms of their material returning to the initial state of stable equilibrium, often obey Hooke's law.
Hooke's law only holds for some materials under certain loading conditions. Steel exhibits linear-elastic behavior in most engineering applications; Hooke's law is valid for it throughout its elastic range (i.e., for stresses below the yield strength). For some other materials, such as aluminium, Hooke's law is only valid for a portion of the elastic range. For these materials a proportional limit stress is defined, below which the errors associated with the linear approximation are negligible.
Rubber is generally regarded as a "non-hookean" material because its elasticity is stress dependent and sensitive to temperature and loading rate.
Tensional stiffness of a uniform bar
We may view a rod of any elastic material as a linear spring. The rod has length L and cross-sectional area A. Its extension (strain) is linearly proportional to its tensile stress σ by a constant factor , the inverse of its modulus of elasticity E, such that
(i.e., [change in length] as a fraction or percentage of total length),
this relationship may also be expressed as
The potential energy stored in a spring is given by
which comes from adding up the energy it takes to incrementally compress the spring. That is, the integral of force over displacement. Since the external force has the same general direction as the displacement, the potential energy of a spring is always non-negative.
This potential "U" can be visualized as a [parabola] on the U-x plane such that . As the spring is stretched in the positive x-direction, the potential energy increases parabolically (the same thing happens as the spring is compressed). Since the change in potential energy changes at a constant rate: . Note that the change in the change in U is constant even when the displacement and acceleration are zero.
Relaxed force constants (generalized compliance constants)
Relaxed force constants (the inverse of Grunenberg`s generalized compliance constants) are uniquely defined for molecular systems, in contradistinction to the usual “rigid” force constants, and thus their use allows meaningful correlations to be made between force fields calculated for reactants, transition state, and product of a chemical reaction. Just as the potential energy can be written as a quadratic form in the internal coordinates, so it can also be written in terms of generalized forces. The resulting coefficients are termed compliance constants. The suitability of relaxed force constants (inverse compliance constants) as covalent bond strength descriptors was demonstrated as early as ~1980, at the University of Cambridge. Recently, the suitability as non-covalent bond strength descriptors was demonstrated, too.
A mass m is attached to the end of a spring is the classic example of a harmonic oscillator. By pulling slightly on the mass and then releasing it, the system will be set in sinusoid oscillating motion about the equilibrium position. To the extent that the spring obeys Hooke's law, and that one can neglect friction and the mass of the spring, the amplitude of the oscillation will remain constant; and its frequency will be independent of its amplitude, determined only by the mass and the stiffness of the spring:
Rotation in Gravity-Free Space
If the mass m was attached to a spring with force constant k and rotating in free space, the spring tension (Ft) would balance the required centripetal force (Fc) as follows -
Since Ft = Fc and x = r, therefore:
Given that , this leads to the same frequency equation as above -
Linear elasticity theory for continuous media
- Note: the Einstein summation convention of summing on repeated indices is used below.
(see viscosity for an analogous development for viscous fluids.)
Isotropic materials are characterized by properties which are independent of direction in space. Physical equations involving isotropic materials must therefore be independent of the coordinate system chosen to represent them. The strain tensor is a symmetric tensor. Since the trace of any tensor is independent of any coordinate system, the most complete coordinate-free decomposition of a symmetric tensor is to represent it as the sum of a constant tensor and a traceless symmetric tensor.:Ch. 10 Thus in index notation:
where is the Kronecker delta. In direct tensor notation:
where is the second-order identity tensor. The first term on the right is the constant tensor, also known as the volumetric strain tensor, and the second term is the traceless symmetric tensor, also known as the deviatoric strain tensor or shear tensor.
The most general form of Hooke's law for isotropic materials may now be written as a linear combination of these two tensors:
Using the relationships between the elastic moduli, these equations may also be expressed in various other ways. A common form of Hooke's law for isotropic materials, expressed in direct tensor notation, is
where and are the Lamé constants, is the second-rank identity tensor, and is the symmetric part of the fourth-rank identity tensor. In index notation:
The inverse relationship is
Therefore the compliance tensor in the relation is
This is the form in which the strain is expressed in terms of the stress tensor in engineering. The expression in expanded form is
Derivation of Hooke's law in 3D The 3-D form of Hooke's law can be derived using Poisson's ratio and the 1-D form of Hooke's law as follows.
Consider the strain and stress relation as a superposition of two effects: stretching in direction of the load (1) and shrinking (caused by the load) in perpendicular directions (2 and 3),
Summing the three cases together () we get
or by adding and subtracting one
and further we get by solving
Calculating the sum
and substituting it to the equation solved for gives
where and are the Lamé parameters. Similar treatment of directions 2 and 3 gives the Hooke's law in three dimensions.
In matrix form, Hooke's law for isotropic materials can be written as
where is the engineering shear strain. The inverse relation may be written as
which can be simplified thanks to the Lamé constants :
Under plane stress conditions . In that case Hooke's law takes the form
The inverse relation is usually written in the reduced form
The symmetry of the Cauchy stress tensor () and the generalized Hooke's laws () implies that . Similarly, the symmetry of the infinitesimal strain tensor implies that . These symmetries are called the minor symmetries of the stiffness tensor (). This reduces the number of elastic constants from 81 to 36.
If in addition, since the displacement gradient and the Cauchy stress are work conjugate, the stress-strain relation can be derived from a strain energy density functional (), then
The arbitrariness of the order of differentiation implies that . These are called the major symmetries of the stiffness tensor. This reduces the number of elastic constants to 21 from 36. The major and minor symmetries indicate that the stiffness tensor has only 21 independent components.
Matrix representation (stiffness tensor)
It is often useful to express the anisotropic form of Hooke's law in matrix notation, also called Voigt notation. To do this we take advantage of the symmetry of the stress and strain tensors and express them as six-dimensional vectors in an orthonormal coordinate system () as
Then the stiffness tensor () can be expressed as
and Hooke's law is written as
Similarly the compliance tensor () can be written as
Change of coordinate system
If a linear elastic material is rotated from a reference configuration to another, then the material is symmetric with respect to the rotation if the components of the stiffness tensor in the rotated configuration are related to the components in the reference configuration by the relation
where are the components of an orthogonal rotation matrix . The same relation also holds for inversions.
In matrix notation, if the transformed basis (rotated or inverted) is related to the reference basis by
In addition, if the material is symmetric with respect to the transformation then
The inverse of this relation is commonly written as
- is the Young's modulus along axis
- is the shear modulus in direction on the plane whose normal is in direction
- is the Poisson's ratio that corresponds to a contraction in direction when an extension is applied in direction .
Under plane stress conditions, , Hooke's law for an orthotropic material takes the form
The inverse relation is
The transposed form of the above stiffness matrix is also often used.
Transversely isotropic materials
More frequently, the axis is taken to be the axis of symmetry and the inverse Hooke's law is written as
where is the surface traction vector, is the body force vector, represents the body and represents its surface. Using the relation between the Cauchy stress and the surface traction, (where is the unit outward normal to ), we have
Converting the surface integral into a volume integral via the divergence theorem gives
Using the symmetry of the Cauchy stress and the identity
we have the following
Hence we can write
and therefore the variation in the internal energy density is given by
An elastic material is defined as one in which the total internal energy is equal to the potential energy of the internal forces (also called the elastic strain energy). Therefore the internal energy density is a function of the strains, and the variation of the internal energy can be expressed as
Since the variation of strain is arbitrary, the stress-strain relation of an elastic material is given by
For a linear elastic material, the quantity is a linear function of , and can therefore be expressed as
where is a fourth-rank tensor of material constants, also called the stiffness tensor. We can see why must be a fourth-rank tensor by noting that, for a linear elastic material,
In index notation
Clearly, the right-hand side constant requires four indices and is a fourth-rank quantity. We can also see that this quantity must be a tensor because it is a linear transformation that takes the strain tensor to the stress tensor. We can also show that the constant obeys the tensor transformation rules for fourth-rank tensors.
- Elastic potential energy
- List of scientific laws named after people
- Quadratic form
- Spring system
- Simple harmonic motion of a mass on a spring
- Sine wave
- Solid mechanics
- Spring pendulum
- The anagram was given in alphabetical order, ceiiinosssttuv, representing Ut tensio, sic vis — "As the extension, so the force": Petroski, Henry (1996). Invention by Design: How Engineers Get from Thought to Thing. Cambridge, MA: Harvard University Press. p. 11. ISBN 0674463684.
- See , where one can find also an anagram for the catenary.
- Alla G. Ponomareva, Yevgen P. Yurenko , Roman O. Zhurakivsky, Tanja van Mourik and Dmytro M. Hovorun Phys. Chem. Chem. Phys., 2012,14, 6787-6795
- Symon, Keith (1971). Mechanics. Reading, MA: Addison-Wesley. ISBN 0-201-07392-7.
- Simo, J. C.; Hughes, T. J. R. (1998), Computational Inelasticity, Springer, ISBN 9780387975207
- Milton, Graeme W. (2002), The Theory of Composites, Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, ISBN 9780521781251
- Slaughter, William S. (2001), The Linearized Theory of Elasticity, Birkhäuser, ISBN 978-0817641177
- Boresi, A. P, Schmidt, R. J. and Sidebottom, O. M., 1993, Advanced Mechanics of Materials, Wiley.
- Tan, S. C., 1994, Stress Concentrations in Laminated Composites, Technomic Publishing Company, Lancaster, PA.
- A.C. Ugural, S.K. Fenster, Advanced Strength and Applied Elasticity, 4th ed
- Walter Lewin explains Hooke's law. From Walter Lewin (1 October 1999). Hooke's Law, Simple Harmonic Oscillator. MIT Course 8.01: Classical Mechanics, Lecture 10. (ogg) (videotape) (in English). Cambridge, MA USA: MIT OCW. Event occurs at 1:21–10:10. Retrieved 23 December 2010. "...arguably the most important equation in all of Physics."
- A test of Hooke's law. From Walter Lewin (1 October 1999). Hooke's Law, Simple Harmonic Oscillator. MIT Course 8.01: Classical Mechanics, Lecture 10. (ogg) (videotape) (in English). Cambridge, MA USA: MIT OCW. Event occurs at 10:10–16:33. Retrieved 23 December 2010.
|Homogeneous isotropic linear elastic materials have their elastic properties uniquely determined by any two moduli among these, thus given any two, any other of the elastic moduli can be calculated according to these formulas.|
There are two valid solutions.
|Cannot be used when| |
Introduction to Digital Signature Algorithm
When a person sends data through a document, it becomes important to identify his/her authenticity for security and safety reasons. Digital signatures are used for this identification. Authentication of the documents means to be aware of who created them and that they did not interfere during their transmission. These signatures are created using certain algorithms. The Digital Signature Algorithm (DSA) is one of these. DSA is a type of public-key encryption algorithm, and it is used to generate an electronic signature.
As we have already seen, DSA is one of the many algorithms that are used to create digital signatures for data transmission. In DSA, a pair of numbers is created and used as a digital signature. These are generated using some specific algorithms. They allow the receiver to authenticate the origin of the message. The digital signature, created using DSA, is in private at the starting point of the data transmission while it ends in public. This means that only the person transmitting the data can make the signature, which is to be added to the message, but anyone can authenticate the signature at the other end.
Understanding the Digital Signature Algorithm
Several algorithms are used to create digital signatures. Most of these follow a simple method of using the private keys of a sender to sign the message digests. This is how the digital thumbprint is formed for the data to be sent. Please take note that it is the message digest that is signed and not the data. Therefore, the size of the signature is small. However, this is not the case with the digital signature algorithm. The procedure followed when using DSA is not as simple as using a private and public key at the start and end of the transmission, respectively. On the other hand, it generates two digital signatures by applying complex and unique mathematical functions, about which we will know in detail in the later parts of this article.
So, as it can be understood, DSA is used only to create the signatures. They cannot be used for the encryption of data. Due to this, it is not subjected to import and export restrictions, which is usually the case with RSA.
The Working of Digital Signature Algorithm (DSA)
The DSA algorithm is standard for digital signature, which is based on the algebraic properties of discrete logarithm problem and modular exponentiations and is based on the public-key cryptosystems principal.
Digital signatures are work on the principle of two mutually authenticating cryptographic keys. Signatures are based on public/private key pairs. With a public-key algorithm like RSA, one can create a mathematically linked private key and public key. One can sign a digital message with his private key. A person can encrypt signature related data with the use of a private key. The private key should always be with a person who wants to create a digital signature. Both the public and the private key can always be derived from one another as they are related mathematically. Signer’s public key is the only way to decrypt this data. One can give the public key to anyone who needs verification of the signer’s signature. It is vital to keep private key secret as one can generate your signature on a document with the help of this. In this manner, the authentication digital signature is done. In a digital signature, validly is only assured by public and private keys.
On the other hand, the digital signature algorithm does not use a private key to encrypt data. Also, a digital signature algorithm does use a public key to decrypt this data. To create a digital signature with two 160-bit numbers, DSA works on the principle of a unique mathematical function. These two numbers are made by using the private key and the message digest.
As the public key is not used to authenticate the signature, the verification process is complex. Both keys are used to secure data in a special digital signature algorithm for further security assurance.
Now, a hash function is used to create a message digest. The generated message digest, along with the DSA algorithm, is what gives the digital signature. This signature is then sent along with the message. At the receiving end, the same hash function is used to authenticate the source and the data.
- Keys are generated with the help of the key generation algorithm. Created keys are used to sign a document.
- For generating a signature, a digital signature algorithm is used.
- A hash function is used to make a message digest.
- Message digest with DSA gives the digital signature.
- The digital signature is then transmitted along with the data sent.
- The authentication of the signature is done using verification algorithms. For verification, the same hash function is used.
Advantages of the Digital Signature Algorithm
- Along with having strong strength levels, the signature’s length is smaller compared to other digital signature standards.
- The signature computation speed is less.
- DSA requires less storage to work as compared to other digital standards.
- DSA is patent-free so that it can be used free of cost.
Disadvantages of Digital Signature Algorithm
- It requires a lot of time to authenticate as the verification process includes complicated remainder operators. It requires a lot of time for computation.
- Data in DSA is not encrypted. We can only authenticate data in this.
- The digital signature algorithm firstly computes with SHA1 hash and signs it. Any drawbacks in the cryptographic security of SHA1 are reflected in DSA because implicitly of DSA is dependent on it.
- With applications in both secret and non-secret communications, DSA is of the US National Standard.
In the above script, we have come up with an essential point regarding the digital signature algorithm. This article gives information about the digital signature algorithm, its way of working and advantages & disadvantages.
The digital signature is one of the best authentication tools for electronic record. On account of its cost, security, time, and speed, digital signatures are popular nowadays. In today’s interconnected and digital world, the digital signature algorithm is vital for creating a safer and secure environment.
This has been a guide to Digital Signature Algorithm. Here we discussed the concepts of the Digital Signature Algorithm. You can also go through our other suggested articles to learn more – |
Knowing the perimeter and the side pieces, you can find the other side and square. The perimeter, in turn, can be found in several specified parties or on the corner and sides, depending on the conditions of the problem. Also, in some cases, it is expressed through the area. The most simple is the perimeter of the rectangle. Draw a rectangle with one side equal to a, and a diagonal equal to d. Knowing these two quantities, find the Pythagorean theorem the other side, which is the width of the rectangle. Finding the width of the rectangle, find it's perimeter as follows: p=2(a+b). This formula is valid for all rectangles because each one of those four sides.
Pay attention to the fact that the perimeter of the triangle in most tasks and find if there is information about at least one of its corner. However, there are tasks in which all sides of a triangle are known, then the perimeter can be calculated by simple summation without using trigonometric calculations: p=a+b+c, where a, b and c - side. But such tasks found in textbooks rarely as a way to solve them is obvious. The more difficult task of finding the perimeter of a triangle solve step by step. For example, draw an isosceles triangle whose base is known and the angle. In order to find its perimeter, first find the sides a and b as follows: b=c/2cosα. Since a=b (isosceles triangle), do the following conclusion: a=b=c/2cosα.
The perimeter of a polygon calculated in a similar way, folding the lengths of all its sides: p=a+b+c+d+e+f and so on. If the correct polygon with an inscribed circle or circumscribed around it, calculate the length of one of its sides, and then multiply by their number. For example, to find the sides of a hexagon inscribed in a circle, proceed as follows: a=R where a is the side of the hexagon equals the radius of the circumscribed circle. Accordingly, if the hexagon is correct, then its perimeter is: p=6a=6R. If circle is inscribed in a hexagon, the side of the latter is equal to: a=2r√3/3. Accordingly, the perimeter of a shape find the following: p=12r√3/3. |
COMPONENTS OF LOGARITHMS
The fractional part of a logarithm is usuallywritten as a decimal. The whole number part of a logarithm and the decimal part have been given separate names because each plays a special part in relation to the number which the logarithm represents. The whole number part of a logarithm is called the CHARACTERISTIC. This part of the logarithm shows the position of the decimal point in the associated number. The decimal part of a logarithm is called the MANTISSA.
For a particular sequence of digits makingup a number, the mantissa of a common logarithm is always the same regardless of the position of the decimal point in that number. For example, log 5270 = 3.72181; the mantissa is 0.72181 and the characteristic is 3.
The characteristic of a common logarithmshows the position of the decimal point in the associated number. The characteristic for a given number may be determined by inspection. It will be remembered that a common logarithm is simply an exponent of the base 10. It is the power of 10 when a number is written in scientific notation.
When we write log 360 = 2.55630, we understand this to mean 10 2.55630 = 360. We knowthat the number is 360 and not 36 or 3,600 be cause the characteristic is 2. We know 10 is 10, 102 is 100, and 102 is 1,000. Therefore, the number whose value is 102.55630 must lie between 100 and 1,000 and of course any number in that range has 3 digits.
Suppose the characteristic had been 1: wherewould the decimal point in the number be placed? Since 101 is 10 and 102 is 100, any number whose logarithm is between 1 and 2 must lie between 10 and 100 and will have 2 digits. Notice how the position of the decimal point changes with the value of the characteristic in the following examples:
log 36,000 = 4.55630
Note that it is only the characteristic that changes when the decimal point is moved. An advantage of using the base 10 is thus revealed: If the characteristic is known, the decimal point may easily be placed. If the number is known,the characteristic may be determined by inspection; that is, by observing the location of the decimal point.
Although an understanding of the relationof the characteristic to the powers of 10 is necessary for thorough comprehension of logarithms, the characteristic may be determined mechanically by application of the following rules:
1. For a number greater than 1, the characteristic is positive and is one less than thenumber of digits to the left of the decimal point in the number.
2. For a positive number less than 1, thecharacteristic is negative and has an absolute value one more than the number of zeros between the decimal point and the first nonzero digit of the number.
Table 8-5 contains examples of each type ofcharacteristic.
Practice problems. In problems 1 through4, write the characteristic of the logarithm for each number. In 5 through 8, place the decimal
Table 8-5.-Positive and negative characteristics.
point in each number as indicated by the characteristic (c) given for each.
When a characteristic is negative, such as-2, we do not carry out the subtraction, since this would involve a negative mantissa. There are several ways of indicating a negative characteristic. Mantissas as presented in the table in the appendix are always positive and the sign of the characteristic is indicated separately. For example, where log 0.023 = 2.36173, the bar over the 2 indicates that only the characteristic is negative-that is, the logarithm is -2 + 0.36173.
Another way to show the negative characteristic is to place it after the mantissa. In thiscase we write 0.36173-2.
A third method, which is used where possible throughout this chapter, is to add a certainquantity to the characteristic and to subtract the same quantity to the right of the mantissa. In the case of the example, we may write:
In this way the value of the logarithm remainsthe same but we now have a positive characteristic as well as a positive mantissa.
The mantissa is the decimal part of a logarithm. Tables of logarithms usually containonly mantissas since the characteristic can be readily determined as explained previously. Table 8-8 shows the characteristic, mantissa, and logarithm for several positions of the decimal point using the sequence of digits 4, 5, 6. It will be noted that the mantissa remains the same for that particular sequence of digits, regardless of the position of the decimal point.
Table 8-6.-Effect of changes in the location of the decimal point.
Appendix I of this training course is a tablewhich includes the logarithms of numbers from 1 to 100. For our present purpose in using this table, we are concerned only with the first and sixth columns.
The first column contains the number and the sixth column contains its logarithm. For example, if it is desired to find the logarithm of 45, we would find the number 45 in the first column, look horizontally across the page to column 6 and read the logarithm, 1.65321. A glance down the logarithm column will reveal that the logarithms increase in value as the numbers increase in value.
It must be noted in this particular table that both the mantissa and the characteristic are given for the number in the first column. This is simply an additional aid, since the characteristic can easily be determined by inspection. Suppose that we wish to use the table of Appendix I to find the logarithm of a number not shown in the "number" column. By recalling that the mantissa does not change when the decimal point moves, we may be able to determine the desired logarithm. For example, the number 450 does not appear in the number column of the table. However, the number 45 has the same mantissa as 450; the only difference between the two logs is in their .characteristics. Thus the logarithm of 450 is 2.65321.
Practice problems. Find the logarithms of the following numbers: |
- Charge density
The linear, surface, or volume charge density is the amount of electric charge in a line, surface, or volume, respectively. It is measured in coulombs per meter (C/m), square meter (C/m²), or cubic meter (C/m³), respectively, and represented by the lowercase Greek letter Rho (ρ). Since there are positive as well as negative charges, the charge density can take on negative values. Like any density it can depend on position. It should not be confused with the charge carrier density. As related to chemistry, it can refer to the charge distribution over the volume of a particle, molecule, or atom. Therefore, a lithium cation will carry a higher charge density than a sodium cation due to its smaller ionic radius.
Classical charge density
This relation defines the charge density mathematically. Note that the symbols used to denote the various dimensions of charge density vary between fields of studies. Other commonly used notations are λ, σ, ρ; or ρl, ρs, ρv for (C/m), (C/m²), (C/m³), respectively.
Homogeneous charge density
For the special case of a homogeneous charge density, that is one that is independent of position, equal to ρq,0 the equation simplifies to:
The proof of this is simple. Start with the definition of the charge of any volume:
Then, by definition of homogeneity, is a constant that we will denote ρq,0 to differentiate between the constant and non-constant forms, and thus by the properties of an integral can be pulled outside of the integral resulting in:
The equivalent proofs for linear charge density and surface charge density follow the same arguments as above.
where is the test position， is the charge of the ith charge carrier, whose position is .
If all charge carriers have the same charge q (for electrons q = − e) the charge density can be expressed through the charge carrier density : Again, the equivalent equations for the linear and surface charge densities follow directly from the above relations.
Relative charge density
From the perspective of the theory of relativity, the length of a segment of wire depends on velocity of observer, so charge density is a relative concept. Anthony French has described how the magnetic field force of a current-bearing wire arises from this relative charge density. He used (p 260) a Minkowski diagram to show "how a neutral current-bearing wire appears to carry a net charge density as observed in a moving frame." The approach to electromagnetism through spacetime symmetry is called relativistic electromagnetism.
Quantum charge density
In quantum mechanics, charge density is related to wavefunction by the equation
when the wavefunction is normalized as
- ^ Spacial Charge Distributions - http://faculty.wwu.edu/vawter/PhysicsNet/Topics/Gauss/SpacialCharge.html
- ^ A. French (1968) Special Relativity, chapter 8 Relativity and electricity, pp 229–65, W. W. Norton.
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How to find roots of a quadratic equation by factorising.
A quadratic equation looks like this:
ax² + bx + c = 0Â (where ‘a’ cannot be zero.)
Solving the equation means finding ‘x’ values that make the equation true. These ‘x’ values are called the roots  of the quadratic.
Quadratic equations can have 0, 1 or two roots.
In the complex number system, all quadratic equations have roots, but we will
not discuss complex numbers in this article. Roots of quadratics always come in
pairs, but when there are two roots that are the same we say that there is only
This method requires that you can factorise the quadratic expression on the left hand side. This is not always possible, and if not you would have to use one of the other methods.
Consider this quadratic expression...
4x - 5 = 0
When factorised, it looks like this...
(x + 1)(x -
5) = 0
For the example, this means that if (x+1) or (x-5) is zero, the product will be zero and the equation will be true. We use this fact to find the roots as follows:
1 = 0 so  Â
5 = 0 so  Â
x = 5
 The example quadratic equation has two roots, x = -1 and x = 5.
Step 1Â Enter the equation to solve
Click  and type the quadratic equation into the 'maths' box in the data entry dialog box.
If the ‘EMPTY’ message is
not displayed between the blue buttons, click the
until the message: ‘INSERT’ appears. If
required, use the ‘ * ’ symbol for multiply, and the ‘ / ’ symbol for
     Â
Step 2, Solve...
Keep clicking the  (factorise) button until the equation is factorised, and looks like this:
(x + 1)(x -
5) = 0
If there is a common factor, this will be at the front of the left bracket.
The expressions in brackets must be
equated to zero to find the roots. (See
the theory section at the top of this article.)
In this case, x+1 = 0 and x-5
= 0, so the roots are x = -1 and x = 5.
NOTE: If the equation does not factorise, then you will need to use one of the other methods described in the topic: Factorise quadratics. |
The Lamport timestamp algorithm is a simple logical clock algorithm used to determine the order of events in a distributed computer system. As different nodes or processes will typically not be perfectly synchronized, this algorithm is used to provide a partial ordering of events with minimal overhead, and conceptually provide a starting point for the more advanced vector clock method. The algorithm is named after its creator, Leslie Lamport.
Distributed algorithms such as resource synchronization often depend on some method of ordering events to function. For example, consider a system with two processes and a disk. The processes send messages to each other, and also send messages to the disk requesting access. The disk grants access in the order the messages were received. For example process sends a message to the disk requesting write access, and then sends a read instruction message to process . Process receives the message, and as a result sends its own read request message to the disk. If there is a timing delay causing the disk to receive both messages at the same time, it can determine which message happened-before the other: happens-before if one can get from to by a sequence of moves of two types: moving forward while remaining in the same process, and following a message from its sending to its reception. A logical clock algorithm provides a mechanism to determine facts about the order of such events. Note that if two events happen in different processes that do not exchange messages directly or indirectly via third-party processes, then we say that the two processes are concurrent, that is, nothing can be said about the ordering of the two events.
Lamport invented a simple mechanism by which the happened-before ordering can be captured numerically. A Lamport logical clock is a numerical software counter value maintained in each process.
Conceptually, this logical clock can be thought of as a clock that only has meaning in relation to messages moving between processes. When a process receives a message, it re-synchronizes its logical clock with that sender. The above-mentioned vector clock is a generalization of the idea into the context of an arbitrary number of parallel, independent processes.
The algorithm follows some simple rules:
- A process increments its counter before each local event (e.g., message sending event);
- When a process sends a message, it includes its counter value with the message after executing step 1;
- On receiving a message, the counter of the recipient is updated, if necessary, to the greater of its current counter and the timestamp in the received message. The counter is then incremented by 1 before the message is considered received.
In pseudocode, the algorithm for sending is:
# event is known time = time + 1; # event happens send(message, time);
The algorithm for receiving a message is:
(message, time_stamp) = receive(); time = max(time_stamp, time) + 1;
For every two different events and occurring in the same process, and being the timestamp for a certain event , it is necessary that never equals .
Therefore it is necessary that:
- The logical clock be set so that there is a minimum of one clock "tick" (increment of the counter) between events and ;
- In a multi-process or multi-threaded environment, it might be necessary to attach the process ID (PID) or any other unique ID to the timestamp so that it is possible to differentiate between events and which may occur simultaneously in different processes.
For any two events, and , if there’s any way that could have influenced , then the Lamport timestamp of will be less than the Lamport timestamp of . It’s also possible to have two events where we can’t say which came first; when that happens, it means that they couldn’t have affected each other. If and can’t have any effect on each other, then it doesn’t matter which one came first.
A Lamport clock may be used to create a partial ordering of events between processes. Given a logical clock following these rules, the following relation is true: if then , where means happened-before.
This relation only goes one way, and is called the clock consistency condition: if one event comes before another, then that event's logical clock comes before the other's. The strong clock consistency condition, which is two way (if then ), can be obtained by other techniques such as vector clocks. Using only a simple Lamport clock, only a partial causal ordering can be inferred from the clock.
However, via the contrapositive, it's true that implies . So, for example, if then cannot have happened-before .
Another way of putting this is that means that may have happened-before , or be incomparable with in the happened-before ordering, but did not happen after .
Nevertheless, Lamport timestamps can be used to create a total ordering of events in a distributed system by using some arbitrary mechanism to break ties (e.g., the ID of the process). The caveat is that this ordering is artifactual and cannot be depended on to imply a causal relationship.
Lamport's logical clock in distributed systems
In a distributed system, it is not possible in practice to synchronize time across entities (typically thought of as processes) within the system; hence, the entities can use the concept of a logical clock based on the events through which they communicate.
If two entities do not exchange any messages, then they probably do not need to share a common clock; events occurring on those entities are termed as concurrent events.
Among the processes on the same local machine we can order the events based on the local clock of the system.
When two entities communicate by message passing, then the send event is said to happen-before the receive event, and the logical order can be established among the events.
A distributed system is said to have partial order if we can have a partial order relationship among the events in the system. If 'totality', i.e., causal relationship among all events in the system, can be established, then the system is said to have total order.
A single entity cannot have two events occur simultaneously. If the system has total order we can determine the order among all events in the system. If the system has partial order between processes, which is the type of order Lamport's logical clock provides, then we can only tell the ordering between entities that interact. Lamport addressed ordering two events with the same timestamp (or counter): "To break ties, we use any arbitrary total ordering of the processes." Thus two timestamps or counters may be the same within a distributed system, but in applying the logical clocks algorithm events that occur will always maintain at least a strict partial ordering.
Lamport clocks lead to a situation where all events in a distributed system are totally ordered. That is, if , then we can say actually happened before .
Note that with Lamport’s clocks, nothing can be said about the actual time of and . If the logical clock says , that does not mean in reality that actually happened before in terms of real time.
Lamport clocks show non-causality, but do not capture all causality. Knowing and shows did not cause or but we cannot say which initiated .
This kind of information can be important when trying to replay events in a distributed system (such as when trying to recover after a crash). If one node goes down, and we know the causal relationships between messages, then we can replay those messages and respect the causal relationship to get that node back up to the state it needs to be in.
- ^ "Distributed Systems 3rd edition (2017)". DISTRIBUTED-SYSTEMS.NET. Retrieved 2021-03-20.
- ^ a b Lamport, L. (1978). "Time, clocks, and the ordering of events in a distributed system" (PDF). Communications of the ACM . 21 (7): 558–565. doi:10.1145/359545.359563. S2CID 215822405.
- ^ "Clocks and Synchronization — Distributed Systems alpha documentation". books.cs.luc.edu. Retrieved 2017-12-13. |
English 9 expands upon the fundamentals of reading and writing. Through exposure to a variety of texts, students will construct coherent writing pieces that help them develop their own perspective on different topics. Key concepts: Foundations of reading and writing; fiction and non-fiction text analysis; research skills; literary terms and devices; short stories, poems, epics, and myths; informational, persuasive, synthetic, and narrative writing; media analysis; grammar and punctuation.
English 10 develops literacy skills for college and career readiness through reading and analyzing different texts that prompt critical thinking, comprehension
English 11 builds on student literacy and language arts skills to promote effective writing, critical thinking, and analysis of literature. Using American History, students will analyze various fiction and non-fiction texts, and express opinions orally and in writing. Key Concepts: Reading skills & the writing process; literary text analysis & research; short stories, poetry, & drama; exploring novels, non-fiction, and American History documents; informative
English 12 promotes effective writing, critical thinking, and literary analysis. Material includes British literature as well as examining historical and cultural concepts in order to develop and express their own perspectives in spoken and written arguments. Key Concepts: Reading skills & the writing process; literary text analysis & research; short stories, poetry, & drama; British poems, novels, & plays; informative, persuasive, expository, & narrative writing; word choice & tone; grammar & punctuation.
Algebra I is a comprehensive presentation of algebra that includes solving, writing, and plotting equations and functions. Key Concepts: Equations & functions; real numbers; equations of lines; graphs of equations & functions; writing linear equations; linear inequalities; solutions using the discriminant; solving systems of equation and inequalities; exponential functions; polynomials; quadratic functions & equations; algebra & geometry connections; rational equations & functions; probability & statistics.
Algebra II expands upon equations and functions, with a focus on solving and simplifying complex algebraic expressions. Key Concepts: Equations & inequalities; linear equations & functions; systems of linear equations & inequalities; matrices; quadratic functions; polynomial functions; roots, radicals, & function operations; exponential & logarithmic functions; trigonometry; introduction to probability; sequences & series; conic sections; rational functions.
Geometry connects algebraic concepts to geometric relationships related to the characteristics of shapes. Key Concepts: Basics of geometry including lines, distance, & angles; reasoning & proof; parallel & perpendicular lines; triangles & congruence; relationships with triangles; polygons & quadrilaterals; ratios & proportions; right triangle trigonometry; circles; perimeter & area; surface & area volume; symmetry, reflections & rigid transformations.
Integrated Math I is the first course of a three-course sequence that satisfies the California Common Core Standards. Integrated Math I builds and strengthens students’ conceptual knowledge of Algebra and Geometry. Key Concepts: Functions; equations; inequalities; systems of linear equations & inequalities; one variable descriptive statistics; correlation & residuals; analyzing categorical data; mathematical modeling; coordinate & transformational geometries.
Integrated Math II is the second course of a three-course sequence that satisfies the California Common Core Standards. Integrated Math II builds and strengthens students’ conceptual knowledge of complex algebraic and geometric relationships. Key Concepts: Triangular relationships; similarity; polygons; circles; areas; volumes; right triangle trigonometry; functions; imaginary numbers; higher order polynomials; graphing of functions; irrational expressions; probability & statistics.
Integrated Math III is the third course of a
Precalculus is a thoughtful introduction to advanced studies leading to calculus. Scaffolding rigorous content with clear instruction, the course leads students through an advanced study of trigonometric functions, matrices, and vectors. Key Concepts: Functions & graphs; polynomials; rational functions; logs & exponents; trigonometry; vectors; systems & matrices; conics; polar & parametric equations; probability & statistics; logic
Biology introduces students to the study of living organisms and their environment, engaging them to connect their learnings to everyday life. Students will investigate the roles and dependencies of organisms within populations, communities, ecosystems, and the biosphere. Key Concepts: Introduction to the scientific method; cytology; genetics; botany; zoology; ecology; taxonomy; evolution; chemistry; microbiology.
Earth Science introduces scientific investigations and methods, observations, tools, and methods used for understanding Earth and its characteristics in the atmosphere, on land, and in water. Key Concepts: Principles of science, earth science tools, materials of the earth’s crust; plate tectonics; geological activity; surface processes & landforms; water; atmospheric processes; life on earth; earth’s history; natural resources; the solar system & beyond.
Physical Science introduces scientific investigation and the scope of physical science. This course will explain how scientific investigation is performed, as well as how technology and science go hand-in-hand. Key Concepts: The world of science; matter; atoms; periodic table; chemical bonding & reactions; chemistry of carbon; Newton’s Laws of Motion; forces; work & machines; energy; waves; sound; electromagnetic radiation; visible light; electricity.
American Government provides students with an understanding of civic life, politics, and government, along with a short history of the American government’s foundation and development. Key Concepts: Foundations of American government; political behavior; legislative, executive, & judicial branches; comparative political & economic systems; powers & procedures of national, state, tribal, & local governments.
Economics introduces students to the basics of economic principles and economic systems within the context of today’s economy. Key Concepts: Basics of economics; supply & demand; production technology & costs; monopoly, price discrimination, market entry, monopolistic competition, & oligopoly; external benefits & costs; labor market & distribution of income; money & banking systems.
U.S. History provides a comprehensive overview of the history of the United States, surveying the major events and turning points of U.S. history as it moves from
World History examines human development from the dawn of civilization to the present day. Using primary and secondary sources, students conduct an
French I focuses on basic skills for listening, speaking, reading, and writing in French. Each lesson introduces new vocabulary and grammar concepts through various comprehension activities. Key Concepts: Vocab includes introductions, dates, personal & family life, city life, & time; present-tense verbs & grammar.
French II uses authentic cultural resources, such as movies and songs, to expand reading, writing, listening, and speaking skills so students can communicate effectively in French. Key Concepts: Vocab includes greetings, family, friends, hobbies, shopping, food, travel, & restaurants; complex verb & grammar.
French III focuses on four modes of expression in French,
French IV reinforces the skills and linguistic tools learned in previous French courses. Students will develop receptive and productive skills that will allow them to communicate extensively in French and understand the language through cultural experiences. Key Concepts: Vocab includes science & technology, family & communities, medical care, the arts, & the outdoors; complex verbs & grammar.
Spanish I is an introduction to listening, speaking, reading, and writing in Spanish, as well as the cultural influences of Spanish and Latino heritage at home and abroad. Key Concepts: Introductions; descriptions; school; food; hobbies; families; home; shopping; expressions; cultural comparisons; adjectives.
Spanish II continues language development skills for comprehension, reading, and writing using cultural presentations and interactive activities that reinforce common grammar patterns. Key Concepts: Special events; community; TV; news; cooking; affirmative & negative commands; common & irregular verb tenses.
Spanish III equips students to interact verbally and in writing in varied social and business situations through discussion and analysis of complex topics using irregular grammar structures. Key Concepts: Vocab includes special events, Spanish art & literature; complex grammar (e.g., preterite, imperfect, subjunctive); commands; pronouns.
Students will build on their Spanish knowledge by learning more complex grammatical structures and become equipped to read and understand a variety of literary selections. Key Concepts: Vocab includes art, self-expression, relationships, & careers; complex verb tenses & grammar (e.g., preterite, imperfect, subjunctive).
Art Appreciation is an art survey course designed to increase knowledge and appreciation of the visual arts. Students focus on interpreting and evaluating works of art within formal, cultural, and historical contexts, including a deep look at
Music Appreciation is an introductory course to music’s various functionalities. Throughout the course, students apply their understanding through music composition to gain a deeper understanding and appreciation for all types of music. Key Concepts: Music literacy; musical instruments; sacred music; music for
Engineering helps students understand what engineers do, as well as the processes and skills required. Throughout the duration of the course, students will work in an Engineering lab onsite twice a week for hands-on application in engineering projects. Key Concepts: Engineering techniques and practices; engineering careers; engineering in society; engineering design process; math in engineering; history of engineering; problem-solving with engineering (graphing, programming, loops, & conditionals).
Entrepreneurship is an interdisciplinary course designed to teach students how to start-up and operate a business while in school. The course integrates inquiry-based learning and business tools that enable students to analyze, create, develop and pilot small businesses in a safe campus environment. Key Concepts: Entrepreneurship; entrepreneur roles in society; types of businesses and ownership; business planning; marketing & sales; managing finances; obtaining investment.
Forensic Science focuses on the skills and concepts behind evidence in crime scene investigation. Whether students desire to be forensic pathologists or medical scientists, this course will help them hone their investigative skills. Key Concepts: Observation, investigation, & evidence collection; death examination; trace evidence; fingerprints & DNA; drug identification & toxicology; blood & blood splatter analysis; forensic anthropology; document & voice examination.
Marketing introduces students to the business activities, tools, and methods that are designed to plan, price, promote, and place goods/services for current and potential customers. Key Concepts: Marketing concepts; market analysis; market research; marketing environments; marketing communication & branding; marketing information management; product & service management; promotion; consumer economic buying decisions; college & career planning.
Personal Finance provides students with basic financial tools and knowledge that will enable them to build the lives they envision. The course will help students to understand how to plan for the future by planning for today. Key Concepts: American credit industry; stock market; consumerism; saving & budgeting; credit &
Psychology focuses on individual behavior and why an individual thinks, feels, and reacts to certain stimuli. Emphasis will be placed on research methods, how the brain works, altered states of consciousness, and psychological disorders. Key Concepts: Introduction to psychology; intelligence & learning; sleeping & dreaming; developmental psychology; stages of childhood & adolescence; nature vs. nurture; personality theory; psychological disorders.
Web Design teaches methods, theories, and principles of design through web design projects that help students develop problem-solving and critical thinking skills, artistic perception, critique
Physical Education I focuses on the principles of fitness, including competency in motor skills and movement. Students enrolled in this course are required to complete 36 hours of physical activity that are signed off by an approved fitness professional. Key Concepts: Principles of fitness including balance, agility, coordination, power, & speed; consumer fitness products; occupational fitness requirements; disease prevention; designing a fitness program; evaluating fitness program elements.
This high school Health course helps students develop the knowledge and skills they need to make healthy decisions that allow them to stay active, safe, and informed. Students learn about the components of a healthy lifestyle and learn strategies for making healthy choices. Instructional material introduces students to the concepts of mental health, emotional health, social health, consumer health, and physical health. It presents opportunities for students to apply their value systems to decisions concerning their own health. Students develop communication skills in this one-semester course that allow them to demonstrate healthy choices with respect for self, family, and others. |
Computer-generated map of Pluto
|Discovered by||Clyde W. Tombaugh|
|Discovery date||February 18, 1930|
|MPC designation||134340 Pluto|
0.248 807 66 (mean)
Average orbital speed
Sidereal rotation period
Equatorial rotation velocity
|119.591°±0.014° (to orbit)[g]|
North pole right ascension
North pole declination
|Albedo||0.49 to 0.66 (geometric, varies by 35%)|
|13.65 to 16.3
(mean is 15.1)
|0.065″ to 0.115″[h]|
|0.30 Pa (summer maximum)|
|Composition||nitrogen, methane, carbon monoxide|
Pluto (134340 Pluto) is the largest object in the Kuiper belt,[i][j] the tenth-most-massive known body directly orbiting the Sun, and the second-most-massive known dwarf planet, after Eris. Like other Kuiper belt objects, Pluto is primarily made of rock and ice, and relatively small, about 1/6 the mass of the Moon and 1/3 its volume. It has an eccentric and highly inclined orbit that takes it from 30 to 49 AU (4.4–7.4 billion km) from the Sun. Hence Pluto periodically comes closer to the Sun than Neptune, but an orbital resonance with Neptune prevents the bodies from colliding. In 2014 it was 32.6 AU from the Sun. Light from the Sun takes about 5.5 hours to reach Pluto at its average distance (39.4 AU).
Discovered in 1930, Pluto was originally considered the ninth planet from the Sun. Its status as a major planet fell into question following further study of it and the outer Solar System over the next 75 years. Starting in 1977 with the discovery of the minor planet Chiron, numerous icy objects similar to Pluto with eccentric orbits were found. The scattered disc object Eris, discovered in 2005, is 27% more massive than Pluto. The understanding that Pluto is only one of several large icy bodies in the outer Solar System prompted the International Astronomical Union (IAU) to formally define "planet" in 2006. This definition excluded Pluto and reclassified it as a member of the new "dwarf planet" category (and specifically as a plutoid). Astronomers who oppose this decision hold that Pluto should have remained classified as a planet, and that other dwarf planets and even moons should be added to the list of planets along with Pluto.
Pluto has five known moons: Charon (the largest, with a diameter just over half that of Pluto), Nix, Hydra, Kerberos, and Styx. Pluto and Charon are sometimes described as a binary system because the barycenter of their orbits does not lie within either body. The IAU has yet to formalise a definition for binary dwarf planets, and Charon is officially classified as a moon of Pluto.
On July 14, 2015, the Pluto system is due to be visited by spacecraft for the first time. The New Horizons probe will perform a flyby during which it will attempt to take detailed measurements and images of Pluto and its moons. Afterwards, the probe may visit several other objects in the Kuiper belt.
- 1 Discovery
- 2 Orbit and rotation
- 3 Physical characteristics
- 4 Satellites
- 5 Origins
- 6 Exploration
- 7 Classification
- 8 See also
- 9 Notes
- 10 References
- 11 Bibliography
- 12 External links
In the 1840s, using Newtonian mechanics, Urbain Le Verrier predicted the position of the then-undiscovered planet Neptune after analysing perturbations in the orbit of Uranus. Subsequent observations of Neptune in the late 19th century caused astronomers to speculate that Uranus's orbit was being disturbed by another planet besides Neptune.
In 1906, Percival Lowell—a wealthy Bostonian who had founded the Lowell Observatory in Flagstaff, Arizona, in 1894—started an extensive project in search of a possible ninth planet, which he termed "Planet X". By 1909, Lowell and William H. Pickering had suggested several possible celestial coordinates for such a planet. Lowell and his observatory conducted his search until his death in 1916, but to no avail. Unknown to Lowell, on March 19, 1915, surveys had captured two faint images of Pluto, but they were not recognized for what they were. There are fifteen other known prediscoveries, with the oldest made by the Yerkes Observatory on August 20, 1909.
Because of a ten-year legal battle with Constance Lowell, Percival's widow, who attempted to wrest the observatory's million-dollar portion of his legacy for herself, the search for Planet X did not resume until 1929, when its director, Vesto Melvin Slipher, summarily handed the job of locating Planet X to Clyde Tombaugh, a 23-year-old Kansan who had just arrived at the Lowell Observatory after Slipher had been impressed by a sample of his astronomical drawings.
Tombaugh's task was to systematically image the night sky in pairs of photographs, then examine each pair and determine whether any objects had shifted position. Using a machine called a blink comparator, he rapidly shifted back and forth between views of each of the plates to create the illusion of movement of any objects that had changed position or appearance between photographs. On February 18, 1930, after nearly a year of searching, Tombaugh discovered a possible moving object on photographic plates taken on January 23 and January 29 of that year. A lesser-quality photograph taken on January 21 helped confirm the movement. After the observatory obtained further confirmatory photographs, news of the discovery was telegraphed to the Harvard College Observatory on March 13, 1930.
The discovery made headlines across the globe. The Lowell Observatory, which had the right to name the new object, received over 1,000 suggestions from all over the world, ranging from Atlas to Zymal. Tombaugh urged Slipher to suggest a name for the new object quickly before someone else did. Constance Lowell proposed Zeus, then Percival and finally Constance. These suggestions were disregarded.
The name Pluto, after the god of the underworld, was proposed by Venetia Burney (1918–2009), an eleven-year-old schoolgirl in Oxford, England, who was interested in classical mythology. She suggested it in a conversation with her grandfather Falconer Madan, a former librarian at the University of Oxford's Bodleian Library, who passed the name to astronomy professor Herbert Hall Turner, who cabled it to colleagues in the United States.
The object was officially named on March 24, 1930. Each member of the Lowell Observatory was allowed to vote on a short-list of three: Minerva (which was already the name for an asteroid), Cronus (which had lost reputation through being proposed by the unpopular astronomer Thomas Jefferson Jackson See), and Pluto. Pluto received every vote. The name was announced on May 1, 1930. Upon the announcement, Madan gave Venetia GB£5 (£276 as of 2015), as a reward.
The choice of name was partly inspired by the fact that the first two letters of Pluto are the initials of Percival Lowell, and Pluto's astronomical symbol (, unicode U+2647, ♇) is a monogram constructed from the letters 'PL'. Pluto's astrological symbol resembles that of Neptune (), but has a circle in place of the middle prong of the trident ().
The name was soon embraced by wider culture. In 1930, Walt Disney was apparently inspired by it when he introduced for Mickey Mouse a canine companion named Pluto, although Disney animator Ben Sharpsteen could not confirm why the name was given. In 1941, Glenn T. Seaborg named the newly created element plutonium after Pluto, in keeping with the tradition of naming elements after newly discovered planets, following uranium, which was named after Uranus, and neptunium, which was named after Neptune.
Most languages use the name "Pluto" in various transliterations.[k] In Japanese, Houei Nojiri suggested the translation Meiōsei (冥王星?, "Star of the King(God) of the Underworld"), and this was borrowed into Chinese, Korean, and Vietnamese. Some Indian languages use the name Pluto, but others, such as Hindi, use the name of Yama, the Guardian of Hell in Hindu and Buddhist mythology, as does Vietnamese. Polynesian languages also tend to use the indigenous god of the underworld, as in Maori Whiro.
Demise of Planet X
|1931||1 Earth||Nicholson & Mayall|
|1948||0.1 (1/10) Earth||Kuiper|
|1976||0.01 (1/100) Earth||Cruikshank, Pilcher, & Morrison|
|1978||0.002 (1/500) Earth||Christy & Harrington|
|2006||0.00218 (1/459) Earth||Buie et al.|
Once found, Pluto's faintness and lack of a resolvable disc cast doubt on the idea that it was Lowell's Planet X. Estimates of Pluto's mass were revised downward throughout the 20th century.
Astronomers initially calculated its mass based on its presumed effect on Neptune and Uranus. In 1931 Pluto was calculated to be roughly the mass of Earth, with further calculations in 1948 bringing the mass down to roughly that of Mars. In 1976, Dale Cruikshank, Carl Pilcher and David Morrison of the University of Hawaii calculated Pluto's albedo for the first time, finding that it matched that for methane ice; this meant Pluto had to be exceptionally luminous for its size and therefore could not be more than 1 percent the mass of Earth. (Pluto's albedo is 1.3–2.0 times greater than that of Earth.)
In 1978, the discovery of Pluto's moon Charon allowed the measurement of Pluto's mass for the first time. Its mass, roughly 0.2% that of Earth, was far too small to account for the discrepancies in the orbit of Uranus. Subsequent searches for an alternative Planet X, notably by Robert Sutton Harrington, failed. In 1992, Myles Standish used data from Voyager 2's 1989 flyby of Neptune, which had revised the planet's total mass downward by 0.5%, to recalculate its gravitational effect on Uranus. With the new figures added in, the discrepancies, and with them the need for a Planet X, vanished. Today, the majority of scientists agree that Planet X, as Lowell defined it, does not exist. Lowell had made a prediction of Planet X's position in 1915 that was fairly close to Pluto's position at that time; Ernest W. Brown concluded soon after Pluto's discovery that this was a coincidence, a view still held today.
Orbit and rotation
Pluto's orbital period is 248 Earth years. Its orbital characteristics are substantially different from those of the planets, which follow nearly circular orbits around the Sun close to a flat reference plane called the ecliptic. In contrast, Pluto's orbit is highly inclined relative to the ecliptic (over 17°) and highly eccentric (elliptical). This high eccentricity means a small region of Pluto's orbit lies nearer the Sun than Neptune's. The Pluto–Charon barycenter came to perihelion on September 5, 1989,[l] and was last closer to the Sun than Neptune between February 7, 1979, and February 11, 1999. Pluto and Neptune make their closest approach when it is at 27.960 AU.
In the long term, Pluto's orbit is in fact chaotic. Although computer simulations can be used to predict its position for several million years (both forward and backward in time), after intervals longer than the Lyapunov time of 10–20 million years, calculations become speculative: Pluto is sensitive to unmeasurably small details of the Solar System, hard-to-predict factors that will gradually disrupt its orbit. Millions of years from now, Pluto may well be at aphelion, at perihelion or anywhere in between, with no way for us to predict which. This does not mean Pluto's orbit itself is unstable, but its position on that orbit is impossible to determine so far ahead. Several resonances and other dynamical effects keep Pluto's orbit stable, safe from planetary collision or scattering.
Relationship with Neptune
Despite Pluto's orbit appearing to cross that of Neptune when viewed from directly above, the two objects' orbits are aligned so that they can never collide or even approach closely. There are several reasons why.
At the simplest level, one can examine the two orbits and see that they do not intersect. When Pluto is closest to the Sun, and hence closest to Neptune's orbit as viewed from above, it is also the farthest above Neptune's path. Pluto's orbit passes about 8 AU above that of Neptune, preventing a collision. Pluto's ascending and descending nodes, the points at which its orbit crosses the ecliptic, are currently separated from Neptune's by over 21°.
This alone is not enough to protect Pluto; perturbations from the planets (especially Neptune) could alter aspects of Pluto's orbit (such as its orbital precession) over millions of years so that a collision could be possible. Some other mechanism or mechanisms must therefore be at work. The most significant of these is that Pluto lies in the 2:3 mean-motion resonance with Neptune: for every two orbits that Pluto makes around the Sun, Neptune makes three. The two objects then return to their initial positions and the cycle repeats, each cycle lasting about 500 years. This pattern is such that, in each 500-year cycle, the first time Pluto is near perihelion Neptune is over 50° behind Pluto. By Pluto's second perihelion, Neptune will have completed a further one and a half of its own orbits, and so will be a similar distance ahead of Pluto. Pluto and Neptune's minimum separation is over 17 AU. Pluto comes closer to Uranus (11 AU) than it does to Neptune.
The 2:3 resonance between the two bodies is highly stable, and is preserved over millions of years. This prevents their orbits from changing relative to one another; the cycle always repeats in the same way, and so the two bodies can never pass near to each other. Thus, even if Pluto's orbit were not highly inclined the two bodies could never collide.
Numerical studies have shown that over periods of millions of years, the general nature of the alignment between Pluto and Neptune's orbits does not change. There are several other resonances and interactions that govern the details of their relative motion, and enhance Pluto's stability. These arise principally from two additional mechanisms (besides the 2:3 mean-motion resonance).
First, Pluto's argument of perihelion, the angle between the point where it crosses the ecliptic and the point where it is closest to the Sun, librates around 90°. This means that when Pluto is nearest the Sun, it is at its farthest above the plane of the Solar System, preventing encounters with Neptune. This is a direct consequence of the Kozai mechanism, which relates the eccentricity of an orbit to its inclination to a larger perturbing body—in this case Neptune. Relative to Neptune, the amplitude of libration is 38°, and so the angular separation of Pluto's perihelion to the orbit of Neptune is always greater than 52° (90°–38°). The closest such angular separation occurs every 10,000 years.
Second, the longitudes of ascending nodes of the two bodies—the points where they cross the ecliptic—are in near-resonance with the above libration. When the two longitudes are the same—that is, when one could draw a straight line through both nodes and the Sun—Pluto's perihelion lies exactly at 90°, and hence it comes closest to the Sun at its maximally above Neptune's orbit. This is known as the 1:1 superresonance. All the Jovian planets, particularly Jupiter, play a role in the creation of the superresonance.
To understand the nature of the libration, imagine a polar point of view, looking down on the ecliptic from a distant vantage point where the planets orbit counterclockwise. After passing the ascending node, Pluto is interior to Neptune's orbit and moving faster, approaching Neptune from behind. The strong gravitational pull between the two causes angular momentum to be transferred to Pluto, at Neptune's expense. This moves Pluto into a slightly larger orbit, where it travels slightly slower, according to Kepler's third law. As its orbit changes, this has the gradual effect of changing the perihelion and longitude of Pluto's orbit (and, to a lesser degree, of Neptune). After many such repetitions, Pluto is sufficiently slowed, and Neptune sufficiently speeded up, that Neptune begins to catch up with Pluto at the opposite side of its orbit (near the opposing node to where we began). The process is then reversed, and Pluto loses angular momentum to Neptune, until Pluto is sufficiently speeded up that it begins to catch Neptune again at the original node. The whole process takes about 20,000 years to complete.
Pluto's rotation period, its day, is equal to 6.39 Earth days. Like Uranus, Pluto rotates on its "side" on its orbital plane, with an axial tilt of 120°, and so its seasonal variation is extreme; at its solstices, one-fourth of its surface is in continuous daylight, whereas another fourth is in continuous darkness.
Appearance and surface
Pluto's visual apparent magnitude averages 15.1, brightening to 13.65 at perihelion. To see it, a telescope is required; around 30 cm (12 in) aperture being desirable. It looks star-like and without a visible disk even in large telescopes, because its angular diameter is only 0.11".
The earliest maps of Pluto, made in the late 1980s, were brightness maps created from close observations of eclipses by its largest moon, Charon. Observations were made of the change in the total average brightness of the Pluto–Charon system during the eclipses. For example, eclipsing a bright spot on Pluto makes a bigger total brightness change than eclipsing a dark spot. Computer processing of many such observations can be used to create a brightness map. This method can also track changes in brightness over time.
Current maps have been produced from images from the Hubble Space Telescope (HST), which offers the highest resolution currently available, and show considerably more detail, resolving variations several hundred kilometres across, including polar regions and large bright spots. The maps are produced by complex computer processing, which find the best-fit projected maps for the few pixels of the Hubble images. The two cameras on the HST used for these maps are no longer in service, so these will likely remain the most detailed maps of Pluto until the 2015 flyby of New Horizons.
These maps, together with Pluto's lightcurve and the periodic variations in its infrared spectra, reveal that Pluto's surface is remarkably varied, with large changes in both brightness and color. Pluto is one of the most contrastive bodies in the Solar System, with as much contrast as Saturn's moon Iapetus. The color varies between charcoal black, dark orange and white: Buie et al. term it "significantly less red than Mars and much more similar to the hues seen on Io with a slightly more orange cast".
Pluto's surface has changed between 1994 and 2002–3: the northern polar region has brightened and the southern hemisphere darkened. Pluto's overall redness has also increased substantially between 2000 and 2002. These rapid changes are probably related to seasonal condensation and sublimation of portions of Pluto's atmosphere, amplified by Pluto's extreme axial tilt and high orbital eccentricity.
Spectroscopic analysis of Pluto's surface reveals it to be composed of more than 98 percent nitrogen ice, with traces of methane and carbon monoxide. The face of Pluto oriented toward Charon contains more methane ice, whereas the opposite face contains more nitrogen and carbon monoxide ice.
Observations by the Hubble Space Telescope place Pluto's density at between 1.8 and 2.1 g/cm3, suggesting its internal composition consists of roughly 50–70 percent rock and 30–50 percent ice by mass. Because the decay of radioactive elements would eventually heat the ices enough for the rock to separate from them, scientists expect that Pluto's internal structure is differentiated, with the rocky material having settled into a dense core surrounded by a mantle of ice. The diameter of the core is hypothesized to be approximately 1700 km, 70% of Pluto's diameter. It is possible that such heating continues today, creating a subsurface ocean layer of liquid water some 100 to 180 km thick at the core–mantle boundary. The DLR Institute of Planetary Research calculated that Pluto's density-to-radius ratio lies in a transition zone, along with Neptune's moon Triton, between icy satellites like the mid-sized moons of Uranus and Saturn, and rocky satellites such as Jupiter's Io.
Mass and size
Pluto's mass is 1.31×1022 kg, less than 0.24 percent that of Earth, and its diameter is 2306±20 km, or roughly 66% that of the Moon. Its surface area (1.665×107 km2) is about 10% smaller than that of South America. Pluto's atmosphere complicates determining its true solid size within a certain margin. Pluto's albedo varies from 0.49–0.66.
The discovery of Pluto's satellite Charon in 1978 enabled a determination of the mass of the Pluto–Charon system by application of Newton's formulation of Kepler's third law. Once Charon's gravitational effect was measured, Pluto's true mass could be determined. Observations of Pluto in occultation with Charon allowed scientists to establish Pluto's diameter more accurately, whereas the invention of adaptive optics allowed them to determine its shape more accurately.
|1993||1195 (2390) km||Millis, et al. (If no haze)|
|1993||1180 (2360) km||Millis, et al. (surface & haze)|
|1994||1164 (2328) km||Young & Binzel|
|2006||1153 (2306) km||Buie, et al.|
|2007||1161 (2322) km||Young, Young, & Buie|
|2011||1180 (2360) km||Zalucha, et al.|
|2014||1184 (2368) km||Lellouch, et al.|
Among the objects of the Solar System, Pluto is much less massive than the terrestrial planets, and at less than 0.2 lunar masses, it is also less massive than seven moons: Ganymede, Titan, Callisto, Io, the Moon, Europa and Triton.
Pluto is more than twice the diameter and a dozen times the mass of the dwarf planet Ceres, the largest object in the asteroid belt. It is less massive than the dwarf planet Eris, a trans-Neptunian object discovered in 2005. Given the error bars in the different size estimates, it is currently unknown whether Eris or Pluto has the larger diameter. Both Pluto and Eris are estimated to have solid-body diameters of about 2330 km.
Determinations of Pluto's size are complicated by its atmosphere, and possible hydrocarbon haze. In March, 2014, Lellouch, de Bergh et al. published findings regarding methane mixing ratios in Pluto's atmosphere consistent with a Plutonian diameter greater than 2360 km, with a "best guess" of 2368 km, which would make it slightly larger than Eris.
Pluto's atmosphere consists of a thin envelope of nitrogen, methane, and carbon monoxide gases, which are derived from the ices of these substances on its surface. Its surface pressure ranges from 6.5 to 24 μbar. Pluto's elongated orbit is predicted to have a major effect on its atmosphere: as Pluto moves away from the Sun, its atmosphere should gradually freeze out, and fall to the ground. When Pluto is closer to the Sun, the temperature of Pluto's solid surface increases, causing the ices to sublimate into gas. This creates an anti-greenhouse effect; much as sweat cools the body as it evaporates from the surface of the skin, this sublimation cools the surface of Pluto. In 2006, scientists using the Submillimeter Array discovered that Pluto's temperature is about 43 K (−230 °C), 10 K colder than would otherwise be expected.
The presence of methane, a powerful greenhouse gas, in Pluto's atmosphere creates a temperature inversion, with average temperatures 36 K warmer 10 km above the surface. The lower atmosphere contains a higher concentration of methane than its upper atmosphere.
Evidence of Pluto's atmosphere was first suggested by Noah Brosch and Haim Mendelson of the Wise Observatory in Israel in 1985, and then definitively detected by the Kuiper Airborne Observatory in 1988, from observations of occultations of stars by Pluto. When an object with no atmosphere moves in front of a star, the star abruptly disappears; in the case of Pluto, the star dimmed out gradually. From the rate of dimming, the atmospheric pressure was determined to be 0.15 pascal, roughly 1/700,000 that of Earth.
In 2002, another occultation of a star by Pluto was observed and analysed by teams led by Bruno Sicardy of the Paris Observatory, James L. Elliot of MIT, and Jay Pasachoff of Williams College. Surprisingly, the atmospheric pressure was estimated to be 0.3 pascal, even though Pluto was farther from the Sun than in 1988 and thus should have been colder and had a more rarefied atmosphere. One explanation for the discrepancy is that in 1987 the south pole of Pluto came out of shadow for the first time in 120 years, causing extra nitrogen to sublimate from the polar cap. It will take decades for the excess nitrogen to condense out of the atmosphere as it freezes onto the north pole's now continuously dark ice cap. Spikes in the data from the same study revealed what may be the first evidence of wind in Pluto's atmosphere. Another stellar occultation was observed by the MIT-Williams College team of James L. Elliot, Jay Pasachoff, and a Southwest Research Institute team led by Leslie A. Young on June 12, 2006, from sites in Australia.
In October 2006, Dale Cruikshank of NASA/Ames Research Center (a New Horizons co-investigator) and his colleagues announced the spectroscopic discovery of ethane on Pluto's surface. This ethane is produced from the photolysis or radiolysis (i.e. the chemical conversion driven by sunlight and charged particles) of frozen methane on Pluto's surface and suspended in its atmosphere.
Pluto has five known natural satellites: Charon, first identified in 1978 by astronomer James Christy; Nix and Hydra, both discovered in 2005, Kerberos, discovered in 2011, and Styx, discovered in 2012.
The Plutonian moons are unusually close to Pluto, compared to other observed systems. Moons could potentially orbit Pluto at up to 53% (or 69%, if retrograde) of the Hill radius, the stable gravitational zone of Pluto's influence. For example, Psamathe orbits Neptune at 40% of the Hill radius. In the case of Pluto, only the inner 3% of the zone is known to be occupied by satellites. In the discoverers' terms, the Plutonian system appears to be "highly compact and largely empty", although others have pointed out the possibility of additional objects, including a small ring system.
The Pluto–Charon system is noteworthy for being one of the Solar System's few binary systems, defined as those whose barycenter lies above the primary's surface (617 Patroclus is a smaller example, the Sun and Jupiter the only larger one). This and the large size of Charon relative to Pluto has led some astronomers to call it a dwarf double planet. The system is also unusual among planetary systems in that each is tidally locked to the other: Charon always presents the same face to Pluto, and Pluto always presents the same face to Charon: from any position on either body, the other is always at the same position in the sky, or always obscured. This also means that the rotation period of each is equal to the time it takes the entire system to rotate around its common center of gravity. Just as Pluto revolves on its side relative to the orbital plane, so the Pluto–Charon system does also. In 2007, observations by the Gemini Observatory of patches of ammonia hydrates and water crystals on the surface of Charon suggested the presence of active cryo-geysers.
Two additional moons were imaged by astronomers working with the Hubble Space Telescope on May 15, 2005, and received provisional designations of S/2005 P 1 and S/2005 P 2. The International Astronomical Union officially named Pluto's newest moons Nix (or Pluto II, the inner of the two moons, formerly P 2) and Hydra (Pluto III, the outer moon, formerly P 1), on June 21, 2006.
These small moons orbit Pluto at approximately two and three times the distance of Charon: Nix at 48,700 kilometres and Hydra at 64,800 kilometres from the barycenter of the system. They have nearly circular prograde orbits in the same orbital plane as Charon.
Observations of Nix and Hydra to determine individual characteristics are ongoing. Hydra is sometimes brighter than Nix, suggesting either that it is larger or that different parts of its surface may vary in brightness. Their sizes are estimated from albedos. If their albedo is similar to that of Charon (0.35), then their diameters are 46 kilometres for Nix and 61 kilometres for Hydra. Upper limits on their diameters can be estimated by using the albedo of the darkest Kuiper-belt objects (0.04); these bounds are 137 ± 11 km and 167 ± 10 km, respectively. At the larger end of this range, the inferred masses are less than 0.3% that of Charon, or 0.03% that of Pluto.
The discovery of Nix and Hydra suggests that Pluto may possess a variable ring system. Small-body impacts can create debris that can form into planetary rings. Data from a deep-optical survey by the Advanced Camera for Surveys on the Hubble Space Telescope suggest that no ring system is present. If such a system exists, it is either tenuous like the rings of Jupiter or is tightly confined to less than 1,000 km in width. Similar conclusions have been made from occultation studies.
A fourth moon, Kerberos, was announced on July 20, 2011. It was detected using NASA's Hubble Space Telescope during a survey searching for rings around Pluto. It has an estimated diameter of 13 to 34 km and is located between the orbits of Nix and Hydra. Kerberos was first seen in a photo taken with Hubble's Wide Field Camera 3 on June 28. It was confirmed in subsequent Hubble pictures taken on July 3 and July 18.
A fifth moon, Styx, was announced on July 7, 2012 while looking for potential hazards for New Horizons. Styx is believed to have a diameter of between 10 and 25 km and to orbit Pluto at a distance between Charon and Nix.
Styx, Nix, Kerberos and Hydra are fairly close to 3:1, 4:1, 5:1 and 6:1 mean-motion orbital resonances with Charon, respectively (the ratios approach integral commensurabilities more closely going outward from Pluto). Determining how near any of these orbital period ratios actually is to a true resonance requires accurate knowledge of the satellites' precessions.
|Orbital radius (km)
|Orbital period (d)||Period ratio||Magnitude (mag)|
|Styx||//||2012||10–25||?||~42,000 ± 2,000||20.2 ± 0.1||3.16||27|
Mass of Nix and Hydra assumes icy/porous density of 1.0 g/cm3
At least one minor body is trapped in the 1:1 commensurability with Pluto, (15810) 1994 JR1, specifically in the quasi-satellite dynamical state. The object has been a quasi-satellite of Pluto for about 100,000 years and it will remain in that dynamical state for perhaps another 250,000 years. Its quasi-satellite behavior is recurrent with a periodicity of 2 million years. There may be additional Pluto co-orbitals.
Pluto's origin and identity had long puzzled astronomers. One early hypothesis was that Pluto was an escaped moon of Neptune, knocked out of orbit by its largest current moon, Triton. This notion has been heavily criticized because Pluto never comes near Neptune in its orbit.
Pluto's true place in the Solar System began to reveal itself only in 1992, when astronomers began to find small icy objects beyond Neptune that were similar to Pluto not only in orbit but also in size and composition. This trans-Neptunian population is believed to be the source of many short-period comets. Astronomers now believe Pluto to be the largest[j] member of the Kuiper belt, a somewhat stable ring of objects located between 30 and 50 AU from the Sun. As of 2011, surveys of the Kuiper belt to magnitude 21 were nearly complete and any remaining Pluto-sized objects are expected to be beyond 100 AU from the Sun. Like other Kuiper-belt objects (KBOs), Pluto shares features with comets; for example, the solar wind is gradually blowing Pluto's surface into space, in the manner of a comet. If Pluto were placed as near to the Sun as Earth, it would develop a tail, as comets do.
Though Pluto is the largest of the Kuiper belt objects discovered,[j] Neptune's moon Triton, which is slightly larger than Pluto, is similar to it both geologically and atmospherically, and is believed to be a captured Kuiper belt object. Eris (see below) is about the same size as Pluto (though more massive) but is not strictly considered a member of the Kuiper belt population. Rather, it is considered a member of a linked population called the scattered disc.
Like other members of the Kuiper belt, Pluto is thought to be a residual planetesimal; a component of the original protoplanetary disc around the Sun that failed to fully coalesce into a full-fledged planet. Most astronomers agree that Pluto owes its current position to a sudden migration undergone by Neptune early in the Solar System's formation. As Neptune migrated outward, it approached the objects in the proto-Kuiper belt, setting one in orbit around itself (Triton), locking others into resonances, and knocking others into chaotic orbits. The objects in the scattered disc, a dynamically unstable region overlapping the Kuiper belt, are believed to have been placed in their current positions by interactions with Neptune's migrating resonances. A computer model created in 2004 by Alessandro Morbidelli of the Observatoire de la Côte d'Azur in Nice suggested that the migration of Neptune into the Kuiper belt may have been triggered by the formation of a 1:2 resonance between Jupiter and Saturn, which created a gravitational push that propelled both Uranus and Neptune into higher orbits and caused them to switch places, ultimately doubling Neptune's distance from the Sun. The resultant expulsion of objects from the proto-Kuiper belt could also explain the Late Heavy Bombardment 600 million years after the Solar System's formation and the origin of the Jupiter trojans. It is possible that Pluto had a near-circular orbit about 33 AU from the Sun before Neptune's migration perturbed it into a resonant capture. The Nice model requires that there were about a thousand Pluto-sized bodies in the original planetesimal disk; these may have included the early Triton and Eris.
Pluto presents significant challenges for spacecraft because of its small mass and large distance from Earth. Voyager 1 could have visited Pluto, but controllers opted instead for a close flyby of Saturn's moon Titan, resulting in a trajectory incompatible with a Pluto flyby. Voyager 2 never had a plausible trajectory for reaching Pluto. No serious attempt to explore Pluto by spacecraft occurred until the last decade of the 20th century. In August 1992, JPL scientist Robert Staehle telephoned Pluto's discoverer, Clyde Tombaugh, requesting permission to visit his planet. "I told him he was welcome to it," Tombaugh later remembered, "though he's got to go one long, cold trip." Despite this early momentum, in 2000, NASA cancelled the Pluto Kuiper Express mission, citing increasing costs and launch vehicle delays.
After an intense political battle, a revised mission to Pluto, dubbed New Horizons, was granted funding from the US government in 2003. New Horizons was launched successfully on January 19, 2006. The mission leader, S. Alan Stern, confirmed that some of the ashes of Clyde Tombaugh, who died in 1997, had been placed aboard the spacecraft.
In early 2007 the craft made use of a gravity assist from Jupiter. Its closest approach to Pluto will be on July 14, 2015; scientific observations of Pluto will begin 5 months before closest approach and will continue for at least a month after the encounter. New Horizons captured its first (distant) images of Pluto in late September 2006, during a test of the Long Range Reconnaissance Imager (LORRI). The images, taken from a distance of approximately 4.2 billion kilometres, confirm the spacecraft's ability to track distant targets, critical for maneuvering toward Pluto and other Kuiper Belt objects.
New Horizons will use a remote sensing package that includes imaging instruments and a radio science investigation tool, as well as spectroscopic and other experiments, to characterise the global geology and morphology of Pluto and its moon Charon, map their surface composition and analyse Pluto's neutral atmosphere and its escape rate. New Horizons will also photograph the surfaces of Pluto and Charon.
Pluto's small moons, discovered shortly before or after the probes's launch, may present it with unforeseen challenges. Debris from collisions between Kuiper belt objects and the smaller moons, with their relatively low escape velocities, may produce a tenuous dusty ring. Were New Horizons to fly through such a ring system, there would be an increased potential for micrometeoroid damage that could disable the probe.
A Pluto orbiter/lander/sample return mission was proposed in 2003. The plan included a twelve-year trip from Earth to Pluto, mapping from orbit, multiple landings, a warm water probe, and possible in situ propellant production for another twelve-year trip back to Earth with samples. Power and propulsion would come from the bimodal MITEE nuclear reactor system.
After Pluto's place within the Kuiper belt was determined, its official status as a planet became controversial, with many questioning whether Pluto should be considered together with or separately from its surrounding population.
Museum and planetarium directors occasionally created controversy by omitting Pluto from planetary models of the Solar System. The Hayden Planetarium reopened after renovation in 2000 with a model of only eight planets. The controversy made headlines at the time.
In 2002, the KBO 50000 Quaoar was discovered, with a diameter then thought to be roughly 1280 kilometres, about half that of Pluto. In 2004, the discoverers of 90377 Sedna placed an upper limit of 1800 km on its diameter, nearer to Pluto's diameter of 2320 km, although Sedna's diameter was revised downward to less than 1600 km by 2007. Just as Ceres, Pallas, Juno and Vesta eventually lost their planet status after the discovery of many other asteroids, so, it was argued, Pluto should be reclassified as one of the Kuiper belt objects.
On July 29, 2005, the discovery of a new trans-Neptunian object was announced. Named Eris, it is now known to be approximately the same size as Pluto. This was the largest object discovered in the Solar System since Triton in 1846. Its discoverers and the press initially called it the tenth planet, although there was no official consensus at the time on whether to call it a planet. Others in the astronomical community considered the discovery the strongest argument for reclassifying Pluto as a minor planet.
2006: IAU classification
The debate came to a head in 2006 with an IAU resolution that created an official definition for the term "planet". According to this resolution, there are three main conditions for an object to be considered a 'planet':
- The object must be in orbit around the Sun.
- The object must be massive enough to be a sphere by its own gravitational force. More specifically, its own gravity should pull it into a shape of hydrostatic equilibrium.
- It must have cleared the neighborhood around its orbit.
Pluto fails to meet the third condition, because its mass is only 0.07 times that of the mass of the other objects in its orbit (Earth's mass, by contrast, is 1.7 million times the remaining mass in its own orbit). The IAU further resolved that Pluto be classified in the simultaneously created dwarf planet category, and that it act as the prototype for the plutoid category of trans-Neptunian objects, in which it would be separately, but concurrently, classified.
On September 13, 2006, the IAU included Pluto, Eris, and the Eridian moon Dysnomia in their Minor Planet Catalogue, giving them the official minor planet designations "(134340) Pluto", "(136199) Eris", and "(136199) Eris I Dysnomia". If Pluto had been given a minor planet name upon its discovery, the number would have been about 1,164 rather than 134,340.
There has been some resistance within the astronomical community toward the reclassification. S. Alan Stern, principal investigator with NASA's New Horizons mission to Pluto, publicly derided the IAU resolution, stating that "the definition stinks, for technical reasons". Stern's contention was that by the terms of the new definition Earth, Mars, Jupiter, and Neptune, all of which share their orbits with asteroids, would be excluded. His other claim was that because less than five percent of astronomers voted for it, the decision was not representative of the entire astronomical community. Marc W. Buie, then at Lowell Observatory, voiced his opinion on the new definition on his website and petitioned against the definition. Others have supported the IAU. Mike Brown, the astronomer who discovered Eris, said "through this whole crazy circus-like procedure, somehow the right answer was stumbled on. It's been a long time coming. Science is self-correcting eventually, even when strong emotions are involved."
Researchers on both sides of the debate gathered on August 14–16, 2008, at the Johns Hopkins University Applied Physics Laboratory for a conference that included back-to-back talks on the current IAU definition of a planet. Entitled "The Great Planet Debate", the conference published a post-conference press release indicating that scientists could not come to a consensus about the definition of planet. Just before the conference, on June 11, 2008, the IAU announced in a press release that the term "plutoid" would henceforth be used to describe Pluto and other objects similar to Pluto which have an orbital semimajor axis greater than that of Neptune and enough mass to be of near-spherical shape.
Reception to the IAU decision was mixed. Although many accepted the reclassification, some sought to overturn the decision with online petitions urging the IAU to consider reinstatement. A resolution introduced by some members of the California State Assembly light-heartedly denounced the IAU for "scientific heresy", among other crimes. The U.S. state of New Mexico's House of Representatives passed a resolution in honor of Tombaugh, a longtime resident of that state, which declared that Pluto will always be considered a planet while in New Mexican skies and that March 13, 2007, was Pluto Planet Day. The Illinois State Senate passed a similar resolution in 2009, on the basis that Clyde Tombaugh, the discoverer of Pluto, was born in Illinois. The resolution asserted that Pluto was "unfairly downgraded to a 'dwarf' planet" by the IAU.
Some members of the public have also rejected the change, citing the disagreement within the scientific community on the issue, or for sentimental reasons, maintaining that they have always known Pluto as a planet and will continue to do so regardless of the IAU decision.
- How I Killed Pluto and Why It Had It Coming
- Pluto in astrology
- Pluto in fiction
- Solar eclipses on Pluto
- The HST observations were made in two wavelengths, which is insufficient to directly make a true-color image. The surface maps at each wavelength limit the shape of the spectrum that could be produced by the materials that are potentially on Pluto's surface. These spectra, generated for each resolved point on the surface, are then converted to the RGB color values seen here. See Buie et al, 2010.
- Orbital elements refer to the barycenter of the Pluto system, and are the instantaneous osculating values at the precise J2000 epoch. Barycenter quantities are given because, in contrast to the planetary center, they do not experience appreciable changes on a day-to-day basis from the motion of the moons. The orbital period of Pluto is listed as 248 years because most references use the more stable barycenter of the Solar System (Sun+Jupiter) to list the orbital period of the Pluto-Charon system. A J2000 heliocentric solution would give a value of 246 years.
- Surface area derived from the radius r: .
- Volume v derived from the radius r: .
- Surface gravity derived from the mass M, the gravitational constant G and the radius r: .
- Escape velocity derived from the mass M, the gravitational constant G and the radius r: .
- Based on the orientation of Charon's orbit, which is assumed the same as Pluto's spin axis due to the mutual tidal locking.
- Based on geometry of minimum and maximum distance from Earth and Pluto radius in the factsheet
- Astronomers do not expect to find an unknown object larger than Pluto closer than 100AU from the Sun. Of the 1547 TNOs known, of them have perihelion further out than Neptune (30.1AU).
- The dwarf planet Eris is roughly the same size as Pluto, about 2330 km, but 28% more massive. Eris is a scattered-disc object, often considered a distinct population from Kuiper-belt objects like Pluto; Pluto is the largest body in the Kuiper belt if the scattered objects are excluded.
- The equivalence is less close in languages whose phonology differs widely from Greek's, such as Somali Buluuto and Navajo Tłóotoo.
- The discovery of Charon in 1978 allowed astronomers to accurately calculate the mass of the Plutonian system. But it did not indicate the two bodies' individual masses, which could only be estimated, until the discovery of Pluto's outer moons in late 2005. As a result, because Pluto came to perihelion in 1989, most Pluto perihelion date estimates are based on the Pluto–Charon barycenter. Charon came to perihelion 1989-Sep-04. The Pluto–Charon barycenter came to perihelion 1989-Sep-05. Pluto came to perihelion 1989-Sep-08.
- Drawn from Hubble images, synthesized true color[a] and among the highest resolutions possible with current technology.
- "Horizon Online Ephemeris System for Pluto Barycenter". JPL Horizons On-Line Ephemeris System @ Solar System Dynamics Group. Retrieved 2011-01-16. (set Observer Location to @sun to place the observer at the center of the sun)
- Williams, David R. (September 7, 2006). "Pluto Fact Sheet". NASA. Retrieved 2007-03-24.
- Seligman, Courtney. "Rotation Period and Day Length". Retrieved 2009-08-13.
- Williams, James G.; Standish, E. Myles. "Keplerian Elements for Approximate Positions of the Major Planets". Retrieved 2011-01-12.
- "HORIZONS Web-Interface for Pluto Barycenter (Major Body=9)". JPL Horizons On-Line Ephemeris System. Retrieved 2012-10-11. Select "Ephemeris Type: Elements", "Target Body: Pluto Barycenter" and "Center: @Sun".
- Lellouch, Emmanuel; de Bergh, Catherine; Sicardy, Bruno et al. (13 March 2014). "Exploring the spatial, temporal, and vertical distribution of methane in Pluto's atmosphere". Icarus. arXiv:1403.3208. doi:10.1016/j.icarus.2014.03.027.
- Young, Eliot F.; Young, Leslie A.; Buie, Marc W. (2007). "Pluto's Radius". American Astronomical Society, DPS meeting No. 39, #62.05; Bulletin of the American Astronomical Society 39: 541. Bibcode:2007DPS....39.6205Y.
- Buie, Marc W.; Grundy, William M.; Young, Eliot F. et al. (2006). "Orbits and photometry of Pluto's satellites: Charon, S/2005 P1, and S/2005 P2". Astronomical Journal 132 (1): 290. arXiv:astro-ph/0512491. Bibcode:2006AJ....132..290B. doi:10.1086/504422.
- Seidelmann, P. Kenneth; Archinal, Brent A.; A'Hearn, Michael F. et al. (2007). "Report of the IAU/IAG Working Group on cartographic coordinates and rotational elements: 2006". Celestial Mechanics and Dynamical Astronomy 98 (3): 155–180. Bibcode:2007CeMDA..98..155S. doi:10.1007/s10569-007-9072-y.
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- Stern, S. Alan; Mitton, Jacqueline (2005). "Pluto and Charon: ice worlds on the ragged edge of the solar system". Weinheim:Wiley-VCH. Retrieved July 3, 2013.
- NASA: How fast does light travel from the Sun to each of the planets?
- Ridpath, Ian (December 1978). "Pluto—Planet or Imposter?". Astronomy: 6–11.
- "Astronomers Measure Mass of Largest Dwarf Planet". hubblesite. 2007. Retrieved 2007-11-03.
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- Pluto Profile at NASA's Solar System Exploration site
- NASA Pluto factsheet
- Website of the observatory that discovered Pluto
- Earth telescope image of Pluto system
- Keck infrared with AO of Pluto system
- Gray, Meghan (2009). "Pluto". Sixty Symbols. Brady Haran for the University of Nottingham. |
Researchers from the USC Viterbi School of Engineering say solid fuel particles may be safer for hazardous work environments on earth and burn more efficiently in the microgravity of space than gaseous fuels, which are more combustible and difficult to transport.
In the spring 2004 issue of NASA Space Research, Fokion Egolfopoulos and Charles Campbell of the USC Viterbi School’s department of aerospace and mechanical engineering reported that they have made significant progress toward understanding the complex chemical processes that take place when tiny particles of solid fuels burn.
The duo’s findings could lead to the design of safer and more efficient solid fuels for propulsion in space or for maintaining human outposts on the moon or Mars. Their research could also benefit fire-prevention practices.
“Understanding the thermal effects is a first step toward improving fuel economy in both space vehicles and those we use on Earth,” Egolfopoulos said.
“It’s also a good start towards preventing spontaneous combustion in dangerous work environments, like in lumber milling, in grain elevators or in mine galleries,” he said. “It’s a sort of walk-before-you-run kind of thing.”
Researchers conducted their experiments during each 23-second zero-g interval during the aircraft’s flight.
Funded by NASA, the researchers made detailed studies of solid fuel combustion, including the effects of gravity on the process. They measured the burning characteristics of various solid fuel particles on earth and in microgravity, using NASA’s KC-135 aircraft - known as the “Vomit Comet” - to simulate the weightlessness of space.
“It takes some getting used to, but after a while, you learn to conduct the experiment very precisely,” said Mustafa Gurhan Andac, a postdoctoral research associate from the USC Viterbi School’s combustion and fuels laboratory, who ran the experiments in the nearly weightless environment aboard the NASA aircraft.
“You only have about 23 seconds in zero-g, so you have to be sure to finish the experiment and record the data during those precious seconds of weightlessness.”
In their experiments, the team used two laminar, smooth-burning flames in an “opposed-jet” configuration to compare the consumption of solid fuel and gaseous fuel. The bottom burner slowly spews gas to carry solid fuel pellets to the flame, while the top burner issues particle-free gas to fuel the flame.
“Depending on the prevailing flow conditions and characteristics of the particles, some particles will ignite and burn completely, where others behave as half-inert and burn only partially,” Egolfopoulos said.
The researchers measured particle size, speed and distribution to determine the optimal conditions for efficient combustion.
Researchers are studying how gravity influences the combustion of solid fuels using this opposed jet flame configuration.
“In reduced gravity, a low-speed gas was more effective for complete fuel consumption,” Campbell said. “However, when we ignited the pellets in our laboratory at USC, in earth’s gravity, a much higher gas velocity was needed to carry the pellets to the flame. Increased speed caused some of the fuel pellets to burn incompletely.”
NASA is finding additional applications for the work as the space agency looks to longer spaceflight missions and human exploration of the moon and Mars. In trips to the moon or Mars, solid fuels derived from the lunar or Martian soil, or solid carbon, extracted from the Martian atmosphere, may fuel the astronauts ’ return flights to Earth.
The researchers will present their findings at the 30th International Symposium on Combustion, to be held July 25-30 in Chicago.
Explore further: Yellowstone's thermal springs—their colors unveiled |
GCSE foundation and higher maths students are now expected to find the nth term of a geometric sequence.
When I teach the nth term of geometric sequences I ask the class to work in pairs to categorise a range of sequences into two groups and present their solutions on mini-whiteboards. The students can decide what the categories are based on how they think the sequences are different.
I think it’s important for students to discover for themselves how a geometric sequence differs from an arithmetic sequence. Students are encouraged to use a calculator to aid their calculations. When you consider what is happening to the sequences on a term to term basis this is actually quite a simple concept and one that provokes quite a bit of class discussion.
Moving on to the development phase I introduce the common ratio by considering the term-to-term rule. For the sequence 2, 4, 8, 16, 32, 64 the common ratio is 2. This means the following term is double the previous term. We begin to generalise this on a term to term basis taking ‘a’ as the first term, a, 2a, 4a, 8a, 16a, 32a.
Now we need to find the formula for the coefficient of a. Rather than telling the class the formula I challenge them to derive it independently. The majority of the class know to raise 2 to a power. A common mistake is to raise 2 to the power of n. We discuss what this sequence would look like (2, 4, 8, 16, 32, 64) and after another minute or so most the students arrive at a × rn-1 where a is the first term of the sequence, r is the common ratio and n is the position number.
I find that once students have found the nth term for a geometric sequence they are much more likely to remember it and be able to apply it in the future.
As we work through the remaining questions the common ratio changes from an integer to a fraction. More able students are challenged to find the first term of a sequence when given two other non-consecutive terms.
In the plenary, the class are challenged to apply finding the nth term of a geometric sequence to compound percentage changes. I think it is really important students appreciate the practical, real life aspect of geometric sequences and compound interest links really nicely with this topic. I tend to allow about ten minutes for this question and have a student demonstrate the solution to their peers to feedback at the end.
Students should be able to represent the solutions to an inequality on a number line, using set notation or as a list of integer values. Here’s how I teach using the balance method for solving inequalities using a number line. Matching inequalities, Number sets and Number Lines At the start of the lesson students recap […]
In this blog I will share some practical tips for using mini-whiteboards in a mathematics lesson. I use mini-whiteboards nearly every lesson because they help the students show me the progress they are making. When I understand what the misconceptions are I am able to address them in subsequent examples as part of my feedback. […]
Demonstrating student progression during a mathematics lesson is about understanding the learning objective and breaking that down into explicit success criteria. Using Success Criteria Take, for example, a lesson on calculating the area of compound rectilinear shapes. The intended learning objective was written on the main whiteboard. Success criteria were used to break down the individual […] |
For years, astronomers have tried to place telescopes above atmosphere, to catch a glimpse of an otherwise hidden infrared universe. This section explores the heritage of infrared astronomy, which culminates with NASA's Spitzer Space Telescope, the most sensitive infrared space observatory ever launched. Learn about infrared astronomy's:
NASA's Spitzer Space Telescope is a technological marvel, featuring many innovations never before used on a space mission. It may seem like a contradiction, but Spitzer needs to be simultaneously "cold" and "warm" to function properly. Learn how Spitzer achieves this balance with the:
The Universe is continually radiating a wealth of information to Earth, sending signals in a wide-spectrum of light. However, not all of these messages reach the ground. In space, any object that has a temperature above zero Kelvin (- 459.67 degrees Fahrenheit, or -273.15 degrees Celsius) radiates in the infrared. Learn how NASA's infrared Spitzer Space Telescope contributes to the study of:
NASA's Spitzer Space Telescope has received the 2014 AIAA Space Science Award for its ongoing infrared studies of the hidden cosmos. The American Institute of Aeronautics and Astronautics, or AIAA, a society for the field of aerospace engineering, established the award in 1961 for "individuals demonstrating leadership of innovative scientific investigation associated with space science missions."
Ten years after a Delta II rocket launched NASA's Spitzer Space Telescope, lighting up the night sky over Cape Canaveral, Fla., the fourth of the agency's four Great Observatories continues to illuminate the dark side of the cosmos with its infrared eyes.
NASA is extending three missions affiliated with the Jet Propulsion Laboratory in Pasadena, Calif. -- Kepler, the Spitzer Space Telescope and the U.S. portion of the European Space Agency's Planck mission -- as a result of the 2012 Senior Review of Astrophysics Missions.
NASA's Spitzer Space Telescope has been awarded the prestigious 2011 Stellar Award by the Rotary National Award for Space Achievement Foundation, which recognizes missions whose accomplishments hold the greatest promise for furthering future activities in space.
NASA's Spitzer Space Telescope team has been selected to receive the 2010 Maria and Eric Muhlmann Award from the Astronomical Society of the Pacific.
On Friday, Oct. 23, engineers with NASA's Spitzer Space Telescope successfully swapped the spacecraft from the main nitrogen thruster string to a backup thruster string. |
By the end of this section, you will be able to:
- Explain the process of measurement
- Identify the three basic parts of a quantity
- Describe the properties and units of length, mass, volume, density, temperature, and time
- Perform basic unit calculations and conversions in the metric and other unit systems
Measurements provide much of the information that informs the hypotheses, theories, and laws describing the behavior of matter and energy in both the macroscopic and microscopic domains of chemistry. Every measurement provides three kinds of information: the size or magnitude of the measurement (a number); a standard of comparison for the measurement (a unit); and an indication of the uncertainty of the measurement. While the number and unit are explicitly represented when a quantity is written, the uncertainty is an aspect of the measurement result that is more implicitly represented and will be discussed later.
The number in the measurement can be represented in different ways, including decimal form and scientific notation. (Scientific notation is also known as exponential notation; a review of this topic can be found in Appendix B.) For example, the maximum takeoff weight of a Boeing 777-200ER airliner is 298,000 kilograms, which can also be written as 2.98 105 kg. The mass of the average mosquito is about 0.0000025 kilograms, which can be written as 2.5 10−6 kg.
Units, such as liters, pounds, and centimeters, are standards of comparison for measurements. A 2-liter bottle of a soft drink contains a volume of beverage that is twice that of the accepted volume of 1 liter. The meat used to prepare a 0.25-pound hamburger weighs one-fourth as much as the accepted weight of 1 pound. Without units, a number can be meaningless, confusing, or possibly life threatening. Suppose a doctor prescribes phenobarbital to control a patient’s seizures and states a dosage of “100” without specifying units. Not only will this be confusing to the medical professional giving the dose, but the consequences can be dire: 100 mg given three times per day can be effective as an anticonvulsant, but a single dose of 100 g is more than 10 times the lethal amount.
The measurement units for seven fundamental properties (“base units”) are listed in Table 1.2. The standards for these units are fixed by international agreement, and they are called the International System of Units or SI Units (from the French, Le Système International d’Unités). SI units have been used by the United States National Institute of Standards and Technology (NIST) since 1964. Units for other properties may be derived from these seven base units.
|Property Measured||Name of Unit||Symbol of Unit|
|amount of substance||mole||mol|
Everyday measurement units are often defined as fractions or multiples of other units. Milk is commonly packaged in containers of 1 gallon (4 quarts), 1 quart (0.25 gallon), and one pint (0.5 quart). This same approach is used with SI units, but these fractions or multiples are always powers of 10. Fractional or multiple SI units are named using a prefix and the name of the base unit. For example, a length of 1000 meters is also called a kilometer because the prefix kilo means “one thousand,” which in scientific notation is 103 (1 kilometer = 1000 m = 103 m). The prefixes used and the powers to which 10 are raised are listed in Table 1.3.
|femto||f||10−15||1 femtosecond (fs) = 1 10−15 s (0.000000000000001 s)|
|pico||p||10−12||1 picometer (pm) = 1 10−12 m (0.000000000001 m)|
|nano||n||10−9||4 nanograms (ng) = 4 10−9 g (0.000000004 g)|
|micro||µ||10−6||1 microliter (μL) = 1 10−6 L (0.000001 L)|
|milli||m||10−3||2 millimoles (mmol) = 2 10−3 mol (0.002 mol)|
|centi||c||10−2||7 centimeters (cm) = 7 10−2 m (0.07 m)|
|deci||d||10−1||1 deciliter (dL) = 1 10−1 L (0.1 L )|
|kilo||k||103||1 kilometer (km) = 1 103 m (1000 m)|
|mega||M||106||3 megahertz (MHz) = 3 106 Hz (3,000,000 Hz)|
|giga||G||109||8 gigayears (Gyr) = 8 109 yr (8,000,000,000 yr)|
|tera||T||1012||5 terawatts (TW) = 5 1012 W (5,000,000,000,000 W)|
Link to Learning
Need a refresher or more practice with scientific notation? Visit this site to go over the basics of scientific notation.
SI Base Units
The initial units of the metric system, which eventually evolved into the SI system, were established in France during the French Revolution. The original standards for the meter and the kilogram were adopted there in 1799 and eventually by other countries. This section introduces four of the SI base units commonly used in chemistry. Other SI units will be introduced in subsequent chapters.
The standard unit of length in both the SI and original metric systems is the meter (m). A meter was originally specified as 1/10,000,000 of the distance from the North Pole to the equator. It is now defined as the distance light in a vacuum travels in 1/299,792,458 of a second. A meter is about 3 inches longer than a yard (Figure 1.23); one meter is about 39.37 inches or 1.094 yards. Longer distances are often reported in kilometers (1 km = 1000 m = 103 m), whereas shorter distances can be reported in centimeters (1 cm = 0.01 m = 10−2 m) or millimeters (1 mm = 0.001 m = 10−3 m).
The standard unit of mass in the SI system is the kilogram (kg). The kilogram was previously defined by the International Union of Pure and Applied Chemistry (IUPAC) as the mass of a specific reference object. This object was originally one liter of pure water, and more recently it was a metal cylinder made from a platinum-iridium alloy with a height and diameter of 39 mm (Figure 1.24). In May 2019, this definition was changed to one that is based instead on precisely measured values of several fundamental physical constants.1. One kilogram is about 2.2 pounds. The gram (g) is exactly equal to 1/1000 of the mass of the kilogram (10−3 kg).
Temperature is an intensive property. The SI unit of temperature is the kelvin (K). The IUPAC convention is to use kelvin (all lowercase) for the word, K (uppercase) for the unit symbol, and neither the word “degree” nor the degree symbol (°). The degree Celsius (°C) is also allowed in the SI system, with both the word “degree” and the degree symbol used for Celsius measurements. Celsius degrees are the same magnitude as those of kelvin, but the two scales place their zeros in different places. Water freezes at 273.15 K (0 °C) and boils at 373.15 K (100 °C) by definition, and normal human body temperature is approximately 310 K (37 °C). The conversion between these two units and the Fahrenheit scale will be discussed later in this chapter.
The SI base unit of time is the second (s). Small and large time intervals can be expressed with the appropriate prefixes; for example, 3 microseconds = 0.000003 s = 3 10−6 and 5 megaseconds = 5,000,000 s = 5 106 s. Alternatively, hours, days, and years can be used.
Derived SI Units
We can derive many units from the seven SI base units. For example, we can use the base unit of length to define a unit of volume, and the base units of mass and length to define a unit of density.
Volume is the measure of the amount of space occupied by an object. The standard SI unit of volume is defined by the base unit of length (Figure 1.25). The standard volume is a cubic meter (m3), a cube with an edge length of exactly one meter. To dispense a cubic meter of water, we could build a cubic box with edge lengths of exactly one meter. This box would hold a cubic meter of water or any other substance.
A more commonly used unit of volume is derived from the decimeter (0.1 m, or 10 cm). A cube with edge lengths of exactly one decimeter contains a volume of one cubic decimeter (dm3). A liter (L) is the more common name for the cubic decimeter. One liter is about 1.06 quarts.
A cubic centimeter (cm3) is the volume of a cube with an edge length of exactly one centimeter. The abbreviation cc (for cubic centimeter) is often used by health professionals. A cubic centimeter is equivalent to a milliliter (mL) and is 1/1000 of a liter.
We use the mass and volume of a substance to determine its density. Thus, the units of density are defined by the base units of mass and length.
The density of a substance is the ratio of the mass of a sample of the substance to its volume. The SI unit for density is the kilogram per cubic meter (kg/m3). For many situations, however, this is an inconvenient unit, and we often use grams per cubic centimeter (g/cm3) for the densities of solids and liquids, and grams per liter (g/L) for gases. Although there are exceptions, most liquids and solids have densities that range from about 0.7 g/cm3 (the density of gasoline) to 19 g/cm3 (the density of gold). The density of air is about 1.2 g/L. Table 1.4 shows the densities of some common substances.
|Solids||Liquids||Gases (at 25 °C and 1 atm)|
|ice (at 0 °C) 0.92 g/cm3||water 1.0 g/cm3||dry air 1.20 g/L|
|oak (wood) 0.60–0.90 g/cm3||ethanol 0.79 g/cm3||oxygen 1.31 g/L|
|iron 7.9 g/cm3||acetone 0.79 g/cm3||nitrogen 1.14 g/L|
|copper 9.0 g/cm3||glycerin 1.26 g/cm3||carbon dioxide 1.80 g/L|
|lead 11.3 g/cm3||olive oil 0.92 g/cm3||helium 0.16 g/L|
|silver 10.5 g/cm3||gasoline 0.70–0.77 g/cm3||neon 0.83 g/L|
|gold 19.3 g/cm3||mercury 13.6 g/cm3||radon 9.1 g/L|
While there are many ways to determine the density of an object, perhaps the most straightforward method involves separately finding the mass and volume of the object, and then dividing the mass of the sample by its volume. In the following example, the object's mass is measured using a scale, but its volume is calculated geometrically from length measurements.
Calculation of DensityGold—in bricks, bars, and coins—has been a form of currency for centuries. In order to swindle people into paying for a brick of gold without actually investing in a brick of gold, people have considered filling the centers of hollow gold bricks with lead to fool buyers into thinking that the entire brick is gold. It does not work: Lead is a dense substance, but its density is not as great as that of gold, 19.3 g/cm3. What is the density of lead if a cube of lead has an edge length of 2.00 cm and a mass of 90.7 g?
SolutionThe density of a substance can be calculated by dividing its mass by its volume. The volume of a cube is calculated by cubing the edge length.
(We will discuss the reason for rounding to the first decimal place in the next section.)
Check Your Learning(a) To three decimal places, what is the volume of a cube (cm3) with an edge length of 0.843 cm?
(b) If the cube in part (a) is copper and has a mass of 5.34 g, what is the density of copper to two decimal places?
(a) 0.599 cm3; (b) 8.91 g/cm3
Link to Learning
To learn more about the relationship between mass, volume, and density, use this interactive simulator to explore the density of different materials.
Using Displacement of Water to Determine DensityThis exercise uses a simulation to illustrate an alternative approach to the determination of density that involves measuring the object’s volume via displacement of water. Use the simulator to determine the densities iron and wood.
SolutionClick the “turn fluid into water” button in the simulator to adjust the density of liquid in the beaker to 1.00 g/mL. Remove the red block from the beaker and note the volume of water is 25.5 mL. Select the iron sample by clicking “iron” in the table of materials at the bottom of the screen, place the iron block on the balance pan, and observe its mass is 31.48 g. Transfer the iron block to the beaker and notice that it sinks, displacing a volume of water equal to its own volume and causing the water level to rise to 29.5 mL. The volume of the iron block is therefore:
The density of the iron is then calculated to be:
Remove the iron block from the beaker, change the block material to wood, and then repeat the mass and volume measurements. Unlike iron, the wood block does not sink in the water but instead floats on the water’s surface. To measure its volume, drag it beneath the water’s surface so that it is fully submerged.
Note: The sink versus float behavior illustrated in this example demonstrates the property of “buoyancy” (see end of chapter Exercise 1.42 and Exercise 1.43).
Check Your LearningFollowing the water displacement approach, use the simulator to measure the density of the foam sample.
- 1For details see https://www.nist.gov/pml/weights-and-measures/si-units-mass |
Mensuration and Measurement
What is Mensuration?
Mensuration can be explained as an act of measurement. We live in a three-dimensional world. The concept of measurement plays an important role in primary as well as secondary school mathematics. Moreover, measurement has a direct connection to our everyday lives. When learning to measure objects we learn to do so for both 3D and 2D objects. Mensuration is the branch of mathematics which studies the measurement of the 2D and 3D figures on parameters like length, volume, shape, surface area etc.
Objects or quantities can be measured using both standard and nonstandard units of measurement. For example, a non-standard unit of measuring length would be handspans. You can even do an activity on it. Asking children to measure the length of objects using handspans. Let children notice that while measuring objects using non-standard units there will always be a scope of a discrepancy. Hence the need for standard units of measurement. To measure parameters like length, weight and capacity we now have units like kilometre, metre, kilogram, gram, litre, millilitre etc.
Topics closely related to mensuration and measurement
Given below are two images showing all the topics that are related to concepts of mensuration. As you can see the concepts connect to other higher-order concepts physics, product designing. To be proficient at these concepts it is important for children to be well versed with basics like operating on quantities, understanding lines and angles.
Given below are the topics that come under mensuration as a track. Click on the links below to understand these topics. You can also download Free Cuemath worksheets for practice.
- Measuring length
- Measuring Weight
- Measuring Capacity
- Surface Area
- Perimeter and Area of a Circle
How do Cuemath students learn Mensuration and Measurement?
Mensuration as a topic is introduced in pre-primary. Kids learn about which objects are long & short, heavy & light. They eventually learn to measure objects using non-standrd units of measurement. After they are comfortable and familiar with the concept of measurement they learn to measure objects using standard units of measurement. Eventually, they move on to converting the units and also operating on them.
Why is mensuration important?
Mensuration is an important topic with high applicability in real-life scenarios. Given below are some of the scenarios.
Measurement of agricultural fields, floor areas required for purchase/selling transactions.
Measurement of volumes required for packaging milk, liquids, solid edible food items.
Measurements of surface areas required for estimation of painting houses, buildings etc.
Volumes and heights are useful in knowing water levels and amounts in rivers or lakes.
Optimum cost packaging sachets for milk etc. like tetra packing.
Simple Ways to learn about mensuration and measurement
Using math manipulatives like solid shapes and nets. Solid shapes will help students understand faces, edges and vertices. Nets will help students visualise the structure of 3D shapes.
You can ask children to identify and show you some shapes that resemble the 3D shapes.
Questioning children in everyday life situations. For example, when you are travelling and you see a signboard which says 50kms to the destination how many metres would that be.
Create Charts for students to remember different rules of conversion.
FAQs on Mensuration
1. What is the difference between mensuration and geometry?
Mensuration refers to the calculation of various parameters of shapes like the perimeter, area, volume etc. whereas, geometry deals with the study of properties and relations of points and lines of various shapes.
2. Who introduced mensuration?
Archimedes is remembered as the greatest mathematician of ancient era. He contributed significantly in geometry regarding the area of plane figures and areas as well as volumes of curved surfaces. |
The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason it is the smallest addressable unit of memory in many computer architectures. To disambiguate arbitrarily sized bytes from the common 8-bit definition, network protocol documents such as the Internet Protocol (RFC 791) refer to an 8-bit byte as an octet. Those bits in an octet are usually counted with numbering from 0 to 7 or 7 to 0 depending on the bit endianness. The first bit is number 0, making the eighth bit number 7.
|Unit system||unit derived from bit|
|Unit of||digital information, data size|
|Symbol||B, o (when 8 bits)|
The size of the byte has historically been hardware-dependent and no definitive standards existed that mandated the size. Sizes from 1 to 48 bits have been used. The six-bit character code was an often-used implementation in early encoding systems, and computers using six-bit and nine-bit bytes were common in the 1960s. These systems often had memory words of 12, 18, 24, 30, 36, 48, or 60 bits, corresponding to 2, 3, 4, 5, 6, 8, or 10 six-bit bytes. In this era, bit groupings in the instruction stream were often referred to as syllables[a] or slab, before the term byte became common.
The modern de facto standard of eight bits, as documented in ISO/IEC 2382-1:1993, is a convenient power of two permitting the binary-encoded values 0 through 255 for one byte, as 2 to the power of 8 is 256. The international standard IEC 80000-13 codified this common meaning. Many types of applications use information representable in eight or fewer bits and processor designers commonly optimize for this usage. The popularity of major commercial computing architectures has aided in the ubiquitous acceptance of the 8-bit byte. Modern architectures typically use 32- or 64-bit words, built of four or eight bytes, respectively.
The unit symbol for the byte was designated as the upper-case letter B by the International Electrotechnical Commission (IEC) and Institute of Electrical and Electronics Engineers (IEEE). Internationally, the unit octet, symbol o, explicitly defines a sequence of eight bits, eliminating the potential ambiguity of the term "byte".
Etymology and history Edit
The term byte was coined by Werner Buchholz in June 1956,[b] during the early design phase for the IBM Stretch computer, which had addressing to the bit and variable field length (VFL) instructions with a byte size encoded in the instruction. It is a deliberate respelling of bite to avoid accidental mutation to bit.[c]
Another origin of byte for bit groups smaller than a computer's word size, and in particular groups of four bits, is on record by Louis G. Dooley, who claimed he coined the term while working with Jules Schwartz and Dick Beeler on an air defense system called SAGE at MIT Lincoln Laboratory in 1956 or 1957, which was jointly developed by Rand, MIT, and IBM. Later on, Schwartz's language JOVIAL actually used the term, but the author recalled vaguely that it was derived from AN/FSQ-31.
Early computers used a variety of four-bit binary-coded decimal (BCD) representations and the six-bit codes for printable graphic patterns common in the U.S. Army (FIELDATA) and Navy. These representations included alphanumeric characters and special graphical symbols. These sets were expanded in 1963 to seven bits of coding, called the American Standard Code for Information Interchange (ASCII) as the Federal Information Processing Standard, which replaced the incompatible teleprinter codes in use by different branches of the U.S. government and universities during the 1960s. ASCII included the distinction of upper- and lowercase alphabets and a set of control characters to facilitate the transmission of written language as well as printing device functions, such as page advance and line feed, and the physical or logical control of data flow over the transmission media. During the early 1960s, while also active in ASCII standardization, IBM simultaneously introduced in its product line of System/360 the eight-bit Extended Binary Coded Decimal Interchange Code (EBCDIC), an expansion of their six-bit binary-coded decimal (BCDIC) representations[d] used in earlier card punches. The prominence of the System/360 led to the ubiquitous adoption of the eight-bit storage size, while in detail the EBCDIC and ASCII encoding schemes are different.
In the early 1960s, AT&T introduced digital telephony on long-distance trunk lines. These used the eight-bit μ-law encoding. This large investment promised to reduce transmission costs for eight-bit data.
In Volume 1 of The Art of Computer Programming (first published in 1968), Donald Knuth uses byte in his hypothetical MIX computer to denote a unit which "contains an unspecified amount of information ... capable of holding at least 64 distinct values ... at most 100 distinct values. On a binary computer a byte must therefore be composed of six bits". He notes that "Since 1975 or so, the word byte has come to mean a sequence of precisely eight binary digits...When we speak of bytes in connection with MIX we shall confine ourselves to the former sense of the word, harking back to the days when bytes were not yet standardized."
The development of eight-bit microprocessors in the 1970s popularized this storage size. Microprocessors such as the Intel 8008, the direct predecessor of the 8080 and the 8086, used in early personal computers, could also perform a small number of operations on the four-bit pairs in a byte, such as the decimal-add-adjust (DAA) instruction. A four-bit quantity is often called a nibble, also nybble, which is conveniently represented by a single hexadecimal digit.
Historically, the term octad or octade was used to denote eight bits as well at least in Western Europe; however, this usage is no longer common. The exact origin of the term is unclear, but it can be found in British, Dutch, and German sources of the 1960s and 1970s, and throughout the documentation of Philips mainframe computers.
Unit symbol Edit
In the International System of Quantities (ISQ), B is the symbol of the bel, a unit of logarithmic power ratio named after Alexander Graham Bell, creating a conflict with the IEC specification. However, little danger of confusion exists, because the bel is a rarely used unit. It is used primarily in its decadic fraction, the decibel (dB), for signal strength and sound pressure level measurements, while a unit for one-tenth of a byte, the decibyte, and other fractions, are only used in derived units, such as transmission rates.
The lowercase letter o for octet is defined as the symbol for octet in IEC 80000-13 and is commonly used in languages such as French and Romanian, and is also combined with metric prefixes for multiples, for example ko and Mo.
Multiple-byte units Edit
|Orders of magnitude of data|
More than one system exists to define unit multiples based on the byte. Some systems are based on powers of 10, following the International System of Units (SI), which defines for example the prefix kilo as 1000 (103); other systems are based on powers of 2. Nomenclature for these systems has been the subject of confusion. Systems based on powers of 10 reliably use standard SI prefixes (kilo, mega, giga, ...) and their corresponding symbols (k, M, G, ...). Systems based on powers of 2, however, might use binary prefixes (kibi, mebi, gibi, ...) and their corresponding symbols (Ki, Mi, Gi, ...) or they might use the prefixes K, M, and G, creating ambiguity when the prefixes M or G are used.
While the numerical difference between the decimal and binary interpretations is relatively small for the kilobyte (about 2% smaller than the kibibyte), the systems deviate increasingly as units grow larger (the relative deviation grows by 2.4% for each three orders of magnitude). For example, a power-of-10-based yottabyte is about 17% smaller than power-of-2-based yobibyte.
Units based on powers of 10 Edit
Definition of prefixes using powers of 10—in which 1 kilobyte (symbol kB) is defined to equal 1,000 bytes—is recommended by the International Electrotechnical Commission (IEC). The IEC standard defines eight such multiples, up to 1 yottabyte (YB), equal to 10008 bytes. The additional prefixes ronna- for 10009 and quetta- for 100010 were adopted by the International Bureau of Weights and Measures (BIPM) in 2022.
This definition is most commonly used for data-rate units in computer networks, internal bus, hard drive and flash media transfer speeds, and for the capacities of most storage media, particularly hard drives, flash-based storage, and DVDs. Operating systems that use this definition include macOS, iOS, Ubuntu, and Debian. It is also consistent with the other uses of the SI prefixes in computing, such as CPU clock speeds or measures of performance.
Units based on powers of 2 Edit
A system of units based on powers of 2 in which 1 kibibyte (KiB) is equal to 1,024 (i.e., 210) bytes is defined by international standard IEC 80000-13 and is supported by national and international standards bodies (BIPM, IEC, NIST). The IEC standard defines eight such multiples, up to 1 yobibyte (YiB), equal to 10248 bytes. The natural binary counterparts to ronna- and quetta- were given in a consultation paper of the International Committee for Weights and Measures' Consultative Committee for Units (CCU) as robi- (Ri, 10249) and quebi- (Qi, 102410), but have not yet been adopted by the IEC and ISO.
An alternate system of nomenclature for the same units (referred to here as the customary convention), in which 1 kilobyte (KB) is equal to 1,024 bytes, 1 megabyte (MB) is equal to 10242 bytes and 1 gigabyte (GB) is equal to 10243 bytes is mentioned by a 1990s JEDEC standard. Only the first three multiples (up to GB) are mentioned by the JEDEC standard, which makes no mention of TB and larger. The customary convention is used by the Microsoft Windows operating system[better source needed] and random-access memory capacity, such as main memory and CPU cache size, and in marketing and billing by telecommunication companies, such as Vodafone, AT&T, Orange and Telstra.
Parochial units Edit
Various computer vendors have coined terms for data of various sizes, sometimes with different sizes for the same term even within a single vendor. These terms include double word, half word, long word, quad word, slab, superword and syllable. There are also informal terms. e.g., half byte and nybble for 4 bits, octal K for 10008.
History of the conflicting definitions Edit
Contemporary[e] computer memory has a binary architecture making a definition of memory units based on powers of 2 most practical. The use of the metric prefix kilo for binary multiples arose as a convenience, because 1,024 is approximately 1,000. This definition was popular in early decades of personal computing, with products like the Tandon 51⁄4-inch DD floppy format (holding 368,640 bytes) being advertised as "360 KB", following the 1,024-byte convention. It was not universal, however. The Shugart SA-400 51⁄4-inch floppy disk held 109,375 bytes unformatted, and was advertised as "110 Kbyte", using the 1000 convention. Likewise, the 8-inch DEC RX01 floppy (1975) held 256,256 bytes formatted, and was advertised as "256k". Other disks were advertised using a mixture of the two definitions: notably, 3+1⁄2-inch HD disks advertised as "1.44 MB" in fact have a capacity of 1,440 KiB, the equivalent of 1.47 MB or 1.41 MiB.
In 1995, the International Union of Pure and Applied Chemistry's (IUPAC) Interdivisional Committee on Nomenclature and Symbols attempted to resolve this ambiguity by proposing a set of binary prefixes for the powers of 1024, including kibi (kilobinary), mebi (megabinary), and gibi (gigabinary).
In December 1998, the IEC addressed such multiple usages and definitions by adopting the IUPAC's proposed prefixes (kibi, mebi, gibi, etc.) to unambiguously denote powers of 1024. Thus one kibibyte (1 KiB) is 10241 bytes = 1024 bytes, one mebibyte (1 MiB) is 10242 bytes = 1,048,576 bytes, and so on.
Modern standard definitions Edit
The IEC adopted the IUPAC proposal and published the standard in January 1999. The IEC prefixes are part of the International System of Quantities. The IEC further specified that the kilobyte should only be used to refer to 1,000 bytes.
Lawsuits over definition Edit
Lawsuits arising from alleged consumer confusion over the binary and decimal definitions of multiples of the byte have generally ended in favor of the manufacturers, with courts holding that the legal definition of gigabyte or GB is 1 GB = 1,000,000,000 (109) bytes (the decimal definition), rather than the binary definition (230). Specifically, the United States District Court for the Northern District of California held that "the U.S. Congress has deemed the decimal definition of gigabyte to be the 'preferred' one for the purposes of 'U.S. trade and commerce' [...] The California Legislature has likewise adopted the decimal system for all 'transactions in this state.'"
Earlier lawsuits had ended in settlement with no court ruling on the question, such as a lawsuit against drive manufacturer Western Digital. Western Digital settled the challenge and added explicit disclaimers to products that the usable capacity may differ from the advertised capacity. Seagate was sued on similar grounds and also settled.
Practical examples Edit
|bit||a Boolean variable indicating true (1) or false (0).|
|byte||a basic Latin character.|
|kilobyte||text of "Jabberwocky"|
|a typical favicon|
|megabyte||text of Harry Potter and the Goblet of Fire|
|gigabyte||about half an hour of video|
|CD-quality uncompressed audio of The Lamb Lies Down on Broadway|
|terabyte||the largest consumer hard drive in 2007|
|1080p 4:3 video of Avatar: The Last Airbender animated television series, all 61 episodes[f]|
|petabyte||2000 years of MP3-encoded music|
|exabyte||global monthly Internet traffic in 2004|
|zettabyte||global yearly Internet traffic in 2016|
Common uses Edit
The C and C++ programming languages define byte as an "addressable unit of data storage large enough to hold any member of the basic character set of the execution environment" (clause 3.6 of the C standard). The C standard requires that the integral data type unsigned char must hold at least 256 different values, and is represented by at least eight bits (clause 126.96.36.199.1). Various implementations of C and C++ reserve 8, 9, 16, 32, or 36 bits for the storage of a byte.[g] In addition, the C and C++ standards require that there are no gaps between two bytes. This means every bit in memory is part of a byte.
Java's primitive data type byte is defined as eight bits. It is a signed data type, holding values from −128 to 127.
In data transmission systems, the byte is used as a contiguous sequence of bits in a serial data stream, representing the smallest distinguished unit of data. A transmission unit might additionally include start bits, stop bits, and parity bits, and thus its size may vary from seven to twelve bits to contain a single seven-bit ASCII code.
See also Edit
- The term syllable was used for bytes containing instructions or constituents of instructions, not for data bytes.
- Many sources erroneously indicate a birthday of the term byte in July 1956, but Werner Buchholz claimed that the term would have been coined in June 1956. In fact, the earliest document supporting this dates from 1956-06-11. Buchholz stated that the transition to 8-bit bytes was conceived in August 1956, but the earliest document found using this notion dates from September 1956.
- Some later machines, e.g., Burroughs B1700, CDC 3600, DEC PDP-6, DEC PDP-10 had the ability to operate on arbitrary bytes no larger than the word size.
- There was more than one BCD code page.
- Through the 1970s there were machines with decimal architectures.
- Video is encoded at a bitrate of 27.8 Mbit/s, with a runtime of 1,403 min (84,180 seconds) resulting in an approximate size of 0.2925 TB (0.2661 TiB).
- The actual number of bits in a particular implementation is documented as
CHAR_BITas implemented in the file limits.h.
Blaauw, Gerrit Anne; Brooks, Jr., Frederick Phillips; Buchholz, Werner (1962), "Chapter 4: Natural Data Units" (PDF), in Buchholz, Werner (ed.), Planning a Computer System - Project Stretch, McGraw-Hill Book Company, Inc. / The Maple Press Company, York, PA., pp. 39–40, LCCN 61-10466, archived from the original (PDF) on 2017-04-03, retrieved 2017-04-03
Terms used here to describe the structure imposed by the machine design, in addition to bit, are listed below.
Byte denotes a group of bits used to encode a character, or the number of bits transmitted in parallel to and from input-output units. A term other than character is used here because a given character may be represented in different applications by more than one code, and different codes may use different numbers of bits (i.e., different byte sizes). In input-output transmission the grouping of bits may be completely arbitrary and have no relation to actual characters. (The term is coined from bite, but respelled to avoid accidental mutation to bit.)
A word consists of the number of data bits transmitted in parallel from or to memory in one memory cycle. Word size is thus defined as a structural property of the memory. (The term catena was coined for this purpose by the designers of the Bull GAMMA 60 computer.)
Block refers to the number of words transmitted to or from an input-output unit in response to a single input-output instruction. Block size is a structural property of an input-output unit; it may have been fixed by the design or left to be varied by the program.
- Bemer, Robert William (1959), "A proposal for a generalized card code of 256 characters", Communications of the ACM, 2 (9): 19–23, doi:10.1145/368424.368435, S2CID 36115735
- Postel, J. (September 1981). Internet Protocol DARPA INTERNET PROGRAM PROTOCOL SPECIFICATION. p. 43. doi:10.17487/RFC0791. RFC 791. Retrieved 28 August 2020.
octet An eight bit byte.
Buchholz, Werner (1956-06-11). "7. The Shift Matrix" (PDF). The Link System. IBM. pp. 5–6. Stretch Memo No. 39G. Archived from the original (PDF) on 2017-04-04. Retrieved 2016-04-04.
[…] Most important, from the point of view of editing, will be the ability to handle any characters or digits, from 1 to 6 bits long.
Figure 2 shows the Shift Matrix to be used to convert a 60-bit word, coming from Memory in parallel, into characters, or 'bytes' as we have called them, to be sent to the Adder serially. The 60 bits are dumped into magnetic cores on six different levels. Thus, if a 1 comes out of position 9, it appears in all six cores underneath. Pulsing any diagonal line will send the six bits stored along that line to the Adder. The Adder may accept all or only some of the bits.
Assume that it is desired to operate on 4 bit decimal digits, starting at the right. The 0-diagonal is pulsed first, sending out the six bits 0 to 5, of which the Adder accepts only the first four (0-3). Bits 4 and 5 are ignored. Next, the 4 diagonal is pulsed. This sends out bits 4 to 9, of which the last two are again ignored, and so on.
It is just as easy to use all six bits in alphanumeric work, or to handle bytes of only one bit for logical analysis, or to offset the bytes by any number of bits. All this can be done by pulling the appropriate shift diagonals. An analogous matrix arrangement is used to change from serial to parallel operation at the output of the adder. […]
3600 Computer System - Reference Manual (PDF). K. St. Paul, Minnesota, US: Control Data Corporation (CDC). 1966-10-11 . 60021300. Archived from the original (PDF) on 2017-04-05. Retrieved 2017-04-05.
Byte - A partition of a computer word.
NB. Discusses 12-bit, 24-bit and 48-bit bytes.
Rao, Thammavaram R. N.; Fujiwara, Eiji (1989). McCluskey, Edward J. (ed.). Error-Control Coding for Computer Systems. Prentice Hall Series in Computer Engineering (1 ed.). Englewood Cliffs, NJ, US: Prentice Hall. ISBN 0-13-283953-9. LCCN 88-17892.
NB. Example of the usage of a code for "4-bit bytes".
Tafel, Hans Jörg (1971). Einführung in die digitale Datenverarbeitung [Introduction to digital information processing] (in German). Munich: Carl Hanser Verlag. p. 300. ISBN 3-446-10569-7.
Byte = zusammengehörige Folge von i.a. neun Bits; davon sind acht Datenbits, das neunte ein Prüfbit
NB. Defines a byte as a group of typically 9 bits; 8 data bits plus 1 parity bit.
ISO/IEC 2382-1: 1993, Information technology - Vocabulary - Part 1: Fundamental terms. 1993.
A string that consists of a number of bits, treated as a unit, and usually representing a character or a part of a character.
1 The number of bits in a byte is fixed for a given data processing system.
2 The number of bits in a byte is usually 8.
- "Internet History of 1960s # 1964". Computer History Museum. 2017 . Archived from the original on 2022-06-24. Retrieved 2022-08-17.
- Jaffer, Aubrey (2011) . "Metric-Interchange-Format". Archived from the original on 2017-04-03. Retrieved 2017-04-03.
- Kozierok, Charles M. (2005-09-20) . "The TCP/IP Guide - Binary Information and Representation: Bits, Bytes, Nibbles, Octets and Characters - Byte versus Octet". 3.0. Archived from the original on 2017-04-03. Retrieved 2017-04-03.
ISO 2382-4, Organization of data (2 ed.).
byte, octet, 8-bit byte: A string that consists of eight bits.
Buchholz, Werner (February 1977). "The Word "Byte" Comes of Age..." Byte Magazine. 2 (2): 144.
We received the following from W Buchholz, one of the individuals who was working on IBM's Project Stretch in the mid 1950s. His letter tells the story.
Not being a regular reader of your magazine, I heard about the question in the November 1976 issue regarding the origin of the term "byte" from a colleague who knew that I had perpetrated this piece of jargon [see page 77 of November 1976 BYTE, "Olde Englishe"]. I searched my files and could not locate a birth certificate. But I am sure that "byte" is coming of age in 1977 with its 21st birthday.
Many have assumed that byte, meaning 8 bits, originated with the IBM System/360, which spread such bytes far and wide in the mid-1960s. The editor is correct in pointing out that the term goes back to the earlier Stretch computer (but incorrect in that Stretch was the first, not the last, of IBM's second-generation transistorized computers to be developed).
The first reference found in the files was contained in an internal memo written in June 1956 during the early days of developing Stretch. A byte was described as consisting of any number of parallel bits from one to six. Thus a byte was assumed to have a length appropriate for the occasion. Its first use was in the context of the input-output equipment of the 1950s, which handled six bits at a time. The possibility of going to 8-bit bytes was considered in August 1956 and incorporated in the design of Stretch shortly thereafter.
The first published reference to the term occurred in 1959 in a paper 'Processing Data in Bits and Pieces' by G A Blaauw, F P Brooks Jr and W Buchholz in the IRE Transactions on Electronic Computers, June 1959, page 121. The notions of that paper were elaborated in Chapter 4 of Planning a Computer System (Project Stretch), edited by W Buchholz, McGraw-Hill Book Company (1962). The rationale for coining the term was explained there on page 40 as follows:
Byte denotes a group of bits used to encode a character, or the number of bits transmitted in parallel to and from input-output units. A term other than character is used here because a given character may be represented in different applications by more than one code, and different codes may use different numbers of bits (ie, different byte sizes). In input-output transmission the grouping of bits may be completely arbitrary and have no relation to actual characters. (The term is coined from bite, but respelled to avoid accidental mutation to bit.)
System/360 took over many of the Stretch concepts, including the basic byte and word sizes, which are powers of 2. For economy, however, the byte size was fixed at the 8 bit maximum, and addressing at the bit level was replaced by byte addressing.
Since then the term byte has generally meant 8 bits, and it has thus passed into the general vocabulary.
Are there any other terms coined especially for the computer field which have found their way into general dictionaries of English language?
"Timeline of the IBM Stretch/Harvest era (1956-1961)". Computer History Museum. June 1956. Archived from the original on 2016-04-29. Retrieved 2017-04-03.
1956 Summer: Gerrit Blaauw, Fred Brooks, Werner Buchholz, John Cocke and Jim Pomerene join the Stretch team. Lloyd Hunter provides transistor leadership.
1956 July [sic]: In a report Werner Buchholz lists the advantages of a 64-bit word length for Stretch. It also supports NSA's requirement for 8-bit bytes. Werner's term "Byte" first popularized in this memo.
Buchholz, Werner (1956-07-31). "5. Input-Output" (PDF). Memory Word Length. IBM. p. 2. Stretch Memo No. 40. Archived from the original (PDF) on 2017-04-04. Retrieved 2016-04-04.
[…] 60 is a multiple of 1, 2, 3, 4, 5, and 6. Hence bytes of length from 1 to 6 bits can be packed efficiently into a 60-bit word without having to split a byte between one word and the next. If longer bytes were needed, 60 bits would, of course, no longer be ideal. With present applications, 1, 4, and 6 bits are the really important cases.
With 64-bit words, it would often be necessary to make some compromises, such as leaving 4 bits unused in a word when dealing with 6-bit bytes at the input and output. However, the LINK Computer can be equipped to edit out these gaps and to permit handling of bytes which are split between words. […]
Buchholz, Werner (1956-09-19). "2. Input-Output Byte Size" (PDF). Memory Word Length and Indexing. IBM. p. 1. Stretch Memo No. 45. Archived from the original (PDF) on 2017-04-04. Retrieved 2016-04-04.
[…] The maximum input-output byte size for serial operation will now be 8 bits, not counting any error detection and correction bits. Thus, the Exchange will operate on an 8-bit byte basis, and any input-output units with less than 8 bits per byte will leave the remaining bits blank. The resultant gaps can be edited out later by programming […]
- Raymond, Eric Steven (2017) . "byte definition". Archived from the original on 2017-04-03. Retrieved 2017-04-03.
Bemer, Robert William (2000-08-08). "Why is a byte 8 bits? Or is it?". Computer History Vignettes. Archived from the original on 2017-04-03. Retrieved 2017-04-03.
I came to work for IBM, and saw all the confusion caused by the 64-character limitation. Especially when we started to think about word processing, which would require both upper and lower case.
Add 26 lower case letters to 47 existing, and one got 73 -- 9 more than 6 bits could represent.
I even made a proposal (in view of STRETCH, the very first computer I know of with an 8-bit byte) that would extend the number of punch card character codes to 256 .
Some folks took it seriously. I thought of it as a spoof.
So some folks started thinking about 7-bit characters, but this was ridiculous. With IBM's STRETCH computer as background, handling 64-character words divisible into groups of 8 (I designed the character set for it, under the guidance of Dr. Werner Buchholz, the man who DID coin the term "byte" for an 8-bit grouping). It seemed reasonable to make a universal 8-bit character set, handling up to 256. In those days my mantra was "powers of 2 are magic". And so the group I headed developed and justified such a proposal .
That was a little too much progress when presented to the standards group that was to formalize ASCII, so they stopped short for the moment with a 7-bit set, or else an 8-bit set with the upper half left for future work.
The IBM 360 used 8-bit characters, although not ASCII directly. Thus Buchholz's "byte" caught on everywhere. I myself did not like the name for many reasons. The design had 8 bits moving around in parallel. But then came a new IBM part, with 9 bits for self-checking, both inside the CPU and in the tape drives. I exposed this 9-bit byte to the press in 1973. But long before that, when I headed software operations for Cie. Bull in France in 1965-66, I insisted that 'byte' be deprecated in favor of "octet".
You can notice that my preference then is now the preferred term.
It is justified by new communications methods that can carry 16, 32, 64, and even 128 bits in parallel. But some foolish people now refer to a "16-bit byte" because of this parallel transfer, which is visible in the UNICODE set. I'm not sure, but maybe this should be called a "hextet".
But you will notice that I am still correct. Powers of 2 are still magic!
- Blaauw, Gerrit Anne; Brooks, Jr., Frederick Phillips; Buchholz, Werner (June 1959). "Processing Data in Bits and Pieces". IRE Transactions on Electronic Computers: 121.
Dooley, Louis G. (February 1995). "Byte: The Word". BYTE. Ocala, FL, US. Archived from the original on 1996-12-20.
The word byte was coined around 1956 to 1957 at MIT Lincoln Laboratories within a project called SAGE (the North American Air Defense System), which was jointly developed by Rand, Lincoln Labs, and IBM. In that era, computer memory structure was already defined in terms of word size. A word consisted of x number of bits; a bit represented a binary notational position in a word. Operations typically operated on all the bits in the full word.
We coined the word byte to refer to a logical set of bits less than a full word size. At that time, it was not defined specifically as x bits but typically referred to as a set of 4 bits, as that was the size of most of our coded data items. Shortly afterward, I went on to other responsibilities that removed me from SAGE. After having spent many years in Asia, I returned to the U.S. and was bemused to find out that the word byte was being used in the new microcomputer technology to refer to the basic addressable memory unit.
- Ram, Stefan (17 January 2003). "Erklärung des Wortes "Byte" im Rahmen der Lehre binärer Codes" (in German). Berlin, Germany: Freie Universität Berlin. Archived from the original on 2021-06-10. Retrieved 2017-04-10.
Origin of the term "byte", 1956, archived from the original on 2017-04-10, retrieved 2022-08-17
A question-and-answer session at an ACM conference on the history of programming languages included this exchange:
[ John Goodenough:
You mentioned that the term "byte" is used in JOVIAL. Where did the term come from? ]
[ Jules Schwartz (inventor of JOVIAL):
As I recall, the AN/FSQ-31, a totally different computer than the 709, was byte oriented. I don't recall for sure, but I'm reasonably certain the description of that computer included the word "byte," and we used it. ]
[ Fred Brooks:
May I speak to that? Werner Buchholz coined the word as part of the definition of STRETCH, and the AN/FSQ-31 picked it up from STRETCH, but Werner is very definitely the author of that word. ]
That's right. Thank you. ]
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|*| About bits and bytes: prefixes for binary multiples - IEC
|*| v0: https://web.archive.org/web/20090818042050/http://www.iec.ch/online_news/etech/arch_2003/etech_0503/focus.htm
|*| v1: https://www.iec.ch/prefixes-binary-multiples Archived 2021-08-16 at the Wayback Machine ]
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Further reading Edit
- "2.5 Byte manipulation" (PDF). Programming with the PDP-10 Instruction Set (PDF). PDP-10 System Reference Manual. Vol. 1. Digital Equipment Corporation (DEC). August 1969. pp. 2-15–2-17. Archived (PDF) from the original on 2017-04-05. Retrieved 2017-04-05.
- Ashley Taylor. "Bits and Bytes." Stanford. https://web.stanford.edu/class/cs101/bits-bytes.html |
SL Helicopter Flying Handbook/Aerodynamics
SECTION 2. Aerodynamics
- 1 The Four Forces of Flight
- 2 Lift
- 3 Drag
- 4 The Rotor Disk
- 5 Hovering Flight
- 6 Forward Flight
- 7 Autorotation
1 The Four Forces of Flight
All aircraft are governed by the four force of flight (Figure 1): lift, weight, drag and thrust. When the opposing forces balance each other (lift against weight and thrust against drag) the aircraft will continue with in the same direction and velocity without acceleration. When two opposing forces are different, the aircraft will accelerate until it reaches equilibrium. It is the job of the pilot to control these forces in a way that results in a desired outcome.
Here is a closer look at the four forces in a helicopter:
- Weight - Weight is the force of gravity acting downward. Weight directly opposes lift and is constantly changing during flight as fuel is burned.
- Lift - Lift is produced by the main rotor system(s) and directly opposes weight. Lift is affected by multiple factors including the angle of attack of the rotor blades, the density of the air, the speed of air over the airfoil, etc.
- Thrust - Thrust is the horizontal force, usually in the forward direction, but for a helicopter, can be potentially in any direction. Thrust is controlled by angling the rotor disk so that a portion of the total thrust of the rotors is in a horizontal direction. Thrust directly opposes drag.
- Drag - Drag is the force that is produced by an object moving through the air. Drag is a result of air pushing against the body and all parts of the aircraft. Drag directly opposes thrust.
Every object in the atmosphere is surrounded by a has that exerts a static force of 2,116 pounds per square foot at sea level. When a rotor blade is not moving, that force is exerted equally over the entire blade surface, and thus no useful lift is produced. In a helicopter, this is done by forcing air over the blades through their rotation around a mast.
Figure 2 shows how lift is produced by an airfoil as it moves through the air. Lets take a look at some of the elements in the production of lift:
- Relative Wind – Direction of movement of the air relative to the airflow. Usually opposite to the direction of movement.
- Wing Chord Line – The Line from the leading edge to the training edge of the wing.
- Angle of Attack (AOA) – The angle between the relative wind and the wing chord line. In a helicopter, raising the collective generally increases the AOA of the rotor blades.
- Resultant Force – The force acting on the airfoil as it moves through the air.
- Lift – The vertical component of the resultant force. Increases as AOA or the airspeed increases.
- Induced Drag – The horizontal component of the resultant force. Increases as AOA or the airspeed increases. A byproduct of lift that must be overcome by thrust in level flight. In a helicopter, induced drag is what results in the increased engine power required to maintain RPM as the AOA is increased.
More specifically, the lift produced by an airfoil (e.g., a rotor blade) is governed by the Lift Equation:
L = CL(1/2)ρv2S
The components of this equation are:
- L - Total lift produced by the airfoil
- CL - The coefficient of lift
- ρ - The density of the air
- v - The speed of air over the airfoil
- S - The surface area of the airfoil
The coefficient of lift is generally a function of the profile (edge view) of the airfoil, and the angle of attack. CL typically increases linearly with angle of attack up to a specific critical angle of attack. Once the critical angle of attack is exceeded, the coefficient of lift decreased rapidly as the airfoil enters aerodynamic stall.
Drag is the force that resists the helicopter and/or rotor blades as the move through the air. Drag must be overcome by the engine to turn the rotor. Drag always acts parallel to the relative wind and total drag is comprised of three types of drag: profile, induced and parasite.
3.1 Profile Drag
Profile drag is a mix of skin friction and form drag that results from turbulent airflow that is created as a structure moves through the air. Profile drag is a function of the smoothness of a surface, and the size/shape of the structure that protrudes into the relative wind. It is generally weakly correlated with airspeed.
3.2 Induced Drag
Induced drag is generated by airflow circulation around the rotor blade as it creates lift. When an airfoil creates lift, some of the air is forced downward meaning that the relative wind is angled slightly above the horizontal plane. This results in a force that tends to slow the blades that increases as the angle of attack increases (i.e., with increased collective). Induced drag is the main reason that more engine power is required as collective is increased.
3.3 Parasite Drag
Parasite drag is the drag produced by all the non-lifting surfaces as the helicopter moves through the air (i.e., cabin, rotor mast, tail, landing gear). Parasite drag generally increases as the square of the the airspeed, thus doubling airspeed results in a 4x increase in drag. This means that a 4x increase in thrust is required to achieve a 2x increase in speed.
3.4 Total Drag
Total drag is the total of profile, induced and parasite drag (see Figure 3). Since induced drag decreases with airspeed, while parasite drag increases, there is generally an airspeed at which the lift-to-drag ratio is minimized. This point is referred to as L/DMAX and typically defines the best climb airspeed of the aircraft. In the example shown here L/DMAX is approximately 50 knots meaning 50 knots would be the best climb speed.
4 The Rotor Disk
4.1 Relative Wind
There are two parts to the relative wind as it passes through the rotor system:
- Horizontal part - caused by the blade moving through the rotor plane consisting of the speed of the rotating blade plus the forward airspeed.
- Vertical part - caused by air being moved down through the rotor system, plus any vertical movement of the helicopter. The vertical component is generally larger at slow airspeed.
4.2 Induced Flow
As the pitch of the rotor blades increase, more air is forced down through the rotor system. This induces an downward flow of air which when combined with the horizontal motion of the blade through the air results in a relative wind that is angled downward relative to the path of the blade. This results in a decreased angle of attack, and this less lift. Induced flow is greatest during hover in no-wind conditions.
4.2.1 Ground Effect
Proximity to the ground (land, water, or over a prim) interrupts the downward movement of air, thus reducing the effect induced flow. The effect increased the closer your are to the surface, and diminishes as you increase height over the surface. Ground effect decreases the power needed to hover.
4.2.2 In Ground Effect (IGE) Hover
Hovering near a surface is referred to as an IGE (In Ground Effect) hover. Ground effect permits the relative wind over the rotor blades to be more horizontal thus increasing their efficiency. Ground effect is increased when hovering over smooth surfaces, and decreased over grasses and other rough surfaces.
4.2.3 Out of Ground Effect (OGE) Hover
When hovering outside the range of ground effect (generally above a rotor diameter), the helicopter is said to be in an Out of Ground Effect (OGE) hover. Since you lose the benefits of ground effect in an OGE hover, it requires more power to maintain altitude. At high density altitudes, or in helicopters with less power, it may not be possible to maintain an OGE hover in some cases. Performing an OGE hover also presents the risk of entering vortex ring state if the helicopter is allowed to descend at too great a speed. See #VORTEX RING STATE for more information on vortex ring state.
5 Hovering Flight
Hovering is the most challenging part of flying a helicopter. This is due to the fact that the helicopter is inherently unstable and constant control inputs are needed to maintain a hover. Furthermore, all of these control movements interact with each other such that moving any one control usually requires moving another control as well. That said, the basic principle is relatively simple. The cyclic is used to eliminate horizontal drift, the pedals are used to maintain directional control, and the collective is used to maintain a constant height above the ground.
5.1 Translating Tendency
The primary purpose of tail rotor is to counteract torque from the main rotors. However, a side effect of this is a slight sideward force that would push the helicopter to the right if left uncorrected. This is referred to as "translating tendency" and is illustrated in Figure 4. The counter-clockwise rotating main rotor induces a torque trying to turn the helicopter to the right. The tail rotor pushes air through it to the left, thus creating a thrust to the right. Since this thrust is away from the center of gravity, this causes a counter-clockwise torque (balancing against the torque from the main rotor), and a horizontal component that acts to push the helicopter to the right.
To compensate for translating tendency, the controls on the helicopter are often rigged so that there is a slight left tilt of the main rotor when the cyclic controls are centered. This left force from the main rotor balances the right force from the tail rotor. A side effect of this is that the left skid will hang slightly lower then the right one in a hover.
5.2 Pendular Action
Since the helicopter is suspended from a single point well above the center of mass, it can have a tendency to rock like a pendulum. This is called pendular action and can be exaggerated by poor control technique. When a pilot begins overcontrolling, the pendular action can rapidly increase causing the helicopter to rapidly depart controlled flight. For this reason, it is important for the pilot to use small and smooth control inputs when flying a helicopter.
5.3 Gyroscopic Precession
The spinning blades of a helicopter act like a gyroscope. One of the properties of gyroscopes is gyroscopic precession. Gyroscopic precession causes a spinning object to act 90 degrees in the direction of rotation from where a force is applied. For this reason, the controls on a helicopter are rigged such that the greatest blade pitch occurs 90 degrees before the highest point of the rotor disk.
As an example, consider a helicopter with counter-clockwise rotating blades. Pushing forward on the cyclic will cause the highest blade pitch to occur at the 9 oclock position on the left side of the helicopter. Gyroscopic precession will cause the back of the rotor disk at the 6 oclock position to tilt up, this vectoring some of the thrust in the forward direction.
In single main rotor helicopters, torque is produced by the main rotor whenever the helicopter is under power. In most aircraft, the main rotor turns counter-clockwise when viewed from above, resulting in the body of the helicopter having a tenancy to turn clockwise (to the right) the more power you use. As a result, the pilot must apply right pedal to compensate. This is particularly evident when pulling collective to lift into a hover which requires the most amount of power. Conversely, right pedal must be applied when reducing power/collective. A few aircraft (e.g., Russian and French) have main rotors that turn clockwise when viewed from above. In these aircraft, the effect is reversed and left pedal is needed to compensate as collective is increased.
In aircraft with tandem rotors such as the Chinook, or in aircraft with coaxial rotors such as the Hiller UH-4, the rotors are counter-rotating and thus torque is canceled.
6 Forward Flight
In straight-and-level, unaccelerated forward flight, lift equals weight and thrust equals drag. If lift drops below weight, the helicopter will descend until the forces are in balance again. The same will occur if lift increases above weight. Similarly if thrust increases above drag, forward airspeed will increase thus increasing drag until it exactly balances the new higher thrust.
Figure 5 shows the four forces of a helicopter in forward level flight at constant speed. When the rotor disk tilts forward, the total main rotor thrust (shown by the blue line) is angled forward perpendicular to the rotor disk. In this state, the main rotor thrust can be decomposed into a vertical (green) and a horizontal (red) component. Since we are in level unaccelerated flight, we know that the vertical component (i.e., lift) must equal weight, and the horizontal component (thrust) must equal drag.
As the rotor disk tilts forward more, the horizontal component increases resulting in higher forward airspeed. But since the lift must equal weight in order to maintain altitude, it is necessary to increase the main/rotor thrust as this happens. This is normally done with increased collective and is why more collective is required as forward speed is increased.
6.1 Airflow in Forward Flight
In forward flight, the forward speed of the aircraft combines with the rotor tip speed to determine the speed of the relative air seen around the rotor disk. For example, consider the situation shown in Figure 6. In this example, the airspeed at the rotor tip in a hover is 300 knots, and the aircraft is moving forward at 100 knots. Since the aircraft is moving forward at 100 knots, there is a 100 knot relative wind from the opposite direction. Assuming a helicopter with counter-clockwise rotating blades, the blade on the right side at point A (called the "advancing blade") is moving forward into the relative wind, so the net relative wind it see will be the 300 from its rotation, plus the 100 from the oncoming air from forward motion. This results in a 400 knot relative wind at the blade tip at point A. On the left side of the rotor disk at point B (called the "retreating blade"), the blade is moving backwards. The relative wind seen by the blade at point B will be the 300 knots from the blade rotation, minus the 100 knots for the forward speed. This means the relative wind at point B will be 200 knots.
6.1.1 Dissymmetry of Lift
Dissymmetry of Lift is the apparent unequal lift on the two sides of the rotor disk in forward flight due to the unequal airflow over each half of the disk. Referring back to the example in Figure 6, we see that the advancing blade sees a relative wind of 400 knots, while the retreating blade sees a relative wind of 200 knots. Recall from Section 2.2 - Lift, that lift is proportional to the square of the relative wind. Since the relative wind on the advancing blade is double that on the retreating blade, that would suggest the lift on the right side of the rotor disk should be 4 times that on the left side. If this were true, the helicopter would roll violently to the left as forward speed were increases. Since this does not happen, there must be some other mechanism at play.
What is actually happening, is blade flapping. A hinge at the rotor hub, called the flapping hinge, allows each blade to move up and down. Blades will flap up on the advancing side, and down on the retreating side. The upward motion of the blade on the advancing side causes the angle of attack on that side to decrease, thus reducing the lift. Similarly, the downward motion on the retreating side increase the angle of attack, this increasing the lift on that side. The flapping of the blades allow the forces to balance exactly, equalizing the lift around the rotor disk. This normally happens automatically without any input from the pilot.
6.1.2 Retreating Blade Stall
As the speed of the helicopter increases more, the relative wind over the retreating blade becomes smaller and smaller. At some point, there will not be enough airflow over the retreating blade to maintain lift, and the blade will stall. This is called retreating blade stall. When the aircraft enters retreating blade stall, it will begin to lose lift and roll, sometimes violently, to the left. The pilot must react quickly with aft cyclic to reduce the airspeed and stop the stall. Retreating blade stall is what generally determines the never exceed speed (Vne) in helicopters and is usually marked with a red line on the airspeed indicator. The pilot should not that the red line represents Vne at sea level. The never exceed speed generally decreases with altitude.
6.2 Translational Lift
When a helicopter is in a hover or at a low speed, airflow through the disk is at a right angle to the rotor plane, and the rotors must provide all induced airflow through the rotors. Additionally, some of the flow recirculates through the rotor system as show in Figure 7. As a helicopter accelerates, it moves out of this downward moving/recirculating air and experiences a significant increase in performance.
6.2.1 Effective Translational Lift (ETL)
At approximately 15-20 knots, the helicopter completely overtakes the recirculating air and moves into clean air (Figure 8). This is referred to as Effective Translational Lift (ETL). As a helicopter passes through ETL, it requires significantly less power to maintain altitude, and more power is available for climbs. This is also the reason that less power is required in cruise flight than for hovering. It is also part of the reason that a normal takeoff involves a short ground run to accelerate past ETL before climbing out.
In autorotation, the blades of the helicopter are kept turning by airflow moving up through the rotor system, rather than by engine power. Autorotation allows a helicopter to land safely in the event of an engine failure. A freewheeling unit, or sprag clutch, allows the main rotor blades to continue turning without power from the engine. This is similar to the way a bicycle can coast without constantly turning the pedals.
Aerodynamically, the rotor disk can be divided into three regions during an autorotation as shown in ???. The three regions are:
- Driving Region – Airflow accelerates rotors and greatest lift produced.
- Driven Region – Drag works to slow rotors. Some lift produced here.
- Stall Region – Blade is stalled with no lift and only drag produced.
An autorotation is normally entered by fully lowering the collective. In the event of an engine failure, the pilot must be ready to react by quickly lowering the collective before the rotor RPM decays too much. If the reaction is too late and the RPM is allowed to decay, it may not be possible to recover.
Most autorotations are performed with forward speed. The pilot maintains this forward speed, typically around 60 knots, then conducts a flare just before touchdown, followed by lifting the collective to cushion the landing. |
Presentation on theme: "1 Algorithms Algorithm A set of unambiguous instructions for solving a problem or subproblem in a finite amount of time using a finite amount of data Why."— Presentation transcript:
1 Algorithms Algorithm A set of unambiguous instructions for solving a problem or subproblem in a finite amount of time using a finite amount of data Why must instructions be unambiguous? Why must time and data be finite?
2 Following an Algorithm Figure 6.4 A recipe for Hollandaise sauce
3 Following an Algorithm Algorithm for preparing a Hollandaise sauce If concerned about cholesterol Put butter substitute in a pot Else Put butter in a pot Turn on burner Put pot on the burner While (NOT bubbling) Leave pot on the burner Put other ingredients in the blender Turn on blender While (more in pot) Pour contents into blender in slow stream Turn off blender
4 Pseudocode A mixture of English and formatting to make the steps in an algorithm explicit Algorithm to Convert base-10 number to other bases While ( the quotient is not zero ) Divide the decimal number by the new base Make the remainder the next digit to the left in the answer Replace the original decimal number with the quotient
5 Pseudocode A way of expressing algorithms that uses a mixture of English phrases and indention to make the steps in the solution explicit There are no grammar rules in pseudocode Pseudocode is not case sensitive
6 Pseudocode Functionality Variables Names of places to store values quotient, decimalNumber, newBase Assignment Storing the value of an expression into a variable Set quotient to 64 quotient <-- 64 quotient = 64
7 Pseudocode Functionality Output Printing a value on an output device Write, Print Input Getting values from the outside word and storing them into variables Get, Read
8 Pseudocode Functionality Repetition Repeating a series of statements Set count to 1 While ( count < 10) Write "Enter an integer number" Read aNumber Write "You entered " + aNumber Set count to count + 1 How many values were read?
9 Pseudocode Functionality Selection Making a choice to execute or skip a statement (or group of statements) Read number If (number < 0) Write number + " is less than zero." or Write "Enter a positive number." Read number If (number < 0) Write number + " is less than zero." Write "You didn't follow instructions."
10 Pseudocode Functionality Selection Choose to execute one statement (or group of statements) or another statement (or group of statements) If ( age < 12 ) Write "Pay children's rate" Write "You get a free box of popcorn" else If ( age < 65 ) Write "Pay regular rate" else Write "Pay senior citizens rate"
11 Pseudocode Example Write "How many pairs of values are to be entered?" Read numberOfPairs Set numberRead to 0 While (numberRead < numberOfPairs) Write "Enter two values separated by a blank; press return" Read number1 Read number2 If (number1 < number2) Print number1, " ”, number2 Else Print number2, " ”, number1 Increment numberRead
12 Walk Through DataFill in values during each iteration 3numberReadnumber1number2 55 70 2 1 33 numberOfPairs What is the output? |
A vector is a ray with both magnitude (size) and direction. A vector is different from a scalar in that a scalar has only magnitude. For example, speed is a scalar quantity, but velocity is a vector, because it gives both speed and direction. Vectors are used to show directed quantities, and can be thought of as the motion necessary to get from one point to another. Vectors are typically written as a, or.In two-dimensional Cartesian space, a vector has the form . A unit vector is a vector with a magnitude of 1, and is written as . Any vector can be made into a unit vector in the form , where represents the vector's magnitude.
Vectors are numbers that have both magnitude and direction. A car has a velocity of 30 m/s in the south direction is a vector. There is a magnitude describing the value and a direction describing the motion. Vectors are used to describe 2 and 3-dimensional motion.
A Vector is a geometric object that has both magnitude and direction. A Scalar on the other hand just has magnitude.
Vectors are a wonderful tool in Vectors and Maths. They have a few different
A vector has both a magnitude (which is usually shown through the length of the vector) and a direction (where it's pointing). Velocity, for example, is a vector. Velocity, unlike speed, has a magnitude and a direction.
The direction of a Vector can be broken up into components across your axis
in both 2-dimensional and 3-dimensional space.
For instance, if a velocity vector is in 2-dimension and pointing entirely horizontal in the positive direction, it's x component would be its magnitude, and its y component would be 0. If it was at some angle between 0 and 90 degrees, it would have a positive component of both x and y that
speed is a scalar: I am driving at 10 miles per hour. You know you are moving at a speed but you do not know which direction you are moving.
velocity is a vector: for example, I am driving at 10 miles per hour in the north-west direction. This is an example of a vector as we know how fast we are going and in which direction we are going.
the modulus of a vector, gives you a scalar which has the same magnitude as the vector.
Also, a 2d dimensional vector(x i + y j ) means that the vector as a magnitude x in the 'i' direction and a magnitude 'y' in the j direction. The total or scalar magnitude of the vector is given as √(x2 + y2).
Mathematical objects that have both the magnitude and direction are termed as “Vectors”, which is represented like an arrow. The algebraic representation of vectors is nothing but to perform easy computations. These calculations include addition and scalar multiplication of vectors. For any vectors
2. Associative property of addition:
3. Distributive property over vector addition:
, where α ∈ R
, where α , β ∈ R
, where α , β ∈ R
Write a vector equation for A for each arrangement of vectors. For example, if adding B and c gives A then write A -B+ C. Each answer you give should start with A- 2. C) A A b) e) d)"
A = 1.01 i + 4.75 j
B = 2.79 i + 3.77 j
So, A + B = (1.01 + 2.79) i + (4.75 + 3.77) j
A + B = 3.80 i + 8.52 j Thus, magnitude of (A+B)
= √(3.802 + 8.522) = 9.329
Thus, R = 9.329
Angle = atan(8.52/3.80) = 65.962 deg
given vectors are (25,12,21) and (-2,2,6)
If two vectors are (x1,x2,x3) and (y1,y2,y3) then the distance between two vectors is given by formula
Distance = √ [(x1 - y1)2 + (x2 - y2)2 + (x3 - y3)2]
So, Distance = √ [(25-(-2)) 2 + (12-2)2 + (21-6)2]
= √ (729+100+225)
= √ (1054)
Example 4: Vector addition using the component method
vector A = -Acos45 i + A sin 45 j
= -424.26i + 424.26 j
vector B = Bj= 500j
vector C = C cos45 i- Csin 45j
C= 282.84i - 282.84j
resultant = vector A+vector B+vector C
= (- 424.26+282.84 ) i +(424.26 + 500 -282.84 ) j
= -141.42 i + 641.42 j
magnitude of resultant = √[(-141.42)2+(641.42)2]
= 656.83 m
the resultant force is as shown
tan θ= 641.42/141.42
θ= 77.57o north of west
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In astronomy, stars are classified based on their spectra. Different types of stars (listed below) have different spectral characteristics and, even though they only differ in brightness to the unaided eye, stars are divided into seven basic spectral classes and eight luminosity classes. This division does not include young stellar objects, stellar remnants (white dwarfs, neutron stars) and substellar objects (brown dwarfs).
Spectral types are determined primarily based on the temperature of the stellar photosphere, the outer shell that extends into the stellar surface. The effective temperature of a star depends on the star’s mass – the greater the mass, the hotter the star – and is also linked with the star’s colour. Mass is critical because it is what determines how long the star lives and which evolutionary path it takes. It is closely linked with luminosity. The most massive stars are usually also the most luminous. They appear brighter to the unaided eye from greater distances.
The temperature of a star is estimated based on the star’s ionization state, which is indicated by the presence or absence of particular chemical elements in the stellar spectrum.
The hotter a star is, the rarer it is. More than 76% of stars are cool, M-type stars (red dwarfs), while massive, hot, O-type stars constitute only 0.00003% of all known stars. These hot blue stars are the most short-lived. Due to their high mass, they evolve quickly and their life spans are measured in mere millions of years. In contrast, our Sun is 4.6 billion years old and only about halfway into its lifetime.
The coolest stars appear red because they emit longer wavelengths of visible light, while the hottest ones emit shorter wavelengths and appear blue or bluish-white. Stars emit other colours as well, but they release the most visible light in the so-called “peak wavelength.”
Each star is assigned a spectral type based on the appearance of its spectrum. Stellar classes typically have three elements: a letter (O-B-A-F-G-K-M), an Arabic number between 0 and 9, and a Roman number between I and VII (or a zero).
The letter indicates the spectral class, which is determined based on the star’s effective temperature. In order of decreasing temperature, the seven main spectral classes in the Morgan-Keenan classification system are: O, B, A, F, G, K, and M. The Arabic number subdivides the class further based on the temperature; 0 indicates the hottest stars in each class, while 9 denotes the coolest. The Roman numeral indicates the luminosity class, classifying stars as main sequence stars, subgiants, giants, bright giants, and supergiants.
The foundation for this classification scheme was created by American astronomer Edward C. Pickering along with Williamina Fleming, and later adapted by Annie Jump Cannon and Antonia Maury. It was published in the Henry Draper Catalogue in the 1920s. The catalogue originally included 225,300 stars.
Pickering conducted a survey of stellar spectra at the Harvard College Observatory in Cambridge, Massachusetts in the 1880s. He continued the work of the late astrophotography pioneer Henry Draper, who had studied astronomy using photography. In 1882, Pickering invented a method of photographing the spectra of multiple stars at the same time. He and his team used the method to take photographs of more than 220,000 stars.
The Harvard spectral classification scheme distinguishes between stars of different temperatures, but does not take into account their luminosity. In other words, it does not distinguish between stars on the main sequence, giants and supergiants. For this reason, the Morgan-Keenan (MK or MKK) system was developed by W. W. Morgan, Philip Childs Keenan, and Edith Marie Kellman at Yerkes Observatory in Wisconsin, and published in 1943. The MKK system, which is still in use today, retained the spectral types used in the Harvard system, but added luminosity classes to indicate whether the star was a dwarf, subgiant, giant, bright giant, or supergiant.
Spectral types: O-B-A-F-G-K-M
OBAFGKM is an acronym for the seven main spectral types of stars. The table below shows the effective temperature range, chromaticity, mass, radius, and luminosity of stars in each class, as well as their average life span.
|Life span (years)
The table below shows examples of main sequence stars of different spectral types.
The Morgan-Keenan system of classifying stellar spectra kept the spectral classes introduced in the Harvard classification system, but added luminosity classes to distinguish between different types of stars. A Roman numeral is used to distinguish between different luminosity classes. These are:
|0 or Ia+
|extremely luminous supergiants (hypergiants)
|Cygnus OB2-12 (B3-4 Ia+), V382 Carinae (G0-4 Ia+)
|Deneb (A2 Ia), Rigel (B8 Ia), Alnilam (B0 Ia), Saiph (B0.5 Ia), Wezen (F8 Ia), Aludra (B5 Ia), Mu Cephei (M2 Ia), KY Cygni (M3 Ia)
|luminous supergiants (intermediate size)
|Alnitak (O9.5 Iab), Sadr (F8 Iab), Mu Normae (O9.7 Iab), Rho Leonis (B1 Iab), Sigma Cygni (B9 Iab), Chi Aurigae (B5 Iab)
|less luminous supergiants
|Polaris (F7 Ib), Mirfak (F5 Ib), Aspidiske (A9 Ib), Suhail (K4 Ib)
|Canopus (A9 II), Adhara (B2 II), Sargas (F0 II), Mintaka (O9.5 II)
|Arcturus (K1.5 III), Aldebaran (K5+ III), Dubhe (K0 III), Capella (G3 III), Hadar (B1 III), Mimosa (B0.5 III), Pollux (K0 III), Avior (K3 III), Miaplacidus (A1 III)
|Regulus (B8 IVn), Shaula (B2 IV), Acrux (B0.5 IV), Alhena (A1 IV), Sabik (A1 IV), Markab (A0 IV),
Menkalinan (A1m IV)
|Sun (G2 V), Vega (A0 Va), Altair (A7 V), Fomalhaut (A3 V), Spica (B1 V), TRAPPIST-1 (M8 V), Proxima Centauri (M5.5Ve), Epsilon Eridani (K2 V), Barnard’s Star (M4.0 V)
|VI (or the prefix sd)
|Kapteyn’s Star (sdM1), Groombridge 1830 (Argelander’s Star, G8 VIp)
|VII (or the prefix D)
|Sirius B (DA), Procyon B (DQZ)
Some stars fall between luminosity classes. For instance, Alioth, the brightest star in Ursa Major, is between a subgiant and giant, with the classification A1III-IVp, and Atria, the luminary of Triangulum Australe, is between a giant and bright giant (K2 IIb-IIIa). Enif, the brightest star in Pegasus, is between a bright giant and supergiant (K2 Ib-II).
Stars are also divided based on their evolutionary stages, which are similar to luminosity classes. Throughout its life cycle, a star will be a protostar, a pre-main-sequence star, a main sequence star, and possibly a giant or supergiant. Depending on its initial mass, it will end its life as a white dwarf, a neutron star, or a black hole. When they have cooled sufficiently, white dwarfs may become black dwarfs, hypothetical stellar remnants that have not yet been observed because the universe is not old enough for any remnant to reach this stage.
The main sequence is the longest stage in a star’s lifetime and most true stars are main sequence stars, including the Sun. During this stage, stars generate energy in their cores by fusing hydrogen into helium. The energy is carried to the surface and emitted at the photosphere.
A mass of 0.08 solar masses is generally set as the low limit below which the stellar core does not reach high enough a temperature to ignite hydrogen stably. Objects below this limit are called brown dwarfs. These are substellar objects, or failed stars. However, brown dwarfs are similar to stars in that they burn deuterium in their cores. Low-mass stars also initially burn deuterium.
Stellar masses can be in the range from 0.08 to 150 or more solar masses. The most massive stars known, the Wolf-Rayet stars R136a1 and BAT99-98 in the Large Magellanic Cloud, have estimated masses of 184 – 260 solar masses (R136a1) and around 226 solar masses (BAT99-98). The slash star Westerhout 49-2 in Aquila is another candidate for the most massive star known, with an estimated mass of 90 – 240 solar masses. On the opposite end of the scale, one of the lowest-mass stars known, the red dwarf SCR 1845−6357A in the southern constellation Pavo, has an estimated mass of 0.07 solar masses.
The life cycle of a star is determined primarily by the star’s mass. The more massive a star is, the faster it will burn through its supply of hydrogen fuel. When hydrogen fusion stops, the star evolves away from the main sequence to become a giant. Astronomers divide stars into several groups based on mass:
- very low-mass stars (< 0.5 solar masses)
- low-mass stars (0.5 to 1.8 – 2.5 M☉)
- intermediate-mass stars (1.8-2.5 M☉ to 5-10 M☉)
- massive stars (> 7-10 M☉)
Very low-mass stars never become red giants. Once they have depleted their supply of hydrogen, they become helium white dwarfs and gradually cool. Low-mass stars do evolve into red giants when they exhaust the hydrogen in their cores. They end their lives by ejecting their outer shells as planetary nebulae, leaving behind white dwarfs. This will be the fate of the Sun in about 5 billion years. Intermediate-mass stars have a similar evolutionary path to low-mass stars. Massive stars evolve into supergiants and usually end their lives as supernovae.
The Hertzsprung-Russell diagram (HR diagram) is a diagram that shows the relationship between the stars’ luminosities (absolute magnitudes) and their effective temperatures or spectral classes. It was named after the Danish astronomer Ejnar Hertzsprung and American astronomer Henry Norris Russell, who created it independently in the 1910s.
HR diagrams can take several forms, but they all share the same basic layout. Stars with greater luminosity are placed at the top of the diagram and those with higher surface temperatures are on the left side. The diagram shows stars at different stages of their evolutionary cycle. Most stars are in the region of the main sequence, which stretches from the upper left for hot, luminous stars to the bottom right for cool stars. Red giants and supergiants have low temperatures and high luminosities, so they are found in the region above the main sequence. White dwarfs occupy the bottom left region of the HR diagram, as they have high temperatures but low luminosities.
Since a star’s surface temperature and luminosity change as the star goes through different evolutionary stages, the HR diagram is a useful tool for the study of stellar evolution. Astronomers can tell a star’s evolutionary stage by determining its place in the diagram.
The HR diagram can also be used to estimate distances of galaxies and star clusters. Astronomers do this by comparing the apparent magnitudes of the stars in the galaxy or cluster to the absolute magnitudes of stars whose distances are known.
These are the different types of stars based on spectral type, luminosity class and stage of evolution:
1. Young stellar objects (YSOs)
- Pre-main-sequence stars (T Tauri stars and Herbig Ae/Be stars)
Young stellar objects are stars in an early stage of evolution, one that precedes the main sequence. They can be protostars or pre-main-sequence stars. They are divided into classes 0, I, II and III based on how much infrared radiation they emit.
Class 0 objects are only a few thousand years old and have not yet started undergoing nuclear fusion at their cores. They are fueled solely by gravitational potential energy which is released as they accrete infalling material.
Class I protostars still collect the dust and gas from the surrounding clouds and their luminosity is largely dependent on gravitational energy. However, unlike class 0 objects, they have begun to undergo nuclear fusion in their centres. These stars are invisible at optical wavelengths and can only be detected at infrared and radio wavelengths because they are still embedded in thick clouds of dust and gas.
Class II objects are still shrouded in disks of dust and gas, but the process of accumulating infalling material has mostly finished. These objects are also known as classical T Tauri stars.
Class III objects have lost their disks and roughly correspond to weak-line T Tauri stars.
Protostars are newly formed stars that are still gathering material from the surrounding molecular cloud. They are formed when a fragment of the parent molecular cloud collapses under the force of its own gravity and a core forms within the fragment. This stage lasts until the infalling material is depleted and stars become visible as pre-main-sequence stars.
Stars are formed within dense cores, small molecular clouds that are initially in balance between the force of self-gravity and both gas pressure and magnetic pressure. As these clouds gather material from the surrounding cloud, they become more massive, and the force of gravity overwhelms pressure. As a result, the dense core begins to collapse. The gas that collapses toward the centre of the core first creates a small protostar and then a protoplanetary disk around it.
Protostars can be exceptionally massive. In 2016, a team of scientists discovered a young stellar object with a mass more than 30 times the mass of the Sun. The protostar, designated G11.92–0.61 MM1 (or simply MM1) lies approximately 11,000 light years away and is still in the process of gathering dust and gas from its parent molecular cloud. It will be even more massive when it reaches the main sequence.
Another high-mass protostar, designated G45.47+0.05, was detected in 2020. It has an estimated mass 30 to 50 times that of the Sun. Like MM1, it is still in the process of growing.
Once stellar winds have dissipated the surrounding clouds of dust and gas, stars become visible as pre-main-sequence objects. At this stage, stars have accumulated almost all their mass, but have not yet begun to burn hydrogen in their cores. They contract and their internal temperature increases until they start the nuclear fusion of hydrogen on the zero-age main sequence. The period when the stars contract is known as the pre-main-sequence stage. During this stage, stars are fueled by gravitational contraction. In the early stage, most of them have circumstellar disks where planets may form.
Pre-main-sequence stars can be either T Tauri stars of Herbig Ae/Be stars, depending on their mass. T Tauri stars have masses of up to 2 solar masses, and Herbig Ae/Be stars are in the range between 2 and 8 solar masses. Stars will a higher initial mass do not have a pre-main-sequence stage; by the time they are visible, they are already burning hydrogen and are on the main sequence.
T Tauri stars
T Tauri stars are very young variable stars that are still contracting to the main sequence. They are typically found near molecular clouds. This class includes the youngest visible stars of the spectral types F, G, K and M with masses of up to 2 solar masses. These stars are less than 10 million years old. About half of them have protoplanetary disks which eventually dissipate. Their effective temperatures are comparable to those of main sequence stars with the same mass, but T Tauri stars are more luminous because they are larger. They are fueled by gravitational energy and do not fuse hydrogen in their cores because their central temperatures are not high enough. They take about 100 million years to reach the main sequence stage.
T Tauri stars were named after T Tauri, a young star discovered by the English astronomer John Russell Hind in October 1852. The star illuminates the nebula NGC 1555, also known as Hind’s Variable Nebula. The nebula varies in brightness because its central star is variable. It is a Herbig-Haro object, a bright nebulous patch associated with a very young star. T Tauri is believed to be only 0.4 million years old. It appears in the same area of the sky as the Hyades cluster, not far from Ain (Epsilon Tauri), the star that marks the Bull’s northern eye.
Herbig Ae/Be stars
Herbig Ae/Be stars are pre-main-sequence stars of the spectral types A or B with masses between 2 and 8 times that of the Sun. Like T Tauri stars, they are very young – up to 10 million years old – and still in the process of contracting. They are shrouded in dust and gas and sometimes have circumstellar disks. They can vary in brightness due to planetesimals in the circumstellar disks.
Herbig Ae/Be stars were named after the American astronomer George Herbig, who was the first to identify them in 1960.
2. Main sequence stars
Main sequence stars, or dwarfs, are stars that generate energy through nuclear fusion of hydrogen into helium in their cores. They are the most numerous stars in the universe (not including substellar objects). The energy that they generate in the core is carried to the surface and radiated away at the photosphere.
The main sequence is the longest stage in a star’s lifetime. For low-mass stars like the Sun, it lasts about 10 billion years. The more massive a star is, the less time it spends on the main sequence. The most massive stars spend only a few million years at this stage. They consume the hydrogen in their cores faster and evolve into supergiants.
Depending on their surface temperature, dwarf stars can belong to one of the following classes:
- O-type dwarfs: S Monocerotis, AE Aurigae, Mu Columbae
- B-type dwarfs: Achernar, Alkaid, Algol
- A-type dwarfs: Sirius, Vega, Fomalhaut
- F-type dwarfs: Diadem, Alchiba, Zavijava
- G-type dwarfs: Sun, Alpha Centauri A, Tau Ceti
- K-type dwarfs: Alpha Centauri B, Epsilon Eridani, 61 Cygni
- M-type dwarfs: Proxima Centauri, Barnard’s Star, TRAPPIST-1
O-type main sequence stars are the hottest stars in the known universe. They make up only 0.00003% of all main sequence stars. With effective temperatures of at least 30,000 K, they are at least 30,000 times more luminous than the Sun. They can be as much as a million times more luminous than our star.
Hot blue O-type stars are very rare. It is believed that there are only up to 20,000 of them in our galaxy. They are commonly found in active star forming regions, such as arms of spiral galaxies or in interacting galaxies. They are often components of multiple star systems.
These stars are exceptionally massive. They have masses at least 16 times that of the Sun and radii at least 6.6 times the Sun’s. Due to their high mass, the stars evolve very quickly and have the shortest life spans of all spectral classes. They live only about 10 million years before going out as supernovae.
Notable examples in this class include the irregular variable star S Monocerotis in the Christmas Tree Cluster (NGC 2264) in Monoceros, AE Aurigae in the Flaming Star Nebula (IC 405) in Auriga, Theta1 Orionis C in the Trapezium Cluster in Orion, Upsilon Orionis in Orion, and Mu Columbae in Columba. All these stars are supernova candidates, with masses in the range from 16 solar masses (Mu Columbae) to 33 solar masses (Theta1 Orionis C).
B-type main sequence stars are also exceptionally hot and luminous, but have more modest parameters than O-type stars. They have temperatures in the range from 10,000 to 30,000 K and are between 25 and 30,000 times more luminous than the Sun. Their masses are typically in the range from 2.1 to 16 solar masses, and their sizes between 1.8 and 6.6 solar radii. These stars constitute only 0.13% of all stars on the main sequence.
Examples in this class include Achernar in Eridanus, the ninth brightest star in the sky, with the stellar classification B6 Vep, Alkaid in Ursa Major (B3 V), Alnair in Grus (B6 V), Peacock in Pavo (B3 V), Nunki in Sagittarius (B2.5 V), Eta Centauri in Centaurus (B1.5 Vne), and the famous variable star Algol in Perseus (B8 V).
A-type stars have surface temperatures between 7,600 and 10,000 K and appear white or bluish-white in colour. They typically have masses in the range from 1.4 to 2.1 solar masses and radii between 1.4 and 1.8 times that of the Sun while on the main sequence. Their bolometric luminosity is between 5 and 25 times that of the Sun.
These stars make up 0.6% of all main sequence stars. They are not as rare and O- and B-type stars, but also not as common as cooler types. Several first-magnitude stars belong to this spectral class: Sirius, Vega, Altair, and Fomalhaut. These stars lie in the solar neighbourhood. Sirius is the fifth nearest star system to the Sun at a distance of 8.709 light years. Vega lies 25.04 light years away, Altair is slightly closer at 16.73 light years, and Fomalhaut is roughly at the same distance as Vega, 25.13 light years away.
S5-HVS1, the fastest moving star detected as of November 2019, is also classified as an A-type dwarf. It is believed to be travelling at 1,755 km/s.
F-type stars comprise 3% of all main sequence stars. With effective temperatures between 6,000 and 7,500 K, they appear white or yellow-white in colour. They are slightly larger and more massive than Sun-like stars. They typically have masses in the range between 1.04 and 1.4 solar masses and radii between 1.15 and 1.4 times that of the Sun. They are between 1.5 and 5 times more luminous than the Sun.
Notable examples of this class are Diadem in Coma Berenices (F5 V), Alchiba in Corvus (F1 V), Zavijava in Virgo (F9 V), Porrima in Virgo (F0 V), and Upsilon Andromedae (F8 V) in Andromeda.
G-type stars – yellow dwarfs – comprise 7.6% of all main sequence stars. They have masses in the range from 0.8 to 1.04 solar masses and radii between 0.96 and 1.15 solar radii. Their luminosity is in the range from 0.6 to 1.5 times that of the Sun with surface temperatures between 5,200 and 6,000 K. These stars spend about 10 billion years on the main sequence before evolving into subgiants and then red giants. As they keep expanding, their gravity becomes insufficient to hold their outer layers and they lose a lot of mass. The expelled material forms a planetary nebula, and the remnant core of the star becomes a dense white dwarf.
The Sun and two its close neighbours – Rigil Kentaurus (Alpha Centauri A) and Tau Ceti belong to this class. The Sun is a yellow dwarf with the stellar classification G2V and an effective temperature of 5,772 K. Rigil Kentaurus is the primary component of the nearest star system to the Sun. Located only 4.37 light years away, the star is slightly larger and more massive than the Sun, with a mass of 1.100 solar masses and a radius 1.2234 times solar. With a surface temperature of 5,790 K, it is 1.519 times more luminous than the Sun. It has the same spectral type as the Sun, G2V.
Tau Ceti is older than the Sun, with an estimated age of 5.8 billion years. It is smaller and less massive than our star, with 78% of the Sun’s mass and 79% its radius. It has the stellar classification G8V. It hosts at least four planets, two of which may be in the habitable zone. Tau Ceti lies only 11.912 light years away.
K-type stars – orange dwarfs – make up 12.1% of all main sequence stars. With surface temperatures between 3,700 and 5,200 K, they shine with 0.08 to 0.6 solar luminosities and appear orange in colour. They have masses in the range from 0.45 to 0.8 solar masses and radii between 70% and 96% that of the Sun.
The nearby examples of this class include Toliman (Alpha Centauri B), Ran (Epsilon Eridani), and 61 Cygni. Toliman is an orange dwarf of the spectral type K1V located only 4.37 light years away. It is the secondary component of the nearest star system to the Sun. Epsilon Eridani is the third nearest star to the Sun that is visible to the unaided eye. It shines at magnitude 3.736 from a distance of 10.475 light years. It has the stellar classification K2V. 61 Cygni is a binary system composed of two orange dwarfs of the spectral types K5V and K7V. The system lies 11.404 light years away. 61 Cygni A is a BY Draconis-type variable, a star that varies in brightness due to starspots. It shines at magnitude 5.21. 61 Cygni B is a flare star with an apparent magnitude of 6.05. The stars are about 6.1 billion years old. They orbit each other with a period of 678 years.
M-type main sequence stars, also known as red dwarfs, are the most numerous stars in the universe. They make up 76.45% of all main sequence stars. They are the smallest and least massive of all the stars on the main sequence, with masses between 0.08 and 0.45 solar masses and radii of up to 0.7 solar radii. Red dwarf stars shine with up to 8% of the Sun’s luminosity with surface temperatures between 2,400 and 3,700 K. They appear reddish or orange-red in colour.
Proxima Centauri, the nearest individual star to the Sun, is a red dwarf of the spectral type M5.5Ve. It lies only 4.2465 light years away. It is the faintest component of the Alpha Centauri system. The star has a mass of only 0.1221 solar masses and shines with 0.0017 solar luminosities. It is classified as a flare star. With an apparent magnitude that varies between 10.43 and 11.11, it is invisible to the unaided eye. It hosts three confirmed exoplanets, designated Proxima Centauri b, c, and d.
Barnard’s Star, the fourth individual nearest star to the Sun (after the three components of the Alpha Centauri system), is another example of this spectral class. Classified as an M4.0 dwarf, it lies 5.9629 light years away and shines at magnitude 9.511.
TRAPPIST-1, a class M8 red dwarf, gained attention in 2016 and 2017, when seven planets were discovered orbiting it. Three of the planets are believed to be in the habitable zone. The star lies 40.54 light years away. It has a mass of about 0.898 solar masses and a radius of only 0.1192 solar radii. Its estimated age is about 7.6 billion years.
Subgiants are stars that are brighter than main sequence stars of the same spectral type, but not quite as bright as giants. This definition applies to subgiants as a luminosity class. The term subgiant is also used for an evolutionary stage of low to intermediate mass stars. During this stage, the stars have exhausted the hydrogen in their cores and the hydrogen shells around the cores continue to fuse, without any major visible changes to the exteriors.
Stars that are on the evolutionary subgiant branch do not always have the subgiant spectral type. They can be classified as giants. Similarly, stars may have the spectral class of a subgiant even if they are at a very different stage of evolution. For instance, the star Theta1 Orionis E in the Trapezium Cluster in the Orion Nebula is classified as a yellow subgiant of the spectral type G2 IV even though it is only 500 million years old and not even on the main sequence yet. Evolutionary subgiants are identified by their lithium abundance or strength of coronal emission.
In terms of luminosity, subgiants typically have the stellar classification B, A, F or G. O-type stars, M-type stars, and class K stars cooler than K1 are normally not given subgiant luminosity classes.
There are, however, exceptions to this rule. Zeta Ophiuchi has the stellar classification O9.2IVnn, indicating a hot blue subgiant. It lies 366 light years away and shines at magnitude 2.569. With a mass 20.2 times that of the Sun, the star is a supernova candidate and will meet its end in a few million years even though it is only about 3 million years old. It is 74,100 times more luminous than the Sun and has an effective temperature of 34,000 K. It is sometimes classified as a main sequence star of the spectral type O9.5 V.
Here are some examples of stars with subgiant luminosity classes:
- O-type subgiants: Zeta Ophiuchi, HD 93250
- B-type subgiants: Acrux, Regulus, Shaula
- A-type subgiants: Menkalinan, Alhena, Merak
- F-type subgiants: Wasat, Theta Ursae Majoris, Zeta Herculis
- G-type subgiants: Alshain, Muphrid, Mu Herculis
- K-type subgiants: Eta Cephei, Delta Eridani
Giants are stars that have exhausted the supply of hydrogen in their cores and evolved away from the main sequence. They have considerably higher luminosity and larger radii than main sequence stars with the same surface temperature. Their radii can be up to a few hundred times that of the Sun and their luminosities are in the range between 10 and a few thousand times the Sun’s.
Not all stars become giants. Very low mass stars (< 0.5 M☉) become helium white dwarfs once they exhaust their hydrogen. Due to their low mass, they never become hot enough to fuse helium in their cores. Massive stars with masses of at least 7 to 10 M☉ evolve into supergiants when they burn through their supply of hydrogen. Stars with masses above 12 M☉ on the main sequence briefly evolve into blue giants before becoming blue supergiants. Their spectral features may present as those of giants or supergiants even before the stars have stopped burning hydrogen.
Low and intermediate mass stars do evolve into red giants once they have depleted the hydrogen in their cores. Low-mass stars (0.5 to 1.8-2.5 M☉) like the Sun start to burn helium in a helium flash, a short thermal runaway nuclear fusion of helium into carbon. The Sun will experience a flash about 1.2 billion years after it evolves away from the main sequence. It will spend about 10% of its life on the red giant branch.
Intermediate-mass stars (1.8-2.5 M☉ to 5-10 M☉) spend a short time on the red giant branch before igniting helium without a flash.
Here are some examples of giants of different spectral types:
- O-type giants: Meissa, Hatysa, Menkib
- B-type giants: Hadar, Mimosa, Elnath
- A-type giants: Miaplacidus, Alioth, Rasalhague
- F-type giants: Caph, Adhafera, Alkarab
- G-type giants: Capella, Nekkar, Kappa Geminorum
- K-type giants: Arcturus, Aldebaran, Pollux
- M-type giants: Gacrux, Mirach, Mira
Giants are commonly referred to by their colour, which roughly corresponds to their temperature and spectral class.
Red giants are giant stars of the spectral types M, K, C (carbon stars) and S (S-type stars). The brightest red giant is Arcturus, the fourth brightest star in the sky. Some stars of the spectral type G can also be called red giants. Yed Posterior (Epsilon Ophiuchi) is one of these, with the stellar classification G9.5 IIIb.
Red giant stars are low to intermediate-mass stars that have reached a late stage in their evolution. They typically have masses in the range from 0.3 to 8 solar masses and temperatures lower than 5,000 K.
These stars can be at several different stages of their evolutionary cycle:
- the red-giant branch (RGB)
- the red horizontal branch (red clump)
- the asymptotic giant branch (AGB)
RGB stars are the most common of the three. These are giants that are still fusing hydrogen into helium in a shell around a helium core. Aldebaran, Arcturus and Gacrux belong to this group. Red clump giants (Hamal, Kappa Persei, Delta Andromedae) are fusing helium into carbon in their cores, while stars on the asymptotic giant branch (Mira, Rasalgethi, Chi Cygni) burn helium in a shell around a degenerate carbon-oxygen core and have a hydrogen-burning shell beyond the helium-burning one.
Carbon stars are stars on the asymptotic giant branch whose atmospheres have more carbon than oxygen. These stars appear strikingly red. Classical carbon stars are giants, but there are also dwarf and supergiant carbon stars.
Examples of this class include Hind’s Crimson Star (R Leporis), S Camelopardalis, CW Leonis, and La Superba (Y Canum Venaticorum).
S-type stars are cool giants with equal amounts of carbon and oxygen in their atmospheres. Their spectra also show bands of zirconium monoxide (ZrO). Intrinsic S-type stars are typically in the most luminous phase of the asymptotic giant branch, which lasts less than a million years. They can be long period variables. These stars are quite rare. They make up less than 10% of AGB stars. Extrinsic class S stars are normally less luminous and classified as semiregular or irregular variables. They form an even smaller percentage of AGB giants.
Examples of this class include the Mira variables R Andromedae, W Aquilae, R Cygni, R Geminorum, BH Crucis, and Chi Cygni.
Giant stars of the spectral type K are sometimes called orange giants to distinguish them from class M red giants. The first-magnitude red giants Arcturus, Aldebaran and Pollux are all class K stars. They are smaller and less luminous than M-type giants, and they have warmer atmospheres.
Yellow giants are giant stars of the spectral types G, F and sometimes A. They are not as common as red giants because they spend less time at this stage and only evolve from slightly more massive stars. In terms of evolutionary cycle, they may be stars evolving toward the RGB phase or stars at a later evolutionary stage on the horizontal branch. The latter have more heavy elements and a lower mass, and they are generally unstable. They include many pulsating variable stars classified as classical Cepheids, Delta Scuti variables, RR Lyrae variables, and W Virginis variables.
Blue giants are giant stars of the spectral types O and B. Some early A-type stars may also be called blue giants. These stars are far less common than red giants because they only evolve from more massive stars and because the blue giant stage is very brief. Blue giant stars have initial masses of at least 2 solar masses. With radii between 5 – 10 times that of the Sun, they are not as large as red giants. Because they do not live very long, these stars are often found in OB associations, young stellar associations consisting of stars formed inside the same molecular cloud.
Blue giants can be anything from massive, luminous stars ending their main sequence lifetime to low-mass stars on the horizontal branch. The high-mass stars first evolve into blue giants, then into bright blue giants, and finally into blue supergiants before becoming red supergiants. Stars with the highest masses barely have a giant stage. The stage is very brief, and the stars soon become supergiants.
The lower-mass stars on the horizontal branch evolve back to asymptotic giant branch (AGB) stars. They can become blue giants depending on mass and metallicity.
Some class A stars may be called white giants. Thuban in the constellation Draco is an example of this. It is a giant of the spectral type A0III.
5. Bright giants
Bright giants are stars that are a bit larger and more luminous than regular giants, but not quite as luminous as supergiants. The examples of this luminosity class include:
- O-type bright giants: Mintaka, 63 Ophiuchi, Tau Canis Majoris
- B-type bright giants: Adhara, Muliphein, HD 33203
- A-type bright giants: Canopus, N Carinae, Omicron Scorpii
- F-type bright giants: Sargas, Turais, Albaldah
- G-type bright giants: Delta Trianguli Australis, V723 Monocerotis, V415 Carinae
- K-type bright giants: Almach, Dabih, Hassaleh, Saclateni
- M-type bright giants: CQ Camelopardalis, Delta Sagittae, Delta2 Lyrae
Supergiants are the most luminous stars of different spectral classes. They have absolute magnitudes between -3 and -8. Their temperatures range from 3,400 K for cool, red supergiants to more than 20,000 K for blue supergiants. Supergiants have more heavy elements in their spectra than main sequence stars and are larger than giants of the same spectral type. Red, M-type supergiants are older, more evolved stars, while O- and B-type supergiants are only a few million years old and have evolved quickly due to their high masses.
The Morgan-Keenan classification system makes a distinction between four luminosity classes of supergiants:
- less luminous supergiants (Ib)
- intermediate luminosity supergiants (Iab)
- luminous supergiants (Ia)
- hypergiants (0 or Ia+)
Supergiants are not just a luminosity class, but also represent an evolutionary stage in the life of stars with masses of more than 8 – 10 solar masses. When they exhaust the hydrogen in their cores, these stars quickly start to fuse helium. Once they have exhausted the helium, they continue to fuse heavier elements until they develop an iron core. When this happens, the core rapidly collapses, triggering a Type II supernova.
Stars do not have to be evolutionary supergiants to be classified as supergiants. Evolved stars with spectral features and luminosities similar to those of supergiants can be assigned a supergiant luminosity class. These are mostly red giants on the asymptotic giant branch (AGB) and post-AGB stars. For example, the variable post-AGB star RV Tauri is classified as a bright supergiant (G2eIa-M2Ia), even though it has only 53% of the Sun’s mass.
Here are some examples of supergiants across different spectral classes:
- O-type supergiants: Alnitak, Naos, Alpha Camelopardalis
- B-type supergiants: Rigel, Alnilam, Saiph, Aludra
- A-type supergiants: Deneb, Aspidiske, Eta Leonis
- F-type supergiants: Mirfak, Wezen, Polaris, Sadr, Arneb
- G-type supergiants: Mu Persei, Sadalsuud, Sadalmelik, Mebsuta
- K-type supergiants: Suhail, BG Geminorum, Zeta Cephei
- M-type supergiants: Betelgeuse, Antares, Mu Cephei
Supergiants are found in all the main spectral classes, but most of them are spectral type B. There are more B-type supergiants than those of all other spectral types combined.
Supergiants are generally not cooler than mid-M class at about 3,400 K. Stars cooler than this would be highly unstable. There are, however, exceptions. The luminous red supergiant VX Sagittarii has a temperature of 2,900 K at visual minimum and 3,200 to 3,400 K near maximum. It is classified as a pulsating variable and has an uncommonly high magnitude range.
Like giant stars, supergiants can be referred to by their colour instead of their spectral class.
Blue supergiants are hot, luminous stars of the spectral types O and B. They are sometimes also called OB supergiants. They have surface temperatures between 10,000 and 50,000 K and are at least 10,000 times more luminous than the Sun. For example, the O-type supergiants Alnitak and Naos shine with 250,000 and 813,000 solar luminosities, while their B-type counterparts Alnilam and Rigel have an energy output 537,000 and 120,000 times that of the Sun. The most luminous blue supergiants can be a million times more luminous than the Sun.
Blue supergiants evolve from stars with initial masses of about 10 – 300 solar masses. Because they are exceptionally massive, these stars spend only a few million years on the main sequence. When they become supergiants, they are generally unstable, experiencing a high degree of mass loss. Some of these stars become luminous blue variables (LBVs) and experience episodes of exceptionally high mass loss. Blue supergiants with lower masses continue to expand in size until they evolve into red supergiants. As they grow, they spend some time as yellow supergiants.
Yellow supergiants are supergiant stars of spectral type F or G, with surface temperatures from about 4,000 K to 7,000 K. Some late A of early K-type stars can also be yellow supergiants. These are rare stars and can be found at different evolutionary stages.
Yellow supergiants are much larger than the Sun. Their radii are in the range from 30 to several hundred times that of the Sun. They are typically at least 1,000 times more luminous than the Sun. The most luminous yellow supergiants can exceed 100,000 solar luminosities.
Even though these stars are quite large, they are not necessarily very massive. They can be less massive than the Sun or they can have more than 20 solar masses. Low-mass yellow supergiants have very low surface gravities.
Spectral standards for the yellow supergiant class include Arneb (Alpha Leporis), Mirfak (Alpha Persei), Wezen (Delta Canis Majoris), Mu Persei, Sadalmelik (Alpha Aquarii), and Mebsuta (Epsilon Geminorum).
Many yellow supergiants are variable stars, primarily Cepheid variables. These stars pulsate radially, and their diameter and temperature vary with the pulsations. Because there is a direct relationship between their pulsation period and luminosity, Cepheids are used as standard candles for establishing galactic and extragalactic distances. Stars classified as classical Cepheids include Polaris (F7Ib), Eta Aquilae (F6 Iab), Mekbuda (F7Ib to G3Ib), RT Aurigae (F8Ib), and Delta Cephei (F5Ib-G1Ib), the prototype for this class.
White supergiants are a rare class of supergiant stars of spectral type A to early F. The brightest example of this class is Deneb (Alpha Cygni), a supergiant of the spectral type A2 Iae. The star has a mass 19 times that of the Sun and a radius 203 times solar. With an effective temperature of 8,525 K, it is about 196,000 times more luminous than the Sun. It shines at magnitude 1.25 from an approximate distance of 2,615 light years. It is by far the most distant first-magnitude star. Other bright examples of this class include Eta Leonis (A0 Ib), Aspidiske (Iota Carinae, A9 Ib), and Omicron2 Centauri (A2 Iae).
Some early or hotter class K supergiants are sometimes referred to as orange supergiants. These stars are very rare compared to M-type supergiants because they are in a very brief transition stage. This class includes Zeta Cephei (K1.5 Ib), Suhail (Lambda Velorum, K4 Ib), and BG Geminorum (K0I).
Red supergiants are supergiant stars of spectral types K and M. They develop from main sequence stars with masses between 8 and 30 times that of the Sun. Due to their high mass, they are normally no more than about 25 million years old. The best-known red supergiants in the sky are the two brightest ones: Betelgeuse in the constellation Orion and Antares in Scorpius.
The largest known stars – Stephenson 2-18, UY Scuti, and VY Canis Majoris, among others – belong to this group. These are the coolest and largest supergiant stars. They have surface temperatures below 4,100 K and are usually at least several hundred times larger than the Sun. Even though they are the largest stars in terms of volume, they are not the most massive. Their masses are typically in the range from about 10 to 40 solar masses.
Red supergiants undergo high mass loss through powerful stellar winds. The lost material forms visible nebulae around the stars. By the time they reach the end of their life cycle, red supergiants have lost a substantial portion of their initial mass. By the time their cores collapse, they have typically reached a mass 10 times that of the Sun.
Even though they are much cooler than the Sun, the sheer size of these stars makes them tens or hundreds of thousands of times more luminous than our star. The theoretical upper limit to the radius of a red supergiant is set at about 1,500 solar radii. Stars above this limit are believed to be too unstable. However, the estimated radii of the largest known stars exceed this value. UY Scuti is reported to have a radius 1,708 times that of the Sun and Stephenson 2-18, a radius of about 2,150 solar radii. These values may be overestimated because they exceed the theoretical limit.
Hypergiants are rare stars with the luminosity class 0 or Ia+. They are also commonly classified as Ia-0. These are exceptionally large, massive and luminous stars that experience atmospheric instability and a high degree of mass loss through strong stellar winds. Almost all of them exhibit small variations in luminosity over time. Red supergiants are seldom given this classification because high mass loss is inevitable for them.
Very few hypergiant stars are known because these stars do not live longer than a few million years. Here are some examples across different spectral types:
- B-type hypergiants: BP Crucis, HT Sagittae, V4030 Sagittarii, Cygnus OB2-12, R126 (HD 37974)
- A-type hypergiants: Westerlund 1-243, 6 Cassiopeiae, V509 Cassiopeiae
- F-type hypergiants: V1302 Aquilae
- G-type hypergiants: R Puppis, V382 Carinae, Omicron1 Centauri, V810 Centauri, Rho Cassiopeiae
- K-type hypergiants: V915 Scorpii, RW Cephei, V766 Centauri (HR 5171 A)
- M-type hypergiants: VY Canis Majoris, NML Cygni
Blue hypergiants are the most luminous blue supergiant stars with emission lines in their spectra that indicate strong mass loss. They are found in the same part of the HR diagram as luminous blue variables (LBVs), but do not necessarily exhibit the same variations. Similarly, some luminous blue variables have spectra similar to those of hypergiants and are classified as hypergiants for at least a part of their cycle.
Luminous blue variables
Luminous blue variables (LBVs) are massive, luminous stars that exhibit sudden variations both in brightness and in the appearance of their spectra. These are unstable supergiant or hypergiant stars that show both periodic outbursts and sporadic greater eruptions. They are also known as S Doradus variables after S Doradus, one of the most luminous stars known and one of the brightest stars in the Large Magellanic Cloud (LMC).
With a luminosity 910,000 times that of the Sun, S Doradus shines at magnitude 8.6 – 11.5 from a distance of 169,000 light years (it lies in another galaxy). Observations have showed that the star’s temperature can drop from 20,000 K to 9,000 K and its luminosity of 1.4 million L☉ to 0.708 L☉ over four years, corresponding to an increase in the radius of the star’s surface from 100 to 380 solar radii. These dramatic changes are common among stars of this type.
Eta Carinae, the best-known luminous blue variable in the sky, famously became brighter than Rigel during its “Great Eruption” in 1837. Previously a fourth-magnitude star, Eta Carinae briefly became the second brightest star in the sky from March 11 – 14, 1843 before gradually fading and becoming invisible to the unaided eye. It has been brightening since 1940 and now shines at magnitude 4.3 from a distance of about 7,500 light years, even though it is heavily obscured by material expelled during the Great Eruption. The star has an estimated luminosity between 2.96 and 4.1 million times that of the Sun and is believed to be less than 3 million years old.
Luminous blue variables are thought to be evolved from the main sequence, or from post-red supergiants with lower masses. They are believed to be direct predecessors of Wolf-Rayet stars.
Yellow hypergiants are exceptionally massive, luminous, and unstable yellow supergiants of spectral types from A to K. They are some of the most visually luminous stars known, with absolute magnitudes of about -9. Most of these stars are believed to evolve from post-red supergiants, stars that have expelled a good portion of their outer layers and are in the process of evolving into blue supergiants and Wolf-Rayet stars.
Yellow hypergiants have extended atmospheres and have lost up to half of their initial mass. Their initial masses are in the range from about 20 to 60 solar masses. Their temperatures are between 4,000 K for type A0 stars and 8,000 K for class K2 stars. The luminosities of yellow hypergiants are between 200,000 and 600,000 times that of the Sun. These stars are exceptionally rare; only 17 are known in the Milky Way, six of which are found in the Ara Cluster (Westerlund 1).
Red hypergiants are the most extended and unstable red supergiant stars. Even though hypergiant spectral classifications are seldom used, the term is occasionally used for red supergiants with the most exceptional stellar parameters. These include the stars VY Canis Majoris and NML Cygni.
8. Stellar remnants
When they reach the end of their life cycle, stars can become white dwarfs, neutron stars or black holes. Their ultimate fate is determined by their initial mass. The life cycle of stars can also be affected by the stars’ environment, i.e. by whether they are single or binary stars.
Stellar remnants can be:
- White dwarfs
- Neutron stars
- Black dwarfs
- Black holes
White dwarfs are remnants of low to intermediate mass stars that expelled their outer layers when they reached the end of their life cycle. They are stellar cores consisting mostly of electron-degenerate matter. White dwarfs are the final stage of evolution for stars that are not massive enough to become neutron stars or black holes. These stars constitute more than 97% stars in our galaxy.
White dwarfs are very dense objects. The nearest known white dwarf, Sirius B, has a mass 102% of the Sun packed into a diameter almost that of the Earth. Popularly known as the Pup (because it is the companion to the Dog Star), Sirius B was discovered by the German astronomer Friedrich Wilhelm Bessel in 1844. It lies 8.6 light years away.
Neutron stars are the remnant cores of supergiants with masses between 10 and 25 times that of the Sun, that ended their lives as supernovae. They are even smaller and denser than white dwarfs. Except for black holes, neutron stars are the smallest and densest known type of stellar objects. They pack a mass of about 1.4 solar masses into a radius of about 10 kilometers (6 miles). The Milky Way is believed to contain about a billion neutron stars.
Neutron stars are products of supernova events combined with gravitational collapse. These events leave a condensed core much smaller than a white dwarf. Neutron stars are believed to be composed almost entirely of neutrons, subatomic particles with a neutral charge. They have gravitational fields about 200 billion times that of Earth at their surfaces and spin at up to several hundred times per second. Some emit beams of electromagnetic radiation out of their magnetic poles and are known as pulsars. The fastest spinning pulsar known, PSR J1748-2446ad, spins 716 times per second. It lies within the globular cluster Terzan 5 in Sagittarius.
Black dwarfs are white dwarfs that have cooled down to the point where they do not emit any significant light or heat. Since white dwarfs would take much longer than 13.77 billion years (the age of the universe) to reach this stage, black dwarfs have not yet been observed and are theoretical objects. Some of the coolest white dwarfs detected have temperatures below 3,900 K and are believed to be 11-12 billion years old.
The term “black dwarf” is also applied to theoretical cooled brown dwarfs, substellar objects that are not massive enough to burn hydrogen.
Black holes are defined as dense, massive regions of spacetime with such intense gravity that nothing, including light, can escape from them. Stellar-mass black holes form when very massive stars collapse in supernova events at the end of their lives. They pack a mass 10 times that of the Sun into a radius of 30 kilometers (18.6 miles). They typically have masses in the range from about 5 to several tens of solar masses. Stellar black holes are very difficult to detect but taking into account the number of stars that are massive enough to produce them, scientists believe that there may be between 10 million and a billion such objects in our galaxy.
Wolf-Rayet stars are rare and exceptionally luminous stars with surface temperatures in the range from 20,000 K to about 210,000 K. Only about 500 of these stars have been discovered in the Milky Way. They are a stage in the evolution of highly massive stars. Wolf-Rayet stars are believed to evolve from the most massive red and blue supergiants or directly from the main sequence.
Classic Wolf-Rayet stars are highly evolved and massive stars that have depleted their outer hydrogen and show a surface enhancement of heavy elements. They have strong stellar winds and have luminosities hundreds of thousands of times that of the Sun. Many are surrounded by Wolf-Rayet nebulae. By the time they appear as WR stars, they have lost at least half of their initial mass.
Some Wolf-Rayet stars still show hydrogen lines in their spectra and are still fusing hydrogen at their cores. Their luminosities tend to be more than a million times that of the Sun.
Another group of stars with spectra of Wolf-Rayet stars are the central stars of planetary nebulae that have expelled their outer layers to reveal a carbon-oxygen core. Their bolometric luminosities tend to be thousands of times that of the Sun.
The brightest Wolf-Rayet star in the sky is Regor (Gamma Velorum), which is also the nearest Wolf-Rayet star to the Sun. It shines at magnitude 1.83 from a distance of 1,095 light years. It has a mass about 9 times that of the Sun and a luminosity of 170,000 Suns. Its initial mass is estimated at 40 solar masses.
Wolf-Rayet stars are some of the most luminous stars known. The current record holders – R136a1, R136a2 and BAT99-98 in the Tarantula Nebula in the Large Magellanic Cloud (LMC) – are all Wolf-Rayet stars. They have luminosities of 6,166,000 L☉ (R136a1), 5,623,000 L☉ (R136a2), and 5,000,000 L☉ (BAT99-98). They are also among the most massive stars known, with masses of 184 – 260 M☉, 154 – 210 M☉, and 226 M☉ respectively.
Subdwarfs are stars with luminosity 1.5 to 2 magnitudes lower than that of main sequence stars of the same spectral class. They are found just below the main sequence on the Hertzsprung-Russell diagram. These are mostly old stars, usually found in the Milky Way’s halo.
Cool subdwarfs with the stellar classification G, K or M fuse hydrogen in their cores like regular main sequence stars, but are much less luminous because they have low metal content. Kapteyn’s Star, a red subdwarf of the spectral type M1, is the nearest halo star to the Sun. It lies only 12.83 light years away. It has a diameter 30% that of the Sun, but only 1.2% of the Sun’s luminosity. It has an estimated age of about 11.5 billion years.
Groombridge 1830 (Argelander’s Star) is another example of this class. It is a yellow subdwarf of the spectral type G8, located 29.9 light years away. It has a radius of 0.681 R☉ and a luminosity of 0.212 L☉. Its estimated age is between 4.7 and 5.3 billion years.
Hot subdwarfs with the stellar classification O and B are a completely different class. They represent a late evolutionary stage for red giant stars that lose their outer layers prematurely, before they start to fuse helium in their cores. This typically happens in binary star systems.
If an object is not massive enough to sustain nuclear fusion of hydrogen in its core, but is able to fuse deuterium (heavy hydrogen), it is defined as a brown dwarf. Brown dwarfs have masses of less than about 0.08 solar masses, but are more massive than the most massive planets. Typically, they have a mass 13 to 80 times that of Jupiter. Those with masses of more than 65 Jupiter masses are also able to fuse lithium.
Brown dwarfs are classified as substellar objects. Their temperature declines over time and they pass through later spectral types over the course of their evolutionary cycle.
The nearest brown dwarfs are found in the Luhman 16 system, the third closest system to the Sun. The binary brown-dwarf system lies only 6.516 light years away in the constellation Vela. The components, Luhman 16A and 16B, have masses of 0.032 and 0.027 M☉ (33.5 and 28.6 MJup) and radii of about 0.85 and 1.04 RJup. With effective temperatures of 1,350 and 1,210 K, they shine with only 0.0000219 and 0.0000209 L☉. They are separated by 1.5 arcseconds on the sky, corresponding to a physical distance of 3 astronomical units (Earth – Sun distances). The system has an estimated age of 600 – 800 million years. |
Scientists at the London Centre for Nanotechnology and Department of Physics & Astronomy at UCL have discovered a potential way to make graphene – a single layer of carbon atoms with great promise for future electronics – superconducting.
The study, performed in collaboration with Stanford University and the SLAC National Accelerator Laboratory is published in Nature Communications.
Graphene, a single sheet of carbon atoms arranged in a honeycomb pattern, is the thinnest and strongest known material and a great conductor of electricity, among other remarkable properties. Scientists hope to eventually use it to make ultra fast transistors, sensors and transparent electrodes. Despite its array of exciting properties, superconducting graphene, in which electricity is conducted without resistance, is yet to be achieved.
The classic way to make graphene is by peeling atomically thin sheets from a block of graphite. But it is possible to isolate these carbon sheets by chemically interweaving graphite with arrays of calcium atoms to form calcium intercalated graphite or CaC6. While it’s been known for nearly a decade that this material is superconducting the new study uncovers the mechanism of superconductivity in unprecedented detail. The work therefore points to a pathway to make graphene itself superconducting – something the scientific community has dreamed about for a long time, but failed to achieve.
The combination of high purity samples and state-of-the-art light scattering experiments permitted the scientists to distinguish what the electrons in each layer were doing, revealing details of their behaviour that had not been seen before. Before now researchers were unable to confirm whether CaC6’s superconductivity came from the calcium layer, the graphene layer or both. The new discovered that electronic states associated both the calcium layer and graphene together with the resulting interaction between the two are essential for superconductivity. Thus to realise superconductivity in single graphene sheets, arrays of metal atoms must be first arranged on its surface.
Although applications of superconducting graphene are speculative and far in the future they could include ultra-high frequency analogue transistors, nanoscale sensors and electromechanical devices and quantum computing devices.
Learn more: A Potential Way to Make Graphene Superconducting
The Latest on: Superconducting graphene
via Google News
The Latest on: Superconducting graphene
- Dirac electrons come back to life in magic-angle grapheneon June 22, 2020 at 1:03 pm
Graphene is a flat crystal of carbon, just one atom thick. When two sheets of this material are placed on top of each other, misaligned at small angle, a periodic "moiré" pattern appears. This pattern ...
- ‘Magic-angle’ graphene doubles upon June 22, 2020 at 11:46 am
Jarillo-Herrero and colleagues made the first magic-angle graphene by stacking two sheets of 2D carbon on top of each other to form a moiré lattice. When they twisted these sheets so that the ...
- A new symmetry-broken parent state discovered in twisted bilayer grapheneon June 22, 2020 at 10:07 am
In 2018 it was discovered that two layers of graphene twisted one with respect to the other by a "magic" angle show a variety of interesting quantum phases, including superconductivity, magnetism and ...
- Dirac electrons come back to life in magic-angle grapheneon June 20, 2020 at 5:00 pm
Graphene is a flat crystal of carbon ... that we discovered appear at temperatures well above the onset of the superconducting and correlated insulating states observed so far," says Ilani.
- Dirac electrons come back to life in magic-angle grapheneon June 15, 2020 at 1:50 am
In magic-angle graphene, on the other hand ... transitions and Dirac revivals that we discovered appear at temperatures well above the onset of the superconducting and correlated insulating states ...
- The Graphene Councilon June 12, 2020 at 9:02 am
In this interview, AZoNano speaks to Frank Deppe, Junior Group Leader for Superconducting Quantum Circuits at the Walther-Meißner-Institut, about QMiCS. This page details the capabilities of the ...
- Paragraf Partners with CERN to Demonstrate Unique Properties of Paragraf’s New Graphene Hall Effect Sensoron June 11, 2020 at 6:29 am
Paragraf has embarked on a working partnership with the Magnetic Measurement section at CERN, the European Organization for Nuclear Research, to demonstrate how new opportunities for magnetic ...
- Cascade sets the stage for superconductivity in magic-angle twisted bilayer grapheneon June 11, 2020 at 3:06 am
(Image: Yazdani lab at Princeton University) "This study shows that the electrons in magic-angle graphene are in a highly correlated state even before the material becomes superconducting, "said Ali ...
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Physics for Kids
When we discussed velocity and speed, we assumed a constant velocity. However, this is rarely the case in the real world. In the real world the velocity of an object in motion is often changing.
What is acceleration?
Acceleration is the measurement of change in an object's velocity. When you press down on the gas pedal in a car, the car surges forward going faster and faster. This change in velocity is acceleration.
The equation for calculating acceleration is:
Acceleration = (change in velocity)/(change in time)
a = Δv ÷ Δt
How to Measure Acceleration
The standard unit of measurement for acceleration is meters per second squared or m/s2. You can calculate this from the above formula where velocity is meters per second and time is in seconds.
Acceleration is a Vector
In physics acceleration not only has a magnitude (which is the m/s2 number we discussed above), but also has a direction. This makes acceleration a vector.
Force and Acceleration
Newton's second law of motion states that the force on an object equals the mass times the acceleration. This is written in the following equation:
Force = mass * acceleration
F = ma
We can use this formula to also figure out the acceleration if we know the mass and force on an object. This formula is:
acceleration = force/mass
a = F/m
When an object is changing velocity by a constant amount over time, this is called constant acceleration. An object with constant positive acceleration will be going faster and faster. Its velocity will be increasing constantly.
An example of constant acceleration of 5 m/s2
Free Fall: A Type of Acceleration
One example of constant acceleration is an object in free fall. During free fall, gravity applies a constant force on the object causing a constant increase in velocity. If you were to measure the distance an object fell, each second it would fall further because it is constantly picking up speed.
Note: In the real world there would be the additional force of air friction on the object. At some point the object would reach "terminal velocity". This means that it would no longer accelerate and the speed of the fall would stay the same. The terminal velocity of a skydiver falling face down is around 122 miles per hour.
The average acceleration is the total change in velocity divided by the total time. This can be found using the equation a = Δv ÷ Δt.
For example, if the velocity of an object changes from 20 m/s to 50 m/s over the course of 5 seconds the average acceleration would be:
a = (50 m/s - 20 m/s) ÷ 5s
a = 30 ms ÷ 5s
a = 6 m/s2
Deceleration or Negative Acceleration
When the velocity of an object decreases (slows down) this is called deceleration. It may also be represented by a negative acceleration. This means the direction or vector of the acceleration is pointing in the opposite direction of the movement of the object.
For example, if the velocity of an object changes from 40 m/s to 10 m/s over a time interval of 2 seconds the average acceleration would be:
a = (10 m/s - 40 m/s) ÷ 2s
a = -30 ms ÷ 2s
a = -15 m/s2
This could also be called a deceleration of 15 m/s2.
More Physics Subjects on Motion, Work, and Energy
Science >> Physics for Kids |
5.1 Vector Addition and Subtraction: Graphical Methods
True or False—We can use Pythagorean theorem to calculate the length of the resultant vector obtained from the addition of two vectors which are at right angles to each other.
True or False—The direction of the resultant vector depends on both the magnitude and direction of added vectors.
5.2 Vector Addition and Subtraction: Analytical Methods
What is the dimensionality of vectors used in the study of atmospheric sciences?
5.3 Projectile Motion
After a projectile is launched in the air, in which direction does it experience constant, non-zero acceleration, ignoring air resistance?
- The x direction
- The y direction
- Both the x and y directions
- Neither direction
A ball is thrown in the air at an angle of 40°. If the maximum height it reaches is 10 m, what must be its initial speed?
- 17.46 m/s
- 21.78 m/s
- 304.92 m/s
- 474.37 m/s
5.4 Inclined Planes
For objects of identical masses but made of different materials, which of the following experiences the most static friction?
- Shoes on ice
- Metal on wood
- Teflon on steel
If an object sits on an inclined plane and no other object makes contact with the object, what is typically equal in magnitude to the component of the weight perpendicular to the plane?
- The normal force
- The total weight
- The parallel force of weight
A 5 kg box is at rest on the floor. The coefficient of static friction between the box and the floor is 0.4. A horizontal force of 50 N is applied to the box. Will it move?
- No, because the applied force is less than the maximum limiting static friction.
- No, because the applied force is more than the maximum limiting static friction.
- Yes, because the applied force is less than the maximum limiting static friction.
- Yes, because the applied force is more than the maximum limiting static friction.
A skier with a mass of 67 kg is skiing down a snowy slope with an incline of 37°. Find the friction if the coefficient of kinetic friction is 0.07.
- 27.66 N
- 34.70 N
- 36.71 N
- 45.96 N
5.5 Simple Harmonic Motion
A change in which of the following is an example of deformation?
The units of amplitude are the same as those for which of the following measurements?
- Oscillation will not happen in the absence of friction.
- Oscillation will continue forever in the absence of friction.
- Oscillation will have changing amplitude in the absence of friction.
- Oscillation will cease after a certain amount of time in the absence of friction. |
- 1. SE Introduction - TI
A brief overview of the following chapters.
- 2. SE Functions, Limits, and Continuity
This chapter informs students about basic graphing techniques, allowing them to better understand the beginning principles of Calculus, including compound interest, the Fundamental Theorem of Calculus and limits.
- 3. SE Differentiation - TI
This chapter students investigate the sinusoidal function, map a pendulum’s acceleration and velocity using a cosine function, and explore the Chain Rule.
- 4. SE Applications of Derivatives - TI
This chapter explores relative maximums and minimums, the second derivative test, and optimization.
- 5. SE Integration - TI
This chapter covers Riemann sums and definitive integration in order to find or approximate the area under a curve. Students are also led to discover the Fundamental Theorem of Calculus.
- 6. SE Applications of Integration - TI
This chapter introduces students to the Solve and Integral commands in order to find areas as well as finding cross plane volumes and arc lengths.
- 7. SE Transcendental Functions - TI
This chapter allows students to find the inverse of a function through various methods. Also covered are logarithmic derivatives.
- 8. SE Integration Techniques - TI
This chapter covers the methods of integration by substitution and by parts. Finally, students will use the deSolve command to solve differential equations.
- 9. SE Infinite Series - TI
This chapter completes the course by exploring series and infinite series, with emphasis on the Taylor polynomial. Also covered is a brief review of the course material in preparation for the AP Calculus exam. |
1 What is a nested loop
The so-called nested loop is that the main part of an outer loop is an inner loop . Inner loop or outer loop can be any type , for example while Cycle or for loop . for example , external for
A loop can contain a while loop , vice versa . The outer loop can contain multiple inner loops . There is no limit to the cycle chain .
In nested loops , The number of iterations will be equal to the number of iterations in the outer loop multiplied by the number of iterations in the inner loop . In each iteration of the outer loop , The inner loop performs all its iterations .
For each iteration of the outer loop , The inner loop restarts and completes its execution before the outer loop can continue to the next iteration . Nested loops are often used to handle multidimensional data structures , For example, print a two-dimensional array , Iterates over a list that contains nested lists . Nested loops are part of the control flow statement , Can help you understand
Python Basic knowledge of .
2 Python nesting for loop
stay Python in ,for Loops are used to iterate sequences , Example list , character string , tuple , And other iteratable objects , For example, scope . stay Python Use nesting in for Circular syntax ：
# outer for loop for element in sequence # inner for loop for element in
sequence: body of inner for loop body of outer for loop
In this example , We are for Used in the loop for loop . In this case , We print the multiplication table of the first ten numbers .
* external for Recycling range() First ten digits of function iteration .
* For each external number , inside for The loop will be executed ten times .
* In the body of the inner loop , We will print the product of the external number and the current number .
* The inner loop is just the main body of the outer loop .
Examples ： Write a nested for Loop program to Python Print multiplication table in .
# outer loop for i in range(1, 11): # nested loop # to iterate from 1 to 10
for j in range(1, 11): # print multiplication print(i * j, end=' ') print()
* In this program , external for The loop is from 1 reach 10 Iterative number . range() return 10 Number . So the total number of iterations of the outer loop is 10.
* Nested in the first iteration , The number is 1. Next time , It is 2. And so on , until 10.
* next , For each iteration of the outer loop , The inner loop will be executed ten times . The internal loop will also be executed 10 second , Because the multiplication table we print is at most 10.
* In each iteration of the internal loop , We calculated the multiplication of two numbers .
2.1 Nested loop print pattern
Another of the most common uses of nested loops is to print various star and number patterns . Let's see how to use nested loops in Python Print the following modes in .
rows = 5 # outer loop for i in range(1, rows + 1): # inner loop for j in
range(1, i + 1): print("*", end=" ") print('')
* In this program , The outer loop is the number of lines printed .
* The number of rows is five , So the outer loop will be executed five times .
* next , The inner loop is the total number of columns in each row .
* For each iteration of the external loop , The column count increases 1.
* In the first iteration of the outer loop , The number of columns is 1, Next time 2. And so on .
* The internal loop iteration is equal to the number of columns .
* In each iteration of the internal loop , We print star.
2.2 stay for In loop while loop
Using another type of loop in one loop is very common and helpful . We can for Place one in the loop while loop . Suppose we want to repeat each name in the list five times ：
* here , We will use external for Loop iteration list .
* Outer layer for Loop each iteration , Inner layer for Loop execution 5 second , Print current name 5 second . names = ['Kelly', 'Jessa', 'Emma'] #
outer loop for name in names: # inner while loop count = 0 while count < 5:
print(name, end=' ') # print(name) # increment counter count = count + 1 print()
2.3 practice ： Print a with 5 that 's ok 3 Rectangular pattern of column stars
Print the following star rectangle ：
# 5 rows for name in range(5): # 3 column for j in range(3): print('*',
3 Breaking nested loops
break Statement is used to exit a loop inside a loop . If used within a nested loop break sentence （ Cycle in another cycle ）, It will terminate the innermost loop .
In the following example , We have two cycles . external for Recycling range() First four digits of function iteration , inside for The loop also iterates over the first four digits .
If the external number is the same as the current number of the internal cycle , Then interrupt the internal （ nesting ） loop .
for i in range(4): for j in range(4): if j == i: break print(i, j)
4 Continue nested loop
continue Statement skips the current iteration and moves to the next iteration . stay Python in , When encountered in the loop continue
Statement time , It skips all statements below it and immediately jumps to the next iteration .
In the following example , We have two cycles . external for
Loop iteration first list , The inner loop also iterates over the second numeric list . If the external number is the same as the current number of the internal cycle , Then move to the next iteration of the internal loop .
first = [2, 4, 6] second = [2, 4, 6] for i in first: for j in second: if i ==
j: continue print(i, '*', j, '= ', i * j)
5 Single line nested loops understood using lists
for example , If you have two lists and want to get all their combinations , To achieve this , You need to use two nested loops , As described below .
first = [2, 3, 4] second = [20, 30, 40] final = for i in first: for j in
second: final.append(i+j) print(final)
You can write faster using list compression and nested loops , More compact code , As shown below .
first = [2, 3, 4] second = [20, 30, 40] final = [i+j for i in first for j in
Coding ideas ：
* first , Write an external for loop , It iterates over the first list , as [for i in first].
* next , Write an internal loop , It iterates over the second list after the external loop , for example [for i in first for j in second].
* last , Calculate the sum of outer and inner numbers , as [i+j for i in first for j in second].
* last , Store the results in a new list , for example final = [i+j for i in first for j in second].
Let's look at other examples ：
In this example , We will use two in the list for loop , The end result will be a list . We will not include the same number in each list . We will use if Filter them conditionally .
final = [[x, y] for x in [10, 20, 30] for y in [30, 10, 50] if x != y]
6 Python Nesting in while loop
stay Python in ,while A loop statement repeats a block of code when a particular condition is true . When the number iteration is not fixed , We use while loop . In this section , We'll learn how to work in another
while Use in circulation while loop . stay Python Write nested while The syntax of the loop statement is as follows ：
while expression: while expression: statement(s) statement(s)
In the following example , We will print before each line 10 Number 5 second .
i = 1 while i <= 5: j = 1 while j <= 10: print(j, end='') j = j + 1 i = i + 1
6.1 While In cycle for loop
Sometimes it's helpful to use one loop in another . We can while Put one in the loop for loop . Suppose we want to print from 1 reach 100 All the perfect numbers .
* here , We will use while Before loop iteration 100 Number .
Outside while In each iteration of the loop , inside for Cycle from 1 To current external digital execution , To check if the current number is perfect .（ Perfect number is a mathematical concept , Interested readers can further inquire ）
print('Show Perfect number fom 1 to 100') n = 2 # outer while loop while n <=
100: x_sum = 0 # inner for loop for i in range(1, n): if n % i == 0: x_sum += i
if x_sum == n: print('Perfect number:', n) n += 1
7 When Python Using nested loops in ?
* When you have nested arrays or lists that need to loop through the same function , Nested loops are convenient .
* When you want to print different star and number patterns using rows and columns .
Remember time complexity . Let's pass Python Nested in for An example of how a loop works to understand this . We use for A cyclic iterative sequence or a given element that can be iterated .
Just like I'm on the list . The time complexity here is
O(n), Because we are iterating over all the items in the list . Perform steps （ iteration ） The number of determines the time complexity of the loop . When you use nested loops and there are no external and internal loops if
Run time under conditions , The time complexity is O(n^2), Because for all n Elements , The code will execute n second .
numbers = [[1, 2, 3], [4, 5, 6]] cnt = 0 for i in numbers: for j in i:
print('iteration', cnt, end=': ') print(j) cnt = cnt + 1
If you give a condition in the inner loop , This condition will stop executing after some elements , And does not execute all of the internal or external loops n Second iteration , Then its time complexity will be less .
Use nested loops when you don't have a better choice , Remember that writing efficient and compact code is far better than writing complex code . |
function of the algebra of logic
A function whose arguments, as well as the function itself, assume values from a two-element set (usually ). Boolean functions are one of the main subjects of discrete mathematics, in particular, of mathematical logic and mathematical cybernetics. Boolean functions first occurred in the mathematical formulation of logical problems, and were named after G. Boole, who laid the foundation for the applications of mathematics in logic in the middle of the 19th century; cf. Algebra of logic.
One such problem is the construction of an algebra of propositions. To this purpose, one of the two values 0 ( "false" ) or 1 ( "true" ) is assigned to each proposition; the principal logical relations "and" , "or" , "not" , "if … then" , etc., can then be regarded as the respective "elementary" Boolean functions: , , , , etc. When this is done, the value of any complex proposition, constructed with the aid of the fundamental logical connectives from given propositions, is a Boolean function of the values of these propositions. Such a Boolean function is a composition of elementary Boolean functions corresponding to the logical connectives forming part of the complex proposition. It became clear later that the language of Boolean functions is suited for a description of the operation of discrete control systems (cf. Control system) such as contact schemes, diagrams of functional elements, logical networks, switching networks, etc. These control systems are constructed in accordance with certain rules from a number of initial elements, just as complex statements are constructed from simple ones. The rules governing the construction of such control systems as well as the operation of the initial elements are such that the operation of complex control systems can be described with the aid of Boolean functions. Boolean functions are also used in certain problems of integer programming that reduce to solving a system of Boolean equations of the form
where the , are Boolean functions. There are also other ways of using Boolean functions in discrete mathematics, so that the study of Boolean functions is of interest in its own right.
An essential feature in solving problems related to Boolean functions is the method of specifying Boolean functions. There are several such methods: tables, formulas, special classes of formulas known as normal forms (cf. Boolean functions, normal forms of), subsets of the vertices of an -dimensional unit cube, etc. In the last-named case every selection of length of values of the arguments (0 or 1) is regarded as a vertex of the -dimensional unit cube, in which case a Boolean function of arguments can be defined by the subset of the corners at which it assumes the value "1" . This subset, when written out as a matrix whose rows are selections of values of the arguments of the Boolean function, is known as a Boolean matrix. If a Boolean function describes the operation of control systems, the latter can also be regarded as a method of specifying the Boolean function. One usually says that this control system realizes the given Boolean function. The realization of Boolean functions by many kinds of control systems is closely related to a large number of problems, such as synthesis, minimization, control and reliability problems, etc. Another type of problem arises in the study of properties and classes of Boolean functions specified by different methods; this is the study of the metric characterizations of various classes of normal forms of Boolean functions and the related geometrical properties of the -dimensional unit cube (cf. Boolean functions, metric theory of), as well as of the various algebras of Boolean functions (cf. Many-valued logic; Equivalent transformations). The system of all classes of Boolean functions that are closed under composition was described by E. Post. It forms a countably-infinite lattice with five maximal (pre-complete) classes.
In certain cases it may be necessary to consider partial (i.e. not everywhere-defined) Boolean functions for which the problems listed have a specific character.
|||P.S. Novikov, "Elements of mathematical logic" , Oliver & Boyd and Acad. Press (1964) (Translated from Russian) MR0164868 Zbl 0113.00301|
|||S.V. Yablonskii, G.P. Gavrilov, V.B. Kudryavtsev, "Functions of the algebra of logic and Post classes" , Moscow (1964) (In Russian)|
|[a1]||P.L. Hammer, S. Rudeanu, "Boolean methods in operations research" , Springer (1968) MR0235830 Zbl 0155.28001|
|[a2]||S. Rudeanu, "Boolean functions and equations" , North-Holland (1974) MR0484821 Zbl 0321.06013|
Boolean function. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Boolean_function&oldid=24380 |
What is the use of Startswith function?
STARTSWITH is a string manipulation function that manipulates all string data types (BIT, BLOB, and CHARACTER), and returns a Boolean value to indicate whether one string begins with another.
How do I use Startswith and Endswith in Python?
There are two built-in methods in Python to do the task. These are startswith() and endswith() methods. If any string starts with a given prefix then startswith() method will return true otherwise returns false and if any string ending with a given suffix then endswith() method will return true otherwise returns false.
Is Startswith case sensitive Python?
So the startswith() function is case sensitive; that is why It will give us the false in the output. So, the startswith() method returns True if a string starts with the specified prefix(string).
What is return value of function Startswith pattern?
startswith() Return Value
startswith() method returns a boolean. It returns True if the string starts with the specified prefix. It returns False if the string doesn’t start with the specified prefix.
What does find () mean in Python?
Definition and Usage
The find() method finds the first occurrence of the specified value. The find() method returns -1 if the value is not found. The find() method is almost the same as the index() method, the only difference is that the index() method raises an exception if the value is not found. (
Can I use startsWith JS?
The startsWith() method returns true if a string begins with a specified string, otherwise false . The startsWith() method is case sensitive.
What does any () do in Python?
Python any() function returns True if any of the elements of a given iterable( List, Dictionary, Tuple, set, etc) are True else it returns False. Parameters: Iterable: It is an iterable object such as a dictionary, tuple, list, set, etc. Returns: Python any() function returns true if any of the items is True.
Is there a starts with function in Python?
The startswith() string method checks whether a string starts with a particular substring. If the string starts with a specified substring, the startswith() method returns True; otherwise, the function returns False.
What are the 3 types of numbers in Python?
There are three distinct numeric types: integers, floating point numbers, and complex numbers.
How do you lower a function in Python?
lower() is a built-in Python method primarily used for string handling. The . lower() method takes no arguments and returns the lowercased strings from the given string by converting each uppercase character to lowercase. If there are no uppercase characters in the given string, it returns the original string.
How do you use substring in Python?
Python String Substring
- start: The index position at which our slice should begin. This is 0 by default.
- end: The position at which the slice ends. The character at the end position is not included in the slice. …
- step: Instructs the slice to ignore every Nth character. N is equal to the step you specify.
How do you lower a string in Python?
The Python lower() function converts a string to all lowercase. The Python isLower() method will check if the alphabetical characters in a string are all lowercase and return True or False. The lower() and isLower() functions are useful for fields like email where all letters should be lowercase. |
Probability can be used for more than calculating the likelihood of one event; it can summarize the likelihood of all possible outcomes.
A thing of interest in probability is called a random variable, and the relationship between each possible outcome for a random variable and their probabilities is called a probability distribution.
Probability distributions are an important foundational concept in probability and the names and shapes of common probability distributions will be familiar.
The structure and type of the probability distribution varies based on the properties of the random variable, such as continuous or discrete, and this, in turn, impacts how the distribution might be summarized or how to calculate the most likely outcome and its probability.
In this post, you will discover a gentle introduction to probability distributions.
After reading this post, you will know:Let’s get started.
A Gentle Introduction to Probability DistributionsPhoto by Tom Long, some rights reserved.
This tutorial is divided into four parts; they are:A random variable is a quantity that is produced by a random process.
In probability, a random variable can take on one of many possible values, e.
events from the state space.
A specific value or set of values for a random variable can be assigned a probability.
In probability modeling, example data or instances are often thought of as being events, observations, or realizations of underlying random variables.
— Page 336, Data Mining: Practical Machine Learning Tools and Techniques, 4th edition.
A random variable is often denoted as a capital letter, e.
X, and values of the random variable are denoted as a lowercase letter and an index, e.
x1, x2, x3.
Upper-case letters like X denote a random variable, while lower-case letters like x denote the value that the random variable takes.
— Page viii, Probability: For the Enthusiastic Beginner, 2016.
The values that a random variable can take is called its domain, and the domain of a random variable may be discrete or continuous.
Variables in probability theory are called random variables and their names begin with an uppercase letter.
[…] Every random variable has a domain—the set of possible values it can take on.
— Page 486, Artificial Intelligence: A Modern Approach, 3rd edition, 2009.
A discrete random variable has a finite set of states: for example, colors of a car.
A random variable that has values true or false is discrete and is referred to as a Boolean random variable: for example, a coin toss.
A continuous random variable has a range of numerical values: for example, the height of humans.
A value of a random variable can be specified via an equals operator: for example, X=True.
The probability of a random variable is denoted as a function using the upper case P or Pr; for example, P(X) is the probability of all values for the random variable X.
The probability of a value of a random variable can be denoted P(X=True), in this case indicating the probability of the X random variable having the value True.
A probability distribution is a summary of probabilities for the values of a random variable.
As a distribution, the mapping of the values of a random variable to a probability has a shape when all values of the random variable are lined up.
The distribution also has general properties that can be measured.
Two important properties of a probability distribution are the expected value and the variance.
Mathematically, these are referred to as the first and second moments of the distribution.
Other moments include the skewness (3rd moment) and the kurtosis (4th moment).
You may be familiar with the mean and variance from statistics, where the concepts are generalized to random variable distributions other than probability distributions.
The expected value is the average or mean value of a random variable X.
This is the most likely value or the outcome with the highest probability.
It is typically denoted as a function of the uppercase letter E with square brackets: for example, E[X] for the expected value of X or E[f(x)] where the function f() is used to sample a value from the domain of X.
The expectation value (or the mean) of a random variable X is denoted by either E(X)— Page 134, Probability: For the Enthusiastic Beginner, 2016.
The variance is the spread of the values of a random variable from the mean.
This is typically denoted as a function Var; for example, Var(X) is the variance of the random variable X or Var(f(x)) for the variance of values drawn from the domain of X using the function f().
The square root of the variance normalizes the value and is referred to as the standard deviation.
The variance between multiple two variables is called the covariance and summarize the linear relationship for how two random variables change together.
Each random variable has its own probability distribution, although the probability distribution of many different random variables may have the same shape.
Most common probability distributions can be defined using a few parameters and provide procedures for calculating the expected value and the variance.
The structure of the probability distribution will differ depending on whether the random variable is discrete or continuous.
A discrete probability distribution summarizes the probabilities for a discrete random variable.
The probability mass function, or PMF, defines the probability distribution for a discrete random variable.
It is a function that assigns a probability for specific discrete values.
A discrete probability distribution has a cumulative distribution function, or CDF.
This is a function that assigns a probability that a discrete random variable will have a value of less than or equal to a specific discrete value.
The values of the random variable may or may not be ordinal, meaning they may or may not be ordered on a number line, e.
counts can, car color cannot.
In this case, the structure of the PMF and CDF may be discontinuous, or may not form a neat or clean transition in relative probabilities across values.
The expected value for a discrete random variable can be calculated from a sample using the mode, e.
finding the most common value.
The sum of probabilities in the PMF equals to one.
Some examples of well known discrete probability distributions include:Some examples of common domains with well-known discrete probability distributions include:A continuous probability distribution summarizes the probability for a continuous random variable.
The probability distribution function, or PDF, defines the probability distribution for a continuous random variable.
Note the difference in the name from the discrete random variable that has a probability mass function, or PMF.
Like a discrete probability distribution, the continuous probability distribution also has a cumulative distribution function, or CDF, that defines the probability of a value less than or equal to a specific numerical value from the domain.
As a continuous function, the structure forms a smooth curve.
Some examples of well-known continuous probability distributions include:Some examples of domains with well-known continuous probability distributions include:This section provides more resources on the topic if you are looking to go deeper.
In this post, you discovered a gentle introduction to probability distributions.
Specifically, you learned:Do you have any questions?.Ask your questions in the comments below and I will do my best to answer. |
A basic goal of zoology is to explain the distribution and abundance of animals. During 1999, behavioral factors such as feeding and mate selection and environmental factors including temperature and pollution were shown to affect distribution and abundance in animals ranging from zooplankton to insects, amphibians, and seals.
Over the years marine biologists have proposed several explanations to account for the geographic distribution and diversity of zooplankton in the world’s oceans. Until 1999, however, none of the explanations had been quantitatively tested on a large scale. One widely held perception regarding zooplankton was that species diversity of one-celled microbes called planktic foraminifera decreases steadily from the warm tropical seas at the Equator toward the icy waters at each pole. Scott Rutherford and Steven D’Hondt of the University of Rhode Island and Warren Prell of Brown University, Providence, R.I., tested this assumption. They selected 1,252 samples of foraminifera and analyzed many environmental variables to determine which factors were most influential in determining distribution patterns of these animals. Their results showed that the notion of greatest diversity at the Equator was incorrect; planktic foraminifera were most diverse at middle latitudes. This held true in all oceans, along with the lowest diversity’s being seen at the poles and intermediate diversity at the Equator. Analyses of ocean temperatures in the Atlantic revealed that almost 90% of the variation in diversity could be explained by temperature alone. Furthermore, the greater diversity at middle latitudes was found to be the result of that region’s thicker thermocline—the layer of water separating the warm surface from the colder depths below. The thermocline’s greater thickness allows for more ecological niches, which in turn results in a greater diversity of species.
On a more localized scale, Perri K. Eason and Gary A. Cobbs of the University of Louisville, Ky., and Kristin G. Trinca of Northeast Louisiana University conducted field experiments with cicada-killer wasps (Sphecius speciosus) to confirm anecdotal reports that naturally occurring landmarks are used to define territorial boundaries. Adult male wasps emerge in late summer before the females, with the males setting up mating territories that they defend against other males. Emergent females generally mate immediately with an available territorial male. To test the importance of visual landmarks in territorial behaviour, the investigators caught, marked (with patterns of coloured dots), and released 62 male wasps into a flat, grassy lawn with no obvious landmarks. The researchers then laid 30 randomly placed 90-cm (3-ft) dowels on the lawn to serve as landmarks in the otherwise homogeneous habitat. The next morning the researchers found that the wasps had defined 42 territories within the study area, using the dowels as boundaries, and none of the wasps had crossed into another territory. Further observation showed that wasps defending territories marked by dowels on two sides but with no such boundary on the other two spent significantly more time defending the unbounded sides (19% to 3%). One conclusion offered by the investigators was that the use of natural landmarks to define territorial boundaries could have evolved because of the reduction in costs of territorial defense.
Perceived declines of herpetofauna (reptiles and amphibians) worldwide have generated concern among conservation biologists for several years. Declines in population and in the number of species have been reported, and many of these declines had been inexplicable. Research in the past year provided insight into the variety of factors that can negatively affect animal populations, thus emphasizing the complexity of global ecology. Recent warming trends were implicated in herpetofaunal declines by the team of J. Alan Pounds and Michael P. L. Fogden of the University of Miami, Fla., and the Tropical Science Center, Costa Rica, and John H. Campbell of the Tropical Science Center, who used a global climate model to determine if events such as the disappearance of the Costa Rican golden toad (Bufo periglenes) during the late 1980s could be explained. The investigators concluded that population crashes observed in several species of frogs and other vertebrates in the region were linked to a reduction in the frequency of mists during the dry season, which in turn was correlated with ocean surface temperatures in the equatorial Pacific.
A more specific, biological cause for frog deaths was determined by Karen R. Lipps of Southern Illinois University at Carbondale, who reported mass mortality of amphibians along streams in Panama. Frogs of several species were abundant when sampled in 1993–95, but by 1997 few frogs of any species could be found. The researcher necropsied 18 dead specimens and discovered that all were infected with a specific fungus associated with amphibian deaths in other parts of the world. Lipps hypothesized that this fungus—a chytridiomycete—could also be responsible for the declines of frogs in Costa Rica.
Test Your Knowledge
Fish in the Sea: Fact or Fiction?
In the United States a combination of field observations and laboratory experiments was used by two sets of investigators to establish that abnormal limb development in frogs can be caused by parasitic flatworms called trematodes. Stanley K. Sessions, R. Alan Franssen, and Vanessa L. Horner of Hartwick College, Oneonta, N.Y., analyzed deformities (extra legs) found in five species of frogs to determine if retinoids were responsible. Retinoids are potent teratogens, or inducers of deformities, that are similar to some pesticides, and retinoids had previously been implicated in reports of deformed amphibians. Analysis of the abnormal frogs, however, revealed that the deformities were related almost exclusively to infestations of a trematode (Ribeiroia), not to retinoids.
A sample of 1,686 long-toed salamanders (Ambystoma macrodactylum) that also displayed limb deformities supported the conclusion of the frog research. Pieter T.J. Johnson and colleagues at Stanford University and James Cook University, North Queensland, Australia, observed abnormal limb development and low survivorship in Pacific tree frogs (Hyla regilla) experimentally exposed to concentrations of trematodes comparable to those found at field sites. The abnormal limb development was similar to that observed in frogs of the same species at field sites in California that harboured an aquatic snail (Planorbella tenuis). The snail is the primary host of the same trematode, and increases in both snail abundance and parasite infections had previously been shown to occur in response to some forms of pollution. Thus, amphibian deformities may not be caused directly by pollution but as a consequence of it via snails and trematodes.
Although specific causes for declines can be identified in some cases, the intensity of the effects may result from lowered resistance due to other environmental stressors. Evidence of such a sublethal effect was provided by William A. Hopkins and Justin D. Congdon of the University of Georgia Savannah River Ecology Laboratory and Chistopher L. Rowe of the University of Puerto Rico. They compared trace element concentrations of toxic elements arsenic, cadmium, and selenium in two populations of banded water snakes (Nerodia fasciata). Snakes from a site polluted by coal-combustion wastes were compared with snakes of the same species from an unpolluted reference site. Snakes from the polluted habitat were found to have significantly higher levels of all three toxins in their livers than snakes from the unpolluted site. Concentrations of toxic elements at the polluted site were also dramatically higher than normal in tadpoles, a major prey of the snakes. One sublethal effect measured was that snakes from the polluted site had metabolic rates 32% higher than those from the unpolluted habitat. This indicates that a disproportionate amount of the snakes’ energy was being allocated to maintaining their health rather than to reproduction, growth, and energy storage. The resulting lowered resistance would presumably make them more susceptible to other forms of physical, chemical, or biological hazards.
In Antarctica, Randall W. Davis of Texas A&M University at Galveston and colleagues provided information on the underwater hunting behaviour of Weddell seals (Leptonychotes weddellii). Although extensive research had been conducted on the predation strategies used by carnivores on land, little comparable information was available for large marine carnivores. Weddell seals commonly dive to depths of 100–350 m (330–1,300 ft) for periods of up to 25 minutes. Consequently, where and how these seals find prey during the dive was unknown. The investigators placed data-collection equipment (video systems and data recorders for depth, speed, direction, and sound) on four adult seals to record their hunting behaviour beneath the Antarctic ice. The seals were found to stalk cod and other fish by diving beneath them to take advantage of backlighting from the surface ice and even blowing bubbles into ice crevices to flush out small fish (Pagothenia borchgrevinki). The study not only revealed previously unobserved behaviour in seals but underscored the research opportunities available through use of customized technologies.
The politics surrounding the genetic engineering of plants became rancorous in 1999. In many Western European countries, trials of genetically modified (GM) crops were destroyed by protesters concerned about the impact of the plants on the environment as well as on human health. For the first time, the European Union’s scientific advisers recommended that a GM potato plant be withheld from commercial use because the group could not guarantee that the potato’s marker gene, which provides resistance to an antibiotic, would not spread to other organisms. France withdrew consent for a GM corn (maize) plant pending a review of the dangers of antibiotic resistance in human health.
In this volatile atmosphere, scientists at Cornell University, Ithaca, N.Y., made headline news when they revealed that in their experiments pollen from corn that had been genetically engineered to protect GM crops against insect pests also killed monarch butterfly caterpillars, which are harmless. The toxin used, called Bt, is produced naturally by a bacterium (Bacillus thuringiensis) and had been used for years as a biopesticide. The Bt in the experiment, however, was engineered into corn so that the plant itself produced the toxin. “This is a warning bell,” said one of the authors, Linda Rayor. “What is really new in this research is that we have shown that toxins can float in the wind.”
Further worries over GM safety were raised by research suggesting that unrelated plants can, in exceptionally rare instances, exchange DNA by means of go-betweens such as fungi, viruses, or aphids. In late 1998 it was reported that Jeff Palmer and his team at Indiana University had discovered a “stowaway” gene segment in a number of unrelated plants. They suggested that the gene segment may have originated in fungi and subsequently been transported between plants by aphids or viruses.
Genetic Engineering: Putting Plants to Work
Despite the controversy, GM crop research advanced, with some of it actually promising to benefit the environment. GM tobacco plants were designed at the University of Cambridge to break down soil residues of the explosives TNT and nitroglycerin. A plant gene that allows plants to soak up toxic heavy metals from soils and store them in leaves was identified by researchers at the University of California, San Diego. The goal was to breed plants that could be harvested with the metals locked inside them and thus eliminate these pollutants from the environment.
One plant’s power to take up minerals could also be used for extracting gold from the ground. Ecologists in New Zealand reported late in 1998 that Indian mustard plants readily absorb gold dissolved in ammonium thiocyanate, a liquid commonly used in traditional mining to process gold ore. They hoped the method could one day be used commercially by harvesting the gold-loaded mustard plants, burning them in incinerators, and extracting gold from the ash.
The ability of plants to concentrate and store minerals from the soil could also be used to ward off anemia in people who suffer diet-related iron deficiency. By adding a gene for an iron-storing protein to rice plants, Japanese scientists hoped to develop a GM rice that would be rich in iron.
Scientists at CBD Technologies of Rehovot, Israel, claimed to have developed GM trees and other plants that grow up to 50% faster than usual. They inserted a bacterial gene, called the cellulose-binding domain, that affects the way that cellulose is manufactured and thereby results in faster and broader growth. The company expected the technique to be commercially available within five years.
A new generation of “designer flowers” was already on the way, thanks to genetic engineering. An Australian company, Florigene of Melbourne, developed GM violet carnations for sale in late 1999, and they hoped to develop a black carnation in 2000. Meanwhile, geneticists at the Salk Institute for Biological Studies, La Jolla, Calif., discovered a gene, called LEAFY, that acts as a master switch for flower development, telling the plant when and where to make a flower. By altering reproductive organs, the gene also determines what the flower will look like.
At a conference on floral scents at the University of Oxford, it was announced that different scents could be engineered into flowers. Philadelphia-based NovaFlora inserted a gene into roses that was to make them smell of lemons. The gene codes for an enzyme called limonene synthase, which citrus plants use to make scent molecules.
Physiology, Ecology, and Evolution
Plant physiologists continued to throw fascinating new light on the way plants combat disease. Belgian scientists detected “hot spots” on the leaves of plants infected with tobacco mosaic virus. These areas were about 0.4° C (0.72° F) warmer than their surroundings and corresponded to areas where the plant was killing its own cells with salicyclic acid, a hormone that prevents the invading virus from spreading. How the extra heat was created was not certain, but the effect appeared eight hours before any other symptom and could therefore be useful for early diagnosis of infection.
Ecologists revealed that plants create a type of smog that had previously been thought to be man-made. According to German researchers, plants release toluene when they are suffering injury or lack of nutrients, and whole forests may be creating their own clouds of natural “pollution.”
Australian scientists dated the origins of complex cells to 2.7 billion years ago, a billion years earlier than previously thought. In western Australia they discovered modified steroids within ancient shales. Steroid compounds are produced only by eukaryotes, organisms with complex cells containing a nucleus. The organism that produced the compounds may be the ancestor of all algae, fungi, plants, and animals. The discovery thus opened a new window on the earliest forms of life.
The extinction of plant species continued to send shock waves through international conservation organizations as the World Conservation Union announced in 1999 that a quarter of the world’s coniferous species were under threat. Many of these trees had changed little since the age of the dinosaurs, and some of the oldest living plants on Earth were conifers.
The aphorism “Like dissolves like” is a useful guide to solubility. Accordingly, polar molecules such as sugar will dissolve in a polar solvent such as water, whereas nonpolar molecules, such as fats and oils, will dissolve in nonpolar solvents, such as benzene. Bipolar molecules, with one end polar and the other nonpolar, present a special case. When placed in water, these bipolar, or amphiphilic, molecules seek to expose the polar end to water while hiding the nonpolar end from it. Bipolar molecules accomplish this by aggregating in two layers, with the polar ends facing the water on both sides and the nonpolar ends facing each other in the middle. This two-layer arrangement forms spontaneously and is the basic structure of cellular membranes. Water should not be able to pass through such a membrane because it would be excluded from the hydrophobic core. Water commonly permeates—enters and leaves—cells, however. How does this happen?
Real cell membranes permit the permeation of numerous substances, such as salts, nutrients, and hormones, in addition to water. Moreover, some of these substances are taken up against a concentration gradient, while the membrane continues to transmit signals in response to various molecules that bind to the outside of the membrane. This is achieved by proteins that are incorporated into the membrane. These proteins are themselves amphiphilic, having hydrophobic portions that insert into the nonpolar core of the membrane, as well as hydrophilic portions that extend into the water on both sides of the membrane. An analogy can be drawn between cellular membranes and brick walls with thick mortar seams. The membrane bilayer would act as the mortar seams, with the inserted proteins being the bricks. Whereas mortar is rigid, however, biological membranes are flexible, even semifluid, which allows the component molecules (the bricks) to drift freely within the membrane (the mortar).
Study of water movement through membranes reveals that different types of cells differ greatly as to permeability, a phenomenon that cannot be explained on the basis of simple diffusion. Control over the rates of water movement through cell membranes is important to all cells, from bacterial to human. It is now known that a family of membrane-associated proteins called aquaporins controls the rate of water permeation. A single molecule of aquaporin 1 (molecular weight 28,000) allows three billion water molecules per second to pass through the membrane. Aquaporin 1 is amazingly specific for water; in addition to blocking transport of other small molecules, it even blocks protons. Knowledge of the aquaporins has provided explanations for both normal and pathological processes. For example, a person’s kidneys filter almost 150 litres (about 40 gal) of liquid from the blood per day, with all but one litre or so being reabsorbed within the kidneys almost immediately. Aquaporin 2 is responsible for this massive reabsorption of water, but its activity is regulated by a hormone called vasopressin. Vasopressin causes the aquaporin to be delivered to the membranes of kidney duct cells responsible for reabsorbing water. Upon reaching the duct cell membrane, aquaporin 2 increases the flow of water into these cells. The small amount of fluid not reabsorbed is urine.
Diabetes insipidus, a disease characterized by excessive urination, is caused by faulty reabsorption of water by the kidney duct cells. It can be brought on by subnormal amounts of aquaporin 2 or by mutations in the aquaporin gene. Lithium salts, which are widely used to treat bipolar disorder (manic depression), have the side effect of causing excessive urination (polyuria). The cause is now clear; lithium salts interfere with the production of aquaporin 2. Although vasopressin operates by regulating aquaporin’s delivery to and from cell membranes, the cell can also control the concentrations of aquaporins by changing their rates of biosynthesis and degradation. Moreover, the activities of aquaporins can be modulated by slight chemical changes in the proteins themselves, giving cells, from the simplest to the most complex, a finely tuned and versatile system of controlling water transport.
Muscular Dystrophy: The NO Connection
Nitric oxide (NO), naturally produced from an amino acid by enzymes called NO synthases, serves as a signaling molecule within the body. One NO synthase in nerve cells produces NO that functions as a neurotransmitter. Another is found in certain white blood cells, and the NO that it produces helps these cells to kill invading microorganisms and virus-infected cells. The NO synthase in blood-vessel endothelial cells is responsive to the rate of blood flow, and the NO made by this enzyme causes relaxation of the vessel walls. The resultant vasodilation (increase in the diameter of the vessel) lowers blood pressure.
New evidence suggests that there is also an NO synthase in skeletal muscle cells. The NO made by this enzyme is extremely important in increasing blood flow to the working muscles so that the vital functions of waste removal and delivery of oxygen and nutrients can be met. Without the vasodilation caused by NO, muscle contraction would actually decrease blood flow to the muscle.
Muscular dystrophies of both the Duchenne and Becker varieties are linked to defects in a membrane-associated protein called dystrophin. NO synthase binds to a protein called syntropin that in turn binds to dystrophin. In this way the NO synthase is localized to the membranes of the muscle fibres—a position optimal for the delivery of NO to the surrounding blood vessels. In the Duchenne and Becker muscular dystrophies, the defective dystrophin fails to bind the syntropin-NO synthase complex, and the NO synthase remains within the cell rather than migrating to the muscle fibre membrane. The blood vessels fail to dilate; the muscles do not get the increased blood flow they need; and the muscles suffer damage.
Plants “See” Red
Not only is light a source of energy for plants, but the quality and quantity of light also provide growth signals—when seeds should germinate and when mature plants should blossom. One of the proteins that allows plants to “see” the light and to respond appropriately is phytochrome. This pigmented protein can exist in two forms, each of which can be converted to the other by light of specific wavelengths. It now appears that one of these forms of phytochrome modulates the activities of other proteins. Red light converts the inactive form of phytochrome to the active form. Far red light—longer wavelengths of red light—can convert the active phytochrome back to its inactive form. The phytochrome thus acts very much as a light-activated two-position switch, allowing the plant to sense the ratio of red to far red light and control its physiology appropriately.
How Plants Send an SOS
Plants have a very clever defense against the insects that eat them—they synthesize and secrete large amounts of volatile compounds that attract enemies (either predators or parasites) of the eater. Moreover, plants can distinguish herbivory (plant eating) from simple mechanical damage and can even tell one herbivorous insect from another, which keeps the plant from responding to a potentially beneficial herbivore (such as a seed-dispersing mammal) and allows for the attraction of only those species that prey on the insect damaging the plant. These volatile calls for help are produced by the plants in response to specific compounds, called elicitors, produced by the herbivorous insects. Sometimes an elicitor is a compound made entirely by the insect, and sometimes it is something that the insect obtained from the plant and then modified. Either way, the predators and parasites attracted to the site significantly decrease the life span and reproductive potential of the herbivore and thus provide the plant with a delayed, but effective, defense.
Recent Advances in Plant Genetics and Culture
Although Gregor Mendel may have been the first to study formally the origins and transmission of specific traits in plants, the practice of selective breeding to enhance desirable traits in “domesticated” crops has been pursued by human populations since at least the beginning of recorded time. In recent years recombinant techniques have joined the arsenal of tools applied to the task.
Recombinant DNA technology in plants has come a long way in recent years through the combined efforts of academy and industry. Improvements include new techniques for introducing foreign or modified DNA sequences into plant genomes and more efficient ways to regenerate whole plants from recombinant clones of cells cultured in the laboratory. Research goals have ranged from growing healthier grains to making plants that produce biodegradable plastic, and many of these efforts are finally beginning to bear fruit.
Potatoes for Latin America
In the past 50 years, U.S. potato yields have doubled through the combined successes of breeding, irrigation, pesticides, and fertilizers. Unfortunately, cultivation practices for the potato varieties common in many climates other than North America have not kept pace. Researchers in Latin American and European laboratories are closing the gap by using genetic engineering to modify varieties of potato commonly grown in Chile, Argentina, Uruguay, Brazil, and Cuba. For example, field tests are currently under way in Chile and Brazil for several genetically engineered lines that are resistant to the Erwinia bacterium, a serious potato pathogen. Additional strains engineered for resistance to insects and a variety of fungal, viral, or bacterial assaults also are in the works.
Improving the Cassava
Cassava is not generally considered a mainstay of nutrition in Western societies, but the leaves and starchy roots of this shrub constitute the third largest source of calories for human consumption worldwide (following rice and corn). More than 50 years ago, a group of British scientists working in East Africa initiated a program of selective breeding for cassavas that was designed to increase the size and number of edible roots per plant. Although the results of these efforts were impressive, further improvements proved difficult owing to losses from bacterial, fungal, and viral infection. Using recent improvements in plant biotechnology, however, a number of research groups are now addressing these issues. For example, one group has succeeded in creating cassava plants resistant to viral infection by engineering the plants to express replicase, an enzyme that disrupts the normal life cycle of the invading virus. If efforts such as these succeed in the field, scientists predict that yields of cassava could increase as much as 10-fold.
Engineering a Better Soybean
Soybeans are a source of a wide variety of food products in many countries. One problem with natural soy oil is its high content of polyunsaturated fatty acids, which makes it unsuitable for frying and cooking. Chemical hydrogenation has been used to convert these compounds to their monounsaturated form, oleic acid. One unfortunate side effect of this process is the production of increased concentrations of trans fatty acids, which have been linked to a number of health risks. As an alternative, researchers at the DuPont Co. have succeeded in genetically modifying soybean plants so that the all-cis oleic acid concentrations in natural seeds are raised from 25% to 85%, which thereby precludes the need for chemical hydrogenation. In short, they have developed a healthier soybean.
Vaccines from Potatoes
Recombinant vaccines, such as the popular hepatitis B series given to all children and to most adults in the U.S. and many other countries, are produced and purified from genetically modified hosts, such as yeast. These vaccines offer undeniable benefits over their predecessors, heat-killed or attenuated live virus, because there are few if any risks associated with receiving the vaccine. Unfortunately, these injectable recombinant vaccines are also expensive to produce, ship, store, and administer, so many children and adults in less-developed nations who may need them the most are least likely to receive them. In 1998 scientists in Ithaca, N.Y., engineered potatoes to express an Escherichia coli (bacterial) protein that elicited an immune response from human volunteers who ate the raw potatoes. They are now working on potatoes to provide immunity against other pathogens, such as the Norwalk virus. The benefits of such edible vaccines are clear; they should be cheap to produce, ship, and store, and no needle is needed for administration. One drawback is that the recombinant plant must be eaten raw, which has inspired researchers to look beyond potatoes for a tastier host, such as the banana.
Biotechnology—Blessing or Curse?
Recent advances in plant biotechnology have produced a stunning array of seemingly hardier plants, growing in more climates and producing more and better fruits. Some view this second generation of modified crops as a bountiful blessing, but others see it as a disguised curse. Some fear hidden dangers to those who consume the recombinant crops, whereas others worry about damage to the environment, including potential compromises of biodiversity. Similar concerns must have been raised generations ago when the first hybrid grains and chemical fertilizers were introduced. In recent years the furor over genetically modified foods in the marketplace has been particularly keen in Great Britain and other nations of the European Union, with ripples in the U.S. and other parts of Europe.
Public acceptance of genetically modified foodstuffs might be expected to be sluggish as long as the benefits of genetic engineering were enjoyed mainly by the producers rather than the consumers. Food prices in the developed world were already low enough that consumers had no real reason to care whether a particular crop was easier or cheaper to grow. Now that more of the benefits of genetic modification—improved taste, longer shelf life, and enhanced health benefits—are oriented directly toward the consumer, however, the public may prove more receptive. |
Are you looking for a way to reinforce place value concepts in an engaging way that helps your students make connections? “Run a Candy Store” is a real-life math project where students will complete eleven different place value tasks involving base ten blocks, expanded form, comparing, ordering and sorting, and more.
Ideas for Use
Math projects are an ideal way to consolidate learning. I recommend using them as an engaging activity AFTER skills have been learned rather than during learning. You will likely find that engagement is very high and that your students ask to do more of these!
There are many ways to use math projects in your classroom. Some of the most popular are:
•a small-group or pairs activity
•a guided math activity to allow you to see where your students are struggling
•a fun, rewarding way to engage your early finishers
•a low-prep, easy-to-implement activity for a substitute teacher
You might choose to print specific tasks to use during Math centers, or you might make a booklet out of all of the tasks and let your students choose which one to do when.
This resource is included in PDF format for printing and in Google Slides™️ format for digital learning. This makes it useable with Google Classroom™️.
Take a look at what you’ll find inside this math project:
TASK #1: THE PLAN
You can’t believe it! Your family is buying a candy store and YOU get to help run it! Let’s think of a name for the candy store and design a poster to advertise.
TASK#2: STOCKING THE SHELVES
Your first shipment has come in and it’s your job to stock the shelves with candy! Figure out how many of each candy was ordered.
Skills: place value chart, comparing and ordering
TASK#3: SURVEY YOUR CUSTOMERS
You decide to survey 100 kids in your school to see what kind of candy is their favorite. Interpret the graph and represent the candy with base 10 blocks.
Skills: skip-counting, base 10 blocks, graphing and data interpretation, addition, subtraction
TASK #4: THE GRAND OPENING
It’s time for the Grand Opening Event at your candy store! You have lots of fun things planned for the day. First up, spin the wheel to see what each person wins! Next, guess the number of candies in the jar!
Skills: base 10 blocks, expanded form, comparing and ordering, addition, subtraction, number words
TASK #5: THE MYSTERY GUEST
You are SO excited about the mystery guest who is handing out candy at the Grand Opening! Use the place value clues to shade the picture and discover who the mystery guest is!
Skills: tens and ones
TASK#6: THE FIRST BIG ORDER
You just got your first big customer order! Let’s take a look at the graphs to see what she would like!
Skills: skip-counting, picture graphs, data interpretation, addition
TASK#7: INVENTORY DAY
Inventory is important when you own a business! This means that we count all of the candies to see what we have available.
Skills: number words, expanded form, comparing and ordering, adding multiples of 10 and 100
TASK #8: SURPRISE BAGS
You decide to make up some surprise bags to sell! Inside each surprise bag will be a variety of candy.
Skills: skip-counting, addition
TASK #9: WORKING THE CASH REGISTER
Working at the cash register is an important job at the candy store! Figure out how much each person’s candy will cost.
Skills: skip-counting, addition, money
TASK#10: CANDY SPILL!
Oh no! The gumball machine fell over and ALL of the gumballs fell. Out! As you clean up the gumball mess, you count each color of gumball.
Skills: skip-counting, number words, addition
TASK#11: GUMMY SALES
Gummy bears and gummy fish have been the most popular candies at the store so far. Interpret the tally charts to show how many packages have sold this week.
Skills: addition, tens and ones
⭐️⭐️⭐️⭐️⭐️ "As a team we noticed a need for place value review, especially for upcoming state assessments. I used this resource during our intervention time. The students were so excited to create their candy store and I loved that they were able to work at their own pace! :)" Eric C.
⭐️⭐️⭐️⭐️⭐️ "Another fantastic project. My students loved working on this at home! One of my students even sent me a picture of an actual candy store she made! How adorable!" Chantal M.
⭐️⭐️⭐️⭐️⭐️ "I have two highly capable first graders in my math small groups, and this has been the perfect resource for them. They worked together to complete the project and it kept them engaged and gave them just the right challenge." Ashley J. |
Crystallins: A heterogeneous family of water-soluble structural proteins found in cells of the vertebrate lens. The presence of these proteins accounts for the transparency of the lens. The family is composed of four major groups, alpha, beta, gamma, and delta, and several minor groups, which are classed on the basis of size, charge, immunological properties, and vertebrate source. Alpha, beta, and delta crystallins occur in avian and reptilian lenses, while alpha, beta, and gamma crystallins occur in all other lenses.Lens, Crystalline: A transparent, biconvex structure of the EYE, enclosed in a capsule and situated behind the IRIS and in front of the vitreous humor (VITREOUS BODY). It is slightly overlapped at its margin by the ciliary processes. Adaptation by the CILIARY BODY is crucial for OCULAR ACCOMMODATION.Antibodies: Immunoglobulin molecules having a specific amino acid sequence by virtue of which they interact only with the ANTIGEN (or a very similar shape) that induced their synthesis in cells of the lymphoid series (especially PLASMA CELLS).beta-Crystallins: A class of crystallins that provides refractive power and translucency to the lens (LENS, CRYSTALLINE) in VERTEBRATES. Beta-crystallins are similar in structure to GAMMA-CRYSTALLINS in that they both contain Greek key motifs. Beta-crystallins exist as oligomers formed from acidic (BETA-CRYSTALLIN A CHAIN) and basic (BETA-CRYSTALLIN B CHAIN) subunits.beta-Crystallin B Chain: The basic subunit of beta-crystallins.gamma-Crystallins: A subclass of crystallins that found in the lens (LENS, CRYSTALLINE) of VERTEBRATES. Gamma-crystallins are similar in structure to BETA-CRYSTALLINS in that they both form into a Greek key-like structure. They are composed of monomeric subunits.Antibody Specificity: The property of antibodies which enables them to react with some ANTIGENIC DETERMINANTS and not with others. Specificity is dependent on chemical composition, physical forces, and molecular structure at the binding site.beta-Crystallin A Chain: The acidic subunit of beta-crystallins.alpha-Crystallins: A subclass of crystallins that provides the majority of refractive power and translucency to the lens (LENS, CRYSTALLINE) in VERTEBRATES. Alpha-crystallins also act as molecular chaperones that bind to denatured proteins, keep them in solution and thereby maintain the translucency of the lens. The proteins exist as large oligomers that are formed from ALPHA-CRYSTALLIN A CHAIN and ALPHA-CRYSTALLIN B CHAIN subunits.Antibodies, Viral: Immunoglobulins produced in response to VIRAL ANTIGENS.Cataract: Partial or complete opacity on or in the lens or capsule of one or both eyes, impairing vision or causing blindness. The many kinds of cataract are classified by their morphology (size, shape, location) or etiology (cause and time of occurrence). (Dorland, 27th ed)Antibodies, Bacterial: Immunoglobulins produced in a response to BACTERIAL ANTIGENS.Antibodies, Monoclonal: Antibodies produced by a single clone of cells.alpha-Crystallin A Chain: One of the subunits of alpha-crystallins. Unlike ALPHA-CRYSTALLIN B CHAIN the expression of ALPHA-CRYSTALLIN A CHAIN is limited primarily to the lens (LENS, CRYSTALLINE).Antibody Formation: The production of ANTIBODIES by proliferating and differentiated B-LYMPHOCYTES under stimulation by ANTIGENS.Antibodies, Neutralizing: Antibodies that reduce or abolish some biological activity of a soluble antigen or infectious agent, usually a virus.Antibody Affinity: A measure of the binding strength between antibody and a simple hapten or antigen determinant. It depends on the closeness of stereochemical fit between antibody combining sites and antigen determinants, on the size of the area of contact between them, and on the distribution of charged and hydrophobic groups. It includes the concept of "avidity," which refers to the strength of the antigen-antibody bond after formation of reversible complexes.Fluorescent Antibody Technique: Test for tissue antigen using either a direct method, by conjugation of antibody with fluorescent dye (FLUORESCENT ANTIBODY TECHNIQUE, DIRECT) or an indirect method, by formation of antigen-antibody complex which is then labeled with fluorescein-conjugated anti-immunoglobulin antibody (FLUORESCENT ANTIBODY TECHNIQUE, INDIRECT). The tissue is then examined by fluorescence microscopy.Antibodies, Anti-Idiotypic: Antibodies which react with the individual structural determinants (idiotopes) on the variable region of other antibodies.alpha-Crystallin B Chain: One of the alpha crystallin subunits. In addition to being expressed in the lens (LENS, CRYSTALLINE), alpha-crystallin B chain has been found in a variety of tissues such as HEART; BRAIN; MUSCLE; and KIDNEY. Accumulation of the protein in the brain is associated with NEURODEGENERATIVE DISEASES such as CREUTZFELDT-JAKOB SYNDROME and ALEXANDER DISEASE.Binding Sites, Antibody: Local surface sites on antibodies which react with antigen determinant sites on antigens (EPITOPES.) They are formed from parts of the variable regions of FAB FRAGMENTS.Lens Nucleus, Crystalline: The core of the crystalline lens, surrounded by the cortex.Amino Acid Sequence: The order of amino acids as they occur in a polypeptide chain. This is referred to as the primary structure of proteins. It is of fundamental importance in determining PROTEIN CONFORMATION.Molecular Sequence Data: Descriptions of specific amino acid, carbohydrate, or nucleotide sequences which have appeared in the published literature and/or are deposited in and maintained by databanks such as GENBANK, European Molecular Biology Laboratory (EMBL), National Biomedical Research Foundation (NBRF), or other sequence repositories.Octopodiformes: A superorder in the class CEPHALOPODA, consisting of the orders Octopoda (octopus) with over 200 species and Vampyromorpha with a single species. The latter is a phylogenetic relic but holds the key to the origins of Octopoda.HIV Antibodies: Antibodies reactive with HIV ANTIGENS.Cross Reactions: Serological reactions in which an antiserum against one antigen reacts with a non-identical but closely related antigen.Epitopes: Sites on an antigen that interact with specific antibodies.Antibodies, Neoplasm: Immunoglobulins induced by antigens specific for tumors other than the normally occurring HISTOCOMPATIBILITY ANTIGENS.Antibodies, Protozoan: Immunoglobulins produced in a response to PROTOZOAN ANTIGENS.Antibodies, Antinuclear: Autoantibodies directed against various nuclear antigens including DNA, RNA, histones, acidic nuclear proteins, or complexes of these molecular elements. Antinuclear antibodies are found in systemic autoimmune diseases including systemic lupus erythematosus, Sjogren's syndrome, scleroderma, polymyositis, and mixed connective tissue disease.Electrophoresis, Gel, Two-Dimensional: Electrophoresis in which a second perpendicular electrophoretic transport is performed on the separate components resulting from the first electrophoresis. This technique is usually performed on polyacrylamide gels.Cattle: Domesticated bovine animals of the genus Bos, usually kept on a farm or ranch and used for the production of meat or dairy products or for heavy labor.Autoantibodies: Antibodies that react with self-antigens (AUTOANTIGENS) of the organism that produced them.Electrophoresis, Polyacrylamide Gel: Electrophoresis in which a polyacrylamide gel is used as the diffusion medium.Bufonidae: The family of true toads belonging to the order Anura. The genera include Bufo, Ansonia, Nectophrynoides, and Atelopus.Immunoglobulin M: A class of immunoglobulin bearing mu chains (IMMUNOGLOBULIN MU-CHAINS). IgM can fix COMPLEMENT. The name comes from its high molecular weight and originally being called a macroglobulin.Antibodies, Fungal: Immunoglobulins produced in a response to FUNGAL ANTIGENS.Solubility: The ability of a substance to be dissolved, i.e. to form a solution with another substance. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed)Fluorescent Antibody Technique, Indirect: A form of fluorescent antibody technique commonly used to detect serum antibodies and immune complexes in tissues and microorganisms in specimens from patients with infectious diseases. The technique involves formation of an antigen-antibody complex which is labeled with fluorescein-conjugated anti-immunoglobulin antibody. (From Bennington, Saunders Dictionary & Encyclopedia of Laboratory Medicine and Technology, 1984)Titrimetry: The determination of the concentration of a given component in solution (the analyte) by addition of a liquid reagent of known strength (the titrant) until an equivalence point is reached (when the reactants are present in stoichiometric proportions). Often an indicator is added to make the equivalence point visible (e.g., a change in color).Aging: The gradual irreversible changes in structure and function of an organism that occur as a result of the passage of time.Molecular Weight: The sum of the weight of all the atoms in a molecule.Neutralization Tests: The measurement of infection-blocking titer of ANTISERA by testing a series of dilutions for a given virus-antiserum interaction end-point, which is generally the dilution at which tissue cultures inoculated with the serum-virus mixtures demonstrate cytopathology (CPE) or the dilution at which 50% of test animals injected with serum-virus mixtures show infectivity (ID50) or die (LD50).Blotting, Western: Identification of proteins or peptides that have been electrophoretically separated by blot transferring from the electrophoresis gel to strips of nitrocellulose paper, followed by labeling with antibody probes.Chromatography, Gel: Chromatography on non-ionic gels without regard to the mechanism of solute discrimination.Antigen-Antibody Reactions: The processes triggered by interactions of ANTIBODIES with their ANTIGENS.Antibodies, Bispecific: Antibodies, often monoclonal, in which the two antigen-binding sites are specific for separate ANTIGENIC DETERMINANTS. They are artificial antibodies produced by chemical crosslinking, fusion of HYBRIDOMA cells, or by molecular genetic techniques. They function as the main mediators of targeted cellular cytotoxicity and have been shown to be efficient in the targeting of drugs, toxins, radiolabeled haptens, and effector cells to diseased tissue, primarily tumors.Deamination: The removal of an amino group (NH2) from a chemical compound.Immune Sera: Serum that contains antibodies. It is obtained from an animal that has been immunized either by ANTIGEN injection or infection with microorganisms containing the antigen.Rabbits: The species Oryctolagus cuniculus, in the family Leporidae, order LAGOMORPHA. Rabbits are born in burrows, furless, and with eyes and ears closed. In contrast with HARES, rabbits have 22 chromosome pairs.KynurenineSingle-Chain Antibodies: A form of antibodies consisting only of the variable regions of the heavy and light chains (FV FRAGMENTS), connected by a small linker peptide. They are less immunogenic than complete immunoglobulin and thus have potential therapeutic use.Mice, Inbred BALB CAntibodies, Blocking: Antibodies that inhibit the reaction between ANTIGEN and other antibodies or sensitized T-LYMPHOCYTES (e.g., antibodies of the IMMUNOGLOBULIN G class that compete with IGE antibodies for antigen, thereby blocking an allergic response). Blocking antibodies that bind tumors and prevent destruction of tumor cells by CYTOTOXIC T-LYMPHOCYTES have also been called enhancing antibodies. (Rosen et al., Dictionary of Immunology, 1989)Eye ProteinsRecombinant Proteins: Proteins prepared by recombinant DNA technology.Immunoglobulin G: The major immunoglobulin isotype class in normal human serum. There are several isotype subclasses of IgG, for example, IgG1, IgG2A, and IgG2B.Decapodiformes: A superorder of CEPHALOPODS comprised of squid, cuttlefish, and their relatives. Their distinguishing feature is the modification of their fourth pair of arms into tentacles, resulting in 10 limbs.Molecular Chaperones: A family of cellular proteins that mediate the correct assembly or disassembly of polypeptides and their associated ligands. Although they take part in the assembly process, molecular chaperones are not components of the final structures.Antigen-Antibody Complex: The complex formed by the binding of antigen and antibody molecules. The deposition of large antigen-antibody complexes leading to tissue damage causes IMMUNE COMPLEX DISEASES.Base Sequence: The sequence of PURINES and PYRIMIDINES in nucleic acids and polynucleotides. It is also called nucleotide sequence.Invertebrates: Animals that have no spinal column.Proto-Oncogene Proteins c-maf: Maf proto-oncogene protein is the major cellular homolog of the V-MAF ONCOGENE PROTEIN. It was the first of the mammalian MAF TRANSCRIPTION FACTORS identified, and it is induced in activated T-LYMPHOCYTES and regulates GENETIC TRANSCRIPTION of INTERLEUKIN-4. c-maf is frequently translocated to an immunoglobulin locus in MULTIPLE MYELOMA.Immunoglobulin Fab Fragments: Univalent antigen-binding fragments composed of one entire IMMUNOGLOBULIN LIGHT CHAIN and the amino terminal end of one of the IMMUNOGLOBULIN HEAVY CHAINS from the hinge region, linked to each other by disulfide bonds. Fab contains the IMMUNOGLOBULIN VARIABLE REGIONS, which are part of the antigen-binding site, and the first IMMUNOGLOBULIN CONSTANT REGIONS. This fragment can be obtained by digestion of immunoglobulins with the proteolytic enzyme PAPAIN.Maillard Reaction: One of a group of nonenzymatic reactions in which aldehydes, ketones, or reducing sugars react with amino acids, peptides, or proteins. Food browning reactions, such as those that occur with cooking of meats, and also food deterioration reactions, resulting in decreased nutritional value and color changes, are attributed to this reaction type. The Maillard reaction is studied by scientists in the agriculture, food, nutrition, and carbohydrate chemistry fields.Antibodies, Heterophile: Antibodies elicited in a different species from which the antigen originated. These antibodies are directed against a wide variety of interspecies-specific antigens, the best known of which are Forssman, Hanganutziu-Deicher (H-D), and Paul-Bunnell (P-B). Incidence of antibodies to these antigens--i.e., the phenomenon of heterophile antibody response--is useful in the serodiagnosis, pathogenesis, and prognosis of infection and latent infectious states as well as in cancer classification.Immunoblotting: Immunologic method used for detecting or quantifying immunoreactive substances. The substance is identified by first immobilizing it by blotting onto a membrane and then tagging it with labeled antibodies.Antibodies, Catalytic: Antibodies that can catalyze a wide variety of chemical reactions. They are characterized by high substrate specificity and share many mechanistic features with enzymes.Poecilia: A genus of livebearing cyprinodont fish comprising the guppy and molly. Some species are virtually all female and depend on sperm from other species to stimulate egg development. Poecilia is used in carcinogenicity studies as well as neurologic and physiologic research.Protein Denaturation: Disruption of the non-covalent bonds and/or disulfide bonds responsible for maintaining the three-dimensional shape and activity of the native protein.Refractometry: Measurement of the index of refraction (the ratio of the velocity of light or other radiation in the first of two media to its velocity in the second as it passes from one into the other).Spectrometry, Mass, Matrix-Assisted Laser Desorption-Ionization: A mass spectrometric technique that is used for the analysis of large biomolecules. Analyte molecules are embedded in an excess matrix of small organic molecules that show a high resonant absorption at the laser wavelength used. The matrix absorbs the laser energy, thus inducing a soft disintegration of the sample-matrix mixture into free (gas phase) matrix and analyte molecules and molecular ions. In general, only molecular ions of the analyte molecules are produced, and almost no fragmentation occurs. This makes the method well suited for molecular weight determinations and mixture analysis.Scattering, Radiation: The diversion of RADIATION (thermal, electromagnetic, or nuclear) from its original path as a result of interactions or collisions with atoms, molecules, or larger particles in the atmosphere or other media. (McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed)Enzyme-Linked Immunosorbent Assay: An immunoassay utilizing an antibody labeled with an enzyme marker such as horseradish peroxidase. While either the enzyme or the antibody is bound to an immunosorbent substrate, they both retain their biologic activity; the change in enzyme activity as a result of the enzyme-antibody-antigen reaction is proportional to the concentration of the antigen and can be measured spectrophotometrically or with the naked eye. Many variations of the method have been developed.Immunoglobulin A: Represents 15-20% of the human serum immunoglobulins, mostly as the 4-chain polymer in humans or dimer in other mammals. Secretory IgA (IMMUNOGLOBULIN A, SECRETORY) is the main immunoglobulin in secretions.Antibodies, Monoclonal, Humanized: Antibodies from non-human species whose protein sequences have been modified to make them nearly identical with human antibodies. If the constant region and part of the variable region are replaced, they are called humanized. If only the constant region is modified they are called chimeric. INN names for humanized antibodies end in -zumab.Hybridomas: Cells artificially created by fusion of activated lymphocytes with neoplastic cells. The resulting hybrid cells are cloned and produce pure MONOCLONAL ANTIBODIES or T-cell products, identical to those produced by the immunologically competent parent cell.Species Specificity: The restriction of a characteristic behavior, anatomical structure or physical system, such as immune response; metabolic response, or gene or gene variant to the members of one species. It refers to that property which differentiates one species from another but it is also used for phylogenetic levels higher or lower than the species.Lens Cortex, Crystalline: The portion of the crystalline lens surrounding the nucleus and bound anteriorly by the epithelium and posteriorly by the capsule. It contains lens fibers and amorphous, intercellular substance.Epitope Mapping: Methods used for studying the interactions of antibodies with specific regions of protein antigens. Important applications of epitope mapping are found within the area of immunochemistry.Antibodies, Antiphospholipid: Autoantibodies directed against phospholipids. These antibodies are characteristically found in patients with systemic lupus erythematosus (LUPUS ERYTHEMATOSUS, SYSTEMIC;), ANTIPHOSPHOLIPID SYNDROME; related autoimmune diseases, some non-autoimmune diseases, and also in healthy individuals.Circular Dichroism: A change from planar to elliptic polarization when an initially plane-polarized light wave traverses an optically active medium. (McGraw-Hill Dictionary of Scientific and Technical Terms, 4th ed)Immunization: Deliberate stimulation of the host's immune response. ACTIVE IMMUNIZATION involves administration of ANTIGENS or IMMUNOLOGIC ADJUVANTS. PASSIVE IMMUNIZATION involves administration of IMMUNE SERA or LYMPHOCYTES or their extracts (e.g., transfer factor, immune RNA) or transplantation of immunocompetent cell producing tissue (thymus or bone marrow).Immunohistochemistry: Histochemical localization of immunoreactive substances using labeled antibodies as reagents.Antigens: Substances that are recognized by the immune system and induce an immune reaction.Immunoenzyme Techniques: Immunologic techniques based on the use of: (1) enzyme-antibody conjugates; (2) enzyme-antigen conjugates; (3) antienzyme antibody followed by its homologous enzyme; or (4) enzyme-antienzyme complexes. These are used histologically for visualizing or labeling tissue specimens.Cell Line: Established cell cultures that have the potential to propagate indefinitely.Peptide Fragments: Partial proteins formed by partial hydrolysis of complete proteins or generated through PROTEIN ENGINEERING techniques.Calpain: Cysteine proteinase found in many tissues. Hydrolyzes a variety of endogenous proteins including NEUROPEPTIDES; CYTOSKELETAL PROTEINS; proteins from SMOOTH MUSCLE; CARDIAC MUSCLE; liver; platelets; and erythrocytes. Two subclasses having high and low calcium sensitivity are known. Removes Z-discs and M-lines from myofibrils. Activates phosphorylase kinase and cyclic nucleotide-independent protein kinase. This enzyme was formerly listed as EC 220.127.116.11.Antigens, Bacterial: Substances elaborated by bacteria that have antigenic activity.Chromatography, High Pressure Liquid: Liquid chromatographic techniques which feature high inlet pressures, high sensitivity, and high speed.Protein Binding: The process in which substances, either endogenous or exogenous, bind to proteins, peptides, enzymes, protein precursors, or allied compounds. Specific protein-binding measures are often used as assays in diagnostic assessments.Antigens, Surface: Antigens on surfaces of cells, including infectious or foreign cells or viruses. They are usually protein-containing groups on cell membranes or walls and may be isolated.Protein Processing, Post-Translational: Any of various enzymatically catalyzed post-translational modifications of PEPTIDES or PROTEINS in the cell of origin. These modifications include carboxylation; HYDROXYLATION; ACETYLATION; PHOSPHORYLATION; METHYLATION; GLYCOSYLATION; ubiquitination; oxidation; proteolysis; and crosslinking and result in changes in molecular weight and electrophoretic motility.Glycosylation: The chemical or biochemical addition of carbohydrate or glycosyl groups to other chemicals, especially peptides or proteins. Glycosyl transferases are used in this biochemical reaction.Immunization, Passive: Transfer of immunity from immunized to non-immune host by administration of serum antibodies, or transplantation of lymphocytes (ADOPTIVE TRANSFER).Protein Conformation: The characteristic 3-dimensional shape of a protein, including the secondary, supersecondary (motifs), tertiary (domains) and quaternary structure of the peptide chain. PROTEIN STRUCTURE, QUATERNARY describes the conformation assumed by multimeric proteins (aggregates of more than one polypeptide chain).Immunoassay: A technique using antibodies for identifying or quantifying a substance. Usually the substance being studied serves as antigen both in antibody production and in measurement of antibody by the test substance.Immunoglobulin Fragments: Partial immunoglobulin molecules resulting from selective cleavage by proteolytic enzymes or generated through PROTEIN ENGINEERING techniques.DucksModels, Molecular: Models used experimentally or theoretically to study molecular shape, electronic properties, or interactions; includes analogous molecules, computer-generated graphics, and mechanical structures.Aldehyde Dehydrogenase: An enzyme that oxidizes an aldehyde in the presence of NAD+ and water to an acid and NADH. This enzyme was formerly classified as EC 18.104.22.168.Cloning, Molecular: The insertion of recombinant DNA molecules from prokaryotic and/or eukaryotic sources into a replicating vehicle, such as a plasmid or virus vector, and the introduction of the resultant hybrid molecules into recipient cells without altering the viability of those cells.Ranidae: The family of true frogs of the order Anura. The family occurs worldwide except in Antarctica.Antigens, Viral: Substances elaborated by viruses that have antigenic activity.Cornea: The transparent anterior portion of the fibrous coat of the eye consisting of five layers: stratified squamous CORNEAL EPITHELIUM; BOWMAN MEMBRANE; CORNEAL STROMA; DESCEMET MEMBRANE; and mesenchymal CORNEAL ENDOTHELIUM. It serves as the first refracting medium of the eye. It is structurally continuous with the SCLERA, avascular, receiving its nourishment by permeation through spaces between the lamellae, and is innervated by the ophthalmic division of the TRIGEMINAL NERVE via the ciliary nerves and those of the surrounding conjunctiva which together form plexuses. (Cline et al., Dictionary of Visual Science, 4th ed)Radioimmunoassay: Classic quantitative assay for detection of antigen-antibody reactions using a radioactively labeled substance (radioligand) either directly or indirectly to measure the binding of the unlabeled substance to a specific antibody or other receptor system. Non-immunogenic substances (e.g., haptens) can be measured if coupled to larger carrier proteins (e.g., bovine gamma-globulin or human serum albumin) capable of inducing antibody formation.Sequence Homology, Amino Acid: The degree of similarity between sequences of amino acids. This information is useful for the analyzing genetic relatedness of proteins and species.Isoelectric Focusing: Electrophoresis in which a pH gradient is established in a gel medium and proteins migrate until they reach the site (or focus) at which the pH is equal to their isoelectric point.Cells, Cultured: Cells propagated in vitro in special media conducive to their growth. Cultured cells are used to study developmental, morphologic, metabolic, physiologic, and genetic processes, among others.Mass Spectrometry: An analytical method used in determining the identity of a chemical based on its mass using mass analyzers/mass spectrometers.B-Lymphocytes: Lymphoid cells concerned with humoral immunity. They are short-lived cells resembling bursa-derived lymphocytes of birds in their production of immunoglobulin upon appropriate stimulation.Complement Fixation Tests: Serologic tests based on inactivation of complement by the antigen-antibody complex (stage 1). Binding of free complement can be visualized by addition of a second antigen-antibody system such as red cells and appropriate red cell antibody (hemolysin) requiring complement for its completion (stage 2). Failure of the red cells to lyse indicates that a specific antigen-antibody reaction has taken place in stage 1. If red cells lyse, free complement is present indicating no antigen-antibody reaction occurred in stage 1.RNA, Messenger: RNA sequences that serve as templates for protein synthesis. Bacterial mRNAs are generally primary transcripts in that they do not require post-transcriptional processing. Eukaryotic mRNA is synthesized in the nucleus and must be exported to the cytoplasm for translation. Most eukaryotic mRNAs have a sequence of polyadenylic acid at the 3' end, referred to as the poly(A) tail. The function of this tail is not known for certain, but it may play a role in the export of mature mRNA from the nucleus as well as in helping stabilize some mRNA molecules by retarding their degradation in the cytoplasm.Hemagglutination Tests: Sensitive tests to measure certain antigens, antibodies, or viruses, using their ability to agglutinate certain erythrocytes. (From Stedman, 26th ed)Hemagglutination Inhibition Tests: Serologic tests in which a known quantity of antigen is added to the serum prior to the addition of a red cell suspension. Reaction result is expressed as the smallest amount of antigen which causes complete inhibition of hemagglutination.Spectrometry, Mass, Fast Atom Bombardment: A mass spectrometric technique that is used for the analysis of a wide range of biomolecules, such as glycoalkaloids, glycoproteins, polysaccharides, and peptides. Positive and negative fast atom bombardment spectra are recorded on a mass spectrometer fitted with an atom gun with xenon as the customary beam. The mass spectra obtained contain molecular weight recognition as well as sequence information.Chickens: Common name for the species Gallus gallus, the domestic fowl, in the family Phasianidae, order GALLIFORMES. It is descended from the red jungle fowl of SOUTHEAST ASIA.Antibodies, Antineutrophil Cytoplasmic: Autoantibodies directed against cytoplasmic constituents of POLYMORPHONUCLEAR LEUKOCYTES and/or MONOCYTES. They are used as specific markers for GRANULOMATOSIS WITH POLYANGIITIS and other diseases, though their pathophysiological role is not clear. ANCA are routinely detected by indirect immunofluorescence with three different patterns: c-ANCA (cytoplasmic), p-ANCA (perinuclear), and atypical ANCA.Immunoglobulin Variable Region: That region of the immunoglobulin molecule that varies in its amino acid sequence and composition, and comprises the binding site for a specific antigen. It is located at the N-terminus of the Fab fragment of the immunoglobulin. It includes hypervariable regions (COMPLEMENTARITY DETERMINING REGIONS) and framework regions.Proteomics: The systematic study of the complete complement of proteins (PROTEOME) of organisms.Seroepidemiologic Studies: EPIDEMIOLOGIC STUDIES based on the detection through serological testing of characteristic change in the serum level of specific ANTIBODIES. Latent subclinical infections and carrier states can thus be detected in addition to clinically overt cases.Immunoglobulin Idiotypes: Unique genetically-controlled determinants present on ANTIBODIES whose specificity is limited to a single group of proteins (e.g., another antibody molecule or an individual myeloma protein). The idiotype appears to represent the antigenicity of the antigen-binding site of the antibody and to be genetically codetermined with it. The idiotypic determinants have been precisely located to the IMMUNOGLOBULIN VARIABLE REGION of both immunoglobin polypeptide chains.T-Lymphocytes: Lymphocytes responsible for cell-mediated immunity. Two types have been identified - cytotoxic (T-LYMPHOCYTES, CYTOTOXIC) and helper T-lymphocytes (T-LYMPHOCYTES, HELPER-INDUCER). They are formed when lymphocytes circulate through the THYMUS GLAND and differentiate to thymocytes. When exposed to an antigen, they divide rapidly and produce large numbers of new T cells sensitized to that antigen.Immunologic Techniques: Techniques used to demonstrate or measure an immune response, and to identify or measure antigens using antibodies.Protein Structure, Secondary: The level of protein structure in which regular hydrogen-bond interactions within contiguous stretches of polypeptide chain give rise to alpha helices, beta strands (which align to form beta sheets) or other types of coils. This is the first folding level of protein conformation.Antigens, Neoplasm: Proteins, glycoprotein, or lipoprotein moieties on surfaces of tumor cells that are usually identified by monoclonal antibodies. Many of these are of either embryonic or viral origin.DNA: A deoxyribonucleotide polymer that is the primary genetic material of all cells. Eukaryotic and prokaryotic organisms normally contain DNA in a double-stranded state, yet several important biological processes transiently involve single-stranded regions. DNA, which consists of a polysugar-phosphate backbone possessing projections of purines (adenine and guanine) and pyrimidines (thymine and cytosine), forms a double helix that is held together by hydrogen bonds between these purines and pyrimidines (adenine to thymine and guanine to cytosine).Immunosorbent Techniques: Techniques for removal by adsorption and subsequent elution of a specific antibody or antigen using an immunosorbent containing the homologous antigen or antibody.Spectrometry, Fluorescence: Measurement of the intensity and quality of fluorescence.Perciformes: The most diversified of all fish orders and the largest vertebrate order. It includes many of the commonly known fish such as porgies, croakers, sunfishes, dolphin fish, mackerels, TUNA, etc.Haptens: Small antigenic determinants capable of eliciting an immune response only when coupled to a carrier. Haptens bind to antibodies but by themselves cannot elicit an antibody response.Sequence Analysis: A multistage process that includes the determination of a sequence (protein, carbohydrate, etc.), its fragmentation and analysis, and the interpretation of the resulting sequence information.Antibody Diversity: The phenomenon of immense variability characteristic of ANTIBODIES. It enables the IMMUNE SYSTEM to react specifically against the essentially unlimited kinds of ANTIGENS it encounters. Antibody diversity is accounted for by three main theories: (1) the Germ Line Theory, which holds that each antibody-producing cell has genes coding for all possible antibody specificities, but expresses only the one stimulated by antigen; (2) the Somatic Mutation Theory, which holds that antibody-producing cells contain only a few genes, which produce antibody diversity by mutation; and (3) the Gene Rearrangement Theory, which holds that antibody diversity is generated by the rearrangement of IMMUNOGLOBULIN VARIABLE REGION gene segments during the differentiation of the ANTIBODY-PRODUCING CELLS.Peptide Library: A collection of cloned peptides, or chemically synthesized peptides, frequently consisting of all possible combinations of amino acids making up an n-amino acid peptide.DNA Primers: Short sequences (generally about 10 base pairs) of DNA that are complementary to sequences of messenger RNA and allow reverse transcriptases to start copying the adjacent sequences of mRNA. Primers are used extensively in genetic and molecular biology techniques.Polymerase Chain Reaction: In vitro method for producing large amounts of specific DNA or RNA fragments of defined length and sequence from small amounts of short oligonucleotide flanking sequences (primers). The essential steps include thermal denaturation of the double-stranded target molecules, annealing of the primers to their complementary sequences, and extension of the annealed primers by enzymatic synthesis with DNA polymerase. The reaction is efficient, specific, and extremely sensitive. Uses for the reaction include disease diagnosis, detection of difficult-to-isolate pathogens, mutation analysis, genetic testing, DNA sequencing, and analyzing evolutionary relationships.Intermediate Filament Proteins: Filaments 7-11 nm in diameter found in the cytoplasm of all cells. Many specific proteins belong to this group, e.g., desmin, vimentin, prekeratin, decamin, skeletin, neurofilin, neurofilament protein, and glial fibrillary acid protein.Hepatitis C Antibodies: Antibodies to the HEPATITIS C ANTIGENS including antibodies to envelope, core, and non-structural proteins.Isoantibodies: Antibodies from an individual that react with ISOANTIGENS of another individual of the same species.Immunoglobulin Isotypes: The classes of immunoglobulins found in any species of animal. In man there are nine classes that migrate in five different groups in electrophoresis; they each consist of two light and two heavy protein chains, and each group has distinguishing structural and functional properties.Flow Cytometry: Technique using an instrument system for making, processing, and displaying one or more measurements on individual cells obtained from a cell suspension. Cells are usually stained with one or more fluorescent dyes specific to cell components of interest, e.g., DNA, and fluorescence of each cell is measured as it rapidly transverses the excitation beam (laser or mercury arc lamp). Fluorescence provides a quantitative measure of various biochemical and biophysical properties of the cell, as well as a basis for cell sorting. Other measurable optical parameters include light absorption and light scattering, the latter being applicable to the measurement of cell size, shape, density, granularity, and stain uptake.Immunoglobulins: Multi-subunit proteins which function in IMMUNITY. They are produced by B LYMPHOCYTES from the IMMUNOGLOBULIN GENES. They are comprised of two heavy (IMMUNOGLOBULIN HEAVY CHAINS) and two light chains (IMMUNOGLOBULIN LIGHT CHAINS) with additional ancillary polypeptide chains depending on their isoforms. The variety of isoforms include monomeric or polymeric forms, and transmembrane forms (B-CELL ANTIGEN RECEPTORS) or secreted forms (ANTIBODIES). They are divided by the amino acid sequence of their heavy chains into five classes (IMMUNOGLOBULIN A; IMMUNOGLOBULIN D; IMMUNOGLOBULIN E; IMMUNOGLOBULIN G; IMMUNOGLOBULIN M) and various subclasses.Binding Sites: The parts of a macromolecule that directly participate in its specific combination with another molecule.Epithelium, Corneal: Stratified squamous epithelium that covers the outer surface of the CORNEA. It is smooth and contains many free nerve endings.Protein Structure, Tertiary: The level of protein structure in which combinations of secondary protein structures (alpha helices, beta sheets, loop regions, and motifs) pack together to form folded shapes called domains. Disulfide bridges between cysteines in two different parts of the polypeptide chain along with other interactions between the chains play a role in the formation and stabilization of tertiary structure. Small proteins usually consist of only one domain but larger proteins may contain a number of domains connected by segments of polypeptide chain which lack regular secondary structure.Mutation: Any detectable and heritable change in the genetic material that causes a change in the GENOTYPE and which is transmitted to daughter cells and to succeeding generations.Antibodies, Monoclonal, Murine-Derived: Antibodies obtained from a single clone of cells grown in mice or rats.Glycoproteins: Conjugated protein-carbohydrate compounds including mucins, mucoid, and amyloid glycoproteins.Vaccination: Administration of vaccines to stimulate the host's immune response. This includes any preparation intended for active immunological prophylaxis.
The molecular mass of crystallin and ubiquitin based Affilin proteins is only one eighth or one sixteenth of an IgG antibody, ... They resemble antibodies in their affinity and specificity to antigens but not in structure, which makes them a type of ... In both types, the binding region is typically located in a beta sheet structure, whereas the binding regions of antibodies, ... Two proteins, gamma-B crystallin and ubiquitin, have been described as scaffolds for Affilin proteins. Certain amino acids in ...
"Mass spectrometry of Lens Crystallins: Bovine β-crystallins." Rapid Communications in Mass Spectrometry (1996) 10,123-129 G. ... "Monitoring papain digestion of a monoclonal antibody by electrospray ionisation mass spectrometry" Analytical Biochemistry ( ... lens crystallin" Protein Science (1997) 6, 909-912 K.L. Bennett, S.V. Smith, R.M. Lambrecht, R.J.W. Truscott and M.M. Sheil* " ...
Muto, A (2004). "The transcriptional programme of antibody class switching involves the repressor Bach2". Nature. 429 (6991): ... "Compound mouse mutants of bZIP transcription factors Mafg and Mafk reveal a regulatory network of non-crystallin genes ...
September 2007). "Affilin-novel binding molecules based on human gamma-B-crystallin, an all beta-sheet protein". J. Mol. Biol. ... but not artificial antibodies, antibody fragments and fusion proteins composed from these. Common advantages over antibodies ... Antibody mimetics are organic compounds that, like antibodies, can specifically bind antigens, but that are not structurally ... Antibodies are ~150 kDa.) Nucleic acids and small molecules are sometimes considered antibody mimetics as well, ...
This helped identify genes required for vision and pigmentation, such as crystallins and the melanocortin 1 receptor. Similarly ... such as modified enzymes or new antibodies, in a process called directed evolution. Antibiotic resistance can be a result of ...
... alpha-crystallin b chain MeSH D12.776.306.366.300.100 - beta-crystallin a chain MeSH D12.776.306.366.300.200 - beta-crystallin ... antibodies MeSH D12.776.377.715.548.114.071 - antibodies, anti-idiotypic MeSH D12.776.377.715.548.114.107 - antibodies, ... antibodies, bispecific MeSH D12.776.377.715.548.114.143 - antibodies, blocking MeSH D12.776.377.715.548.114.167 - antibodies, ... antibodies, helminth MeSH D12.776.377.715.548.114.191 - antibodies, heterophile MeSH D12.776.377.715.548.114.224 - antibodies, ...
... , in addition, functions as a structural lens protein (tau-crystallin) in the monomeric form. Alternative splicing ... "Human alpha-enolase from endothelial cells as a target antigen of anti-endothelial cell antibody in Behçet's disease". ... "Measurement and evaluation of isotypes of anti-citrullinated fibrinogen and anti-citrullinated alpha-enolase antibodies in ... identified it as an autoantigen associated with severe asthma and a putative target antigen of anti-endothelial cell antibody ...
"Protein antigen-monoclonal antibody contact sites investigated by limited proteolysis of monoclonal antibody-bound antigen: ... Shum, Wai-Kei; Maleknia, Simin D.; Downard, Kevin M. (2005). "Onset of oxidative damage in α-crystallin by radical probe mass ... "Homology-modelled structure of the βB2B3-crystallin heterodimer studied by ion mobility and radical probe MS". FEBS Journal. ... was originally coined in reference to the use of limited proteolysis to investigate contact sites within a monoclonal antibody ...
All teeth are in use by 8 years. The lenses of the eyes contain crystallin, which constitutes 8 to 13% of the protein ... dromedaries were found to have natural antibodies against the rinderpest and ovine rinderpest viruses. ... Garland, D.; Rao, P.V.; Del Corso, A.; Mura, U.; Zigler Jr., J.S. (1991). "zeta-Crystallin is a major protein in the lens of ... "Detection of antibodies of rinderpest and peste des petits ruminants viruses (Paramyxoviridae, Morbillivirus) during a new ...
In this process antibodies to Aβ are used to decrease cerebral plaque levels. This is accomplished by promoting microglial ... "Monitoring the prevention of amyloid fibril formation by alpha-crystallin. Temperature dependence and the nature of the ... One sensitive method is ELISA which is an immunosorbent assay which utilizes a pair of antibodies that recognize amyloid beta. ... This stimulates the host immune system to recognize and attack Aβ, or provide antibodies that either prevent plaque deposition ...
... and antibody response of active Aβ immunotherapy with CAD106 in patients with Alzheimer's disease: randomised, double-blind, ... "Monitoring the prevention of amyloid fibril formation by alpha-crystallin. Temperature dependence and the nature of the ...
... and alpha B crystallin. Tau proteins may also be present, and Lewy bodies may occasionally be surrounded by neurofibrillary ... Stains used: mouse monoclonal alpha-synuclein antibody; counterstained with Mayer's haematoxylin. Lewy bodies ...
241-250 Wistow, Graeme (August 1993). "Lens crystallins: gene recruitment and evolutionary dynamism". Trends in Biochemical ... for example modified enzymes and new antibodies) in a process called directed evolution. Understanding the changes that have ... "Recruitment of enzymes and stress proteins as lens crystallins". In Jansson, Bengt; Jörnvall, Hans; Rydberg, Ulf; et al. Toward ... is the recruitment of enzymes from glycolysis and xenobiotic metabolism to serve as structural proteins called crystallins ...
High levels of anti-nuclear antibodies are found normally in patients with MS. Antibodies against Neurofascins ... Bsibsi M, Holtman IR, Gerritsen WH, Eggen BJ, Boddeke E, van der Valk P, van Noort JM, Amor S (Sep 2013). "Alpha-B-Crystallin ... Currently antibodies to lipids and peptides in sera, detected by microarrays, can be used as markers of the pathological ... The anti-MOG antibody has been investigated and finally led to the description of a new disease, AntiMOG associated ...
Rabbit polyclonal Alpha B Crystallin antibody. Validated in WB, IHC and tested in Mouse, Human, Pig. Immunogen corresponding to ... Anti-Alpha B Crystallin antibody. See all Alpha B Crystallin primary antibodies. ... Anti-Alpha B Crystallin antibody (ab231268) at 2 µg/ml + Recombinant human Alpha B Crystallin protein.. Predicted band size: 20 ... Primary antibodies. Secondary antibodies. ELISA and Matched Antibody Pair Kits. Cell and tissue imaging tools. Cellular and ...
Rabbit polyclonal Alpha B Crystallin antibody. Validated in WB, IP, IHC, ICC and tested in Mouse, Rat, Chicken, Cow, Human, Pig ... Anti-Alpha B Crystallin antibody. See all Alpha B Crystallin primary antibodies. ... Primary antibodies. Secondary antibodies. ELISA and Matched Antibody Pair Kits. Cell and tissue imaging tools. Cellular and ... Anti-Alpha B Crystallin antibody (ab13497) at 1/1000 dilution + Human spinal cord tissue lysate - total protein (ab29188) at 10 ...
Mouse Monoclonal Anti-AlphaA Crystallin/CRYAA Antibody (1H3.B8). Validated: WB, ELISA, IB, ICC/IF. Tested Reactivity: Human. ... Home » AlphaA Crystallin/CRYAA » AlphaA Crystallin/CRYAA Antibodies » AlphaA Crystallin/CRYAA Antibody (1H3.B8) ... PTMs for AlphaA Crystallin/CRYAA Antibody (NBP2-12875). Learn more about PTMs related to AlphaA Crystallin/CRYAA Antibody (NBP2 ... Reviews for AlphaA Crystallin/CRYAA Antibody (NBP2-12875) (0) There are no reviews for AlphaA Crystallin/CRYAA Antibody (NBP2- ...
... read details of BioLegend antibodies in the SelectScience.net Antibody products and suppliers directory ... Alpha-crystallin B chain, alpha B crystallin, heat shock protein beta-5, rosenthal fiber component, heat-shock 20 kD like- ... Purified anti-Alpha Crystallin B. Be the first to review this product ... Purified anti-Alpha Crystallin B; Clone: Poly9079; Reactivity: Human, Mouse; Apps: IHC, WB; Size: 200 μl ...
... is replaced by a more specific monoclonal antibody, αB-crystallin (F-10) that gives a stronger signal & consistent results ... α A-crystallin, α B-crystallin, α C-crystallin, β-crystallin, β B1-crystallin, β B2-crystallin, β B3-crystallin, γ-crystallin, ... γ B-crystallin and γ D-crystallin * Learn more about our ImmunoCruz® Antibody Conjugates and Cruz Marker™ MW Standards ... αB-crystallin (K-20) has been discontinued and replaced by αB-crystallin (F-10): sc-137129.. ...
Primary Antibodies. Catalog No.. Host. Iso.. Clone. Pres.. React.. Applications. TA344266. Lambda-crystallin homolog antibody. ... Background of Lambda-crystallin homolog antibody. Kit Component:. - KN212304G1, CRYL1 gRNA vector 1 in pCas-Guide vector. - ... Rabbit Polyclonal Anti-CRYL1 Antibody - N-terminal region. Rabbit. IgG. Purified. Can, Eq, GP, Hu, Ms, Rt, Ye. WB. 50 µg / € ... Acris Antibodies Inc. (North America) Choose this store if you are located in… *America (e.g. United-States, Canada, Mexico, ...
Crystallins are separated into two classes: taxon-specific, or enzyme, and ubiquitous. The latter class constitutes the major ... Rabbit Polyclonal antibody to Beta crystallin A4 (crystallin, beta A4). Rabbit. Aff - Purified. Hu, Ms. ICC/IF, WB. 0.1 ml / € ... Primary Antibodies. Catalog No.. Host. Iso.. Clone. Pres.. React.. Applications. TA308870. Beta-crystallin A4 (1-185) antibody ... Background of Beta-crystallin A4 antibody. Crystallins are separated into two classes: taxon-specific, or enzyme, and ...
Shop QEDs high-quality Alpha B Crystallin antibodies, for use in WB & ELISA applications. With 20+ years of expertise, you can ... It does not cross-react with alpha A crystallin, beta- L crystallin, beta-H crystallin, gamma crystallin, Hsp25, Hsp27, or ... Antibody Class: IgG1. Preservatives: None. SPECIFICITY. This antibody recognizes human and bovine alpha B crystallin. ... Anti-Alpha B Crystallin Monoclonal Antibody. ORDERING INFORMATION. Catalog No.: 11083 (clone 3A10.C9). Size: 100ug in PBS, pH ...
Recombinant Protein and Alpha-crystallin Antibody at MyBioSource. Custom ELISA Kit, Recombinant Protein and Antibody are ... Alpha-crystallin. Alpha-crystallin ELISA Kit. Alpha-crystallin Recombinant. Alpha-crystallin Antibody. Also known as Alpha- ... Custom Antibody. Antibody Matched Pairs. Antibody Peptide Pairs. Phospho Antibodies. Products by Disease. Products by Pathway. ... Alpha-crystallin A chain ELISA Kit. Alpha-crystallin A chain Recombinant. Alpha-crystallin A chain Antibody. CRYA1: a major ...
Antibodies. Anti-Caspase-3 antibody and anti-VDAC were obtained from Calbiochem and anti-activated caspase-3 from Abcam, Inc. ... Expression of R120G-alphaB-crystallin causes aberrant desmin and alphaB-crystallin aggregation and cardiomyopathy in mice. Circ ... Mutations in desmin, α-B-crystallin (CryAB), and other genes result in the desmin-related myopathies (DRM).1,2 The ... Golenhofen N, Htun P, Ness W, Koob R, Schaper W, Drenckhahn D. Binding of the stress protein alpha B-crystallin to cardiac ...
Rat A crystallin A Monoclonal Antibody (Clone c9F2)-NP_000385 (MBS200007) product datasheet at MyBioSource, Primary Antibodies ... LIMP2 (SCARB2) Antibody. • IFT52 Antibody. • PPP4R1 Antibody. • ILK Antibody. • HAO2 Antibody. • RGS4 ELISA Kit. more .... ... Custom Antibody. Antibody Matched Pairs. Antibody Peptide Pairs. Phospho Antibodies. Products by Disease. Products by Pathway. ... This antibody is not shown cross-activity about Crystallin alpha B. A : Crystallin-alpha A recombinant protein B : Crystallin- ...
... αB-crystallin was also associated with worse survival (3.0 versus 4.7 months, P=0.007). αB-crystallin is a promising biomarker ... In addition, αB-crystallin positive protein expression were linked to poorer survival and early spread to the brain. The ... We examined αB-crystallin expression in primary breast carcinomas with metastatic data to evaluate its association with ... αB-crystallin gene (CRYAB) expression was examined using publically available global-gene expression data (n=855 breast tumors ...
A missense mutation in the alphaB-crystallin chaperone gene causes a desmin-related myopathy.. Vicart P1, Caron A, Guicheney P ... AlphaB-crystallin is a member of the small heat shock protein (shsp) family and possesses molecular chaperone activity. We ... This region contains the alphaB-crystallin gene (CRYAB), a candidate gene encoding a 20-kD protein that is abundant in lens and ... lines transfected with the mutant CRYAB cDNA showed intracellular aggregates that contain both desmin and alphaB-crystallin as ...
Antibodies. , Anti-mu Crystallin Rabbit Polyclonal Antibody. Anti-mu Crystallin Rabbit Polyclonal Antibody. Supplier: ... mu Crystallin(thiomorpholine-carboxylate dehydrogenase) is also named as THBP, CRYM, ketimine reductase and belongs to the ... Antigen: mu Crystallin. Clonality: Polyclonal. Clone: Conjugation: Unconjugated. Epitope: Host: Rabbit. Isotype: IgG. ...
Supporting Information Table 3. Primary antibodies for western blot, IHC and co-IP. ... Chuanbing Shi, Xiaojun Yang, Xiaodong Bu, Ning Hou, Pingsheng Chen, Alpha B-crystallin promotes the invasion and metastasis of ... αB-Crystallin complexes with and elevates 14-3-3ζ protein, leading to up-regulation of ERK1/2 activity. Moreover, ... αB-crystallin complexes with 14-3-3ζ to induce epithelial-mesenchymal transition and resistance to sorafenib in hepatocellular ...
Fluorescent Antibody Technique * Genes * Lens, Crystalline / analysis * Lens, Crystalline / cytology * Lens, Crystalline / ... alpha-crystallin is the first crystallin to be detected and is localized in some lens pit cells at 12 days of development. By ... beta- and gamma-crystallins are detected later at 12 1/2 days and are localized in some cells situated primarily in the ... Cell Division, Cell Elongation and the Co-Ordination of Crystallin Gene Expression During Lens Morphogenesis in the Rat J ...
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g) The anti-HA antibody specifically recognized αB-crystallin-HA in the Western Blot of the eye imaginal discs of gmr-gal4; uas ... Alpha-crystallins (α-crystallins) are major protein components of the vertebrate eye lens. The α-crystallins and especially αB- ... a, b) Transgenic flies coexpressing α-synuclein and αB-crystallin (gmr-gal4/+; uas-αB-crystallin-HA/+; uas-α-synuclein/+). (c, ... c, f) Transgenic flies coexpressing Q92 peptides and αB-crystallin (gmr-gal4; gmr-Q92/+; uas-αB-crystallin-HA). (b, e) ...
Primary anti-CRYAA antibody (1:1000, ab5595; Abcam plc, Cambridge, UK) and secondary anti-rabbit polyclonal antibodies (1:600, ... Results: We found αA-crystallin gene mutations in all 19 F0-generation pups (100%) with indel mutations in the αA-crystallin ... Production of the αA-crystallin protein was determined to be dramatically reduced in αA-crystallin gene knockout rabbits. We ... αA-crystallin gene (CRYAA) and αB-crystallin gene (CRYAB), which have been shown to be associated with autosomal dominant or ...
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Recombinant Crystallin, alpha A (CRYAA) Protein (His tag). Species: Sheep (Ovine). Source: Yeast. Order product ABIN1630960. ... proteins produced by yeast expression system has been used as raw materials for downstream preparation of monoclonal antibodies ... Crystallin, alpha A (CRYAA) (AA 1-173) protein (His tag) Crystallin, alpha A (CRYAA) (AA 1-173) protein (His tag). Details for ... Crystallin, alpha A (CRYAA) Background Recommended name: Alpha-crystallin A chain Cleaved into the following chain: 1.. Alpha- ...
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Polyclonal antibodyAntigenCRYABReactivityMouse monoclonal antibodyWater-solubleHeat shock pHSP27SerumWestern BlotSpeciesPeptidesCRYAAGenesDilutionAntigensPeptideImmunofluorescenceCatalogPolypeptideMonoclonal antibodiesChaperonesIgG1ImmunoblotHuman Crystallin alphaHSP25Gene in inducing cStructuralDatasheetExpressionSecondary antibody conjugatedSpecificityLysatesDetectionLens epithelial cellsVertebrate eyeEpithelialAffinity
- The following antibody was used in this experiment: HSP20 Polyclonal Antibody from Thermo Fisher Scientific, catalog # PA5-89649. (thermofisher.com)
- Mouse polyclonal antibody raised against a full-length human HSPB9 protein. (abnova.com)
- Western Blot analysis of HSPB9 expression in transfected 293T cell line ( H00094086-T01 ) by HSPB9 MaxPab polyclonal antibody. (abnova.com)
- Immunoblot analysis using a polyclonal antibody against CryAB detected a single protein with molecular mass of 21kDa in Syrian hamster left ventricle. (go.jp)
- Also known as Alpha-crystallin (Acr) (14 kDa antigen) (16 kDa antigen) (HSP 16.3) (Nox16). (mybiosource.com)
- Mouse anti Human alpha B crystallin antibody recognizes alpha B crystallin, also known as heat shock protein beta-5, heat-shock 20 kD like-protein and renal carcinoma antigen NY-REN-27, rosenthal fiber component. (bio-rad-antibodies.com)
- The technique involves formation of an antigen-antibody complex which is labeled with fluorescein-conjugated anti-immunoglobulin antibody. (labome.org)
- Each antibody is crafted with care according to rigorous protocols for immunogen design and preparation, presentation to host animal, and high-affinity purification against the antigen. (abgent.com)
- Expression of α-crystallin, the antigen 85 complex, PstS-1, L-alanine dehydrogenase and the 65 kDa antigen was analysed by Western blotting and enzyme-linked immunosorbent assays, using mouse monoclonal antibodies. (degruyter.com)
- the sample is added to the well, and the immobilized antibody binds to the protein antigen. (thermofisher.com)
- Antibodies to alphaB-Crystallin, Vimentin, and Heat Shock Protein 70 in Aqueous Humor of patients with Normal Tension Glaucoma and IgG Antibody Patterns Against Retinal Antigen in Aqueous Humor. (vision-research.eu)
- The stress protein αB-crystallin is an immunodominant antigen in multiple sclerosis (MS)-affected myelin for human T cells and is expressed at elevated levels in MS lesions. (tudelft.nl)
- Defects in CRYAB are the cause of myofibrillar alpha-B crystallin-related (MFM-CRYAB) [MIM: (abcam.com)
- An R120G missense mutation in the small heat shock protein α-B-crystallin (CryAB) causes desmin-related cardiomyopathy. (ahajournals.org)
- Mutations in desmin, α-B-crystallin (CryAB), and other genes result in the desmin-related myopathies (DRM). (ahajournals.org)
- In the 855Met data set, αB-crystallin gene ( CRYAB) expression was an independent predictor of brain as the first distant site of relapse (hazards ratio, HR=1.2, (95% confidence interval, CI 1.0-1.4), P =0.021). (nature.com)
- This region contains the alphaB-crystallin gene (CRYAB), a candidate gene encoding a 20-kD protein that is abundant in lens and is also present in a number of non-ocular tissues, including cardiac and skeletal muscle. (nih.gov)
- Muscle cell lines transfected with the mutant CRYAB cDNA showed intracellular aggregates that contain both desmin and alphaB-crystallin as observed in muscle fibers from DRM patients. (nih.gov)
- Alpha B-Crystallin (CRYAB) is purported to be a metastasis suppressor protein, and lack or lower CRYAB expression is a prognostic biomarker for several types of cancer, such as that of the prostate and head and neck. (cdc.gov)
- αB-Crystallin (CryAB) is a major stress protein in cardiac myocytes. (go.jp)
- N.B. Antibody reactivity and working conditions may vary between species. (bio-rad-antibodies.com)
- Van Noort and colleagues ( 2 , 3 ) first proposed the protein to be an autoantigen in 1995 based on the reactivity of PBMCs from MS patients and healthy control subjects to proliferate in response to a fraction of myelin from MS brains containing α B-crystallin. (jimmunol.org)
- When bovine serum albumin was incubated with various concentrations of fructose, the reactivity of thee antibody increased in a dose- and time-dependent manner. (nii.ac.jp)
- This antibody is predicted to have no cross-reactivity to Aldh3A2. (prosci-inc.com)
- Mouse anti Human Alpha A Crystallin antibody, clone c9F2 recognizes alpha A crystallin, a 20 kDa water-soluble major structural protein and member of the heat shock protein family, designated HSPB4, which acts as a molecular chaperone and is believed to play a role in the maintenance of ocular lens transparency/refractive index. (bio-rad-antibodies.com)
- Aleinikova, K. 2004-10-13 00:00:00 The major water-soluble polypeptide with molecular weight of approximately 23 kDa (the 23 kDa polypeptide) was identified in the lens of common frog Rana temporaria L. According to the gel filtration data, the peptide is a part of an oligomeric protein with molecular weight over than 300 kDa (α-crystallin fraction). (deepdyve.com)
- alpha-crystallins can be induced by heat shock and are members of the small heat shock protein (sHSP). (mybiosource.com)
- Alpha crystallins can be induced by heat shock and are members of the small heat shock protein (HSP20) family. (mybiosource.com)
- αB-crystallin is a widely expressed member of the small heat shock protein family that protects cells from stress by its dual function as a molecular chaperone to preserve proteostasis and as a cell death antagonist that inhibits caspase-3 activation and oxidative stress. (nature.com)
- AlphaB-crystallin is a member of the small heat shock protein (shsp) family and possesses molecular chaperone activity. (nih.gov)
- The α B-crystallin protein is a member of the small heat shock protein family, and it has a chaperone-like function [ 12 - 15 ]. (hindawi.com)
- peptides in heat-shock protein Hsp20 (G71HFSVLLDVKHFSPEEIAVK91) and Hsp27 (D93RWRVSLDVNHFAPDELTVK113) with sequence homology to alpha-crystallin also have robust chaperone and anti-apoptotic activities. (antibodies-online.com)
- For 15 y, α B-crystallin (heat shock protein [Hsp] B5) has been labeled an autoantigen in multiple sclerosis (MS) based on humoral and cellular responses found in humans and animal models. (jimmunol.org)
- The association of α B-crystallin (heat shock protein [Hsp] B5) with multiple sclerosis (MS) has been a puzzling story ( 1 ). (jimmunol.org)
- HSP27 and alphaB-crystallin are both members of the small heat shock protein family. (wikigenes.org)
- αB-Crystallin is a member of the small heat shock protein family. (bioportfolio.com)
- The alpha-crystallins possess structural and functional similarities with Hsp25 and Hsp27 (1). (biovendor.com)
- Correlative immunofluorescence and immunoelectron microscopy showed that two small HSPs (HSP27 and αB-crystallin) and the ATP-dependent chaperone HSP90 translocated to the titin springs in myopathy. (pubmedcentralcanada.ca)
- HSP27 antibody revealed that HSP27 was not detectable in cultured kidney epithelial cells. (uwaterloo.ca)
- The alpha-crystallin-related heat shock (stress) protein hsp27 is expressed in absence of heat shock during Drosophila melanogaster development. (rupress.org)
- A form of fluorescent antibody technique commonly used to detect serum antibodies and immune complexes in tissues and microorganisms in specimens from patients with infectious diseases. (labome.org)
- Serum samples were collected and analyzed with the enzyme-linked immunosorbent assay (ELISA) technique for antibodies to myelin basic protein, myelin-associated glycoprotein, ganglioside GM1, sulfatide, myelin oligodendrocyte glycoprotein, alpha-B-crystallin, chondroitin sulfate, tubulin, and neurofilament. (ei-resource.org)
- Almost every tested serum with high levels of antibodies against modified food antigens showed very high levels of antibodies against myelin basic protein, oxidized low density lipoprotein, AGE-human serum albumin and AGE-hemoglobin. (biomedcentral.com)
- Serum antibody responses to i.p. immunisation with chicken gama globulin in BALB/c mice are also modulated by oral application of Lactobacillus. (tudelft.nl)
- Product Description:Bovine Beta- crystallin B2, CRYBB2 ELISA KIT allows for the in vitro quantitative determination of Bovine Beta-crystallin B2, CRYBB2 concentrations in serum, plasma, tissue homogenates, cell culture supernates or other biological fluids. (lifescience-market.com)
- The present study was performed to elucidate the roles of serum anti-Sm antibodies in the pathogenesis of systemic lupus erythematosus (SLE). (bioportfolio.com)
- Western blot analysis of whole cell lysates probed with alpha B crystallin antibody followed by detection with HRP conjugated Goat anti Mouse IgG (1/10,000, STAR207P ) and visualized on the ChemiDoc MP with 4 second exposure. (bio-rad-antibodies.com)
- Western blot analysis of extracts (35ug) from 9 different cell lines by using anti-CRYM monoclonal antibody. (genetex.com)
- Western blot analysis of Aldh3A1 in human stomach lysate with Aldh3A1 antibody at (A) 1 and (B) 2 μg/mL. (prosci-inc.com)
- Aldh3A1 antibody can be used for detection of Aldh3A1 by Western blot at 1 - 2 μg/mL. (prosci-inc.com)
- Antibody validated: Western Blot in human samples. (prosci-inc.com)
- Abgent's experienced staff custom validates more than 1,000 antibodies each month in Western Blot (WB), Immunofluorescence (IF), Immunohistochemistry (IHC), Flow Cytometry (FC) and additional applications. (abgent.com)
- It may block above mentioned antibody from binding to its target protein in western blot and/or immunohistochecmistry under proper experimental settings. (absave.com)
- Immunocytochemistry/ Immunofluorescence: AlphaA Crystallin/CRYAA Antibody (1H3.B8) [NBP2-- Tissue: Neuroblastoma cell line SK-N-BE. (novusbio.com)
- Small volumes of anti-CRYAA antibody vial(s) may occasionally become entrapped in the seal of the product vial during shipment and storage. (mybiosource.com)
- It has been demonstrated previously that Pax-6, a paired domain (PD)/homeodomain (HD) transcription factor critical for eye development, contributes to the activation of the αB-, αA-, δ1-, and ζ-crystallin genes in the lens. (asm.org)
- Here we have examined the possibility that the inverse relationship between the expression of Pax-6 and β-crystallin genes within the developing chicken lens reflects a negative regulatory role of Pax-6. (asm.org)
- The genes encoding crystallins are generally expressed either specifically or preferentially in the lens and are independently regulated at the transcriptional level ( 11 , 38 ). (asm.org)
- A hallmark of the microarray analysis is that the antagonist seems to be a novel stage-specific regulator of crystallin genes. (molvis.org)
- The late, sustained cluster also contained the upregulated crystallin genes. (pubmedcentralcanada.ca)
- Genes associated with the development of lens include crystallin genes. (bjbms.org)
- Antibody mimetics are organic compounds that, like antibodies, can specifically bind antigens, but that are not structurally related to antibodies. (wikipedia.org)
- They resemble antibodies in their affinity and specificity to antigens but not in structure, which makes them a type of antibody mimetic. (wikipedia.org)
- Patients with documented, measured exposure to molds had elevated titers of antibodies (immunoglobulin [Ig]A, IgM, and IgG) to neural-specific antigens. (ei-resource.org)
- All groups showed significantly increased autoantibody titers for all isotypes (IgA, IgM, and IgG) of antibodies to neural antigens when compared with 500 healthy controls. (ei-resource.org)
- We developed an enzyme-linked immunosorbent assay for the measurement of IgE, IgG, IgA and IgM antibodies against raw and processed food antigens. (biomedcentral.com)
- Compared to raw food antigens, IgE antibodies showed a 3-8-fold increase against processed food antigens in 31% of the patients. (biomedcentral.com)
- Similarly, IgG, IgA and IgM antibodies against modified food antigens overall were found at much higher levels than antibody reactions against raw food antigens. (biomedcentral.com)
- We conclude that the determination of food allergy, intolerance and sensitivity would be improved by testing IgE, IgG, IgA and IgM antibodies against both raw and processed food antigens. (biomedcentral.com)
- Retinal ganglion cell loss is accompanied by antibody depositions and increased levels of microglia after immunization with retinal antigens. (vision-research.eu)
- Autoreactive antibodies and loss of retinal ganglion cells in rats induced by immunization with ocular antigens. (vision-research.eu)
- Seven protein regions exist in crystallins: four homologous motifs, a connecting peptide, and N- and C-terminal extensions. (acris-antibodies.com)
- The anti-αB-C antibody was made by the injection of a synthet … More ic peptide from the carboxyl terminal of αB-C to rabbits (Tamaoka et al, 1995). (nii.ac.jp)
- Aldh3A1 antibody was raised against a 13 amino acid synthetic peptide near the carboxy terminus of the human Aldh3A1. (prosci-inc.com)
- Aldh3A1 Antibody is affinity chromatography purified via peptide column. (prosci-inc.com)
- This is a synthetic peptide designed for use in combination with anti-CRYGN Antibody (ARP67062_P050), made by Aviva Systems Biology. (absave.com)
- A monoclonal antibody targeted to the functional peptide of αB-crystallin inhibits the chaperone and anti-apoptotic activities. (bioportfolio.com)
- Previous studies have shown that the peptide (DRFSVNLDVKHFSPEELKVKV, hereafter referred to as peptain-1) from the core domain of αB-crystallin exhibits both chaperone and anti-apoptotic properties similar to the parent protein. (bioportfolio.com)
- A highly pure fraction of the 23 kDa polypeptide was isolated by two-step ion-exchange chromatography and SDS electrophoresis and the specific antibodies were obtained. (deepdyve.com)
- Immunochemical analysis showed that the 23 kDa polypeptide was different from all known crystallins of frogs and other animals (bull, mouse, rat, and chicken). (deepdyve.com)
- 0.5 ug/ml was sufficient for detection of 100 ng purified alphaA crystalline by colorimetric immunoblot analysis using Goat Anti-Mouse IgG:HRP as the secondary.Alpha A Crystallin Antibody.Use in Immunoblotting reported in scientific literature (PMID 28546921). (novusbio.com)
- Immunoblot analysis demonstrated that Ang II increased renal expression of HSP70 and HSP25, as well as HO-1, but that expression of αB-crystallin was unaffected by this treatment. (ahajournals.org)
- Immunoblot analysis showed that lens crystallin reacted highly with this antibody. (nii.ac.jp)
- Anti-human Crystallin alpha A mAb, clone c9F2, is derived from hybridization of mouse SP2/O myeloma cells with spleen cells from BALB/c mice immunized with recombinant Crystallin alpha A. (mybiosource.com)
- This antibody is not shown cross-activity about Crystallin alpha B. A : Crystallin-alpha A recombinant protein B : Crystallin-alpha B recombinant protein C : Mouse eye lysates The Cell lysates (5ug) were resolved by SDS-PAGE, transferred to PVDF membrane and probed with anti-human Crystallin alpha A antibody (1:3000). (mybiosource.com)
- E. coli -derived recombinant protein corresponding to full-length (aa1-173) human crystallin alpha A. (bio-rad-antibodies.com)
- Here, we investigated the regulation of expression and localization of other HSPs, including HSP70, HSP25, and αB-crystallin, in the kidney of rats undergoing long-term administration of Ang II (0.7 mg · kg −1 · d −1 ). (ahajournals.org)
- Note that in comparison to neurons astrocytes constitutively express high amounts of HSP25 and B-crystallin, while HSP60 and HSC 70 are similarly prominent in both cell types. (hindawi.com)
- In response to cellular stress, alpha crystallin is phosphorlyated and may serve a structural control function and play a role in protein maintenance. (qedbio.com)
- When cellular stress occurs, alpha-crystallin enters its' phosphorylated state and may serve a structural control function and play a role in protein maintenance (2). (biovendor.com)
- Alpha-enolase in addition, functions as a structural lens protein (tau-crystallin) in the monomeric form. (genecards.org)
- Crystallins are the dominant structural components of the vertebrate eye lens. (ptglab.com)
- it encodes alpha-enolase, a homodimeric soluble enzyme, and also encodes a shorter monomeric structural lens protein, tau-crystallin. (avivasysbio.com)
- We examined αB-crystallin expression in primary breast carcinomas with metastatic data to evaluate its association with prognosis and site-specific metastases. (nature.com)
- αB-crystallin protein expression was determined by immunohistochemistry using the clinically annotated British Columbia Cancer Agency (BCCA) tissue microarray ( n =3,987 breast tumors). (nature.com)
- In the BCCA series, αB-crystallin protein expression was an independent prognostic marker of poor breast cancer-specific survival (HR=1.3, (95% CI 1.1-1.6), P =0.014). (nature.com)
- We thus suggest that the relatively high concentration of Pax-6 contributes to the absence of βB1-crystallin gene expression in lens epithelial cells and that diminishing amounts of Pax-6 in lens fiber cells during development allow activation of this gene. (asm.org)
- We show that the transcription factor Pax6 expressed in dopaminergic neurons of the olfactory bulb regulates the survival of these neurons by directly controlling the expression of crystallin αA (CryαA), which blocks apoptosis by inhibition of procaspase-3 activation. (nih.gov)
- Also these results suggest that crystallin gene expression can be regulated by pro-inflammatory events in the eye. (molvis.org)
- αB-crystallin (αB-C) is a subunit of α-crystallin, a major protein component of the vertebrate lens, and αB-C expression has been reported in extra-lenticular tissues. (nii.ac.jp)
- Since most of previous studies using this antibody have primarily dealt with ballooned neurons, we investigated such αB-C expression in neuronal abnormalities of various neurological diseases. (nii.ac.jp)
- We set out to assess whether αB-crystallin expression is correlated with worse prognosis and whether this is related to VEGF secretion and cell motility in head and neck squamous cell carcinoma (HNSCC). (biomedcentral.com)
- αB-crystallin expression was determined immunohistochemically in tumor biopsies of 38 HNSCC patients. (biomedcentral.com)
- Locoregional control (LRC) and metastasis-free survival (MFS) of the patients were analyzed in relation to αB-crystallin expression. (biomedcentral.com)
- Our data suggest that αB-crystallin expression is associated with distant metastases formation in HNSCC patients. (biomedcentral.com)
- αB-crystallin expression levels were immunohistochemically determined in HNSCC biopsies and correlated with clinicopathological characteristics and outcome. (biomedcentral.com)
- The mechanism of this resistance appears to involve the increased expression of Hsp 27 and alphaB-crystallin. (unboundmedicine.com)
- Characterization of Antibodies to Identify Cellular Expression of Dopamine Receptor 4 Adv Exp Med Biol. (usc.edu)
- The lack of encephalitogenicity of whole protein and dominant epitopes may be due to the low constitutive expression of αB-crystallin in the CNS combined with a state of peripheral tolerance suggested by the constitutive expression of αB-crystallin in secondary lymphoid tissues in ABH mice. (tudelft.nl)
- These findings demonstrate the potential for new-generation antibody-based tests for the early detection of M. bovis infection in cattle. (asm.org)
- In contrast, the poor sensitivity of antibody-based tests has prevented the widespread use of these assays for the early detection of tuberculous cattle ( 14 ). (asm.org) |
A function can take multiple arguments, these arguments can be objects, variables(of same or different data types) and functions. Python functions are first class objects. In the example below, a function is assigned to a variable. This assignment doesn’t call the function. It takes the function object referenced by shout and creates a second name pointing to it, yell.
Higher Order Functions
Because functions are objects we can pass them as arguments to other functions. Functions that can accept other functions as arguments are also called higher-order functions. In the example below, a function greet is created which takes a function as an argument.
HI, I AM CREATED BY A FUNCTION PASSED AS AN ARGUMENT. hi, i am created by a function passed as an argument.
Wrapper function or decorator allows us to wrap another function in order to extend the behavior of the wrapped function, without permanently modifying it. In Decorators, functions are taken as the argument into another function and then called inside the wrapper function. To know more about decorator click here.
Below is the example of a simple decorator.
Hello, this is before function execution This is inside the function !! This is after function execution
Lambda wrapper function
In Python, anonymous function means that a function is without a name. As we already know that
def keyword is used to define the normal functions and the
lambda keyword is used to create anonymous functions. This function can have any number of arguments but only one expression, which is evaluated and returned. Lambda function can also have another function as an argument. The below example shows a basic lambda function where another lambda function is passed as an argument.
square of 2 is :4 The cube of 4 is 64
Attention geek! Strengthen your foundations with the Python Programming Foundation Course and learn the basics.
To begin with, your interview preparations Enhance your Data Structures concepts with the Python DS Course.
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We know that the grammar of a language is a set of rules that explain how words are used in a language to form meaningful sentences. Similarly, grammar of graphics defines rules for structuring mathematics and aesthetic elements into a meaningful graph, i.e., graphics are built based on an underlying grammar.
The grammar of graphics in
ggplot is a plotting framework developed by Leland Wilkinson in his book ‘Grammar of Graphics’ published in 1999.
There are two important principles here:
- Graphics are made of distinct layers of grammatical elements
- Plots are built with appropriate aesthetic mappings to makes these plots meaningful
In brief, the grammar tells us that a statistical graphic is a mapping from data to aesthetic attributes (colour, shape, size) of geometric objects (points, lines, bars). The plot may also contain statistical transformations of the data and is drawn on a specific coordinate systemFrom ggplot2 book
Components of Grammar of Graphics
There are 7 grammatical elements in
ggplot2 with 3 being essential. The following table summarizes these elements:
|Data||This is the dataset being plotted containing the variables to be plotted on the graph.This is an essential element.|
|Aesthetics||Aesthetics refers to the scales on which we map our data. For example, we will map one variable to the x-axis, and another to y-axis. We may use to differentiate different attributes by color. Some common aesthetics to consider are axis, shape, size and color.This is an essential element.|
|Geometries||Geom refers to the actual visual elements used for the data in the plot, such as points, lines, and bars.|
This is an essential element.
|Facets||Faceting refers to splitting the data into multiple subsets and then displaying plots for the specific subsets in a panel. Such plots are also called small-multiple plots. The facet approach partitions a plot into a matrix of panels. Each panel shows a different subset of the data.This is an optional element.|
|Statistics||This refers to representing statistical information about the data, such as mean and variance, to help in understanding the data.This is an optional element.|
|Coordinates||This refers to the space on which the data is plotted (E.g., Cartesian coordinates). Most popular graphs such as line and bar charts are drawn using Cartesian coordinates.|
This is an optional element.
|Themes||Themes are used to change the appearance of non-data elements. Themes enable you to design with a particular visual identity using fonts, colours and other design elements.This is an optional element.|
It is useful to think of plots made up of layers. A layer can be thought of as consisting of the data, a mapping of data to aesthetics, and a geometry to visually display the data. Sometimes you can also use additional parameters to customize the display.
The grammar of graphics is implemented in R using the ggplot2 package. Essentially we develop plots by layering graphical elements on top of each other and use aesthetic mappings to refine our visualizations.
The following diagram provides an Ariel view of choices we will make while defining each layer in a plot. So, when we are making a plot with
ggplot2, we are making choices from these items (Note: These are examples of choices. there are more choices that are not shown.)
In the next few lessons, we will learn about how we can create a variety of meaningful data visualizations using ggplot2 by implementing these 7 layers of grammar of graphics. |
A NASA satellite designed to precisely measure changes in Earth’s ice sheets, glaciers, sea ice and vegetation was launched into polar orbit from California early on September 15. A Delta 2 rocket carrying ICESat-2 lifted off from Vandenberg Air Force Base at 6:02 AM and headed over the Pacific Ocean.
NASA Earth Science Division director Michael Freilich says that the mission, in particular, will advance knowledge of how the ice sheets of Greenland and Antarctica contribute to sea level rise. The melt from those ice sheets alone has raised global sea level by more than 1 millimetre (0.04 inch) a year recently, according to NASA.
The mission is a successor to the original Ice, Cloud and Land Elevation Satellite that operated from 2003 to 2009. Measurements continued since then with airborne instruments in NASA’s Operation IceBridge.
Built by Northrop Grumman, ICESat-2 carries a single instrument, a laser altimeter that measures height by determining how long it takes photons to travel from the spacecraft to Earth and back. According to NASA, it will collect more than 250 times as many measurements as the first ICESat.
The laser is designed to fire 10,000 times per second, divided into six beams of hundreds of trillions of photons. The round trip is timed to a billionth of a second.
In addition to ice, the satellite’s other measurements, such as the tops of trees, snow and river heights, may help with research into the amount of carbon stored in forests, flood and drought planning and wildfire behaviour, among other uses.
The launch was the last for a Delta 2 rocket, United Launch Alliance said. The first Delta 2 lifted off on February 14,1989, and since then it has been the launch vehicle for Global Positioning System orbiters, Earth observing and commercial satellites, and interplanetary missions including the twin Mars rovers Spirit and Opportunity. |
A 30-60-90 triangle is a right triangle with angles that measure 30 degrees, 60 degrees, and 90 degrees. It has some special properties. One of them is that if we know the length of only one side, we … [Read more...] about 30-60-90 Triangle
A triangle in which one of the edges is perpendicular to another, forming a 90° angle is called a “Right triangle”:
The two edges which form the right angle (a and b) are called the “legs”, and the third edge (c), opposite the right angle, is called the hypotenuse.
The properties of right triangles, which we will prove, are the things we will use in problems involving right triangles. These include:
1. The Pythagorean theorem: a2+b2 = c2 – this will be useful in any problem that asks us to find the edge lengths or areas of shapes made up of one or more right triangles.
2. The length of the median – a line that connects a vertice (or corner) of a triangle to the mid-point of the opposite side – to the hypotenuse is equal to half the length of the hypotenuse. We will use this whenever we see the median in a problem or the mid-point of the hypotenuse being used.
3. The sum of the two angles that are not the right angle is 90° (since the sum of all the angles is 180 °, and the right angle is 90°, so the other two must sum up to 180°-90°= 90°). We’ll use these in problems involving finding angle sizes in right triangles.
Now that we've explained the basic concept of right triangles in geometry, let's scroll down to work on specific geometry problems relating to this topic.
In today's geometry lesson, we will prove that in a right triangle, the median to the hypotenuse is equal to half the hypotenuse. The median of a triangle is a line drawn from one of the vertices … [Read more...] about Right Triangles: Median to the Hypotenuse is Equal to Half the Hypotenuse
A 45 45 90 triangle has unique properties. Here's a good strategy for solving multiple-step geometry problems that involve it. A right triangle has one angle which is 90°, so the sum of the other … [Read more...] about 45 45 90 Triangle |
Relative density, or specific gravity,12 is the ratio of the density (mass of a unit volume) of a substance to the density of a given reference material. Specific gravity usually means relative density with respect to water. The term "relative density" is often preferred in modern scientific usage.
If a substance's relative density is less than one then it is less dense than the reference; if greater than 1 then it is denser than the reference. If the relative density is exactly 1 then the densities are equal; that is, equal volumes of the two substances have the same mass. If the reference material is water then a substance with a relative density (or specific gravity) less than 1 will float in water. For example, an ice cube, with a relative density of about 0.91, will float. A substance with a relative density greater than 1 will sink.
Temperature and pressure must be specified for both the sample and the reference. Pressure is nearly always 1 atm equal to 101.325 kPa. Where it is not, it is more usual to specify the density directly. Temperatures for both sample and reference vary from industry to industry. In British brewing practice the specific gravity as specified above is multiplied by 1000.3 Specific gravity is commonly used in industry as a simple means of obtaining information about the concentration of solutions of various materials such as brines, sugar solutions (syrups, juices, honeys, brewers wort, must, etc.) and acids.
Relative density (RD) or specific gravity (SG) is a dimensionless quantity, as it is the ratio of either densities or weights
where RD is relative density, ρsubstance is the density of the substance being measured, and ρreference is the density of the reference. (By convention ρ, the Greek letter rho, denotes density.)
The reference material can be indicated using subscripts: RDsubstance/reference, which means "the relative density of substance with respect to reference". If the reference is not explicitly stated then it is normally assumed to be water at 4 °C (or, more precisely, 3.98 °C, which is the temperature at which water reaches its maximum density). In SI units, the density of water is (approximately) 1000 kg/m3 or 1 g/cm3, which makes relative density calculations particularly convenient: the density of the object only needs to be divided by 1000 or 1, depending on the units.
The relative density of gases is often measured with respect to dry air at a temperature of 20 °C and a pressure of 101.325 kPa absolute, which has a density of 1.205 kg/m3. Relative density with respect to air can be obtained by
Where M is the molar mass and the approximately equal sign is used because equality pertains only if 1 mol of the gas and 1 mol of air occupy the same volume at a given temperature and pressure i.e. they are both Ideal gases. Ideal behaviour is usually only seen at very low pressure. For example, one mol of an ideal gas occupies 22.414 L at 0 °C and 1 atmosphere whereas carbon dioxide has a molar volume of 22.259 L under those same conditions.
- See Density for a table of the measured densities of water at various temperatures.
The density of substances varies with temperature and pressure so that it is necessary to specify the temperatures and pressures at which the densities or weights were determined. It is nearly always the case that measurements are made at nominally 1 atmosphere (101.325 kPa the variations caused by changing weather patterns) but as specific gravity usually refers to highly incompressible aqueous solutions or other incompressible substances (such as petroleum products) variations in density caused by pressure are usually neglected at least where apparent specific gravity is being measured. For true (in vacuo) specific gravity calculations air pressure must be considered (see below). Temperatures are specified by the notation Ts/Tr) with Ts representing the temperature at which the sample's density was determined and Tr the temperature at which the reference (water) density is specified. For example SG (20°C/4°C) would be understood to mean that the density of the sample was determined at 20 °C and of the water at 4 °C. Taking into account different sample and reference temperatures we note that while SGH2O = 1.000000 (20°C/20°C) it is also the case that SGH2O = 0.998203/0.998840 = 0.998363 (20°C/4°C). Here temperature is being specified using the current ITS-90 scale and the densities4 used here and in the rest of this article are based on that scale. On the previous IPTS-68 scale the densities at 20 °C and 4 °C are, respectively, 0.9982071 and 0.9999720 resulting in an SG (20°C/4°C) value for water of 0.9982343.
The temperatures of the two materials may be explicitly stated in the density symbols; for example:
- relative density: or specific gravity:
where the superscript indicates the temperature at which the density of the material is measured, and the subscript indicates the temperature of the reference substance to which it is compared.
Relative density can also help quantify the buoyancy of a substance in a fluid, or determine the density of an unknown substance from the known density of another. Relative density is often used by geologists and mineralogists to help determine the mineral content of a rock or other sample. Gemologists use it as an aid in the identification of gemstones. Water is preferred as the reference because measurements are then easy to carry out in the field (see below for examples of measurement methods).
As the principal use of specific gravity measurements in industry is determination of the concentrations of substances in aqueous solutions and these are found in tables of SG vs concentration it is extremely important that the analyst enter the table with the correct form of specific gravity. For example, in the brewing industry, the Plato table, which lists sucrose concentration by weight against true SG, were originally (20 °C/4 °C)5 that is based on measurements of the density of sucrose solutions made at laboratory temperature (20 °C) but referenced to the density of water at 4 °C which is very close to the temperature at which water has its maximum density of ρ(H2O) equal to 0.999972 g/cm3 (or 62.43 lbm·ft−3). The ASBC table6 in use today in North America, while it is derived from the original Plato table is for apparent specific gravity measurements at (20 °C/20 °C) on the IPTS-68 scale where the density of water is 0.9982071 g/cm3. In the sugar, soft drink, honey, fruit juice and related industries sucrose concentration by weight is taken from this work3 which uses SG (17.5 °C/17.5 °C). As a final example, the British SG units are based on reference and sample temperatures of 60°F and are thus (15.56°C/15.56°C).3
Relative density can be calculated directly by measuring the density of a sample and dividing it by the (known) density of the reference substance. The density of the sample is simply its mass divided by its volume. Although mass is easy to measure, the volume of an irregularly shaped sample can be more difficult to ascertain. One method is to put the sample in a water-filled graduated cylinder and read off how much water it displaces. Alternatively the container can be filled to the brim, the sample immersed, and the volume of overflow measured. The surface tension of the water may keep a significant amount of water from overflowing, which is especially problematic for small samples. For this reason it is desirable to use a water container with as small a mouth as possible.
For each substance, the density, ρ, is given by
When these densities are divided, references to the spring constant, gravity and cross-sectional area simply cancel, leaving
Relative density is more easily and perhaps more accurately measured without measuring volume. Using a spring scale, the sample is weighed first in air and then in water. Relative density (with respect to water) can then be calculated using the following formula:
- Wair is the weight of the sample in air (measured in pounds-force, newtons, or some other unit of force)
- Wwater is the weight of the sample in water (measured in the same units).
This technique cannot easily be used to measure relative densities less than one, because the sample will then float. Wwater becomes a negative quantity, representing the force needed to keep the sample underwater.
Another practical method uses three measurements. The sample is weighed dry. Then a container filled to the brim with water is weighed, and weighed again with the sample immersed, after the displaced water has overflowed and been removed. Subtracting the last reading from the sum of the first two readings gives the weight of the displaced water. The relative density result is the dry sample weight divided by that of the displaced water. This method works with scales that can't easily accommodate a suspended sample, and also allows for measurement of samples that are less dense than water.
The relative density of a liquid can be measured using a hydrometer. This consists of a bulb attached to a stalk of constant cross-sectional area, as shown in the diagram to the right.
First the hydrometer is floated in the reference liquid (shown in light blue), and the displacement (the level of the liquid on the stalk) is marked (blue line). The reference could be any liquid, but in practice it is usually water.
The hydrometer is then floated in a liquid of unknown density (shown in green). The change in displacement, Δx, is noted. In the example depicted, the hydrometer has dropped slightly in the green liquid; hence its density is lower than that of the reference liquid. It is, of course, necessary that the hydrometer floats in both liquids.
The application of simple physical principles allows the relative density of the unknown liquid to be calculated from the change in displacement. (In practice the stalk of the hydrometer is pre-marked with graduations to facilitate this measurement.)
In the explanation that follows,
- ρref is the known density (mass per unit volume) of the reference liquid (typically water).
- ρnew is the unknown density of the new (green) liquid.
- RDnew/ref is the relative density of the new liquid with respect to the reference.
- V is the volume of reference liquid displaced, i.e. the red volume in the diagram.
- m is the mass of the entire hydrometer.
- g is the local gravitational constant.
- Δx is the change in displacement. In accordance with the way in which hydrometers are usually graduated, Δx is here taken to be negative if the displacement line rises on the stalk of the hydrometer, and positive if it falls. In the example depicted, Δx is negative.
- A is the cross sectional area of the shaft.
Since the floating hydrometer is in static equilibrium, the downward gravitational force acting upon it must exactly balance the upward buoyancy force. The gravitational force acting on the hydrometer is simply its weight, mg. From the Archimedes buoyancy principle, the buoyancy force acting on the hydrometer is equal to the weight of liquid displaced. This weight is equal to the mass of liquid displaced multiplied by g, which in the case of the reference liquid is ρrefVg. Setting these equal, we have
Exactly the same equation applies when the hydrometer is floating in the liquid being measured, except that the new volume is V - AΔx (see note above about the sign of Δx). Thus,
Combining (1) and (2) yields
But from (1) we have V = m/ρref. Substituting into (3) gives
This equation allows the relative density to be calculated from the change in displacement, the known density of the reference liquid, and the known properties of the hydrometer. If Δx is small then, as a first-order approximation of the geometric series equation (4) can be written as:
This shows that, for small Δx, changes in displacement are approximately proportional to changes in relative density.
A pycnometer (from Greek: πυκνός (puknos) meaning "dense"), also called pyknometer or specific gravity bottle, is a device used to determine the density of a liquid. A pycnometer is usually made of glass, with a close-fitting ground glass stopper with a capillary tube through it, so that air bubbles may escape from the apparatus. This device enables a liquid's density to be measured accurately by reference to an appropriate working fluid, such as water or mercury, using an analytical balancecitation needed.
If the flask is weighed empty, full of water, and full of a liquid whose specific gravity is desired, the specific gravity of the liquid can easily be calculated. The particle density of a powder, to which the usual method of weighing cannot be applied, can also be determined with a pycnometer. The powder is added to the pycnometer, which is then weighed, giving the weight of the powder sample. The pycnometer is then filled with a liquid of known density, in which the powder is completely insoluble. The weight of the displaced liquid can then be determined, and hence the specific gravity of the powder.
There is also a gas-based manifestation of a pycnometer known as a gas pycnometer. It compares the change in pressure caused by a measured change in a closed volume containing a reference (usually a steel sphere of known volume) with the change in pressure caused by the sample under the same conditions. The difference in change of pressure represents the volume of the sample as compared to the reference sphere, and is usually used for solid particulates that may dissolve in the liquid medium of the pycnometer design described above, or for porous materials into which the liquid would not fully penetrate.
When a pycnometer is filled to a specific, but not necessarily accurately known volume, V and is placed upon a balance, it will exert a force
where mb is the mass of the bottle and g the gravitational acceleration at the location at which the measurements are being made. ρa is the density of the air at the ambient pressure and ρb is the density of the material of which the bottle is made (usually glass) so that the second term is the mass of air displaced by the glass of the bottle whose weight, by Archimedes Principle must be subtracted. The bottle is, of course, filled with air but as that air displaces an equal amount of air the weight of that air is canceled by the weight of the air displaced. Now we fill the bottle with the reference fluid e.g. pure water. The force exerted on the pan of the balance becomes:
If we subtract the force measured on the empty bottle from this (or tare the balance before making the water measurement) we obtain.
where the subscript n indicated that this force is net of the force of the empty bottle. The bottle is now emptied, thoroughly dried and refilled with the sample. The force, net of the empty bottle, is now:
where ρs is the density of the sample. The ratio of the sample and water forces is:
This is called the Apparent Specific Gravity, denoted by subscript A, because it is what we would obtain if we took the ratio of net weighings in air from an analytical balance or used a hydrometer (the stem displaces air). Note that the result does not depend on the calibration of the balance. The only requirement on it is that it read linearly with force. Nor does SGA depend on the actual volume of the pycnometer.
Further manipulation and finally substitution of SGV, the true specific gravity (the subscript V is used because this is often referred to as the specific gravity in vacuo), for ρs/ρw gives the relationship between apparent and true specific gravity.
In the usual case we will have measured weights and want the true specific gravity. This is found from
Since the density of dry air at 101.325 kPa at 20 °C is7 0.001205 g/cm3 and that of water is 0.998203 g/cm3 we see that the difference between true and apparent specific gravities for a substance with specific gravity (20°C/20°C) of about 1.100 would be 0.000120. Where the specific gravity of the sample is close to that of water (for example dilute ethanol solutions) the correction is even smaller.
The pycnometer is used in ISO standard: ISO 1183-1:2004, ISO 1014–1985 and ASTM standard: ASTM D854.
- Gay-Lussac, pear shaped, with perforated stopper, adjusted, capacity 1, 2, 5, 10, 25, 50 and 100 ml
- as above, with ground-in thermometer, adjusted, side tube with cap
- Hubbard, for bitumen and heavy oils, cylindrical type, ASTM D 70, 24 ml
- as above, conical type, ASTM D 115 and D 234, 25 ml
- Boot, with vacuum jacket and thermometer, capacity 5, 10, 25 and 50 ml
Hydrostatic Pressure-based Instruments: This technology relies upon Pascal's Principle which states that the pressure difference between two points within a vertical column of fluid is dependent upon the vertical distance between the two points, the density of the fluid and the gravitational force. This technology is often used for tank gaging applications as a convenient means of liquid level and density measure.
Vibrating Element Transducers: This type of instrument requires a vibrating element to be placed in contact with the fluid of interest. The resonant frequency of the element is measured and is related to the density of the fluid by a characterization that is dependent upon the design of the element. In modern laboratories precise measurements of specific gravity are made using oscillating U-tube meters. These are capable of measurement to 5 to 6 places beyond the decimal point and are used in the brewing, distilling, pharmaceutical, petroleum and other industries. The instruments measure the actual mass of fluid contained in a fixed volume at temperatures between 0 and 80 °C but as they are microprocessor based can calculate apparent or true specific gravity and contain tables relating these to the strengths of common acids, sugar solutions, etc. The vibrating fork immersion probe is another good example of this technology. This technology also includes many coriolis-type mass flow meters which are widely used in chemical and petroleum industry for high accuracy mass flow measurement and can be configured to also output density information based on the resonant frequency of the vibrating flow tubes.8
Ultrasonic Transducer: Ultrasonic waves are passed from a source, through the fluid of interest, and into a detector which measures the acoustic spectroscopy of the waves. Fluid properties such as density and viscosity can be inferred from the spectrum.
Radiation-based Gauge: Radiation is passed from a source, through the fluid of interest, and into a scintillation detector, or counter. As the fluid density increases, the detected radiation "counts" will decrease. The source is typically the radioactive isotope cesium-137, with a half-life of about 30 years. A key advantage for this technology is that the instrument is not required to be in contact with the fluid—typically the source and detector are mounted on the outside of tanks or piping.9
Buoyant Force Transducer: the buoyancy force produced by a float in a homogeneous liquid is equal to the weight of the liquid that is displaced by the float. Since buoyancy force is linear with respect to the density of the liquid within which the float is submerged, the measure of the buoyancy force yields a measure of the density of the liquid. One commercially available unit claims the instrument is capable of measuring specific gravity with an accuracy of ± 0.005 SG units. The submersible probe head contains a mathematically characterized spring-float system. When the head is immersed vertically in the liquid, the float moves vertically and the position of the float controls the position of a permanent magnet whose displacement is sensed by a concentric array of Hall-effect linear displacement sensors. The output signals of the sensors are mixed in a dedicated electronics module that provides a single output voltage whose magnitude is a direct linear measure of the quantity to be measured.10
Substances with a specific gravity of 1 are neutrally buoyant, those with SG greater than one are denser than water, and so (ignoring surface tension effects) will sink in it, and those with an SG of less than one are less dense than water, and so will float.
(Samples may vary, and these figures are approximate.)
- Dana, Edward Salisbury (1922). A text-book of mineralogy: with an extended treatise on crystallography.... New York, London(Chapman Hall): John Wiley and Sons. pp. 195–200, 316.
- Schetz, Joseph A.; Allen E. Fuhs (1999-02-05). Fundamentals of fluid mechanics. Wiley, John & Sons, Incorporated. pp. 111,142,144,147,109,155,157,160,175. ISBN 0-471-34856-2.
- Hough, J.S., Briggs, D.E., Stevens, R and Young, T.W. Malting and Brewing Science, Vol. II Hopped Wort and Beer, Chapman and Hall, London, 1991, p. 881
- Bettin, H.; Spieweck, F.: (1990). Die Dichte des Wassers als Funktion der Temperatur nach Einführung des Internationalen Temperaturskala von 1990 (in German). PTB=Mitt. 100. pp. 195–196.
- ASBC Methods of Analysis Preface to Table 1: Extract in Wort and Beer, American Society of Brewing Chemists, St Paul, 2009
- ASBC Methods of Analysis op. cit. Table 1: Extract in Wort and Beer
- DIN51 757 (04.1994): Testing of mineral oils and related materials; determination of density
- dead link
- Density – VEGA Americas, Inc. Ohmartvega.com. Retrieved on 2011-09-30.
- Process Control Digital Electronic Hydrometer. Gardco. Retrieved on 2011-09-30.
- Fundamentals of Fluid Mechanics Wiley, B.R. Munson, D.F. Young & T.H. Okishi
- Introduction to Fluid Mechanics Fourth Edition, Wiley, SI Version, R.W. Fox & A.T. McDonald
- Thermodynamics: An Engineering Approach Second Edition, McGraw-Hill, International Edition, Y.A. Cengel & M.A. Boles
- Munson, B. R.; D. F. Young, T. H. Okishi (2001). Fundamentals of Fluid Mechanics (4th ed.). Wiley. ISBN 978-0-471-44250-9.
- Fox, R. W.; McDonald, A. T. (2003). Introduction to Fluid Mechanics (4th ed.). Wiley. ISBN 0-471-20231-2. |
Differential geometry, branch of mathematics that studies the geometry of curves, surfaces, and manifolds (the higher-dimensional analogs of surfaces). The discipline owes its name to its use of ideas and techniques from differential calculus, though the modern subject often uses algebraic and purely geometric techniques instead. Although basic definitions, notations, and analytic descriptions vary widely, the following geometric questions prevail: How does one measure the curvature of a curve within a surface (intrinsic) versus within the encompassing space (extrinsic)? How can the curvature of a surface be measured? What is the shortest path within a surface between two points on the surface? How is the shortest path on a surface related to the concept of a straight line?
While curves had been studied since antiquity, the discovery of calculus in the 17th century opened up the study of more complicated plane curves—such as those produced by the French mathematician René Descartes (1596–1650) with his “compass” (see History of geometry: Cartesian geometry). In particular, integral calculus led to general solutions of the ancient problems of finding the arc length of plane curves and the area of plane figures. This in turn opened the stage to the investigation of curves and surfaces in space—an investigation that was the start of differential geometry.
Some of the fundamental ideas of differential geometry can be illustrated by the strake, a spiraling strip often designed by engineers to give structural support to large metal cylinders such as smokestacks. A strake can be formed by cutting an annular strip (the region between two concentric circles) from a flat sheet of steel and then bending it into a helix that spirals around the cylinder, as illustrated in the figure. What should the radius r of the annulus be to produce the best fit? Differential geometry supplies the solution to this problem by defining a precise measurement for the curvature of a curve; then r can be adjusted until the curvature of the inside edge of the annulus matches the curvature of the helix.
An important question remains: Can the annular strip be bent, without stretching, so that it forms a strake around the cylinder? In particular, this means that distances measured along the surface (intrinsic) are unchanged. Two surfaces are said to be isometric if one can be bent (or transformed) into the other without changing intrinsic distances. (For example, because a sheet of paper can be rolled into a tube without stretching, the sheet and tube are “locally” isometric—only locally because new, and possibly shorter, routes are created by connecting the two edges of the paper.) Thus, the second question becomes: Are the annular strip and the strake isometric? To answer this and similar questions, differential geometry developed the notion of the curvature of a surface.
Curvature of curves
Although mathematicians from antiquity had described some curves as curving more than others and straight lines as not curving at all, it was the German mathematician Gottfried Leibniz who, in 1686, first defined the curvature of a curve at each point in terms of the circle that best approximates the curve at that point. Leibniz named his approximating circle (as shown in the figure) the osculating circle, from the Latin osculare (“to kiss”). He then defined the curvature of the curve (and the circle) as 1/r, where r is the radius of the osculating circle. As a curve becomes straighter, a circle with a larger radius must be used to approximate it, and so the resulting curvature decreases. In the limit, a straight line is said to be equivalent to a circle of infinite radius and its curvature defined as zero everywhere. The only curves in ordinary Euclidean space with constant curvature are straight lines, circles, and helices. In practice, curvature is found with a formula that gives the rate of change, or derivative, of the tangent to the curve as one moves along the curve. This formula was discovered by Isaac Newton and Leibniz for plane curves in the 17th century and by the Swiss mathematician Leonhard Euler for curves in space in the 18th century. (Note that the derivative of the tangent to the curve is not the same as the second derivative studied in calculus, which is the rate of change of the tangent to the curve as one moves along the x-axis.)
With these definitions in place, it is now possible to compute the ideal inner radius r of the annular strip that goes into making the strake shown in the figure. The annular strip’s inner curvature 1/r must equal the curvature of the helix on the cylinder. If R is the radius of the cylinder and H is the height of one turn of the helix, then the curvature of the helix is 4π2R/[H2 + (2πR)2]. For example, if R = 1 metre and H = 10 metres, then r = 3.533 metres.
Curvature of surfaces
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To measure the curvature of a surface at a point, Euler, in 1760, looked at cross sections of the surface made by planes that contain the line perpendicular (or “normal”) to the surface at the point (see figure). Euler called the curvatures of these cross sections the normal curvatures of the surface at the point. For example, on a right cylinder of radius r, the vertical cross sections are straight lines and thus have zero curvature; the horizontal cross sections are circles, which have curvature 1/r. The normal curvatures at a point on a surface are generally different in different directions. The maximum and minimum normal curvatures at a point on a surface are called the principal (normal) curvatures, and the directions in which these normal curvatures occur are called the principal directions. Euler proved that for most surfaces where the normal curvatures are not constant (for example, the cylinder), these principal directions are perpendicular to each other. (Note that on a sphere all the normal curvatures are the same and thus all are principal curvatures.) These principal normal curvatures are a measure of how “curvy” the surface is.
The theory of surfaces and principal normal curvatures was extensively developed by French geometers led by Gaspard Monge (1746–1818). It was in an 1827 paper, however, that the German mathematician Carl Friedrich Gauss made the big breakthrough that allowed differential geometry to answer the question raised above of whether the annular strip is isometric to the strake. The Gaussian curvature of a surface at a point is defined as the product of the two principal normal curvatures; it is said to be positive if the principal normal curvatures curve in the same direction and negative if they curve in opposite directions. Normal curvatures for a plane surface are all zero, and thus the Gaussian curvature of a plane is zero. For a cylinder of radius r, the minimum normal curvature is zero (along the vertical straight lines), and the maximum is 1/r (along the horizontal circles). Thus, the Gaussian curvature of a cylinder is also zero.
If the cylinder is cut along one of the vertical straight lines, the resulting surface can be flattened (without stretching) onto a rectangle. In differential geometry, it is said that the plane and cylinder are locally isometric. These are special cases of two important theorems:
- Gauss’s “Remarkable Theorem” (1827). If two smooth surfaces are isometric, then the two surfaces have the same Gaussian curvature at corresponding points. (Athough defined extrinsically, Gaussian curvature is an intrinsic notion.)
- Minding’s theorem (1839). Two smooth (“cornerless”) surfaces with the same constant Gaussian curvature are locally isometric.
As corollaries to these theorems:
- A surface with constant positive Gaussian curvature c has locally the same intrinsic geometry as a sphere of radius √1/c. (This is because a sphere of radius r has Gaussian curvature 1/r2).
- A surface with constant zero Gaussian curvature has locally the same intrinsic geometry as a plane. (Such surfaces are called developable).
- A surface with constant negative Gaussian curvature c has locally the same intrinsic geometry as a hyperbolic plane. (See non-Euclidean geometry.)
The Gaussian curvature of an annular strip (being in the plane) is constantly zero. So to answer whether or not the annular strip is isometric to the strake, one needs only to check whether a strake has constant zero Gaussian curvature. The Gaussian curvature of a strake is actually negative, hence the annular strip must be stretched—although this can be minimized by narrowing the shapes.
Shortest paths on a surface
From an outside, or extrinsic, perspective, no curve on a sphere is straight. Nevertheless, the great circles are intrinsically straight—an ant crawling along a great circle does not turn or curve with respect to the surface. About 1830 the Estonian mathematician Ferdinand Minding defined a curve on a surface to be a geodesic if it is intrinsically straight—that is, if there is no identifiable curvature from within the surface. A major task of differential geometry is to determine the geodesics on a surface. The great circles are the geodesics on a sphere.
A great circle arc that is longer than a half circle is intrinsically straight on the sphere, but it is not the shortest distance between its endpoints. On the other hand, the shortest path in a surface is not always straight, as shown in the figure. An important theorem is:
On a surface which is complete (every geodesic can be extended indefinitely) and smooth, every shortest curve is intrinsically straight and every intrinsically straight curve is the shortest curve between nearby points. |
Moons of Saturn
The moons of Saturn are numerous and diverse ranging from tiny moonlets less than 1 kilometer across to the enormous Titan, which is larger than the planet Mercury. Saturn has 62 moons with confirmed orbits, 53 of which have names and only 13 of which have diameters larger than 50 kilometers. Seven Saturnian moons are large enough to be ellipsoidal in shape, though only two of those, Titan and Rhea, are currently in hydrostatic equilibrium, as well as dense rings with complex orbital motions of their own. Particularly notable among Saturn's moons are Titan, the second-largest moon in the Solar System, with a nitrogen-rich Earth-like atmosphere and a landscape including hydrocarbon lakes and dry river networks; and Enceladus, which emits jets of gas and dust and may harbor liquid water under its south pole region.
Twenty-four of Saturn's moons are regular satellites; they have prograde orbits not greatly inclined to Saturn's equatorial plane. They include the seven major satellites, four small moons that exist in a trojan orbit with larger moons, two mutually co-orbital moons and two moons that act as shepherds of Saturn's F Ring. Two other known regular satellites orbit within gaps in Saturn's rings. The relatively large Hyperion is locked in a resonance with Titan. The remaining regular moons orbit near the outer edge of the A Ring, within G Ring and between the major moons Mimas and Enceladus. The regular satellites are traditionally named after Titans and Titanesses or other figures associated with the mythological Saturn.
The remaining 38, all small except one, are irregular satellites, whose orbits are much farther from Saturn, have high inclinations, and are mixed between prograde and retrograde. These moons are probably captured minor planets, or debris from the breakup of such bodies after they were captured, creating collisional families. The irregular satellites have been classified by their orbital characteristics into the Inuit, Norse, and Gallic groups, and their names are chosen from the corresponding mythologies. The largest of the irregular moons is Phoebe, the ninth moon of Saturn, discovered at the end of the 19th century.
The rings of Saturn are made up of objects ranging in size from microscopic to moonlets hundreds of meters across, each in its own orbit around Saturn. Thus a precise number of Saturnian moons cannot be given, because there is no objective boundary between the countless small anonymous objects that form Saturn's ring system and the larger objects that have been named as moons. Over 150 moonlets embedded in the rings have been detected by the disturbance they create in the surrounding ring material, though this is thought to be only a small sample of the total population of such objects.
- 1 Discovery and naming
- 2 Sizes
- 3 Orbital groups
- 4 Tables of moons
- 5 Formation
- 6 Notes
- 7 References
- 8 External links
Discovery and naming
Before the advent of telescopic photography, eight moons of Saturn were discovered by direct observation using optical telescopes. Saturn's largest moon, Titan, was discovered in 1655 by Christiaan Huygens using a 57-millimeter (2.2 in) objective lens on a refracting telescope of his own design. Tethys, Dione, Rhea and Iapetus (the "Sidera Lodoicea") were discovered between 1671 and 1684 by Giovanni Domenico Cassini. Mimas and Enceladus were discovered in 1789 by William Herschel. Hyperion was discovered in 1848 by W.C. Bond, G.P. Bond and William Lassell.
The use of long-exposure photographic plates made possible the discovery of additional moons. The first to be discovered in this manner, Phoebe, was found in 1899 by W.H. Pickering. In 1966 the tenth satellite of Saturn was discovered by Audouin Dollfus, when the rings were observed edge-on near an equinox. It was later named Janus. A few years later it was realized that all observations of 1966 could only be explained if another satellite had been present and that it had an orbit similar to that of Janus. This object is now known as Epimetheus, the eleventh moon of Saturn. It shares the same orbit with Janus—the only known example of co-orbitals in the Solar System. In 1980 three additional Saturnian moons were discovered from the ground and later confirmed by the Voyager probes. They are trojan moons of Dione (Helene) and Tethys (Telesto and Calypso).
Observations by spacecraft
The study of the outer planets has since been revolutionized by the use of unmanned space probes. The arrival of the Voyager spacecraft at Saturn in 1980–1981 resulted in the discovery of three additional moons—Atlas, Prometheus and Pandora, bringing the total to 17. In addition, Epimetheus was confirmed as distinct from Janus. In 1990, Pan was discovered in archival Voyager images.
The Cassini mission, which arrived at Saturn in the summer of 2004, initially discovered three small inner moons including Methone and Pallene between Mimas and Enceladus as well as the second Lagrangian moon of Dione—Polydeuces. It also observed three suspected but unconfirmed moons in the F Ring. In November 2004 Cassini scientists announced that the structure of Saturn's rings indicates the presence of several more moons orbiting within the rings, although only one, Daphnis, has been visually confirmed so far (in 2005). In 2007 Anthe was announced. In 2008 it was reported that Cassini observations of a depletion of energetic electrons in Saturn's magnetosphere near Rhea might be the signature of a tenuous ring system around Saturn's second largest moon. In March 2009, Aegaeon, a moonlet within the G Ring, was announced. In July of the same year, S/2009 S 1, the first moonlet within the B Ring, was observed. In April 2014, the possible beginning of a new moon, within the A Ring, was reported. (related image)
Study of Saturn's moons has also been aided by advances in telescope instrumentation, primarily the introduction of digital charge-coupled devices which replaced photographic plates. For the entire 20th century, Phoebe stood alone among Saturn's known moons with its highly irregular orbit. Beginning in 2000, however, three dozen additional irregular moons have been discovered using ground-based telescopes. A survey starting in late 2000 and conducted using three medium-size telescopes found thirteen new moons orbiting Saturn at a great distance, in eccentric orbits, which are highly inclined to both the equator of Saturn and the ecliptic. They are probably fragments of larger bodies captured by Saturn's gravitational pull. In 2005, astronomers using the Mauna Kea Observatory announced the discovery of twelve more small outer moons. In 2006, astronomers using the Subaru 8.2 m telescope reported the discovery of further nine irregular moons. In April 2007, Tarqeq (S/2007 S 1) was announced. In May of the same year S/2007 S 2 and S/2007 S 3 were reported.
The modern names for Saturnian moons were suggested by John Herschel in 1847. He proposed to name them after mythological figures associated with the Roman god of agriculture and harvest, Saturn (equated to the Greek Cronus). In particular, the then known seven satellites were named after Titans and Titanesses—brothers and sisters of Saturn. In 1848 Lassell proposed that the eighth satellite of Saturn was named Hyperion after another Titan. When in the 20th century the names of Titans were exhausted, the moons were named after different characters of the Greco-Roman mythology or giants from other mythologies. All the irregular moons (except Phoebe) are named after Inuit and Gallic gods and after Norse ice giants.
Some asteroids share the same names as moons of Saturn: 55 Pandora, 106 Dione, 577 Rhea, 1809 Prometheus, 1810 Epimetheus, and 4450 Pan. In addition, two more asteroids previously shared the names of Saturnian moons until spelling differences were made permanent by the International Astronomical Union (IAU): Calypso and asteroid 53 Kalypso; and Helene and asteroid 101 Helena.
The Saturnian moon system is very lopsided: one moon, Titan, comprises more than 96% of the mass in orbit around the planet. The six other planemo (ellipsoidal) moons constitute roughly 4%, while the remaining 55 small moons, together with the rings, comprise only 0.04%.[a]
|Saturn's major satellites, compared to Earth's Moon|
Although the boundaries may be somewhat vague, Saturn's moons can be divided into ten groups according to their orbital characteristics. Many of them, such as Pan and Daphnis, orbit within Saturn's ring system and have orbital periods only slightly longer than the planet's rotation period. The innermost moons and most regular satellites all have mean orbital inclinations ranging from less than a degree to about 1.5 degrees (except Iapetus, which has an inclination of 7.57 degrees) and small orbital eccentricities. On the other hand, irregular satellites in the outermost regions of Saturn's moon system, in particular the Norse group, have orbital radii of millions of kilometers and orbital periods lasting several years. The moons of the Norse group also orbit in the opposite direction to Saturn's rotation.
During late July 2009, a moonlet was discovered in the B Ring, 480 km from the outer edge of the ring, by the shadow it cast. It is estimated to be 300 m in diameter. Unlike the A Ring moonlets (see below), it does not induce a 'propeller' feature, probably due to the density of the B Ring.
In 2006, four tiny moonlets were found in Cassini images of the A Ring. Before this discovery only two larger moons had been known within gaps in the A Ring: Pan and Daphnis. These are large enough to clear continuous gaps in the ring. In contrast, a moonlet is only massive enough to clear two small—about 10 km across—partial gaps in the immediate vicinity of the moonlet itself creating a structure shaped like an airplane propeller. The moonlets themselves are tiny, ranging from about 40 to 500 meters in diameter, and are too small to be seen directly. In 2007, the discovery of 150 more moonlets revealed that they (with the exception of two that have been seen outside the Encke gap) are confined to three narrow bands in the A Ring between 126,750 and 132,000 km from Saturn's center. Each band is about a thousand kilometers wide, which is less than 1% the width of Saturn's rings. This region is relatively free from the disturbances related to resonances with larger satellites, although other areas of the A Ring without disturbances are apparently free of moonlets. The moonlets were probably formed from the breakup of a larger satellite. It is estimated that the A Ring contains 7,000–8,000 propellers larger than 0.8 km in size and millions larger than 0.25 km.
Similar moonlets may reside in the F Ring. There, "jets" of material may be due to collisions, initiated by perturbations from the nearby small moon Prometheus, of these moonlets with the core of the F Ring. One of the largest F-Ring moonlets may be the as-yet unconfirmed object S/2004 S 6. The F Ring also contains transient "fans" which are thought to result from even smaller moonlets, about 1 km in diameter, orbiting near the F Ring core.
One of the recently discovered moons, Aegaeon, resides within the bright arc of G Ring and is trapped in the 7:6 mean motion resonance with Mimas. This means that it makes exactly seven revolutions around Saturn while Mimas makes exactly six. The moon is the largest among the population of bodies that are sources of dust in this ring.
Shepherd satellites are small moons that orbit within, or just beyond, a planet's ring system. They have the effect of sculpting the rings: giving them sharp edges, and creating gaps between them. Saturn's shepherd moons are Pan (Encke gap), Daphnis (Keeler gap), Atlas (A Ring), Prometheus (F Ring) and Pandora (F Ring). These moons together with co-orbitals (see below) probably formed as a result of accretion of the friable ring material on preexisting denser cores. The cores with sizes from one-third to one-half the present day moons may be themselves collisional shards formed when a parental satellite of the rings disintegrated.
Janus and Epimetheus are called co-orbital moons. They are of roughly equal size, with Janus being slightly larger than Epimetheus. Janus and Epimetheus have orbits with only a few kilometers difference in semi-major axis, close enough that they would collide if they attempted to pass each other. Instead of colliding, however, their gravitational interaction causes them to swap orbits every four years.
Inner large moons
The innermost large moons of Saturn orbit within its tenuous E Ring, along with three smaller moons of the Alkyoniods group.
- Mimas is the smallest and least massive of the inner round moons, although its mass is sufficient to alter the orbit of Methone. It is noticeably ovoid-shaped, having been made shorter at the poles and longer at the equator (by about 20 km) by the effects of Saturn's gravity. Mimas has a large impact crater one-third its diameter, Herschel, situated on its leading hemisphere. Mimas has no known past or present geologic activity, and its surface is dominated by impact craters. The only tectonic features known are a few arcuate and linear troughs, which probably formed when Mimas was shattered by the Herschel impact.
- Enceladus is one of the smallest of Saturn's moons that is spherical in shape—only Mimas is smaller—yet is the only small Saturnian moon that is currently endogenously active, and the smallest known body in the Solar System that is geologically active today. Its surface is morphologically diverse; it includes ancient heavily cratered terrain as well as younger smooth areas with few impact craters. Many plains on Enceladus are fractured and intersected by systems of lineaments. The area around its south pole was found by Cassini to be unusually warm and cut by a system of fractures about 130 km long called "tiger stripes", some of which emit jets of water vapor and dust. These jets form a large plume off its south pole, which replenishes Saturn's E ring and serves as the main source of ions in the magnetosphere of Saturn. The gas and dust are released with a rate of more than 100 kg/s. Enceladus may have liquid water underneath the south-polar surface. The source of the energy for this cryovolcanism is thought to be a 2:1 mean-motion resonance with Dione. The pure ice on the surface makes Enceladus one of the brightest known objects in the Solar System—its geometrical albedo is more than 140%.
- Tethys is the third largest of Saturn's inner moons. Its most prominent features are a large (400 km diameter) impact crater named Odysseus on its leading hemisphere and a vast canyon system named Ithaca Chasma extending at least 270° around Tethys. The Ithaca Chasma is concentric with Odysseus, and these two features may be related. Tethys appears to have no current geological activity. A heavily cratered hilly terrain occupies the majority of its surface, while a smaller and smoother plains region lies on the hemisphere opposite to that of Odysseus. The plains contain fewer craters and are apparently younger. A sharp boundary separates them from the cratered terrain. There is also a system of extensional troughs radiating away from Odysseus. The density of Tethys (0.985 g/cm3) is less than that of water, indicating that it is made mainly of water ice with only a small fraction of rock.
- Dione is the second-largest inner moon of Saturn. It has a higher density than the geologically dead Rhea, the largest inner moon, but lower than that of active Enceladus. While the majority of Dione's surface is heavily cratered old terrain, this moon is also covered with an extensive network of troughs and lineaments, indicating that in the past it had global tectonic activity. The troughs and lineaments are especially prominent on the trailing hemisphere, where several intersecting sets of fractures form what is called "wispy terrain". The cratered plains have a few large impact craters reaching 250 km in diameter. Smooth plains with low impact-crater counts are present as well on a small fraction its surface. They were probably tectonically resurfaced relatively later in the geological history of Dione. At two locations within smooth plains strange landforms (depressions) resembling oblong impact craters have been identified, both of which lie at the centers of radiating networks of cracks and troughs; these features may be cryovolcanic in origin. Dione may be geologically active even now, although on a scale much smaller than the cryovolcanism of Enceladus. This follows from Cassini magnetic measurements that show Dione is a net source of plasma in the magnetosphere of Saturn, much like Enceladus.
Three small moons orbit between Mimas and Enceladus: Methone, Anthe, and Pallene. Named after the Alkyonides of Greek mythology, they are some of the smallest moons in the Saturn system. Anthe and Methone possess very faint ring arcs along their orbits while Pallene possesses a faint complete ring. Of these three moons, only Methone has been photographed at close range, showing it to be egg-shaped with very few or no craters.
Trojan moons are a unique feature only known from the Saturnian system. A trojan body orbits at either the leading L4 or trailing L5 Lagrange point of a much larger object, such as a large moon or planet. Tethys has two trojan moons, Telesto (leading) and Calypso (trailing), and Dione also has two, Helene (leading) and Polydeuces (trailing). Helene is by far the largest trojan moon, while Polydeuces is the smallest and has the most chaotic orbit. These moons are coated with dusty material that has smoothened out their surfaces.
Outer large moons
These moons all orbit beyond the E Ring. They are:
- Rhea is the second-largest of Saturn's moons. In 2005 Cassini detected a depletion of electrons in the plasma wake of Rhea, which forms when the co-rotating plasma of Saturn's magnetosphere is absorbed by the moon. The depletion was hypothesized to be caused by the presence of dust-sized particles concentrated in a few faint equatorial rings. Such a ring system would make Rhea the only moon in the Solar System known to have rings. However, subsequent targeted observations of the putative ring plane from several angles by Cassini's narrow-angle camera turned up no evidence of the expected ring material, leaving the origin of the plasma observations unresolved. Otherwise Rhea has rather a typical heavily cratered surface, with the exceptions of a few large Dione-type fractures (wispy terrain) on the trailing hemisphere and a very faint "line" of material at the equator that may have been deposited by material deorbiting from present or former rings. Rhea also has two very large impact basins on its anti-Saturnian hemisphere, which are about 400 and 500 km across. The first, Tirawa, is roughly comparable to the Odysseus basin on Tethys. There is also a 48 km-diameter impact crater called Inktomi[b] at 112°W that is prominent because of an extended system of bright rays, which may be one of the youngest craters on the inner moons of Saturn. No evidence of any endogenic activity has been discovered on the surface of Rhea.
- Titan, at 5,150 km diameter, is the second largest moon in the Solar System and Saturn's largest. Out of all the large moons, Titan is the only one with a dense (surface pressure of 1.5 atm), cold atmosphere, primarily made of nitrogen with a small fraction of methane. The dense atmosphere frequently produces bright white convective clouds, especially over the south pole region. On June 6, 2013, scientists at the IAA-CSIC reported the detection of polycyclic aromatic hydrocarbons in the upper atmosphere of Titan. On June 23, 2014, NASA claimed to have strong evidence that nitrogen in the atmosphere of Titan came from materials in the Oort cloud, associated with comets, and not from the materials that formed Saturn in earlier times. The surface of Titan, which is difficult to observe due to persistent atmospheric haze, shows only a few impact craters and is probably very young. It contains a pattern of light and dark regions, flow channels and possibly cryovolcanoes. Some dark regions are covered by longitudinal dune fields shaped by tidal winds, where sand is made of frozen water or hydrocarbons. Titan is the only moon with large bodies of a liquid on its surface, in the form of methane/ethane lakes in Titan's north and south polar regions. The largest lake, Kraken Mare, is larger than the Caspian Sea. Like Europa and Ganymede, it is believed that Titan has a subsurface ocean made of water mixed with ammonia, which can erupt to the surface of the moon and lead to cryovolcanism. On July 2, 2014, NASA reported the ocean inside Titan may be "as salty as the Earth's Dead Sea".
- Hyperion is Titan's nearest neighbor in the Saturn system. The two moons are locked in a 4:3 mean motion resonance with each other, meaning that while Titan makes four revolutions around Saturn, Hyperion makes exactly three. With an average diameter of about 270 km, Hyperion is smaller and lighter than Mimas. It has an extremely irregular shape, and a very odd, tan-colored icy surface resembling a sponge, though its interior may be partially porous as well. The average density of about 0.55 g/cm3 indicates that the porosity exceeds 40% even assuming it has a purely icy composition. The surface of Hyperion is covered with numerous impact craters—those with diameters 2–10 km are especially abundant. It is the only moon known to have a chaotic rotation, which means Hyperion has no well-defined poles or equator. While on short timescales the satellite approximately rotates around its long axis at a rate of 72–75° per day, on longer timescales its axis of rotation (spin vector) wanders chaotically across the sky. This makes the rotational behavior of Hyperion essentially unpredictable.
- Iapetus is the third-largest of Saturn's moons. Orbiting the planet at 3.5 million km, it is by far the most distant of Saturn's large moons, and also possesses the greatest orbital inclination, at 15.47°. Iapetus has long been known for its unusual two-toned surface; its leading hemisphere is pitch-black and its trailing hemisphere is almost as bright as fresh snow. Cassini images showed that the dark material is confined to a large near equatorial area on the leading hemisphere called Cassini Regio, which extends approximately from 40°N to 40°S. The pole regions of Iapetus are as bright as its trailing hemisphere. Cassini also discovered a 20 km tall equatorial ridge, which spans nearly the moon's entire equator. Otherwise both dark and bright surfaces of Iapetus are old and heavily cratered. The images revealed at least four large impact basins with diameters from 380 to 550 km and numerous smaller impact craters. No evidence of any endogenic activity has been discovered. A clue to the origin of the dark material covering part of Iapetus's starkly dichromatic surface may have been found in 2009, when NASA's Spitzer Space Telescope discovered a vast, nearly invisible disk around Saturn, just inside the orbit of the moon Phoebe—the Phoebe ring. Scientists believe that the disk originates from dust and ice particles kicked up by impacts on Phoebe. Because the disk particles, like Phoebe itself, orbit in the opposite direction to Iapetus, Iapetus collides with them as they drift in the direction of Saturn, darkening its leading hemisphere slightly. Once a difference in albedo, and hence in average temperature, was established between different regions of Iapetus, a thermal runaway process of water ice sublimation from warmer regions and deposition of water vapor onto colder regions ensued. Iapetus's present two-toned appearance results from the contrast between the bright, primarily ice-coated areas and regions of dark lag, the residue left behind after the loss of surface ice.
Irregular moons are small satellites with large-radii, inclined, and frequently retrograde orbits, believed to have been acquired by the parent planet through a capture process. They often occur as collisional families or groups. The precise size as well as albedo of the irregular moons are not known for sure because the moons are very small to be resolved by a telescope, although the latter is usually assumed to be quite low—around 6% (albedo of Phoebe) or less. The irregulars generally have featureless visible and near infrared spectra dominated by water absorption bands. They are neutral or moderately red in color—similar to C-type, P-type, or D-type asteroids, though they are much less red than Kuiper belt objects.[c]
The Inuit group includes five prograde outer moons that are similar enough in their distances from the planet (186–297 radii of Saturn), their orbital inclinations (45–50°) and their colors that they can be considered a group. The moons are Ijiraq, Kiviuq, Paaliaq, Siarnaq, and Tarqeq. The largest among them is Siarnaq with an estimated size of about 40 km.
The Gallic group are four prograde outer moons that are similar enough in their distance from the planet (207–302 radii of Saturn), their orbital inclination (35–40°) and their color that they can be considered a group. They are Albiorix, Bebhionn, Erriapus, and Tarvos. Tarvos, as of 2009, is the most distant of Saturn's moons with a prograde orbit. The largest among these moons is Albiorix with an estimated size of about 32 km.
The Norse (or Phoebe) group consists of 29 retrograde outer moons. They are Aegir, Bergelmir, Bestla, Farbauti, Fenrir, Fornjot, Greip, Hati, Hyrrokkin, Jarnsaxa, Kari, Loge, Mundilfari, Narvi, Phoebe, Skathi, Skoll, Surtur, Suttungr, Thrymr, Ymir, S/2004 S 7, S/2004 S 12, S/2004 S 13, S/2004 S 17, S/2006 S 1, S/2006 S 3, S/2007 S 2, and S/2007 S 3. After Phoebe, Ymir is the largest of the known retrograde irregular moons, with an estimated diameter of only 18 km. The Norse group may itself consist of several smaller subgroups.
- Phoebe, at 214 km in diameter, is by far the largest of Saturn's irregular satellites. It has a retrograde orbit and rotates on its axis every 9.3 hours. Phoebe was the first moon of Saturn to be studied in detail by Cassini, in June 2004; during this encounter Cassini was able to map nearly 90% of the moon's surface. Phoebe has a nearly spherical shape and a relatively high density of about 1.6 g/cm3. Cassini images revealed a dark surface scarred by numerous impacts—there are about 130 craters with diameters exceeding 10 km. Spectroscopic measurement showed that the surface is made of water ice, carbon dioxide, phyllosilicates, organics and possibly iron bearing minerals. Phoebe is believed to be a captured centaur that originated in the Kuiper belt. It also serves as a source of material for the largest known ring of Saturn, which darkens the leading hemisphere of Iapetus (see above).
Tables of moons
Major icy moons
|Name||Pronunciation (key)||Image||Diameter (km)[e]||Mass
(×1015 kg) [f]
|Semi-major axis (km) [g]||Orbital period (d)[g][h]||Inclination [g][i]||Eccentricity||Position||Discovery
|0||S/2009 S/2009 S 1||—||≈ 0.3||< 0.0001||≈ 117000||≈ 0.47||≈ 0°||≈ 0||outer B Ring||2009||Cassini–Huygens|
|0||(moonlets)||—||0.04 to 0.4 (Earhart)||< 0.0001||≈ 130000||≈ 0.55||≈ 0°||≈ 0||Three 1000 km bands within A Ring||2006||Cassini–Huygens|
(34 × 31 × 20)
|4.95±0.75||133584||+0.57505||0.001°||0.000035||in Encke Division||1990||M. Showalter|
(9 × 8 × 6)
|0.084±0.012||136505||+0.59408||≈ 0°||≈ 0||in Keeler Gap||2005||Cassini–Huygens|
(41 × 35 × 19)
|6.6±0.045||137670||+0.60169||0.003°||0.0012||outer A Ring shepherd||1980||Voyager 2|
(136 × 79 × 59)
|159.5±1.5||139380||+0.61299||0.008°||0.0022||inner F Ring shepherd||1980||Voyager 2|
(104 × 81 × 64)
|137.1±1.9||141720||+0.62850||0.050°||0.0042||outer F Ring Shepherd||1980||Voyager 2|
(130 × 114 × 106)
|526.6±0.6||151422||+0.69433||0.335°||0.0098||co-orbital with Janus||1977||J. Fountain, and S. Larson|
(203 × 185 × 153)
|1897.5±0.6||151472||+0.69466||0.165°||0.0068||co-orbital with Epimetheus||1966||A. Dollfus|
|8||LIII||Aegaeon Aegaeon||iːˈdʒiːən||≈ 0.5||≈ 0.0001||167500||+0.80812||0.001°||0.0002||G Ring moonlet||2008||Cassini–Huygens|
(416 × 393 × 381)
|10||XXXII||Methone Methone||mɨˈθoʊniː||3.2±1.2||≈ 0.02||194440||+1.00957||0.007°||0.0001||Alkyonides||2004||Cassini–Huygens|
|11||XLIX||Anthe Anthe||ˈænθiː||≈ 1||≈ 0.007||197700||+1.03650||0.1°||0.001||Alkyonides||2007||Cassini–Huygens|
(6 × 6 × 4)
(513 × 503 × 497)
|108022±101||237950||+1.370218||0.010°||0.0047||Generates the E ring||1789||W. Herschel|
(1077 × 1057 × 1053)
(33 × 24 × 20)
|≈ 9.41||294619||+1.887802||1.158°||0.000||leading Tethys trojan||1980||B. Smith, H. Reitsema, S. Larson, and J. Fountain|
(30 × 23 × 14)
|≈ 6.3||294619||+1.887802||1.473°||0.000||trailing Tethys trojan||1980||D. Pascu, P. Seidelmann, W. Baum, and D. Currie|
(1128 × 1123 × 1119)
(43 × 38 × 26)
|≈ 24.46||377396||+2.736915||0.212°||0.0022||leading Dione trojan||1980||P. Laques and J. Lecacheux|
(3 × 2 × 1)
|≈ 0.03||377396||+2.736915||0.177°||0.0192||trailing Dione trojan||2004||Cassini–Huygens|
(1530 × 1526 × 1525)
|21||VI||Titan ♠Titan||ˈtaɪtən||5151||134520000±20000||1221930||+15.94542||0.3485°||0.0288||1655||C. Huygens|
(360 × 266 × 205)
|5620±50||1481010||+21.27661||0.568°||0.123006||in 4:3 resonance with Titan||1848||W. Bond
(1491 × 1491 × 1424)
|24||XXIV||Kiviuq ‡Kiviuq||ˈkɪviək||≈ 16||≈ 2.79||11294800||+448.16||49.087°||0.3288||Inuit group||2000||B. Gladman, J. Kavelaars, et al.|
|25||XXII||Ijiraq ‡Ijiraq||ˈiː.ɨrɒk||≈ 12||≈ 1.18||11355316||+451.77||50.212°||0.3161||Inuit group||2000||B. Gladman, J. Kavelaars, et al.|
(219 × 217 × 204)
|8292±10||12869700||−545.09||173.047°||0.156242||Norse group||1899||W. Pickering|
|27||XX||Paaliaq ‡Paaliaq||ˈpɑːliɒk||≈ 22||≈ 7.25||15103400||+692.98||46.151°||0.3631||Inuit group||2000||B. Gladman, J. Kavelaars, et al.|
|28||XXVII||Skathi ♣Skathi||ˈskɒði||≈ 8||≈ 0.35||15672500||−732.52||149.084°||0.246||Norse (Skathi) Group||2000||B. Gladman, J. Kavelaars, et al.|
|29||XXVI||Albiorix ♦Albiorix||ˌælbiˈɒrɪks||≈ 32||≈ 22.3||16266700||+774.58||38.042°||0.477||Gallic group||2000||M. Holman|
|30||S/2007A ♣S/2007 S 2||—||≈ 6||≈ 0.15||16560000||−792.96||176.68°||0.2418||Norse group||2007||S. Sheppard, D. Jewitt, J. Kleyna, B. Marsden|
|31||XXXVII||Bebhionn ♦Bebhionn||bɛˈviːn, ˈvɪvi.ɒn||≈ 6||≈ 0.15||17153520||+838.77||40.484°||0.333||Gallic group||2004||S. Sheppard, D. Jewitt, J. Kleyna|
|32||XXVIII||Erriapus ♦Erriapus||ˌɛriˈæpəs||≈ 10||≈ 0.68||17236900||+844.89||38.109°||0.4724||Gallic group||2000||B. Gladman, J. Kavelaars, et al.|
|33||XLVII||Skoll ♣Skoll||ˈskɒl, ˈskɜːl||≈ 6||≈ 0.15||17473800||−862.37||155.624°||0.418||Norse (Skathi) group||2006||S. Sheppard, D. Jewitt, J. Kleyna|
|34||XXIX||Siarnaq ‡Siarnaq||ˈsiːɑrnək||≈ 40||≈ 43.5||17776600||+884.88||45.798°||0.24961||Inuit group||2000||B. Gladman, J. Kavelaars, et al.|
|35||LII||Tarqeq ‡Tarqeq||ˈtɑrkeɪk||≈ 7||≈ 0.23||17910600||+894.86||49.904°||0.1081||Inuit group||2007||S. Sheppard, D. Jewitt, J. Kleyna|
|36||S/2004B ♣S/2004 S 13||—||≈ 6||≈ 0.15||18056300||−905.85||167.379°||0.261||Norse group||2004||S. Sheppard, D. Jewitt, J. Kleyna|
|37||LI||Greip ♣Greip||ˈɡreɪp||≈ 6||≈ 0.15||18065700||−906.56||172.666°||0.3735||Norse group||2006||S. Sheppard, D. Jewitt, J. Kleyna|
|38||XLIV||Hyrrokkin ♣Hyrrokkin||hɪˈrɒkɨn||≈ 8||≈ 0.35||18168300||−914.29||153.272°||0.3604||Norse (Skathi) group||2006||S. Sheppard, D. Jewitt, J. Kleyna|
|39||L||Jarnsaxa ♣Jarnsaxa||jɑrnˈsæksə||≈ 6||≈ 0.15||18556900||−943.78||162.861°||0.1918||Norse group||2006||S. Sheppard, D. Jewitt, J. Kleyna|
|40||XXI||Tarvos ♦Tarvos||ˈtɑrvɵs||≈ 15||≈ 2.3||18562800||+944.23||34.679°||0.5305||Gallic group||2000||B. Gladman, J. Kavelaars, et al.|
|41||XXV||Mundilfari ♣Mundilfari||ˌmʊndəlˈvɛri||≈ 7||≈ 0.23||18725800||−956.70||169.378°||0.198||Norse group||2000||B. Gladman, J. Kavelaars, et al.|
|42||S/2006 ♣S/2006 S 1||—||≈ 6||≈ 0.15||18930200||−972.41||154.232°||0.1303||Norse (Skathi) group||2006||S. Sheppard, D.C. Jewitt, J. Kleyna|
|43||S/2004C ♣S/2004 S 17||—||≈ 4||≈ 0.05||19099200||−985.45||166.881°||0.226||Norse group||2004||S. Sheppard, D. Jewitt, J. Kleyna|
|44||XXXVIII||Bergelmir ♣Bergelmir||bɛərˈjɛlmɪər||≈ 6||≈ 0.15||19104000||−985.83||157.384°||0.152||Norse (Skathi) group||2004||S. Sheppard, D. Jewitt, J. Kleyna|
|45||XXXI||Narvi ♣Narvi||ˈnɑrvi||≈ 7||≈ 0.23||19395200||−1008.45||137.292°||0.320||Norse (Narvi) group||2003||S. Sheppard, D. Jewitt, J. Kleyna|
|46||XXIII||Suttungr ♣Suttungr||ˈsʊtʊŋɡər||≈ 7||≈ 0.23||19579000||−1022.82||174.321°||0.131||Norse group||2000||B. Gladman, J. Kavelaars, et al.|
|47||XLIII||Hati ♣Hati||ˈhɑːti||≈ 6||≈ 0.15||19709300||−1033.05||163.131°||0.291||Norse group||2004||S. Sheppard, D. Jewitt, J. Kleyna|
|48||S/2004A ♣S/2004 S 12||—||≈ 5||≈ 0.09||19905900||−1048.54||164.042°||0.396||Norse group||2004||S. Sheppard, D. Jewitt, J. Kleyna|
|49||XL||Farbauti ♣Farbauti||fɑrˈbaʊti||≈ 5||≈ 0.09||19984800||−1054.78||158.361°||0.209||Norse (Skathi) group||2004||S. Sheppard, D. Jewitt, J. Kleyna|
|50||XXX||Thrymr ♣Thrymr||ˈθrɪmər||≈ 7||≈ 0.23||20278100||−1078.09||174.524°||0.453||Norse group||2000||B. Gladman, J. Kavelaars, et al.|
|51||XXXVI||Aegir ♣Aegir||ˈaɪ.ɪər||≈ 6||≈ 0.15||20482900||−1094.46||167.425°||0.237||Norse group||2004||S. Sheppard, D. Jewitt, J. Kleyna|
|52||S/2007B ♣S/2007 S 3||—||≈ 5||≈ 0.09||20518500||≈ −1100||177.22°||0.130||Norse group||2007||S. Sheppard, D. Jewitt, J. Kleyna|
|53||XXXIX||Bestla ♣Bestla||ˈbɛstlə||≈ 7||≈ 0.23||20570000||−1101.45||147.395°||0.5145||Norse (Narvi) group||2004||S. Sheppard, D. Jewitt, J. Kleyna|
|54||S/2007C ♣S/2004 S 7||—||≈ 6||≈ 0.15||20576700||−1101.99||165.596°||0.5299||Norse group||2004||S. Sheppard, D. Jewitt, J. Kleyna|
|55||S/2006 ♣S/2006 S 3||—||≈ 6||≈ 0.15||21076300||−1142.37||150.817°||0.4710||Norse (Skathi) group||2006||S. Sheppard, D. Jewitt, J. Kleyna|
|56||XLI||Fenrir ♣Fenrir||ˈfɛnrɪər||≈ 4||≈ 0.05||21930644||−1212.53||162.832°||0.131||Norse group||2004||S. Sheppard, D. Jewitt, J. Kleyna|
|57||XLVIII||Surtur ♣Surtur||ˈsɜrtər||≈ 6||≈ 0.15||22288916||−1242.36||166.918°||0.3680||Norse group||2006||S. Sheppard, D. Jewitt, J. Kleyna|
|58||XLV||Kari ♣Kari||ˈkɑri||≈ 7||≈ 0.23||22321200||−1245.06||148.384°||0.3405||Norse (Skathi) group||2006||S. Sheppard, D. Jewitt, J. Kleyna|
|59||XIX||Ymir ♣Ymir||ˈɪmɪər||≈ 18||≈ 3.97||22429673||−1254.15||172.143°||0.3349||Norse group||2000||B. Gladman, J. Kavelaars, et al.|
|60||XLVI||Loge ♣Loge||ˈlɔɪ.eɪ||≈ 6||≈ 0.15||22984322||−1300.95||166.539°||0.1390||Norse group||2006||S. Sheppard, D. Jewitt, J. Kleyna|
|61||XLII||Fornjot ♣Fornjot||ˈfɔrnjɒt||≈ 6||≈ 0.15||24504879||−1432.16||167.886°||0.186||Norse group||2004||S. Sheppard, D. Jewitt, J. Kleyna|
|S/2004 S 6||≈ 3–5||≈ 140130||+0.61801||uncertain objects around the F Ring||2004|
|S/2004 S 3/S 4[j]||≈ 3−5||≈ 140300||≈ +0.619||2004|
- Chiron which was supposedly sighted by Hermann Goldschmidt in 1861, but never observed by anyone else.
- Themis was allegedly discovered in 1905 by astronomer William Pickering, but never seen again. Nevertheless it was included in numerous almanacs and astronomy books until the 1960s.
It is thought that the Saturnian system of Titan, mid-sized moons, and rings developed from a set-up closer to the Galilean moons of Jupiter, though the details are unclear. It has been proposed either that a second Titan-sized moon broke up, producing the rings and inner mid-sized moons, or that two large moons fused to form Titan, with the collision scattering icy debris that formed the mid-sized moons. On June 23, 2014, NASA claimed to have strong evidence that nitrogen in the atmosphere of Titan came from materials in the Oort cloud, associated with comets, and not from the materials that formed Saturn in earlier times.
- The mass of the rings is about the mass of Mimas, while the combined mass of Janus, Hyperion and Phoebe—the most massive of the remaining moons—is about one-third of that. The total mass of the rings and small moons is around 5.5×1019 kg.
- Inktomi was once known as "The Splat".
- The photometric color may be used as a proxy for the chemical composition of satellites' surfaces.
- A confirmed moon is given a permanent designation by the IAU consisting of a name and a Roman numeral. The nine moons that were known before 1900 (of which Phoebe is the only irregular) are numbered in order of their distance from Saturn; the rest are numbered in the order by which they received their permanent designations. Nine small moons of the Norse group and S/2009 S 1 have not yet received a permanent designation.
- The diameters and dimensions of the inner moons from Pan through Janus, Methone, Pallene, Telepso, Calypso, Helene, Hyperion and Phoebe were taken from Thomas 2010, Table 3. Diameters and dimensions of Mimas, Enceladus, Tethys, Dione, Rhea and Iapetus are from Thomas 2010, Table 1. The approximate sizes of other satellites are from the website of Scott Sheppard.
- Masses of the large moons were taken from Jacobson, 2006. Masses of Pan, Daphnis, Atlas, Prometheus, Pandora, Epimetheus, Janus, Hyperion and Phoebe were taken from Thomas, 2010, Table 3. Masses of other small moons were calculated assuming a density of 1.3 g/cm3.
- The orbital parameters were taken from Spitale, et al. 2006, IAU-MPC Natural Satellites Ephemeris Service, and NASA/NSSDC.
- Negative orbital periods indicate a retrograde orbit around Saturn (opposite to the planet's rotation).
- To Saturn's equator for the regular satellites, and to the ecliptic for the irregular satellites
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|Wikimedia Commons has media related to Moons of Saturn.|
- "Simulation showing the position of Saturn's Moon". Retrieved 26 May 2010.
- "Saturn's Rings". NASA's Solar System Exploration. Retrieved 26 May 2010.
- "Saturn's Moons". Astronomy Cast episode No. 61, includes full transcript. Retrieved 26 May 2010.
- Carolyn Porco. Fly me to the moons of Saturn. Retrieved 26 May 2010.
- "The Top 10 Largest Planetary Moons". |
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- Ten ‘Calculate the Area and Perimeter’ Challenges – Ask your students to work out the area and perimeter of these shapes. Available with different shapes and a variety of difficulty levels, with answers for teachers and self-checking.
- Ten ‘Farmer’s Field’ Investigations – Challenge your children to design new fields for the farmer that have a specific area or perimeter. Ten variations are available (at different levels of difficulty) with squared paper templates to use for working out the solutions.
- Two Playground Plans – Can your children calculate the area and perimeter of each piece of playground equipment? Two different playground plans are included (with squares / rectangles or compound shapes) and a blank version is also available so your children can design their own!
- Five Mechanical Maths Challenges – Ask your pupils to calculate the area and perimeter of each body part on these robots! A blank version is also included so that they can design their own.
- Fifteen ‘When do we use Area and Perimeter?’ Posters – A set of fifteen posters that give examples of people using area and perimeter outside of the classroom. Can your children think of any more?
- Two Area and Perimeter Posters – Two handy posters to help your children remember the difference between the area and the perimeter of a shape.
- Five Area and Perimeter Display Banners – A set of eye-catching banners to add to the Maths display boards in your classroom.
Watch the video below to view samples of resources from the Area and Perimeter Pack.
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I teach children at a bilingual school and am always looking for pictorial ways to show them why learning about maths is relevant to their real lives. The photographs of the ways in which people with real jobs use area and perimeter, along with simple, short explanatory sentences, really helps them to engage without overwhelming them with information. Very hard to find this kind of resource elsewhere!
I really found this pack useful. I was having difficulty explaining real life applications for use of area and perimeter but the set of photographs clarified it so much. The activity to estimate and measure the robot body parts was just the right level for my class, and I'm planning the zoo activity for after Easter holidays. Delighted I signed up to Teaching Packs.
My year 3s loved using the challenges in this pack. Worked well across all abilities.
Fantastic resource to use with year 4, 5, 6 students when covering this maths topic. Great to use for displays and also to initiate discussions and encourage kids to verbalise their understanding of concepts.
As always the presentation of this is outstanding.
What is disappointing is the lack of either scaffolding or space for students to show their working out- especially when it comes to calculating Area of shapes/compound shapes.
It is important we demonstrate how kids should set out their work
If a child is asked to calculate the area of a triangle, there should be 3 lines of working out
1. A line for the formula (this helps reinforce this knowledge into long term for the individual through repetition)
2.A line for students to substitute the numbers
3. The answer with correct units
Just my thoughts - I appreciate others may not mind if things are not so structured
Allow us the ability to edit the work sheets once they have been downloaded.
That way we can set play with the structure and formulae ourselves.
I prefer to teach area of squares/rectangles as
base times height
this then assists with leading into
area of a triangle is a half times base times height
This can also be demonstrated for the students visually through drawing a square/rectangle drawing a diagonal and cutting creating triangles-allowing the students to realise you are only using half a square/rectangle.
Thanks for this feedback Dimi. We will definitely take this into account as we make future packs and update existing ones.
Absolutely love all of your packs, but especially the booklets that accompany the maths packs. They are clear and concise and contain all of the information you need in a progressive manner. The display posters are clear and eye catching. Wouldn't be without my teaching packs. Thank you.
I can't remember how I stumbled across your website, but I found it in my first month as an NQT. In a single entry school, with no planning in place, and four children of my own at home I was finding things tough! I have now used many of your packs - Area and perimeter, Fractions, Time, Instructional texts and the Egyptians - and have recommended you to my Year 5 and 6 colleagues who are studying the Victorians. They, like me, have been delighted with the quality of your resources, the lovely photographs and story starters, and clear explanations. I now always go to your site first in the hope that you will have a pack waiting for me for my next topic! (Volcanoes and Tudors next!!). I am recommending you to all my fellow ex-students and the lecturers at St Mary's University, and would like to thank you very much for your fantastic products.
Along with all the other packs I am so happy to have found this website and resources. As a graduating teacher I have been looking for resources that are vibrant, dynamic, informative and easy to understand - not only for the students but also for me. Thank you Teaching Packs. Your hard work in preparing these great resources is much appreciated.
Teaching year 5 and 6 students is a challenge! To be able to access such a quality resource is fantastic! This pack has it all- the content is relevant to our curriculum and the activities, charts and challenges are engaging for students. Thank you for creating such fun learning experiences that are easy for teachers to apply! Teaching is hard enough without having to make all your own resources as well!
Used the perimeter downloads last week with my year 3 class. The playground activity sheet was very well received and they calculated the perimeters with enthusiasm. There is differentiation and extension included in the activities. A good resource pack. Looking forward to using angle resources this week. |
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|Annexation of the Republic of Texas to the United States|
Boundaries of Texas as annexed, 1845
|Drafted||27 February 1844|
|Signed||29 December 1845|
|Effective||19 February 1846|
|Condition||Ratification by Republic of Texas (including plebiscite) and US Congress|
|Annexation of Texas at Wikisource|
After declaring their independence from the Republic of Mexico in 1836, the vast majority of Texas citizens favored the annexation of the Lone Star Republic by the United States. The leadership of both major American political parties, the Democrats and the Whigs, strenuously objected to introducing Texas, a vast slave-holding region, into the volatile political climate of the pro- and anti-slavery sectional controversies in Congress. Moreover, they wished to avoid a war with Mexico, whose government refused to acknowledge the sovereignty of its rebellious northern province. With Texas's economic fortunes declining by the early 1840s, the President of the Texas Republic, Sam Houston, arranged talks with Mexico to explore the possibility of securing official recognition of independence, with Great Britain mediating.
In 1843, President of the United States John Tyler, unaligned with any political party, decided, as chief executive, to independently pursue the annexation of Texas in a bid to gain a base of popular support for another four years in office. His official motivation was to outmaneuver suspected diplomatic efforts by the British government to promote a general emancipation of slaves in Texas that would weaken the institution of human bondage in the United States. Initiating and impelling secret annexation negotiations with the Houston administration, Tyler secured a treaty of annexation in April 1844. When the documents were submitted to the US Senate for ratification, the details of the terms of annexation became public and the question of acquiring Texas took center stage in the presidential election of 1844. Pro-Texas annexationist southern Democratic delegates denied their anti-annexationist leader Martin Van Buren the nomination at their party's convention in May 1844. In alliance with pro-expansionist northern Democratic colleagues, they secured the unanimous nomination of James K. Polk, who ran on a pro-Texas Manifest Destiny platform.
In June 1844, the Senate, with its Whig majority, soundly rejected the Tyler-Texas treaty. The pro-annexationist Democrat Polk would defeat the anti-annexationist Whig Henry Clay for the presidency by a small margin in November of 1844. In December 1844, the lame-duck President Tyler called on Congress to pass his treaty by simple majorities in each house. The Democratic-dominated House of Representatives complied with his request by passing an amended bill expanding on the pro-slavery provisions of the Tyler treaty. The Senate's minority Democrats narrowly passed a compromise version of the House bill, with critical support from several southern Whigs, designed to provide the incoming President-elect Polk the option to effect immediate annexation of Texas or open new talks to revise the annexation terms of the House amended bill.
On March 3, 1845, shortly after signing the legislation, President Tyler preempted Polk and forwarded the House legislative alternative to Texas, offering immediate annexation to the republic. When Polk entered the White House the next day, he proceeded to encourage Texas to accept the Tyler offer. The Lone Star Republic ratified the treaty with popular approval from Texans. The bill was signed by United States President Polk on December 29, 1845, accepting Texas as the 28th state of the Union. Texas formally relinquished its sovereignty to the United States on February 19, 1846.
|Part of a series on the|
|History of Texas|
- 1 Background
- 2 Jackson and Van Buren Administrations
- 3 John Tyler Administration
- 4 Tyler-Texas Treaty and the Election of 1844
- 5 Congressional Debate over Annexation
- 6 Tyler's Preemption of Texas Annexation
- 7 Joint Resolution Precedent and Legacy: Hawaii
- 8 Notes
- 9 References
- 10 External links
Territorial Expansion and Texas
First mapped by Spain in 1519, Texas was part of the Spanish empire for over 300 years. When the Louisiana territory was acquired by the United States from France in 1803, many people believed the new territory included parts or all of present day Texas. The US-Spain border along the northern frontier of Texas took shape in the 1817–1819 negotiations between Secretary of State John Quincy Adams and the Spanish ambassador to the United States Luis de Onís y González-Vara. The boundaries of Texas were determined within the larger geostrategic struggle to demarcate the limits of the United States' extensive western lands and of Spain's vast possessions in North America. The Florida Treaty of February 22, 1819 emerged as a compromise that excluded Spain from the lower Columbia River watershed, but established southern boundaries at the Sabine and Red Rivers, "legally extinguish[ing]" any American claims to Texas. Nonetheless, Texas remained an object of fervent interest to American expansionists, among them Thomas Jefferson, who anticipated the eventual acquisition of its fertile lands.
The Missouri crisis of 1819–1821 sharpened commitments to expansionism among the country's slaveholding interests, when the so-called Thomas proviso established the 36°30' parallel imposing free-soil and slave-soil futures in the Louisiana Purchase lands. While a majority of southern congressmen acquiesced to the exclusion of slavery from the bulk of the Louisiana Purchase, a significant minority objected. Virginian editor Thomas Ritchie of the Richmond Enquirer predicted that with the proviso restrictions, the South would ultimately require Texas: "If we are cooped up on the north, we must have elbow room to the west." Representative John Floyd of Virginia in 1824 accused Secretary of State Adams of conceding Texas to Spain in 1819 in the interests of Northern anti-slavery advocates, and so depriving the South of additional slave states. Congressman John Tyler of Virginia invoked the Jeffersonian precepts of territorial and commercial growth as a national goal to counter the rise of sectional differences over slavery. His "diffusion" theory declared that with Missouri open to slavery, the new state would encourage the transfer of underutilized slaves westward, emptying the eastern states of bondsmen and making emancipation feasible in the old South. This doctrine would be revived during the Texas annexation controversy.
When Mexico won its independence from Spain in 1821, the United States did not contest the new republic's claims to Texas, and both presidents John Quincy Adams (1825–1829) and Andrew Jackson (1829–1837) persistently sought, through official and unofficial channels, to procure all or portions of provincial Texas from the Mexican government, without success.
Texas Settlement and Independence
Anglo-American immigrants, primarily from the Southern United States, began emigrating to Mexican Texas in the early 1820s at the invitation of the Mexican government, which sought to populate the sparsely inhabited lands of its northern frontier. Colonizing empresario Stephen F. Austin managed the regional affairs of the mostly American-born population – 20% of them slaves – under the terms of the generous government land grants. Mexican authorities were initially content to govern the remote province through salutary neglect, "permitting slavery under the legal fiction of 'permanent indentured servitude', similar to Mexico's peonage system.
A general lawlessness prevailed in the vast Texas frontier, and Mexico's civic laws went largely unenforced. Mexican authorities, perceiving that they were losing control over Texas and alarmed by the unsuccessful Fredonia Rebellion of 1826, abandoned the policy of benign rule. New restrictions were imposed in 1829–1830, outlawing slavery throughout the nation and terminating further American immigration to Texas. Military occupation followed, sparking local uprisings and a civil war. Texas conventions in 1832 and 1833 submitted petitions for redress of grievances to overturn the restrictions, with limited success. In 1835, an army under Mexican President Santa Anna entered Texas and abolished self-government. Texans responded by declaring their independence from Mexico on March 2, 1836. On April 20–21, rebel forces under Texas General Sam Houston defeated the Mexican army at the Battle of San Jacinto. The Mexican government refused to honor the terms granting the Lone Star Republic its independence agreed to by President Santa Anna in June 1836. Texans, now in possession of a de facto republic, recognized that their security and prosperity could never be achieved while Mexico denied the legitimacy of their revolution.
In the years following independence, the migration of white settlers and importation of black slave labor into the vast republic was deterred by Texas's unresolved international status and the threat of renewed warfare with Mexico. American citizens who considered migrating to the new republic perceived that "life and property were safer within the United States" than in an independent Texas. The situation led to labor shortages, reduced tax revenue, large national debts and a diminished Texas militia.
Jackson and Van Buren Administrations
The Anglo-American immigrants residing in newly-independent Texas overwhelmingly desired immediate annexation by the United States. But, despite his strong support for Texas independence, then-President Andrew Jackson delayed recognizing the new republic until the last day of his presidency to avoid raising the issue during the 1836 general election. Jackson's political caution was informed by northern concerns that Texas could potentially form several new slave states and undermine the North-South balance in Congress.
Jackson's successor, President Martin Van Buren, viewed Texas annexation as an immense political liability that would empower the anti-slavery northern Whig opposition – especially if annexation provoked a war with Mexico. Presented with a formal annexation proposal from Texas minister Memucan Hunt, Jr. in August 1837, Van Buren summarily rejected it. Annexation resolutions presented separately in each house of Congress were either soundly defeated or tabled through filibuster. After the election of 1838, new Texas president Mirabeau B. Lamar withdrew his republic's offer of annexation due to these failures. Texans were at an annexation impasse when John Tyler entered the White House in 1841.
John Tyler Administration
William Henry Harrison, Whig Party presidential nominee, defeated US President Martin Van Buren in the 1840 general election. Upon Harrison's death shortly after his inauguration, Vice-President John Tyler assumed the presidency. President Tyler was expelled from the Whig party in 1841 for repeatedly vetoing their domestic finance legislation. Tyler, isolated and outside the two-party mainstream, turned to foreign affairs to salvage his presidency, aligning himself with a southern states' rights faction that shared his fervent slavery expansionist views.
In his first address to Congress in special session on June 1, 1841, Tyler set the stage for Texas annexation by announcing his intention to pursue an expansionist agenda so as to preserve the balance between state and national authority and to protect American institutions, including slavery, so as to avoid sectional conflict. Tyler's closest advisors counseled him that obtaining Texas would assure him a second term in the White House, and it became a deeply personal obsession for the president, who viewed the acquisition of Texas as the "primary objective of his administration". Tyler delayed direct action on Texas to work closely with his Secretary of State Daniel Webster on other pressing diplomatic initiatives.
With the Webster-Ashburton Treaty ratified in 1843, Tyler was ready to make the Texas his "top priority". Congressman Thomas W. Gilmer of Virginia was authorized by the administration to make the case for annexation to the American electorate. In a widely circulated open letter, understood as an announcement of the executive branch's designs for Texas, Gilmer described Texas as a panacea for North-South conflict and an economic boon to all commercial interests. The slavery issue, however divisive, would be left for the states to decide as per the US Constitution. Domestic tranquility and national security, Tyler argued, would result from an annexed Texas; a Texas left outside American jurisdiction would imperil the Union. Tyler adroitly arranged the resignation of his anti-annexationist Secretary of State Daniel Webster, and on June 23, 1843 filled the post with Abel P. Upshur, a Virginia states' rights champion and ardent proponent of Texas annexation. This shift in cabinet appointment signaled Tyler's intent to aggressively pursue Texas annexation.
Tyler-Upshur-Calhoun Campaign for Texas
In late September 1843, in an effort to cultivate public support for Texas, Secretary Upshur dispatched a letter to his ambassador to London, Edward Everett, conveying his displeasure with Britain's global anti-slavery posture, and warning their government that forays into Texas's affairs would be regarded as "tantamount to direct interference 'with the established institutions of the United States'". In a breach of diplomatic norms, Upsher leaked the communique to the press in order to inflame popular Anglophobic sentiments among American citizens.
In the spring of 1843, the Tyler administration had sent executive agent Duff Green to Europe to gather intelligence and arrange territorial treaty talks with Great Britain regarding Oregon; he also worked with American minister to France, Lewis Cass, to thwart efforts by major European powers to suppress the maritime slave trade. Green, as secret envoy, alleged in executive reports reaching Secretary Upshur in July 1843 the he had discovered a "loan plot" by American abolitionists, in league with Lord Aberdeen, British Foreign Secretary, to provide funds to the Lone Star Republic in exchange for the emancipation of its slaves. Minister to London Everett was charged with determining the substance of these confidential reports alleging a Texas plot. His investigations, including personal interviews with Lord Aberdeen, concluded that British interest in abolitionist intrigues was weak, contradicting Secretary of State Upshur's conviction that Great Britain was manipulating Texas. Though unsubstantiated, Green's unofficial intelligence so alarmed Tyler that he requested verification from his minister in Mexico, Waddy Thompson.
John C. Calhoun, a South Carolina pro-slavery extremist, counseled Secretary of State Upshur that British designs on American slavery were real and required immediate action to preempt a takeover of Texas by Great Britain. When Tyler confirmed in September that the British Foreign Secretary Aberdeen had encouraged détente between Mexico and Texas, allegedly pressing Mexico to maneuver Texas towards emancipation of its slaves, Tyler acted at once. On September 18, 1843, in consultation with Secretary Upshur, he ordered secret talks opened with Texas Minister to the United States Isaac Van Zandt to negotiate the annexation of Texas. Face-to-face negotiations commenced on October 16, 1843.
Texas-Mexico-Great Britain Negotiations
By the summer of 1843 Sam Houston's Texas administration had returned to negotiations with the Mexican government to consider a rapprochement that would permit Texas self-governance, possibly as a state of Mexico, with Great Britain acting as mediator. Texas officials felt compelled by the fact that the Tyler administration appeared unequipped to mount an effective campaign for Texas annexation. With the 1844 general election in the United States approaching, the leadership in both the Democratic and Whig parties remained unequivocally anti-Texas. Texas-Mexico treaty options under consideration included an autonomous Texas within Mexico's borders, or an independent republic with the provision that Texas should emancipate its slaves upon recognition.
Van Zandt, though he personally favored annexation by the United States, was not authorized to entertain any overtures from the US government on the subject. Texas officials were at the moment deeply engaged in exploring settlements with Mexican diplomats, facilitated by Great Britain. Texas's predominant concern was not British interference with the institution of slavery – English diplomats had not alluded to the issue – but the avoidance of any resumption of hostilities with Mexico. Still, US Secretary of State Upshur vigorously courted Texas diplomats to begin annexation talks, finally dispatching an appeal to President Sam Houston in January 1845. In it, he assured Houston that, in contrast to previous attempts, the political climate in the United States, including sections of the North, was amenable to Texas statehood, and that a two-thirds majority in Senate could be obtained to ratify a Texas treaty.
Texans were hesitant to pursue a US-Texas treaty without a written commitment of military defense from America, since a full-scale military retaliation by Mexico seemed likely when the negotiations became public. If ratification of the annexation measure stalled in the US Senate, the Lone Star Republic could face a war alone against Mexico. Because only Congress could declare war, the Tyler administration lacked the constitutional authority to commit its support to Texas. But, when Secretary Upshur provided a verbal assurance of a military defense, President Houston, responding to urgent calls for annexation from the Texas Congress of December 1843, authorized the reopening of annexation negotiations.
The US-Texas Treaty Negotiations
As Secretary Abel P. Upshur accelerated the secret treaty discussions, Mexican diplomatic circles became aware that US-Texas talks were taking place. Mexican minister to the US Juan Almonte confronted Upshur with these reports, warning him that if Congress sanctioned a treaty of annexation, Mexico would break diplomatic ties and immediately declare war. Secretary Upshur evaded and dismissed the charges, and pressed forward with the negotiations. In tandem with moving forward with Texas diplomats, Upshur was secretly lobbying US Senators to gain support for annexation, providing lawmakers with persuasive arguments linking Texas acquisition to national security and domestic peace. By early 1844, Upshur was able to assure Texas officials that 40 of the 52 members of the Senate were pledged to ratify the Tyler-Texas treaty, enough to secure the two-thirds majority required for passage. Tyler, in his annual address to Congress in December 1844, maintained his silence on the secret treaty, so as not to damage relations with the wary Texas diplomats. Throughout, Tyler did his utmost to keep the negotiations secret, making no public reference to his administration's singleminded quest for Texas.
The treaty was in its final stages when the chief architects the of the Tyler-Texas treaty, Secretary Upshur and Secretary of the Navy Thomas W. Gilmer, died in an accident aboard the USS Princeton (1843) on February 28, 1844, just a day after achieving a preliminary treaty draft agreement with the Texas Republic. The Princeton disaster proved a major setback for Texas annexation, in that Tyler expected Secretary Upshur to elicit critical support from Whig and Democratic Senators during the upcoming treaty ratification process. Tyler selected John C. Calhoun to replace Upshur as Secretary of State and to finalize the treaty with Texas. The choice of Calhoun, a highly regarded but controversial American statesman, risked introducing a politically polarizing element into the Texas debates, but Tyler prized him as a strong advocate of annexation.
Robert J. Walker and the "Safety-Valve"
With the Tyler-Upshur secret annexation negotiations with Texas near consummation, Senator Robert J. Walker of Mississippi, a key Tyler ally, issued a widely distributed and highly influential letter, reproduced as a pamphlet, making the case for the Lone Star Republic's immediate annexation. In it, Walker argued that Texas could be acquired by Congress in a number of ways – all constitutional – and that the moral authority to do so was based on the precepts for territorial expansion established by Jefferson and Madison, and promulgated as doctrine by James Monroe in 1823. Senator Walker's polemic offered analysis on the significance of Texas with respect to slavery and race. He envisioned Texas as a corridor through which both free and enslaved African-Americans could be "diffused" southward in a gradual exodus that would ultimately supply labor to the Central American tropics, and in time, empty the United States of its slave population.
This "safety-valve" theory "appealed to the racial fears of northern whites" who dreaded the prospect of absorbing emancipated slaves into their communities in the event that the institution of slavery collapsed in the South. This scheme for racial cleansing was consistent, on a pragmatic level, with colonization proposals for blacks, pursued by a number of American presidents, from Jefferson to Lincoln. Walker bolstered his position by raising national security concerns, warning that in the event annexation failed, imperialist Great Britain would maneuver the Republic of Texas into emancipating its slaves, forecasting a dangerous destabilizing influence on southwestern slaveholding states. The pamphlet characterized abolitionists as traitors who conspired with the British to overthrow the United States.
A variation of the Tyler's "diffusion" theory, it played on economic fears in a period when slave-based staple crop markets had not yet recovered from the Panic of 1837. The Texas "escape route" conceived by Walker promised to increase demand for slaves in fertile cotton growing regions of Texas, as well as the monetary value of slaves. Cash poor plantation owners in the older eastern South were promised a market for superfluous slaves at a profit. Texas annexation, wrote Walker, would eliminate all these dangers and "fortify the whole Union."
Walker's pamphlet brought forth strident demands for Texas from pro-slavery expansionists in the South; in the North, it allowed anti-slavery expansionists to embrace Texas without appearing to be aligned with pro-slavery extremists. His assumptions and analysis "shaped and framed the debates on annexation but his premises went largely unchallenged among the press and public.
Tyler-Texas Treaty and the Election of 1844
The Tyler-Texas treaty, signed on April 12, 1844 was framed so as to induct Texas into the Union as a territory, following constitutional protocols. To wit, Texas would cede all its public lands to the United States, and the federal government would assume all its bonded debt, up to $10 million. The boundaries of the Texas territory were left unspecified. Four new states could ultimately be carved from the former republic – three of them likely to become slave states. Any allusion to slavery was omitted from the document so as not to antagonize anti-slavery sentiments during Senate debates, but it provided for the "preservation of all [Texas] property as secured in our domestic institutions."
Upon the signing of the treaty, Tyler complied with the Texans' demand for military and naval protection, deploying troops to Fort Jesup in Louisiana and a fleet of warships to the Gulf of Mexico. In the event that the Senate failed to pass the treaty, Tyler promised the Texas diplomats that he would officially exhort both houses of Congress to establish Texas as a state of the Union upon provisions authorized in the US Constitution. Tyler's cabinet was split on the administration's handling of the Texas agreement. Secretary of War William Wilkins praised the terms of annexation publicly, touting the economic and geostrategic benefits with relation to Great Britain. Secretary of the Treasury John C. Spencer was alarmed at the constitutional implications of Tyler's application of military force without congressional approval, a violation of the separation of powers. Refusing to transfer contingency funds for the naval mobilization, he resigned.
Tyler submitted his Texas-US treaty for annexation to the US Senate, delivered April 22, 1844, where a two-thirds majority was required for ratification. Secretary of State John C. Calhoun of South Carolina (assuming his post March 29, 1844) included a document known as the Packenham Letter with the Tyler bill that was calculated to create a sense of crisis in Southern Democrats of the Deep South. In it, he characterized slavery as a social blessing and the acquisition of Texas as an emergency measure necessary to safeguard the "peculiar institution" in the United States. In doing so, Tyler and Calhoun sought to unite the South in a crusade that would present the North with an ultimatum: support Texas annexation or lose the South.
Tyler and the Polk Presidential Nomination
President Tyler expected that his treaty would be debated secretly in Senate executive session. However, less than a week after debates opened, the treaty, its associated internal correspondence and the Packenham letter were leaked to the public. The nature of the Tyler-Texas negotiations caused a national outcry, in that "the documents appeared to verify that the sole objective of Texas annexation was the preservation of slavery". A mobilization of anti-annexation forces in the North strengthened both major parties' hostility toward Tyler's agenda. The leading presidential hopefuls of both parties, Democrat Martin Van Buren and Whig Henry Clay, publicly denounced the treaty. Texas annexation and the reoccupation of Oregon territory emerged as the central issues in the 1844 general election.
In response, Tyler, already ejected from the Whig party, quickly began to organize a third party in hopes of inducing the Democrats to embrace a pro-expansionist platform. By running as a third-party candidate, Tyler threatened to siphon off pro-annexation Democratic voters; Democratic party disunity would mean the election of Henry Clay, a staunchly anti-Texas Whig. Pro-annexationist delegates among southern Democrats, with assistance from a number of northern delegates, succeeded in ousting the anti-expansionist presidential candidate Martin Van Buren at their convention, nominating the pro-expansionist champion of Manifest Destiny, James K. Polk of Tennessee. Polk would unify his party under the banner of Texas and Oregon acquisition.
In August 1844, in the midst of the election campaign for president, Tyler withdrew from the race. The Democratic party was by then unequivocally committed to Texas annexation, and Tyler, assured by Polk's envoys that as president he would effect Texas annexation, urged his supporters to cast their votes for the Democratic Party. Polk narrowly defeated Whig Henry Clay in the November election. The victorious Democrats were poised to acquire Texas under the leadership of their president-elect James K. Polk, the pro-Texas annexation champion of Manifest Destiny, rather than on the pro-slavery agenda favored by the Tyler-Calhoun expansionists.
Congressional Debate over Annexation
Tyler-Texas Treaty Defeat in the Senate
As a treaty document with a foreign nation, the Tyler-Texas annexation treaty required the support of a two-thirds majority in the Senate for passage. But in fact, when the Senate voted on the measure on June 8, 1844, fully two-thirds voted against the treaty. The vote went largely along party lines: Whigs had opposed it almost unanimously (27-1), while Democrats split, but voted overwhelmingly in favor (15-8). The election campaign had hardened partisan positions on Texas among Democrats. Tyler had anticipated that the measure would fail, due largely to the divisive effects of Secretary Calhoun's Packenham letter. Undeterred, he formally asked the House of Representatives to consider other constitutional means to authorize passage of the treaty. Congress adjourned before debating the matter.
Reintroduction as a Joint Resolution
The same Senate that had rejected the Tyler-Calhoun treaty by a margin of 2:1 in June 1844 reassembled in December 1844 in short (lame-duck) session. (Though pro-annexation Democrats had made gains in the fall congressional races, those legislators – the 29th Congress – would not assume office until March 1845.) Lame-duck President John Tyler, persisting in his efforts to annex Texas in the final months of his administration, wished to avoid another overwhelming Senate rejection of his treaty. In his annual address to Congress on December 4, he declared the Polk victory a mandate for Texas annexation and proposed that congress adopt a joint resolution procedure by which simple majorities in each house could secure ratification for the Tyler treaty. This method would avoid the constitutional necessity of a two-thirds majority for international treaties in the Senate. Bringing the House of Representatives into the equation boded well for Texas annexation, as the pro-annexation Democratic Party possessed nearly a 2:1 majority in that chamber.
By resubmitting the discredited treaty through a House-sponsored bill, the Tyler administration reignited sectional hostilities over Texas admission. Both northern Democratic and southern Whig Congressmen had been bewildered by local political agitation in their home states during the 1844 presidential campaigns. Now, Democratic legislators found themselves vulnerable to charges of appeasement to their southern wing if they capitulated to Tyler's slavery expansion provisions. On the other hand, Manifest Destiny enthusiasm in the north placed politicians under pressure to admit Texas immediately to the Union.
Constitutional objections were raised in House debates as to whether both houses of Congress could constitutionally authorize admission of territories, rather than states. Moreover, if the Republic of Texas, a nation in its own right, were admitted as a state, its territorial boundaries, property relations (including slave property), debts and public lands would require a Senate-ratified treaty. Democrats were particularly uneasy about shouldering the United States with $10 million in Texas debt, resenting the deluge of speculators, who, in possession of inflated Texas bonds, lobbied Congress in favor of the Texas House bill. House Democrats, at an impasse, relinquished the legislative initiative to the southern Whigs.
Brown-Foster House Amendment
Anti-Texas Whig legislators had lost more than the White House in the general election of 1844. In the southern states of Tennessee and Georgia, Whig strongholds in the 1840 general election, voter support dropped precipitously due to the pro-annexation excitement in the Deep South – and Henry Clay lost every Southern state to James K. Polk. Northern Whigs' uncompromising hostility to slavery expansion increasingly characterized the party, and southern members, by association, had suffered from charges of being "soft on Texas, therefore soft on slavery" by Southern Democrats. Facing congressional and gubernatorial races in 1845 in their home states, a number of Southern Whigs sought to erase that impression with respect to the Tyler-Texas bill.
Southern Whig legislators in the House, including Representative Milton Brown and Senator Ephraim Foster, both of Tennessee, and Representative Alexander Stephens of Georgia collaborated to introduce a House amendment on January 13, 1845 that was designed to enhance slaveowner gains in Texas beyond those offered by the Democratic-sponsored Tyler-Calhoun treaty bill. The legislation proposed to recognize Texas as a slave state which would retain all its vast public lands, as well as its bonded debt accrued since 1836. Furthermore, the Brown amendment would delegate to the US government responsibility for negotiating the disputed Texas-Mexico boundary. The issue was a critical one, as the size of Texas would be immensely increased if the international border were set at the Rio Grande River, with its headwaters in the Rocky Mountains, rather than the traditionally recognized boundary at the Nueces River, 100 miles to the north. While the Tyler-Calhoun treaty provided for the organization of a total of four states from the Texas lands – three likely to qualify as slave states – Brown's plan would permit Texas state lawmakers to configure a total of five states from its western region, south of the 36°30' Missouri Compromise line, each pre-authorized to permit slavery upon statehood, if Texas designated them as such.
Politically, the Brown amendment was designed to portray Southern Whigs as "even more ardent champions of slavery and the South, than southern Democrats." The bill also served to distinguish themselves from their northern Whig colleagues who cast the controversy, as Calhoun did, in strictly pro- versus anti-slavery terms. While almost all Northern Whigs spurned Brown's amendment, the Democrats quickly co-opted the legislation, providing the votes necessary to attach the proviso to Tyler's joint resolution, passing 118-101. Southern Democrats supported the bill almost unanimously (59-1), while Northern Democrats split strongly in favor (50-30). Eight of eighteen Southern Whigs cast their votes in favor. Northern Whigs unanimously rejected it. The House proceeded to approve the amended Texas treaty 120-98 on January 25, 1845. The vote in the House had been one in which party affiliation prevailed over sectional allegiance. The bill was forwarded the same day to the Senate for debate.
Benton Senate Compromise
By early March 1845, when the Senate began to debate the Brown-amended Tyler treaty, its passage seemed unlikely, as support was "perishing". The partisan alignments in the Senate were near parity, 28-24, slightly in favor of the Whigs. The Senate Democrats would require undivided support among their colleagues, and three or more Whigs who would be willing to cross party lines to pass the House-amended treaty. The fact that Senator Foster had drafted the House amendment under consideration improved Senate Democratic prospects to pass the measure.
Thomas Hart Benton, an anti-annexation Senator from Missouri, had been the only Southern Democrat to vote against the Tyler Texas measure in June 1844. His original proposal for an annexed Texas had embodied a national compromise, whereby Texas would be divided in two, half slave-soil and half free-soil. As pro-annexation sentiment grew in his home state, Benton retreated from this compromise offer. By February 5, 1845, in the early debates on the Brown amended House bill, he advanced an alternative resolution that, unlike the Brown scenario, made no reference whatsoever to the ultimate free-slave apportionment for an annexed Texas and simply called for five bipartisan commissioners to resolve border disputes with Texas and Mexico and set conditions for the Lone Star Republic's acquisition by the United States.
The Benton proposal was intended to calm his party's northern anti-slavery wing, which wished to eliminate the Tyler-Calhoun treaty altogether, as it had been negotiated on behalf of the slavery expansionists, and allow the decision to devolve upon the soon-to-be-inaugurated Democratic president-elect James K. Polk. President-elect Polk had expressed his ardent wish that Texas annexation should be accomplished before he entered Washington in advance of his inauguration on March 4, 1845, the same day Congress would end its session. With his arrival in the capital, he discovered the Benton and Brown factions in the Senate "paralyzed" over the Texas annexation legislation. On the advice of his soon-to-be Secretary of the Treasury Robert J. Walker, Polk urged Senate Democrats to unite under a dual resolution that would include both the Benton and Brown versions of annexation, leaving enactment of the legislation to Polk's discretion when he assumed the presidency. In private and separate talks with supporters of both the Brown and Benton plans, Polk left each side with the "impression he would administer their [respective] policy. Polk meant what he said to Southerners and meant to appear friendly to the Van Burenite faction." Polk's handling of the matter had the effect of uniting Senate northern Democrats in favor of the dual alternative treaty bill.
On February 27, 1845, less than a week before Polk's inauguration, the Senate voted 27-25 to admit Texas, based on the Tyler protocols of simple majority passage. All twenty-four Democrats voted for the measure, joined by three southern Whigs. Benton and his allies were assured that Polk would act to establish the eastern portion of Texas as a slave state; the western section was to remain unorganized territory, not committed to slavery. On this understanding, the northern Democrats had conceded their votes for the dichotomous bill. The next day, in an almost strict party line vote the Benton-Milton measure was passed in the Democrat-controlled House of Representatives. President Tyler signed the bill the following day, March 1, 1845.
Tyler's Preemption of Texas Annexation
Senate and house legislators who had favored Benton's renegotiated version of the Texas annexation bill had been assured that President Tyler would sign the joint house measure, but leave its implementation to the incoming Polk administration. But, during his last day in office, President Tyler, with the urging of his Secretary of State Calhoun, decided to act decisively to improve the odds for the immediate annexation of Texas. On March 3, 1845, with his cabinet's assent, he dispatched an offer of annexation to the Republic of Texas by courier, exclusively under the terms of the Brown-Foster option of the joint house measure. Secretary Calhoun apprised president-elect Polk of the action, who demurred without comment. Tyler justified his preemptive move on the grounds that Polk was likely to come under pressure to abandon immediate annexation and reopen negotiations under the Benton alternative.
When President Polk entered the White House the following day, March 4, 1845, he was in a position to recall Tyler's dispatch to Texas and reverse his decision. On March 10, after conferring with his cabinet, Polk upheld Tyler's action and allowed the courier to proceed with the offer of immediate annexation to Texas. The only modification was to exhort Texans to accept the annexation terms unconditionally. Polk's decision was based on his concern that a protracted negotiation by US commissioners would expose annexation efforts to foreign intrigue and interference. While President Polk kept his annexation endeavors confidential, Senators passed a resolution requesting formal disclosure of the administration's Texas policy. Polk stalled, and when the Senate special session had adjourned on March 20, 1845, no names for US commissioners to Texas had been submitted by the White House. Polk denied charges from Senator Benton that he had misled him on his intention to support the new negotiations option, declaring "if any such pledges were made, it was in a total misconception of what I said or meant."
A Texas annexation convention debated the Tyler-Polk annexation offer and almost unanimously passed it on July 4, 1845. President James K. Polk signed the legislation making the former Lone Star Republic a state of the Union on December 29, 1845. Texas formally relinquished its sovereignty to the United States on February 14, 1846.
Joint Resolution Precedent and Legacy: Hawaii
The formal controversy over the legality of the annexation of Texas stems from the fact that Congress approved the annexation of Texas as a state, rather than a territory, with simple majorities in each house, instead of annexing the land by Senate treaty, as was done with Native American lands. Tyler's extralegal joint resolution maneuver in 1844 exceeded strict constructionist precepts, but was passed by Congress in 1845 as part of a compromise bill. The success of the joint house Texas annexation set a precedent that would be applied to Hawaii's annexation in 1897.
Lame-duck Republican President Benjamin Harrison (1889–1893) attempted, in 1893, to annex Hawaii through a Senate treaty. When this failed, he was asked to consider the Tyler joint house precedent; he declined. Democratic President Grover Cleveland (1893–1897) did not pursue the annexation of Hawaii. When President William McKinley took office in 1897, he quickly revived expectations among territorial expansionists when he resubmitted legislation to acquire Hawaii. When the two-thirds Senate support was not forthcoming, committees in the House and Senate explicitly invoked the Tyler precedent for the joint house resolution, which was successfully applied to approve the annexation of Hawaii in July 1898.
- Malone, 1960, p. 545: "... Texas was now actually free [after] ... the Texas Declaration of Independence on March 2, 1836 ... and its people avidly desired annexation by the United States."
- Wilentz, 2008, p. 558: "... the heightening of sectional tensions in Congress made it imperative that [the Whigs] find some compromise ground in the 1844 election ... the same intersectional logic held true for the Democrats ..." and p. 560: 'Texas annexation had long been a taboo subject for Whigs and Democrats alike."
- Freehling, 1991, p. 355: "Immediately before annexation, both major parties remained frozen in their decade-long position that Texas was not worth a foreign war or sectional combat."
- Freehling, 1991, p. 369: "Sam Houston ... the Texas president apparently swerved from seeking an apparently unattainable annexation [to the US]" and "would negotiate independence from Mexico. England, Houston hoped, might aid in the negotiations."
- Wilentz, 2009, p. 566: "President Sam Houston truly was interested in the British option [to negotiate a peace with Mexico] and was pursuing it vigorously and openly."
- Varon, 2008, p. 166: "President Tyler cherished annexation as a measure that could redeem his administration and enable him to build a loyal political constituency in the South."
- Freehling, 1991, p. 398: "Tyler and [Secretary of State] Upshur opted for annexation only after a public parliamentary exchange confirmed ... that England had 'earnestly' pressed Mexico to pressure Texas towards abolition [of slavery]."
- Merk, 1978, p. 308: "The course of [Texas] history was changed by new forces: the emergence in the South of the doctrine that slavery was a beneficent form of labor – that it was necessary to the southern economy, to southern democracy, and to well-being of the slaves – a way of life threatened by international abolitionism."
- Merk, 1978, p. 308: In the early 1840s "there developed in the Northwest and in eastern urban centers the doctrine of Manifest Destiny, which could be brought to the support of slavery expansion."
- Wilentz, 2008, p. 575: "Tyler and Calhoun, determined to win [annexation of Texas] before leaving office, arrived at the ... constitutionally dubious strategy of immediately annexing Texas by joint congressional resolution, which would require a mere simple majority in both houses of Congress."
- Merk, 1978, p.308: "In Texas, on February 19, 1846, [Texas President] Anson Jones presided over the ceremony of the transfer of his state's sovereignty to the United States."
- Meacham, 2008, p. 315
- Merry, 2009, p. 69–70: The Texas annexation issue "emerged atop a history stretching back to 1803 and the Thomas Jefferson's celebrated purchase of the Louisiana Territory from France. One problem was that the precise boundaries of the vast lands were unknown."
Crapol, 2006, p. 176: "... many people thought that all or at least part of Texas was included in the bargain."
Remini, 2002, p. 55: "When the French sold Louisiana to the United States the western and northern boundaries were not defined and some Americans claimed that Texas was included in the purchase and they wanted it occupied."
- Dangerfield, 1952, p. 129: "... Adams took up the [Louisiana] negotiations in December 1817."
- Merry, 2009, p. 70: "Spain and the United States found themselves in dispute over Louisiana's western border and extent to which Jefferson's purchase included portion of Texas." And "[I]n 1819, the matter was incorporated into the two countries' efforts to settle the status of Florida."
Dangerfield, 1952, p. 128–129: "The cession of Florida was, of course, not the only bargaining point at the disposal of [Onis] in his attempt to prevent the United States from recognizing ... Spanish revolutionaries in South America. He was also ready to discuss the boundaries of the Louisiana Purchase in their relation to the Empire of Spain.
- Crapol, 2006, p. 176: "... the Adams-Onis Treaty ... also known as the Florida treaty ..."
- Dangerfield, 1952, p. 152: "On February 22 , the great Transcontinental Treaty was signed and sealed."
- Crapol, 2006, p. 176: "... the Sabine River ... today is the boundary between [the states of] Louisiana and Texas." P. 176: The US claim to Texas"was legally extinguished ..."
- Dangerfield, 1952, p. 156:"It was by no means a perfect Treaty – by excluding Texas [from US possession], it bequeathed to the United States a legacy of trouble and war – but was certainly a great Treaty."
- Crapol, 2006, p. 176: "Among diehard expansionists unwilling to give up hope of getting Texas at a future date was Thomas Jefferson. He assured his friend President James Monroe that, when acquired, Texas would become "the richest State of our Union, without any exception."
Merry, 2009, p. 70: "[E]stablishing [Texas] west of the Sabine ... enraged many US expansionists" and "[a]nger over the treaty would linger for decades."
- Brown, 1966, p.24: The "architects of Southern power [objected to] the so-called Thomas Proviso, amending the Missouri bill to draw the ill-fated 36°30' line across the Louisiana Purchase, prohibiting slavery in the territory to the north, giving up the lion's share to freedom."
- Holt, 2004, p. 6: "In short, in 1820, a majority of southern congressmen accepted congressional prohibition of slavery from almost all of the western territories."
- Brown, 1966, p. 25–26: "In fact, the vote on the [Thomas] Proviso illuminated an important division in Southern sentiment. Thirty-seven slave state congressmen opposed it, white thirty-nine voted for it ..." a harbinger that the opposition would "in due time rectify the Thomas Proviso."
- Brown, 1966, p. 25: "As the [Missouri] debates thundered to their climax, Ritchie in two separate editorials predicted the if the Proviso passed, the South must in due time have Texas".
- Freehling, 1991, p. 152: "The Thomas plan angered some Southerners. They denounced the unequal division of turf and constitutional precedent."
- Brown, 1966, p. 28: "In 1823–1824 some Southerners suspected that an attempt by Secretary of State Adams to conclude a slave trade convention with Great Britain was an attempt to reap the benefit of Northern anti-slavery sentiments; and some, notably John Floyd of Virginia, sought to turn the tables on Adams by attacking him for allegedly ceding Texas to Spain in the Florida treaty, thus ceding what Floyd called "two slaveholding states" and costing "the Southern interest" four Senators."
- Crapol, 2006, p. 37–38: Tyler "believed in a theory of'diffusion' as a way to end slavery gradually and peacefully ... so as to "thin out and diffuse the slave population and, with fewer blacks in some of the older slave states of the upper South, it might become politically feasible to abolish slavery states like Virginia" ... and "Tyler voted against proposals that restricted slavery in Missouri or any other portion of the remaining territory of the Louisiana Purchase."
- Freehling, 1991, p. 151: "The Southerner [John Tyler] who best defended diffusion during the Missouri Crisis would become a key actor in the Texas [annexation] epic.", p. 195: "... the diffusion argument had emerged in the Missouri Controversy of the 1820s and would remain in the Texas Controversy of the 1840s."
- Crapol, 2006, p. 206: Pro-Texas arguments made by Senator Walker in 1843 were "remarkably similar to [Tyler's] diffusion theory he earlier had formulated at the time of the Missouri controversy."
- Freehling, 1991, p. 365
- Crapol, 2006, p. 176: "In fact, Mexican sovereignty [over Texas] was openly acknowledged" by the Adams and Jackson administrations, both of whom "tried to purchase all or part of Texas from the Mexicans."
Merk, 1978, p. 270: "Mexican fears were ... aroused because of the persistence with which the United States government tried to buy Texas."
Merry, 2009, p. "Jackson ... had sought to purchase the province from Mexico before Texas independence."
- Crapol, 2006, p. 176:"... Texans, mostly Americans who had emigrated to the province ..."
- Merk, 1978, p. 270: "The Anglo-Americans who went to Texas were attracted by the prospect of beautiful agricultural lands virtually free.", Meacham, 2008, p. 315, Ray Allen Billington,The Far Western Frontier, 1830–1860 (New York: Harper & Row, 1956), p. 116.
- Freehling, 1991, p. 368–369
Merry, 2009, p. 70: "Stephen [Austin] arrived in 1821 and established sway over 100,000 acres of [Mexican land grants]."
- Malone, 1960, p. 543: "Stephen F. Austin ... the chief promoter of colonization [in Texas]" and "... the basic reason for the migration of Americans" was the "liberal colonization law under which a league [7 square miles] of land was made available to each married settler ... for less than $200."
- Freehling, 1991, p. 365: "The Mexican government ... considered southwestern [US] entrepreneurs the most likely migrants" and invited them "to bring along their despotic alternative to Mexican economic peonage, black slavery ..."
- Malone, 1960, p. 543: "The vast distances in Texas, the premium that space paid to the individualism" contributed to "the disrespect of settlers for Mexican authority" and "Private violence was common ... and public violence was endemic."
- Merk, 1978, p. 270: "The Texan revolt was the result primarily of the initial Mexican error of admitting into the rich prairies of Texas a race of aggressive and unruly American frontiersmen who were contemptuous of Mexico and Mexican authority."
- Merk, 1978, p. 270: Mexican authorities feared that "... Texas was developing into an American state ...", Malone, 1960, p. 544: "... the Colonization Law of 1830 ... forbade further American migration to Texas."
- Freehling, 1991, p.545: "Neglected sovereign power [in Texas] was creating a vacuum" and Mexico "accordingly emancipated slaves" nationwide on "September 15, 1829"
- Varon, 2008, p. 127: ""... Texans had earned the reputation as defenders of slavery – they had vehemently protested efforts by successive Mexican administrations to restrict and gradually dismantle the institution, winning concessions such as the 1828 decree that allowed Texans to register their slaves, in name only, as 'indentured servants'".
Malone, 1960, p. 544
- Freehling, 1991, p. 365: "... On April 21, 1836, General Sam Houston ambushed Santa Anna at San Jacinto ..."
- Malone, 1960, p. 544: "... the Texas Declaration of Independence of March 2, 1836 ..."
- Freehling, 1991, p. 365, Merk, 1978, p. 275–276
- Freehling, 1991, p. 365
- Merry, 2009, p.71: "... an official state of war existed between the two entities, although it never erupted into full scale fighting."
- Freehling, 1991, p. 365: "... prospective American settlers [did not] have to be told that life and property were safer in the United States than in Texas ..." and slave-owners "considered slave property particularly unsafe across the border."
- Freehling, 1991, p. 365: "Imminent war hung heavily over the Texas Republic's prospects": though "Few Texans feared that Mexico might win such a war," it would disrupt Texas's economy and society, making "slave property particularly unsafe." P. 367: "Texas's population shortage victimized more than the economy. Slim populations made for low tax revenue, a large national debt, and an undermanned army."
- Finkelman, 2011, p. 29–30: "As long as Texas remained an independent republic, the Mexican government had no strong incentive to actively assert its claim of ownership. In the years since declaring independence, Texas had hardly prospered; its government was weak, its treasury was empty, and its debt was mounting every year. Mexico knew that eventually the independent government would fail."
- Malone, 1960, p. 545: Texans "avidly desired annexation by the United States.", Crapol, 2006, p. 176: Texans "overwhelmingly supported immediate annexation by the United States."
- Freehling, 1991, p. 367: "President Jackson was indeed a partisan of Texas annexation ... He recognized the independence of Texas ... on the last day of his administration ..." and "later claimed his greatest mistake was in failing to celebrate annexation as well as recognition."
- Freehling, 1991, p. 367: "On the last day of his administration ... he recognized the independence of Texas."
- Malone, 1960, p. 545: Jackson maintained "correct neutrality" towards Texas independence., Crapol, 2006, p. 53: "Unwilling to jeopardize the election of Van Buren ... Jackson had not sought immediate annexation ... although recognition was granted in early 1837 after Van Buren was safely elected ..." Merk, 1978, p. 279
- Crapol, 2006, p. 53: "... a widespread northern uneasiness that taking Texas would add a number of slave states and upset the congressional balance between North and South." Malone, 1960, p. 545: "... the American Anti-Slavery Society" charged that "Texas would make half a dozen [slave] states ... and annexation would give the South dominance in the Union." Merk, 1978, p. 279: "... it would precipitate a clash over the extension of slavery in the United States."
- Merry, 2009, p. 71: Van Buren "particularly feared any sectional flare-ups over slavery that would ensue from an annexation effort."
- Freehling, 1991, p. 367–368: Van Buren "considered Texas potentially poisonous to American Union," and Whigs "could generate mammoth political capitol out of any war with Mexico which was fought to gain a huge slaveholding republic and still more land for the Slavepower." "Van Buren would not even allow the Texas [minister to the US] to present an annexation proposal ... until months after his inauguration, then swiftly turned it down."
Crapol, 2006, p. 177: "... in August 1837, the Texans officially requested annexation, but Van Buren, fearing an anti-slavery backlash and domestic turmoil, rebuffed them.", Malone, 1960, p. 545: Van Buren "facing a financial crisis [Panic of 1837] ... did not want to add to his diplomatic and political difficulties, rebuffed it." Merk, 1978, p. 279–280
- Richard Bruce Winders, Crisis in the Southwest: The United States, Mexico, and the Struggle over Texas (Lanham: Rowman & Littlefield, 2002), p. 41.
Malone, 1960, p. 545: "In 1838, an annexation resolution that was presented in the Senate by a South Carolinian was voted down, while another that had been similarly introduced in the House was smothered by three-weeks filibustering speech by John Quincy Adams ... soon after the Texans withdrew their offer and turned their eyes toward Great Britain."
Crapol, 2006, p. 177: "Texas withdrew their [annexation] offer in October 1838."
- Crapol, 2006, p. 177: "[A series of failures to annex Texas] was more of less where matters [on annexation] stood when John Tyler entered the White House."
- Crapol, 2006, p. 10: "Three days after taking the symbolic oath-taking [April 6, 1841], John Tyler issued an inaugural address to further buttress the legitimacy of his presidency."
- Freehling, 1991, p. 364: "Tyler vetoed [the Whigs] banking bill" and "again ... vetoed [it]." The Whigs congressional caucus "... excommunicated the President from the party ..." Tyler recruited "extreme States' Rights Whigs" to fill cabinet posts ..." p. 357: As the "first and last States' Rights Whig President" he would form a "coalition uncompromisingly for states' rights.",Merk, 1978, p. 280: Tyler ..."a president without a party ... turned to foreign affairs, where executive authority was greater ..."
- Merk, 1978, p. 280–281: "... opportunities were open in foreign affairs – the annexation of Texas and a settlement of the Oregon dispute with England. The acquisition of Texas also beckoned.", Crapol, 2006, p. 24–25: "John Tyler recognized, as his fellow Virginians Jefferson and Monroe ... that expansion was the republican key to preserving the delicate balance between national and state power" and"... bringing Texas into the Union headed Tyler's acquisitive agenda." P. 177: Tyler's "Madisonian formula, [where] empire and liberty became inseparable in order to sustain the incongruity of a slaveholding republic."
- Merk, 1978, p. 281: "The temper of the period was expansionist and its tide might carry the statesman [Tyler] riding it into a term of his own in the White House."
- Crapol, 2006, p. 177
- Crapol, 2006, p. 178:"Despite being preoccupied by these more urgent diplomatic initiatives, the president kept Texas uppermost on his long-term expansionist agenda."
- Crapol, 2006, p. 180
- Merk, 1978, p. 281: "The letter was recognized at once as a major pronouncement on the Texas issue." "And [Gilmer] was a believer in the new creed of the beneficence of slavery and also in the doctrine of Manifest Destiny.", Crapol, 2006, p. 180–181
- Merk, 1978, p. 281: "[Daniel Webster's] presence in the Cabinet had become an embarrassment to Tyler as the annexation issue emerged." And "[Upshur] ... a devotee of strict construction and ... the beneficence of Negro slavery." And "[Upshur's] appointment was an omen of the coming drive for the annexation of Texas."
Crapol, 2006, p. 194: Upshur agreed with Tyler "that bringing the Lone Star Republic in the Union as a slave state should be the administration's number one diplomatic priority."
Freehling, 1991, p. 364: "... his Secretary of State [Upshur] could suggest a foreign policy [on Texas] fit to reassert executive authority and build a presidential party."
- Crapol, 2006, p. 197: Upshur's letter was an "effort to rally the American public in opposition to British machinations in Texas ..."
Freehling, 1991, p. 399–400: "... American Ambassador to London Edward Everett told Aberdeen of the Tyler-Upshur fury about English 'earnest pressing'... [encouraging] a Texas-Mexico emancipation rapprochement."
- Crapol, 2006, p. 197: Upshur's letter "a breach of diplomatic protocol ..."
- Varon, 2008, p. 166: "In 1841, Tyler had dispatched Green as an emissary to London, to move stealthily in diplomatic circles in search of 'proof' that England had designs on Texas
Merk, 1978, p. 281–282: "The subjects of negotiation" included "adjustments of territorial issues ... of the Oregon dispute ..." and p. 282: "Green busied himself, in collaboration with ... Lewis Cass ... to defeat ratification of the ... Quintuple Treaty to suppress the maritime slave trade" which France approved.
- Merk, 1978, p. 282: "... the discovery of a British 'plot' to abolitionize Texas ... promised a government guarantee of interest on a loan to Texas ... devoted to abolitionizing Texas."
- Merk, 1978, p. 284: "Everett's report ... constituted a negation of the Duff Green letter and the charges Upshur wished to fasten to the British ministry ..." and expressed the opinion that Britain "was less committed to antislavery causes than had been its predecessor, or the British public."
Merry, 2009, p. 74: "The British minister to Mexico ... Charles Elliot, had actually formulated a plan for extensive British loans to Texas in exchange for abolition and a free trade policy between the two countries. His clear aim was to detach Texas completely from United States influence ... Lord Aberdeen, British foreign secretary, on three occasions sought to assure America that Britain harbored no such ambitions ... But ... Duff Green, Tyler's man in London, chose to ignore Aberdeen's assurances. His motive is discernible in his private warnings to his friend Calhoun that, without the Texas issue, the Calhoun forces would be over whelmed by the presidential momentum of their rival Van Buren."
- Merry, 2009, p. 72: Duff Green's claims of a British loan plot, "though false ... was highly incendiary throughout the South – and also in the White House, occupied by a Virginia slaveholder and longtime Calhoun confidant."
- Merk, 1978, p. 282: "... the tidings from Green ... also went to Calhoun ... the mentor of southern extremists." And "[Calhoun] ... believed the "British were determined to abolish slavery ... throughout the continent ... a disaster," and he would "lead a campaign of propaganda on behalf of annexation."
- Merk, 1978, p. 282–283: "On August 18, 1843 ... Lord Aberdeen was questioned in the House of Lords as to what the [British] government was doing regarding the trade in slaves to Texas and ... war between Mexico and Texas" he said that "an armistice had been arranged ..." and that "the British government hoped to see slavery abolished in Texas and everywhere else in the world" and to see "peace between Mexico and Texas."
- Freehling, 1991, p. 382
- Crapol, 2006, p. 195
Merk, 1991, p. 283: "Prompt action was necessary to meet the threat. Tyler at once authorized Upshur to open negotiations with the Texas government ... on September 18, 1843 ..." and "word passed to Isaac Van Zandt ..."
- Wilentz, 2008, p. 561
- Finkelman, 2011, p. 30: "By 1843, the government in Austin [Texas] was negotiating with Great Britain to intercede with Mexico to recognize Texas independence."
Freehling, 1991, p. 370–371
- Finkelman, 2011, p. 30: "It is hard to imagine that the slaveholding republic would have actually consented to any significant British influence in Texas because Britain was deeply hostile to slavery and had abolished it everywhere in its empire."
Malone, 1960, p. 545: "Things were not going well in Texas ... in 1843 ... and [Sam Houston] had little choice but to flirt with the British for their backing."
- Freehling, 1991, p. 369
- Freehling, 1991, p. 369: "An American presidential election loomed ... [both parties] were determined to keep annexation out of the canvass."
- Freehling, 1991, p. 396: "... Texas could govern themselves if they conceded Mexicans' theoretical sovereignty" or Britain's minister to Mexico Doyle "[could] suggest that Mexico grant Texas independence if Texas should make [its] blacks independent."
- Merk, 1978, p. 284: "Van Zandt ... favored annexation ..." but had been instructed "to take no action on the matter ... and declined Upshur's invitation to enter" into talks. "The Texas government had no fear of British interference with its form of labor ... never so much as alluded to by British representatives in Texas." "What Texans really feared was reopening by Mexico of hostilities in the event of attempted annexation to the United States and a resulting withdrawal of [Britain]" as mediator.
- Merk, 1978, p. 285: Upshur wrote Houston "earlier American failures ... had been due to a misunderstanding of the issue." "Annexation was now favored even in the North to a great extent ..." and it would be feasible to win "a clear constitutional majority" in "the Senate for ratification."
- Merk, 1978, p. 285: "The question [of American military commitment] went to the heart of Texan hesitation about entering into American negotiation, and also at the heart of the American constitutional principle of separation of powers."
- Merk, 1978, p. 285: "Houston ... reversed his stand ... and recommended to [Texas] Congress the opening of an annexation negotiation."
Crapol, 2006, p. 196: "After five months of hard bargaining, [Upshur] convinced enough members of Sam Houston's government of the sincerity of the Tyler administration's overtures and cajoled them into accepting American guarantees of protection and quick action."
- Crapol, 2006, p. 198: "... Almonte bluntly warned [Upshur], Mexico would sever diplomatic relations and immediately declare war."
- Crapol, 2006, p. 199: Uphsur denied "any knowledge of US-Texas negotiations to Minister Almonte ..."
- Crapol, 2006, p. 203: "... Upshur ... inform[ed] Texas officials that at least forty of fifty-two senators were solid for ratification ..."
- Crapol, 2006, p. 199: "It was the prudent thing to do if he hoped to retain the trust of the Texans and keep them at the negotiating table."
- Crapol, 2006, p. 200–201
- Crapol, 2006, p. 207
- Crapol, 2006, p. 209: "The deaths of Upshur and Gilmer deprived [Tyler] of two of his best people and the most important architects of the administration's annexation policy ... the political landscape had been rocked."
- Crapol, 2006, p. 211: Calhoun "ranked with Daniel Webster and Henry Clay as America's leading political icons of the early republic."
- Crapol, 2006, p. 211: "... Tyler momentarily balked at the idea of appointing Calhoun as secretary of state because the South Carolinian might adversely polarize public opinion on the Texas question ... It was a decision he later came to regret."
- Merk, 1978, p. 285–286: Calhoun "was known to be eager for Texas ... [and] had been Upsher's counselor on the issue."
Merry, 2009, p. 67: Calhoun's appointment as Secretary of State was "guaranteed to generate controversy and disruption" on the Texas issue.
- Varon, 2008, p. 168
- Freehling, 1991, p. 418: "Once [Sam] Houston agreed to negotiate with Upshur, Walker authored an enormously influential pro-Texas pamphlet."
Crapol, 2006, p. 204: "... Senator Walker published a lengthy pro-annexation letter" in a leading newspaper, "... a message to the American people outlining the manifold reasons why the United States should annex Texas," and "millions of copies were circulated" in pamphlet form.
Merry, 2009, p. 85: Walker "had published a long pro-annexation treatise that had helped galvanize the issue and get [Texas annexation] into the public consciousness."
- Crapol, 2006, p. 22: "... the Monroe Doctrine [was] a restatement of the Madisonian/Jeffersonian faith in territorial expansion ..." also see p. 205.
- Freehling, 1991, p. 418: Walker asserted that "an annexed Texas, instead of helping to perpetuate slavery, would beneficially diffuse blacks away, first from the oldest [US] South, eventually from an emancipated North America." And p. 419–420: The country would be emptied of blacks, 'not by abolition ... but slowly and gradually ...'
Wilentz, 2008, p. 563: Walker "argued that annexation would lead to a dispersal of slave populations through the West and into Latin America, hasten slavery's demise" and create "an all-white United States – a rehashing of the old Jeffersonian 'diffusion' idea."
- Crapol, 2006, p. 205: "... in an appeal to the racial fears of northern whites ..." Walker warned that "the only safety-valve for the whole Union, and the only practicable outlet for the African population is through Texas, into Mexico and Central and South America".
- Crapol, 2006, p. 206: "The idea of shipping blacks to Africa ... was a solution Jefferson, Madison and John Tyler had embraced, and later pursued by Abraham Lincoln during the first year of the Civil War when he attempted to launch a Haitian colonization scheme."
- Crapol, 2006, p. 206: Walker warned of "the ever-threatening British who were intent on preventing annexation ... as part of their overall plan to undercut American national destiny."
- Freehling, 1991, p. 418: Failure to annex Texas, according to Walker "would lead to British-induced emancipation in Texas, then to Yankee-induced emancipation in the South, then to freed slaves swarming northwards towards their liberators."
- Freehling, 1991, p. 423: "Nowhere was the economic tremor of the 1840s more evident than in the older eastern South" where poor cotton yields "intensified the search for a way out." and "... in Texas, went the dream ... demand for slaves might increase slave prices, bailing out the less prosperous southeast. But close the safety valve, heap up redundant slaves back on the decaying older South, and black hands would be increasingly idle." And p. 424: "... the claustrophobia of the Southeast, pent up with too many increasingly dispensable" slaves.
- Crapol, 2006, p. 206: "Senator Walker ... once again proposed the all-purpose remedy of annexation [which would] 'strengthen and fortify the whote Union.'"
- Freehling, 1991, p. 418: "The Walker thesis transformed sorely pressed Northern Democrats from traitors who knuckled under to the Slavepower into heroes who would diffuse blacks further from the North."
- Crapol, 2006, p. 207: In the weeks and months following its publication, his letter "shaped and framed" the public debate.
Freehling, 1991, p. 422: "No one called Walker's [analysis] 'untrue'."
- Merk, 1978, p. 286: "Texas ... admitted as a territory subject to the same constitutional provisions as other territories ..."
- Holt, 2005, p. 13: "Under the original terms of the Democratic resolution, Texas would be admitted to the Union as a territory, not as a state; furthermore, in return for paying off the bonded debt Texas had accrued since 1836, the United States would own all the unsold public land in the huge republic.
Freehling, 1991, p. 440
- Crapol, 2006, p. 213
Merk, 1978, p. 286: "What the Senate would ratify was kept constantly in mind" during the Tyler-Texas negotiation.
- Crapol, 2006, p. 213: "This garrison ... named the Army of Observation" and "... a powerful naval force to the Gulf of Mexico."
- Crapol, 2006, p. 213: "Tyler was true to his word."
- Crapol, 2006, p. 217: Cabinet members "were split on the wisdom of [Tyler's] Texas machinations ... Wilkins, a Democrat, was solidly behind Tyler on Texas ..." and "stressed the economic benefits for [his home state Pennsylvania] ..." and the need to prevent Texas from "becoming a commercial dependency of Great Britain."
- Crapol, 2006, p. 217: "Spencer thought Tyler's directive [to supply funds without Congressional sanction] was illegal ... After twice refusing to execute the president's order, Secretary Spencer resigned his cabinet post on May 2, 1844."
- Freehling, 1991, p. 408: "On April 22, 1844, the Senate received the pre-treaty correspondence [and] the [Tyler] treaty ..."
- Finkelman, 2011, p. 29: "A treaty required a two-thirds majority [in the Senate] for ratification."
- Freehling, 1991, p. 407: "The new Secretary of State [Calhoun] reached Washington March 29, 1844."
- Freehling, 1991, p. 415: "... Calhoun could only begin to provoke a 'sense of crisis' with southern Democrats.", and "The Packenham Letter could rally southern Democrats against the party's northern establishment ..."
May, 2008, p. 113: "The Packenham Letter proved the claims of anti-annexationists and abolitionists that the Texas question was only about slavery – its expansion and preservation – despite Tyler's protestations to the contrary."
Varon, 2008, p. 167: Calhoun "unabashedly cast Texas as a stronghold for slavery."
- Freehling, 1991, p. 408: The Packenham Letter "declared the national [Texas] treaty a sectional weapon, designed to protect slavery's blessings from England's documented interference" and "aimed at driving southerners to see England's soft threat in a hard-headed way."
May 2008, p. 112–113: ""Calhoun ... insisted that the 'peculiar institution' was, in fact, 'a political institution necessary to peace, safety and prosperity."
- Merry, 2009, p. 67–68: Calhoun "wanted to expand the country's slave territory and thus retain the South's numerical and political advantage in regional disputes. He also wanted to force a slave issue confrontation within the country ... if that confrontation should split the Union, Texas would add luster and power to an independent South."
Freehling, 2008, p. 409–410: "Nothing would have made Northern Whigs tolerate the [Packenham] document, and Northern Democrats would have to be forced to swallow their distaste for the accord. Calhoun's scenario of rallying enough slaveholders to push enough Northern Democrats to stop evading the issue was exactly the way the election of 1844 and annexation aftermath transpired."
- Crapol, 2006, p. 216: "... the Tyler administration assumed that the Senate would consider annexation in executive session ... which meant the text of the treaty and accompanying documents would not be made public until after the vote on ratification."
- Crapol, 2006, p. 214
- Crapol, 2006, p. 216–217: "As opposition to the Texas treaty mounted, the two leading candidates for the Whig and Democratic presidential nominations came out against immediate annexation."
- Merk, 1978, p. 288: Tyler moved the annexation issue "into the presidential campaign of 1844, which was underway."
- Crapol, 2006, p. 218: "In an attempt to salvage his presidential candidacy and to gain approval of his Texas annexation treaty ... Tyler sanctioned a third-party movement ... [A] band of Tyler followers, many of them postmasters and other recipients of his executive patronage ..." and "... a tactical maneuver [to] pressure Democrats to adopt an expansionist platform favoring the annexation of Texas."
- Crapol, 2006, p. 218: "Tyler explained ... that the third-party ploy worked because it made Democrats realize that a '[Pro-]Texas man or defeat was the only choice.'"
May, 2008, p. 114: "If Tyler stayed in the race, he threatened to draw enough votes from Polk to elect Clay, which handed Tyler an opportunity to secure his [Texas] legacy."
- Finkelman, 2011, p. 27: "This was a superb strategy, because while Polk was much more interested in Texas, asserting expansive claims in the Pacific Northwest made him palatable to many northerners."
Crapol, 2006, p. 218: "After bitter wrangling they denied Martin Van Buren the nomination and chose ... James K. Polk ... an outspoken expansionist, and his campaign platform called for the reannexation of Texas and the reoccupation of Oregon."
- May, 2008, p. 119: "If Polk or his representative could give Tyler that guarantee [to annex Texas], he promised to 'withdraw' and support Polk enthusiastically." and p. 120: "Tyler's supporters easily switched their allegiance to Polk [because] 'Polk would be the advocate of most of [his] measures.'"
- Crapol, 2006, p. 219: "In November Polk narrowly defeated Henry Clay in the popular vote by just over 38,000 out of 2.7 million votes cast ..."
- Holt, 2005, p. 12: "The Democrats' triumph in the 1844 elections [the Polk victory] increased the odds of Texas annexation ... [and with] their heavy majority in the House, Democrats could easily pass the resolution containing the same terms as Tyler's rejected treaty."
- Sellers, 1966, p. 168: "Even Benton's allies of the Wright-Van Buren persuasion had argued during the campaign for annexation in the proper manner, objecting only to [the Tyler-Calhoun treaty, with emphasis on slavery expansion]" and p. 168: Pro-annexation Northern Democrats "came to Washington [D.C.] 'prepared to vote for admission [of Texas] as a state ... saying nothing about slavery."
- May, 2008, p. 114–115
Freehling, 1991, p. 443
- Sellers, 1966, p. 168: "The chain of events running back through the Baltimore convention to Calhoun's Packenham letter had finally polarized the Democrats along North-South lines."
- Merry, 2009, p. 72–73: Calhoun's "letter to British minister Richard Packenham ... contained language so incendiary and politically audacious that it would render Senate ratification nearly impossible ..."
- Crapol, 2006, p. 218–219: "Untroubled by the initial failure, Tyler had carefully prepared for just such a contingency ... recommending [Congress] consider another path to annexation."
- Holt, 2005, p. 10–11
- Freehling, 1991, p. 440: "... the lame-duck Congress returned to Washington in December 1844 ..." and p. 443: "The previous June, this same Senate had scuttled Tyler's treaty of annexation, 35-16."
Holt, 2005, p. 12
- Wilentz, 2008, p. 575
- Wilentz, 2008, p. 575
Holt, 2005, p. 12: '... Lame-duck president Tyler [asked Congress] for a joint resolution that would require only a simple majority vote in the House and Senate. This tack would avoid the far-more-elusive two-thirds Senate majority required to ratify a treaty."
- May, 2008, p. 121–122
- Freehling, 1991, p. 440
Wilentz, 2008, p. 575
Holt, 2005, p. 12
- Sellers, 1966, p. 171: "... Benton and others maintained that if Texas were admitted as a state, with any stipulation of terms, this would be a treaty requiring the assent of two thirds of the Senate."
- Holt, 2005, p. 12: "With their heavy majority in the House, Democrats could easily pass the [Tyler] resolution containing the same terms as Tyler's rejected treaty. Anti-Texas Whigs controlled the Senate narrowly, 28-24.
- Freehling, 1991, p. 443, Freehling, 1978, p. 443: "The South-leaning Democratic Party controlled the House by almost a two-to-one majority."
- Varon, 2008, p. 173: "The joint resolution sparked nearly three months of acrimonious debate."
Sellers, 1978, p. 168: "But instead of welcoming the large body of [northern Democrat] converts [to Texas annexation], who would have made annexation irresistible, the [Tyler] administration and Calhounites in Congress insisted on a vindication of the rejected treaty of the previous spring [of 1844], with all its Packenham associations."
- Sellers, 1966, p. 170: "[Texas] agitation ... had shaken both northern Democrats and Southern Whigs" during the 1844 elections."
- Sellers, 1966, p. 170–171: "Yet, apart from slavery, annexation was popular in much of the North ..." with some politicians under "heavy pressure" to proceed with Texas annexation.
- Sellers, 1966, p. 171: "One major problem was finding constitutional justification" for Tyler's request "for annexation through..simple a majority in both houses of Congress, rather than by treaty. Some thought that Congress could not annex Texas as a territory, but only as a state, under the constitutional provision that Congress could admit new states. On the contrary, [Senator] Benton and others maintained that if Texas were admitted as a state, without any stipulation of terms, this would be a treaty requiring the assent of two-thirds of the Senate. Yet the status of Texas as an independent nation made it necessary to stipulate terms with regard to her public property, lands, and debts, to say nothing of the extent of states that might be created from her territory and the status of slavery in them"
Crapol, 2006, p. 220: "When Congress reconvened it acted upon Tyler's request, but not before considerable debate on the issue of the legality and constitutionality of annexing Texas by joint resolution."
- Sellers, 1978, p. 168: "Particularly objectionable to the Benton-Van Buren men was the provision that the US become responsible for the inflated Texas debt, speculators in which had been most active lobbyists for annexation." and "Many opponents [of the Texas bill] resented the lobbying of Texas bondholders ... who hoped that the US would assume the Texas unpaid debt."
- Sellers, 1966, p. 172: "With Democrats in hopeless disagreement, the equally beleaguered southern Whigs now took a hand."
- Freehling, 1991, p. 437: "... Clay lost every state in the Deep South."
- Freehling, 1991, p. 437, 440: "... Southern Whigs suffered from being labeled soft on Texas."
- Holt, 2005, p. 12: "Aware ... that their party had been damaged in the South by the annexation issue in 1844, a few southern Whigs were now eager to annex Texas."
- Varon, 2008, p. 175: "A small but aggressive cadre of Southern Whigs ... certain that annexation had decimated them in the recent election, broke ranks and joined the Democrats [on the Texas annexation issue]."
- Freehling, 1991, p. 441: "Both Whig Senator Ephraim Foster ... who wrote Brown's amendment, and Whig Congressman Alexander Stephens ... who helped guide the measure through the House ..."
- Freehling, 1991, p. 440
- Wilentz, 2008, p. 575
- Freehling, 1991, p. 455: "Mexican officials believed that Texas ended at the Nueces River. Texans claimed instead that their empire sprawled 100 miles further south, to the Rio Grande; [this] would swell [Texas] thousands of square miles" into the Mexican interior.
- Sellers, 1966, p. 205: By extending the Missouri Compromise line, the amendment would "guarantee slavery in most of Texas."
Holt, 2005, p. 13: "... Brown stipulated that as many as four additional states could be carved from Texas and that future Congresses must admit as slave states if Texans so desired."
- Holt, 2005, p. 13
- Sellers, 1966, p.172: "But the great camouflaged issue was by now slavery" with neither North nor South willing to compromise on the matter.
- Sellers, 1978, p. 173: Democratic "annexationists seiz[ed] upon the opportunity [and] took up the proposition of the surprised southern Whigs at the 'first hop' and passed it January 25 with their support."
Freehling, 1991, p. 442–443: "Southern Democrats, as usual, would not allow Whigs to become more successfully aggressive on slavery-related issues ... Democrats saved [Representative] Milton Brown Whiggery, [voting] to add Brown's amendment to the joint congressional resolution admitting slavery.
- Freehling, 1991, p. 443
- Sellers, 1966, p. 186: "Texas was still far more a party question than a sectional question.", May, 2008, p. 123, Holt, 2005, p. 13–14
- Holt, 2005, p. 14: "The division over annexation remained more partisan than sectional."
- Holt, 2005, p. 14
- Freehling, 1991, p. 443
- Sellers, 1966, p. 186: "The situation in the Senate was extremely complex."
Freehling, 1991, p. 443: "the amended joint resolution now faced a harder test in the Senate."
- Freehling, 1991, p. 446: "... the only Southern Democrat who had voted no on the annexation treaty ..."
- Wilentz, 2008, p. 575
- Wilentz, 2008, p. 572: "In the Senate, Thomas Hart Benton offered his own plan which would split Texas into two equal districts, one slave and one free, and require Mexico's consent."
- Freehling, 1991, p. 446: "... Benton's freeing of half a slave republic seemed too Yankee."
- Wilentz, 2008, p. 575
- Freehling, 1991, p. 447
- Sellers, 1966, p. 173
- Freeling, 1991, p. 447: "The impasse paralyzed the Polk administration before the President-elect could take office."
Sellers, 1966, p. 205
- Crapol, 2006, p. 220: "... a number of the senators had voted for the compromise resolution with the expectation that President-elect Polk would be the one to choose between the options of immediate annexation or renewed negotiations."
Freehling, 1991, p. 447: "Polk supported a sleight of hand [which would] authorized the President to administer either the ... Benton ... or Brown versions of annexation."
- Freehling, 1991, p. 447
- Sellers, 1966, p. 447: "Neither Polk's contemporaries nor late historians have appreciated the extent to which he was responsible for the narrow passage of the joint resolution ... four days before his inauguration. It was at his suggestion that the House resolution, providing for immediate annexation ... was combined with Benton's bill, providing for a five-member commission to negotiate with Texas the terms of annexation. And it was his persuasion, convincing Bentonites that he would choose the Benton alternative, that procured the votes to pass the compromise measure."
- Holt, 2005, p. 15
Freehling, 1991, p. 447–448: "All Democrats and three turncoat Whigs" voted for the compromise treaty bill.
- Holt, 2005, p. 14–15: The Benton-Van Burenite Senators "expected Polk to pursue [their] option because Polk explicitly promised Benton that he would do so. Only that promise brought northern Democrats on board."
- Crapol, 2006, p. 220
- Sellers, 1966, p. 215
- Sellers, 1966, p. 215: "The Bentonian Senators had voted for the compromise relying on the assurance of Calhoun's friend Senator George McDuffie that the Tyler administration" would not 'meddle' with the bill and "that the choice between the alternative methods of annexation would be left to Polk."
May, 2008, p. 124
- Wilentz, 2008, p. 577
- Freehling, 1991, p. 448: "... under Calhoun's urging, President Tyler, on the eve of departing the White House, dispatched a courier to Houston City, offering Texas admission to the Union under the Milton Brown formula for possible future division" into several slave states.
Crapol, 2006, p. 220: Tyler "signed the joint resolution on March 1 and two days later, after first touching base with Polk, sent a dispatch to the Texans offering annexation and admission on the House plan."
- Sellers, 1966, p. 216: "Tyler did insist that Calhoun get Polk's reaction to the plan. But Polk cagily 'declined to express any opinion or to make any suggestion in reference to the subject', as Calhoun reported to Tyler ..."
- Wilentz, 2008, p. 577
- Sellers, 1966, p. 215–216
- Holt, 2004, p. 15: "[Tyler] dispatched a courier to Texas offering annexation under the Brown-amended version of the House bill. Rather than recall this courier, Polk broke his promise to the Van Burenites and endorsed Tyler's action."
- Sellers, 1966, p. 221: United States envoy to Texas Donelson "was now told [by Polk] to warn the Texans that the United States Congress might not accept ... amendments, and to urge that they accept the terms unconditionally."
Wilentz, 2008, p. 577
- Holt, 2004, p. 15: "... rather than seek new negotiations to settle the boundary dispute between Texas and Mexico, as even Brown's amendment had called for, he declared the Rio Grande the recognized boundary and announced he would deploy American military forces to defend it."
Sellers, 1966, p. 221: Polk in footnote: "... if negotiations had been opened by Commissioners great delay would necessarily have taken place, giving ample opportunity to British and French intrigues to have seriously embarrassed, if not defeated, annexation." (emphasis in original)
- Wilentz, 2008, p. 578
- Holt, 2005, p. 15
- Merk, 1978, p.308: "In Texas, on February 14, 1846, [Texas President] Anson Jones presided over the ceremony of the transfer of his state's sovereignty to the United States."
- Crapol, 2006, p. 279: "Tyler's extralegal joint resolution ploy, which belied his pretensions to being a strict constructionist when it came to interpreting the Constitution, appealed to late-nineteenth century imperialists who sought ways to circumvent Senate opposition to a Hawaii annexation treaty."
- Crapol, 2006, p. 279–280
- Brown, Richard H. 1966. The Missouri Crisis, Slavery, and the Politics of Jacksonianism. South Atlantic Quarterly. pp. 55–72 in Essays on Jacksonian America, Ed. Frank Otto Gatell. Holt, Rinehart and Winston, Inc. New York . 1970.
- Crapol, Edward P. 2006. John Tyler: the accidental president. The University of North Carolina Press. Chapel Hill. ISBN 978-0-8078-3041-3
- Finkelman, Paul. 2011. Millard Fillmore. New York: Times Books
- Freehling, William W. 1991. The Road to Disunion: Volume I: Secessionists at Bay, 1776–1854. Oxford University Press. 1991. ISBN 978-0-19-507259-4.
- Holt, Michael F. 2005. The fate of their country: politicians, slavery extension, and the coming of the Civil War. New York: Hill and Wang. ISBN 978-0-8090-4439-9
- Malone, Dumas and Rauch, Basil. 1960. Empire for Liberty: The Genesis and Growth of the United States of America. Appleton-Century Crofts, Inc. New York.
- May, Gary. 2008. John Tyler. New York: Times Books ISBN 978-8050-8238-8
- Meacham, Jon. 2008. American Lion: Andrew Jackson in the White House. Random House, New York.
- Merk, Frederick. 1978. History of the Westward Movement. Alfred A. Knopf. New York. ISBN 978-0-394-41175-0
- Merry, Robert W. 2009. A Country of Vast Designs: James K. Polk, the Mexican War and the Conquest of the American Continent. Simon & Schuster. New York. ISBN 978-0-7432-9743-1
- Remini, Robert V. 2002. John Quincy Adams. New York: Times Books
- Sellers, Charles. 1966. James K. Polk, Continentalist. Princeton University Press. Princeton, New Jersey. ISBN 978-0-8090-6051-1
- Varon, Elizabeth R. Disunion!: The Coming of the American Civil War, 1789–1859. Chapel Hill, NC: University of North Carolina Press, 2008. ISBN 978-0-8078-3232-5
- Wilentz, Sean. 2008. The Rise of American Democracy: Jefferson to Lincoln. W.W. Horton and Company. New York. ISBN 978-0-393-32921-6
- Avalon Project at Yale Law School. Texas from Independence to Annexation.
- Joint Resolution for Annexing Texas to the United States, Approved March 1, 1845.
- Jones, Anson. Letters, Relating to the History of Annexation. Galveston: Civilian Office, 1848.
- Ordinance of Annexation, Approved by the Texas Convention on July 4, 1845.
- Dewey, Orville. Discourse on Slavery and the Annexation of Texas. New York: C.S. Francis & Co., 1844.
- "Annexation." Handbook of Texas Online.
- Carefoot, Jean. "Narrative History of Texas Annexation." Texas State Library and Archives Commission.
- Silbey, Joel H. Storm over Texas: The Annexation Controversy and the Road to Civil War. New York: Oxford University Press, 2005.
- Smith, Justin H. The Annexation of Texas. Unknown publisher, 1911. |
Start by understanding PEMDAS. This is the acronym on how the operation in algebra should follow one another. It stands for Parentheses, Exponent, Multiplication, Division, Addition and then Subtraction. When you are solving any problem, you have to start on expression found within parentheses and follow up the order of the acronym and finish up with subtraction.
To solve any problem in algebra homework, you will have to base yourself on PEMDAS. Sometime, the problems may include parentheses to show the operations that have to be performed before others. Division and multiplication are at the same rank, and you can solve them in any order based from the left toward the right. This is the same for the subtraction and addition. When you practice more, you will be able to solve more problems and much easier. When you use such order for the operation, it will be your second nature and it will not be hard to solve problems in algebra. You can work on different problems, and you will feel more confident when it comes to work on your algebra homework.
When you feel that the homework is overwhelming, you should ask someone to help you. You can ask your teacher, or you can get a tutor. You can even ask a friend who is better in algebra than you. Consider algebra like a puzzle that you have to solve. Just like the puzzle, you have to bring together different pieces. You should learn how to recognize symbols and numbers for a placeholder and ensure that you make a solution to be easier to understand. While solving algebra problems, you need to know that if you change one side in equations, you have to do the same at the second side. When you divide, multiply, subtract or add to one side, then you have to do it at the second side.
Bring the variable at one side of an equation. If you are given algebraic expression, you will notice that they will be variables and constants. The constant is a given number while a variable is a letter which represents any unknown number. While isolating the number, you will need to subtract or add terms so that you may end up with variables at just one side. When the variable has some coefficients, you have to divide with it at both sides in order to get variables on their own. Put together all terms that looks the same so that you may simplify the problem. It helps in keeping the equation at a manageable and easy to solve the level. |
Remote sensing (archaeology)
Remote sensing techniques in archaeology are an increasingly important component of the technical and methodological tool set available in archaeological research. The use of remote sensing techniques allows archaeologists to uncover unique data that is unobtainable using traditional archaeological excavation techniques.
Remote Sensing methods employed in the service of archaeological investigations include:
- Aerial, UAV and Satellite Imaging
Ground-based geophysical methods such as Ground Penetrating Radar and Magnetometry are also used for archaeological imaging. Although these are sometimes classed as remote sensing, they are usually considered a separate discipline (see Geophysical survey (archaeology)).
Satellite archaeology is an emerging field of archaeology that uses high resolution satellites with thermal and infrared capabilities to pinpoint potential sites of interest in the earth around a meter or so in depth. The infrared light used by these satellites have longer wavelengths than that of visible light and are therefore capable of penetrating the earth's surface. The images are then taken and processed by an archaeologist who specializes in satellite remote sensing in order to find any subtle anomalies on the earth's surface.
Landscape features such as soil, vegetation, geology, and man-made structures of possible cultural interest have specific signatures that the multi-spectral satellites can help to identify. The satellites can then make a 3D image of the area to show if there are any man-made structures beneath soil and vegetation that can not be seen by the naked eye. Commercially available satellites have a .4m-90m resolution that make it possible to see most ancient sites and their associated features in such places as Egypt, Perù and Mexico. It is a hope of archaeologists that in the next few decades resolutions will improve to the point where they are capable of zooming in on a single pottery shard buried beneath the earth's surface.
Satellite archaeology is a non-invasive method for mapping and monitoring potential archaeological sites in an ever changing world that faces issues such as urbanization, looting, and groundwater pollution that could pose threats to such sites. In spite of this, satellites in archaeology are mostly a tool for broad scale survey and focused excavation. All archaeological projects need ground work in order to verify any potential findings.
Examples of regional applications
Some of the most prominent remote sensing research has been done in regard to Maya studies in Mesoamerica. The Petén region of northern Guatemala is of particular focus because remote sensing technology is of very definite use there. The Petén is a densely forested region and it lacks modern settlements and infrastructure. As a result, it is extremely difficult to survey, and because of this remote sensing offers a solution to this research problem. The use of remote sensing techniques in this region is a great example of the applications these methods have for archaeologists. The Petén is a hilly, karstic, thickly forested landscape which offers an incredible barrier for field archaeologists to penetrate. With the advent of remote sensing techniques, a plethora of information has been uncovered about the region and about the people that inhabited it.
The Petén is arguably one of the most difficult of the Maya landscapes in which to subsist. It is questions regarding subsistence patterns and related problems that have driven remote sensing methodology in the hopes of understanding the complex adaptations that the Maya developed. Remote sensing methods have also proven invaluable when working to discover features, cisterns, and temples. Archaeologists have identified vegetative differentiation associated with such features. With the advent of remote sensing, archaeologists are able to pinpoint and study the features hidden beneath this canopy without ever visiting the jungle.
A pioneer in the use of remote sensing in Maya research is NASA archaeologist Tom Sever, who has applied remote sensing to research in Maya site discovery as well as mapping causeways (sacbeob) and roads. Sever has stressed the enormous use of remote sensing in uncovering settlement patterns, population densities, societal structure, communication, and transportation. Sever has done much of his research in the Petén region of northern Guatemala, where he and his research team have used satellite imagery and GIS to map undiscovered roads and causeways the ancient Maya built to connect cities and settlements. These landscape artifacts represent the advantage of using remote sensing as these causeways are not visible from the ground. By mapping these forms, Sever is able to locate new sites and further uncover ancient Maya methods of communicated and transportation. Sever and his team also use remote sensing methods to gather data on deforestation. The rain forests of the Petén are undergoing massive deforestation, and Sever's remote sensing offers another window into this understanding and halting this problem. Monitoring the rate of deforestation not only has important ecological value, but the use of remote sensing can detect landscape change. By measuring the magnitude of landscape change in terms of vegetative cover and soil geography, as well as shifting land use patterns and the associated cultural diversity, archaeologists are given a window into depletion rates and trends in anthropogenic landscape alteration.
Much attention has been devoted to the mapping of canals and irrigation systems. Synthetic Aperture Radar (SAR) has proved particularly useful in this research. SAR is a type of radar that is sensitive to linear and geometric features on the ground. It is also important to include a method called ground truthing, or the process of physically visiting (on foot) the localities surveyed to verify the data and help inform the interpretation. GPS is often used to aid in this process.
Ground-based geophysical methods have also been employed in Maya research. Ground Penetrating Radar (GPR) has been performed on a number of sites, including Chichen Itza. The GPR research has detected buried causeways and structures that might have otherwise gone unnoticed.
One of Sever's research goals is understanding the comparatively sudden decline of many Maya centers in the central Lowlands region by the end of the 1st millennium CE, a happenstance often referred to as the "(Classic) Maya collapse". Sever's research on communication and transportation systems points to an extensive societal infrastructure capable of supporting the building and maintenance of the causeways and roadways. Using satellite imagery, researchers have been able to map canals and reservoirs. These offer a glimpse into Maya cultural adaptations during the period of their highest population density. At the height of the classic period, the population in the Maya lowlands was 500 - 1300 people per square mile in rural areas, and even more in urban regions. This far outweighs the carrying capacity for this region, but this follows centuries of successful adaptation. Other data shows that by the end of the classic period, the Maya had already depleted much of the rain forest. Understanding how the ancient Maya adapted to this karst topography could shed light on solutions to modern ecological problems that modern peoples in the Petén currently face, which is much the same, except there are fewer people who are causing even more damage to the biodiversity and cultural diversity. Sever believes that the Maya collapse was a primarily ecological disaster. By detecting deforestation rates and trends can help us to understand how these same processes affected the Maya. An important contribution to the study of Maya has been provided by LiDAR thanks to its ability to penetrate dense tropical canopies. LiDAR has been applied to the site of Caracol, Belize in 2009, revaling an impressive monumental complex covered by jungle.
Satellite archaeology in Peru
In Peru, an Italian scientific mission of CNR, directed by Nicola Masini, provided important results by using satellite imagery for both site discovery and the protection of archaeological heritage. In particular, by processing QuickBird images a large buried settlement, including a pyramid, in the Nasca riverbed (Southern Peru), near the Ceremonial Center of Cahuachi, has been detected. In the region of Lambayeque (Northern Peru), which is strongly affected by clandestine excavations, satellite imagery have been also employed for mapping and monitoring archaeological looting.
Location of ancient Iram
Iram of the Pillars is a lost city (or region surrounding the lost city) on the Arabian Peninsula. In the early 1980s a group of researchers interested in the history of Iram used NASA remote sensing satellites, ground penetrating radar, Landsat program data and images taken from the Space Shuttle Challenger as well as SPOT data to identify old camel train routes and points where they converged. These roads were used as frankincense trade routes around 2800 BC to 100 BC.
One area in the Dhofar province of Oman was identified as a possible location for an outpost of the lost civilization. A team including adventurer Ranulph Fiennes, archaeologist Juris Zarins, filmmaker Nicholas Clapp, and lawyer George Hedges, scouted the area on several trips, and stopped at a water well called Ash Shisar. Near this oasis was located a site previously identified as the 16th century Shis'r fort. Excavations uncovered an older settlement, and artifacts traded from far and wide were found. This older fort was found to have been built on top of a large limestone cavern which would have served as the water source for the fort, making it an important oasis on the trade route to Iram. As the residents of the fort consumed the water from underground, the water table fell, leaving the limestone roof and walls of the cavern dry. Without the support of the water, the cavern would have been in danger of collapse, and it seems to have done so some time between 300-500 AD, destroying the oasis and covering over the water source.
Four subsequent excavations were conducted by Dr. Juris Zarins, tracing the historical presence by the people of 'Ad, the assumed ancestral builders of Iram.
Egypt and the Roman Empire
Archaeologist Dr Sarah Parcak uses satellites to search for sub-surface remains. Parcak uses these satellites to hunt to for lost settlements, tombs, and pyramids in Egypt's Nile Delta. She has also prospectively identified several significant sites in various parts of the ancient Roman Empire.
- Rindfuss,Ronald R and Stern, Paul C. Linking Remote Sensing and Social Science: The Need and the New Challenges.People and Pixels: Linking Remote Sensing and Social Science.National Academy Press. Washington D.C.1998. ,
- "Satellite archaeology". National Geographic. Retrieved 13 February 2014.
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- Sever, Thomas L.Validating Prehistoric and Current Social Phenomena upon the Landscape of the Peten, Guatemala.People and Pixels: Linking Remote Sensing and Social Science.National Academy Press. Washington D.C.1998.,
- Pope, Kevin O. and Dahlin, Bruce H.Ancient Maya wetland agriculture: new insights from ecological and remote sensing research.Journal of field archaeology.Vol. 16 p. 87-106. 1989
- Desmond, Lawrence G. and William A. Sauck.Entering the Maya Underworld: A ground penetrating radar Survey at Chichen Itza, Yucatan, Mexico. Innovation et Technologie au Service de Patrimoine de l'Humanite, Actes du colloque organise par Admitech en collaboration avec l'Unesco, Paris, 24 June 1996, pp. 23-30.
- Sever, Thomas and L and Irwin, Daniel E.LANDSCAPE ARCHAEOLOGY: Remote-sensing investigation of the ancient Maya in the Peten rainforest of northern Guatemala. Ancient Mesoamerica. Issue 1, vol.14. January 2003
- Protecting Peru's ancient past http://www.bbc.co.uk/news/world-latin-america-16190824
- "The Frankincense Route Emerges From the Desert". New York Times. 1992-04-21. Retrieved 2007-12-06.
- Said-Moorhouse,Lauren. "Space archaeologist unlocks secrets to ancient civilizations". CNN Travel. 20 Sep. 2013. Website. 28 Jan. 2014.http://www.cnn.com/2013/09/02/travel/space-archaeologist-unlocks-secrets/
- "What is space archaeology?". Sarah Parcak. Website. 28 Jan. 2014. http://www.sarahparcak.com/index2.php#/multi-text_5/1/.
- "Rome's Lost Empire, BBC One, review". Telegraph. Dec 10, 2012.
- BBC 4, 31 December 2013, Rome's Lost Empire |
Schematic representation of rotating disc galaxies in the early Universe (right) and the present day (left). Observations with ESO’s Very Large Telescope suggest that such massive star-forming disc galaxies in the early Universe were less influenced by dark matter (shown in red), as it was less concentrated. As a result the outer parts of distant galaxies rotate more slowly than comparable regions of galaxies in the local Universe.
We see normal matter as brightly shining stars, glowing gas and clouds of dust. But the more elusive dark matter does not emit, absorb or reflect light and can only be observed via its gravitational effects. The presence of dark matter can explain why the outer parts of nearby spiral galaxies rotate more quickly than would be expected if only the normal matter that we can see directly were present.
Now, an international team of astronomers led by Reinhard Genzel at the Max Planck Institute for Extraterrestrial Physics in Garching, Germany have used the KMOS and SINFONI instruments at ESO’s Very Large Telescope in Chile to measure the rotation of six massive, star-forming galaxies in the distant Universe, at the peak of galaxy formation 10 billion years ago.
What they found was intriguing: unlike spiral galaxies in the modern Universe, the outer regions of these distant galaxies seem to be rotating more slowly than regions closer to the core — suggesting there is less dark matter present than expected.
“Surprisingly, the rotation velocities are not constant, but decrease further out in the galaxies,” comments Reinhard Genzel, lead author of the Nature paper. “There are probably two causes for this. Firstly, most of these early massive galaxies are strongly dominated by normal matter, with dark matter playing a much smaller role than in the Local Universe. Secondly, these early discs were much more turbulent than the spiral galaxies we see in our cosmic neighbourhood.”
Both effects seem to become more marked as astronomers look further and further back in time, into the early Universe. This suggests that 3 to 4 billion years after the Big Bang , the gas in galaxies had already efficiently condensed into flat, rotating discs, while the dark matter halos surrounding them were much larger and more spread out. Apparently it took billions of years longer for dark matter to condense as well, so its dominating effect is only seen on the rotation velocities of galaxy discs today.
This explanation is consistent with observations showing that early galaxies were much more gas-rich and compact than today’s galaxies.
The six galaxies mapped in this study were among a larger sample of a hundred distant, star-forming discs imaged with the KMOS and SINFONI instruments at ESO’s Very Large Telescope at the Paranal Observatory in Chile. In addition to the individual galaxy measurements described above, an average rotation curve was created by combining the weaker signals from the other galaxies. This composite curve also showed the same decreasing velocity trend away from the centres of the galaxies. In addition, two further studies of 240 star forming discs also support these findings.
Detailed modelling shows that while normal matter typically accounts for about half of the total mass of all galaxies on average, it completely dominates the dynamics of galaxies at the highest redshifts.
R. Genzel, N. M. Förster Schreiber, H. Übler, P. Lang, T. Naab, R. Bender, L. J. Tacconi, E. Wisnioski, S. Wuyts, T. Alexander, A. Beifiori, S. Belli, G. Brammer, A. Burkert, C. M. Carollo, J. Chan, R. Davies, M. Fossati, A. Galametz, S. Genel, O. Gerhard, D. Lutz, J. T. Mendel, I. Momcheva, E. J. Nelson, A. Renzini, R. Saglia, A. Sternberg, S. Tacchella, K. Tadaki, D. Wilman. Strongly baryon-dominated disk galaxies at the peak of galaxy formation ten billion years ago.. Nature, 2017; 543 (7645): 397 DOI: : 10.1038/nature21685 |
Across the UK there are many laws which aim to keep children safe and protect their rights. These laws:
We've put together an overview of the key legislation in these areas, to help people who work with children.
Definitions of a child
The United Nations Convention on the Rights of the Child (UNCRC) defines a child as everyone under 18 unless, "under the law applicable to the child, majority is attained earlier".
In England a child is defined as anyone who has not yet reached their 18th birthday. Child protection guidance points out that even if a child has reached 16 years of age and is:
they are still legally children and should be given the same protection and entitlements as any other child (Department for Education, 2018a).
In Northern Ireland the The Children (Northern Ireland) Order 1995 defines a 'child' as a person under the age of 18.
In Scotland, a child legally becomes an adult when they turn 16, but statutory guidance which supports the Children and Young People (Scotland) Act 2014, includes all children and young people up to the age of 18. Where concerns are raised about a 16- or 17-year-old, agencies will need to consider which legislation or guidance is appropriate to follow, given the age and situation of the young person at risk.
Paragraph 21 of the National guidance for child protection in Scotland explains how professionals should act to protect young people from harm in different circumstances (Scottish Government, 2014).
Section 3 of the Social Services and Well-being (Wales) Act 2014 states that a child is a person who is aged under 18.
Children's rights are protected by law internationally and within the UK.
Some rights are recognised at international level through agreements between governments. The UK has signed up to the United Nations Convention on the Rights of the Child (UNCRC) and the European Convention on Human Rights (ECHR) (PDF), both of which set out a number of children's rights.
UN Convention on the Rights of the Child
The UN Convention on the Rights of the Child (UNCRC) sets out the rights of every child in the world to:
It sets standards for education, health care, social services and penal laws, and establishes the right of children to have a say in decisions that affect them .
The UK signed this convention in 1990. However the Rights of Children and Young Persons (Wales) Measure 2011 made Wales the first, and so far only, country in the UK to make the UNCRC part of its domestic law. This means that Welsh Ministers have a duty to include the UNCRC in all policymaking.
European Convention on Human Rights (ECHR)
The 1950 European Convention on Human Rights (ECHR) (PDF) is an international treaty which gives a set of rights to both adults and children. The Human Rights Act 1998 made most of the ECHR UK law. This means that children can complain to a UK court if their rights have been broken, and if the claim is rejected, take their claim to the European Court of Human Rights.
Rights set out in the convention include:
Children's rights in the UK
The Human Rights Act 1998
The Human Rights Act 1998 sets out the fundamental rights and freedoms that everyone in the UK is entitled to. It incorporates the rights set out in the European Convention on Human Rights (ECHR) (PDF) into domestic British law. The Human Rights Act came into force in the UK in October 2000.
The Equality Act 2010
The Equality Act 2010 protects children, young people and adults against discrimination, harassment and victimisation in relation to housing, education, clubs, the provision of services and work. The Act applies to England, Scotland and Wales.
Northern Ireland has a number of different anti-discrimination laws relating to the provision of services.
Rights of Children and Young Persons (Wales) Measure 2011
In 2011 the Rights of Children and Young Persons (Wales) Measure 2011 made Wales the first, and so far only, country in the UK to make the United Nations Convention on the Rights of the Child part of its domestic law. This ensures that children's rights are included in all policy making in Wales.
Each of the four nations in the UK has a Children's Commissioner who is responsible for promoting and protecting the rights and best interests of children and young people:
Gillick competency and Fraser guidelines
Most child protection guidance emphasises the importance of listening to the wishes of the child.
The Gillick competency and Fraser guidelines help to balance children's rights and wishes with the responsibility to keep children safe from harm.
They refer to a legal case in the 1980's which looked specifically at whether doctors should be able to give contraceptive advice or treatment to under 16-year-old girls without parental consent.
Since then, the guidelines have been used more widely to help assess whether a child has the maturity to make their own decisions and to understand the implications of those decisions.
School leaving age varies across the UK.
In England pupils can leave school on the last Friday in June if they'll be 16 by the end of the summer holidays.
Young people must then do one of the following until they're 18:
In Northern Ireland if a pupil turns 16 during the school year (between 1 September and 1 July) they can leave school after 30 June of that year.
If a pupil turns 16 between 2 July and 31 August they can't leave school until 30 June the following year (Gov.uk, 2018a).
In Scotland, if a pupil turns 16 between 1 March and 30 September they can leave school after 31 May of that year.
If a pupil turns 16 between 1 October and the end of February they can leave at the start of the Christmas holidays in that school year (Gov.uk, 2018a).
In Wales pupils can leave school on the last Friday in June, as long as they'll be 16 by the end of that school year's summer holidays (Gov.uk, 2018a).
As young people get older they may start to think about moving out and living independently, for various reasons. They may:
In some cases parents may ask their children to leave the home, for example for financial reasons or a breakdown in relationships.
Support for children who need to leave home
If a child under 16 is made to leave or doesn't feel safe in their home, local children's services can help.
Children's services should provide a family with support so that the child doesn't have to leave home. But if it's in the child's best interests to live somewhere else, they can arrange for them to live with another family member or friend, or provide emergency accommodation, such as a foster placement.
A child or young person aged 16 or 17 should contact their local children's services team if they are considering leaving home. Children's services should discuss the matter with them to see what support they need. Children's services may be able to work with the family to enable the young person to stay at home, or arrange alternative accommodation such as with another family member or friend. But they should also respect the child's wishes about where they want to live.
A child or young person may be considered homeless when their home is not suitable or they do not have the right to stay where they live. For example they may be living somewhere that is dangerous or overcrowded.
A homeless child is entitled to accommodation from their local authority children's services, regardless of their nationality or immigration status.
In England, statutory guidance for supporting homeless 16- and 17-year-olds is set out in Prevention of homelessness and provision of accommodation for 16 and 17 year old young people who may be homeless and/or require accommodation (PDF) (Ministry of Housing, Communities and Local Government, 2018).
In Northern Ireland, Health and Social Care Trusts have a duty under The Children (Northern Ireland) Order 1995 to provide services for persons under 18 who are children in need (Housing Executive, 2017).
In Scotland, chapter 6 of the Code of Guidance on Homelessness (PDF) (Scottish Government, 2005) refers to 16- and 17-year-olds as having priority need for housing.
In Wales statutory guidance for homeless 16- and 17-year-olds is Provision of accommodation for 16 and 17 year old young people who may be homeless (PDF) (Welsh Government, 2010).
If a child or young person wants to live independently it's important to consider their ability to support themselves financially. They may not be in a position to put down a deposit on a property, pay rent and bills, or buy food.
In England, Northern Ireland and Wales, young people are not legally entitled to have a tenancy agreement to rent a property in their own name until they are 18. In Scotland this is possible from 16.
Children who are aged 16 or 17 and who have little or no income may be eligible to claim Income Support (IS) or jobseeker's allowance (JSA).
Universal Credit will replace six benefits across the UK, including Income Support and Jobseeker's Allowance. 16- and 17-year-olds will only be able to claim Universal Credit if they:
The local Citizen's Advice Bureau can help work out what support a child is entitled to. More information is also available from Jobcentre Plus in England, Scotland and Wales or the Jobs & Benefits office in Northern Ireland.
If a child or young person needs confidential help and advice direct them to Childline. Calls to 0800 1111 are free and children can also contact Childline online or read about homelessness on the Childline website. You can also download or order Childline posters and wallet cards.
In all nations of the UK, children leaving care at 18 are entitled to support from their local authority until they are at least 21.
Young people who have their own children are entitled to support. The local children's services or the Citizen's Advice Bureau can advise about what help is available.
The youngest age a child can work part-time is 13, except for children involved in specific areas such as television, theatre or modelling (Gov.uk, 2018b). Children working in these areas will need a performance licence.
Children can only start working full-time once they've reached the minimum school leaving age � after this they can work up to 40 hours per week (Gov.uk, 2018b).
Young people can work as apprentices from the age of 16. However, there is also a Young Apprenticeship scheme for 14- to 16-year-olds. Apprentices are paid a salary for their work and also pay tax and national insurance.
In England, a young person must be in part-time education or training until they're 18 (Gov.uk, 2018a).
Rules about child employment
To help keep children safe and protect their rights, there are laws governing what kinds of work they can do, how they are paid, and when they can work. An employer can be prosecuted for breaking these laws.
In most cases, businesses intending to employ school-aged children need to apply to their local authority for a child employment permit before the child can start work.
Children are only allowed to work:
The local authority won't allow a child to do any job they think may be harmful to them.
Local bylaws may also restrict the kind of work children can do (Gov.uk, 2018b).
Keeping children safe at work
Employers have a responsibility to keep all the children they work with safe. This includes providing a safe environment and making sure they are doing a job which is suitable for their physical and psychological capabilities.
Employers must carry out a risk assessment before a child starts work, and take measures to reduce any risks identified. In most cases, if the child is below school leaving age, the employer must inform the child's parents about the results of the risk assessment.
The Health and Safety Executive (HSE) provides guidance on health and safety considerations for young people in the workplace (HSE, 2018a).
Young people who work with other children
Although there is no law in the UK saying how old a babysitter should be, we recommend they should be at least 16.
Child care establishments like nurseries, cr�ches, and out-of-school clubs are heavily regulated to ensure that children in their care are safe.
In general, only people aged 18 or over should be included as adults when calculating adult to child ratios.
If over-16-year-olds are doing work that is classed as "regulated activity" they need to have a criminal records check.
Work experience placements
The Department for Education (DfE) has published non-statutory advice to help schools, colleges and other training providers in England deliver work experience, including information on health and safety and accountability (DfE, 2015).
The HSE have published information on their website for employers who have young people doing work experience with them (HSE, 2018b).
Age of consent
In each UK nation, the age of consent (the legal age when people can engage in sexual activity) is 16-years-old. This is the same regardless of the person's gender identity, sexual identity and whether the sexual activity is between people of the same or different gender.
The law is there to protect children from abuse or exploitation, rather than to prosecute under-16s who participate in mutually consenting sexual activity. Underage sexual activity should always be seen as a possible indicator of child sexual exploitation.
Children aged under 13
The law says anyone under the age of 13 can never legally give consent. (Sexual Offences Act 2003; Sexual Offences (Northern Ireland) Order 2008; Sexual Offences (Scotland) Act 2009; Protection of Children and Prevention of Sexual Offences (Scotland) Act 2005).
Any sexual activity with a child under 13 should always result in a child protection referral.
Young people aged 16 to 18
The law gives extra protection to young people who are over the age of consent but under 18. It is illegal:
Age of criminal responsibility
The age of criminal responsibility in England, Wales and Northern Ireland is 10-years-old (Crime and Disorder Act 1998, Criminal Justice (Northern Ireland) Order 1998). The age of criminal responsibility in Scotland is 8-years-old.
England and Wales
In England and Wales children between 10 and 17 can be arrested and taken to court if they commit a crime. They are treated differently from adults:
In England and Wales, children under 10 cannot be charged with committing a criminal offence. However, they can be given a:
Children under 10 who break the law regularly can sometimes be taken into care, or their parents could be held responsible (Crime and Disorder Act 1998).
Young people aged 18-25 are treated as an adult by the law in England and Wales. However, if they're sent to prison, they'll be sent to a special centre for 18- to 25-year-olds, not an adult prison (Crime and Disorder Act 1998).
In Scotland, the age of criminal responsibility is 8, but the minimum age for criminal prosecution is 12-years-old (Criminal Justice and Licensing (Scotland) Act 2010). This means if a child aged between 8 and 11 breaks the law, their case can't be heard in a criminal court. Instead their behaviour will be addressed by a Children's Hearing.
Children aged 12 to 16 can be taken to court but only for serious crimes. Most offences committed by children of this age will be dealt with by early intervention (like a warning or help from a support organisation) or the children's hearings system (Criminal Procedure (Scotland) Act 1995).
The Scottish Parliament has published the Age of Criminal Responsibility (Scotland) Bill 2018, which will raise the age of criminal responsibility to 12.
The General Data Protection Regulation (GDPR)
The General Data Protection Regulation (GDPR) came in to force on 25th May 2018. It is an EU law that sets out guidelines for the collection and processing of personal information and aims to give individuals more rights over how their data is used. GDPR is incorporated into the UK's Data Protection Act 2018.
Why is GDPR important and what impact does it have on children?
The GDPR explicitly states that children's personal data merits specific protection. It also introduces new requirements for the online processing of a child's personal data.
Children have the same rights as adults over their personal data. These include the right to:
A child may exercise these rights on their own behalf as long as they are competent to do so. In Scotland, a person aged 12 or over is presumed to be of sufficient age and maturity to be able to exercise their data protection rights. In England and Wales and Northern Ireland, competence is assessed depending upon the level of understanding of the child.
Even if a child is too young to understand the implications of their rights, they are still their rights, rather than anyone else's such as a parent or guardian (Information Commissioners Office, 2018).
GDPR and online data
The provisions of GDPR help children to keep themselves safe online by giving them more control over the information they share.
GDPR gives children the 'right to erasure'. This means they can request online platforms to remove their personal data, including pictures, text or status updates.
If a child has shared any material online that they no longer wish anyone to see, they have a legal right to get this material removed, even if the content was posted by someone else.
Apps, sites and games must make it clear to users how and why they are using data.
Under this law, children aged 12 or under need to seek parental consent to open a social media account, because they need to be 13 years or older to meaningfully understand how their data might be used (O2/NSPCC Net Aware, 2018).
GDPR and child protection
GDPR emphasises the importance of asking children for consent before sharing personal information.
If a child is mature enough you should give them the opportunity to decide whether they agree to their confidential information being shared. If a child doesn't have the capacity to make their own decisions, you should ask their parent or carer (unless this would put the child at risk).
However, if you have a child protection concern, you must share information with the relevant agencies, even if you haven't been given consent. GDPR does not affect this principle. |
19, Jun 19 . To let a function return a value, use the returnstatement: Example. These are most useful when you do not know how many numbers of arguments are to be passed into a function. As an example, define a function that returns a string and a number as follows: Just write each value after the return, separated by commas. In Python, you can return multiple values by simply return them separated by commas. This tutorial shows how multiple values can be returned from Python functions with multiple variables, objects, tuples, lists, and dictionaries. A return statement is used to end the execution of the function call and “returns” the result (value of the expression following the return keyword) to the caller. Then look at what is printed when the function returns. In today’s article, we’ll be looking at Python’s in-built hash() function. Step 1) Here - we see when function is not "return". Sometimes, you need to perform a task multiple times in a program. The return keyword is to exit a function and return a value. Return to Content. 01, May 20. In this tutorial, we will learn how to return a tuple from a function in Python. map() is useful when you need to apply a transformation function to each item in an iterable and transform them into a new iterable.map() is one of the tools that support a functional programming style in Python. Of course, specifying an index that exceeds the number of defined return values will occur an error. The statements after the return statements are not executed. Note: The return statement within a function does not print the value being returned to the caller. Attention geek! A function in Python is defined with the def keyword. This is possible because funcitons are treated as first class objects in Python. To do so, return a data structure that contains multiple values, like a list containing the number of miles to run each week. Active 1 month ago. See the following article for the basics of functions in Python. Well, one possibility is to use function return values. This is because return statements send values from a function to a main program. play_arrow. This is a unique property of Python, other programming languages such as C++ or Java do not support this by default. More Control Flow Tools - Defining Functions — Python 3.7.4rc1 documentation Let's understand this with the following example . So, if we have to return, for example, 3 integer values, we can return a list or a tuple with these three integer values. Python Return Tuple. Functions can have parameters and return values. Python Function Return Value. Python: Return Multiple Values with Commas. We learned that we can also return a function from another function. Return value policies¶ Python and C++ use fundamentally different ways of managing the memory and lifetime of objects managed by them. Python Function with argument and No Return value. A function is not required to return a variable, it can return zero, one, two or more variables. How to write an empty function in Python - pass statement? To understand python return statement, you can refer to this tutorial.. Python … You can return multiple values by separating the values you want to return with commas. Viewed 107 times -2. To know more about first class objects click here. 3. 1. Function with no argument and with Return value 3. Return Multiple Values. It accepts an argument returns the class of the argument the object belongs to. Return Values. Visualization for Function Optimization in Python. Functions do not have declared return types. Function with no argument and with a Return value. What is a function. Python functions can return multiple variables. Remember! Any input parameters or arguments should be placed within these parentheses. Closed. How do i return a boolean value from a function? A return value is a result of the function's execution. Otherwise, the value False is returned. Consider the following common mistake made by beginning Python programmers. So, when you type in the return statement within the function the result is different than when the return statement is mentioned outside. Like any other object, you can return a tuple from a function. Recursion is a common mathematical and programming concept. Note that this… By Jason Brownlee on January 15, 2021 in Optimization. code. edit Function optimization involves finding the input that results in the optimal value from an objective function. generate link and share the link here. Python allows function to return multiple values. 2. def my_function(x): return 5 * x. print(my_function(3)) print(my_function(5)) print(my_function(9)) Try it Yourself ». But it can also be e.g. A function without an explicit return statement returns None. It is best to check your indentation properly before executing a function … This can lead to issues when creating bindings for functions that return a non-trivial type. An object can be a numerical value, like an integer or a float. The python return statement is used in a function to return something to the caller program. Check the example below to find the square of the number using Python. It can be returned to the block of code that called the function, and then used as needed. edit. You can define functions to provide the required functionality. ), numpy.delete(): Delete rows and columns of ndarray, Create transparent png image with Python, Pillow (putalpha). The return statement. Our function can return two values: True or False. You might have encountered some functions written in python which have a return keyword in the end of the function. Python functions can return both single and multiple values. filter_none. brightness_4 link brightness_4 code # A Python program to return multiple # values from a method using class . How to select first object in object in AngularJS? Understand Python Return Statement for Python Beginners – Python Tutorial ; If the return statement contains an expression, it’s evaluated first and then the value is returned. This tutorial shows how multiple values can be returned from Python functions with multiple variables, objects, tuples, lists, and dictionaries. futures module provides a higher-level API to threading, including passing return values or exceptions from a worker thread back to the main thread: Note: Return statement can not be used outside the function. These variables can be stored in variables directly. Notre programme va être composé de différentes fonctions qui vont se charger d’effectuer ces différents calculs à la suite les unes des autres. 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python function return value 2021 |
"There are many strategies a teacher can implement in the classroom to help a Dyslexic student do well and understand the different skill sets such as spelling, reading, writing, arithmetic and understanding time. Most of these suggestions are beneficial for any student but especially important for Dyslexics."
* If one or both of a child's parents are Dyslexic the odds are 50% their children will be too. Dyslexia can also skip generations from grandparent to grandchild. There is a gene that indicates Dyslexia. Visit the article CAUSE OF DYSLEXIA ON CHROMOSOME 18 which we have quoted on our website from the Indepentent.co.uk
* Help right-brain learners (Dyslexics) understand their thinking and the learning differences from left brain thinkers (big picture and concrete images versus abstracts such numbers, letters and words). They will understand they can be taught how to use their processing style to their advantage for success in school.
* Help Dyslexic students discover their personal learning style (auditory, visual or kinesthetic) and teach them how to use their strongest sense to process information and perform new skills with greater understanding.
* These students think in wholes: spelling whole words, thinking in whole words, whole chapters and stories, whole lessons, whole assignments and whole concepts. Their school work should reflect this focus on wholes. Breaking a word into individual letters and sounds is not the best way for these students to learn how to spell them.
*Skills or information taught with steps over a series of days, without a preliminary overview or "Big Picture", can be very difficult for Dyslexic students to follow and comprehend. The constant memory loss of information covered over several days is one way a Dyslexic can be labeled as having "short term memory loss".
An example is teaching the process of long division using brackets, often taught in steps over a number of days. Without an overview explanation of what long division is or what it is used for the sequence or set of steps of a long division problem becomes very abstract. The average student is taught to follow them and they will have a correct answer.
A Dyslexic student needs to understand what is happening in these steps and why the answer is right otherwise they won't understand what long division is and why they need to do it. Dyslexics and right-brained thinkers need to see the whole process and its meaning at the beginning of the lessons.
A more appropriate way to approach long division would be to begin with a discussion about what it is. We would start with a demonstration talking about how multiplication is about counting in groups (which they should know) and long division is about subtracting in groups.
Then we would practice subtracting in groups with objects and then start to introduce the bracket. Each number position in the bracket would be associated with the practice of subtracting in groups so they understand what each position represents. A complete problem would be shown and all the steps.
After that we would practice division problems with real objects and the brackets over a series of days. This method will be very vivid in their minds and they will completely understand.
* Try to complete a lesson at one sitting. An incomplete lesson is entirely lost on them. If this is not possible, then provide a written summary, extra time during the same day to answer the student's questions or find ways to teach the complete lesson in one sitting, or give them the start and ending first and then fill in the middle.
* Dyslexic students can be identified as early as 6 years of age. Their struggles with school work are noticeable when compared to the rest of the class along with their above average intelligence. It is very important to identify them early. If this is delayed and they are being taught with methodologies that work well with left-brain learners they can lose a lot of ground, get behind in class and have difficulty catching up.
* Studies have shown that Dyslexics tend to be above average to genius level in intelligence. It is not uncommon for gifted children to have Dyslexic issues. Often this can make it difficult to identify them and they can be regarded as "lazy and not living up to their potential".
* These students think and reason starting with a fact or conclusion and analyze the parts that prove or disprove the conclusion. They need to see the "forest before the trees" with everything they are learning and processing. Just as many essays are based on analyzing a stated conclusion.
*Always design your questions and assignments around a given conclusion or fact. Dyslexic students think in concrete wholes, that is, they work backwards from a conclusion or fact to fill in all the parts. "Top/down processing."
"Top-Down Processing: Top-Down Processing is also known as "large chunk" processing and states that we form perceptions (or focus our attention) by starting with the larger concept or idea (it can even be the concept or idea of an object) and then working our way down to the finer details of that concept or idea. If you're the type of person who learns new ideas and concepts (or forms impressions) by starting first with the high-level aspects and then working your way down to the fine details, then you're a top-down processor." ~ quoted from AlleyDog.com
*Do not give them open-ended questions that involve abstract or incomplete instructions.
*Do not base the student's marks on spelling, punctuation or grammatical errors. Errors in assignments should be corrected for them. Spelling, punctuation and grammar are very abstract concepts for them that the right brain does not easily process and cannot visualize them as concrete images. If these errors must be corrected before a student hands in an assignment then permit someone else to edit the mistakes in spelling, grammar and punctuation. Parents are often helpful in this.
* Look for ideas, not clerical errors. Getting ideas down on paper is much more important than fretting over spelling, grammar and punctuation. If they do not achieve what they are capable of they soon become depressed and give up. Using recording devices to get their ideas down are a great tool.
* Their ability to use the correct grammar, punctuation and spelling forms may or may not improve with age, depending on the their ability to understand these concepts and the type of teaching methods the Dyslexic student receives.
* They ask a lot of questions and they need them answered. Without these answers they can be paralyzed in the classroom and can't proceed with their school work. Answer the student's questions as often as possible, but keep your answers very short, clear and specific. Be precise. Do not repeat your answers unless the student asks you to do so. Then answer only what the student asks. Long explanations, different approaches, wordy definitions, or abstract thinking are all very tiring and difficult for these students who are looking for a concrete answer.
* Do not criticize your students for not paying attention or being lazy. If they look like they are daydreaming, they may be learning by listening or they can no longer understand the lesson and are trying to cope with the situation. They are actually working hard to understand what you are saying. Sometimes the student has already solved the problem and is thinking about other solutions or aspects of the problem.
* Instead of long, written assignments, turn these tasks into projects that involve all the senses. These could be done on any large piece of coloured paper they could add real objects, pictures, drawing, sketches, photos, words of explanation and an oral report. The Dyslexic student learns best doing projects that involve seeing, listening, discussing and using their hands.
* Help facilitate a Dyslexic student who has been assessed for their best colour for dealing with reading issues caused by reading black text on white paper. This can be accomplished by using coloured plastic overlays over printed text, a similar colour on their computer background and coloured paper for their worksheets and other school materials. Many times we have seen great changes in a students reading speed and comprehension just by changing the colour of the paper they are working on or by placing a coloured transparent acetate over a worksheet or page of a book.(Refer to information about Scotopic Sensitivity Syndrome)
* Encourage these students to expand and use their natural right-brain traits and talents such as: artistic abilities in different mediums, researching topics for projects. Some are proficient and exceptional at arithmetic and mathematics and yet other Dyslexics can have great difficulty with arithmetic and math. Most Dyslexic individuals show good leadership abilities, problem solving skills, have wonderful imagination and terrific story-telling skills. Many have natural mechanical abilities, are talented athletes, possess photographic memories and show a strong logical sensibility. They can be assessed to discover their natural talents, interests and hobbies.
* Teach the students how to put individual parts in a sequential order. The right-brained student needs to be trained in sequencing skills by using concrete materials and visual procedures such as the order of letters in words. This can be accomplished by using mind maps to show them how to find the parts and their order in the "big picture".
Eg: The seasons of the year could be printed in big simple letters on a large cardboard sheet with pictures of what the weather is like during those seasons, special holidays and day-to-day life such as school and summer activities. The mind map concept can be taken further and add the months of the year that fall in each season. This type of visual can help a Dyslexic anchor what "seasons of the year" means, what order they come in and how they are spelled. Many teenage Dyslexic students we assess still don't know the seasons or months of the year let alone their order.
* Mind maps should be used for all subjects. Dyslexics understand many concepts more completely when presented in mind maps and diagrams. The computer program, "Inspirations" is ideal for this. An example of a mind map created from the "Inspirations" program is shown below:
* Writing notes from the board can be very difficult so placing a Dyslexic child close to the front of the classroom or giving them notes pre-printed can be very helpful.
* Many Dyslexics need to read the beginning, then the end, and then the middle of chapter stories and best followed up with a movie of the book. Presenting the end of the story after the beginning gives the Dyslexic the "big picture" and their comprehension of the story increases. Some Dyslexics do not like this approach and prefer beginning, middle and end.
* Arithmetic, math, the concept of time, money, clock faces and measurement are very abstract and difficult ideas for Dyslexics but if concrete images and physical demonstrations are used to explain them they will catch on quickly. They should not be discouraged to count with their fingers or use other aids such as an abacus. The Dyslexic student may never be able to work arithmetic or math problems without these aids. These students also do better with drawing out a word problem rather than trying to work the details of the math equation from the text of the problem.
* They will always want to know the schedule for the day and will point it out if it changes.
* They can become obsessed about one subject so if this can be used in any school work at all it will help them learn the new skill sets. We had one boy we assessed who loved volcanoes. He could tell you all about them and spell difficult words like; magma, mantle, eruption. But he could not spell; then, would, other, into.
* Some Dyslexic children who are displaying ADHD behaviours are possibly suffering from frustration, confusion and fear. They don't understand what is going on in the class, they want to desperately and they are humiliated by their peers. Their inability to sit still and focus can be due to exasperation. More than one mother has told me her child was suicidal and they have been as young as third grade. We are not saying a child does not have ADHD, we are suggesting medical testing should be done along with examining the school background and emotional state of the child for other factors.
* And speaking of being wiggly and talking out in class; Dyslexic children tend to be very connected to experiencing the world through their senses and don't sit well to focus quietly on their schoolwork. They want to feel it, see it, touch it, smell it and hear everything. They experience life in the present - the past and the future belongs to the left brain.
If you can integrate movement and other sensory experiences consistently into the classroom they will be avid learners. Sitting, listening and writing for long periods of time can be almost impossible for them. More schools are starting to introduce accommodations in the classroom such as chewing gum, squeeze balls, plastic straws to tap instead of pencils and getting up and moving often.
* If you have a Dyslexic class clown try letting them have 5 minutes of stand-up comedy if they agree not to disturb the class for the rest of the day. This was the answer for my Dyslexic son in grade four who came up with the idea. I ran into his teacher a few years later and she said she still used this with other class clowns. Dyslexics are often very quick mentally and verbally and will use humour to deflect attention away from their learning problems and negative attention from their fellow class mates (Jim Carrey, Robin Williams, Jay Leno, Whoopi Goldberg to name a few).
* Dyslexics need a reason for everything. If you want them to stop a certain behaviour or demand they have, they often respond well to a logical explanation or solution.
If they want something now but you want them to wait until later such as a treat like icecream, tell them your plan. They are often able to understand and accept the delay. But if you change the day's activities you will probably be dealing with some strong objections.
Another would be denying them something they want but you don't think is good for them. When my three dyslexic children were growing up in the '80's I decided I didn't like the nintendos that were becoming popular. I told my children I thought they weren't a healthy substitute for going outside for exercise. I knew they would fight me if I banned them completely so I worked out a fair solution. If they were at a friend's house who had a nindtendo or an arcade they could play the games. But I would not buy one for our house. They accepted this option. We didn't fight about it.
Older dyslexic students will often have issues with tasks they have to do in school. They won't see the sense of repetitive exercises or following steps to a process such as those in a math problem or writing the steps down.
We have a fifteen year old we are working with who was failing because he was resistant to show his work. He saw answers in his head and didn't feel he needed to write the steps down to get the answer. We explained to him these steps confirm to the teacher he knew what he was doing and not just guessing. Also if he was making mistakes his work would help the teacher see where they were.
This would also help him get what he wanted which was passing grades, a diploma and the ability to go onto what he wanted to do with his life.
After these explanations the young man became more accommodating. We have this conversation with many of our older Dyslexic students and once they have a reason to comply, they do. These students don't like to accept direction unless there is a reason.
So try working out negotiations or reasons for or not doing certain things.
* Many Dyslexics have a terrible time with being on time and completion dates. They live in the present and do not comprehend a schedule easily. Team up with their parents to work out a schedule for their schoolwork. They could have a white board at home with homework dates that the parent could help them remember.
They respond well to colour. Give them an agenda done in colours. Red could mean hand in "tomorrow", blue could be the "end of the week". This could be written on their white board at home. The colours could be updated daily on their calendar for consideration of their home work due dates.
The other side of the spectrum are Dyslexics who are obsessed about schedules. This is what we have found to be typical, nothing in the middle. Either they can be on time and sometimes obsessively or not at all. We have found working with a Dyslexic student on schedules can help them build a lifelong skill.
* These students are reality based because they think in whole concrete images they can see, hear, touch, smell and taste. All abstract materials should be related to something they can see, feel, touch, hear or smell.
We have parents tell us that the teachers their children had that were focused on multi-sensory teaching methods, lots of movement and projects were usually their Dyslexic child's most successful and happy years.
* Dyslexics have great difficulty with letters and phonemes without the presence of the whole image of the word and an image or picture that relates to the word when learning to copy and memorize words. Most Dyslexics have difficulty understanding what letters are individually. C - A - T are three sounds that bring up no image on their own but the word "cat" brings up the image of a cat. An illustration would be to ask them to point to the "back of a chair". They will wonder if you mean the back of the chair where they lean their backs on or the "back" behind the chair. This problem occurs for them with many instructions they receive during the day in a classroom.
* Try to assist them in focusing ideas and organizing a large body of work. Know they need special training in writing procedures and gathering tools such as note-taking, note making, outlining, clustering or mind map information, using pictures, diagrams, drawings and composition procedures.
* Recognize their abilities to think emotionally, intuitively, creatively and "big picture" and incorporate into class work.
* Be sympathetic with their fears of being ridiculed when reading out loud, oral discussion and being able to follow written directions. One way to help with reading out loud is to give them a passage to practice reading at home and then reading it aloud in the classroom when they are comfortable.
* Recognize they may excel in oral discussions and group projects.
* Recognize they may be a good organizer and excel in leadership skills if they are not suffering from a loss of self-esteem.
* Dyslexics should be allowed and encouraged to use laptop computers in the classroom. Printing or writing is usually agonizing for a Dyslexic student. They generally have Dysgraphia to some degree so writing can affect their comprehension, their ability to write notes from the board, and complete an exercise or test on time.
Another option is using a scribe (a teaching assistant who writes a student's words or answers down for them in the classroom).
* Dyslexic students should be allowed to use assistive technologies such as computer programs like Dragon Naturally Speaking, Kurzweil, TextHelp Inspirations.
* Dyslexics should be given more time to complete class work and tests or do them orally. The purpose of their completed schoolwork is to be sure they understand it and having to write their answers can effect their ability to convey their knowledge of the subject. Written formats can make it impossible for them to print their thoughts and answers adequately when they are usually very articulate speakers. Recording machines can also help with getting their ideas and answers saved and then typed or hand written.
* Dyslexia changes from a Learning Difference to a Learning Disability when a child cannot learn in school due to inappropriate teaching methods and having become frustrated, exhausted, humiliated and despondent. When a child loses their self-esteem and begins to believe they are "stupid" they are filled with "self-limiting beliefs". They shut down and can no longer learn many new skills in school in a normal and timely manner - if it all.
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Students learn geometry at almost every grade level. Elementary students learn the basics of geometry: shapes and counting the number of sides. Middle school student begin learning how to find the volume and area of circles and squares. High school students jump into geometry with Euclidean/Plane Geometry and Symmetry & Tessellations. College students can take their knowledge from high school geometry to the next level and learn about Spherical Geometry, Hyperbolic Geometry, as well as Riemannian Geometry and Fourth Dimensional Geometry. No matter the grade level your student is in, we have expert tutors that will help students understand and conceptualize what they need to know in their geometry class.
What is it?
Euclidean/Plane Geometry is the study of flat space. Between every pair of points there is a unique line segment which is the shortest curve between those two points. These line segments can be extended to lines. Lines are infinitely long in both directions and for every pair of points on the line the segment of the line between them is the shortest curve that can be drawn between them. All of these ideas can be described by drawing on a flat piece of paper. From the laws of Euclidean Geometry, we get the famous Pythagorean Theorem.
Non-Euclidean Geometry is any geometry that is different from Euclidean geometry. It is a consistent system of definitions, assumptions, and proofs that describe such objects as points, lines and planes. The two most common non-Euclidean geometries are spherical geometry and hyperbolic geometry. The essential difference between Euclidean geometry and these two non-Euclidean geometries is the nature of parallel lines: In Euclidean geometry, given a point and a line, there is exactly one line through the point that is in the same plane as the given line and never intersects it. In spherical geometry there are no such lines. In hyperbolic geometry there are at least two distinct lines that pass through the point and are parallel to (in the same plane as and do not intersect) the given line.
Riemannian Geometry is the study of curved surfaces and higher dimensional spaces. For example, you might have a cylinder, or a sphere and your goal is to find the shortest curve between any pair of points on such a curved surface, also known as a minimal geodesic. Or you may look at the universe as a three dimensional space and attempt to find the distance between/around several planets.
Practice. Practice. Practice. For most students success in any math course comes from regular studying and practicing habits. However, we find that geometry is the one math class can be a foreign language for many students. No matter the level of the geometry class that the student is taking, we have expert tutors available and ready to help. All of our geometry tutors have a degree in mathematics, science, or a related field like engineering. Our goal is to provide a geometry tutor that can make understanding the concepts simple and straightforward and to help the student achieve success in the classroom.
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Imagine. You are an ancient human and your reliable and faithful sun suddenly and unexpectedly goes dark. This terrifies you. You think, ‘What if it never comes back? Oh gods, WHAT HAVE WE DONE TO DESER…oh, it’s back. Phew.’ But then, over the years, it keeps happening. You begin to lose trust in the sun’s loyalty and start recording when these events happen. Centuries go by and eventually enough of a pattern has built up that early civilizations are able to predict when these crazy events might occur.
“The idea that it’s not just random is pretty incredible,” says Jonathan Seitz, an associate professor of history at Drexel. “The Mesopotamians figured it out first in part because they had a habit of writing things down. They were doing this because they felt that these things had meaning—they weren’t just random natural phenomena.”
With records stretching back to about 700 BC, Mesopotamians were able to determine the length of a Saros Cycle—the interval between when the Moon, Earth, and Sun line up for an eclipse. A cycle happens once every 18 years, 10 days (11 days on leap years), and eight hours, tracing a shadow on the Earth. That extra eight hours means that the position of the eclipse shifts over time as the Earth rotates.
Though ancient astronomers wouldn’t have been able to monitor all iterations of a Saros cycle (eclipses can occur in the middle of oceans or uninhabited areas), they were able to figure out parts of the timing well enough to know when one might strike. But at this point in history, they just knew the when. Why and how would have to come much later.
Enter the Greeks. For thinkers like Aristotle and others, it wasn’t enough to know that something was happening. It was equally as important to know why it was occurring. “The Greeks became very interested in causation,” Seitz says. The meaning of the eclipse was less important than other factors: “For them, you don’t understand something until you can explain it.”
Greek observations helped figure out how planets move and that the shape of the Earth is a sphere. Without telescopes, they still thought of the moon as a luminous heavenly body, vastly different from our rocky home, but they figured out its relative motion compared to Earth. And even though they thought that the Earth was the center of the Universe, they figured out that an eclipse is the shadow of a new Moon cast by the sun onto the Earth.
Techniques developed by Aristotle and Ptolemy to understand eclipses were in use all the way up until Copernicus and Newton stepped on the scene hundreds of years later.
“That’s not to say that nothing happened in the intervening time,” Seitz adds. People kept building on ancient cultures’ knowledge, accumulating more data, and starting to refine techniques during the Middle Ages. “In the Islamic world in particular, they paid a lot of attention to astronomy and astrology, developed astrolabes to take angles in the heavens, and tried to refine the system,” Seitz says.
Later, thinkers like Tycho Brahe built giant quadrants to make more accurate measurements of the movement of the Sun during eclipses, and some people used techniques to measure the eclipse that we still use today. “They did use pinhole cameras in the medieval period, which lets you measure the magnitude of the eclipse a little better,” Seitz says.
Europe was far from the only place to notice that eclipses were happening. China developed their own eclipse predictions at around the same time as people in the Mediterranean, paralleling the discovery of the patterns of eclipses thanks to their long history of record-keeping. There is evidence that the Mayans also had ways of measuring eclipses, but virtually all their records were brutally destroyed by conquistadors during the European invasion of the Americas.
Despite greater understanding of eclipses, most cultures still saw them as bad omens. Interpretations (slowly) started to change with the advent of telescopes, which revealed the topography of the Moon and allowed eclipse predictions to get much more precise. In fact, in the 1700’s astronomer Edmond Halley made a map of the path of the coming eclipse and published it in the hopes that the general public wouldn’t panic when the Sun briefly disappeared, and that observers might gather more data on how long the eclipse lasted at different locations. The modern era of eclipse observing had finally begun.
“The method we use now is based on something that people came up with in the 19th century” Ernie Wright, a visualization expert at NASA says. The people who started using more modern calculations to predict the eclipse paths were Friedrich Bessel and William Chauvenet.
“Bessel came up with the basic math that we use around 1820, and Chauvenet put it in its modern form in 1855,” Wright says.
Today, we’re able to get even more specific, thanks to our understanding of the shape of the moon. The moon—contrary to every elementary-school drawing you ever labored over—is not in fact, shaped like a banana or a perfect sphere. Like the Earth, it has mountains and valleys that make its shape a little rough around the edges, and that means that it’s shadow is uneven as well.
“19th century methods assume that he moon is smooth, and assume that all observers [are] at sea level,” Wright says. “You have to make those simplifications when you’re doing it on pencil and paper.”
From the late 1940’s until 1963, an astronomer named Charles Burleigh Watts spent countless hours mapping out the variations that appeared on the moon’s surface, focusing on the landforms that appeared on the outer edge of the moon as seen from Earth. His detailed maps helped eclipse predictions get even more precise. Suddenly, the shadow of the eclipse wasn’t an oval, it was a many sided polygon with each angle aligning with a valley on the Moon’s limb.
Then, NASA took it up a notch. The space agency’s Lunar Reconnaissance Orbiter built on Watt’s work, and captured the topography of the moon in detail that would have been impossible to get from photographs of the moon taken on the ground.
Wright took that data about the shape of the moon, the topography of the Earth, and the positions of the sun, Moon and Earth to create an incredibly detailed and accurate accounting of where the eclipse shadow will pass across the United States.
This eclipse is expected to be the most viewed total eclipse in history. And after humanity has spent thousands of years of watching and recording eclipses, there’s still plenty that researchers hope to learn.
“We’ve been talking recently about the fact that there is some uncertainty about the size of the Sun,” Wright says. “It turns out that eclipses are [a] very sensitive method of measuring the radius of the Sun. The Sun’s radius is about 696,000 km. But if you change that radius by 125 km, you change the duration of totality by a full second.”
If a lot of people along the very outermost edge of the predicted path, like those watching in some areas of Saint Louis, or Kansas City, report that they saw plenty of Bailey’s Beads and that it never got fully, one hundred percent dark, then that lets people know that the sun might just be a little bigger than we thought. If it is, that contribution could help future astronomers refine their predictions even more.
As you look up where the path of the eclipse is, and marvel at how modern science figured out exactly when, where, and how a shadow traveling at speeds between 1400 mph and 2500 mph crosses the country, spare a thought to all the generations of people who helped make that possible; from the observers who didn’t know what was happening over hundreds and hundreds of years but still bothered to write down what they saw, to the people who built the modern satellites that made this year’s eclipse maps so accurate. It took all of them to get to where we are today. |
An influential concept in the study of the relationship between attitudes and behavior.
First proposed by Leon Festinger in 1957, the theory of cognitive dissonance is based on the principle that people prefer their cognitions, or beliefs, to be consistent with each other and with their own behavior.
Inconsistency, or dissonance, among their own ideas makes people uneasy enough to alter these ideas so that they will agree with each other. For example, smokers forced to deal with the opposing thoughts "I smoke" and "smoking is dangerous" are likely to alter one of them by deciding to quit smoking. Alternatively, one can diffuse dissonance by reducing its importance (discounting the evidence against smoking or adopting the view that smoking will not harm you personally); adding new information that gives more weight to one of the dissonant beliefs or appears to reconcile them (deciding that smoking is less dangerous than the stresses it helps alleviate).
In a classic study of cognitive dissonance, subjects were asked to perform a dull task and then to persuade others that this task was interesting and enjoyable. Some were paid one dollar to do this, while others were paid $20, and all of their attitudes toward the task were measured at the conclusion of the experiment. The subjects who had been paid one dollar showed a marked improvement in their attitude toward the task, while the more highly paid subjects did not. The designers of the experiment interpreted their results in the following way. Cognitive dissonance was created in all of the subjects by the conflicting facts that the task had been boring and that they were saying it was interesting—their statements and beliefs did not match. However, those who were paid $20 had been given a justification for lying: they could tell themselves that their actions made some kind of sense. However, the actions of the other group made no sense unless they could persuade themselves that the task had indeed been interesting. Thus they acted to reduce the dissonance by changing their original belief.
Children have shown similar responses to experimental situations involving cognitive dissonance. In one case, children were asked not to play with an appealing toy. One experimenter made this request mildly and politely while another one made it in a threatening fashion. Those children who had accommodated the polite request also became less attracted to the toy, since liking the toy and giving it up were conflicting experiences that created dissonance. However, the children who were threatened felt no pressure to change their opinions about the toy since they had a logical reason for giving it up.
Several types of cognitive dissonance have been identified. In post-decision dissonance, a person must decide between two choices, each of which has both positive and negative components (in other contexts, this type of situation is called a multiple approach-avoidance conflict). Forced compliance dissonance occurs when people are forced to act in ways that conflict with their beliefs and can not find any way to justify their actions to themselves. Dissonance also occurs when people are exposed to new information that threatens or changes their current beliefs. Various group situations also generate cognitive dissonance. It occurs when a person must abandon old beliefs or adopt new ones in order to join a group, when
members disagree with each other, and when the group as a whole has its central beliefs threatened by an external event or by the receipt of new information.
Festinger proposed that some individuals have a higher tolerance for cognitive dissonance than others. Subsequent researchers have found correlations between various personality traits, such as extroversion, and the ability to withstand dissonance.
Festinger, Leon. A Theory of Cognitive Dissonance. Stanford, CA: Stanford University Press, 1957.
- Cognitive Psychology
- Cognitive Development - Piaget's stages of cognitive development, Modern views
- Other Free Encyclopedias |
Millennium Development Goals
The Millennium Development Goals (MDGs) were the eight international development goals for the year 2015 that had been established following the Millennium Summit of the United Nations in 2000, following the adoption of the United Nations Millennium Declaration. All 191 United Nations member states at that time, and at least 22 international organizations, committed to help achieve the following Millennium Development Goals by 2015:
- To eradicate extreme poverty and hunger
- To achieve universal primary education
- To promote gender equality and empower women
- To reduce child mortality
- To improve maternal health
- To combat HIV/AIDS, malaria, and other diseases
- To ensure environmental sustainability
- To develop a global partnership for development
Each goal had specific targets, and dates for achieving those targets. To accelerate progress, the G8 finance ministers agreed in June 2005 to provide enough funds to the World Bank, the International Monetary Fund (IMF) and the African Development Bank (AfDB) to cancel $40 to $55 billion in debt owed by members of the heavily indebted poor countries (HIPC) to allow them to redirect resources to programs for improving health and education and for alleviating poverty.
Critics of the MDGs complained of a lack of analysis and justification behind the chosen objectives, and the difficulty or lack of measurements for some goals and uneven progress, among others. Although developed countries' aid for achieving the MDGs rose during the challenge period, more than half went for debt relief and much of the remainder going towards natural disaster relief and military aid, rather than further development.
As of 2013, progress towards the goals was uneven. Some countries achieved many goals, while others were not on track to realize any. A UN conference in September 2010 reviewed progress to date and adopted a global plan to achieve the eight goals by their target date. New commitments targeted women's and children's health, and new initiatives in the worldwide battle against poverty, hunger and disease.
Among the non-governmental organizations assisting were the United Nations Millennium Campaign, the Millennium Promise Alliance, Inc., the Global Poverty Project, the Micah Challenge, The Youth in Action EU Programme, "Cartoons in Action" video project and the 8 Visions of Hope global art project.
The Sustainable Development Goals (SDGs) replaced the MDGs in 2016.
- 1 Background
- 2 Goals
- 2.1 Goal 1: Eradicate extreme poverty and hunger
- 2.2 Goal 2: Achieve universal primary education
- 2.3 Goal 3: Promote gender equality and empower women
- 2.4 Goal 4: Reduce child mortality rates
- 2.5 Goal 5: Improve maternal health
- 2.6 Goal 6: Combat HIV/AIDS, malaria, and other diseases
- 2.7 Goal 7: Ensure environmental sustainability
- 2.8 Goal 8: Develop a global partnership for development
- 3 Criticism
- 4 Progress
- 5 Improvements
- 6 Post 2015 development agenda
- 7 Related activities/organisations
- 8 See also
- 9 References
- 10 Bibliography
- 11 External links
Preparations for the 2000 Millennium Summit launched with the report of the Secretary-General entitled, "We the people: The Role of the United Nations in the Twenty-First Century". Additional input was prepared by the Millennium Forum, which brought together representatives of over 1,000 non-governmental and civil society organizations from more than 100 countries. The Forum met in May to conclude a two-year consultation process covering issues such as poverty eradication, environmental protection, human rights and protection of the vulnerable.
MDGs derive from earlier development targets, where world leaders adopted the United Nations Millennium Declaration. The approval of the Millennium Declaration was the main outcome of the Millennium Summit.
The MDGs originated from the United Nations Millennium Declaration. The Declaration asserted that every individual has dignity; and hence, the right to freedom, equality, a basic standard of living that includes freedom from hunger and violence and encourages tolerance and solidarity. The MDGs set concrete targets and indicators for poverty reduction in order to achieve the rights set forth in the Declaration.
The Millennium Summit Declaration was, however, only part of the origins of the MDGs. More ideas came from Adam Figueroa, Organization for Economic Cooperation and Development (OECD), the World Bank and the International Monetary Fund. A series of UN‑led conferences in the 1990s focused on issues such as children, nutrition, human rights and women. The OECD criticized major donors for reducing their levels of Official Development Assistance (ODA). UN Secretary-General Kofi Annan signed a report titled, We the Peoples: The Role of the United Nations in the 21st Century. The OECD had formed its International Development Goals (IDGs). The two efforts were combined for the World Bank's 2001 meeting to form the MDGs.
Human capital, infrastructure and human rights
The MDGs emphasized three areas: human capital, infrastructure and human rights (social, economic and political), with the intent of increasing living standards. Human capital objectives include nutrition, healthcare (including child mortality, HIV/AIDS, tuberculosis and malaria, and reproductive health) and education. Infrastructure objectives include access to safe drinking water, energy and modern information/communication technology; increased farm outputs using sustainable practices; transportation; and environment. Human rights objectives include empowering women, reducing violence, increasing political voice, ensuring equal access to public services and increasing security of property rights. The goals were intended to increase an individual’s human capabilities and "advance the means to a productive life". The MDGs emphasize that each nation's policies should be tailored to that country's needs; therefore most policy suggestions are general.
MDGs emphasize the role of developed countries in aiding developing countries, as outlined in Goal Eight, which sets objectives and targets for developed countries to achieve a "global partnership for development" by supporting fair trade, debt relief, increasing aid, access to affordable essential medicines and encouraging technology transfer. Thus developing nations ostensibly became partners with developed nations in the struggle to reduce world poverty.
The MDGs were developed out of several commitments set forth in the Millennium Declaration, signed in September 2000. There are eight goals with 21 targets, and a series of measurable health indicators and economic indicators for each target.
Goal 1: Eradicate extreme poverty and hunger
- Target 1A: Halve, between 1990 and 2015, the proportion of people living on less than $1.25 a day
- Poverty gap ratio [incidence x depth of poverty]
- Share of poorest quintile in national consumption
- Target 1B: Achieve Decent Employment for Women, Men, and Young People
- GDP Growth per Employed Person
- Employment Rate
- Proportion of employed population below $1.25 per day (PPP values)
- Proportion of family-based workers in employed population
- Target 1C: Halve, between 1990 and 2015, the proportion of people who suffer from hunger
- Prevalence of underweight children under five years of age
- Proportion of population below minimum level of dietary energy consumption
Goal 2: Achieve universal primary education
- Target 2A: By 2015, all children can complete a full course of primary schooling, girls and boys
- Enrollment in primary education
- Completion of primary education
Goal 3: Promote gender equality and empower women
- Target 3A: Eliminate gender disparity in primary and secondary education preferably by 2005, and at all levels by 2015
- Ratios of girls to boys in primary, secondary and tertiary education
- Share of women in wage employment in the non-agricultural sector
- Proportion of seats held by women in national parliament
Goal 4: Reduce child mortality rates
- Target 4A: Reduce by two-thirds, between 1990 and 2015, the under-five mortality rate
Goal 5: Improve maternal health
- Target 5A: Reduce by three quarters, between 1990 and 2015, the maternal mortality ratio
- Maternal mortality ratio
- Proportion of births attended by skilled health personnel
- Target 5B: Achieve, by 2015, universal access to reproductive health
Goal 6: Combat HIV/AIDS, malaria, and other diseases
- Target 6A: Have halted by 2015 and begun to reverse the spread of HIV/AIDS
- HIV prevalence among population aged 15–24 years
- Condom use at last high-risk sex
- Proportion of population aged 15–24 years with comprehensive correct knowledge of HIV/AIDS
- Target 6B: Achieve, by 2010, universal access to treatment for HIV/AIDS for all those who need it
- Proportion of population with advanced HIV infection with access to anti-retroviral drugs
- Target 6C: Have halted by 2015 and begun to reverse the incidence of malaria and other major diseases
- Prevalence and death rates associated with malaria
- Proportion of children under 5 sleeping under insecticide-treated bednets
- Proportion of children under 5 with fever who are treated with appropriate anti-malarial drugs
- Incidence, prevalence and death rates associated with tuberculosis
- Proportion of tuberculosis cases detected and cured under DOTS (Directly Observed Treatment Short Course)
Goal 7: Ensure environmental sustainability
- Target 7A: Integrate the principles of sustainable development into country policies and programs; reverse loss of environmental resources
- Target 7B: Reduce biodiversity loss, achieving, by 2010, a significant reduction in the rate of loss
- Proportion of land area covered by forest
- CO2 emissions, total, per capita and per $1 GDP (PPP)
- Consumption of ozone-depleting substances
- Proportion of fish stocks within safe biological limits
- Proportion of total water resources used
- Proportion of terrestrial and marine areas protected
- Proportion of species threatened with extinction
- Target 7C: Halve, by 2015, the proportion of the population without sustainable access to safe drinking water and basic sanitation
- Target 7D: By 2020, to have achieved a significant improvement in the lives of at least 100 million slum-dwellers
Goal 8: Develop a global partnership for development
- Target 8A: Develop further an open, rule-based, predictable, non-discriminatory trading and financial system
- Target 8B: Address the Special Needs of the Least Developed Countries (LDCs)
- Target 8C: Address the special needs of landlocked developing countries and small island developing States
- Through the Programme of Action for the Sustainable Development of Small Island Developing States and the outcome of the twenty-second special session of the General Assembly
- Target 8D: Deal comprehensively with the debt problems of developing countries through national and international measures in order to make debt sustainable in the long term
- Some of the indicators listed below are monitored separately for the least developed countries (LDCs), Africa, landlocked developing countries and small island developing States.
- Official development assistance (ODA):
- Net ODA, total and to LDCs, as percentage of OECD/DAC donors’ GNI
- Proportion of total sector-allocable ODA of OECD/DAC donors to basic social services (basic education, primary health care, nutrition, safe water and sanitation)
- Proportion of bilateral ODA of OECD/DAC donors that is untied
- ODA received in landlocked countries as proportion of their GNIs
- ODA received in small island developing States as proportion of their GNIs
- Market access:
- Proportion of total developed country imports (by value and excluding arms) from developing countries and from LDCs, admitted free of duty
- Average tariffs imposed by developed countries on agricultural products and textiles and clothing from developing countries
- Agricultural support estimate for OECD countries as percentage of their GDP
- Proportion of ODA provided to help build trade capacity
- Debt sustainability:
- Total number of countries that have reached their HIPC decision points and number that have reached their HIPC completion points (cumulative)
- Debt relief committed under HIPC initiative, US$
- Debt service as a percentage of exports of goods and services
- Target 8E: In co-operation with pharmaceutical companies, provide access to affordable, essential drugs in developing countries
- Proportion of population with access to affordable essential drugs on a sustainable basis
- Target 8F: In co-operation with the private sector, make available the benefits of new technologies, especially information and communications
- Telephone lines and cellular subscribers per 100 population
- Personal computers in use per 100 population
- Internet users per 100 Population
General criticisms include a perceived lack of analytical power and justification behind the chosen objectives.
Iterations of proven local successes should be scaled up to address the larger need through human energy and existing resources using methodologies such as participatory rural appraisal, asset-based community development, or SEED-SCALE.
MDG 8 uniquely focuses on donor achievements, rather than development successes. The Commitment to Development Index, published annually by the Center for Global Development in Washington, D.C., is considered the best numerical indicator for MDG 8. It is a more comprehensive measure of donor progress than official development assistance, as it takes into account policies on a number of indicators that affect developing countries such as trade, migration and investment.
Agriculture was not specifically mentioned in the MDGs even though most of the world's poor are farmers.
Alleged lack of legitimacy
The entire MDG process has been accused of lacking legitimacy as a result of failure to include, often, the voices of the very participants that the MDGs seek to assist. The International Planning Committee for Food Sovereignty, in its post 2015 thematic consultation document on MDG 69 states "The major limitation of the MDGs by 2015 was the lack of political will to implement due to the lack of ownership of the MDGs by the most affected constituencies".
The MDGs may under-emphasize local participation and empowerment (other than women’s empowerment). FIAN International, a human rights organization focusing on the right to adequate food, contributed to the Post 2015 process by pointing out a lack of: "primacy of human rights; qualifying policy coherence; and of human rights based monitoring and accountability. Without such accountability, no substantial change in national and international policies can be expected."
MDG 2 focuses on primary education and emphasizes enrollment and completion. In some countries, primary enrollment increased at the expense of achievement levels. In some cases, the emphasis on primary education has negatively affected secondary and post-secondary education.
A publication from 2005 argued that goals related to maternal mortality, malaria and tuberculosis are impossible to measure and that current UN estimates lack scientific validity or are missing. Household surveys are the primary measure for the health MDGs but may be poor and duplicative measurements that consume limited resources. Furthermore, countries with the highest levels of these conditions typically have the least reliable data collection. The study also argued that without accurate measures, it is impossible to determine the amount of progress, leaving MDGs as little more than a rhetorical call to arms.
MDG proponents such as McArthur and Sachs countered that setting goals is still valid despite measurement difficulties, as they provide a political and operational framework to efforts. With an increase in the quantity and quality of healthcare systems in developing countries, more data could be collected. They asserted that non-health related MDGs were often well measured, and that not all MDGs were made moot by lack of data.
The attention to well being other than income helps bring funding to achieving MDGs. Further MDGs prioritize interventions, establish obtainable objectives with useful measurements of progress despite measurement issues and increased the developed world’s involvement in worldwide poverty reduction. MDGs include gender and reproductive rights, environmental sustainability, and spread of technology. Prioritizing interventions helps developing countries with limited resources make decisions about allocating their resources. MDGs also strengthen the commitment of developed countries and encourage aid and information sharing. The global commitment to the goals likely increases the likelihood of their success. They note that MDGs are the most broadly supported poverty reduction targets in world history.
Achieving the MDGs does not depend on economic growth alone. In the case of MDG 4, developing countries such as Bangladesh have shown that it is possible to reduce child mortality with only modest growth with inexpensive yet effective interventions, such as measles immunization. Still, government expenditure in many countries is not enough to meet the agreed spending targets. Research on health systems suggests that a "one size fits all" model will not sufficiently respond to the individual healthcare profiles of developing countries; however, the study found a common set of constraints in scaling up international health, including the lack of absorptive capacity, weak health systems, human resource limitations, and high costs. The study argued that the emphasis on coverage obscures the measures required for expanding health care. These measures include political, organizational, and functional dimensions of scaling up, and the need to nurture local organizations.
Fundamental issues such as gender, the divide between the humanitarian and development agendas and economic growth will determine whether or not the MDGs are achieved, according to researchers at the Overseas Development Institute (ODI).
The International Health Partnership (IHP+) aimed to accelerate MDG progress by applying international principles for effective aid and development in the health sector. In developing countries, significant funding for health came from external sources requiring governments to coordinate with international development partners. As partner numbers increased variations in funding streams and bureaucratic demands followed. By encouraging support for a single national health strategy, a single monitoring and evaluation framework, and mutual accountability, IHP+ attempted to build confidence between government, civil society, development partners and other health stakeholders.
Further developments in rethinking strategies and approaches to achieving the MDGs include research by the Overseas Development Institute into the role of equity. Researchers at the ODI argued that progress could be accelerated due to recent breakthroughs in the role equity plays in creating a virtuous circle where rising equity ensures the poor participate in their country's development and creates reductions in poverty and financial stability. Yet equity should not be understood purely as economic, but also as political. Examples abound, including Brazil's cash transfers, Uganda's eliminations of user fees and the subsequent huge increase in visits from the very poorest or else Mauritius's dual-track approach to liberalization (inclusive growth and inclusive development) aiding it on its road into the World Trade Organization. Researchers at the ODI thus propose equity be measured in league tables in order to provide a clearer insight into how MDGs can be achieved more quickly; the ODI is working with partners to put forward league tables at the 2010 MDG review meeting.
The effects of increasing drug use were noted by the International Journal of Drug Policy as a deterrent to the goal of the MDGs.
Increased focus on gender issues could accelerate MDG progress, e.g. empowering women through access to paid work could help reduce child mortality. In South Asian countries babies often suffered from low birth weight and high mortality due to limited access to healthcare and maternal malnutrition. Paid work could increase women's access to health care and better nutrition, reducing child mortality. Increasing female education and workforce participation increased these effects. Improved economic opportunities for women also decreased participation in the sex market, which decreased the spread of AIDS, MDG 6A. Another way in which women can be empowered is through access to paid work. Kabeer states that this access increases women’s agency in their households, it does so in the economic and political spheres as well. A study of women in rural Mexico found that those of them engaged in industrial work were able to negotiate and obtain a greater degree of respect in their households. Additionally, another study from Tanzania found that increased access to paid work led to a long-term reduction in domestic violence. Lastly, Women’s employment and access to financial resources increased their political participation. Data from Bangladesh indicates that longer membership in microfinance organizations have many positive effects including higher levels of political participation and improved access to government programs.
Although the resources, technology and knowledge exist to decrease poverty through improving gender equality, the political will is often missing. If donor and developing countries focused on seven "priority areas", great progress could be made towards the MDG. These seven priority areas include: increasing girls’ completion of secondary school, guaranteeing sexual and reproductive health rights, improving infrastructure to ease women’s and girl’s time burdens, guaranteeing women’s property rights, reducing gender inequalities in employment, increasing seats held by women in government, and combating violence against women.
It is thought[by whom?] that the current MDGs targets do not place enough emphasis on tracking gender inequalities in poverty reduction and employment as there are only gender goals relating to health, education, and political representation. To encourage women’s empowerment and progress towards the MDGs, increased emphasis should be placed on gender mainstreaming development policies and collecting data based on gender.[according to whom?]
Progress towards reaching the goals has been uneven across countries. Brazil achieved many of the goals, while others, such as Benin, are not on track to realize any. The major successful countries include China (whose poverty population declined from 452 million to 278 million) and India. The World Bank estimated that MDG 1A (halving the proportion of people living on less than $1 a day) was achieved in 2008 mainly due to the results from these two countries and East Asia.
In the early 1990s Nepal was one of the world's poorest countries and remains South Asia's poorest country. Doubling health spending and concentrating on its poorest areas halved maternal mortality between 1998 and 2006. Its Multidimensional Poverty Index has seen the largest decreases of any tracked country. Bangladesh has made some of the greatest improvements in infant and maternal mortality ever seen, despite modest income growth.
Between 1990 and 2010 the population living on less than $1.25 a day in developing countries halved to 21%, or 1.2 billion people, achieving MDG1A before the target date, although the biggest decline was in China, which took no notice of the goal. However, the child mortality and maternal mortality are down by less than half. Sanitation and education targets will also be missed.
Multilateral debt reduction
G‑8 Finance Ministers met in London in June 2005 in preparation for the Gleneagles Summit in July and agreed to provide enough funds to the World Bank, IMF and the African Development Bank (AfDB) to cancel an additional the remaining HIPC multilateral debt ($40 to $55 billion). Recipients would theoretically re-channel debt payments to health and education.
The Gleaneagles plan became the Multilateral Debt Relief Initiative (MDRI). Countries became eligible once their lending agency confirmed that the countries had continued to maintain the reforms they had implemented.
While the World Bank and AfDB limited MDRI to countries that complete the HIPC program, the IMF's eligibility criteria were slightly less restrictive so as to comply with the IMF's unique "uniform treatment" requirement. Instead of limiting eligibility to HIPC countries, any country with per capita income of $380 or less qualified for debt cancellation. The IMF adopted the $380 threshold because it closely approximated the HIPC threshold.
One success was to strengthen rice production in Sub-Saharan Africa. By the mid‑1990s, rice imports reached nearly $1 billion annually. Farmers had not found suitable rice varieties that produce high yields. New Rice for Africa (NERICA), a high-yielding and well adapted strain, was developed and introduced in areas including Congo Brazzaville, Côte d'Ivoire, the Democratic Republic of the Congo, Guinea, Kenya, Mali, Nigeria, Togo and Uganda. Some 18 varieties of this strain became available, enabling African farmers to produce enough rice to feed their families and have extra to sell.
The region also showed progress towards MDG 2. School fees that included Parent-Teacher Association and community contributions, textbook fees, compulsory uniforms and other charges took up nearly a quarter of a poor family’s income and led countries including Burundi, the Democratic Republic of the Congo, Ethiopia, Ghana, Kenya, Malawi, Mozambique, Tanzania, and Uganda to eliminate such fees, increasing enrollment. For instance, in Ghana, public school enrollment in the most deprived districts rose from 4.2 million to 5.4 million between 2004 and 2005. In Kenya, primary school enrollment added 1.2 million in 2003 and by 2004, the number had climbed to 7.2 million.
|Graphs from the Millennium Development Goals Report 2010|
Malaria deaths declined by more than one-third, saving millions of lives.
Although developed countries' financial aid rose during the Millennium Challenge, more than half went towards debt relief. Much of the remainder aid money went towards disaster relief and military aid. According to the United Nations Department of Economic and Social Affairs (2006), the 50 least developed countries received about one third of all aid that flows from developed countries.
Over the past 35 years, UN members have repeatedly "commit[ted] 0.7% of rich-countries' gross national income (GNI) to Official Development Assistance". The commitment was first made in 1970 by the UN General Assembly.
The text of the commitment was:
Each economically advanced country will progressively increase its official development assistance to the developing countries and will exert its best efforts to reach a minimum net amount of 0.7 percent of its gross national product at market prices by the middle of the decade.
In 2005 the European Union reaffirmed its commitment to the 0.7% aid targets, noting that "four out of the five countries, which exceed the UN target for ODA of 0.7%, of GNI are member states of the European Union". Further, the UN "believe[s] that donors should commit to reaching the long-standing target of 0.7 percent of GNI by 2015".
However, the United States as well as other nations disputed the Monterrey Consensus that urged "developed countries that have not done so to make concrete efforts towards the target of 0.7% of gross national product (GNP) as ODA to developing countries".
Many Organisation for Economic Co-operation and Development (OECD) nations, did not donate 0.7% of their GNI. Some nations' contributions fell far short of 0.7%.
The Australian government committed to providing 0.5% of GNI in International Development Assistance by 2015-2016.
Review Summit 2010
A major conference was held at UN headquarters in New York on 20–22 September 2010 to review progress. The conference concluded with the adoption of a global action plan to accelerate progress towards the eight anti-poverty goals. Major new commitments on women's and children's health, poverty, hunger and disease ensued.
According to MDG Monitor, the target under MDG 3 "To eliminate gender disparity in primary and secondary education by 2005, and in all levels of education by 2015" was met.
However MDG monitor points out that while parity has been achieved across the developing world, there are regional and national differences favouring girls in some cases and boys in others. In secondary education in "Western Asia, Oceania, and sub-Saharan Africa, girls are still at a disadvantage, while the opposite is true in Latin America and the Caribbean – boys are at a disadvantage." Similarly in tertiary education there are disparities "at the expense of men in Northern Africa, Eastern Asia, and Latin America and the Caribbean" while conversely they are "at the expense of women in Southern Asia and sub-Saharan Africa."
Improving living conditions in developing countries may encourage healthy workers not to move to other places that offer a better lifestyle.
Cuba, itself a developing country, played a significant role in providing medical personnel to other developing nations; it has trained more than 14,500 medical students from 30 different countries at its Latin American School of Medicine in Havana since 1999. Moreover, some 36,000 Cuban physicians worked in 72 countries, from Europe to Southeast Asia, including 31 African countries, and 29 countries in the Americas. Countries such as Honduras, Guatemala, and Nicaragua benefit from Cuban assistance.
Post 2015 development agenda
Although there has been major advancements and improvements achieving some of the MDGs even before the deadline of 2015, the progress has been uneven between the countries. In 2012 the UN Secretary-General established the "UN System Task Team on the Post-2015 UN Development Agenda", bringing together more than 60 UN agencies and international organizations to focus and work on sustainable development.
At the MDG Summit, UN Member States discussed the Post-2015 Development Agenda and initiated a process of consultations. Civil society organizations also engaged in the post-2015 process, along with academia and other research institutions, including think tanks.
The Sustainable Development Goals (SDGs) have been proposed as targets relating to future international development once they expire at the end of 2015.
In 2014, the UN's Commission on the Status of Women agreed on a document that called for the acceleration of progress towards achieving the millennium development goals, and confirmed the need for a stand-alone goal on gender equality and women's empowerment in post-2015 goals, and for gender equality to underpin all of the post-2015 goals.
The United Nations Millennium Campaign is a UNDP campaign to increase support for the Millennium Development Goals. The Millennium Campaign targets intergovernmental, government, civil society organizations and media at global and regional levels.
The Millennium Promise Alliance, Inc. (or simply the "Millennium Promise") is a U.S.-based non-profit organization founded in 2005 by Jeffrey Sachs and Ray Chambers. Millennium Promise coordinates the Millennium Villages Project in partnership with Columbia's Earth Institute and UNDP; it aims to demonstrate MDG feasibility through an integrated, community-led approach. As of 2012 the Millennium Villages Project operated in 14 sites across 10 countries in sub-Saharan Africa.
The Global Poverty Project is an international education and advocacy organisation that encourages MC support in English-speaking countries.
The World We Want 2015 is a platform and joint venture between the United Nations and Civil Society Organizations that supports citizen participation in defining a new global development framework to replace the Millennium Development Goals.
Accessing Development Education is a web portal. It provides relevant information about development and global education and helps educators share resources and materials that are most suitable for their work.
The Teach MDGs European project aims to increase MDG awareness and public support by engaging teacher training institutes, teachers and pupils in developing local teaching resources that promote the MDGs with a focus on sub-Saharan Africa.
Global Education Magazine is an initiative launched by the teaching team that formulated the proposal most voted in the group "Sustainable Development for the Eradication of Poverty in Rio+20". It is supported by UNESCO and UNHCR and aims to create a common place to disseminate transcultural, transpolitical, transnational and transhumanist knowledge.
UN Goals is a global project dedicated to spreading knowledge of MDG through various internet and offline awareness campaigns.
Libraries and the Millennium Development Goals
Librarians and others in the information professions are in a unique position to help achieve the Millennium Development Goals. It is often the dissemination of key information, e.g., about health, that changes daily life and can affect an entire community.
Millennium Development Goals are not only for the developing world. Maret (2011) specifically addresses how U.S. public libraries can help the United States meet the goals. The work of U.S. librarians has evolved in a manner that incorporates human rights values and precepts without having generally used the language that characterizes the philosophical and ethical goals of human rights and human development. Librarians are able to further the Millennium Development Goals and contribute by providing information and services to all people in varying formats and languages.
Albright and Kwooya (2007) report that cultural and financial barriers in Sub-Saharan Africa impede LIS education programs. As a result, MDG goals for poverty, healthcare, and education fall short. High rates of HIV/AIDS, and escalating child and maternal mortality are the direct result of poverty and substandard medical care. Limited instruction in information access and exchange contributes to this ongoing dilemma.
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- Singer, M (2008). "Drugs and Development: The Global Impact of Drug Use and Trafficking on Social and Economic Development". International Journal of Drug Policy. 19 (6): 467–478. doi:10.1016/j.drugpo.2006.12.007.
- Kabeer, Naila. 2003. Gender Mainstreaming in Poverty Eradication and the Millennium Development Goals: A Handbook for Policy-Makers and Other Stakeholders. Commonwealth Secretariat.
- Kabeer, Naila (2005). "Gender equality and women's empowerment: a critical analysis of the third millennium development goal". Gender and Development. 13 (Gender and Development): 13–24.
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Gender disparity has reduced dramatically at all levels of education in the developing regions since 2000, hitting the MDG target.
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- Eradicate Extreme Poverty and Hunger by 2015 | UN Millennium Development Goal curated by the Center for Latin American and Caribbean Studies at Michigan State University
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- Gillian Sorensen, Senior Advisor to the United Nations Foundation, discusses UN Millennium Development Goals
- ⇒ The Vrinda Project Channel - videos on the work in progress for the achievement of the MDGs connected to the Wikibook Development Cooperation Handbook
- The Millennium Development Goals in Asia and the Pacific: 12 Things to Know Asian Development Bank.
|Wikimedia Commons has media related to Millennium Development Goals.| |
Math FractionsGiven two numbers i and j.
A fraction is of the form, i / j.
i is called Numerator of the fraction.
j is called Denominator of the fraction.
Example: Say we have two numbers 3 and 4. Fraction is 3/4.
Consider three numbers i, j and k.
A mixed fraction is of the form k (i / j).
Where numerator will be k x j + i.
Operations on fractions:
Fractions Addition - Back to topAddition of Fractions:
Consider two fractions i / j and a / b.
The addition of the two fractions is:
i/j + a/b = (i+a)/(j+b)
So the numerator of the addition is the sum of numerators of the operands.
The denominator of the addition is the sum of denomimators of the operands.
Example: 3/4 + 1/7 = (3+1)/(4+7) = 4 / 11
Fractions Subtraction - Back to topSubtraction of Fractions:
The subtraction of two fractions is:
i/j - a/b = (i-a)/(j-b)
So, the numerator is the subtraction of numerators of the operands.
The denominator is the subtraction of denominators of the operands.
Example: 7/10 - 1/3 = (7-1)/(10-3) = 6/7
Fractions Multiplication - Back to topMultiplication of Fractions:
Multiply fraction with whole number:
Multiplication of fraction with whole number is repeated addition as many times are the number.
Consider a number m and fraction i/j.
m x (i / j) = i/j + i/j ... m times.
Example: 2 x (1 / 3) = 1/3 + 1/3 = 2/3
Multiplication of fraction with another fraction:
Consider two fractions: i/j and a/b.
i/j x a/b = (i x a) / (j x b)
Example: 3/4 x 7/5 = (3 x 7) / (4 x 5) = 21/20
Fractions Division - Back to topDivision of Fractions:
Before we understand division of a fraction, we should familiarize ourselves with the concept of reciprocal of a fraction.
Reciprocal of a fraction:
Reciprocal of a fraction is switching of numerator with denomiator, and denominator with numerator.
Consider a fraction i / j. Reciprocal of fraction is j / i.
Example: Consider a fraction 2 / 3. Reciprocal of fraction is 3 / 2.
Divide fraction with whole number:
Division of a fraction with a whole number is multiplying the denominator with that number. Consider a fraction i/j and whole number m.
(i / j) / m = 1 / (j x m)
Example: (1 / 4) / 2 = 1 / (4 x 2) = 1 / 8.
Divide fraction with another fraction:
Division of a fraction with another fraction is multiplication of fraction with reciprocal of the second fraction.
Consider two fractions: i / j and a / b.
(i / j) / (a / b) = i / j x b / a = (i x b) / (i x a)
Example: (3 / 4) / (7 / 8) = 3/4 x 8/7 = (3 x 8) / (4 x 7) = 24 / 28. |
Circle Theorems Worksheet
A, b, c and dare points on the circumference of a circle.blank angle cad and x find the value of x. give reasons for your answer. total for question is marks a, b and c are points on the circumference of a circle.Circle theorem worksheet exercise introductory questions theorem angles standing on the same arc chord are equal theorem angle at the centre is twice the angle at the circumference theorem angles standing on a diameter angles in a semicircle.
find, the marked angles, giving reason a b c d theorems worksheet describes circle theorems in words. circle theorems worksheet calculates angles in circles. circle theorems worksheets calculates angles in circles involving harder questions. circle theorems worksheet involves angles at tangents of circles.
List of Circle Theorems Worksheet
Circle theorems questions, worksheets and revision level. in this topic. revise. take an online exam. worksheets exam questions. learning resources. the circle theorems. you should be familiar with all circle theorems to the point where a you can identify when they should be used.
Circle theorem. circle theorem displaying top worksheets found for this concept. some of the worksheets for this concept are mathematics linear circle theorems, t date, revision circle theorems, circle geometry, similar triangles and circles proofs packet, mixed review on formulas theorems on geometry of circles, circle theorems, circle theorems h.
1. 9 Lesson Circle Theorem Ideas Theorems
You must give reasons for each stage of your working. are several circle theorems that apply to all circles. a tangent and a radius meet at the tangent makes with the radius which it meets at the point at which it touches. two radii form an isosceles theorems about parallelograms.
theorems include opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. hsg.gpe.b. use coordinates to prove simple geometric theorems algebraically.
2. Geometry Circle Theorems Arcs Angles Puzzle Worksheet Education Quotes Teachers Math
Area and perimeter worksheets with answers kenkoman.info. free grade math worksheets peninsulamontejo.com. Unit - circle geometry. math toolbox. new path math to. final exam review. mathematics. unit overview. unit -. unit - integers. unit - fractions.
3. Circle Theorems Review Worksheets Distance Learning Geometry Notes
Now lets use these theorems to find the values of some angles example find the measure of the angle indicated. A circle is a plane figure, a shape in geometry that consists of points which are all equally distant from a given point in space. that distance is called the radius (r) and that given point is called the center (marked by the symbol o ).
a straight line that connects two points on the opposite sides of a circle and goes through the center is called the diameter (d). Geometry circles riddle worksheet and quick reference bundle this is a bundle of my three best selling riddle worksheets that focus on three of the most important concepts of a high school geometry unit on circles.
4. Circle Theorems Workout Teaching Geometry Math
Students can complete this set of questions interactively on the homework platform. also contains answers. dfmfullcoveragecircletheorems. exam about circles. this article talks about some interesting theorems that you will encounter when exploring the geometry of circles.
5. Circle Theorems Worksheet Math Questions
Of course, there are many other theorems about circles. this just gives you an introduction. inscribed angle theorems. an inscribed angle is an angle that is formed by two chords to a circle that meet at a.About this quiz worksheet. find out how much you know about chord theorems of circles in geometry with this study combo.
6. Circles Ideas Geometry High School Teaching Circle Theorems
Circles write a standard equation for each circle. circles match the standard equations and graphs. a circle and compare its radius, circumference, and area. a circle and compare its radius, circumference, and area. grade math. user from international, here is the worksheet with spaces for the students to answer the questions.
best for math. user from. Chords intersect inside a circle. c e d b a f segments of a chord rule (theorem) the product of the segments of one chord is equal to the product of the segments of the other chord. times ac times cf. sophomore math worksheet.
7. Circles Measures Arcs Central Angles Worksheets Worksheet Teaching Methods
8. Circles Quiz Review Day 1 Ideas Resources Secondary Math Classroom Circle
9. Circles Tangent Theorems Worksheet Worksheets
There are many ways in which angles can be used to solve such problems. Displaying top worksheets found for - skills practice angle measures. some of the worksheets for this concept are, nag to, skills practice, lesson triangle sum conjecture, angles and angle measure date period, geom, lesson inscribed angles with, example example answers find.
10. Exterior Angle Theorem Circle Ideas Theorems Angles
11. Find Perimeter Polygon Geometry Worksheets Regular Angles Worksheet
12. Free Download Circle Theorem Flashcards Matching Pairs Game Great Maths Teaching Ideas Theorems Math Geometry
13. Free Printable Maths Posters Geometry Circle Theorems Display Math Tutorials
14. Geometry Circle Theorems Secant Tangent Segments
Unit - prisms. unit - percents etc. class worksheets. ) class reviews. ) re-test packages. cant open the below files. Circle geometry a guide for teachers assumed knowledge introductory plane geometry involving points and lines, parallel lines and, angle sums of triangles and quadrilaterals, and general.
15. Circle Theorems Proof Mills Math Notes
Nbspall content has been designed to gradually build the confidence of the maths learner whilst establishing greater proficiency in completing circle theorems worksheets.pupils are required to use their knowledge of circle theorems to.Lesson overview circle theorems the alternate segment theorem view in classroom learn that an angle made with a chord and tangent is equal to the angle subtended by the chord in This geometry video tutorial provides a basic introduction into the power theorems of circles which is based on chords, secants, and tangents.
16. Geometry Circle Theorems Secant Tangent Segments Puzzle Worksheet
Experience with a logical argument in geometry written as a sequence of steps, each justified by a reason. Explore, prove, and apply important properties of circles that have to do with things like arc length, radians, inscribed angles, and tangents.
17. Geometry Circles Quick Reference Sheets Lesson Plans High School Math Teaching
18. Geometry Secant Tangent Theorem Doodle Notes Graphic Organizer Mathematics Worksheets Interactive Notebook Teaching
After your kid has learned how to count the circles, then should be taught how to add numbers. in these circle addition worksheets, circles are given in two blocks and kids can add them. there is also another way to add it by using the numbers given just before the.
19. Geometry Unit 5 Circles High School Teaching Math Circle Theorems
20. Geometry Worksheets Circle Math
Circles worksheet day write an equation of a circle given the following information. center (.) (-.-) radius equation write an equation of each circle described below. show work. given a circle with center (, -) and passing through (, ). given a circle with the center (, ) and a point on the circle (, -).
21. Ideas Resources Secondary Math Classroom Central Angles Arcs Circle Geometry Worksheets Teaching
22. Love High School Geometry Circumference Circles Maze Students Act Lessons Worksheets
Circles geometry review worksheet. tenth graders solve and complete different geometry problems. first, they find the area and circumference of a circle with a given radius. then, they find the area between a circle and an inscribed equilateral triangle given the measurement of each side.
23. Maths Circle Theorems Educational Poster Size Math Art
24. Monster Circle Puzzle Angles Formed Secants Tangents Geometry Lessons High School Teaching
In geometry and mathematics, the word circumference is used to describe the measurement of the distance around a circle while radius is used to describe the distance across a circles length. in the following eight circumference worksheets, students are provided with the radius of each of the circles listed and asked to find the area and.
25. Properties Circles Maze Arcs Tangents Secants Inscribed Polygons Geometry Lessons High School Math Work
Geometry worksheets on this page you will find a complete list of all of our math worksheets relating to geometry.choose a specific addition topic below to view all of our worksheets in that content area. you will find addition lessons, worksheets, homework, and quizzes in each section.
27. Tangents Circles Maths Worksheet Answers 9 1 Higher Grade 6 Year Circle Theorems Math
28. Circle Theorems Review Worksheets Distance Learning
It covers the.This is perhaps the most complicated theorem, but think of it this way when a triangle is enclosed inside a circle and a tangent meets the circumference as in the example above, the two angles shaded in yellow are equal and the two in blue are equal.
29. Circle Theorems Practice Finding Arcs Angle Measures Formed Secant Tangent Lines High Sch Geometry School Worksheets
Concentric circles are circles within circles. recognize them in these grade worksheets and find the area between the two circles. subtract the inner area from the outer area to find the area of the ring. applying the formula, circumference pi r, find the circumference of each circle.
Before we begin, lets state a few important theorems. theorem if two angles inscribed in a circle intercept the same arc, then they are equal to each other. theorem if an angle inside a circle intercepts a diameter, then the angle has a measure of ( ).
30. Angles Circle Worksheet Calculating Arc Angle Measurements Theorems Template Measuring
Sep, three carefully worksheets that have helped many classes take the first steps working with the circle theorems. included are angles in the same segment and angle at the centre.i have used these sheets for many years and they have always given students an excellent base from which to move onto the more difficult problems.
Arrowback back to circle theorems and parts of a circle circle theorems and parts of a circle worksheets with answers. whether you want a homework, some cover work, or a lovely bit of extra practise, this is the place for you. and best of all they all well, Solutions for the assessment revision circle theorems angle reason angle in a semicircle is angle reason angle between tangent and radius is angle.
31. Circle Theorem Worksheets Theorems Math Sheets
Again, circle theorems feature heavily in the geometry section of the.Dec, circle theorem review worksheets. for each worksheet one theorem is explained with examples before students are asked to solve the problems and match to an answer in the middle.
there are seven worksheets, one of which has mixed questions.answer sheets. Worksheet circle theorems in each question, find the value of the lettered angles y x super challenge question can you prove both the rules you have learnt algebraically j c y ed x y x g f h x i k x n x a x y b x y l z y If two chords of a circle which cut at a point may be inside or outside a circle then if pis a point outside a circle and t, a, b are points on the circle such that a tangent and is a secant then pt these theorems and related results can be investigated through a geometry package such theorems a circle is a set of points in a plane that are a given distance from a given point, called the center.
32. Angles Circle Worksheet Lovely Theorems Match Studying Math
Some of the worksheets below are free circles worksheets, explaining several p of the circle like arcs and chords, inscribed angles, segment relationships in circles, symmetries of a circle, intersecting segments of circles with several interesting problems and solutions.
once you find your worksheet (s), you can either click on the pop-out icon or download button to print or download your desired worksheet (s). Explore, prove, and apply important properties of circles that have to do with things like arc length, radians, inscribed angles, and tangents.
33. Angles Circle Worksheet Lovely Theorems Match Template Geometry Worksheets
Geometry (all content) unit circles. geometry (all content) unit circles. progress. circle basics. learn. circles glossary (opens a modal). The various resources listed below are aligned to the same standard, (g) taken from the (common core standards for mathematics) as the geometry worksheet shown above.
know the formulas for the area and circumference of a circle and use them to solve problems give an informal derivation of the relationship between the circumference and. day review day warm up example in the diagram of circle o below, chord is parallel to diameter and m.
34. Angles Circles Maths Worksheet Answers 9 1 Higher Grade 6 Year Circle Theorems Math Worksheets
Sop is a straight line. angle opt work out the size of the angle marked x. you must give a reason for each stage of your working.On the circumference of a circle, centre o. pa and are tangents to the circle. angle. a i work out the size of angle. ii give a reason for your answer.
b work out the size of angle. p s r q b a p, q, r and s are points on the circle. is a diameter of the circle. angle. a i work out the size of angle.Level level level description help more angles. this is level angles which can be found using one of the angle theorems.
35. Angles Circles Secants Tangents Chords Partner Worksheet Teaching Geometry Circle Theorems Math
36. Angles Circles Secants Tangents Chords Partner Worksheet Teaching Geometry Studying Math Worksheets
It also has many applications to physics, astronomy, and other branches of science. it is a very old subject. many of the geometric results that we worksheets examples, solutions, and videos to help maths students learn the circle theorems. angle subtended at the centre of a circle is twice the angle at the circumference.
the angle between a radius and a tangent is degrees.Theorem if a line is drawn from the centre of a circle perpendicular to a chord, then it bisects the chord. the converse of this theorem theorem if a line is drawn from the centre of a circle to the midpoint of a chord, then the line is perpendicular to the chord.
37. Arcs Angles Circles Task Card Sort Rise Run High School Geometry Circle Theorems Sorting Cards
What is m example in the diagram of circle o below, chord is parallel to diameter and m. what is m. Tangents using equations of circles writing equations of circles display. all. Diameter and radius worksheets. when first studying circles, many students often confuse the diameter and the radius.
even though these two values have a very simply relationship, simple worksheets that practice calculating one from the other can help cement this knowledge before moving on to more complicated circle operations such as calculating the area and circumference.
38. Chords Secants Tangents Circle Math Teaching Geometry Lessons
39. Chords Secants Tangents Teaching Geometry Circle Activities
An arc is a part of a circle. Inscribed angle of a circle. chord, tangent and the circle. angles of intersecting chords theorem. side length of tangent secant of a circle. side splitter theorem. triangle angle bisector theorem. geometry calculator. geometry worksheets (with keys) angles.
Circle worksheets, videos, tutorials and formulas involving arcs, chords, area, angles, secants and more. Save for later. preview and details. files included,. alternate angle theorem.,. angle at centre twice angle at circumference part.,. angle at centre twice angle at circumference part.
40. Circle Basics Graphic Organizer Ideas Resources Secondary Math Classroom Teaching Geometry Organizers
Geometry worksheets circle worksheets. here is a graphic preview for all of the circle worksheets. you can select different variables to customize these circle worksheets for your needs. the circle worksheets are randomly created and will never repeat so you have an endless supply of quality circle worksheets to use in the classroom or at home.
we have identifying radius and diameter for circles worksheets, calculating circumference, area, radius, and diameters worksheets, arcs and central. Circle worksheets. this set of circle worksheets is an important addition to build your knowledge. the worksheets encompass exercises like finding the area and circumference of a circle, area of a segment, finding the radius, diameter, arc length, area of the sector to name a few.
41. Circle Basics Unit Part 1 Ideas Resources Secondary Math Classroom Teaching Geometry Basic
Angles arcs worksheet list circle theorems. angles circle worksheet lovely theorems match template geometry worksheets. angles circle worksheet lovely theorems match template library solution examples.Circle theorems. points a, b and c are all on the circumference of the circle, o represents the centre.
calculate the angle. mark. points a, b and c are all on the circumference of the circle. line a b is a straight line going through the centre o. calculate angle marks diagram not accurately drawn diagram not accurately tangent of a circle definition theorems worksheet.
42. Circle Theorem 4 Theorems Geometry Formulas Math
A tangent to a circle is a line that follows the circumference of a circle. intersects the circle at one point., circle, circle theorems,,,. leave your comment. mathematics worksheet circle theorems. print this post. o level mathematics worksheet sets diagrams mathematics worksheet linear programming o level mathematics worksheet ratio , revision notes on circle theorems.
videos, worksheets, and much, circle theorem past papers free download as word doc.doc., file., text file. or read online for free. a of maths past papers focusing on circle circles angles in circles inc circle theorems worksheets. circle theorems worksheet.
43. Circle Theorem Angles Arc Theorems
Our circle theorems worksheet is aimed at maths pupils who have mastered basic angle rules, such as angles in parallel lines and angles in a circle. all content has been designed to gradually build the confidence of the maths learner whilst establishing greater proficiency in completing circle theorems.
Nov, there was also a question in the paper relating to the power of a point theorem, which now features in specifically the intersecting chords theorem but not. interestingly the wording but not the substance of the circle theorems content on the o level syllabus differs notably from the syllabus.
44. Circle Theorems 1 9 Lessons Revisions Practice Math
The center is often used to name the circle. t this circle shown is described as circle t. as always, when we introduce a new topic we have to define the things we wish to talk about.Circle displaying top worksheets found for this concept. some of the worksheets for this concept are mathematics linear circle theorems, circle geometry, t date, revision circle theorems, circle theorems h, solve for assume that lines which appear tangent are, the theorem date period, similar triangles and circles proofs packet.
The equation of a circle is based upon its definition and the theorem. since a locus for the circle is the set of points equidistant from a single point called the center and that distance between the center and the point on the circle is a constant radius, then we can consider the radius to be the hypotenuse of all right triangles whose sides are the differences between this worksheet, we will practice recognizing and applying circle theorems to find unknown angle measures in circles.
45. Circle Theorems Maths Revision Math
Some of the worksheets displayed are mathematics linear circle theorems, maths, the work, circle theorems answers, the answer book, work foundation and higher questions answers, mathematics linear area circumference of circles, circle theorems Showing top worksheets in the category circle theorems.
46. Circle Theorems 4 Theorem Problems Including Proof Worksheet Math Tutor
Question in the following figure, is a tangent to circle with center at point. find the length of to the nearest tenth.Circle theorem worksheet e z math. theorem angles standing on the same arc chord are equal theorem angle at the centre is twice the angle at the circumference.
two circles intersecting at w z. is a to the circle at v, and are straight lines, and six calculate the size of each folio in the diagram not drawn to, worksheet worksheet worksheet exam questions answers answers answers answers can use principals from geometry to find the lengths of segments inside circles.
47. Circle Theorems Activity High School Geometry Partner Worksheet Math Lessons
). ).). software geometry inscribed circles answer key software answer key fundamentals of physics edition test bank software infinite interior and inscribed angles worksheet free printable , software inscribed angles answers voucherslug.co and arcs answer key central angles and inscribed.
Download inscribed angles software answer key document. on this page you can read or download inscribed angles software answer key in format. if you see any interesting for you, use our search form on bottom. chapter, section inscribed angles - schools.
48. Circle Theorems Angle Puzzles Math Teaching Geometry
A series of free, high school geometry video lessons. videos, worksheets, and activities to help geometry students. in this lesson, we will learn. the locus and definition of a circle and a sphere. about central angles and intercepted arcs. chords and the center of a circle.
Circles - geometry tangent and secant lines in circles riddle worksheet this is a question riddle practice worksheet designed to practice and reinforce the concepts of tangent and secant lines in circles. the concepts cover tangents intersecting at the point of two secant.
49. Circle Theorems Angle Puzzles Teaching Geometry Math
A b c x x x x. there is another theorem that deals with tangents as well. if two tangents to the same circle share a point outside of the circle, then the two tangents are congruent. if a p and b p are tangents, then a Circle theorem worksheet a list of other worksheets is available.
save the planet and give your pupils a better experience by putting your most popular printed worksheets in acetate holders. this ensures the resource can be used on many occasions and lets the pupil easily erase mistakes while working on Circle theorem includes the concept of tangents, sectors, angles, the chord of a circle and proofs.
50. Circle Theorems Cheat Sheet Printable Math Posters Geometry Lessons
A circle is the locus of all points in a plane which are equidistant from a fixed point. the fixed point is called the centre of the circle, and the constant distance between any Circle theorems worksheet. find x find the size of angles. a the x y calculate the size of x calculate the size of x calculate the size of y fir.
the angles x y write dawn the size of of the angle calculate the angle ad. calculate the size of angle x.Circle theorems investigation worksheets pack this pack features seven circle theorems spread over six worksheets. each worksheet requires your students to measure the given angles and lines and try to deduce the circle theorems by themselves.
51. Circle Theorems Complete Lesson 1 Teaching Resources Geometry Lessons
A fantastic entry activity into circle theorems and a fun way of learning this tricky subject.Maths revision video and notes on the topic of circle theorems.May flag comment. i love circle theorems so easy to understand, please update with harder questions so i can get a star.
This page is a shop for all your finding area and circumference of a circle exercises. catering to the learning needs of students in grade through grade, these printable worksheets practice the topic pretty much across the board easy, moderate and hard.
52. Circle Theorems Ideas Maths Revision
53. Circle Theorems Investigation Pack Mathematics Angles
A a, b and c are points on the circumference of a circle, centre, o. ac is the diameter of the circle. write down the size of angle. b given that ab and , work out. httpquestionsexam.comgetmathswatch.answers.circle.theorems.free.In this circles review worksheet, learners answer questions involving arc measures, tangent lines, equations of circles, and inscribed angles.
students complete review questions covering postulates, theorems, quadrilaterals,.Arc an unbroken part of a circle. the endpoints of an arc are on the circle. every chord cuts off two arcs. if the chord is a diameter the arcs are if the chord is not a diameter, one arc is and the other is.
54. Circle Theorems Match Teaching Geometry
Theorems involving chords in the same circle or congruent circles.Circle theorems worksheet and answers author wiki.ctsnet.orglaura subject circle theorems worksheet and answers keywords circle,theorems,worksheet,and,answers created date a, worksheet and assessment.
frost is a maths teacher working at school in. you can find all of his resources at his website drfrostmaths.com, a huge bank of, worksheets and activities spanning year to further maths.This compilation has geometry worksheets to recognize the type of triangles based on sides and angles, finding angles both interior and exterior, length of the sides, the perimeter with congruent properties, the area of a triangle, isosceles, scalene, equilateral inequality theorem and much more.
55. Circle Theorems Math
Circle your class engaged with fun and unique teaching resources is vital in helping them reach their potential. on resources we have a range of tried and tested materials created by teachers for teachers, from through to high school.Angles in a circle worksheet lovely circle theorems match up by template library in circle theorems math worksheet circle geometry.
identify circle radius and diameter worksheets geometry worksheets circle geometry angles worksheet.Geometry circle learn displaying top worksheets found for geometry circle learn. some of the worksheets for this concept are circle geometry, circumference and area of circles, euclidean geometry circles, mathematics workshop euclidean geometry, grade math circles circles circles circles, circle theorems, a guide to advanced analytical geometry, art and geometric design.
56. Circle Theorems Math Revision Maths
Practice measuring angles and arcs worksheet answers. the not so safe category. measuring angles and arcs worksheet answers. measuring angles and arcs answer the following theorems about arcs and central angles are easily proven. measure of a minor arc is defined to be the measure of its central angle p.
continue reading practice measuring angles and arcs worksheet The lesson. the angle between a tangent to a circle and a chord at the point of contact is equal to the angle in the alternate segment. this theorem is called the alternate segment theorem.
57. Circle Theorems Maths Poster Math Charts
More about the alternate segment theorem. this circle theorem deals with a tangent and a chord meeting at a point on a circle, forming an angle between them. the chord the circle into two segments.Circle properties and circle theorems. angle in a semicircle an angle in a semicircle is always.
in proofs quote angle in semicircle is. angles at centre and circumference the angle an arc or chord subtends at the centre is twice the angle it subtends at the circumference. in proofs quote angle at centre is twice angle at.Showing top worksheets in the category circle theorems foundation.
58. Teaches Math Teaching Geometry Circle Theorems
Circle theorems and online worksheet for grades and. you can do the exercises online or download the worksheet as.Circle theorems worksheet applying circle theorems online worksheet for grade. you can do the exercises online or download the worksheet as.
A and b are points on the circumference of a circle, centre o. pa and are tangents to the circle. angle is. work out the size of the angle marked x. marks. r and s are two points on a circle, centre o. ts is a tangent to the circle. angle x. prove that angle. |
A set of 7 polygon puzzles to practice solving multiplication number sentences.
Use this resource when learning to multiply.
How to set up this resource:
- Print out 7 of the polygon puzzle mats on cardstock for added durability.
- Print out each puzzle on cardstock and cut out the pieces. Store each puzzle separately with one of the polygon puzzle mats in a resealable bag to be used again and again.
- TIP: Draw the same shape on the back of each puzzle piece in a set so that you know those pieces belong together.
Students are to put the puzzle back together by connecting the product with the corresponding number sentence. The puzzles start out with basic multiplication facts and move up in complexity. The hardest puzzle includes 2-digit times 2-digit.
A full set of instructions is included in the download.
These puzzles are great to use as math center activities.
Download this resource as part of a larger resource pack or Unit Plan.
Common Core Curriculum alignment
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all pr...
Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.
Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangul...
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Answer sheets now provided for the students to check their answers.
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BackgroundThink fast! It might feel like you think and react instantly, but it actually takes a little bit of time for nerve signals to travel. That's why when someone throws something at you unexpectedly, it's challenging to react quickly enough to catch it. Something that we react to in our environment is called a stimulus.
The amount of time between sensing and responding to a stimulus is called reaction time. Reaction time is usually so fast that we have to measure it in milliseconds. One millisecond is 1/1000 of a second.
QuestionHow fast is your reaction time?
Based on what you know about how fast you and other people can catch balls, stop bicycles, hit volleyballs, etc., how fast do you think your reaction time is? Also base your hypothesis on what you have learned about nerves and nerve signals. (Remember a hypothesis does not have to be right, but it should be based on good logic and on knowledge we have gathered so far.) One second would be 1000 milliseconds, 1/2 of a second would be 500 milliseconds, 1/4 second would be 250 milliseconds. Write your hypothesis in your science notebook.
- Ruler, 30 centimeters long
- Reaction time graph
- Before beginning your experiment, make a data table in your science notebook (See directions in the data section).
- Ask a parent or sibling to help you with this experiment.
- Hold out your thumb and index finger, about three centimeters apart, ready to pinch together.he d
- Have a parent or sibling hold the ruler with the 0 cm mark hanging just between your fingers.
- At a random second, they should drop the ruler, and you should catch it. It is important that you don't know exactly when they are going to drop the ruler.
- Measure to the nearest centimeter, or if you are able, to the nearest tenth of a centimeter, how far the ruler dropped before you caught it.
- Repeat steps 2 through 5 four more times, for a total of 5 trials.
- Find the average number of centimeters the ruler fell.
To find the average:
- Step 1: Estimate your average. The average should be the "normal" amount. It won't be the highest amount or the lowest amount. It will be somewhere in-between them.
- Step 2: Add together all 5 trials.
- Step 3: Divide the total by the number of trials.
- Step 4: Check your answer with your estimate. Does your answer make sense?
- Finally: Enter your average in your data table.
- Use the reaction time graph and your average number of centimeters to figure out how many milliseconds your average reaction time was.
We will be doing 5 trials, and since this is an observational study (not really an experiment), we only have one condition. Try making your data table first; then check to see if it matches one of these. It doesn't need to be exactly the same, but it does need to have an organized place to write each piece of data. Record your data in the data table in your science notebook.
ConclusionBased on your data, what is the answer to our question? What does this teach us about nerve signals? What further questions does it make you want to ask about how nerve signals travel? Write your rough draft of your conclusion in your science notebook. |
Python has gained a lot of spotlights because of its salient features, easy syntax, good readability, availability of various libraries and APIs.
Now every computer geek wants to learn this trending language, but there may be a question “how to start?”. Well, the answer to that question would be having a look at python documentation and knowing the syntax of python.
After learning all the rules and syntax of python our mind may urge us to implement a trivial or hello world program in python. Now let’s satisfy the thirst of our enthusiastic mind by having a look at a trivial code, which is adding two numbers in python.
Let’s have a look at different possible implementations of this code.
1. Addition of Two Numbers
Let’s demonstrate the code of adding two user-defined numbers.
|i = 5
j = 6
sum = i+j
print(“sum of”,i,“and”,j,“is”,sum) #line1
print(“sum of”,i,“and”,j,“is”,i+j) #line2
In the above code variables i and j stores the values which are to be added and the sum variable stores the value of i+j. And then we can print that value. Also here’s a point to be noted, if we don’t want a variable to store the answer we can directly calculate the answer in the print statement itself (as shown in line2).
But what if we want to add numbers that are given as input from the user?
2. Addition of User Input Numbers
This code will be similar to the previous code but the only difference would be assigning the variables with user input. Let’s have a look at the code.
|i = input(” enter the first number “)
j = input(” enter the second number “)
sum = i+j
In the above code, the first line would prompt “enter the first number” in the output screen and the terminal or the console expects an input that will be assigned to the variable i. similarly, the same process will be observed for line 2. Now both the variables i, j are assigned with the user input, and the sum is stored in the sum variable. Feels like a cakewalk right?
3. Addition of Two Float Numbers
Many times we may face a situation to add numbers with decimal precision, lets have a look at that implementation!
|i = 1.5223
j = 1.8365
sum = i+j
print(“sum of”,i,”and”,j,”is”,sum) #line1
print(“sum of”,i,”and”,j,”is”,i+j) #line2
As already discussed we don’t need to mention the data type of the variable we are going to use. Variables i, j are treated as float values and the final result obtained will have decimal precision.
We can also typecast an integer to a float in python, let’s demonstrate the difference between integer addition and float addition.
|i = 3
j = 6
sum = float(i)+float(j) #line1
print(“sum of”,i,”and”,j,”is”,sum) #line2
print(“sum of”,i,”and”,j,”is”,i+j) #line3print(float(i+j)) #line4
In the above snippet, we have two variables i, j which are assigned with two integers. Now if we add these two variables the answer would be of integer type. We can have the answer in float datatype by typecasting the variables into a float (as shown in line 1) or typecasting the answer into the float (as shown in line 4).
The main difference between line 2 and line 3 would be the lack of decimal precision in line 3. The output of line 2 will be 8.0 whereas the output of line 3 will be 8, so if we want to maintain the decimal precision of a variable then we need to use a float datatype.
Also Read: Python Project Ideas & Topics For Beginners
We have walked through various code snippets where we’ve seen the addition of two user-defined numbers, the addition of user input numbers, the addition of float numbers, observed decimal precision of result with float datatype, and typecasting the numbers in python.
Now that you are aware of how to add two numbers in python, try writing the code on your own and try modifying the code with various data types. And try performing a few other trivial tasks in python and explore the fun in python programming 🙂
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What are the pros and cons of programming in Python?
Python is an amazing language that has deep roots in development and is now gaining support in the programming domain. But along with its pros, there are some cons as well that must be considered before opting it out. The pros and cons are as follows:
1. The Python syntax is extremely user-friendly and easy to write. It is nearly equivalent to writing some sentences in the English language with indentation.
2. Problems that are solved in too many lines in other languages can be solved in less than half-line in Python with the help of various inbuilt functions.
3. The code is much cleaner and shorter as the programmer does not have to write much and most of the work is done by the compiler itself.
1. One of the biggest drawbacks of Python is its speed. It is very slow, slower than C++ and even Java.
2. Many programmers recommend avoiding Python because it spoils the logic building as most of the work is done by the inbuilt Python functions.
What do you understand about the numeric data type in Python?
In Python, the numerical data or values are generally represented by the numeric data types. There can be three types of numeric values in Python which are as follows:
The integers like 3, 0, -100, -2, and 25 are represented by the int class. Unlike other programming languages like C++, there is no limit to how long an integer value can be. You can enter a value equivalent to the long long int of C++ in the int class in Python.
The fractional or decimal numerical values are known as float and are represented by the float class. The scientific notation of a float value can be determined by appending “e” or “E” followed by the “+” or “-”.
The values that are in the form of “a+ib” where “a” is the real part and “b” is the imaginary part are considered as complex numbers and are represented by the complex class of Python.
Name some best Python IDEs?
There are a lot of Python IDEs out there that are pretty decent. Some of these are PyCharm by JetBrains, Visual Studio Code by Microsoft, Spyder, Eclipse, Atom, PyDev, and Wing IDE. |
An animation showing when United States territories and states forbade or allowed slavery, 1789–1861
Slavery in the United States was the legal institution of human chattel slavery, comprising the enslavement primarily of Africans and African Americans, that existed in the United States of America from its founding in 1776 until the passage of the Thirteenth Amendment in 1865. Slavery was established throughout European colonization in the Americas. From early colonial days, it was practiced in Britain's colonies, including the Thirteen Colonies which formed the United States. Under the law, an enslaved person was treated as property and could be bought, sold, or given away. Slavery lasted in about half of U.S. states until 1865. As an economic system, slavery was largely replaced by sharecropping and convict leasing.
By the time of the American Revolution (1775–1783), the status of enslaved people had been institutionalized as a racial caste associated with African ancestry. During and immediately following the Revolution, abolitionist laws were passed in most Northern states and a movement developed to abolish slavery. The role of slavery under the U.S. Constitution (1789) was the most contentious issue during its drafting. Although the creators of the Constitution never used the word "slavery", the final document, through the three-fifths clause, gave slave-owners disproportionate political power. All Northern states had abolished slavery in some way by 1805; sometimes, abolition was a gradual process, and hundreds of people were still enslaved in the Northern states as late as the 1840 Census. Some slaveowners, primarily in the Upper South, freed their slaves, and philanthropists and charitable groups bought and freed others. The Atlantic slave trade was outlawed by individual states beginning during the American Revolution. The import-trade was banned by Congress in 1808, although smuggling was common thereafter.:7
The rapid expansion of the cotton industry in the Deep South after the invention of the cotton gin greatly increased demand for slave labor, and the Southern states continued as slave societies. The United States became ever more polarized over the issue of slavery, split into slave and free states. Driven by labor demands from new cotton plantations in the Deep South, the Upper South sold more than a million slaves who were taken to the Deep South. The total slave population in the South eventually reached four million. As the United States expanded, the Southern states attempted to extend slavery into the new western territories to allow proslavery forces to maintain their power in the country. The new territories acquired by the Louisiana Purchase and the Mexican Cession were the subject of major political crises and compromises. By 1850, the newly rich, cotton-growing South was threatening to secede from the Union, and tensions continued to rise. Slavery was defended in the South as a "positive good", and the largest religious denominations split over the slavery issue into regional organizations of the North and South.
When Abraham Lincoln won the 1860 election on a platform of halting the expansion of slavery, seven slave states broke away to form the Confederacy. Shortly afterward, the Civil War began when Confederate forces attacked the U.S. Army's Fort Sumter in South Carolina. Four additional slave states then joined the confederacy after Lincoln requested arms from them to make a retaliatory strike. Due to Union measures such as the Confiscation Acts and the Emancipation Proclamation in 1863, the war effectively ended chattel slavery in most places. Following the Union victory, the institution was banned in the whole territory of the United States upon the ratification of the Thirteenth Amendment in December 1865.
In 1508, Ponce de León established the Spanish settlement in Puerto Rico, which used the native Taínos for labor. The Taínos were largely exterminated by war, overwork and diseases brought by the Spanish. In 1513, to supplement the dwindling Taíno population, the first enslaved African people were imported to Puerto Rico. The abolition of Indian slavery in 1542 with the New Laws increased the demand for African slaves.
A century and a half later, the British conducted enslaving raids in what is now Georgia, Tennessee, North Carolina, South Carolina, Florida and possibly Alabama. The Charles Town slave trade, which included both trading and direct raids by colonists, was the largest among the British colonies in North America. Between 1670 and 1715, between 24,000 and 51,000 captive Native Americans were exported from South Carolina—more than the number of Africans imported to the colonies of the future United States during the same period. Additional enslaved Native Americans were exported from South Carolina to Virginia, Pennsylvania, New York, Rhode Island and Massachusetts.
The historian Alan Gallay says, "the trade in Indian slaves was at the center of the English empire's development in the American South. The trade in Indian slaves was the most important factor affecting the South in the period 1670 to 1715"; intertribal wars to capture slaves destabilized English colonies, Spanish Florida, and French Louisiana.
First continental African enslaved people
The first Africans enslaved within continental North America arrived via Santo Domingo to the San Miguel de Gualdape colony (most likely located in the Winyah Bay area of present-day South Carolina), founded by Spanish explorer Lucas Vázquez de Ayllón in 1526. The ill-fated colony was almost immediately disrupted by a fight over leadership, during which the enslaved people revolted and fled the colony to seek refuge among local Native Americans. De Ayllón and many of the colonists died shortly afterward of an epidemic and the colony was abandoned. The settlers and the enslaved people who had not escaped returned to Santo Domingo.
On August 28, 1565, St. Augustine, Florida was founded by the Spanish conquistador Don Pedro Menendez de Aviles and he brought three enslaved Africans with him. During the 16th and 17th centuries, St. Augustine was the hub of the trade in enslaved people in Spanish colonial Florida and the first permanent settlement in what would become the continental United States to include enslaved Africans. The first birth of an enslaved African in what is now the United States was Agustin, who was born there in 1606.
Decades later, in the early years of the Chesapeake Bay settlements, colonial officials found it difficult to attract and retain laborers under the harsh frontier conditions, and there was a high mortality rate. Most laborers came from Britain as indentured laborers, signing contracts of indenture to pay with work for their passage, their upkeep and their training, usually on a farm. The colonies had agricultural economies. These indentured laborers were often young people who intended to become permanent residents. In some cases, convicted criminals were transported to the colonies as indentured laborers, rather than being imprisoned. The indentured laborers were not slaves, but were required to work for four to seven years in Virginia to pay the cost of their passage and maintenance.
Destination of enslaved Africans (1519–1867)
|British mainland North America
|British Leeward Islands
|British Windward Islands and Trinidad (British 1797–1867)
|Jamaica (Spanish 1519–1655, British 1655–1867)
|The Guianas (British, Dutch, French)
|French Windward Islands
|Spanish mainland North and South America
|Spanish Caribbean islands
|Dutch Caribbean islands
|Northeastern Brazil (Portuguese)
|Bahia, Brazil (Portuguese)
|Southeastern Brazil (Portuguese)
|Elsewhere in the Americas
The first Africans to reach the colonies that England was struggling to establish were a group of some 20 enslaved people who arrived at Point Comfort, Virginia, near Jamestown, in August 1619, brought by British privateers who had seized them from a captured Portuguese slave ship. Colonists do not appear to have made indenture contracts for most Africans. Although it is possible that some of them were freed after a certain period, most of them remained enslaved for life. The historian Ira Berlin noted that what he called the "charter generation" in the colonies was sometimes made up of mixed-race men (Atlantic Creoles) who were indentured servants and whose ancestry was African and Iberian. They were descendants of African women and Portuguese or Spanish men who worked in African ports as traders or facilitators in the trade of enslaved people. The transformation of the status of Africans, from indentured servitude to slaves in a racial caste which they could not leave or escape, happened over the next generation.
First slave laws
There were no laws regarding slavery early in Virginia's history, but in 1640, a Virginia court sentenced John Punch, an African, to life in servitude after he attempted to flee his service. The two whites with whom he fled were sentenced only to an additional year of their indenture, and three years' service to the colony. This marked the first de facto legal sanctioning of slavery in the English colonies, and was one of the first legal distinctions made between Europeans and Africans.
Slaves processing tobacco in 17th-century Virginia
Slaves shipped to those regions that are part of the present-day United States
In 1641, Massachusetts became the first colony to authorize slavery through enacted law. Massachusetts passed the Body of Liberties, which prohibited slavery in many instances but allowed people to be enslaved if they were captives of war, if they sold themselves into slavery or were purchased elsewhere, or if they were sentenced to slavery as punishment by the governing authority. The Body of Liberties used the word "strangers" to refer to people bought and sold as slaves; they were generally not English subjects. Colonists came to equate this term with Native Americans and Africans.
In 1654, John Casor, a black indentured servant in colonial Virginia, was the first man to be declared a slave in a civil case. He had claimed to an officer that his master, Anthony Johnson, had held him past his indenture term. Johnson himself was a free black, who had arrived in Virginia in 1621 from Angola. A neighbor, Robert Parker, told Johnson that if he did not release Casor, he would testify in court to this fact. Under local laws, Johnson was at risk for losing some of his headright lands for violating the terms of indenture. Under duress, Johnson freed Casor. Casor entered into a seven years' indenture with Parker. Feeling cheated, Johnson sued Parker to repossess Casor. A Northampton County, Virginia court ruled for Johnson, declaring that Parker illegally was detaining Casor from his rightful master who legally held him "for the duration of his life".
First inherited status laws
During the colonial period, the status of enslaved people was affected by interpretations related to the status of foreigners in England. England had no system of naturalizing immigrants to its island or its colonies. Since persons of African origins were not English subjects by birth, they were among those peoples considered foreigners and generally outside English common law. The colonies struggled with how to classify people born to foreigners and subjects. In 1656 Virginia, Elizabeth Key Grinstead, a mixed-race woman, successfully gained her freedom and that of her son in a challenge to her status by making her case as the baptized Christian daughter of the free Englishman Thomas Key. Her attorney was an English subject, which may have helped her case. (He was also the father of her mixed-race son, and the couple married after Key was freed.)
In 1662, shortly after the Elizabeth Key trial and similar challenges, the Virginia royal colony approved a law adopting the principle of partus sequitur ventrem (called partus, for short), stating that any children born in the colony would take the status of the mother. A child of an enslaved mother would be born into slavery, regardless if the father were a freeborn Englishman or Christian. This was a reversal of common law practice in England, which ruled that children of English subjects took the status of the father. The change institutionalized the skewed power relationships between those who enslaved people and enslaved women, freed white men from the legal responsibility to acknowledge or financially support their mixed-race children, and somewhat confined the open scandal of mixed-race children and miscegenation to within the slave quarters.
Increasing slave trade
In 1672, King Charles II rechartered the Royal African Company (it had initially been set up in 1660) as an English monopoly for the African slave and commodities trade. In 1698, by statute, the English parliament opened the trade to all English subjects. The trade of enslaved people to the mid-Atlantic colonies increased substantially in the 1680s, and by 1710 the African population in Virginia had increased to 23,100 (42% of total); Maryland contained 8,000 Africans (14.5% of total). In the early 18th century, England passed Spain and Portugal to become the world's leading trader of enslaved people. From the early 18th century British colonial merchants, especially in Charleston, South Carolina, challenged the monopoly of the Royal African Company, and Joseph Wragg and Benjamin Savage became the first independent traders of enslaved people to break through the monopoly by the 1730s.
First religious status laws
The Virginia Slave codes of 1705 further defined as slaves those people imported from nations that were not Christian. Native Americans who were sold to colonists by other Native Americans (from rival tribes), or captured by Europeans during village raids, were also defined as slaves. This codified the earlier principle of non-Christian foreigner enslavement.
First anti-slavery causes
In 1735, the Georgia Trustees enacted a law prohibiting slavery in the new colony, which had been established in 1733 to enable the "worthy poor" as well as persecuted European Protestants to have a new start. Slavery was then legal in the other 12 English colonies. Neighboring South Carolina had an economy based on the use of enslaved labor. The Georgia Trustees wanted to eliminate the risk of slave rebellions and make Georgia better able to defend against attacks from the Spanish to the south, who offered freedom to escaped enslaved people. James Edward Oglethorpe was the driving force behind the colony, and the only trustee to reside in Georgia. He opposed slavery on moral grounds as well as for pragmatic reasons, and vigorously defended the ban on slavery against fierce opposition from Carolina merchants of enslaved people and land speculators.
The Protestant Scottish highlanders who settled what is now Darien, Georgia, added a moral anti-slavery argument, which became increasingly rare in the South, in their 1739 "Petition of the Inhabitants of New Inverness". By 1750 Georgia authorized slavery in the colony because it had been unable to secure enough indentured servants as laborers. As economic conditions in England began to improve in the first half of the 18th century, workers had no reason to leave, especially to face the risks in the colonies.
Slavery in British colonies
During most of the British colonial period, slavery existed in all the colonies. People enslaved in the North typically worked as house servants, artisans, laborers and craftsmen, with the greater number in cities. Many men worked on the docks and in shipping. In 1703, more than 42% of New York City households enslaved people, the second-highest proportion of any city in the colonies, behind only Charleston, South Carolina. But enslaved people were also used as agricultural workers in farm communities, including in areas of upstate New York and Long Island, Connecticut and New Jersey. By 1770, there were 397,924 blacks in a population of 2.17 million. They were unevenly distributed: There were 14,867 in New England, where they were 2.7% of the population; 34,679 in the mid-Atlantic colonies, where they were 6% of the population (19,000 were in New York or 11%); and 347,378 in the five Southern Colonies, where they were 31% of the population
The South developed an agricultural economy dependent on commodity crops. Its planters rapidly acquired a significantly higher number and proportion of enslaved people in the population overall, as its commodity crops were labor-intensive. Early on, enslaved people in the South worked primarily on farms and plantations growing indigo, rice and tobacco; cotton did not become a major crop until after the 1790s. Before then long-staple cotton was cultivated primarily on the Sea Islands of Georgia and South Carolina.
The invention of the cotton gin in 1793 enabled the cultivation of short-staple cotton in a wide variety of mainland areas, leading to the development of large areas of the Deep South as cotton country in the 19th century. Rice and tobacco cultivation were very labor-intensive. In 1720, about 65% of South Carolina's population was enslaved. Planters (defined by historians in the Upper South as those who held or more slaves) used enslaved workers to cultivate commodity crops. They also worked in the artisanal trades on large plantations and in many Southern port cities. The later wave of settlers in the 18th century who settled along the Appalachian Mountains and backcountry were backwoods subsistence farmers, and they seldom held enslaved people.
Some of the British colonies attempted to abolish the international slave trade, fearing that the importation of new Africans would be disruptive. Virginia bills to that effect were vetoed by the British Privy Council. Rhode Island forbade the import of enslaved people in 1774. All of the colonies except Georgia had banned or limited the African slave trade by 1786; Georgia did so in 1798. Some of these laws were later repealed.
About 600,000 slaves were transported to the United States, or 5% of the twelve million slaves taken from Africa. About 310,000 of these persons were imported into the Thirteen Colonies before 1776: 40% directly and the rest from the Caribbean.
Slaves transported to the United States:
- Total .............597,000
They constituted less than 5% of the 12 million enslaved people brought from Africa to the Americas. The great majority of enslaved Africans were transported to sugar colonies in the Caribbean and to Brazil. As life expectancy was short, their numbers had to be continually replenished. Life expectancy was much higher in the United States, and the enslaved population was successful in reproduction. The number of enslaved people in the United States grew rapidly, reaching 4 million by the 1860 Census. From 1770 to 1860, the rate of natural growth of North American enslaved people was much greater than for the population of any nation in Europe, and it was nearly twice as rapid as that of England.
The number of enslaved and free blacks rose from 759,000 (60,000 free) in the 1790 U.S. Census to 4,450,000 (480,000, or 11%, free) in the 1860 U.S. Census, a 580% increase. The white population grew from 3.2 million to 27 million, an increase of 1,180% due to high birth rates and 4.5 million immigrants, overwhelmingly from Europe, and 70% of whom arrived in the years 1840–1860. The percentage of the black population dropped from 19.3% to 14.1%, as follows: 1790: 757,208 .. 19.3% of population, of whom 697,681 (92%) were enslaved. 1860: 4,441,830 .. 14.1% of population, of whom 3,953,731 (89%) were enslaved.
Slavery in French Louisiana
Louisiana was founded as a French colony. Colonial officials in 1724 implemented Louis XIV of France's Code Noir, which regulated the slave trade and the institution of slavery in New France and French Caribbean colonies. This resulted in a different pattern of slavery in Louisiana, purchased in 1803, compared to the rest of the United States. As written, the Code Noir gave some rights to slaves, including the right to marry. Although it authorized and codified cruel corporal punishment against slaves under certain conditions, it forbade slave owners from torturing them or separating married couples (or separating young children from their mothers). It also required the owners to instruct slaves in the Catholic faith.
Together with a more permeable historic French system that allowed certain rights to gens de couleur libres (free people of color), who were often born to white fathers and their mixed-race concubines, a far higher percentage of African Americans in Louisiana were free as of the 1830 census (13.2% in Louisiana compared to 0.8% in Mississippi, whose population was dominated by white Anglo-Americans). Most of Louisiana's "third class" of free people of color, situated between the native-born French and mass of African slaves, lived in New Orleans. The Louisiana free people of color were often literate and educated, with a significant number owning businesses, properties, and even slaves. Although Code Noir forbade interracial marriages, interracial unions were widespread. Whether there was a formalized system of concubinage known as plaçage, is subject to debate. The mixed-race offspring (Creoles of color) from these unions were among those in the intermediate social caste of free people of color. The English colonies, in contrast, operated within a binary system that treated mulatto and black slaves equally under the law, and discriminated against equally if free. But many free people of African descent were mixed race.
When the U.S. took over Louisiana, Americans from the Protestant South entered the territory and began to impose their norms. They officially discouraged interracial relationships (although white men continued to have unions with black women, both enslaved and free.) The Americanization of Louisiana gradually resulted in a binary system of race, causing free people of color to lose status as they were grouped with the slaves. They lost certain rights as they became classified by American whites as officially "black".
|Origins and percentages of Africans
imported into British North America
and Louisiana (1700–1820)
|Amount % |
|West-central Africa (Kongo, N. Mbundu, S. Mbundu)
|Bight of Biafra (Igbo, Tikar, Ibibio, Bamileke, Bubi)
|Sierra Leone (Mende, Temne)
|Senegambia (Mandinka, Fula, Wolof)
|Gold Coast (Akan, Fon)
|Windward Coast (Mandé, Kru)
|Bight of Benin (Yoruba, Ewe, Fon, Allada and Mahi)
|Southeast Africa (Macua, Malagasy)
Prince Estabrook memorial in front of Buckman Tavern
on Lexington Green in Lexington, Massachusetts. Prince Estabrook, who was wounded in the Battle of Lexington and Concord
, was the first black casualty of the Revolutionary War.
As historian Christopher L. Brown put it, slavery "had never been on the agenda in a serious way before," but the American Revolution "forced it to be a public question from there forward."
Freedom offered as incentive by British
This postage stamp, which was created at the time of the Bicentennial, honors Salem Poor
, who was an enslaved African American man who purchased his freedom, became a soldier, and rose to fame as a war hero during the Battle of Bunker Hill
Continental soldiers at Yorktown. On the left, an African American soldier of the 1st Rhode Island Regiment.
While a small number of African slaves were kept and sold in England and Scotland, slavery in England had not been authorized by statute there, though it had in Scotland. In 1772, in the case of Somerset v Stewart, it was found that slavery was no part of the common law in England and Wales. The British role in the international slave trade continued until it abolished its slave trade in 1807. Slavery flourished in most of Britain's North American and Caribbean colonies, with many wealthy slave owners living in England and wielding considerable power.
In early 1775 Lord Dunmore, royal governor of Virginia and a slave-owner, wrote to Lord Dartmouth of his intent to free slaves owned by patriots in case of rebellion. On November 7, 1775, Lord Dunmore issued Lord Dunmore's Proclamation which declared martial law in Virginia and promised freedom for any slaves of American patriots who would leave their masters and join the royal forces. Slaves owned by Loyalist masters, however, were unaffected by Dunmore's Proclamation. About 1500 slaves owned by patriots escaped and joined Dunmore's forces. Most died of disease before they could do any fighting. Three hundred of these freed slaves made it to freedom in Britain.
Many slaves used the very disruption of war to escape their plantations and fade into cities or woods, or to the British lines. Upon their first sight of British vessels, thousands of slaves in Maryland and Virginia ran away from their owners.:21 In South Carolina, nearly 25,000 slaves (30% of the total enslaved population) fled, migrated, or died during the war. Throughout the South, losses of slaves were high, with many due to escapes. Slaves also escaped throughout New England and the mid-Atlantic, with many joining the British who had occupied New York.
In the closing months of the war the British evacuated freedmen and also removed slaves owned by loyalists. The British evacuated 20,000 freedmen from major coastal cities, transporting more than 3,000 for resettlement in Nova Scotia, where they were registered as black loyalists and eventually granted land. They transported others to the Caribbean islands, and some to England. Over 5,000 enslaved Africans owned by loyalists were transported in 1782 with their owners from Savannah to Jamaica and St. Augustine, Florida (then a British colony). Similarly, over half of the black people evacuated in 1782 from Charleston by the British to the West Indies and Florida were slaves owned by white loyalists.
Slaves and free blacks who supported the rebellion
The rebels began to offer freedom as an incentive to motivate slaves to fight on their side. Washington authorized slaves to be freed who fought with the American Continental Army. Rhode Island started enlisting slaves in 1778, and promised compensation to owners whose slaves enlisted and survived to gain freedom. During the course of the war, about one-fifth of the Northern army was black. In 1781, Baron Closen, a German officer in the French Royal Deux-Ponts Regiment at the Battle of Yorktown, estimated the American army to be about one-quarter black. These men included both former slaves and Blacks born free. Thousands of free blacks in the Northern states fought in the state militias and Continental Army. In the South, both sides offered freedom to slaves who would perform military service. Roughly 20,000 slaves fought in the American Revolution.
The birth of abolitionism in the new United States
In the first two decades after the American Revolution, state legislatures and individuals took actions to free slaves. Northern states passed new constitutions that contained language about equal rights or specifically abolished slavery; some states, such as New York and New Jersey, where slavery was more widespread, passed laws by the end of the 18th century to abolish slavery incrementally. By 1804, all the Northern states had passed laws outlawing slavery, either immediately or over time. In New York, the last slaves were freed in 1827 (celebrated with a big July 4 parade). Indentured servitude (temporary slavery), which had been widespread in the colonies (half the population of Philadelphia had once been indentured servants), dropped dramatically, and disappeared by 1800. However, there were still forcibly indentured servants in New Jersey in 1860. No Southern state abolished slavery, but some individual owners, more than a handful, freed their slaves by personal decision, often providing for manumission in wills but sometimes filing deeds or court papers to free individuals. Numerous slaveholders who freed their slaves cited revolutionary ideals in their documents; others freed slaves as a promised reward for service. The number of free blacks as a proportion of the black population in the Upper South increased from less than one percent to nearly ten percent between 1790 and 1810 as a result of these actions.
Starting in 1777, the rebels outlawed the importation of slaves state by state. They all acted to end the international trade, but after the war it was later reopened in South Carolina and Georgia.
In 1807 Congress acted on President Jefferson's advice and, without controversy, made importing slaves from abroad a federal crime, effective the first day that the Constitution permitted this prohibition: January 1, 1808.
During the Revolution and in the following years, all states north of Maryland took steps towards abolishing slavery. In 1777, the Vermont Republic, which was still unrecognized by the United States, passed a state constitution prohibiting slavery. The Pennsylvania Abolition Society, led in part by Benjamin Franklin, was founded in 1775, and in 1780, Pennsylvania began gradual abolition. In 1783, the Supreme Judicial Court of Massachusetts ruled in Commonwealth v. Jennison that slavery was unconstitutional under the state's new 1780 constitution. New Hampshire began gradual emancipation in 1783, while Connecticut and Rhode Island followed in 1784. The New York Manumission Society was founded in 1785, and was led by John Jay, Alexander Hamilton and Aaron Burr. New York state began gradual emancipation in 1799, and New Jersey followed in 1804.
Shortly after the Revolution, the Northwest Territory was established, by Manasseh Cutler and Rufus Putnam (who had been George Washington's chief engineer). Both Cutler and Putnam came from Puritan New England. The Puritans strongly believed that slavery was morally wrong. Their influence on the issue of slavery was long-lasting, and this was provided significantly greater impetus by the Revolution. The Northwest Territory (which became Ohio, Michigan, Indiana, Illinois, Wisconsin and part of Minnesota) doubled the size of the United States, and it was established at the insistence of Cutler and Putnam as "free soil" – no slavery. This was to prove crucial a few decades later. Had those states been slave states, and their electoral votes gone to Abraham Lincoln's main opponent, Lincoln would not have become President. The Civil War would not have been fought. Even if it eventually had been, the North might well have lost.
Constitution of the United States
Slavery was a contentious issue in the writing and approval of the Constitution of the United States. The words "slave" and "slavery" did not appear in the Constitution as originally adopted, although several provisions clearly referred to slaves and slavery. Until the adoption of the 13th Amendment in 1865, the Constitution did not prohibit slavery.
Section 9 of Article I forbade the Federal government from preventing the importation of slaves, described as "such Persons as any of the States now existing shall think proper to admit", for twenty years after the Constitution's ratification (until January 1, 1808). The Act Prohibiting Importation of Slaves of 1807, adopted by Congress and signed into law by President Thomas Jefferson (who had called for its enactment in his 1806 State of the Union address), went into effect on January 1, 1808, the earliest date on which the importation of slaves could be prohibited under the Constitution.
The delegates approved Section 2 of Article IV, which prohibited states from freeing slaves who fled to them from another state, and required the return of chattel property to owners.
In a section negotiated by James Madison of Virginia, Section 2 of Article I designated "other persons" (slaves) to be added to the total of the state's free population, at the rate of three-fifths of their total number, to establish the state's official population for the purposes of apportionment of Congressional representation and federal taxation. The "Three-Fifths Compromise" was reached after a debate in which delegates from Southern (slaveholding) states argued that slaves should be counted in the census just as all other persons were while delegates from Northern (free) states countered that slaves should not be counted at all. The compromise strengthened the political power of Southern states, as three-fifths of the (non-voting) slave population was counted for congressional apportionment and in the Electoral College, although it did not strengthen Southern states as much as it would have had the Constitution provided for counting all persons, whether slave of free, equally.
In addition, many parts of the country were tied to the Southern economy. As the historian James Oliver Horton noted, prominent slaveholder politicians and the commodity crops of the South had a strong influence on United States politics and economy. Horton said,
in the 72 years between the election of George Washington and the election of Abraham Lincoln, 50 of those years [had] a slaveholder as president of the United States, and, for that whole period of time, there was never a person elected to a second term who was not a slaveholder.
The power of Southern states in Congress lasted until the Civil War, affecting national policies, legislation, and appointments. One result was that justices appointed to the Supreme Court were also primarily slave owners. The planter elite dominated the Southern congressional delegations and the United States presidency for nearly fifty years.
1790 to 1860
The U.S. Constitution barred the federal government from prohibiting the importation of slaves for twenty years. Various states passed bans on the international slave trade during that period; by 1808, the only state still allowing the importation of African slaves was South Carolina. After 1808, legal importation of slaves ceased, although there was smuggling via Spanish Florida and the disputed Gulf Coast to the west.:48–49:138 This route all but ended after Florida became a U.S. territory in 1821 (but see Wanderer and Clotilda).
The replacement for the importation of slaves from abroad was increased domestic production. Virginia and Maryland had little new agricultural development, and their need for slaves was mostly for replacements for decedents. Normal reproduction more than supplied these: Virginia and Maryland had surpluses of slaves. Their tobacco farms were "worn out" and the climate was not suitable for cotton or sugar cane. The surplus was even greater because slaves were encouraged to reproduce (though they could not marry). The white supremacist Virginian Thomas Roderick Dew wrote in 1832 that Virginia was a "negro-raising state"; i.e. Virginia "produced" slaves.:2 According to him, in 1832 Virginia exported "upwards of 6,000 slaves" per year, "a source of wealth to Virginia".:198 Another writer gives the figure in 1836 as 40,000, earning for Virginia an estimated $24,000,000 per year.:201 Where demand for slaves was the strongest in what was then the southwest of the country: Alabama, Mississippi, and Louisiana, and later Texas, Arkansas, and Missouri. Here there was abundant land suitable for plantation agriculture, which young men with some capital established. This was expansion of the white, monied population: younger men seeking their fortune.
The most valuable crop that could be grown on a plantation in that climate was cotton. That crop was labor-intensive, and the least-costly laborers were slaves. Demand for slaves exceeded the supply in the southwest; therefore slaves, never cheap if they were productive, went for a higher price. As portrayed in Uncle Tom's Cabin (the "original" cabin was in Maryland), "selling South" was greatly feared. A recently (2018) publicized example of the practice of "selling South" is the 1838 sale by Jesuits of 272 slaves from Maryland, to plantations in Louisiana, to benefit Georgetown University, which has been described as "ow[ing] its existence" to this transaction.
Traders responded to the demand, including John Armfield and his uncle Isaac Franklin, who were "reputed to have made over half a million dollars (in 19th-century value)" in the slave trade.
In the United States in the early 19th century, owners of female slaves could freely and legally use them as sexual objects. This follows free use of female slaves on slaving vessels by the crews.:83
The slaveholder has it in his power, to violate the chastity of his slaves. And not a few are beastly enough to exercise such power. Hence it happens that, in some families, it is difficult to distinguish the free children from the slaves. It is sometimes the case, that the largest part of the master's own children are born, not of his wife, but of the wives and daughters
of his slaves, whom he has basely prostituted as well as enslaved.:38
"This vice, this bane of society, has already become so common, that it is scarcely esteemed a disgrace."
"Fancy" was a code word which indicated that the girl or young woman was suitable for or trained for sexual use.:56 In some cases, children were also abused in this manner. The sale of a 13-year-old "nearly a fancy" is documented. Zephaniah Kingsley, Jr., bought his wife when she was 13.:191
Furthermore, enslaved women who were old enough to bear children were encouraged to procreate, which raised their value as slaves, since their children would eventually provide labor or be sold, enriching the owners. Enslaved women were sometimes medically treated in order to enable or encourage their fertility. The variations in skin color found in the United States make it obvious how often black women were impregnated by whites.:78–79 For example, in the 1850 Census, 75.4% of "free negros" in Florida were described as mulattos, of mixed race.:2 Nevertheless, it is only very recently, with DNA studies, that any sort of reliable number can be provided, and the research has only begun. Light-skinned girls, who contrasted with the darker field workers, were preferred.
The sexual use of black slaves by either slave owners or by those who could purchase the temporary services of a slave took various forms. A slaveowner, or his teenage son, could go to the slave quarters area of the plantation and do what he wanted, usually in front of the rest of the slaves, or with minimal privacy. It was common for a "house" female (housekeeper, maid, cook, laundress, or nanny) to be raped by one or more members of the household. Houses of prostitution throughout the slave states were largely staffed by female slaves providing sexual services, to their owners' profit. There were a small number of free black females engaged in prostitution, or concubinage, especially in New Orleans.:41
Slave owners who engaged in sexual activity with female slaves "were often the elite of the community. They had little need to worry about public scorn." These relationships "appear to have been tolerated and in some cases even quietly accepted." "Southern women ... do not trouble themselves about it". Franklin and Armfield, who were definitely the elite of the community, joked frequently in their letters about the black women and girls that they were raping. It never occurred to them that there was anything wrong in what they were doing.
Light-skinned young girls were sold openly for sexual use; their price was much higher than that of a field hand.:38, 55 Special markets for the fancy girl trade existed in New Orleans:55 and Lexington, Kentucky. Historian Philip Shaw describes an occasion when Abraham Lincoln and Allen Gentry witnessed such sales in New Orleans in 1828:
Gentry vividly remembered a day in New Orleans when he and the nineteen-year-old Lincoln came upon a slave market. Pausing to watch, Gentry recalled looking down at Lincoln's hands and seeing that he "doubled his fists tightly; his knuckles went white." Men wearing black coats and white hats buy field hands, "black and ugly," for $500 to 800. And then the real horror begins: "When the sale of "fancy girls" began, Lincoln, "unable to stand it any longer," muttered to Gentry "Allen that's a disgrace. If I ever get a lick at that thing I'll hit it hard."
Those girls who were "considered educated and refined, were purchased by the wealthiest clients, usually plantation owners, to become personal sexual companions." "There was a great demand in New Orleans for 'fancy girls'."
The issue which did come up frequently was the threat of sexual intercourse between black males and white females. Just as the black women were perceived as having "a trace of Africa, that supposedly incited passion and sexual wantonness",:39 the men were perceived as savages, unable to control their lust, given an opportunity.:212–213
Another approach to the question was offered by Quaker and Florida planter Zephaniah Kingsley, Jr. He advocated, and personally practiced, deliberate racial mixing through marriage, as part of his proposed solution to the slavery issue: racial integration, called "amalgamation" at the time. In an 1829 Treatise, he stated that mixed-race people were healthier and often more beautiful, that interracial sex was hygienic, and slavery made it convenient.:190 Because of these views, tolerated in Spanish Florida, he found it impossible to remain long in Territorial Florida, and moved with his slaves and multiple wives to a plantation in Haiti (now in the Dominican Republic). There were many others who less flagrantly practiced interracial, common-law marriages with slaves (see Partus sequitur ventrem).
Justifications in the South
"A necessary evil"
In the 19th century, proponents of slavery often defended the institution as a "necessary evil". At that time, it was feared that emancipation of black slaves would have more harmful social and economic consequences than the continuation of slavery. On April 22, 1820, Thomas Jefferson, one of the Founding Fathers of the United States, wrote in a letter to John Holmes, that with slavery,
We have the wolf by the ear, and we can neither hold him, nor safely let him go. Justice is in one scale, and self-preservation in the other.
The French writer and traveler Alexis de Tocqueville, in his influential Democracy in America (1835), expressed opposition to slavery while observing its effects on American society. He felt that a multiracial society without slavery was untenable, as he believed that prejudice against blacks increased as they were granted more rights (for example, in northern states). He believed that the attitudes of white Southerners, and the concentration of the black population in the South, were bringing the white and black populations to a state of equilibrium, and were a danger to both races. Because of the racial differences between master and slave, he believed that the latter could not be emancipated.
In a letter to his wife dated December 27, 1856, in reaction to a message from President Franklin Pierce, Robert E. Lee wrote,
There are few, I believe, in this enlightened age, who will not acknowledge that slavery as an institution is a moral and political evil. It is idle to expatiate on its disadvantages. I think it is a greater evil to the white than to the colored race. While my feelings are strongly enlisted in behalf of the latter, my sympathies are more deeply engaged for the former. The blacks are immeasurably better off here than in Africa, morally, physically, and socially. The painful discipline they are undergoing is necessary for their further instruction as a race, and will prepare them, I hope, for better things. How long their servitude may be necessary is known and ordered by a merciful Providence.
"A positive good"
However, as the abolitionist movement's agitation increased and the area developed for plantations expanded, apologies for slavery became more faint in the South. Leaders then described slavery as a beneficial scheme of labor management. John C. Calhoun, in a famous speech in the Senate in 1837, declared that slavery was "instead of an evil, a good – a positive good". Calhoun supported his view with the following reasoning: in every civilized society one portion of the community must live on the labor of another; learning, science, and the arts are built upon leisure; the African slave, kindly treated by his master and mistress and looked after in his old age, is better off than the free laborers of Europe; and under the slave system conflicts between capital and labor are avoided. The advantages of slavery in this respect, he concluded, "will become more and more manifest, if left undisturbed by interference from without, as the country advances in wealth and numbers".
South Carolina Army officer, planter, and railroad executive James Gadsden called slavery "a social blessing" and abolitionists "the greatest curse of the nation". Gadsden was in favor of South Carolina's secession in 1850, and was a leader in efforts to split California into two states, one slave and one free.
Other Southern writers who also began to portray slavery as a positive good were James Henry Hammond and George Fitzhugh. They presented several arguments to defend the practice of slavery in the South. Hammond, like Calhoun, believed that slavery was needed to build the rest of society. In a speech to the Senate on March 4, 1858, Hammond developed his "Mudsill Theory," defending his view on slavery by stating: "Such a class you must have, or you would not have that other class which leads progress, civilization, and refinement. It constitutes the very mud-sill of society and of political government; and you might as well attempt to build a house in the air, as to build either the one or the other, except on this mud-sill." Hammond believed that in every class one group must accomplish all the menial duties, because without them the leaders in society could not progress. He argued that the hired laborers of the North were slaves too: "The difference ... is, that our slaves are hired for life and well compensated; there is no starvation, no begging, no want of employment," while those in the North had to search for employment.
George Fitzhugh used assumptions about white superiority to justify slavery, writing that, "the Negro is but a grown up child, and must be governed as a child." In The Universal Law of Slavery, Fitzhugh argues that slavery provides everything necessary for life and that the slave is unable to survive in a free world because he is lazy, and cannot compete with the intelligent European white race. He states that "The negro slaves of the South are the happiest, and in some sense, the freest people in the world." Without the South, "He (slave) would become an insufferable burden to society" and "Society has the right to prevent this, and can only do so by subjecting him to domestic slavery."
On March 21, 1861, Alexander Stephens, Vice President of the Confederacy, delivered his Cornerstone Speech. He explained the differences between the Constitution of the Confederate States and the United States Constitution, laid out the cause for the American Civil War, as he saw it, and defended slavery:
The new Constitution has put at rest forever all the agitating questions relating to our peculiar institutions – African slavery as it exists among us – the proper status of the negro in our form of civilization. This was the immediate cause of the late rupture and present revolution. Jefferson, in his forecast, had anticipated this, as the "rock upon which the old Union would split." He was right. What was conjecture with him, is now a realized fact. But whether he fully comprehended the great truth upon which that rock stood and stands, may be doubted. The prevailing ideas entertained by him and most of the leading statesmen at the time of the formation of the old Constitution were, that the enslavement of the African was in violation of the laws of nature; that it was wrong in principle, socially, morally and politically. It was an evil they knew not well how to deal with; but the general opinion of the men of that day was, that, somehow or other, in the order of Providence, the institution would be evanescent and pass away ... Those ideas, however, were fundamentally wrong. They rested upon the assumption of the equality of races. This was an error. It was a sandy foundation, and the idea of a Government built upon it – when the "storm came and the wind blew, it fell."
Our new Government is founded upon exactly the opposite ideas; its foundations are laid, its cornerstone rests, upon the great truth that the negro is not equal to the white man; that slavery, subordination to the superior race, is his natural and moral condition.
This view of the Negro "race" was backed by pseudoscience. The leading researcher was Dr. Samuel A. Cartwright, inventor of the mental illnesses of drapetomania (the desire of a slave to run away) and dysaesthesia aethiopica ("rascality"), both cured by whipping. The Medical Association of Louisiana set up a committee, of which he was chair, to investigate "the Diseases and Physical Peculiarities of the Negro Race". Their report, first delivered to the Medical Association in an address, was published in their journal, and then reprinted in part in the widely circulated DeBow's Review.
Proposed expansion of slavery
Whether or not slavery was to be limited to the Southern states that already had it, or whether it was to be permitted in new states made from the lands of the Louisiana Purchase and Mexican Cession, was a major issue in the 1840s and 1850s. Results included the Compromise of 1850 and the Bleeding Kansas period.
Also relatively well known are the proposals, including the Ostend Manifesto, to annex Cuba as a slave state. There was also talk of making slave states of Mexico, Nicaragua (see Walker affair), and other lands around the so-called Golden Circle. Less well known today (2019), though well known at the time, is that pro-slavery Southerners:
- Wanted to reintroduce slavery in the Northern states, through federal action or Constitutional amendment making slavery legal nationwide, thus overriding state anti-slavery laws. (See Crittenden Compromise.) This was described as "well underway" by 1858.
- Said openly that slavery should by no means be limited to Negros, since in their view it was beneficial. Northern white workers, who were allegedly "wage slaves" already, would allegedly have better lives if they were enslaved.
None of these ideas got very far, but they alarmed Northerners and contributed to the growing polarization of the country.
Abolitionism in the North
Slavery is a volcano, the fires of which cannot be quenched, nor its ravishes controlled. We already feel its convulsions, and if we sit idly gazing upon its flames, as they rise higher and higher, our happy republic will be buried in ruin, beneath its overwhelming energies.
Beginning during the Revolution and in the first two decades of the postwar era, every state in the North abolished slavery. These were the first abolitionist laws in the Atlantic World. However, the abolition of slavery did not necessarily mean that existing slaves became free. In some states they were forced to remain with their former owners as indentured servants: free in name only, although they could not be sold and thus families could not be split, and their children were born free. The end of slavery did not come in New York until July 4, 1827, when it was celebrated with a big parade. However, in the 1830 census, the only state with no slaves was Vermont. In the 1840 census, there were still slaves in New Hampshire (1), Rhode Island (5), Connecticut (17), New York (4), Pennsylvania (64), Ohio (3), Indiana (3), Illinois (331), Iowa (16), and Wisconsin (11). There were none in these states in the 1850 census.
In Massachusetts, slavery was successfully challenged in court in 1783 in a freedom suit by Quock Walker; he said that slavery was in contradiction to the state's new constitution of 1780 providing for equality of men. Freed slaves were subject to racial segregation and discrimination in the North, and in many cases they did not have the right to vote until ratification of the Fifteenth Amendment in 1870.
Most Northern states passed legislation for gradual abolition, first freeing children born to slave mothers (and requiring them to serve lengthy indentures to their mother's owners, often into their 20s as young adults). In 1845, the Supreme Court of New Jersey received lengthy arguments towards "the deliverance of four thousand persons from bondage". Pennsylvania's last ex-slaves were freed in 1847, Connecticut's in 1848, and while neither New Hampshire nor New Jersey had any slaves in the 1850 Census, and New Jersey only one and New Hampshire none in the 1860 Census, slavery was never prohibited in either state until ratification of the 13th Amendment in 1865 (and New Jersey was one of the last states to ratify it).
None of the Southern states abolished slavery before 1865, but it was not unusual for individual slaveholders in the South to free numerous slaves, often citing revolutionary ideals, in their wills. Methodist, Quaker, and Baptist preachers traveled in the South, appealing to slaveholders to manumit their slaves, and there were "manumission societies" in some Southern states. By 1810, the number and proportion of free blacks in the population of the United States had risen dramatically. Most free blacks lived in the North, but even in the Upper South, the proportion of free blacks went from less than one percent of all blacks to more than ten percent, even as the total number of slaves was increasing through imports.
One of the early Puritan writings on this subject was "The Selling of Joseph," by Samuel Sewall in 1700. In it, Sewall condemned slavery and the slave trade and refuted many of the era's typical justifications for slavery. The Puritan influence on slavery was still strong at the time of the American Revolution and up until the Civil War. Of America's first seven presidents, the two who did not own slaves, John Adams and John Quincy Adams, came from Puritan New England. They were wealthy enough to own slaves, but they chose not to because they felt it was morally wrong. In 1765, colonial leader Samuel Adams and his wife were given a slave girl as a gift. They immediately freed her. Just after the Revolution, in 1787, the Northwest Territory (which became the states of Ohio, Michigan, Indiana, Illinois, Wisconsin, and part of Minnesota) was opened up for settlement. The two men responsible for establishing this territory were Manasseh Cutler and Rufus Putnam. They came from Puritan New England, and they insisted that this new territory, which doubled the size of the United States, was going to be "free soil" – no slavery. This was to prove crucial in the coming decades. If those states had become slave states, and their electoral votes had gone to Abraham Lincoln's main opponent, Lincoln would not have been elected president. The Civil War would not have been fought. Even if it eventually had been, the North would likely have lost.
Statue of abolitionist and crusading minister Theodore Parker
in front of the Theodore Parker Church in West Roxbury, Massachusetts.
In the decades leading up to the Civil War, the abolitionists, such as Theodore Parker, Ralph Waldo Emerson, Henry David Thoreau and Frederick Douglass, repeatedly used the Puritan heritage of the country to bolster their cause. The most radical anti-slavery newspaper, The Liberator, invoked the Puritans and Puritan values over a thousand times. Parker, in urging New England Congressmen to support the abolition of slavery, wrote that "The son of the Puritan ... is sent to Congress to stand up for Truth and Right ..."
Northerners predominated in the westward movement into the Midwestern territory after the American Revolution; as the states were organized, they voted to prohibit slavery in their constitutions when they achieved statehood: Ohio in 1803, Indiana in 1816, and Illinois in 1818. What developed was a Northern block of free states united into one contiguous geographic area that generally shared an anti-slavery culture. The exceptions were the areas along the Ohio River settled by Southerners: the southern portions of Indiana, Ohio, and Illinois. Residents of those areas generally shared in Southern culture and attitudes. In addition, these areas were devoted to agriculture longer than the industrializing northern parts of these states, and some farmers used slave labor. In Illinois, for example, while the trade in slaves was prohibited, it was legal to bring slaves from Kentucky into Illinois and use them there, as long as the slaves left Illinois one day per year (they were "visiting"). The emancipation of slaves in the North led to the growth in the population of Northern free blacks, from several hundred in the 1770s to nearly 50,000 by 1810.
Agitation against slavery
There was legal agitation against slavery in the thirteen colonies starting in 1752 by lawyer Benjamin Kent, whose cases were recorded by one of his understudies, the future president John Adams. Kent represented numerous slaves in their attempts to gain their freedom. He handled the case of a slave, Pompey, suing his master. In 1766, Kent was the first lawyer in the United States to win a case to free a slave, Jenny Slew. He also won a trial in the Old County Courthouse for a slave named Ceasar Watson (1771). Kent also handled Lucy Pernam's divorce and the freedom suits of Rose and Salem Orne.
Simon Legree and Uncle Tom: a scene from Uncle Tom's Cabin
(1852), an influential abolitionist novel
Throughout the first half of the 19th century, abolitionism, a movement to end slavery, grew in strength; most abolitionist societies and supporters were in the North. They worked to raise awareness about the evils of slavery, and to build support for abolition.
This struggle took place amid strong support for slavery among white Southerners, who profited greatly from the system of enslaved labor. But slavery was entwined with the national economy; for instance, the banking, shipping, and manufacturing industries of New York City all had strong economic interests in slavery, as did similar industries in other major port cities in the North. The Northern textile mills in New York and New England processed Southern cotton and manufactured clothes to outfit slaves. By 1822 half of New York City's exports were related to cotton.
Slaveholders began to refer to slavery as the "peculiar institution" to differentiate it from other examples of forced labor. They justified it as less cruel than the free labor of the North.
The principal organized bodies to advocate abolition and anti-slavery reforms in the north were the Pennsylvania Abolition Society and the New York Manumission Society. Before the 1830s the antislavery groups called for gradual emancipation. By the late 1820s, under the impulse of religious evangelicals such as Beriah Green, the sense emerged that owning slaves was a sin and the owner had to immediately free himself from this grave sin by immediate emancipation.
In the early part of the 19th century, other organizations were founded to take action on the future of black Americans. Some advocated removing free black people from the United States to places where they would enjoy greater freedom; some endorsed colonization in Africa, while others advocated emigration, usually to Haiti. During the 1820s and 1830s, the American Colonization Society (ACS) was the primary organization to implement the "return" of black Americans to Africa. The ACS was made up mostly of Quakers and slaveholders, and they found uneasy common ground in support of what was incorrectly called "repatriation". By this time, however, most black Americans were native-born and did not want to emigrate, saying they were no more African than white Americans were British. Rather, they wanted full rights in the United States, where their families had lived and worked for generations.
In 1822 the ACS and affiliated state societies established what would become the colony of Liberia, in West Africa. The ACS assisted thousands of freedmen and free blacks (with legislated limits) to emigrate there from the United States. Many white people considered this preferable to emancipation in the United States. Henry Clay, one of the founders and a prominent slaveholder politician from Kentucky, said that blacks faced
unconquerable prejudice resulting from their color, they never could amalgamate with the free whites of this country. It was desirable, therefore, as it respected them, and the residue of the population of the country, to drain them off.
Deportation would also be a way to prevent reprisals against former slaveholders and white people in general, as had occurred in the 1804 Haiti massacre. After 1830, abolitionist and newspaper publisher William Lloyd Garrison promoted emancipation, characterizing slaveholding as a personal sin. He demanded that slaveowners repent and start the process of emancipation. His position increased defensiveness on the part of some Southerners, who noted the long history of slavery among many cultures. A few abolitionists, such as John Brown, favored the use of armed force to foment uprisings among the slaves, as he attempted to do at Harper's Ferry. Most abolitionists tried to raise public support to change laws and to challenge slave laws. Abolitionists were active on the lecture circuit in the North, and often featured escaped slaves in their presentations. Writer and orator Frederick Douglass became an important abolitionist leader after escaping from slavery. Harriet Beecher Stowe's novel Uncle Tom's Cabin (1852) was an international bestseller and aroused popular sentiment against slavery. It also provoked the publication of numerous anti-Tom novels by Southerners in the years before the American Civil War.
Prohibiting the international trade
While under the Constitution, Congress could not prohibit the import slave trade that was allowed in South Carolina, until 1808, the third Congress regulated against it in the Slave Trade Act of 1794, which prohibited American shipbuilding and outfitting for the trade. Subsequent acts in 1800 and 1803 sought to discourage the trade by banning American investment in the trade, and American employment on ships in the trade, as well as prohibiting importation into states that had abolished slavery, which most in the North had by that time. The final Act Prohibiting Importation of Slaves was adopted in 1807, effective in 1808. However, illegal importation of African slaves (smuggling) was common. The Cuban slave trade between 1796 and 1807 was dominated by American slave ships. Despite the 1794 Act, Rhode Island slave ship owners found ways to continue supplying the slave-owning states. The overall US slave ship fleet in 1806 was estimated to be almost 75% the size of that of the British.:63, 65
After Great Britain and the United States outlawed the international slave trade in 1807, British slave trade suppression activities began in 1808 through diplomatic efforts and the formation of the Royal Navy's West Africa Squadron in 1809. The USA denied the Royal Navy the right to stop and search US suspected slave ships, so not only were American ships unhindered by British patrols, but slavers from other countries would fly the American flag to try and avoid being stopped. Co-operation between the US and Britain was not possible during the War of 1812 nor the period of poor relations in the following years. In 1820, the United States Navy sent USS Cyane, under the command of Captain Trenchard, to patrol the slave coasts of West Africa. Cyane seized 4 American slave ships in her first year on station. Trenchard developed a good level of co-operation with the Royal Navy. Four additional US warships were sent to the African coast in 1820 and 1821. A total of 11 US slave ships were taken by the US Navy over this period. Then American enforcement activity reduced. There was still no agreement between the USA and Britain on a mutual right to board suspected slave traders sailing under each other's flag. Attempts to reach such an agreement stalled in 1821 and 1824 in the Senate. A US Navy presence, however sporadic, did result in American slavers sailing under the Spanish flag, but still as an extensive trade. The Webster-Ashburton Treaty of 1842 set a guaranteed minimum level of patrol activity by the US Navy and the Royal Navy, and formalised the level of co-operation that had existed in 1820. Its effects were, however, minimal whilst opportunities for greater co-operation were not taken. The US transatlantic slave trade was not effectively suppressed until Lincoln's presidency of 1861, when a treaty with Britain was signed whose provisions included allowing the Royal Navy to board, search and arrest slavers operating under the American flag.:399-400, 449, 1144, 1149
Post-revolution Southern manumissions
Although Virginia, Maryland and Delaware were slave states, the latter two already had a high proportion of free blacks by the outbreak of war. Following the Revolution, the three legislatures made manumission easier, allowed by deed or will. Quaker and Methodist ministers particularly urged slaveholders to free their slaves. The number and proportion of freed slaves in these states rose dramatically until 1810. More than half of the number of free blacks in the United States were concentrated in the Upper South. The proportion of free blacks among the black population in the Upper South rose from less than 1% in 1792 to more than 10% by 1810. In Delaware, nearly 75% of blacks were free by 1810.
In the United States as a whole, the number of free blacks reached 186,446, or 13.5% of all blacks, by 1810. After that period, few slaves were freed, as the development of cotton plantations featuring short-staple cotton in the Deep South drove up the internal demand for slaves in the domestic slave trade and high prices being paid for them.
South Carolina made manumission more difficult, requiring legislative approval of every instance of manumission. Several Southern states
required manumitted slaves to leave the state within thirty days.
Domestic slave trade and forced migration
Movement of slaves between 1790 and 1860
The growing international demand for cotton led many plantation owners further west in search of suitable land. In addition, the invention of the cotton gin in 1793 enabled profitable processing of short-staple cotton, which could readily be grown in the uplands. The invention revolutionized the cotton industry by increasing fifty-fold the quantity of cotton that could be processed in a day. At the end of the War of 1812, fewer than 300,000 bales of cotton were produced nationally. By 1820, the amount of cotton produced had increased to 600,000 bales, and by 1850 it had reached 4,000,000. There was an explosive growth of cotton cultivation throughout the Deep South and greatly increased demand for slave labor to support it. As a result, manumissions decreased dramatically in the South.
Slaves Waiting for Sale: Richmond, Virginia
. Painted upon the sketch of 1853
Most of the slaves sold from the Upper South were from Maryland, Virginia and the Carolinas, where changes in agriculture decreased the need for their labor and the demand for slaves. Before 1810, primary destinations for the slaves who were sold were Kentucky and Tennessee, but after 1810 the Deep South states of Georgia, Alabama, Mississippi, Louisiana and Texas received the most slaves. This is where cotton became "king." Meanwhile, the Upper South states of Kentucky and Tennessee joined the slave-exporting states.
By 1815, the domestic slave trade had become a major economic activity in the United States; it lasted until the 1860s. Between 1830 and 1840 nearly 250,000 slaves were taken across state lines. In the 1850s, more than 193,000 enslaved persons were transported, and historians estimate nearly one million in total took part in the forced migration of this new "Middle Passage." By 1860, the slave population in the United States had reached four million. Of the 1,515,605 free families in the fifteen slave states in 1860, nearly 400,000 held slaves (roughly one in four, or 25%), amounting to 8% of all American families.
is a cloth that recounts a slave sale separating a mother and her daughter. The sack belonged to a nine-year-old girl Ashley and was a parting gift from her mother, Rose, after Ashley had been sold. Rose filled the sack with a dress, braid of her hair, pecans, and "my love always"
The historian Ira Berlin called this forced migration of slaves the "Second Middle Passage" because it reproduced many of the same horrors as the Middle Passage (the name given to the transportation of slaves from Africa to North America). These sales of slaves broke up many families and caused much hardship. Characterizing it as the "central event" in the life of a slave between the American Revolution and the Civil War, Berlin wrote that, whether slaves were directly uprooted or lived in fear that they or their families would be involuntarily moved, "the massive deportation traumatized black people, both slave and free." Individuals lost their connection to families and clans. Added to the earlier colonists combining slaves from different tribes, many ethnic Africans lost their knowledge of varying tribal origins in Africa. Most were descended from families that had been in the United States for many generations.
The firm of Franklin and Armfield was a leader in this trade. In the 1840s, almost 300,000 slaves were transported, with Alabama and Mississippi receiving 100,000 each. During each decade between 1810 and 1860, at least 100,000 slaves were moved from their state of origin. In the final decade before the Civil War, 250,000 were transporteded. Michael Tadman wrote in Speculators and Slaves: Masters, Traders, and Slaves in the Old South (1989) that 60–70% of inter-regional migrations were the result of the sale of slaves. In 1820, a slave child in the Upper South had a 30% chance of being sold South by 1860. The death rate for the slaves on their way to their new destination across the American South was less than that suffered by captives shipped across the Atlantic Ocean, but mortality nevertheless was higher than the normal death rate.
Slave traders transported two-thirds of the slaves who moved West. Only a minority moved with their families and existing master. Slave traders had little interest in purchasing or transporting intact slave families; in the early years, planters demanded only the young male slaves needed for heavy labor. Later, in the interest of creating a "self-reproducing labor force", planters purchased nearly equal numbers of men and women. Berlin wrote:
The internal slave trade became the largest enterprise in the South outside the plantation itself, and probably the most advanced in its employment of modern transportation, finance, and publicity. The slave trade industry developed its own unique language, with terms such as "prime hands, bucks, breeding wenches, and "fancy girls" coming into common use.
The expansion of the interstate slave trade contributed to the "economic revival of once depressed seaboard states" as demand accelerated the value of slaves who were subject to sale.
Some traders moved their "chattels" by sea, with Norfolk to New Orleans being the most common route, but most slaves were forced to walk overland. Others were shipped downriver from such markets as Louisville on the Ohio River, and Natchez on the Mississippi. Traders created regular migration routes served by a network of slave pens, yards and warehouses needed as temporary housing for the slaves. In addition, other vendors provided clothes, food and supplies for slaves. As the trek advanced, some slaves were sold and new ones purchased. Berlin concluded, "In all, the slave trade, with its hubs and regional centers, its spurs and circuits, reached into every cranny of southern society. Few southerners, black or white, were untouched."
Once the trip ended, slaves faced a life on the frontier significantly different from most labor in the Upper South. Clearing trees and starting crops on virgin fields was harsh and backbreaking work. A combination of inadequate nutrition, bad water and exhaustion from both the journey and the work weakened the newly arrived slaves and produced casualties. New plantations were located at rivers' edges for ease of transportation and travel. Mosquitoes and other environmental challenges spread disease, which took the lives of many slaves. They had acquired only limited immunities to lowland diseases in their previous homes. The death rate was so high that, in the first few years of hewing a plantation out of the wilderness, some planters preferred whenever possible to use rented slaves rather than their own.
The harsh conditions on the frontier increased slave resistance and led owners and overseers to rely on violence for control. Many of the slaves were new to cotton fields and unaccustomed to the "sunrise-to-sunset gang labor" required by their new life. Slaves were driven much harder than when they had been in growing tobacco or wheat back East. Slaves had less time and opportunity to improve the quality of their lives by raising their own livestock or tending vegetable gardens, for either their own consumption or trade, as they could in the East.
In Louisiana, French colonists had established sugar cane plantations and exported sugar as the chief commodity crop. After the Louisiana Purchase in 1803, Americans entered the state and joined the sugar cultivation. Between 1810 and 1830, planters bought slaves from the North and the number of slaves increased from fewer than 10,000 to more than 42,000. Planters preferred young males, who represented two-thirds of the slave purchases. Dealing with sugar cane was even more physically demanding than growing cotton. The largely young, unmarried male slave force made the reliance on violence by the owners "especially savage".
New Orleans became nationally important as a slave market and port, as slaves were shipped from there upriver by steamboat to plantations on the Mississippi River; it also sold slaves who had been shipped downriver from markets such as Louisville. By 1840, it had the largest slave market in North America. It became the wealthiest and the fourth-largest city in the nation, based chiefly on the slave trade and associated businesses. The trading season was from September to May, after the harvest.
Slave traders were men of low reputation, even in the South. In the 1828 presidential election, candidate Andrew Jackson was strongly criticized by opponents as a slave trader who transacted in slaves in defiance of modern standards or morality.
The treatment of slaves in the United States varied widely depending on conditions, time, and place, but in general it was brutal, especially on plantations. Whippings and rape were routine. The power relationships of slavery corrupted many whites who had authority over slaves, with children showing their own cruelty. Masters and overseers resorted to physical punishments to impose their wills. Slaves were punished by whipping, shackling, hanging, beating, burning, mutilation, branding and imprisonment. Punishment was most often meted out in response to disobedience or perceived infractions, but sometimes abuse was carried out to re-assert the dominance of the master or overseer of the slave. Treatment was usually harsher on large plantations, which were often managed by overseers and owned by absentee slaveholders, conditions permitting abuses.
William Wells Brown, who escaped to freedom, reported that on one plantation, slave men were required to pick eighty pounds per day of cotton, while women were required to pick seventy pounds; if any slave failed in his or her quota, they were subject to whip lashes for each pound they were short. The whipping post stood next to the cotton scales. A New York man who attended a slave auction in the mid-19th century reported that at least three-quarters of the male slaves he saw at sale had scars on their backs from whipping. By contrast, small slave-owning families had closer relationships between the owners and slaves; this sometimes resulted in a more humane environment but was not a given.
Historian Lawrence M. Friedman wrote: "Ten Southern codes made it a crime to mistreat a slave. ... Under the Louisiana Civil Code of 1825 (art. 192), if a master was "convicted of cruel treatment," the judge could order the sale of the mistreated slave, presumably to a better master." Masters and overseers were seldom prosecuted under these laws. No slave could give testimony in the courts.
According to Adalberto Aguirre, there were 1,161 slaves executed in the U.S. between the 1790s and 1850s. Quick executions of innocent slaves as well as suspects typically followed any attempted slave rebellions, as white militias overreacted with widespread killings that expressed their fears of rebellions, or suspected rebellions.
Although most slaves had lives that were very restricted in terms of their movements and agency, exceptions existed to virtually every generalization; for instance, there were also slaves who had considerable freedom in their daily lives: slaves allowed to rent out their labor and who might live independently of their master in cities, slaves who employed white workers, and slave doctors who treated upper-class white patients. After 1820, in response to the inability to import new slaves from Africa and in part to abolitionist criticism, some slaveholders improved the living conditions of their slaves, to encourage them to be productive and to try to prevent escapes. It was part of a paternalistic approach in the antebellum era that was encouraged by ministers trying to use Christianity to improve the treatment of slaves. Slaveholders published articles in Southern agricultural journals to share best practices in treatment and management of slaves; they intended to show that their system was better than the living conditions of northern industrial workers.
Medical care for slaves was limited in terms of the medical knowledge available to anyone. It was generally provided by other slaves or by slaveholders' family members, although sometimes "plantation physicians", like J. Marion Sims, were called by the owners to protect their investment by treating sick slaves. Many slaves possessed medical skills needed to tend to each other, and used folk remedies brought from Africa. They also developed new remedies based on American plants and herbs.
According to Andrew Fede, an owner could be held criminally liable for killing a slave only if the slave he killed was "completely submissive and under the master's absolute control". For example, in 1791 the North Carolina legislature defined the willful killing of a slave as criminal murder, unless done in resisting or under moderate correction (that is, corporal punishment).
Because of the power relationships at work, slave women in the United States were at high risk for rape and sexual abuse. Their children were repeatedly taken away from them and sold as farm animals; usually they never saw each other again. Many slaves fought back against sexual attacks, and some died resisting. Others carried psychological and physical scars from the attacks. Sexual abuse of slaves was partially rooted in a patriarchal Southern culture that treated black women as property or chattel. Southern culture strongly policed against sexual relations between white women and black men on the purported grounds of racial purity but, by the late 18th century, the many mixed-race slaves and slave children showed that white men had often taken advantage of slave women. Wealthy planter widowers, notably such as John Wayles and his son-in-law Thomas Jefferson, took slave women as concubines; each had six children with his partner: Elizabeth Hemings and her daughter Sally Hemings (the half-sister of Jefferson's late wife), respectively. Both Mary Chesnut and Fanny Kemble, wives of planters, wrote about this issue in the antebellum South in the decades before the Civil War. Sometimes planters used mixed-race slaves as house servants or favored artisans because they were their children or other relatives. As a result of centuries of slavery and such relationships, DNA studies have shown that the vast majority of African Americans also have historic European ancestry, generally through paternal lines.
While slaves' living conditions were poor by modern standards, Robert Fogel argued that all workers, free or slave, during the first half of the 19th century were subject to hardship. Unlike free individuals, however, enslaved people were far more likely to be underfed, physically punished, sexually abused, or killed, with no recourse, legal or otherwise, against those who perpetrated these crimes against them.
To help regulate the relationship between slave and owner, including legal support for keeping the slave as property, states established slave codes, most based on laws existing since the colonial era. The code for the District of Columbia defined a slave as "a human being, who is by law deprived of his or her liberty for life, and is the property of another".
While each state had its own slave code, many concepts were shared throughout the slave states. According to the slave codes, some of which were passed in reaction to slave rebellions, teaching a slave to read or write was illegal. This prohibition was unique to American slavery, believed to reduce slaves forming aspirations that could lead to escape or rebellion. Informal education occurred when white children taught slave companions what they were learning; in other cases, adult slaves learned from free artisan workers, especially if located in cities, where there was more freedom of movement.
In Alabama, slaves were not allowed to leave their master's premises without written consent or passes. This was a common requirement in other states as well, and locally run patrols (known to slaves as pater rollers) often checked the passes of slaves who appeared to be away from their plantations. In Alabama slaves were prohibited from trading goods among themselves. In Virginia, a slave was not permitted to drink in public within one mile of his master or during public gatherings. Slaves were not permitted to carry firearms in any of the slave states.
Slaves were generally prohibited by law from associating in groups, with the exception of worship services (a reason why the Black Church is such a notable institution in black communities today). Following Nat Turner's rebellion in 1831, which raised white fears throughout the South, some states also prohibited or restricted religious gatherings of slaves, or required that they be officiated by white men. Planters feared that group meetings would facilitate communication among slaves that could lead to rebellion. Slaves held private, secret "brush meetings" in the woods.
In Ohio, an emancipated slave was prohibited from returning to the state in which he or she had been enslaved. Other Northern states discouraged the settling of free blacks within their boundaries. Fearing the influence of free blacks, Virginia and other Southern states passed laws to require blacks who had been freed to leave the state within a year (or sometimes less time) unless granted a stay by an act of the legislature.
High demand and smuggling
U.S. brig Perry
confronting the slave ship Martha
on June 6, 1850
The United States Constitution, adopted in 1787, prevented Congress from completely banning the importation of slaves until 1808, although Congress regulated against the trade in the Slave Trade Act of 1794, and in subsequent Acts in 1800 and 1803. During and after the Revolution, the states individually passed laws against importing slaves. By contrast, the states of Georgia and South Carolina reopened their trade due to demand by their upland planters, who were developing new cotton plantations: Georgia from 1800 until December 31, 1807, and South Carolina from 1804. In that period, Charleston traders imported about 75,000 slaves, more than were brought to South Carolina in the 75 years before the Revolution. Approximately 30,000 were imported to Georgia.
By January 1, 1808, when Congress banned further imports, South Carolina was the only state that still allowed importation of enslaved people. The domestic trade became extremely profitable as demand rose with the expansion of cultivation in the Deep South for cotton and sugar cane crops. Slavery in the United States became, more or less, self-sustaining by natural increase among the current slaves and their descendants. Maryland and Virginia viewed themselves as slave producers, seeing "producing slaves" as resembling animal husbandry. Workers, including many children, were relocated by force from the upper to the lower South.
Despite the ban, slave imports continued through smugglers bringing in slaves past the U.S. Navy's African Slave Trade Patrol to South Carolina, and overland from Texas and Florida, both under Spanish control. Congress increased the punishment associated with importing slaves, classifying it in 1820 as an act of piracy, with smugglers subject to harsh penalties, including death if caught. After that, "it is unlikely that more than 10,000 [slaves] were successfully landed in the United States." But, some smuggling of slaves into the United States continued until just before the start of the Civil War; see slave ships Wanderer and Clotilda.
War of 1812
During the War of 1812, British Royal Navy commanders of the blockading fleet were instructed to offer freedom to defecting American slaves, as the Crown had during the Revolutionary War. Thousands of escaped slaves went over to the Crown with their families. Men were recruited into the Corps of Colonial Marines on occupied Tangier Island, in the Chesapeake Bay. Many freed American slaves were recruited directly into existing West Indian regiments, or newly created British Army units. The British later resettled a few thousand freed slaves to Nova Scotia. Their descendants, together with descendants of the black people resettled there after the Revolution, have established the Black Loyalist Heritage Museum.
Slaveholders, primarily in the South, had considerable "loss of property" as thousands of slaves escaped to the British lines or ships for freedom, despite the difficulties. The planters' complacency about slave "contentment" was shocked by seeing that slaves would risk so much to be free. Afterward, when some freed slaves had been settled at Bermuda, slaveholders such as Major Pierce Butler of South Carolina tried to persuade them to return to the United States, to no avail.
The Americans protested that Britain's failure to return all slaves violated the Treaty of Ghent. After arbitration by the Tsar of Russia, the British paid $1,204,960 in damages (about $27.6 million in today's money) to Washington, which reimbursed the slaveowners.
Prior to the American Revolution, masters and revivalists spread Christianity to slave communities, supported by the Society for the Propagation of the Gospel. In the First Great Awakening of the mid-18th century, Baptists and Methodists from New England preached a message against slavery, encouraged masters to free their slaves, converted both slaves and free blacks, and gave them active roles in new congregations. The first independent black congregations were started in the South before the Revolution, in South Carolina and Georgia. Believing that, "slavery was contrary to the ethics of Jesus", Christian congregations and church clergy, especially in the North, played a role in the Underground Railroad, especially Wesleyan Methodists, Quakers and Congregationalists.
Over the decades and with the growth of slavery throughout the South, some Baptist and Methodist ministers gradually changed their messages to accommodate the institution. After 1830, white Southerners argued for the compatibility of Christianity and slavery, with a multitude of both Old and New Testament citations. They promoted Christianity as encouraging better treatment of slaves and argued for a paternalistic approach. In the 1840s and 1850s, the issue of accepting slavery split the nation's largest religious denominations (the Methodist, Baptist and Presbyterian churches) into separate Northern and Southern organizations; see Methodist Episcopal Church, South, Southern Baptist Convention, and Presbyterian Church in the Confederate States of America). Schisms occurred, such as that between the Wesleyan Methodist Church and the Methodist Episcopal Church.
Southern slaves generally attended their masters' white churches, where they often outnumbered the white congregants. They were usually permitted to sit only in the back or in the balcony. They listened to white preachers, who emphasized the obligation of slaves to keep in their place, and acknowledged the slave's identity as both person and property. Preachers taught the master's responsibility and the concept of appropriate paternal treatment, using Christianity to improve conditions for slaves, and to treat them "justly and fairly" (Col. 4:1). This included masters having self-control, not disciplining under anger, not threatening, and ultimately fostering Christianity among their slaves by example.
Slaves also created their own religious observances, meeting alone without the supervision of their white masters or ministers. The larger plantations with groups of slaves numbering 20, or more, tended to be centers of nighttime meetings of one or several plantation slave populations. These congregations revolved around a singular preacher, often illiterate with limited knowledge of theology, who was marked by his personal piety and ability to foster a spiritual environment. African Americans developed a theology related to Biblical stories having the most meaning for them, including the hope for deliverance from slavery by their own Exodus. One lasting influence of these secret congregations is the African American spiritual.
Illustration from History of American conspiracies – a record of treason, insurrection, rebellion and c., in the United States of America, from 1760 to 1860 (1863)
James Hopkinson's Plantation.
Planting sweet potatoes. ca. 1862/63
According to Herbert Aptheker, "there were few phases of ante-bellum Southern life and history that were not in some way influenced by the fear of, or the actual outbreak of, militant concerted slave action."
Historians in the 20th century identified 250 to 311 slave uprisings in U.S. and colonial history. Those after 1776, include:
In 1831, Nat Turner, a literate slave who claimed to have spiritual visions, organized a slave rebellion in Southampton County, Virginia; it was sometimes called the Southampton Insurrection. Turner and his followers killed nearly sixty white inhabitants, mostly women and children. Many of the men in the area were attending a religious event in North Carolina. Eventually Turner was captured with 17 other rebels, who were subdued by the militia. Turner and his followers were hanged, and Turner's body was flayed. In a frenzy of fear and retaliation, the militia killed more than 100 slaves who had not been involved in the rebellion. Planters whipped hundreds of innocent slaves to ensure resistance was quelled.
This rebellion prompted Virginia and other slave states to pass more restrictions on slaves and free people of color, controlling their movement and requiring more white supervision of gatherings. In 1835 North Carolina withdrew the franchise for free people of color, and they lost their vote.
In a feature unique to American slavery, legislatures across the South enacted new laws to curtail the already limited rights of African Americans. For example, Virginia prohibited blacks, free or slave, from practicing preaching, prohibited them from owning firearms, and forbade anyone to teach slaves or free blacks how to read. It specified heavy penalties for both student and teacher if slaves were taught, including whippings or jail.
[E]very assemblage of negroes for the purpose of instruction in reading or writing, or in the night time for any purpose, shall be an unlawful assembly. Any justice may issue his warrant to any office or other person, requiring him to enter any place where such assemblage may be, and seize any negro therein; and he, or any other justice, may order such negro to be punished with stripes.
Unlike in the South, slave owners in Utah were required to send their slaves to school. Black slaves did not have to spend as much time in school as Indian slaves.
There were approximately 15,000 slaves in New England in 1770 of 650,000 inhabitants. 35,000 slaves lived in the Mid-Atlantic States of 600,000 inhabitants of whom 19,000 lived in New York where they made up 11% of the population. By 1790 Virginia held 44% (315,000 in a total population of 750,000 the State). It was common in agriculture, with a more massive presence in the South, where climate was more propitious for widescale agricultural activity. By 1790 slavery in the New England States was abolished in Massachusetts, New Hampshire, and Vermont and phased out in Rhode Island and Connecticut. New York introduced gradual emancipation in 1799 (completed in 1827). Pennsylvania abolished slavery during the War for Independence.
Robert Fogel and Stanley Engerman, in their 1974 book Time on the Cross, argued that the rate of return of slavery at the market price was close to ten percent, a number close to investment in other assets. The transition from indentured servants to slaves is cited to show that slaves offered greater profits to their owners. A qualified consensus among economic historians and economists is that "Slave agriculture was efficient compared with free agriculture. Economies of scale, effective management, and intensive utilization of labor and capital made southern slave agriculture considerably more efficient than nonslave southern farming", and it is the near-universal consensus among economic historians and economists that slavery was not "a system irrationally kept in existence by plantation owners who failed to perceive or were indifferent to their best economic interests".
The relative price of slaves and indentured servants in the antebellum period did decrease. Indentured servants became more costly with the increase in the demand of skilled labor in England. At the same time, slaves were mostly supplied from within the United States and thus language was not a barrier, and the cost of transporting slaves from one state to another was relatively low. However, as in Brazil and Europe, slavery at its end in the United States tended to be concentrated in the poorest regions of the United States, with a qualified consensus among economists and economic historians concluding that the "modern period of the South's economic convergence to the level of the North only began in earnest when the institutional foundations of the southern regional labor market were undermined, largely by federal farm and labor legislation dating from the 1930s."
In the decades preceding the Civil War, the black population of the United States experienced a rapid natural increase. Unlike the trans-Saharan slave trade with Africa, the slave population transported by the Atlantic slave trade to the United States was sex-balanced. The slave population multiplied nearly fourfold between 1810 and 1860, despite the passage of the Act Prohibiting Importation of Slaves signed into law by President Thomas Jefferson in 1807 banning the international slave trade. Thus, it is also the universal consensus among modern economic historians and economists that slavery in the United States was not "economically moribund on the eve of the Civil War". In the 2010s, several historians, among them Edward E. Baptist, Sven Beckert, Walter Johnson and Calvin Schermerhorn, have posited that slavery was integral in the development of American capitalism. Other economic historians have rejected that thesis.
Efficiency of slaves
Scholars disagree on how to quantify the efficiency of slavery. In Time on the Cross Fogel and Engerman equate efficiency to total factor productivity (TFP), the output per average unit of input on a farm. Using this measurement, Southern farms that enslaved black people using the gang system were 35% more efficient than Northern farms, which used free labor. Under the gang system, groups of slaves perform synchronized tasks under the constant vigilance of an overseer. Each group was like a part of a machine. If perceived to be working below his capacity, a slave could be punished. Fogel argues that this kind of negative enforcement was not frequent and that slaves and free laborers had a similar quality of life; however, there is controversy on this last point. A critique of Fogel and Engerman's view was published by Paul A. David in 1976.
In 1995, a random survey of 178 members of the Economic History Association sought to study the views of economists and economic historians on the debate. The study found that 72 percent of economists and 65 percent of economic historians would generally agree that "Slave agriculture was efficient compared with free agriculture. Economies of scale, effective management, and intensive utilization of labor and capital made southern slave agriculture considerably more efficient than nonslave southern farming." 48 percent of the economists agreed without provisos, while 24 percent agreed when provisos were included in the statement. On the other hand, 58 percent of economic historians and 42 percent of economists disagreed with Fogel and Engerman's "proposition that the material (not psychological) conditions of the lives of slaves compared favorably with those of free industrial workers in the decades before the Civil War".
Prices of slaves
The U.S. has a capitalist economy so the price of slaves was determine by the law of supply and demand. For example, following bans on the import of slaves after the U.K.'s Slave Trade Act 1807 and the American 1807 Act Prohibiting Importation of Slaves, the prices for slaves increased. The markets for the products produced by slaves also affected the price of slaves (e.g. the price of slaves fell when the price of cotton fell in 1840). Anticipation of slavery's abolition also influenced prices. During the Civil War the price for slave men in New Orleans dropped from $1,381 in 1861 to $1,116 by 1862 (the city was captured by U.S. forces in the Spring of 1862).
Controlling for inflation, prices of slaves rose dramatically in the six decades prior to the Civil War, reflecting demand due to commodity cotton, as well as use of slaves in shipping and manufacturing. Although the prices of slaves relative to indentured servants declined, both got more expensive. Cotton production was rising and relied on the use of slaves to yield high profits. Fogel and Engeman initially argued that if the Civil War had not happened, the slave prices would have increased even more, an average of more than fifty percent by 1890.:96
Prices reflected the characteristics of the slave; such factors as sex, age, nature, and height were all taken into account to determine the price of a slave. Over the life-cycle, the price of enslaved women was higher than their male counterparts up to puberty age, as they would likely bear children who their masters could sell as slaves and could be used as slave laborers. Men around the age of 25 were the most valued, as they were at the highest level of productivity and still had a considerable life-span. Taller male slaves were priced at a higher level, as height was viewed as a proxy for fitness and productivity.
If slaves had a history of fights or escapes, their price was lowered reflecting what planters believed was risk of repeating such behavior. Slave traders and buyers would examine a slave's back for whipping scars; a large number of injuries would be seen as evidence of laziness or rebelliousness, rather than the previous master's brutality, and would lower the slave's price.
Effects on Southern economic development
Five-dollar banknote showing a plantation scene with enslaved people in South Carolina. Issued by the Planters Bank, Winnsboro
, 1853. On display at the British Museum in London.
While slavery brought profits in the short run, discussion continues on the economic benefits of slavery in the long run. In 1995, a random anonymous survey of 178 members of the Economic History Association found that out of the forty propositions about American economic history that were surveyed, the group of propositions most disputed by economic historians and economists were those about the postbellum economy of the American South (along with the Great Depression). The only exception was the proposition initially put forward by historian Gavin Wright that the "modern period of the South's economic convergence to the level of the North only began in earnest when the institutional foundations of the southern regional labor market were undermined, largely by federal farm and labor legislation dating from the 1930s." 62 percent of economists (24 percent with and 38 percent without provisos) and 73 percent of historians (23 percent with and 50 percent without provisos) agreed with this statement. Wright has also argued that the private investment of monetary resources in the cotton industry, among others, delayed development in the South of commercial and industrial institutions. There was little public investment in railroads or other infrastructure. Wright argues that agricultural technology was far more developed in the South, representing an economic advantage of the South over the North of the United States.
In Democracy in America, Alexis de Tocqueville noted that "the colonies in which there were no slaves became more populous and more rich than those in which slavery flourished." Economists Peter H. Lindert and Jeffrey G. Williamson, in a pair of articles published in 2012 and 2013, found that, despite the American South initially having per capita income roughly double that of the North in 1774, incomes in the South had declined 27% by 1800 and continued to decline over the next four decades, while the economies in New England and the Mid-Atlantic states vastly expanded. By 1840, per capita income in the South was well behind the Northeast and the national average (Note: this is also true in the early 21st century).
Lindert and Williamson argue that this antebellum period is an example of what economists Daron Acemoglu, Simon Johnson, and James A. Robinson call "a reversal of fortune". In his essay "The Real History of Slavery", economist Thomas Sowell reiterated and augmented the observation made by de Tocqueville by comparing slavery in the United States to slavery in Brazil. He notes that slave societies reflected similar economic trends in those and other parts of the world, suggesting that the trend Lindert and Williamson identify may have continued until the American Civil War:
Both in Brazil and in the United States – the countries with the two largest slave populations in the Western Hemisphere – the end of slavery found the regions in which slaves had been concentrated poorer than other regions of these same countries. For the United States, a case could be made that this was due to the Civil War, which did so much damage to the South, but no such explanation would apply to Brazil, which fought no Civil War over this issue. Moreover, even in the United States, the South lagged behind the North in many ways even before the Civil War.
Although slavery in Europe died out before it was abolished in the Western Hemisphere, as late as 1776 slavery had not yet died out all across the continent when Adam Smith wrote in The Wealth of Nations that it still existed in some eastern regions. But, even then, Eastern Europe was much poorer than Western Europe. The slavery of North Africa and the Middle East, over the centuries, took more slaves from sub-Saharan Africa than the Western Hemisphere did ... But these remained largely poor countries until the discovery and extraction of their vast oil deposits.
Sowell also notes in Ethnic America: A History, citing historians Clement Eaton and Eugene Genovese, that three-quarters of Southern white families owned no slaves at all. Most slaveholders lived on farms rather than plantations, and few plantations were as large as the fictional ones depicted in Gone with the Wind. In "The Real History of Slavery," Sowell also notes in comparison to slavery in the Arab world and the Middle East (where slaves were seldom used for productive purposes) and China (where the slaves consumed the entire output they created), Sowell observes that many commercial slaveowners in the antebellum South tended to be spendthrift and many lost their plantations due to creditor foreclosures, and in Britain, profits by British slave traders only amounted to two percent of British domestic investment in the 18th century. Sowell draws the following conclusion regarding the macroeconomic value of slavery:
In short, even though some individual slaveowners grew rich and some family fortunes were founded on the exploitation of slaves, that is very different from saying that the whole society, or even its non-slave population as a whole, was more economically advanced than it would have been in the absence of slavery. What this means is that, whether employed as domestic servants or producing crops or other goods, millions suffered exploitation and dehumanization for no higher purpose than the ... aggrandizement of slaveowners.
Eric Hilt noted that, while some historians have suggested slavery was necessary for the Industrial Revolution (on the grounds that American slave plantations produced most of the raw cotton for the British textiles market and the British textiles market was the vanguard of the Industrial Revolution), it is not clear if this is actually true; there is no evidence that cotton could not have been mass-produced by yeoman farmers rather than slave plantations if the latter had not existed (as their existence tended to force yeoman farmers into subsistence farming) and there is some evidence that they certainly could have. The soil and climate of the American South were excellent for growing cotton, so it is not unreasonable to postulate that farms without slaves could have produced substantial amounts of cotton; even if they did not produce as much as the plantations did, it could still have been enough to serve the demand of British producers. Similar arguments have been made by other historians.
Sexual economy of American slavery
Scholar Adrienne Davis articulates how the economics of slavery also can be defined as a sexual economy, specifically focusing on how black women were expected to perform physical, sexual and reproductive labor to provide a consistent enslaved workforce and increase the profits of white slavers. Davis writes that black women were needed for their "sexual and reproductive labor to satisfy the economic, political, and personal interest of white men of the elite class" articulating that black women's reproductive capacity was important in the maintenance of the system of slavery due to its ability to perpetuate an enslaved workforce. She is also drawing attention to black women's labor being needed to maintain the aristocracy of a white ruling class, due to the intimate nature of reproduction and its potential for producing more enslaved peoples.
Due to the institution of partus sequitur ventrem, black women's wombs became the site where slavery was developed and transferred, meaning that black women were not only used for their physical labor, but for their sexual and reproductive labor as well.
"The rule that the children's status follows their mothers' was a foundational one for our economy. It converted enslaved women's reproductive capacity into market capital"
This articulation by Davis illustrates how black women's reproductive capacity was commodified under slavery, and that an analysis of the economic structures of slavery requires an acknowledgment of how pivotal black women's sexuality was in maintaining slavery's economic power. Davis writes how black women performed labor under slavery, writing: "[black women were] male when convenient and horrifically female when needed" The fluctuating expectations of black women's gendered labor under slavery disrupted the white normative roles that were assigned to white men and white women. This ungendering black women received under slavery contributed to the systemic dehumanization experienced by enslaved black women, as they were unable to receive the expectations or experiences of either gender within the white binary.
Davis's arguments addresses the fact that under slavery, black women's sexuality became linked to the economic and public sphere, making their intimate lives into public institutions. Black women's physical labor was gendered as masculine under slavery when they were needed to yield more profit, but their reproductive capacities and sexual labor was equally as important in maintaining white power over black communities and perpetuating an enslaved workforce. This blurring of the line between the private and public sphere is another way Davis articulates how black women's sexuality and reproduction was commodified and exploited for capitalist gain, as their private and intimate lives became disrupted by the violence at the hands of white men, and their sexual capacities became an important part of the public marketplace and United States economy.
Despite this, the slave population transported by the Atlantic slave trade to the United States was sex-balanced and most survived the passage. Despite lacking legal recognition, most slaves in the antebellum South lived in families, unlike the trans-Saharan slave trade with Africa, which was overwhelmingly female and in which the majority died en route crossing the Sahara (with the large majority of the minority of male African slaves dying as a result of crude castration procedures to produce eunuchs, who were in demand as harem attendants).
In 1850, Congress passed the Fugitive Slave Act, as part of the Compromise of 1850, which required law enforcement and citizens of free states to cooperate in the capture and return of slaves. This met with considerable overt and covert resistance in free states and cities such as Philadelphia, New York, and Boston. Refugees from slavery continued to flee the South across the Ohio River and other parts of the Mason–Dixon line dividing North from South, to the North and Canada via the Underground Railroad. Some white Northerners helped hide former slaves from their former owners or helped them reach freedom in Canada.
As part of the Compromise of 1850, Congress abolished the slave trade (though not the ownership of slaves) in the District of Columbia; fearing this would happen, Alexandria, regional slave trading center and port, successfully sought its removal from the District of Columbia and devolution to Virginia. After 1854, Republicans argued that the "Slave Power", especially the pro-slavery Democratic Party in the South, controlled two of the three branches of the Federal government.
The abolitionists, realizing that the total elimination of slavery was unrealistic as an immediate goal, worked to prevent the expansion of slavery into the western territories which eventually would be new states. The Missouri Compromise, the Compromise of 1850, and the Bleeding Kansas period dealt with whether new states would be slave or free, or how that was to be decided. Both sides were anxious about effects of these decisions on the balance of power in the Senate.
After the passage of the Kansas–Nebraska Act in 1854, border fighting broke out in the Kansas Territory, where the question of whether it would be admitted to the Union as a slave or free state was left to the inhabitants. Migrants from both free and slave states moved into the territory to prepare for the vote on slavery. Abolitionist John Brown, the most famous of the anti-slavery immigrants, was active in the fighting in "Bleeding Kansas," but so too were many white Southerners (many from adjacent Missouri) who opposed abolition.
Abraham Lincoln's and the Republicans' political platform in 1860 was to stop slavery's expansion. Historian James McPherson says that in his famous "House Divided" speech in 1858, Lincoln said American republicanism can be purified by restricting the further expansion of slavery as the first step to putting it on the road to 'ultimate extinction.' Southerners took Lincoln at his word. When he won the presidency, they left the Union to escape the 'ultimate extinction' of slavery."
Freedom suits and Dred Scott
With the development of slave and free states after the American Revolution, and far-flung commercial and military activities, new situations arose in which slaves might be taken by masters into free states. Most free states not only prohibited slavery, but ruled that slaves brought and kept there illegally could be freed. Such cases were sometimes known as transit cases. Dred Scott and his wife Harriet Scott each sued for freedom in St. Louis after the death of their master, based on their having been held in a free territory (the northern part of the Louisiana Purchase from which slavery was excluded under the terms of the Missouri Compromise). (Later the two cases were combined under Dred Scott's name.) Scott filed suit for freedom in 1846 and went through two state trials, the first denying and the second granting freedom to the couple (and, by extension, their two daughters, who had also been held illegally in free territories). For 28 years, Missouri state precedent had generally respected laws of neighboring free states and territories, ruling for freedom in such transit cases where slaves had been held illegally in free territory. But in the Dred Scott case, the State Supreme Court ruled against the slaves.
After Scott and his team appealed the case to the U.S. Supreme Court, Chief Justice Roger B. Taney, in a sweeping decision, denied Scott his freedom. The 1857 decision, decided 7–2, held that a slave did not become free when taken into a free state; Congress could not bar slavery from a territory; and people of African descent imported into the United States and held as slaves, or their descendants, could never be citizens and thus had no status to bring suit in a U.S. court. A state could not bar slaveowners from bringing slaves into that state. Many Republicans, including Abraham Lincoln, considered the decision unjust and evidence that the Slave Power had seized control of the Supreme Court. Anti-slavery groups were enraged and slave owners encouraged, escalating the tensions that led to civil war.
Civil War and emancipation
1860 presidential election
The divisions became fully exposed with the 1860 presidential election. The electorate split four ways. The Southern Democrats endorsed slavery, while the Republicans denounced it. The Northern Democrats said democracy required the people to decide on slavery locally, state by state and territory by territory. The Constitutional Union Party said the survival of the Union was at stake and everything else should be compromised.
Lincoln, the Republican, won with a plurality of popular votes and a majority of electoral votes. Lincoln, however, did not appear on the ballots of ten southern slave states. Many slave owners in the South feared that the real intent of the Republicans was the abolition of slavery in states where it already existed, and that the sudden emancipation of four million slaves would be disastrous for the slave owners and for the economy that drew its greatest profits from the labor of people who were not paid. The slave owners feared that ending the balance could lead to the domination of the federal government by the northern free states. This led seven southern states to secede from the Union. When the southern forces attacked a U.S. Army installation at Fort Sumter, the American Civil War began and four additional slave states seceded. Northern leaders had viewed the slavery interests as a threat politically, but with secession, they viewed the prospect of a new Southern nation, the Confederate States of America, with control over the Mississippi River and parts of the West, as politically unacceptable. Most of all, they could not accept this repudiation of American nationalism.
The consequent American Civil War, beginning in 1861, led to the end of chattel slavery in America. Not long after the war broke out, through a legal maneuver credited to Union General Benjamin F. Butler, a lawyer by profession, slaves who came into Union "possession" were considered "contraband of war". General Butler ruled that they were not subject to return to Confederate owners as they had been before the war. Soon word spread, and many slaves sought refuge in Union territory, desiring to be declared "contraband". Many of the "contrabands" joined the Union Army as workers or troops, forming entire regiments of the U.S. Colored Troops. Others went to refugee camps such as the Grand Contraband Camp near Fort Monroe or fled to northern cities. General Butler's interpretation was reinforced when Congress passed the Confiscation Act of 1861, which declared that any property used by the Confederate military, including slaves, could be confiscated by Union forces.
At the beginning of the war, some Union commanders thought they were supposed to return escaped slaves to their masters. By 1862, when it became clear that this would be a long war, the question of what to do about slavery became more general. The Southern economy and military effort depended on slave labor. It began to seem unreasonable to protect slavery while blockading Southern commerce and destroying Southern production. As Congressman George W. Julian of Indiana put it in an 1862 speech in Congress, the slaves "cannot be neutral. As laborers, if not as soldiers, they will be allies of the rebels, or of the Union." Julian and his fellow Radical Republicans put pressure on Lincoln to rapidly emancipate the slaves, whereas moderate Republicans came to accept gradual, compensated emancipation and colonization. Copperheads, the border states and War Democrats opposed emancipation, although the border states and War Democrats eventually accepted it as part of total war needed to save the Union.
The Emancipation Proclamation was an executive order issued by President Lincoln on January 1, 1863. In a single stroke it changed the legal status, as recognized by the U.S. government, of three million slaves in designated areas of the Confederacy from "slave" to "free". It had the practical effect that as soon as a slave escaped the control of the Confederate government, by running away or through advances of federal troops, the slave became legally and actually free. Plantation owners, realizing that emancipation would destroy their economic system, sometimes moved their slaves as far as possible out of reach of the Union army. By June 1865, the Union Army controlled all of the Confederacy and had liberated all of the designated slaves.
In 1861, Lincoln expressed the fear that premature attempts at emancipation would mean the loss of the border states. He believed that "to lose Kentucky is nearly the same as to lose the whole game." At first, Lincoln reversed attempts at emancipation by Secretary of War Simon Cameron and Generals John C. Fremont (in Missouri) and David Hunter (in South Carolina, Georgia and Florida) to keep the loyalty of the border states and the War Democrats.
Escaped slaves, ca. 1862, at the headquarters of General Lafayette
Lincoln mentioned his Emancipation Proclamation to members of his cabinet on July 21, 1862. Secretary of State William H. Seward told Lincoln to wait for a victory before issuing the proclamation, as to do otherwise would seem like "our last shriek on the retreat". In September 1862 the Battle of Antietam provided this opportunity, and the subsequent War Governors' Conference added support for the proclamation. Lincoln had already published a letter encouraging the border states especially to accept emancipation as necessary to save the Union. Lincoln later said that slavery was "somehow the cause of the war".
Lincoln issued his preliminary Emancipation Proclamation on September 22, 1862, and said that a final proclamation would be issued if his gradual plan, based on compensated emancipation and voluntary colonization, was rejected. Only the District of Columbia accepted Lincoln's gradual plan, and Lincoln issued his final Emancipation Proclamation on January 1, 1863. In his letter to Hodges, Lincoln explained his belief that
If slavery is not wrong, nothing is wrong ... And yet I have never understood that the Presidency conferred upon me an unrestricted right to act officially upon this judgment and feeling ... I claim not to have controlled events, but confess plainly that events have controlled me.
Lincoln's Emancipation Proclamation of January 1, 1863 was a powerful action that promised freedom for slaves in the Confederacy as soon as the Union armies reached them, and authorized the enlistment of African Americans in the Union Army. The Emancipation Proclamation did not free slaves in the Union-allied slave-holding states that bordered the Confederacy. Since the Confederate States did not recognize the authority of President Lincoln, and the proclamation did not apply in the border states, at first the proclamation freed only those slaves who had escaped behind Union lines. The proclamation made the abolition of slavery an official war goal that was implemented as the Union took territory from the Confederacy. According to the Census of 1860, this policy would free nearly four million slaves, or over 12% of the total population of the United States.
Based on the President's war powers, the Emancipation Proclamation applied to territory held by Confederates at the time. However, the Proclamation became a symbol of the Union's growing commitment to add emancipation to the Union's definition of liberty. Lincoln played a leading role in getting the constitutionally required two-thirds majority of both houses of Congress to vote for the Thirteenth Amendment, which made emancipation universal and permanent.
Enslaved African Americans had not waited for Lincoln before escaping and seeking freedom behind Union lines. From the early years of the war, hundreds of thousands of African Americans escaped to Union lines, especially in Union-controlled areas such as Norfolk and the Hampton Roads region in 1862 Virginia, Tennessee from 1862 on, the line of Sherman's march, etc. So many African Americans fled to Union lines that commanders created camps and schools for them, where both adults and children learned to read and write. The American Missionary Association entered the war effort by sending teachers south to such contraband camps, for instance, establishing schools in Norfolk and on nearby plantations.
In addition, nearly 200,000 African-American men served with distinction in the Union forces as soldiers and sailors; most were escaped slaves. The Confederacy was outraged by armed black soldiers and refused to treat them as prisoners of war. They murdered many, as at the Fort Pillow Massacre, and re-enslaved others.
The Arizona Organic Act abolished slavery on February 24, 1863, in the newly formed Arizona Territory. Tennessee and all of the border states (except Kentucky and Delaware) abolished slavery by early 1865. Thousands of slaves were freed by the operation of the Emancipation Proclamation as Union armies marched across the South. Emancipation came to the remaining southern slaves after the surrender of all Confederate troops in spring 1865.
In spite of the South's shortage of manpower, until 1865, most Southern leaders opposed arming slaves as soldiers. However, a few Confederates discussed arming slaves. Finally in early 1865 General Robert E. Lee said black soldiers were essential, and legislation was passed. The first black units were in training when the war ended in April.
End of slavery
Booker T. Washington remembered Emancipation Day in early 1863, when he was a boy of 9 in Virginia:
As the great day drew nearer, there was more singing in the slave quarters than usual. It was bolder, had more ring, and lasted later into the night. Most of the verses of the plantation songs had some reference to freedom. ... Some man who seemed to be a stranger (a United States officer, I presume) made a little speech and then read a rather long paper – the Emancipation Proclamation, I think. After the reading we were told that we were all free, and could go when and where we pleased. My mother, who was standing by my side, leaned over and kissed her children, while tears of joy ran down her cheeks. She explained to us what it all meant, that this was the day for which she had been so long praying, but fearing that she would never live to see.
Abolition of slavery in the various states of the US over time:
Abolition of slavery during or shortly after the American Revolution
The Northwest Ordinance, 1787
Gradual emancipation in New York (starting 1799) and New Jersey (starting 1804)
The Missouri Compromise, 1821
Effective abolition of slavery by Mexican or joint US/British authority
Abolition of slavery by Congressional action, 1861
Abolition of slavery by Congressional action, 1862ff.
Emancipation Proclamation as originally issued, 1 Jan 1863
Subsequent operation of the Emancipation Proclamation in 1863
Abolition of slavery by state action during the Civil War
Operation of the Emancipation Proclamation in 1864
Operation of the Emancipation Proclamation in 1865
Thirteenth Amendment to the US constitution, 18 Dec 1865
Territory incorporated into the US after the passage of the Thirteenth Amendment
The war ended on June 22, 1865, and following that surrender, the Emancipation Proclamation was enforced throughout remaining regions of the South that had not yet freed the slaves. Slavery officially continued for a couple of months in other locations. Federal troops arrived in Galveston, Texas, on June 19, 1865, to enforce the emancipation. The commemoration of that event, Juneteenth National Independence Day, has been declared a national holiday in 2021.
The Thirteenth Amendment, abolishing slavery except as punishment for a crime, had been passed by the Senate in April 1864, and by the House of Representatives in January 1865.
The amendment did not take effect until it was ratified by three-fourths of the states, which occurred on December 6, 1865, when Georgia ratified it. On that date, the last 40,000–45,000 enslaved Americans were freed in the remaining two slave states of Kentucky and Delaware, and the 200 or so perpetual apprentices in New Jersey, left from the very gradual emancipation process begun in 1804.
The American historian R. R. Palmer opined that the abolition of slavery in the United States without compensation to the former slave owners was an "annihilation of individual property rights without parallel ...in the history of the Western world". Economic historian Robert E. Wright argues that it would have been much cheaper, with minimal deaths, if the federal government had purchased and freed all the slaves, rather than fighting the Civil War. Another economic historian, Roger Ransom, writes that Gerald Gunderson compared compensated emancipation to the cost of the war and "notes that the two are roughly the same order of magnitude – 2.5 to 3.7 billion dollars". Ransom also writes that compensated emancipation would have tripled federal outlays if paid over the period of 25 years and was a program that had no political support within the United States during the 1860s.
Reconstruction to the present
Journalist Douglas A. Blackmon reported in his Pulitzer Prize-winning book Slavery By Another Name that many black persons were virtually enslaved under convict leasing programs, which started after the Civil War. Most Southern states had no prisons; they leased convicts to businesses and farms for their labor, and the lessee paid for food and board. The incentives for abuse were satisfied.
The continued involuntary servitude took various forms, but the primary forms included convict leasing, peonage, and sharecropping, with the latter eventually encompassing poor whites as well. By the 1930s, whites constituted most of the sharecroppers in the South. Mechanization of agriculture had reduced the need for farm labor, and many black people left the South in the Great Migration. Jurisdictions and states created fines and sentences for a wide variety of minor crimes and used these as an excuse to arrest and sentence black people. Under convict leasing programs, African American men, often guilty of no crime at all, were arrested, compelled to work without pay, repeatedly bought and sold, and coerced to do the bidding of the leaseholder. Sharecropping, as it was practiced during this period, often involved severe restrictions on the freedom of movement of sharecroppers, who could be whipped for leaving the plantation. Both sharecropping and convict leasing were legal and tolerated by both the North and South. However, peonage was an illicit form of forced labor. Its existence was ignored by authorities while thousands of African Americans and poor Anglo-Americans were subjugated and held in bondage until the mid-1960s to the late 1970s. With the exception of cases of peonage, beyond the period of Reconstruction, the federal government took almost no action to enforce the 13th Amendment until December 1941 when President Franklin Delano Roosevelt summoned his attorney general. Five days after Pearl Harbor, at the request of the President, Attorney General Francis Biddle issued Circular No. 3591 to all federal prosecutors, instructing them to actively investigate and try any case of involuntary servitude or slavery. Several months later, convict leasing was officially abolished. But aspects have persisted in other forms. Historians argue that other systems of penal labor were all created in 1865, and convict leasing was simply the most oppressive form. Over time a large civil rights movement arose to bring full civil rights and equality under the law to all Americans.
With emancipation a legal reality, white Southerners were concerned with both controlling the newly freed slaves and keeping them in the labor force at the lowest level. The system of convict leasing began during Reconstruction and was fully implemented in the 1880s and officially ending in the last state, Alabama, in 1928. It persisted in various forms until it was abolished in 1942 by President Franklin D. Roosevelt during World War II, several months after the attack on Pearl Harbor involved the U.S. in the conflict. This system allowed private contractors to purchase the services of convicts from the state or local governments for a specific time period. African Americans, due to "vigorous and selective enforcement of laws and discriminatory sentencing," made up the vast majority of the convicts leased. Writer Douglas A. Blackmon writes of the system:
It was a form of bondage distinctly different from that of the antebellum South in that for most men, and the relatively few women drawn in, this slavery did not last a lifetime and did not automatically extend from one generation to the next. But it was nonetheless slavery – a system in which armies of free men, guilty of no crimes and entitled by law to freedom, were compelled to labor without compensation, were repeatedly bought and sold, and were forced to do the bidding of white masters through the regular application of extraordinary physical coercion.
The constitutional basis for convict leasing is that the Thirteenth Amendment, while abolishing slavery and involuntary servitude generally, expressly permits it as a punishment for crime.
An industrial school set up for ex-slaves in Richmond during Reconstruction
The anti-literacy laws after 1832 contributed greatly to the problem of widespread illiteracy facing the freedmen and other African Americans after Emancipation and the Civil War 35 years later. The problem of illiteracy and need for education was seen as one of the greatest challenges confronting these people as they sought to join the free enterprise system and support themselves during Reconstruction and thereafter.
Consequently, many black and white religious organizations, former Union Army officers and soldiers, and wealthy philanthropists were inspired to create and fund educational efforts specifically for the betterment of African Americans; some African Americans had started their own schools before the end of the war. Northerners helped create numerous normal schools, such as those that became Hampton University and Tuskegee University, to generate teachers, as well as other colleges for former slaves. Blacks held teaching as a high calling, with education the first priority for children and adults. Many of the most talented went into the field. Some of the schools took years to reach a high standard, but they managed to get thousands of teachers started. As W. E. B. Du Bois noted, the black colleges were not perfect, but "in a single generation they put thirty thousand black teachers in the South" and "wiped out the illiteracy of the majority of black people in the land".
Northern philanthropists continued to support black education in the 20th century, even as tensions rose within the black community, exemplified by Booker T. Washington and W. E. B. Du Bois, as to the proper emphasis between industrial and classical academic education at the college level. An example of a major donor to Hampton Institute and Tuskegee was George Eastman, who also helped fund health programs at colleges and in communities. Collaborating with Washington in the early decades of the 20th century, philanthropist Julius Rosenwald provided matching funds for community efforts to build rural schools for black children. He insisted on white and black cooperation in the effort, wanting to ensure that white-controlled school boards made a commitment to maintain the schools. By the 1930s local parents had helped raise funds (sometimes donating labor and land) to create over 5,000 rural schools in the South. Other philanthropists, such as Henry H. Rogers and Andrew Carnegie, each of whom had arisen from modest roots to become wealthy, used matching fund grants to stimulate local development of libraries and schools.
On February 24, 2007, the Virginia General Assembly passed House Joint Resolution Number 728 acknowledging "with profound regret the involuntary servitude of Africans and the exploitation of Native Americans, and call for reconciliation among all Virginians". With the passing of this resolution, Virginia became the first state to acknowledge through the state's governing body their state's negative involvement in slavery. The passing of this resolution was in anticipation of the 400th anniversary commemoration of the founding of Jamestown, Virginia (the first permanent English settlement in North America), which was an early colonial slave port. Apologies have also been issued by Alabama, Florida, Maryland, North Carolina and New Jersey.
On July 29, 2008, during the 110th United States Congress session, the United States House of Representatives passed a resolution 'HR. 194' apologizing for American slavery and subsequent discriminatory laws.
The U.S. Senate unanimously passed a similar resolution on June 18, 2009, apologizing for the "fundamental injustice, cruelty, brutality, and inhumanity of slavery". It also explicitly states that it cannot be used for restitution claims.
A 2016 study, published in The Journal of Politics, finds that "Whites who currently live in Southern counties that had high shares of slaves in 1860 are more likely to identify as a Republican, oppose affirmative action, and express racial resentment and colder feelings toward blacks." The study contends that "contemporary differences in political attitudes across counties in the American South in part trace their origins to slavery's prevalence more than 150 years ago. " The authors argue that their findings are consistent with the theory that "following the Civil War, Southern whites faced political and economic incentives to reinforce existing racist norms and institutions to maintain control over the newly freed African American population. This amplified local differences in racially conservative political attitudes, which in turn have been passed down locally across generations."
A 2017 study in the British Journal of Political Science argued that the British American colonies without slavery adopted better democratic institutions in order to attract migrant workers to their colonies.
Native Americans as slaves
During the 17th and 18th centuries, Indian slavery, the enslavement of Native Americans by European colonists, was common. Many of these Native slaves were exported to the Northern colonies and to off-shore colonies, especially the "sugar islands" of the Caribbean. The exact number of Native Americans who were enslaved is unknown because vital statistics and census reports were at best infrequent. Historian Alan Gallay estimates that from 1670 to 1715, British slave traders sold between 24,000 and 51,000 Native Americans from what is now the southern part of the U.S. Andrés Reséndez estimates that between 147,000 and 340,000 Native Americans were enslaved in North America, excluding Mexico. Even after the Indian Slave Trade ended in 1750 the enslavement of Native Americans continued in the west, and also in the Southern states mostly through kidnappings.
Slavery of Native Americans was organized in colonial and Mexican California through Franciscan missions, theoretically entitled to ten years of Native labor, but in practice maintaining them in perpetual servitude, until their charge was revoked in the mid-1830s. Following the 1847–48 invasion by U.S. troops, the "loitering or orphaned Indians" were de facto enslaved in the new state from statehood in 1850 to 1867. Slavery required the posting of a bond by the slave holder and enslavement occurred through raids and a four-month servitude imposed as a punishment for Indian "vagrancy".
Native Americans holding African-American slaves
After 1800, some of the Cherokee and the other four civilized tribes of the Southeast started buying and using black slaves as labor. They continued this practice after removal to Indian Territory in the 1830s, when as many as 15,000 enslaved blacks were taken with them.
The nature of slavery in Cherokee society often mirrored that of white slave-owning society. The law barred intermarriage of Cherokees and enslaved African Americans, but Cherokee men had unions with enslaved women, resulting in mixed-race children. Cherokee who aided slaves were punished with one hundred lashes on the back. In Cherokee society, persons of African descent were barred from holding office even if they were also racially and culturally Cherokee. They were also barred from bearing arms and owning property. The Cherokee prohibited the teaching of African Americans to read and write.
By contrast, the Seminole welcomed into their nation African Americans who had escaped slavery (Black Seminoles). Historically, the Black Seminoles lived mostly in distinct bands near the Native American Seminole. Some were held as slaves of particular Seminole leaders. Seminole practice in Florida had acknowledged slavery, though not the chattel slavery model common elsewhere. It was, in fact, more like feudal dependency and taxation. The relationship between Seminole blacks and natives changed following their relocation in the 1830s to territory controlled by the Creek who had a system of chattel slavery. Pro slavery pressure from Creek and pro-Creek Seminole and slave raiding led to many Black Seminoles escaping to Mexico.
The Haida and Tlingit Indians who lived along the southeastern Alaskan coast were traditionally known as fierce warriors and slave-traders, raiding as far as California. Slavery was hereditary after slaves were taken as prisoners of war. Among some Pacific Northwest tribes, about a quarter of the population were slaves. Other slave-owning tribes of North America were, for example, Comanche of Texas, Creek of Georgia, the fishing societies, such as the Yurok, that lived along the coast from what is now Alaska to California; the Pawnee, and Klamath.
Some tribes held people as captive slaves late in the 19th century. For instance, "Ute Woman", was a Ute captured by the Arapaho and later sold to a Cheyenne. She was kept by the Cheyenne to be used as a prostitute to serve American soldiers at Cantonment in the Indian Territory. She lived in slavery until about 1880. She died of a hemorrhage resulting from "excessive sexual intercourse".
Black slave owners
Slave owners included a comparatively small number of people of at least partial African ancestry, in each of the original thirteen colonies and later states and territories that allowed slavery; in some early cases black Americans also had white indentured servants. An African former indentured servant who settled in Virginia in 1621, Anthony Johnson, became one of the earliest documented slave owners in the mainland American colonies when he won a civil suit for ownership of John Casor. In 1830 there were 3,775 black (including, mixed race) slaveholders in the South who owned a total of 12,760 slaves, which was a small percentage of a total of over two million slaves then held in the South. 80% of the black slaveholders were located in Louisiana, South Carolina, Virginia and Maryland.
There were economic and ethnic differences between free blacks of the Upper South and the Deep South, with the latter fewer in number, but wealthier and typically of mixed race. Half of the black slaveholders lived in cities rather than the countryside, with most living in New Orleans and Charleston. In particular, New Orleans had a large, relatively wealthy free black population (gens de couleur) composed of people of mixed race, who had become a third social class between whites and enslaved blacks, under French and Spanish colonial rule. Relatively few non-white slaveholders were substantial planters; of those who were, most were of mixed race, often endowed by white fathers with some property and social capital. For example, Andrew Durnford of New Orleans was listed as owning 77 slaves. According to Rachel Kranz: "Durnford was known as a stern master who worked his slaves hard and punished them often in his efforts to make his Louisiana sugar plantation a success." In the years leading up to the Civil War, Antoine Dubuclet, who owned over a hundred slaves, was considered the wealthiest black slaveholder in Louisiana.
The historians John Hope Franklin and Loren Schweninger wrote:
A large majority of profit-oriented free black slaveholders resided in the Lower South. For the most part, they were persons of mixed racial origin, often women who cohabited or were mistresses of white men, or mulatto men ... Provided land and slaves by whites, they owned farms and plantations, worked their hands in the rice, cotton, and sugar fields, and like their white contemporaries were troubled with runaways.
The historian Ira Berlin wrote:
In slave societies, nearly everyone – free and slave – aspired to enter the slaveholding class, and upon occasion some former slaves rose into slaveholders' ranks. Their acceptance was grudging, as they carried the stigma of bondage in their lineage and, in the case of American slavery, color in their skin.
African-American history and culture scholar Henry Louis Gates Jr. wrote:
... the percentage of free black slave owners as the total number of free black heads of families was quite high in several states, namely 43 percent in South Carolina, 40 percent in Louisiana, 26 percent in Mississippi, 25 percent in Alabama and 20 percent in Georgia.
Free blacks were perceived "as a continual symbolic threat to slaveholders, challenging the idea that 'black' and 'slave' were synonymous". Free blacks were sometimes seen as potential allies of fugitive slaves and "slaveholders bore witness to their fear and loathing of free blacks in no uncertain terms." For free blacks, who had only a precarious hold on freedom, "slave ownership was not simply an economic convenience but indispensable evidence of the free blacks' determination to break with their slave past and their silent acceptance – if not approval – of slavery."
The historian James Oakes in 1982 stated that "[t]he evidence is overwhelming that the vast majority of black slaveholders were free men who purchased members of their families or who acted out of benevolence". After 1810, Southern states made it increasingly difficult for any slaveholders to free slaves. Often the purchasers of family members were left with no choice but to maintain, on paper, the owner–slave relationship. In the 1850s "there were increasing efforts to restrict the right to hold bondsmen on the grounds that slaves should be kept 'as far as possible under the control of white men only.'"
In his 1985 statewide study of black slaveholders in South Carolina, Larry Koger challenged this benevolent view. He found that the majority of mixed-race or black slaveholders appeared to hold at least some of their slaves for commercial reasons. For instance, he noted that in 1850 more than 80% of black slaveholders were of mixed race, but nearly 90% of their slaves were classified as black. Koger also noted that many South Carolina free blacks operated small businesses as skilled artisans, and many owned slaves working in those businesses. "Koger emphasizes that it was all too common for freed slaves to become slaveholders themselves."
Some free black slaveholders in New Orleans offered to fight for Louisiana in the Civil War. Over 1,000 free black people volunteered and formed the 1st Louisiana Native Guard (CSA), which was disbanded without even seeing combat.
Distribution of slaves
Percentage of slaves in each county of the slave states in 1860
|Source:"Distribution of Slaves in US History". Retrieved May 13, 2010.
Evolution of the enslaved population of the United States as a percentage of the population of each state, 1790–1860
Total Slave Population in US 1790–1860, by State and Territory
|District of Columbia
For various reasons, the census did not always include all of the slaves, especially in the West. California was admitted as a free state and reported no slaves. However, there were many slaves that were brought to work in the mines during the California Gold Rush. Some Californian communities openly tolerated slavery, such as San Bernardino, which was mostly made up of transplants from the neighboring slave territory of Utah. New Mexico Territory never reported any slaves on the census, yet sued the government for compensation for 600 slaves that were freed when Congress outlawed slavery in the territory. Utah was actively trying to hide its slave population from Congress and did not report slaves in several communities. Additionally, the census did not traditionally include Native Americans, and hence did not include Native American slaves or Native African slaves owned by Native Americans. There were hundreds of Native American slaves in California, Utah and New Mexico that were never recorded in the census.
Distribution of slaveholders
As of the 1860 Census, one may compute the following statistics on slaveholding:
- Enumerating slave schedules by county, 393,975 named persons held 3,950,546 unnamed slaves, for an average of about ten slaves per holder. As some large holders held slaves in multiple counties and are thus multiply counted, this slightly overestimates the number of slaveholders.
- Excluding slaves, the 1860 U.S. population was 27,167,529; therefore, approximately 1.45% of free persons (roughly one in 69) was a named slaveholder (393,975 named slaveholders among 27,167,529 free persons). By counting only named slaveholders, this approach does not acknowledge people who benefited from slavery by being in a slaveowning household, e.g., the wife and children of an owner; in 1850, there was an average of 5.55 people per household, so on average, around 8.05% of free persons lived in a slave-owning household. In the South, 33% of families owned at least one slave. According to historian Joseph Glatthaar, the number of soldiers of the Confederacy's Army of Northern Virginia who either owned slaves or came from slave owning households is "almost one of every two 1861 recruits". In addition he notes that, "Untold numbers of enlistees rented land from, sold crops to, or worked for slaveholders. In the final tabulation, the vast majority of the volunteers of 1861 had a direct connection to slavery."
- It is estimated by the transcriber Tom Blake, that holders of 200 or more slaves, constituting less than 1% of all U.S. slaveholders (fewer than 4,000 persons, one in 7,000 free persons, or 0.015% of the population) held an estimated 20–30% of all slaves (800,000 to 1,200,000 slaves). Nineteen holders of 500 or more slaves have been identified. The largest slaveholder was Joshua John Ward, of Georgetown, South Carolina, who in 1850 held 1,092 slaves, and whose heirs in 1860 held 1,130 or 1,131 slaves – he was dubbed "the king of the rice planters", and one of his plantations is now part of Brookgreen Gardens.
- The percentage of families that owned slaves in 1860 in various groupings of states was as follows:
|Group of States
||States in Group
|15 states where slavery was legal
||Alabama, Arkansas, Delaware, Florida, Georgia, Kentucky, Louisiana, Maryland, Mississippi, Missouri, North Carolina, South Carolina, Tennessee, Texas, Virginia
|11 states that seceded
||Alabama, Arkansas, Florida, Georgia, Louisiana, Mississippi, North Carolina, South Carolina, Tennessee, Texas, Virginia
|7 states that seceded before Lincoln's inauguration
||Alabama, Florida, Georgia, Louisiana, Mississippi, South Carolina, Texas
|4 states that seceded later
||Arkansas, North Carolina, Tennessee, Virginia
|4 slave states that did not secede
||Delaware, Kentucky, Maryland, Missouri
The historian Peter Kolchin, writing in 1993, noted that until the latter decades of the 20th century, historians of slavery had primarily concerned themselves with the culture, practices and economics of the slaveholders, not with the slaves. This was in part due to the circumstance that most slaveholders were literate and left behind written records, whereas slaves were largely illiterate and not in a position to leave written records. Scholars differed as to whether slavery should be considered a benign or a "harshly exploitive" institution.
Much of the history written prior to the 1950s had a distinctive racist slant to it. By the 1970s and 1980s, historians were using archaeological records, black folklore and statistical data to develop a much more detailed and nuanced picture of slave life. Individuals were shown to have been resilient and somewhat autonomous in many of their activities, within the limits of their situation and despite its precariousness. Historians who wrote in this era include John Blassingame (Slave Community), Eugene Genovese (Roll, Jordan, Roll), Leslie Howard Owens (This Species of Property), and Herbert Gutman (The Black Family in Slavery and Freedom).
History of slavery in individual states and territories
- ^ Wood, Peter (2003). "The Birth of Race-Based Slavery". Slate. (May 19, 2015): Reprinted from Strange New Land: Africans in Colonial America by Peter H. Wood with permission from Oxford University Press. ©1996, 2003.
- ^ Douglass, Frederick (1849). "The Constitution and Slavery".
- ^ a b Smith, Julia Floyd (1973). Slavery and Plantation Growth in Antebellum Florida, 1821–1860. Gainesville: University of Florida Press. pp. 44–46. ISBN 978-0-8130-0323-8.
- ^ McDonough, Gary W. (1993). The Florida Negro. A Federal Writers' Project Legacy. University Press of Mississippi. ISBN 978-0878055883.
- ^ Stephen D. Behrendt, David Richardson, and David Eltis, W. E. B. Du Bois Institute for African and African-American Research, Harvard University. Based on "records for 27,233 voyages that set out to obtain slaves for the Americas". Stephen Behrendt (1999). "Transatlantic Slave Trade". Africana: The Encyclopedia of the African and African American Experience. New York: Basic Civitas Books. ISBN 978-0-465-00071-5.
- ^ Introduction – Social Aspects of the Civil War Archived July 14, 2007, at the Wayback Machine, National Park Service.
- ^ López León, Dorian. "Puerto Rico in the 16th century – History". Encyclopedia de Puerto Rico. Puerto Rico Endowment for the Humanities, and the National Endowment for the Humanities. Retrieved June 29, 2020.
- ^ Ethridge, From Chicaza to Chickasaw (2010), pp. 97–98.
- ^ Ethridge, From Chicaza to Chickasaw (2010), p. 109.
- ^ Ethridge, From Chicaza to Chickasaw (2010), p. 65.
- ^ a b c Gallay, Alan. (2002) The Indian Slave Trade: The Rise of the English Empire in the American South 1670–1717. Yale University Press: New York. ISBN 0-300-10193-7, pg. 299
- ^ Figures cited in Ethridge, From Chicaza to Chickasaw (2010), p. 237.
- ^ a b Robert Wright, Richard (1941). "Negro Companions of the Spanish Explorers". Phylon. 2 (4).
- ^ "St. Augustine, Florida founded". African American Registry. Retrieved November 15, 2019.
- ^ "Civil Rights in Colonial St. Augustine (U.S. National Park Service)". www.nps.gov. Retrieved August 7, 2020.
- ^ Richard Hofstadter, "White Servitude" Archived October 9, 2014, at the Wayback Machine, n.d., Montgomery College. Retrieved January 11, 2012.
- ^ 1.Deborah Gray White, Mia Bay, and Waldo E. Martin, Jr., Freedom on My Mind: A History of African Americans (New York: Bedford/St. Martin's, 2013), 59.
- ^ Behrendt, Stephen (2005). "Transatlantic Slave Trade". In Appiah, Kwame Anthony; Gates Jr., Henry Louis (eds.). Africana: The Encyclopedia of the African and African American Experience. 5 (Second ed.). Oxford: Oxford University Press. p. 199. ISBN 978-0-19-517055-9. Retrieved April 9, 2017.
- ^ "African Americans at Jamestown". National Park Service. February 26, 2015. Retrieved June 4, 2019.
Arrival of "20 and odd" Africans in late August 1619, not aboard a Dutch ship as reported by John Rolfe, but an English warship, White Lion, sailing with a letters of marque issued to the British Captain Jope by the Protestant Dutch Prince Maurice, son of William of Orange. A letters of marque legally permitted the White Lion to sail as a privateer attacking any Spanish or Portuguese ships it encountered. The 20 and odd Africans were captives removed from the Portuguese slave ship, San Juan Bautista, following an encounter the ship had with the White Lion and her consort, the Treasurer, another British ship, while attempting to deliver its African prisoners to Mexico. Rolfe's reporting the White Lion as a Dutch warship was a clever ruse to transfer blame away from the British for piracy of the slave ship to the Dutch.
- ^ Rein, Lisa (September 3, 2006). "Mystery of Va.'s First Slaves Is Unlocked 400 Years Later". The Washington Post. Retrieved June 4, 2019.
- ^ Knight, Kathryn (2010). "The First Africans". Historic Jamestowne. Retrieved June 4, 2019.
Nearing her destination, the slave ship was attacked by two English privateers, the White Lion and the Treasurer, in the Gulf of Mexico and robbed of 50–60 Africans.
- ^ Beth Austin (December 2019). "1619: Virginia's First Africans". Hampton History Museum. Retrieved June 29, 2021.
- ^ a b Donoghue, John (2010). Out of the Land of Bondage": The English Revolution and the Atlantic Origins of Abolition. The American Historical Review. Archived from the original on September 4, 2015.
- ^ Higginbotham, A. Leon (1975). In the Matter of Color: Race and the American Legal Process: The Colonial Period. Greenwood Press. ISBN 9780195027457.
- ^ Tom Costa (2011). "Runaway Slaves and Servants in Colonial Virginia". Encyclopedia Virginia.
- ^ "Assessing the Slave Trade: Estimates". The Trans-Atlantic Slave Trade Database. Emory University, Atlanta, Georgia.
- ^ a b Higginbotham, A. Leon (1975). In the Matter of Color: Race and the American Legal Process: The Colonial Period. Greenwood Press. ISBN 9780195027457.
- ^ William M. Wiecek (1977). "the Statutory Law of Slavery and Race in the Thirteen Mainland Colonies of British America". The William and Mary Quarterly. 34 (2): 258–280. doi:10.2307/1925316. JSTOR 1925316.
- ^ William J. Wood. "The Illegal Beginning of American Negro Slavery," American Bar Association Journal, January 1970.
- ^ Taunya Lovell Banks, "Dangerous Woman: Elizabeth Key's Freedom Suit – Subjecthood and Racialized Identity in Seventeenth Century Colonial Virginia", Digital Commons Law, University of Maryland Law School. Retrieved April 21, 2009.
- ^ "Africans in America | Part 1 | Narrative | from Indentured Servitude to Racial Slavery".
- ^ Wood, Origins of American Slavery (1997), p. 88.
- ^ a b c d "Interview: James Oliver Horton: Exhibit Reveals History of Slavery in New York City", PBS Newshour, January 25, 2007. Retrieved February 11, 2012.
- ^ "European traders". International Slavery Museum. National Museums Liverpool. Retrieved November 15, 2019.
- ^ Pamela Chase Hain, A Confederate Chronicle: The Life of a Civil War Survivor, p. 2, 2005
- ^ Seybert, Tony (August 4, 2004). "Slavery and Native Americans in British North America and the United States: 1600 to 1865". Slavery in America. Archived from the original on August 4, 2004. Retrieved June 14, 2011.
- ^ Wilson, Thomas D., The Oglethorpe Plan: Enlightenment Design in Savannah and Beyond, Charlottesville: University of Virginia Press, 2012, chapter 3
- ^ Scott, Thomas Allan (July 1995). Cornerstones of Georgia history. University of Georgia Press. ISBN 978-0-8203-1743-4.
- ^ "Thurmond: Why Georgia's founder fought slavery". Archived from the original on July 15, 2012. Retrieved October 4, 2009.
- ^ "It is shocking to human Nature, that any Race of Mankind and their Posterity should be sentanc'd to perpetual Slavery; nor in Justice can we think otherwise of it, that they are thrown amongst us to be our Scourge one Day or other for our Sins: And as Freedom must be as dear to them as it is to us, what a Scene of Horror must it bring about! And the longer it is unexecuted, the bloody Scene must be the greater."
—Inhabitants of New Inverness, s:Petition against the Introduction of Slavery
- ^ "Slavery in New York", The Nation, November 7, 2005
- ^ Ira Berlin, Generations of Captivity: A History of African-American Slaves, 2003
- ^ "The First Black Americans" Archived February 2, 2011, at the Wayback Machine, Hashaw, Tim; US News and World Report, 1/21/07
- ^ a b "Slavery in America", Encyclopædia Britannica's Guide to Black History. Retrieved October 24, 2007.
- ^ Trinkley, M. "Growth of South Carolina's Slave Population", South Carolina Information Highway. Retrieved October 24, 2007.
- ^ Morison and Commager: Growth of the American Republic, pp. 212–220.
- ^ Source: Miller and Smith, eds. Dictionary of American Slavery (1988) p. 678
- ^ Includes 10,000 to Louisiana before 1803.
- ^ Michael Tadman, "The Demographic Cost of Sugar: Debates on Slave Societies and Natural Increase in the Americas," The American Historical Review, December 2000, 105:5 online Archived August 1, 2012, at archive.today
- ^ This table gives the African-American population in the United States over time, based on U.S. Census figures. (Numbers from years 1920–2000 are based on U.S. Census figures as given by the Time Almanac of 2005, p. 377.)
- ^ a b c Martin H. Steinberg, Disorders of Hemoglobin: Genetics, Pathophysiology, and Clinical Management, pp. 725–726 Google Books
- ^ a b Rodney Stark, For the Glory of God: How Monotheism Led to Reformations, Science, Witch-hunts, and the End of Slavery, p. 322 Internet Archive Note that the hardcover edition has a typographical error stating "31.2 percent"; it is corrected to 13.2 in the paperback edition. The 13.2% value for the percentage of free people of color (see below) is confirmed with 1830 census data.
- ^ a b Cook, Samantha; Hull, Sarah (March 1, 2011). The Rough Guide to the USA. ISBN 9781405389525.
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Representatives and direct taxes shall be apportioned among the several states ... by adding to the whole number of free persons, including those bound to service for a term of years, and excluding Indians not taxed, three-fifths of all other persons.
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Through the domestic slave trade, about one million enslaved African Americans were forcibly removed from the Upper South to the Deep South, with some transported by ship in the coastwise trade. In 1834, Alabama, Mississippi and Louisiana grew half the nation's cotton; by 1859, along with Georgia, they grew 78%. By 1859, cotton growth in the Carolinas had fallen to just 10% of the national total. Berlin p. 166.
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mishandle historical evidence and mischaracterize important events in ways that affect their major interpretations on the nature of slaveryAlan L. Olmstead; Paul W. Rhode (January 2018). "Cotton, slavery, and the new history of capitalism". Explorations in Economic History. 67: 1–17. doi:10.1016/j.eeh.2017.12.002.
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- ^ Davis, Adrienne (2002). ""Don't Let Nobody Bother Yo' Principle" The Sexual Economy of American Slavery". Sister Circle: Black Women and Work. Rutgers University Press. pp. 109. ISBN 978-0813530611.
- ^ a b Davis, Adrienne (2002). ""Don't Let Nobody Bother Yo' Principle" The Sexual Economy of American Slavery". Sister Circle: Black Women and Work. Rutgers University Press. pp. 119. ISBN 978-0813530611.
- ^ Sowell, Thomas (2005). "The Real History of Slavery". Black Rednecks and White Liberals. New York: Encounter Books. p. 126. ISBN 978-1-59403-086-4.
- ^ Larry Gara, The Liberty Line: The Legend of the Underground Railroad (University Press of Kentucky, 2013).
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- ^ McPherson, Battle Cry, pp. 355, 494–6, quote from George Julian on 495.
- ^ Litwack, Leon F. (1979). Been in the Storm So Long: The Aftermath of Slavery. New York: Knopf. ISBN 978-0-394-50099-7.
- ^ Lincoln's letter to O. H. Browning, September 22, 1861.
- ^ Stephen B. Oates, Abraham Lincoln: The Man Behind the Myths, page 106.
- ^ Images of America: Altoona, by Sr. Anne Francis Pulling, 2001, 10.
- ^ Letter to Greeley, August 22, 1862.
- ^ Abraham Lincoln, Second Inaugural Address, March 4, 1865.
- ^ Lincoln's Letter to A. G. Hodges, April 4, 1864.
- ^ James McPherson, The War that Never Goes Away.
- ^ James McPherson, "Drawn With the Sword", from the article "Who Freed the Slaves?"
- ^ Doyle, Robert C. C. (2010). The Enemy in Our Hands: America's Treatment of Prisoners of War from the Revolution to the War on Terror. University Press of Kentucky. p. 76. ISBN 978-0-8131-3961-6.
- ^ Bruce C. Levine, Confederate Emancipation: Southern Plans to Free and Arm Slaves during the Civil War (2007).
- ^ Up from Slavery (1901), pp. 19–21.
- ^ "History of Juneteenth". Juneteenth World Wide Celebration. Archived from the original on May 27, 2007. Retrieved March 9, 2014.
- ^ Charters of Freedom – The Declaration of Independence, The Constitution, The Bill of Rights
Section 1. Neither slavery nor involuntary servitude, except as a punishment for crime whereof the party shall have been duly convicted, shall exist within the United States, or any place subject to their jurisdiction.
Section 2. Congress shall have power to enforce this article by appropriate legislation.
- ^ E. Merton Coulter. The Civil War and Readjustment in Kentucky (1926), pp. 268–270; James J. Gigantino, The Ragged Road to Abolition; Slavery and Freedom in New Jersey, 1775-1865.
- ^ Palmer, R.R.; Colton, Joel (1995). A History of the Modern World. New York: McGraw-Hill. pp. 572–573. ISBN 978-0-07-040826-5.
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- ^ Gunderson, Gerald (1974). "The Origin of the American Civil War". Journal of Economic History. 34 (4): 915–950. doi:10.1017/S0022050700089361. JSTOR 2116615.
- ^ a b Ransom, Roger (August 24, 2001). Whaples, Robert (ed.). "Economics of the Civil War". EH.Net Encyclopedia. Retrieved July 16, 2014.
- ^ Thomas C. Holt, ed. Major Problems in African-American History: From Freedom to "Freedom Now," 1865–1990s (2000),
- ^ Litwack (1998), p. 271.
- ^ Blackmon (2008), p. 4.
- ^ Anderson, James D. (1988). The Education of Blacks in the South, 1860–1935. Chapel Hill, NC: University of North Carolina Press. pp. 244–45. ISBN 978-0-8078-1793-3.
- ^ Ford, Carin T. (2004). George Eastman: The Kodak Camera Man. Enslow Publishers, INC.
- ^ O'Dell, Larry (February 25, 2007). "Virginia Apologizes for Role in Slavery". The Washington Post.
- ^ "Florida apologizes for role in slavery". Tampa Bay Times. Archived from the original on August 10, 2017. Retrieved August 28, 2017.
- ^ "House apologizes for slavery, 'Jim Crow' injustices – CNN.com". www.cnn.com. CNN. Retrieved September 21, 2019.
- ^ Cohen, Steve (July 29, 2008). "H.Res.194 – 110th Congress (2007–2008): Apologizing for the enslavement and racial segregation of African-Americans". www.congress.gov. Retrieved September 21, 2019.
- ^ "Apologizing for the enslavement and racial segregation of African-Americans. (2008 – H.Res. 194)". GovTrack.us.
- ^ "H. Res. 194: Apologizing for the enslavement and racial segregation of African-Americans" (PDF). Retrieved September 21, 2019.
- ^ Congress Apologizes for Slavery, Jim Crow npr.org
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- ^ Thompson, Krissah (June 19, 2009). "Senate Backs Apology for Slavery". The Washington Post. Retrieved June 21, 2009.
- ^ a b Acharya, Avidit; Blackwell, Matthew; Sen, Maya (May 19, 2016). "The Political Legacy of American Slavery". The Journal of Politics. 78 (3): 000. CiteSeerX 10.1.1.397.3549. doi:10.1086/686631. ISSN 0022-3816. S2CID 222442945.
- ^ Nikolova, Elena (January 1, 2017). "Destined for Democracy? Labour Markets and Political Change in Colonial British America". British Journal of Political Science. 47 (1): 19–45. doi:10.1017/S0007123415000101. ISSN 0007-1234. S2CID 17112994.
- ^ Lauber, Almon Wheeler (1913). Indian Slavery in Colonial Times Within the Present Limits of the United States Chapter 1: Enslavement by the Indians Themselves. 53. Columbia University. pp. 25–48.
- ^ Gallay, Alan (2009). "Introduction: Indian Slavery in Historical Context". In Gallay, Alan (ed.). Indian Slavery in Colonial America. Lincoln, NE: University of Nebraska Press. pp. 1–32. Retrieved March 8, 2017.
- ^ Lauber (1913), "The Number of Indian Slaves" [Ch. IV], in Indian Slavery, pp. 105–117.
- ^ Gallay, Alan. (2002) The Indian Slave Trade: The Rise of the English Empire in the American South 1670–171. New York: Yale University Press. ISBN 0-300-10193-7.
- ^ Reséndez, Andrés (2016). The other slavery: The uncovered story of Indian enslavement in America. Boston: Houghton Mifflin Harcourt. p. 324. ISBN 978-0-544-94710-8.
- ^ Yarbrough, Fay A. (2008). "Indian Slavery and Memory: Interracial sex from the slaves' perspective". Race and the Cherokee Nation. University of Pennsylvania Press. pp. 112–123.
- ^ Castillo, E.D. 1998. "Short Overview of California Indian History" Archived 2006-12-14 at the Wayback Machine, California Native American Heritage Commission, 1998. Retrieved October 24, 2007.
- ^ Castillo, E. D. 1998. "Short Overview of California Indian History" Archived December 14, 2006, at the Wayback Machine, California Native American Heritage Commission, 1998. Retrieved October 24, 2007.
- ^ Beasley, Delilah L. (1918). "Slavery in California," The Journal of Negro History, Vol. 3, No. 1. (January), pp. 33–44.
- ^ A history of the descendants of the slaves of Cherokee can be found at Sturm, Circe (1998). "Blood Politics, Racial Classification, and Cherokee National Identity: The Trials and Tribulations of the Cherokee Freedmen". American Indian Quarterly. 22 (1/2): 230–58. JSTOR 1185118. In 1835, 7.4% of Cherokee families held slaves. In comparison, nearly one-third of white families living in Confederate states owned slaves in 1860. Further analysis of the 1835 Federal Cherokee Census can be found in McLoughlin, W. G.; Conser, W. H. (1977). "The Cherokees in Transition: a Statistical Analysis of the Federal Cherokee Census of 1835". Journal of American History. 64 (3): 678–703. doi:10.2307/1887236. JSTOR 1887236. A discussion on the total number of Slave holding families can be found in Olsen, Otto H. (December 2004). "Historians and the extent of slave ownership in the Southern United States". Civil War History. Archived from the original on July 20, 2007. Retrieved June 8, 2007.
- ^ Perdue, Theda (1979). Slavery and the Evolution of Cherokee Society, 1540–1866. University of Tennessee Press. pp. 207 pages. ISBN 9780870495304. Retrieved February 28, 2019.
Perdue, Theda. Slavery and the Evolution of Cherokee Society, 1540–1866.
- ^ Katz, William Loren (January 3, 2012). Black Indians: A Hidden Heritage. Simon and Schuster. pp. 254. ISBN 9781442446373. Retrieved March 1, 2019.
- ^ Duncan, J. W. (1928). "Interesting ante-bellum laws of the Cherokee, now Oklahoma history". Chronicles of Oklahoma. 6 (2): 178–180. Archived from the original on December 19, 2007. Retrieved July 13, 2007.
- ^ Davis, J. B. (1933). "Slavery in the Cherokee nation". Chronicles of Oklahoma. 11 (4): 1056–1072. Archived from the original on March 10, 2015. Retrieved July 13, 2007.
- ^ Watson W. Jennison (January 18, 2012). Cultivating Race: The Expansion of Slavery in Georgia, 1750–1860. University Press of Kentucky. p. 132. ISBN 978-0-8131-4021-6.
- ^ McCall, George A. (1868). Letters from the Frontiers. Philadelphia: J.B. Lippincott. p. 160. ISBN 9781429021586.
- ^ Kevin Mulroy (January 18, 2016). The Seminole Freedmen: A History. University of Oklahoma Press. p. 25. ISBN 978-0-8061-5588-3.
- ^ Philip Deloria; Neal Salisbury (April 15, 2008). A Companion to American Indian History. John Wiley & Sons. pp. 348–349. ISBN 978-1-4051-4378-3.
- ^ Bruce G. Trigger; Wilcomb E. Washburn (October 13, 1996). The Cambridge History of the Native Peoples of the Americas. Cambridge University Press. p. 525. ISBN 978-0-521-57392-4.
- ^ Wolfgang Binder (1987). Westward Expansion in America (1803–1860). Palm & Enke. p. 147. ISBN 978-3-7896-0171-2.
- ^ James Shannon Buchanan (1955). Chronicles of Oklahoma. Oklahoma Historical Society. p. 522.
- ^ Kevin Mulroy (2007). The Seminole Freedmen: A History. University of Oklahoma Press. p. 79. ISBN 978-0-8061-3865-7.
- ^ Digital "African American Voices" Archived July 15, 2007, at the Wayback Machine, Digital History. Retrieved October 24, 2007.
- ^ "Haida Warfare", civilization.ca. Retrieved October 24, 2007.
- ^ Berthrong, Donald J. (1976). The Cheyenne and Arapaho Ordeal: Reservation and Agency Life in the Indian Territory, 1875 to 1907. University of Oklahoma Press. p. 124. ISBN 978-0-8061-1277-0.
- ^ a b Henry Louis Gates Jr. (March 4, 2013). "Did Black People Own Slaves?". Archived from the original on March 8, 2013.
- ^ Hewitt, D (May 17, 2018). "Ten Black Slaveowners That Will Tear Apart Historical Perception". History Collection. Retrieved July 26, 2021.
- ^ Breen, T. H. (2004). "Myne Owne Ground" : Race and Freedom on Virginia's Eastern Shore, 1640–1676. New York: Oxford University Press. pp. 13–15. ISBN 978-0-19-972905-0.
- ^ a b Conlin, Joseph (2011). The American Past: A Survey of American History. Cengage Learning. p. 370. ISBN 978-1-111-34339-2.
- ^ Stampp p. 194. Oakes pp. 47–48.
- ^ Kranz, Rachel (2004). African-American Business Leaders and Entrepreneurs. Infobase Publishing. p. 72. ISBN 978-1-4381-0779-0.
- ^ Franklin and Schweninger, p. 201.
- ^ Berlin, Generations of Captivity, p. 9.
- ^ Gates Jr.; Henry Louis (March 4, 2013). "Did Black People Own Slaves?". The Root. Archived from the original on January 23, 2014.
- ^ Mason p. 17
- ^ Mason pp. 19–20.
- ^ Berlin, Generations of Captivity, p. 138.
- ^ Oakes pp. 47–48.
- ^ Oakes pp. 47–49.
- ^ Koger, Larry (1985). "Foreword". Black Slaveowners: Free Black Masters in South Carolina, 1790–1860. Columbia, SC: University of South Carolina Press. ISBN 978-0-7864-5128-9.
- ^ Joyner, Charles (October 1986). "Review of Black Slaveowners: Free Black Slave Masters in South Carolina, 1790–1860, by Larry Koger". South Carolina Historical Magazine. 87 (4): 251–253. JSTOR 27567980.
- ^ "Total Slave Population in US, 1790–1860, by State". Archived from the original on August 22, 2007. Retrieved December 28, 2007.
- ^ Jason B. Johnson, "Slavery in Gold Rush Days – New Discoveries Prompt Exhibition, Re-examination of State's Involvement," SFGate, January 27, 2007.
- ^ Mark Gutglueck. "Mormons Created And Then Abandoned San Bernardino". San Bernardino County Sentinel.
- ^ a b Mary Ellen Snodgrass (March 26, 2015). The Civil War Era and Reconstruction: An Encyclopedia of Social, Political, Cultural and Economic History. p. 556. ISBN 9781317457916.
- ^ Nathaniel R. Ricks (2007). A Peculiar Place for the Peculiar Institution: Slavery and Sovereignty in Early Territorial Utah.
- ^ Reeve, W. Paul; Parshall, Ardis E (2010). Mormonism: A Historical Encyclopedia. p. 26. ISBN 9781598841077.
- ^ Ronald G. Coleman. Blacks in Utah History: An Unknown Legacy (PDF).
- ^ Castillo, E.D. 1998. "Short Overview of California Indian History" Archived December 14, 2006, at the Wayback Machine, California Native American Heritage Commission, 1998. Retrieved October 24, 2007.
- ^ United States. Congress (1857). The Congressional Globe, Part 2. Blair & Rives. pp. 287–288.
- ^ Large Slaveholders of 1860 and African American Surname Matches from 1870 Archived September 5, 2015, at the Wayback Machine, by Tom Blake, 2001–2005.
- ^ Pew Research Center: The number of people in the average U.S. household is going up for the first time in over 160 years
- ^ Glatthaar, Joseph (2009). General Lee's Army: From Victory to Collapse. New York: Free Press. pp. 20, 474. ISBN 978-1416596974.
- ^ a b The Sixteen Largest American Slaveholders from 1860 Slave Census Schedules Archived July 19, 2013, at the Wayback Machine, Transcribed by Tom Blake, April to July 2001, (updated October 2001 and December 2004; now includes 19 holders)
- ^ a b c Pargas, Damian Alan (2008). "Boundaries and Opportunities: Comparing Slave Family Formation in the Antebellum South" (PDF). Journal of Family History. 33 (3): 316–345. doi:10.1177/0363199008318919. PMID 18831111. S2CID 22302394.
- ^ Bonekemper III, Edward H. (2015). The Myth of the Lost Cause: Why the South Fought the Civil War and Why the North Won. Washington, D.C.: Regnery Publishing. p. 39.
- ^ a b Kolchin p. 134.
- ^ Kolchin pp. 137–143. Horton and Horton p. 9.
National and comparative studies
- Berlin, Ira. Generations of Captivity: A History of African American Slaves. (2003) ISBN 0-674-01061-2.
- Berlin, Ira. Many Thousands Gone: The First Two Centuries of Slavery in North America. Harvard University Press, 1998. ISBN 0-674-81092-9
- Berlin, Ira and Ronald Hoffman, eds. Slavery and Freedom in the Age of the American Revolution University Press of Virginia, 1983. essays by scholars
- Blackmon, Douglas A. Slavery by Another Name: The Re-Enslavement of Black Americans from the Civil War to World War II. (2008) ISBN 978-0-385-50625-0.
- Blassingame, John W. The Slave Community: Plantation Life in the Antebellum South Oxford University Press, 1979. ISBN 0-19-502563-6.
- David, Paul A. and Temin, Peter. "Slavery: The Progressive Institution?", Journal of Economic History. Vol. 34, No. 3 (September 1974)
- Davis, David Brion. Inhuman Bondage: The Rise and Fall of Slavery in the New World (2006)
- Elkins, Stanley. Slavery : A Problem in American Institutional and Intellectual Life. University of Chicago Press, 1976. ISBN 0-226-20477-4
- Fehrenbacher, Don E. Slavery, Law, and Politics: The Dred Scott Case in Historical Perspective Oxford University Press, 1981
- Fogel, Robert W. Without Consent or Contract: The Rise and Fall of American Slavery W.W. Norton, 1989. Econometric approach
- Foner, Eric (2005). Forever Free. ISBN 978-0-375-40259-3.
- Foner, Eric. The Fiery Trial: Abraham Lincoln and American Slavery (2010), Pulitzer Prize excerpt and text search
- Franklin, John Hope and Loren Schweninger. Runaway Slaves: Rebels on the Plantation. (1999) ISBN 0-19-508449-7.
- Gallay, Alan. The Indian Slave Trade (2002).
- Genovese, Eugene D. Roll, Jordan, Roll: The World the Slaves Made Pantheon Books, 1974.
- Genovese, Eugene D. The Political Economy of Slavery: Studies in the Economy and Society of the Slave South (1967)
- Genovese, Eugene D. and Elizabeth Fox-Genovese, Fruits of Merchant Capital: Slavery and Bourgeois Property in the Rise and Expansion of Capitalism (1983)
- Hahn, Steven. "The Greatest Slave Rebellion in Modern History: Southern Slaves in the American Civil War." Southern Spaces (2004)
- Higginbotham, A. Leon, Jr. In the Matter of Color: Race and the American Legal Process: The Colonial Period. Oxford University Press, 1978. ISBN 0-19-502745-0
- Horton, James Oliver and Horton, Lois E. Slavery and the Making of America. (2005) ISBN 0-19-517903-X
- Kolchin, Peter. American Slavery, 1619–1877 Hill and Wang, 1993. Survey
- Litwack, Leon F. Been in the Storm So Long: The Aftermath of Slavery (1979), social history of how slavery ended in the Confederacy
- Mason, Matthew. Slavery and Politics in the Early American Republic. (2006) ISBN 978-0-8078-3049-9.
- Moon, Dannell, "Slavery", article in Encyclopedia of rape, Merril D. Smith (Ed.), Greenwood Publishing Group, 2004
- Moore, Wilbert Ellis, American Negro Slavery and Abolition: A Sociological Study, Ayer Publishing, 1980
- Morgan, Edmund S. American Slavery, American Freedom: The Ordeal of Colonial Virginia W.W. Norton, 1975.
- Morris, Thomas D. Southern Slavery and the Law, 1619–1860 University of North Carolina Press, 1996.
- Oakes, James. The Ruling Race: A History of American Slaveholders. (1982) ISBN 0-393-31705-6.
- Ransom, Roger L. "Was It Really All That Great to Be a Slave?" Agricultural History, Vol. 48, No. 4 (1974) in JSTOR
- Rodriguez, Junius P., ed. Encyclopedia of Emancipation and Abolition in the Transatlantic World. Armonk, NY: M.E. Sharpe, 2007.
- Rodriguez, Junius P., ed. Encyclopedia of Slave Resistance and Rebellion. Westport, CT: Greenwood, 2007.
- Scarborough, William K. The Overseer: Plantation Management in the Old South (1984)
- Schermerhorn, Calvin. The Business of Slavery and the Rise of American Capitalism, 1815–1860. New Haven, CT: Yale University Press, 2015.
- Snyder, Terri L. The Power to Die: Slavery and Suicide in British North America. Chicago: University of Chicago Press, 2015.
- Stampp, Kenneth M. The Peculiar Institution: Slavery in the Ante-Bellum South (1956) Survey
- Stampp, Kenneth M. "Interpreting the Slaveholders' World: a Review." Agricultural History 1970 44(4): 407–12. ISSN 0002-1482
- Tadman, Michael. Speculators and Slaves: Masters, Traders, and Slaves in the Old South University of Wisconsin Press, 1989.
- Wright, W. D. Historians and Slavery; A Critical Analysis of Perspectives and Irony in American Slavery and Other Recent Works Washington, D.C.: University Press of America (1978)
State and local studies
- Fields, Barbara J. Slavery and Freedom on the Middle Ground: Maryland During the Nineteenth Century Yale University Press, 1985.
- Jewett, Clayton E. and John O. Allen; Slavery in the South: A State-By-State History Greenwood Press, 2004
- Jennison, Watson W. Cultivating Race: The Expansion of Slavery in Georgia, 1750–1860 (University Press of Kentucky; 2012)
- Kulikoff, Alan. Tobacco and Slaves: The Development of Southern Cultures in the Chesapeake, 1680–1800 University of North Carolina Press, 1986.
- Minges, Patrick N.; Slavery in the Cherokee Nation: The Keetoowah Society and the Defining of a People, 1855–1867 2003 deals with Indian slave owners.
- Mohr, Clarence L. On the Threshold of Freedom: Masters and Slaves in Civil War Georgia University of Georgia Press, 1986.
- Mutti Burke, Diane (2010). On Slavery's Border: Missouri's Small Slaveholding Households, 1815–1865. University of Georgia Press. ISBN 978-0-8203-3683-1.
- Mooney, Chase C. Slavery in Tennessee Indiana University Press, 1957.
- Olwell, Robert. Masters, Slaves, & Subjects: The Culture of Power in the South Carolina Low Country, 1740–1790 Cornell University Press, 1998.
- Reidy, Joseph P. From Slavery to Agrarian Capitalism in the Cotton Plantation South, Central Georgia, 1800–1880 University of North Carolina Press, 1992.
- Ripley, C. Peter. Slaves and Freemen in Civil War Louisiana Louisiana State University Press, 1976.
- Rivers, Larry Eugene. Slavery in Florida: Territorial Days to Emancipation University Press of Florida, 2000.
- Sellers, James Benson; Slavery in Alabama University of Alabama Press, 1950
- Sydnor, Charles S. Slavery in Mississippi. 1933
- Takagi, Midori. Rearing Wolves to Our Own Destruction: Slavery in Richmond, Virginia, 1782–1865 University Press of Virginia, 1999.
- Taylor, Joe Gray. Negro Slavery in Louisiana. Louisiana Historical Society, 1963.
- Trexler, Harrison Anthony. Slavery in Missouri, 1804–1865 (Johns Hopkins University Press, 1914) online edition
- Wood, Peter H. Black Majority: Negroes in Colonial South Carolina from 1670 through the Stono Rebellion W.W. Norton & Company, 1974.
- Ayers, Edward L. "The American Civil War, Emancipation, and Reconstruction on the World Stage," OAH Magazine of History, January 2006, Vol. 20, Issue 1, pp. 54–60
- Berlin, Ira. "American Slavery in History and Memory and the Search for Social Justice," Journal of American History, March 2004, Vol. 90, Issue 4, pp. 1251–1268
- Boles, John B. and Evelyn T. Nolen, eds., Interpreting Southern History: Historiographical Essays in Honor of Sanford W. Higginbotham (1987).
- Brown, Vincent. "Social Death and Political Life in the Study of Slavery," American Historical Review, December 2009, Vol. 114, Issue 5, pp. 1231–1249, examined historical and sociological studies since the influential 1982 book Slavery and Social Death by American sociologist Orlando Patterson
- Campbell, Gwyn. "Children and slavery in the new world: A review," Slavery & Abolition, August 2006, Vol. 27, Issue 2, pp. 261–285
- Collins, Bruce. "Review: American Slavery and Its Consequences" Historical Journal (1979) 33#4 pp. 997–1015 online
- Dirck, Brian. "Changing Perspectives on Lincoln, Race, and Slavery," OAH Magazine of History, October 2007, Vol. 21, Issue 4, pp. 9–12
- Farrow, Anne; Lang, Joel; Frank, Jenifer. Complicity: How the North Promoted, Prolonged, and Profited from Slavery. Ballantine Books, 2006 ISBN 0-345-46783-3
- Fogel, Robert W. The Slavery Debates, 1952–1990: A Retrospective (2007)
- Ford, Lacy K. (2009). Deliver Us from Evil. The Slavery Question in the Old South. Oxford University Press. ISBN 9780195118094.
- Frey, Sylvia R. "The Visible Church: Historiography of African American Religion since Raboteau," Slavery & Abolition, January 2008, Vol. 29 Issue 1, pp. 83–110
- Hettle, Wallace. "White Society in the Old South: The Literary Evidence Reconsidered," Southern Studies: An Interdisciplinary Journal of the South, Fall/Winter 2006, Vol. 13, Issue 3/4, pp 29–44
- King, Richard H. "Marxism and the Slave South", American Quarterly 29 (1977), 117–31. focus on Genovese
- Kolchin, Peter. "American Historians and Antebellum Southern Slavery, 1959–1984", in William J. Cooper, Michael F. Holt, and John McCardell, eds., A Master's Due: Essays in Honor of David Herbert Donald (1985), 87–111
- Laurie, Bruce. "Workers, Abolitionists, and the Historians: A Historiographical Perspective," Labor: Studies in Working Class History of the Americas, Winter 2008, Vol. 5, Issue 4, pp. 17–55
- Neely Jr., Mark E. "Lincoln, Slavery, and the Nation," Journal of American History, September 2009, Vol. 96 Issue 2, pp. 456–458
- Parish; Peter J. Slavery: History and Historians Westview Press. 1989
- Penningroth, Dylan. "Writing Slavery's History," OAH Magazine of History, April 2009, Vol. 23 Issue 2, pp. 13–20, basic overview
- Rael, Patrick. Eighty-Eight Years: The Long Death of Slavery in the United States, 1777–1865. Athens, GA: University of Georgia Press, 2015.
- Sidbury, James. "Globalization, Creolization, and the Not-So-Peculiar Institution," Journal of Southern History, August 2007, Vol. 73, Issue 3, pp. 617–630, on colonial era
- Stuckey, P. Sterling. "Reflections on the Scholarship of African Origins and Influence in American Slavery," Journal of African American History, Fall 2006, Vol. 91 Issue 4, pp. 425–443
- Sweet, John Wood. "The Subject of the Slave Trade: Recent Currents in the Histories of the Atlantic, Great Britain, and Western Africa," Early American Studies, An Interdisciplinary Journal, Spring 2009, Vol. 7 Issue 1, pp. 1–45
- Tadman, Michael. "The Reputation of the Slave Trader in Southern History and the Social Memory of the South," American Nineteenth Century History, September 2007, Vol. 8, Issue 3, pp. 247–271
- Tulloch, Hugh. The Debate on the American Civil War Era (1998), ch. 2–4
- Albert, Octavia V. Rogers. The House of Bondage Or Charlotte Brooks and Other Slaves. Oxford University Press, 1991. Primary sources with commentary. ISBN 0-19-506784-3
- An American (1855). Cotton is king: or, The culture of cotton, and its relation to Agriculture, Manufactures and Commerce; to the free colored people; and to those who hold that slavery is in itself sinful. Cincinnati: Moore, Wilstach, Keys.
- Berlin, Ira, Joseph P. Reidy, and Leslie S. Rowlands, eds. Freedom: A Documentary History of Emancipation, 1861–1867 5 vol Cambridge University Press, 1982. Very large collection of primary sources regarding the end of slavery.
- Berlin, Ira, Marc Favreau, and Steven F. Miller, eds. Remembering Slavery: African Americans Talk About Their Personal Experiences of Slavery and Emancipation The New Press: 2007. ISBN 978-1-59558-228-7
- Blassingame, John W., ed. Slave Testimony: Two Centuries of Letters, Speeches, Interviews, and Autobiographies. Louisiana State University Press, 1977.
- Burke, Diane Mutti, On Slavery's Border: Missouri's Small Slaveholding Households, 1815–1865,
- De Tocqueville, Alexis. Democracy in America. (1994 Edition by Alfred A Knopf, Inc) ISBN 0-679-43134-9
- A Narrative of the Life of Frederick Douglass, an American Slave (1845) (Project Gutenberg), (Audio book at FreeAudio.org)
- "The Heroic Slave." Autographs for Freedom. Ed. Julia Griffiths Boston: Jewett and Company, 1853. 174–239. Available at the Documenting the American South website.
- Frederick Douglass My Bondage and My Freedom (1855) (Project Gutenberg)
- Frederick Douglass Life and Times of Frederick Douglass (1892)
- Frederick Douglass Collected Articles Of Frederick Douglass, A Slave (Project Gutenberg)
- Frederick Douglass: Autobiographies by Frederick Douglass, Henry Louis Gates, Jr. Editor. (Omnibus of all three) ISBN 0-940450-79-8
- Litwack, Leon Been in the Storm So Long: The Aftermath of Slavery. (1979) Winner of the 1981 National Book Award for history and the 1980 Pulitzer Prize for History.
- Litwack, Leon North of Slavery: The Negro in the Free States, 1790–1860 (University of Chicago Press: 1961)
- Document: "List Negroes at Spring Garden with their ages taken January 1829" (title taken from document)
- Missouri History Museum Archives Slavery Collection
- Rawick, George P., ed. The American Slave: A Composite Autobiography. 19 vols. Greenwood Publishing Company, 1972. Collection of WPA interviews made in the 1930s with ex-slaves |
Extreme storms can be defined as intense storm events characterised by strong winds blowing over the surface of the sea, large and long waves that can travel long distances until they reach the shore and high water levels known as storm surge . Such storms can significantly affect navigation and petroleum platforms and can cause a range of potential hazards to coastal areas, such as overwash and/or inundation, beach or shore erosion, as well as damages to coastal protection structures or to infrastructure of developed coastal areas (see Figs. 1a-1f). The most frequent natural hazards to coastal areas, namely flooding and erosion are usually induced by extreme storm events, resulting in lives lost, human injuries and damage to property or to the environment.
Extreme storms are usually defined as the sources of coastal flooding or erosion risk, transmitted to the receptors (society, economy, environmental values) through the pathways of the respective coastal hazard. The intensity of storm-induced coastal processes and the morphodynamic response of a coastal area to an extreme storm event depend strongly on the characteristics of the storm (i.e. storm peak, duration, directionality, energetic content), as well as on the characteristics of the coastal area (i.e. beach profile, gain size, relative orientation of the shoreline)
The description of risk sources in coastal areas helps to deliver the hydrologic and hydraulic boundary conditions needed to describe the loading of defences or can be used as key input to calculate the probability of occurrence of a certain coastal hazard (i.e. coastal flooding or erosion). Main coastal risk sources include both intense meteorological synoptic-scale cyclonic events, the tropical cyclones which form almost exclusively over tropical seas, as well as marine storm events resulting from severe wave conditions and/or high sea levels (tide and storm surge) offshore and transformed to nearshore. Tsunamis, namely very long waves most often generated by seismic activity, also belong to coastal risk sources characterised by a high damage potential.
Tropical cyclones are intense local meteorological systems characterised by extremely low pressure in the cyclone center near the sea surface and caused by a combination of warm water, evaporation, swirling winds and other factors. The drag on the sea surface causes the wind to spiral in towards the center of the storm, transferring heat from the ocean surface to the air and therefore refuelling and perhaps strengthening the system (Fig. 2). The intensity of the tropical cyclone increases with lower sea-level pressures in the core of the storm, as well as with stronger winds near the sea surface.
In the Atlantic and Northeast Pacific, tropical cyclones are called hurricanes, while the terms typhoons and cyclones are used for similar types of disturbances in the Northwest Pacific and in the South Pacific and Indian Ocean, respectively (see Fig. 3). Therefore, aside from slightly different wind speeds, there is no difference between a hurricane, a typhoon, and a cyclone.
Most tropical cyclones form within the trade wind region, tracking from east to west, turning poleward under the influence of monsoon circulation and then continuing to turn towards the northeast due to western winds in the mid-latitudes. The intensification stages leading to fully developed tropical cyclones include tropical disturbances, tropical depressions and tropical storms, distinctly separated based on the maximum wind speed near the sea surface. For a tropical cyclone to form and develop there are seven main requirements:
- Sufficiently warm deep sea-surface temperatures,
- Enough Coriolis force to cause the tangential flow of air around the eye of the tropical cyclone,
- Atmospheric instability developed non locally to support deep thunderstorm convection,
- High humidity in the lower to middle levels of the troposphere,
- Low vertical wind shear allowing to create a low-pressure center at the sea surface where thunderstorm clusters can be formed,
- Enough relative vorticity at the lower part of the troposphere enabling the clustering of thunderstorms,
- A pre-existing low level focus or disturbance enabling horizontal convergence in the atmospheric boundary layer.
The reduced atmospheric pressure in the eye of the tropical cyclone combined with wind blowing towards the coast could form large propagating storm surges able to inundate very large areas of the shore and cause significant damages. High surface waves, generated by the total wind speed of the tropical cyclone relative to the surface, resulting as a vector sum of the translation and the rotation speed of the storm, could significantly increase the damage caused. The main coastal hazards resulting from a tropical cyclone include flooding caused by the fast propagating storm surge, high wind speeds causing significant damages inland, beach erosion, as well as wave scour at the toe of structures protecting coastal areas and wave battering of such structures.
Wave storms and storm surges
A storm can be simply defined as an intense atmospheric perturbation, which impacts directly on the sea surface causing significantly increased wave heights and sometimes high storm surges. Strong winds over the sea, especially those with large fetches acting for long durations, favor the air-sea momentum transfer, possibly leading to high and long sea waves. Wave storms are usually defined as events of significant wave height, [math]H_s[/math], exceeding a predefined threshold (critical [math]H_s[/math]) with a minimum duration. The duration of the storm starts when [math]H_s[/math] exceeds the threshold and ends when [math]H_s[/math] goes below it. Both the threshold of the storm event and its minimum duration are defined based on the objective of the study i.e. storms with a high flooding or erosion potential to the adjacent coastal area. Studies performed for the Spanish coast in the Mediterranean, define a wave storm as an event during which [math]H_s[/math] overpasses the threshold of 2 m with a minimum duration of 6 h, as the limiting conditions required to significantly erode the Catalan coast. Therefore, wave storms are considered to be sufficiently intense and durable to produce substantial impacts based on the objectives of each study. It is also quite common to define a maximum time interval for which the wave data fall below the threshold within a single wave storm event. For longer time intervals the storm is splitted in two different wave storm events, allowing for suites of low energetic events to be treated as independent wave storms. To determine wave storm events, long time series of wave data at quite a high temporal resolution (i.e. hourly data) should be made available. Such data can be acquired from a wave buoy network, measuring significant wave height, [math]H_s[/math], peak spectral wave period, [math]T_p[/math], and prevailing wave direction, [math]\theta[/math], or hindcast wave data can be utilised. Sea level is composed of three components, namely the mean sea level, the tidal level and zero mean surge level (i.e. the meteorological residual). The storm surge is the stochastic component of sea level mainly induced by the inverse barometer effect and strong winds. A storm surge event is defined in a similar manner to the wave storm event. Therefore, an appropriate threshold is defined and the event starts when the storm surge overpasses it and terminates when it gets below this minimum value. A minimum duration of each storm event is also considered. Sea level variations can be acquired from tide gauge records and satellite-altimeter data.
Methods to analyse extreme storms and predict return periods
Once storm events (wave storms, storm surge events or wind storms) are identified, time series of storm peaks can be constructed defined by means of the maximum value within each event. These maxima should belong to independent storm events, therefore it is quite common to consider a minimum separation time interval between consecutive peak values . Extreme Value Analysis (EVA) can then be performed to extract return levels of wave/ storm surge/ wind characteristics corresponding to defined return periods i.e. 50, 100, 1000 years. Extreme Value methods are utilized for the purpose of extrapolation to levels more extreme than those observed. Univariate Extreme Value Theory (EVT) includes models for:
- Block maxima (the block size is usually considered equal to one year)
- Exceedances over high thresholds (Peaks Over Threshold (POT) models)
and are used according to data availability. The former models correspond to the family of the Generalized Extreme Value (GEV) distribution, where the largest storms (i.e. the storm with the highest peak [math]H_s[/math]) within each year are selected. The POT method, where all events exceeding a defined threshold [math]u[/math] are considered, defines a two dimensional point process ([math]y, \; N_u[/math]), where the excesses, [math]y[/math], of the threshold [math]u[/math] follow a Generalised Pareto Distribution (GPD), while the number of storms, [math]N_u[/math], is Poisson distributed (Fig. 4, Fig. 5).
The most frequent natural hazards to coastal areas, such as coastal flooding and coastal erosion, are particularly likely when high tides, storm surge and/or large waves occur at the same time. Where the source of a hazard consists of more than one variables (i.e. coastal flooding caused by extreme wave heights and sea levels), it is necessary to consider the joint probability distribution of these variables. Joint exceedance combinations of wave heights and sea levels with a given probability of occurrence are defined in terms of sea conditions in which a given wave height is exceeded at the same time as a given water level (or its surge component) being exceeded. There are different levels of complexity for joint probability methods but all require some assessment of the dependence between variables:
- A relatively simple method uses the marginal distributions of the variables involved and an assessment of their dependence. The joint return period is expressed in terms of combinations of the marginal return periods.
- A more sophisticated approach involves fitting a probability distribution to the joint distribution of variables and extrapolating the joint density function. The benefit of this approach is that the return period of the response function can be easily determined, but a large amount of concurrent data of the variables is needed. For this approach Multivariate Extreme Value Theory and copula functions can be used to extract joint exceedance probabilities and joint return levels. Approaches based on copula functions are able to model multivariate datasets with mixed marginal distributions and complex dependence structures.
Joint probability approaches have been used in the literature to model the pair of extreme wave height, [math]H_s[/math], and peak period, [math]T_p[/math] , [math]H_s[/math] and associated mean period, [math]T_m[/math] , maximum water level (storm surge), [math]S[/math] and associated fullness, [math]F[/math], of the entire storm surge curve defined as the energetic content of the event within the storm duration (Fig. 6). Corbella and Stretch investigate dependencies between wave height, wave period, storm duration, water level and storm inter-arrival time and use trivariate copulas to jointly analyze the variables that are significantly associated.
Extreme storms in coastal engineering practice
Extreme storms are usually related to cross-shore profile changes and longshore changes of the coastline and are considered to induce a range of hazards to coastal areas, the most common of which are flooding and coastal erosion. Population growth, concentration of economic activities, asset concentration, urbanization and tourism lead to an increasing vulnerability of such areas to the aforementioned hazards. The above mentioned challenges coupled with the general inception of a changing climate, with extreme marine events of higher intensity and frequency and mean sea level rise are expected to increase exposure of coastal societies to the associated hazards. Especially when coastal environments are highly urbanised or developed, extreme storm events can induce serious impacts on infrastructure, coastal communities and recreational activities of the affected coastal areas. The increasing potential to predict or forecast such events and to attain reliable estimates of future severe sea states can significantly contribute to reduce flooding and/or erosion risks by prevention or preparedness of the risk receptors.
Extreme storms are also used in the design of coastal protection works, port and harbour structures. Return levels of wave height, wave period, wave run-up and storm surge corresponding to defined return periods (complying with the design standards of each country) are utilised to provide design values of crest characteristics, berm height and width, mean nominal diameter of armour elements and windward slope angle of such structures. They are also used to define the number of layers of coastal structures, to select the appropriate types of armour units, as well as to provide design estimates of toe protection characteristics. During the last few years, probabilistic design approaches based on reliability and risk-based design concepts have been increasingly proposed and applied in the fields of civil engineering and water defences, because of their ability to provide an explicit measure of the safety level of structured systems. More specifically, safety assessments of flood defence assets are increasingly performed with the technique of structural reliability. Reliability-based design optimization deals with obtaining optimal designs characterized by low costs and by a low probability of failure. Risk-based design of structures is defined as the approach in which the costs of protection are explicitly weighted against the risk reduction in the protected area. In contrast with reliability-based design, the failure probability for which the structure is designed depends on the consequences of failure. To determine the failure probability of a structure is critical for both methods. When the source of the failure consists of a single variable, i.e. extreme wave height or extreme sea level, the failure probability can be computed from a distribution function by a given value of the source variable (failure condition). When the source of failure consists of more than one variables, their joint exceedance probability is determined by integrating the joint probability density of the variables over the failure region (Fig. 7).
Failure probability referring to the occurrence of a particular response (i.e. overtopping, force on the structure) can be obtained by intersecting the equal response curve with the joint exceedance probability curve of a certain joint return period. The intersection point is referred to as the worst case loading combination (critical condition) for the response under study. The area within the response curve represents the failure probability of the structure for this particular response (Fig. 8).
References – Further reading
- U.S. Geological Survey (USGS), 2016. Coastal Change Hazards: Hurricanes and Extreme Storms, Available from: http://coastal.er.usgs.gov/hurricanes/extreme-storms, National Assessment of Storm-Induced Coastal Change Hazards, Available from: http://coastal.er.usgs.gov/hurricanes/sandy/ [accessed on 31-10-2016]
- Cooper, J.A.G., Jackson, D.W.T., Navas, F., McKenna, J. and Malvarez, G., 2004. “Identifying storm impacts on an embayed, high-energy coastline: examples from western Ireland”. Marine Geology, Vol. 210(1), 261-280.
- Mendoza, E.T. and Jiménez, J.A., 2006. “Storm-Induced Beach Erosion Potential on the Catalonian Coast”, Journal of Coastal Research, SI 48, 81-88.
- Stull, R.B., 2011. “Meteorology for Scientists and Engineers”, 3rd Edition, 938 pp, Free online for everyone worldwide under a Creative Commons license, ISBN 978-0-88865-178-5
- Bosom, E. and Jiménez, J.A., 2011. “Probabilistic coastal vulnerability assessment to storms at regional scale: application to Catalan beaches (NW Mediterranean)”, Natural Hazards and Earth System Sciences, Vol. 11(2), 475-484.
- Guimarães, P.V., Farina, L. and Toldo Jr, E.E., 2014. “Analysis of extreme wave events on the southern coast of Brazil”, Natural Hazards and Earth System Sciences, Vol. 14(12), 3195-3205.
- Pugh, D.T., 1987. “Tides, Surges and Mean Sea Level: a Handbook for Engineers and Scientists”, Wiley, Chichester, 472 pp.
- Menéndez, M., Méndez, F.J. and Losada, I.J., 2009. “Forecasting seasonal to interannual variability in extreme sea levels”, ICES Journal of Marine Science, Vol. 66, 1490-1496.
- Makris, C., Galiatsatou, P., Tolika, K., Anagnostopoulou, C., Kombiadou, K., Prinos, P., Velikou, K., Kapelonis, Z., Tragou, E., Androulidakis, Y., Athanassoulis, G., Vagenas, C., Tegoulias, I., Baltikas, V., Krestenitis, Y., Gerostathis, T., Belibassakis, K. and Rusu, E., 2016. “Climate change effects on the marine characteristics of the Aegean and Ionian Seas”, Ocean Dynamics, 1-33.
- Coles, S., 2001. “An introduction to statistical modeling of extreme values”, Springer Series in Statistics, Springer, Berlin, 209 pp.
- Galiatsatou, P., Prinos, P. and Sánchez-Arcilla, A., 2008. “Estimation of extremes. Conventional versus Bayesian techniques”, Journal of Hydraulic Research, Vol. 46(2), 211-223.
- Hawkes, P.J., Gouldby, B.P., Tawn, J.A. and Owen, M.W., 2002. “The joint probability of waves and water levels in coastal defence design”, Journal of Hydraulic Research, Vol. 40(3), 241-251.
- DEFRA/ Environment Agency Flood and Coastal Defence R&D Programme, 2005. “Joint Probability: Dependence Mapping and Best Practice”, Technical report on dependence mapping, R&D Technical Report FD2308/TR1.
- Wahl, T., Mudersbach, C. and Jensen, J., 2015. “Statistical assessment of storm surge scenarios within integrated risk analyses”, Coastal Engineering Journal, Elsevier, Vol. 57(1), 1540003.
- Oumeraci, H., Kortenhaus, A., Burzel, A., Naulin, M., Dassanayake, D.R., Jensen, J., Wahl, T., Mudersbach, C., Gönnert, G., Gerkensmeir, B., Fröhle, P. and Ujeyl, G., 2015. “XtremRisK -Integrated flood risk analysis for extreme storm surges at open coasts and in estuaries: Methodology, key results and lessons learned”, Coastal Engineering Journal, Vol. 57(1), 1540001.
- Repko, A., Van Gelder, P.H.A.J.M., Voortman, H.G. and Vrijling, J.K., 2004. “Bivariate description of offshore wave conditions with physics-based extreme value statistics”, Applied Ocean Research, Vol. 26, 162-170.
- Ferreira, J.A. and Guedes Soares, C., 2002. “Modelling bivariate distributions of significant wave height and mean period”, Applied Ocean Research, Vol. 24, 31-45.
- Corbella, A. and Stretch, D.D., 2013. “Simulating a multivariate sea storm using Archimedean copulas”, Coastal Engineering, Vol. 76, 68–78.
- Yeh, S-P., Ou, S-H., Doong, D-J., Kao, C.C. and Hsieh, D.W.J., 2006. “Joint probability analysis of waves and water level during typhoons”, Proc 3rd Chinese-German Joint Symposium on Coastal and Ocean Engineering. Citefout: Ongeldig label
<ref>; de naam "Yeh" wordt meerdere keren met andere inhoud gedefinieerd.
- Galiatsatou, P. and Prinos, P., 2011. “Bivariate Analysis of Extreme Wave and Storm Surge Events. Determining the Failure Area of Structures”, The Open Journal of Ocean Engineering, Vol. 4(1), 4-13.
- Dai Viet, N., Verhagen, H.J., van Gelder, P.H.A.J.M. and Vrijling, J.K., 2008. “Conceptual design for the breakwater system of the south of Doson Naval Base: Optimization versus deterministic design”, Proc. COPEDEC VII, Dubai, UAE, Paper No:053
- Van Gelder, P., Buijs, F., Horst, W., Kanning, W., Mai Van, C., Rajabalinejad, M., de Boer, E., Gupta, S., Shams, R., van Erp, N., Gouldby, B.P., Kingston, G., Sayers, P.B., Willis, M., Kortenhaus, A. and Lambrecht, H.J., 2009. “Reliability analysis of flood defence structures and systems in Europe”, Flood Risk Management: Research and Practice-Samuels et al. (eds), Taylor & Francis Group, London, ISBN 978-0-415-48507-4.
- Mai Van, C., van Gelder, P. H. A. J. M. and Vrijling, J. K., 2010. “Risk based design of coastal flood defences-A vietnam case”, In: Reliability, Risk and Safety: Theory and Applications – Briš, Guedes Soares & Martorell (eds), Taylor & Francis Group, London, ISBN 978-0-415-55509-8
- Voortman, H. G., 2002. “Risk-based design of large scale flood defence systems”, PhD thesis. Delft University of Technology, the Netherlands. |
Big Data Lesson Plans (1 result)
"Big data" is exactly what it sounds like, a really large amount of data. Science has always been at the forefront of gathering, visualizing, and trying to make sense of massive data sets. For example, think of the more than 661,000 (and counting) asteroids that have been discovered in our solar system. Or ponder that 1.2 million species have been caught, identified, classified, and catalogued on Earth. And then there are the approximately 3 billion base pairs sequenced from the human genome. Even before there was a term for it, scientists have been amassing and analyzing big data.
Scientists are concerned that climate change could cause the spread of mosquito populations that carry diseases like malaria, West Nile virus, Zika virus, and dengue fever. In this lesson plan, your students will access real-world data on mosquitoes at different locations throughout the United States, and examine the effects of temperature on mosquito populations.
Remote learning adaptation: This lesson plan can be conducted remotely. Students can work independently on the Explore section of…
NGSS Performance Expectations:
Construct an argument supported by empirical evidence that changes to physical or biological components of an ecosystem affect populations.
Use mathematical and/or computational representations of phenomena or design solutions to support explanations of factors that affect carrying capacity of ecosystems at different scales.
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Stretchy Balloons! Fun STEM Activity |
arithmeticArticle Free Pass
If three positive integers a, b, and c are in the relation ab = c, it is said that a and b are divisors or factors of c, or that a divides c (written a|c), and b divides c. The number c is said to be a multiple of a and a multiple of b.
The number 1 is called the unit, and it is clear that 1 is a divisor of every positive integer. If c can be expressed as a product ab in which a and b are positive integers each greater than 1, then c is called composite. A positive integer neither 1 nor composite is called a prime number. Thus, 2, 3, 5, 7, 11, 13, 17, 19, … are prime numbers. The ancient Greek mathematician Euclid proved in his Elements (c. 300 bc) that there are infinitely many prime numbers.
The fundamental theorem of arithmetic was proved by Gauss in his Disquisitiones Arithmeticae. It states that every composite number can be expressed as a product of prime numbers and that, save for the order in which the factors are written, this representation is unique. Gauss’s theorem follows rather directly from another theorem of Euclid to the effect that if a prime divides a product, then it also divides one of the factors in the product; for this reason the fundamental theorem is sometimes credited to Euclid.
For every finite set a1, a2, …, ak of positive integers, there exists a largest integer that divides each of these numbers, called their greatest common divisor (GCD). If the GCD = 1, the numbers are said to be relatively prime. There also exists a smallest positive integer that is a multiple of each of the numbers, called their least common multiple (LCM).
A systematic method for obtaining the GCD and LCM starts by factoring each ai (where i = 1, 2, …, k) into a product of primes p1, p2, …, ph, with the number of times that each distinct prime occurs indicated by qi; thus,
Then the GCD is obtained by multiplying together each prime that occurs in every ai as many times as it occurs the fewest (smallest power) among all of the ai. The LCM is obtained by multiplying together each prime that occurs in any of the ai as many times as it occurs the most (largest power) among all of the ai. An example is easily constructed. Given a1 = 3,000 = 23 × 31 × 53 and a2 = 2,646 = 21 × 33 × 72, the GCD = 21 × 31 = 6 and the LCM = 23 × 33 × 53 × 72 = 1,323,000. When only two numbers are involved, the product of the GCD and the LCM equals the product of the original numbers. (See the table for useful divisibility tests.)
If a and b are two positive integers, with a > b, two whole numbers q and r exist such that a = qb + r, with r less than b. The number q is called the partial quotient (the quotient if r = 0), and r is called the remainder. Using a process known as the Euclidean algorithm, which works because the GCD of a and b is equal to the GCD of b and r, the GCD can be obtained without first factoring the numbers a and b into prime factors. The Euclidean algorithm begins by determining the values of q and r, after which b and r assume the role of a and b and the process repeats until finally the remainder is zero; the last positive remainder is the GCD of the original two numbers. For example, starting with 544 and 119:
- 1. 544 = 4 × 119 + 68;
- 2. 119 = 1 × 68 + 51;
- 3. 68 = 1 × 51 + 17;
- 4. 51 = 3 × 17.
Thus, the GCD of 544 and 119 is 17.
From a less abstract point of view, the notion of division, or of fraction, may also be considered to arise as follows: if the duration of a given process is required to be known to an accuracy of better than one hour, the number of minutes may be specified; or, if the hour is to be retained as the fundamental unit, each minute may be represented by 1/60 or by
In general, the fractional unit 1/d is defined by the property d × 1/d = 1. The number n × 1/d is written n/d and is called a common fraction. It may be considered as the quotient of n divided by d. The number d is called the denominator (it determines the fractional unit or denomination), and n is called the numerator (it enumerates the number of fractional units that are taken). The numerator and denominator together are called the terms of the fraction. A positive fraction n/d is said to be proper if n < d; otherwise it is improper.
The numerator and denominator of a fraction are not unique, since for every positive integer k, the numerator and denominator of a fraction can each simultaneously be multiplied by the integer k without altering the fractional value. Every fraction can be written as the quotient of two relatively prime integers, however. In this form it is said to be in lowest terms.
The integers and fractions constitute what are called the rational numbers. The five fundamental laws stated earlier with regard to the positive integers can be generalized to apply to all rational numbers.
Adding and subtracting fractions
From the definition of fraction it follows that the sum (or difference) of two fractions having the same denominator is another fraction with this denominator, the numerator of which is the sum (or difference) of the numerators of the given fractions. Two fractions having different denominators may be added or subtracted by first reducing them to fractions with the same denominator. Thus, to add a/b and c/d, the LCM of b and d, often called the least common denominator of the fractions, must be determined. It follows that there exist numbers k and l such that kb = ld, and both fractions can be written with this common denominator, so that the sum or difference of the fractions is obtained by the simple operation of adding or subtracting the new numerators and placing the value over the new denominator.
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Functional programming is a programming paradigm in which we try to bind everything in pure mathematical functions style. It is a declarative type of programming style. Its main focus is on “what to solve” in contrast to an imperative style where the main focus is “how to solve”. It uses expressions instead of statements. An expression is evaluated to produce a value whereas a statement is executed to assign variables. Those functions have some special features discussed below.
Functional Programming is based on Lambda Calculus:
Lambda calculus is framework developed by Alonzo Church to study computations with functions. It can be called as the smallest programming language of the world. It gives the definition of what is computable. Anything that can be computed by lambda calculus is computable. It is equivalent to Turing machine in its ability to compute. It provides a theoretical framework for describing functions and their evaluation. It forms the basis of almost all current functional programming languages.
Fact: Alan Turing was a student of Alonzo Church who created Turing machine which laid the foundation of imperative programming style.
Concepts of functional programming:
- Pure functions
- Referential transparency
- Functions are First-Class and can be Higher-Order
- Variables are Immutable
Pure functions: These functions have two main properties. First, they always produce the same output for same arguments irrespective of anything else.
Secondly, they have no side-effects i.e. they do modify any argument or global variables or output something.
Later property is called immutability. The pure functions only result is the value it returns. They are deterministic.
Programs done using functional programming are easy to debug because pure functions have no side effect or hidden I/O. Pure functions also make it easier to write parallel/concurrent applications. When the code is written in this style, a smart compiler can do many things – it can parallelize the instructions, wait to evaluate results when need them, and memorize the results since the results never change as long as the input doesn’t change.
example of the pure function:
sum(x, y) // sum is function taking x and y as arguments return x + y // sum is returning sum of x and y without changing them
Recursion: There are no “for” or “while” loop in functional languages. Iteration in functional languages is implemented through recursion. Recursive functions repeatedly call themselves, until it reaches the base case.
example of the recursive function:
fib(n) if (n <= 1) return 1; else return fib(n - 1) + fib(n - 2);
Referential transparency: In functional programs variables once defined do not change their value throughout the program. Functional programs do not have assignment statements. If we have to store some value, we define new variables instead. This eliminates any chances of side effects because any variable can be replaced with its actual value at any point of execution. State of any variable is constant at any instant.
x = x + 1 // this changes the value assigned to the variable x. // So the expression is not referentially transparent.
Functions are First-Class and can be Higher-Order: First-class functions are treated as first-class variable. The first class variables can be passed to functions as parameter, can be returned from functions or stored in data structures. Higher order functions are the functions that take other functions as arguments and they can also return functions.
show_output(f) // function show_output is declared taking argument f // which are another function f(); // calling passed function print_gfg() // declaring another function print("hello gfg"); show_output(print_gfg) // passing function in another function
Variables are Immutable: In functional programming, we can’t modify a variable after it’s been initialized. We can create new variables – but we can’t modify existing variables, and this really helps to maintain state throughout the runtime of a program. Once we create a variable and set its value, we can have full confidence knowing that the value of that variable will never change.
Advantages and Disadvantages of Functional programming
- Pure functions are easier to understand because they don’t change any states and depend only on the input given to them. Whatever output they produce is the return value they give. Their function signature gives all the information about them i.e. their return type and their arguments.
- The ability of functional programming languages to treat functions as values and pass them to functions as parameters make the code more readable and easily understandable.
- Testing and debugging is easier. Since pure functions take only arguments and produce output, they don’t produce any changes don’t take input or produce some hidden output. They use immutable values, so it becomes easier to check some problems in programs written uses pure functions.
- It is used to implement concurrency/parallelism because pure functions don’t change variables or any other data outside of it.
- It adopts lazy evaluation which avoids repeated evaluation because the value is evaluated and stored only when it is needed.
- Sometimes writing pure functions can reduce the readability of code.
- Writing programs in recursive style instead of using loops can be bit intimidating.
- Writing pure functions are easy but combining them with rest of application and I/O operations is the difficult task.
- Immutable values and recursion can lead to decrease in performance.
- It is used in mathematical computations.
- It is needed where concurrency or parallelism is required.
Fact: Whatsapp needs only 50 engineers for its 900M user because Erlang is used to implement its concurrency needs. Facebook uses Haskell in its anti-spam system.
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TeachersFirst's US Census Resources
This collection of reviewed resources from TeachersFirst is selected to help teachers and students learn about the United States census and to plan related projects and classroom activities for both math and social studies classes at all levels. The census gives us a new lens to view geography, economics, history, current events, pop culture, and-- of course-- math! Whether you spend one class or an entire unit on the census, the ideas included within the "In the Classroom" portion of reviews will launch discussions and meaningful projects for student-centered learning.
GradesK to 3
In the ClassroomInclude this video when teaching students about gathering and sharing data to help them understand a census. Then, expand students' knowledge by conducting a census of your class. First, use Pear Deck, reviewed here, to build an interactive lesson to teach students about gathering and sharing data that includes this video as an introduction and includes questions to gather data on your class, such as how many boys and girls are in your class, how many students have siblings, etc. Next, use the Data Gif Maker, reviewed here, to quickly build graphs representing the data you collect in different formats.
Grades6 to 9
In the ClassroomUse the ideas shared in this article to create an interdisciplinary lesson to teach math, social studies, and writing objectives. For example, in this article, students work in groups to explore how many people in different states speak a language other than English at home. Take advantage of technology tools to engage and enhance this activity. For example, have students collect data using Microsoft Forms or Google Forms, then create and share charts and graphs using ChartGizmo, reviewed here. Use Google My Maps, reviewed here, to create an interactive map that includes all information created and shared by students.
Grades4 to 8
In the ClassroomTake advantage of this free lesson plan and the included ideas to introduce and reinforce the concept of statistical questions to your students. Integrate statistical questions with your lessons using Microsoft Excel or Google Sheets spreadsheets to visualize and analyze data. Ask students to share their data using Displayr, reviewed here to view the information in many different formats, including line graphs, bar charts, infographics, and much more. Extend learning by asking students to become statisticians by creating questions, gathering data, and sharing their analyses with peers. Use Microsoft Forms or Google Forms for students to collect data to begin their investigation.
Grades7 to 12
In the ClassroomPropose reasons for the differences in median income in a particular area or state. Research industry, agriculture, level of education, and other factors to determine the reasons. Investigate at the nearby ports and natural resources. Why do certain parts of the country have higher incomes and/or costs of living? How is income connected to education level? Students can identify patterns that exist among the data. They can form hypotheses about why. Create a campaign to bridge the wage gap by suggesting ideas to increase salaries in areas. Have students create a simple infographic sharing their findings using Easel.ly, reviewed here or Venngage reviewed here. Teachers of gifted will find "rich" possibilities for discussion from this site.
Grades7 to 12
This site includes advertising.
In the ClassroomUse this tool to determine how far a dollar goes in various locations. Allow students the opportunity to play with a standard salary and occupation to look at the differences in costs of living. Report on trends for cities in different areas of the country. Create a list locally of the various items that would be found in each category and the salary for that occupation where you live. Create a budget that allows for savings and vacation or large purchases. Use the data for practice with graphing and creating infographics. In government classes, use this tool and census data to make hypotheses or draw conclusions about patterns of population movement and economic trends in various areas of the country, especially in connection with political trends and election data.
Grades3 to 12
tag(s): thanksgiving (23)
In the ClassroomChoose a statistic your students can estimate then use this site to help develop estimation and number sense--all in a holiday spirit. Gobble, Gobble! Perhaps create an infographic to display your favorite data. An interesting question to ask: what other data would you like to learn from the U.S. census the next time they do one?
Grades6 to 12
In the ClassroomFirst, it's important for students to know that the US Constitution requires a census, and second, that the information gathered is used in a variety of important ways that affect them directly. The first data posted looks at how shifts in population density will change the way various geographic areas of the country are represented in the US government. Consider reading the Director's blog for further analysis of how census data is being used on a local, state, and national level. Of course, the data are perfect for using in math and civics classes for teaching graph reading and creation, and for providing real-life information to use in statistical analysis. A civics or sociology class might download a copy of the census form and consider what the questions tell us about how families live in the 21st century. What questions might students add to a future census form that would reflect how things are changing for their generation?
Grades6 to 12
There are two lesson plans for this site. The first one, "World Portrait" is where students survey and select 100 people to represent their community and the world's population. There are also suggestions for how a class might select one person. The plan is download-able and has ideas that include criteria for the people who are nominated, discussion topics and activities, questions for the community profile, a questionnaire for the people nominated, an image release form, just to name a few. Student results are to be captured in film, photography, music and text. The other lesson plan on this site is titled "100 People Under the Sun." In order to download this lesson you must register, it is free, but you will have to log in when viewing the plan. With this lesson "...students will develop key leadership skills to help raise their community's awareness of its energy use, as well as its motivation to advance sustainable approaches."
In the ClassroomThis project is the perfect opportunity to collaborate with others in your building! Math students could complete a school and community survey (which could tie in with 2010 U.S. census). Social Studies students could interpret data collected in the survey (also could be tied into the 2010 census) and extrapolate parameters for nominations. Language Arts students would finalize the nominations and develop the essays. Technology, yearbook, and art classes can draw the portraits or produce them digitally, create a video for submission to 100 People project, and your more advanced technology students can create a website for content display. WebNode, reviewed here, or a wiki would be great tools to use for the website! Not familiar with wikis? Check out the TeachersFirst's Wiki Walk-Through.
Of course, you don't have to collaborate with others. This unit would work well in any world culture class at any level, or even in language arts when studying multicultural literature and settings. Here's another idea: Many of us have seen the video Did You Know? Predicting Future Statistics>. The beginning states "If you are one in a million in China there are 1,300 people just like you." But it also gives statistics like "During the course of this presentation 60 babies will be born in the U.S., 244 babies will be born in China, and 351 babies will be born in India..." You can use your and your student's ideas to come up with your own statistics. Something like how many people will be working and sleeping between the hours of midnight and 6:00 A.M. in the U.S., China, and India (or any other country you wish to include). Use this to lead to discussions of time zones and all sorts of other peripheral ideas and decisions students will have to think about.
Grades2 to 12
In the ClassroomShare this video and song on your projector and screen, or whiteboard, as students come into the classroom. Use it as a lead-in to a discussion about the importance of the census. You can post some of the information from "Statistics - Census in Schools," reviewed here. From this same site you can go to "Fun Facts," that you can use in elementary, middle school, and high school classrooms. One last suggestion: Once you've completed your census unit, discussion, etc. You might want to have your class participate in the "100 People: A World Portrait" reviewed here. Don't forget about the possibility of using the census in math class to understand data and graphing, as well.
GradesK to 12
In the ClassroomThe K-4 lessons are perfect to use the way they are, or you might want to do some comparing of information between the different grade levels within your school. Another idea is to pair up third and fourth graders with the kindergartners or first and second graders to read the story and work on the worksheets together. Of course, using your projector and interactive whiteboard with the whole class is a must for explanations of the lessons. This site is very colorful, so project what you can! You may want to introduce this unit with a catchy, educational song and video about the census reviewed here. For teachers of older students there are "Lessons Using the 2000 Census Data," "Quick Facts," and much more. One last suggestion: Once you've completed your census unit, discussion, etc. You might want to have your class participate in the "100 People: A World Portrait" project reviewed here.
Grades3 to 6
tag(s): states (120) |
Sierra had to pay the school for two textbooks that she lost. Is this a true statement? Problem Set For each of the relationships described below, write an inequality that relates the rational numbers. Order the Changes in Total Rainfall: Sixteen degrees Celsius is warmer than zero degrees Celsius.
In 7 years, Ellie will be old enough to vote in an election. For example, here is a problem where we can use the Subtraction Property to help us find a range of possible solutions: Fill in the blanks below to create inequality statements that compare the Changes in Total Rainfall for each month the right-most column of the table.
This pattern holds true for all inequalities—if they are multiplied by a negative number, the inequality flips. Writing Inequality Statements Involving Rational Numbers Write one inequality statement to show the relationship between the following shoe sizes: The resulting value of AC Graph your answer from the Opening Exercise, part a on the number line below.
From Greatest to Least: Common Core For Grade 6 Examples, solutions, videos, and worksheets to help Grade 6 students learn to write and explain inequality statements involving rational numbers.
What can you say about how old she is now? Write a real-world situation that is represented by the following inequality: What happens if we multiply both numbers by the same value c? Then write an inequality statement that shows the relationship between these two numbers. Her mother wrote two separate checks for each expense.
Explain the position of the numbers on a number line. What relationship would she expect to see between the two stocks at the end of Tuesday? We can then use the Subtraction Property of Inequality to solve for e. We could write this inequality as: The data is reflected in the table below.
Also graph the points associated with 4 and 5 on the number line. Students justify inequality statements involving rational numbers. On this number line, points B and A are our original values of 2 and 5.
They lost yard on the second play. For each of the following, use the information given by the inequality to describe the relative position of the numbers on a horizontal number line. You must be at least 18 years old to vote. In December, the total snowfall was One possible value for the amount of money in my pocket is: On a vertical number line?
They lost 3 yards on the first play. For example, explain the process for writing one inequality statement comparing ,-3 ,8 and Closing What can you do before writing an inequality statement involving three numbers that makes it easier to write the inequality statement?
If we divide both sides by a positive number, the inequality is preserved. The Division Properties of Inequality work the same way. This is written formally as: Write one inequality statement that shows the relationship among all three numbers.
If we take the same two numbers and multiply them by If you know the order of a set of numbers, how can you represent the order using inequality symbols?Write an inequality that represents the statement “x is greater than 2 and less than 8.” - /5(1).
Example 1. A number minus 4 is greater than 2. The words "a number" tell us that we need a variable in our inequality, and that the result of the variable less "4" is more than 2. We're writing inequalities by using information from the word problems.
He mixed 3/2 cups of wheat flour.
3/2 is the exact same thing as 1 and 1/2, if we were to write it as a mixed number. To make the batter, he mixes 11/16 cups tapioca flour with 3/8 rice flour and some water.
Write an inequality to express the relationship between. Write a fraction inequality statement for the sixths and tenths bars from your mat. Ask a few students for their inequalities.! Find three bars on your mat that are side-by-side and which decrease in shaded For any fraction equal to 1/2, you may place a marker on all the half-bars on your mat, regardless of their color.!
The first player. mi-centre.com5, mi-centre.com8 Lesson 7 Write and Graph Inequalities 27 Main Idea Write and graph inequalities. Write and Graph Inequalities FAIR Jessica is trying to County State Examples 1–3 Write an inequality for each sentence.
The movie will be no more than 90 minutes in length. 2. The mountain is at least feet tall. Inequalities An inequality is a statement that one amount or quantity is greater than (or equal to) or less than (or equal to) another amount or quantity.
The following symbols are used to represent inequalities.Download |
4 and 5-Digit Addition. This page has resources for teaching addition with 4 and 5-digit numbers. Includes column addition exercises, an addition crossword, and word problems. (Approx. level: 3rd grade, 4th grade, 5th grade).
Fraction Addition & Subtraction. On these worksheets, students will practice adding and subtracting fractions and mixed numbers. Includes fractions with same denominator, and different denominators. (Approx. levels: 3rd, 4th, 5th, and 6th grades)
We have all types of measurement worksheets. There are worksheets for linear measurement with a ruler - yards, feet, inches. There are capacity worksheets for measuring gallons, quarts, pints, and cups. We even have Fahrenheit and Celsius temperature worksheets.
Writing Algebraic Expressions. Write simple expressions in algebraic form with a variable. 5th through 7th Grades. |
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In economics, demand is the utility for a good or service of an economic agent, relative to his/her income. (Note: This distinguishes "demand" from "quantity demanded", where demand is a listing or graphing of quantity demanded at each possible price. In contrast to demand, quantity demanded is the exact quantity demanded at a certain price. Changing the actual price will change the quantity demanded, but it will not change the demand, because demand is a listing of quantities that would be bought at various prices, not just the actual price.)
Demand is a buyer's willingness and ability to pay a price for a specific quantity of a good or service. Demand refers to how much (quantity) of a product or service is desired by buyers at various prices. The quantity demanded is the amount of a product people are willing to buy at a certain price; the relationship between price and quantity demanded is known as the demand. (see also supply and demand). The term demand signifies the ability or the willingness to buy a particular commodity at a given point of time, ceteris paribus. Utility preferences and choices underlying demand can be represented as functions of cost, benefit, odds and other variables.
- 1 Overview
- 2 Factors affecting elasticity of demand
- 3 Demand function and demand equation
- 4 Demand curve
- 5 Price elasticity of demand (PED)
- 6 Market structure and the demand curve
- 7 Inverse demand function
- 8 Residual demand curve
- 9 Is the demand curve for PC firm really flat?
- 10 Demand management in economics
- 11 Different types of goods demand
- 12 See also
- 13 Notes
- 14 Further reading
- 15 External links
Economists record demand on a demand schedule and plot it on a graph as a demand curve that is usually downward sloping. The downward slope reflects the negative or inverse relationship between price and quantity demanded: as price decreases, quantity demanded increases. Changing market price would move the equilibrium point for quantity demanded up and down ALONG the demand curve, but would not shift the demand curve - and would not change demand for the good. An actual change in demand means that the whole curve of quantity-demanded vs. price, has shifted. This curve is the demand, sometimes also called the demand curve. Change in demand and not just quantity-demanded could come from changes in consumer wealth, from consumer preferences, or from the prices of substitutes or complements for the product.
In principle, each consumer has a demand curve for any product that he or she is willing and able to buy, and the consumer's demand curve is equal to the marginal utility (benefit) curve, assuming full information and the lack of frictions that would perturb the consumer's choice. When the demand curves of all consumers are added up, the result is the market demand curve for that product which also indicates a negative or inverse relationship between the price and quantity demanded. If there are no externalities, the market demand curve is also equal to the social utility (benefit) curve.
Factors affecting elasticity of demand
Innumerable factors and circumstances could affect a buyer's willingness or ability to buy a good. Some of the more common factors are:
- Good's own price: The basic demand relationship is between potential prices of a good and the quantities that would be purchased at those prices. Generally the relationship is negative meaning that an increase in price will induce a decrease in the quantity demanded. This negative relationship is embodied in the downward slope of the consumer demand curve. The assumption of a negative relationship is reasonable and intuitive. If the price of a new novel is high, a person might decide to borrow the book from the public library rather than buy it.
- Price of related goods: The principal related goods are complements and substitutes. A complement is a good that is used with the primary good. Examples include hotdogs and mustard, beer and pretzels, automobiles and gasoline.(Perfect complements behave as a single good.) If the price of the complement goes up the quantity demanded of the other good goes down. Mathematically, the variable representing the price of the complementary good would have a negative coefficient in the demand function. For example, Qd = a - P - Pg where Q is the quantity of automobiles demanded, P is the price of automobiles and Pg is the price of gasoline. The other main category of related goods are substitutes. Substitutes are goods that can be used in place of the primary good. The mathematical relationship between the price of the substitute and the demand for the good in question is positive. If the price of the substitute goes down the demand for the good in question goes down.
- Personal Disposable Income: In most cases, the more disposable income (income after tax and receipt of benefits) a person has the more likely that person is to buy.
- Tastes or preferences: The greater the desire to own a good the more likely one is to buy the good. There is a basic distinction between desire and demand. Desire is a measure of the willingness to buy a good based on its intrinsic qualities. Demand is the willingness and ability to put one's desires into effect. It is assumed that tastes and preferences are relatively constant.
- Consumer expectations about future prices, income and availability: If a consumer believes that the price of the good will be higher in the future, he/she is more likely to purchase the good now. If the consumer expects that his/her income will be higher in the future, the consumer may buy the good now. Availability (supply side) as well as predicted or expected availability also affects both price and demand.
- Population:If the population grows this means that demand will also increase.
- Nature of the good:If the good is a basic commodity, it will lead to a higher demand
- This list is not exhaustive. All facts and circumstances that a buyer finds relevant to his willingness or ability to buy goods can affect demand. For example, a person caught in an unexpected storm is more likely to buy an umbrella than if the weather were bright and sunny.
Demand function and demand equation
The demand equation is the mathematical expression of the relationship between the quantity of a good demanded and those factors that affect the willingness and ability of a consumer to buy the good. For example, Qd = f(P; Prg, Y) is a demand equation where Qd is the quantity of a good demanded, P is the price of the good, Prg is the price of a related good, and Y is income; the function on the right side of the equation is called the demand function. The semi-colon in the list of arguments in the demand function means that the variables to the right are being held constant as one plots the demand curve in (quantity, price) space. A simple example of a demand equation is Qd = 325 - P - 30Prg + 1.4Y. Here 325 is the repository of all relevant non-specified factors that affect demand for the product. P is the price of the good. The coefficient is negative in accordance with the law of demand. The related good may be either a complement or a substitute. If a complement, the coefficient of its price would be negative as in this example. If a substitute, the coefficient of its price would be positive. Income, Y, has a positive coefficient indicating that the good is a normal good. If the coefficient was negative the good in question would be an inferior good meaning that the demand for the good would fall as the consumer's income increased. Specifying values for the non price determinants, Prg = 4.00 and Y = 50, results in the demand equation Q = 325 - P - 30(4) +1.4(50) or Q = 275 - P. If income were to increase to 55 the new demand equation would be Q = 282 - P. Graphically this change in a non price determinant of demand would be reflected in an outward shift of the demand function caused by a change in the x intercept. Devon Clarke
In economics, the demand curve is the graph depicting the relationship between the price of a certain commodity and the amount of it that consumers are willing and able to purchase at that given price.
Price elasticity of demand (PED)
PED is a measure of the sensitivity of the quantity variable, Q, to changes in the price variable, P. Elasticity answers the question of the percent by which the quantity demanded will change relative to (divided by) a given percentage change in the price. For infinitesimal changes the formula for calculating PED is the absolute value of (∂Q/∂P)×(P/Q).
Determinants of PED
The overriding factor in determining PED is the willingness and ability of consumers after a price changes to postpone immediate consumption decisions concerning the good and to search for substitutes (wait and look).
Elasticity along linear demand curve
The slope of a linear demand curve is constant. The elasticity of demand changes continuously as one moves down the demand curve because the ratio of price to quantity continuously falls. At the point the demand curve intersects the y-axis PED is infinitely elastic, because the variable Q appearing in the denominator of the elasticity formula is zero there. At the point the demand curve intersects the x-axis PED is zero, because the variable P appearing in the numerator of the elasticity formula is zero there. At one point on the demand curve PED is unitary elastic: PED equals one. Above the point of unitary elasticity is the elastic range of the demand curve (meaning that the elasticity is greater than one). Below is the inelastic range, in which the elasticity is less than one. The decline in elasticity as one moves down the curve is due to the falling P/Q ratio.
Constant price elasticity demand
where a and c are parameters, and the constant price elasticity is c and .
Market structure and the demand curve
In perfectly competitive markets the demand curve, the average revenue curve, and the marginal revenue curve all coincide and are horizontal at the market-given price. The demand curve is perfectly elastic and coincides with the average and marginal revenue curves. Economic actors are price-takers. Perfectly competitive firms have zero market power; that is, they have no ability to affect the terms and conditions of exchange. A perfectly competitive firm's decisions are limited to whether to produce and if so, how much. In less than perfectly competitive markets the demand curve is negatively sloped and there is a separate marginal revenue curve. A firm in a less than perfectly competitive market is a price-setter. The firm can decide how much to produce or what price to charge. In deciding one variable the firm is necessarily determining the other variable
Inverse demand function
In its standard form a linear demand equation is Q = a - bP. That is, quantity demanded is a function of price. The inverse demand equation, or price equation, treats price as a function g of quantity demanded: P = f(Q). To compute the inverse demand equation, simply solve for P from the demand equation. For example, if the demand equation is Q = 240 - 2P then the inverse demand equation would be P = 120 - .5Q, the right side of which is the inverse demand function.
The inverse demand function is useful in deriving the total and marginal revenue functions. Total revenue equals price, P, times quantity, Q, or TR = P×Q. Multiply the inverse demand function by Q to derive the total revenue function: TR = (120 - .5Q) × Q = 120Q - 0.5Q². The marginal revenue function is the first derivative of the total revenue function; here MR = 120 - Q. Note that the MR function has the same y-intercept as the inverse demand function in this linear example; the x-intercept of the MR function is one-half the value of that of the demand function, and the slope of the MR function is twice that of the inverse demand function. This relationship holds true for all linear demand equations. The importance of being able to quickly calculate MR is that the profit-maximizing condition for firms regardless of market structure is to produce where marginal revenue equals marginal cost (MC). To derive MC the first derivative of the total cost function is taken. For example assume cost, C, equals 420 + 60Q + Q2. Then MC = 60 + 2Q. Equating MR to MC and solving for Q gives Q = 20. So 20 is the profit maximizing quantity: to find the profit-maximizing price simply plug the value of Q into the inverse demand equation and solve for P.
Residual demand curve
The demand curve facing a particular firm is called the residual demand curve. The residual demand curve is the market demand that is not met by other firms in the industry at a given price. The residual demand curve is the market demand curve D(p), minus the supply of other organizations, So(p): Dr(p) = D(p) - So(p )
Is the demand curve for PC firm really flat?
Practically every introductory microeconomics text describes the demand curve facing a perfectly competitive firm as being flat or horizontal. A horizontal demand curve is perfectly elastic. If there are n identical firms in the market then the elasticity of demand PED facing any one firm is
- PEDmi = nPEDm - (n - 1) PES
where PEDm is the market elasticity of demand, PES is the elasticity of supply of each of the other firms, and (n -1) is the number of other firms. This formula suggests two things. The demand curve is not perfectly elastic and if there are a large number of firms in the industry the elasticity of demand for any individual firm will be extremely high and the demand curve facing the firm will be nearly flat.
- PEDmi = -1(80) - (79 x 3)
- PEDmi = -80 - 237 = - 317
That is the firm PED is 317 times as elastic as the market PED. If a firm raised its price "by one tenth of one percent demand would drop by nearly one third." if the firm raised its price by three tenths of one percent the quantity demanded would drop by nearly 100%. Three tenths of one percent marks the effective range of pricing power the firm has because any attempt to raise prices by a higher percentage will effectively reduce quantity demanded to zero.
Demand management in economics
Demand management in economics is the art or science of controlling economic or aggregate demand to avoid a recession. Such management is inspired by Keynesian macroeconomics, and Keynesian economics is sometimes referred to as demand-side economics.
Different types of goods demand
Negative demand: If the market response to a product is negative, it shows that people are not aware of the features of the service and the benefits offered. Under such circumstances, the marketing unit of a service firm has to understand the psyche of the potential buyers and find out the prime reason for the rejection of the service. For example: if passengers refuse a bus conductor's call to board the bus. The service firm has to come up with an appropriate strategy to remove the misunderstandings of the potential buyers. A strategy needs to be designed to transform the negative demand into a positive demand.
No demand: If people are unaware, have insufficient information about a service or due to the consumer's indifference this type of a demand situation could occur. The marketing unit of the firm should focus on promotional campaigns and communicating reasons for potential customers to use the firm's services. Service differentiation is one of the popular strategies used to compete in a no demand situation in the market.
Latent demand: At any given time it is impossible to have a set of services that offer total satisfaction to all the needs and wants of society. In the market there exists a gap between desirables and the availables. There is always a search on for better and newer offers to fill the gap between desirability and availability. Latent demand is a phenomenon of any economy at any given time, it should be looked upon as a business opportunity by service firms and they should orient themselves to identify and exploit such opportunities at the right time. For example a passenger traveling in an ordinary bus dreams of traveling in a luxury bus. Therefore, latent demand is nothing but the gap between desirability and availability.
Seasonal demand:Some services do not have an all year round demand, they might be required only at a certain period of time. Seasons all over the world are very diverse. Seasonal demands create many problems to service organizations, such as:- idling the capacity, fixed cost and excess expenditure on marketing and promotions. Strategies used by firms to overcome this hurdle are like - to nurture the service consumption habit of customers so as to make the demand unseasonal, or other than that firms recognize markets elsewhere in the world during the off-season period. Hence, this presents and opportunity to target different markets with the appropriate season in different parts of the world. For example the need for Christmas cards comes around once a year. Or the, seasonal fruits in a country.
Demand patterns need to be studied in different segments of the market. Service organizations need to constantly study changing demands related to there service offerings over various time periods. They have to develop a system to chart these demand fluctuations, which helps them in predicting the demand cycles. Demands do fluctuate randomly, therefore, they should be followed on a daily, weekly or a monthly basis.
- Demand chain
- Demand curve
- Demand schedule
- Derived demand
- Planned obsolescence
- Law of demand
- Law of supply
- Supply (economics)
- Supply-side economics
- Supply and demand
- Sullivan, Arthur; Steven M. Sheffrin (2003). Economics: Principles in action. Upper Saddle River, New Jersey 07458: Pearson Prentice Hall. p. 79. ISBN 0-13-063085-3.
- Colander, David C. Microeconomics 7th ed. pp. 132-33 McGraw-Hill 2008.
- Colander, David C. Microeconomics 7th ed. pp. 132-33. McGraw-Hill 2008.
- The perfectly competitive firm's demand curve is not in fact flat. However, if there are numerous firms in the industry the demand curve of an individual firm is likely to be extremely elastic, for a discussion of residual demand curves see Perloff (2008) at pp. 245–246.
- The form of the inverse linear demand equation is P = a/b - 1/bQ.
- Samuelson, W & Marks, S. Managerial Economics 4th ed. p. 37. Wiley 2003.
- Perloff (2008) p. 243.
- Perloff (2008) p. 245–246
- Perloff (2008) p. 244.
- Prloff (2008) p. 243.
- Ehrbar, Al (2008). "Supply". In David R. Henderson. Concise Encyclopedia of Economics (2nd ed.). Indianapolis: Library of Economics and Liberty. ISBN 978-0865976658. OCLC 237794267.
- Henderson, David R. (2008). "Demand". Concise Encyclopedia of Economics (2nd ed.). Indianapolis: Library of Economics and Liberty. ISBN 978-0865976658. OCLC 237794267.
- Friedman, Milton (December 1949). "The Marshallian Demand Curve". Journal of Political Economy 57 (6): 463. doi:10.1086/256879. JSTOR 1826553.
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Outer space, commonly shortened to space, is the expanse that exists beyond Earth and its atmosphere and between celestial bodies. Outer space is not completely empty—it is a near perfect vacuum containing a low density of particles, predominantly a plasma of hydrogen and helium, as well as electromagnetic radiation, magnetic fields, neutrinos, dust, and cosmic rays. The baseline temperature of outer space, as set by the background radiation from the Big Bang, is 2.7255 kelvins (−270.4245 °C; −454.7641 °F) +/-0.002 K. The plasma between galaxies is thought to account for about half of the baryonic (ordinary) matter in the universe, having a number density of less than one hydrogen atom per cubic metre and a temperature of millions of kelvins. Local concentrations of matter have condensed into stars and galaxies. Studies indicate that 90% of the mass in most galaxies is in an unknown form, called dark matter, which interacts with other matter through gravitational but not electromagnetic forces. Observations suggest that the majority of the mass-energy in the observable universe is dark energy, a type of vacuum energy that is poorly understood. Intergalactic space takes up most of the volume of the universe, but even galaxies and star systems consist almost entirely of empty space.
Outer space does not begin at a definite altitude above the Earth's surface. The Kármán line, an altitude of 100 km (62 mi) above sea level, is conventionally used as the start of outer space in space treaties and for aerospace records keeping. The framework for international space law was established by the Outer Space Treaty, which entered into force on 10 October 1967. This treaty precludes any claims of national sovereignty and permits all states to freely explore outer space. Despite the drafting of UN resolutions for the peaceful uses of outer space, anti-satellite weapons have been tested in Earth orbit.
Humans began the physical exploration of space during the 20th century with the advent of high-altitude balloon flights. This was followed by crewed rocket flights and, then, crewed Earth orbit, first achieved by Yuri Gagarin of the Soviet Union in 1961. Due to the high cost of getting into space, human spaceflight has been limited to low Earth orbit and the Moon. On the other hand, uncrewed spacecraft have reached all of the known planets in the Solar System.
Outer space represents a challenging environment for human exploration because of the hazards of vacuum and radiation. Microgravity also has a negative effect on human physiology that causes both muscle atrophy and bone loss. In addition to these health and environmental issues, the economic cost of putting objects, including humans, into space is very high.
Formation and stateEdit
The size of the whole universe is unknown, and it might be infinite in extent. According to the Big Bang theory, the very early Universe was an extremely hot and dense state about 13.8 billion years ago which rapidly expanded. About 380,000 years later the Universe had cooled sufficiently to allow protons and electrons to combine and form hydrogen—the so-called recombination epoch. When this happened, matter and energy became decoupled, allowing photons to travel freely through the continually expanding space. Matter that remained following the initial expansion has since undergone gravitational collapse to create stars, galaxies and other astronomical objects, leaving behind a deep vacuum that forms what is now called outer space. As light has a finite velocity, this theory also constrains the size of the directly observable universe.
The present day shape of the universe has been determined from measurements of the cosmic microwave background using satellites like the Wilkinson Microwave Anisotropy Probe. These observations indicate that the spatial geometry of the observable universe is "flat", meaning that photons on parallel paths at one point remain parallel as they travel through space to the limit of the observable universe, except for local gravity. The flat Universe, combined with the measured mass density of the Universe and the accelerating expansion of the Universe, indicates that space has a non-zero vacuum energy, which is called dark energy.
Estimates put the average energy density of the present day Universe at the equivalent of 5.9 protons per cubic meter, including dark energy, dark matter, and baryonic matter (ordinary matter composed of atoms). The atoms account for only 4.6% of the total energy density, or a density of one proton per four cubic meters. The density of the Universe is clearly not uniform; it ranges from relatively high density in galaxies—including very high density in structures within galaxies, such as planets, stars, and black holes—to conditions in vast voids that have much lower density, at least in terms of visible matter. Unlike matter and dark matter, dark energy seems not to be concentrated in galaxies: although dark energy may account for a majority of the mass-energy in the Universe, dark energy's influence is 5 orders of magnitude smaller than the influence of gravity from matter and dark matter within the Milky Way.
Outer space is the closest known approximation to a perfect vacuum. It has effectively no friction, allowing stars, planets, and moons to move freely along their ideal orbits, following the initial formation stage. The deep vacuum of intergalactic space is not devoid of matter, as it contains a few hydrogen atoms per cubic meter. By comparison, the air humans breathe contains about 1025 molecules per cubic meter. The low density of matter in outer space means that electromagnetic radiation can travel great distances without being scattered: the mean free path of a photon in intergalactic space is about 1023 km, or 10 billion light years. In spite of this, extinction, which is the absorption and scattering of photons by dust and gas, is an important factor in galactic and intergalactic astronomy.
Stars, planets, and moons retain their atmospheres by gravitational attraction. Atmospheres have no clearly delineated upper boundary: the density of atmospheric gas gradually decreases with distance from the object until it becomes indistinguishable from outer space. The Earth's atmospheric pressure drops to about 0.032 Pa at 100 kilometres (62 miles) of altitude, compared to 100,000 Pa for the International Union of Pure and Applied Chemistry (IUPAC) definition of standard pressure. Above this altitude, isotropic gas pressure rapidly becomes insignificant when compared to radiation pressure from the Sun and the dynamic pressure of the solar wind. The thermosphere in this range has large gradients of pressure, temperature and composition, and varies greatly due to space weather.
The temperature of outer space is measured in terms of the kinetic activity of the gas, as it is on Earth. The radiation of outer space has a different temperature than the kinetic temperature of the gas, meaning that the gas and radiation are not in thermodynamic equilibrium. All of the observable universe is filled with photons that were created during the Big Bang, which is known as the cosmic microwave background radiation (CMB). (There is quite likely a correspondingly large number of neutrinos called the cosmic neutrino background.) The current black body temperature of the background radiation is about 3 K (−270 °C; −454 °F). The gas temperatures in outer space can vary widely. For example, the temperature in the Boomerang Nebula is 1 K, while the solar corona reaches temperatures over 1.2–2.6 million K.
Magnetic fields have been detected in the space around just about every class of celestial object. Star formation in spiral galaxies can generate small-scale dynamos, creating turbulent magnetic field strengths of around 5–10 μG. The Davis–Greenstein effect causes elongated dust grains to align themselves with a galaxy's magnetic field, resulting in weak optical polarization. This has been used to show ordered magnetic fields exist in several nearby galaxies. Magneto-hydrodynamic processes in active elliptical galaxies produce their characteristic jets and radio lobes. Non-thermal radio sources have been detected even among the most distant, high-z sources, indicating the presence of magnetic fields.
Outside a protective atmosphere and magnetic field, there are few obstacles to the passage through space of energetic subatomic particles known as cosmic rays. These particles have energies ranging from about 106 eV up to an extreme 1020 eV of ultra-high-energy cosmic rays. The peak flux of cosmic rays occurs at energies of about 109 eV, with approximately 87% protons, 12% helium nuclei and 1% heavier nuclei. In the high energy range, the flux of electrons is only about 1% of that of protons. Cosmic rays can damage electronic components and pose a health threat to space travelers. According to astronauts, like Don Pettit, space has a burned/metallic odor that clings to their suits and equipment, similar to the scent of an arc welding torch.
Effect on biology and human bodiesEdit
Despite the harsh environment, several life forms have been found that can withstand extreme space conditions for extended periods. Species of lichen carried on the ESA BIOPAN facility survived exposure for ten days in 2007. Seeds of Arabidopsis thaliana and Nicotiana tabacum germinated after being exposed to space for 1.5 years. A strain of Bacillus subtilis has survived 559 days when exposed to low-Earth orbit or a simulated martian environment. The lithopanspermia hypothesis suggests that rocks ejected into outer space from life-harboring planets may successfully transport life forms to another habitable world. A conjecture is that just such a scenario occurred early in the history of the Solar System, with potentially microorganism-bearing rocks being exchanged between Venus, Earth, and Mars.
Even at relatively low altitudes in the Earth's atmosphere, conditions are hostile to the human body. The altitude where atmospheric pressure matches the vapor pressure of water at the temperature of the human body is called the Armstrong line, named after American physician Harry G. Armstrong. It is located at an altitude of around 19.14 km (11.89 mi). At or above the Armstrong line, fluids in the throat and lungs boil away. More specifically, exposed bodily liquids such as saliva, tears, and liquids in the lungs boil away. Hence, at this altitude, human survival requires a pressure suit, or a pressurized capsule.
Out in space, sudden exposure of an unprotected human to very low pressure, such as during a rapid decompression, can cause pulmonary barotrauma—a rupture of the lungs, due to the large pressure differential between inside and outside the chest. Even if the subject's airway is fully open, the flow of air through the windpipe may be too slow to prevent the rupture. Rapid decompression can rupture eardrums and sinuses, bruising and blood seep can occur in soft tissues, and shock can cause an increase in oxygen consumption that leads to hypoxia.
As a consequence of rapid decompression, oxygen dissolved in the blood empties into the lungs to try to equalize the partial pressure gradient. Once the deoxygenated blood arrives at the brain, humans lose consciousness after a few seconds and die of hypoxia within minutes. Blood and other body fluids boil when the pressure drops below 6.3 kPa, and this condition is called ebullism. The steam may bloat the body to twice its normal size and slow circulation, but tissues are elastic and porous enough to prevent rupture. Ebullism is slowed by the pressure containment of blood vessels, so some blood remains liquid. Swelling and ebullism can be reduced by containment in a pressure suit. The Crew Altitude Protection Suit (CAPS), a fitted elastic garment designed in the 1960s for astronauts, prevents ebullism at pressures as low as 2 kPa. Supplemental oxygen is needed at 8 km (5 mi) to provide enough oxygen for breathing and to prevent water loss, while above 20 km (12 mi) pressure suits are essential to prevent ebullism. Most space suits use around 30–39 kPa of pure oxygen, about the same as on the Earth's surface. This pressure is high enough to prevent ebullism, but evaporation of nitrogen dissolved in the blood could still cause decompression sickness and gas embolisms if not managed.
Humans evolved for life in Earth gravity, and exposure to weightlessness has been shown to have deleterious effects on human health. Initially, more than 50% of astronauts experience space motion sickness. This can cause nausea and vomiting, vertigo, headaches, lethargy, and overall malaise. The duration of space sickness varies, but it typically lasts for 1–3 days, after which the body adjusts to the new environment. Longer-term exposure to weightlessness results in muscle atrophy and deterioration of the skeleton, or spaceflight osteopenia. These effects can be minimized through a regimen of exercise. Other effects include fluid redistribution, slowing of the cardiovascular system, decreased production of red blood cells, balance disorders, and a weakening of the immune system. Lesser symptoms include loss of body mass, nasal congestion, sleep disturbance, and puffiness of the face.
During long-duration space travel, radiation can pose an acute health hazard. Exposure to high-energy, ionizing cosmic rays can result in fatigue, nausea, vomiting, as well as damage to the immune system and changes to the white blood cell count. Over longer durations, symptoms include an increased risk of cancer, plus damage to the eyes, nervous system, lungs and the gastrointestinal tract. On a round-trip Mars mission lasting three years, a large fraction of the cells in an astronaut's body would be traversed and potentially damaged by high energy nuclei. The energy of such particles is significantly diminished by the shielding provided by the walls of a spacecraft and can be further diminished by water containers and other barriers. The impact of the cosmic rays upon the shielding produces additional radiation that can affect the crew. Further research is needed to assess the radiation hazards and determine suitable countermeasures.
Space is a partial vacuum: its different regions are defined by the various atmospheres and "winds" that dominate within them, and extend to the point at which those winds give way to those beyond. Geospace extends from Earth's atmosphere to the outer reaches of Earth's magnetic field, whereupon it gives way to the solar wind of interplanetary space. Interplanetary space extends to the heliopause, whereupon the solar wind gives way to the winds of the interstellar medium. Interstellar space then continues to the edges of the galaxy, where it fades into the intergalactic void.
Geospace is the region of outer space near Earth, including the upper atmosphere and magnetosphere. The Van Allen radiation belts lie within the geospace. The outer boundary of geospace is the magnetopause, which forms an interface between the Earth's magnetosphere and the solar wind. The inner boundary is the ionosphere. The variable space-weather conditions of geospace are affected by the behavior of the Sun and the solar wind; the subject of geospace is interlinked with heliophysics—the study of the Sun and its impact on the planets of the Solar System.
The day-side magnetopause is compressed by solar-wind pressure—the subsolar distance from the center of the Earth is typically 10 Earth radii. On the night side, the solar wind stretches the magnetosphere to form a magnetotail that sometimes extends out to more than 100–200 Earth radii. For roughly four days of each month, the lunar surface is shielded from the solar wind as the Moon passes through the magnetotail.
Geospace is populated by electrically charged particles at very low densities, the motions of which are controlled by the Earth's magnetic field. These plasmas form a medium from which storm-like disturbances powered by the solar wind can drive electrical currents into the Earth's upper atmosphere. Geomagnetic storms can disturb two regions of geospace, the radiation belts and the ionosphere. These storms increase fluxes of energetic electrons that can permanently damage satellite electronics, interfering with shortwave radio communication and GPS location and timing. Magnetic storms can also be a hazard to astronauts, even in low Earth orbit. They also create aurorae seen at high latitudes in an oval surrounding the geomagnetic poles.
Although it meets the definition of outer space, the atmospheric density within the first few hundred kilometers above the Kármán line is still sufficient to produce significant drag on satellites. This region contains material left over from previous crewed and uncrewed launches that are a potential hazard to spacecraft. Some of this debris re-enters Earth's atmosphere periodically.
Earth's gravity keeps the Moon in orbit at an average distance of 384,403 km (238,857 mi). The region outside Earth's atmosphere and extending out to just beyond the Moon's orbit, including the Lagrange points, is sometimes referred to as cislunar space.
Deep space is defined by the United States government and others as any region beyond cislunar space. The International Telecommunication Union responsible for radio communication (including satellites) defines the beginning of deep space at about 5 times that distance (2×106 km).
The region where Earth's gravity remains dominant against gravitational perturbations from the Sun is called the Hill sphere. This extends into translunar space to a distance of roughly 1% of the mean distance from Earth to the Sun, or 1.5 million km (0.93 million mi).
Interplanetary space is defined by the solar wind, a continuous stream of charged particles emanating from the Sun that creates a very tenuous atmosphere (the heliosphere) for billions of kilometers into space. This wind has a particle density of 5–10 protons/cm3 and is moving at a velocity of 350–400 km/s (780,000–890,000 mph). Interplanetary space extends out to the heliopause where the influence of the galactic environment starts to dominate over the magnetic field and particle flux from the Sun. The distance and strength of the heliopause varies depending on the activity level of the solar wind. The heliopause in turn deflects away low-energy galactic cosmic rays, with this modulation effect peaking during solar maximum.
The volume of interplanetary space is a nearly total vacuum, with a mean free path of about one astronomical unit at the orbital distance of the Earth. This space is not completely empty, and is sparsely filled with cosmic rays, which include ionized atomic nuclei and various subatomic particles. There is also gas, plasma and dust, small meteors, and several dozen types of organic molecules discovered to date by microwave spectroscopy. A cloud of interplanetary dust is visible at night as a faint band called the zodiacal light.
Interplanetary space contains the magnetic field generated by the Sun. There are also magnetospheres generated by planets such as Jupiter, Saturn, Mercury and the Earth that have their own magnetic fields. These are shaped by the influence of the solar wind into the approximation of a teardrop shape, with the long tail extending outward behind the planet. These magnetic fields can trap particles from the solar wind and other sources, creating belts of charged particles such as the Van Allen radiation belts. Planets without magnetic fields, such as Mars, have their atmospheres gradually eroded by the solar wind.
Interstellar space is the physical space within a galaxy beyond the influence each star has upon the encompassed plasma. The contents of interstellar space are called the interstellar medium. Approximately 70% of the mass of the interstellar medium consists of lone hydrogen atoms; most of the remainder consists of helium atoms. This is enriched with trace amounts of heavier atoms formed through stellar nucleosynthesis. These atoms are ejected into the interstellar medium by stellar winds or when evolved stars begin to shed their outer envelopes such as during the formation of a planetary nebula. The cataclysmic explosion of a supernova generates an expanding shock wave consisting of ejected materials that further enrich the medium. The density of matter in the interstellar medium can vary considerably: the average is around 106 particles per m3, but cold molecular clouds can hold 108–1012 per m3.
A number of molecules exist in interstellar space, as can tiny 0.1 μm dust particles. The tally of molecules discovered through radio astronomy is steadily increasing at the rate of about four new species per year. Large regions of higher density matter known as molecular clouds allow chemical reactions to occur, including the formation of organic polyatomic species. Much of this chemistry is driven by collisions. Energetic cosmic rays penetrate the cold, dense clouds and ionize hydrogen and helium, resulting, for example, in the trihydrogen cation. An ionized helium atom can then split relatively abundant carbon monoxide to produce ionized carbon, which in turn can lead to organic chemical reactions.
The local interstellar medium is a region of space within 100 parsecs (pc) of the Sun, which is of interest both for its proximity and for its interaction with the Solar System. This volume nearly coincides with a region of space known as the Local Bubble, which is characterized by a lack of dense, cold clouds. It forms a cavity in the Orion Arm of the Milky Way galaxy, with dense molecular clouds lying along the borders, such as those in the constellations of Ophiuchus and Taurus. (The actual distance to the border of this cavity varies from 60 to 250 pc or more.) This volume contains about 104–105 stars and the local interstellar gas counterbalances the astrospheres that surround these stars, with the volume of each sphere varying depending on the local density of the interstellar medium. The Local Bubble contains dozens of warm interstellar clouds with temperatures of up to 7,000 K and radii of 0.5–5 pc.
When stars are moving at sufficiently high peculiar velocities, their astrospheres can generate bow shocks as they collide with the interstellar medium. For decades it was assumed that the Sun had a bow shock. In 2012, data from Interstellar Boundary Explorer (IBEX) and NASA's Voyager probes showed that the Sun's bow shock does not exist. Instead, these authors argue that a subsonic bow wave defines the transition from the solar wind flow to the interstellar medium. A bow shock is the third boundary of an astrosphere after the termination shock and the astropause (called the heliopause in the Solar System).
Intergalactic space is the physical space between galaxies. Studies of the large scale distribution of galaxies show that the Universe has a foam-like structure, with groups and clusters of galaxies lying along filaments that occupy about a tenth of the total space. The remainder forms huge voids that are mostly empty of galaxies. Typically, a void spans a distance of (10–40) h−1 Mpc, where h is the Hubble constant in units of 100 km s−1 Mpc−1, or the dimensionless Hubble constant.
Surrounding and stretching between galaxies, there is a rarefied plasma that is organized in a galactic filamentary structure. This material is called the intergalactic medium (IGM). The density of the IGM is 5–200 times the average density of the Universe. It consists mostly of ionized hydrogen; i.e. a plasma consisting of equal numbers of electrons and protons. As gas falls into the intergalactic medium from the voids, it heats up to temperatures of 105 K to 107 K, which is high enough so that collisions between atoms have enough energy to cause the bound electrons to escape from the hydrogen nuclei; this is why the IGM is ionized. At these temperatures, it is called the warm–hot intergalactic medium (WHIM). (Although the plasma is very hot by terrestrial standards, 105 K is often called "warm" in astrophysics.) Computer simulations and observations indicate that up to half of the atomic matter in the Universe might exist in this warm–hot, rarefied state. When gas falls from the filamentary structures of the WHIM into the galaxy clusters at the intersections of the cosmic filaments, it can heat up even more, reaching temperatures of 108 K and above in the so-called intracluster medium (ICM).
A spacecraft enters orbit when its centripetal acceleration due to gravity is less than or equal to the centrifugal acceleration due to the horizontal component of its velocity. For a low Earth orbit, this velocity is about 7,800 m/s (28,100 km/h; 17,400 mph); by contrast, the fastest piloted airplane speed ever achieved (excluding speeds achieved by deorbiting spacecraft) was 2,200 m/s (7,900 km/h; 4,900 mph) in 1967 by the North American X-15.
To achieve an orbit, a spacecraft must travel faster than a sub-orbital spaceflight. The energy required to reach Earth orbital velocity at an altitude of 600 km (370 mi) is about 36 MJ/kg, which is six times the energy needed merely to climb to the corresponding altitude. Spacecraft with a perigee below about 2,000 km (1,200 mi) are subject to drag from the Earth's atmosphere, which decreases the orbital altitude. The rate of orbital decay depends on the satellite's cross-sectional area and mass, as well as variations in the air density of the upper atmosphere. Below about 300 km (190 mi), decay becomes more rapid with lifetimes measured in days. Once a satellite descends to 180 km (110 mi), it has only hours before it vaporizes in the atmosphere. The escape velocity required to pull free of Earth's gravitational field altogether and move into interplanetary space is about 11,200 m/s (40,300 km/h; 25,100 mph).
There is no clear boundary between Earth's atmosphere and space, as the density of the atmosphere gradually decreases as the altitude increases. There are several standard boundary designations, namely:
- The Fédération Aéronautique Internationale has established the Kármán line at an altitude of 100 km (62 mi) as a working definition for the boundary between aeronautics and astronautics. This is used because at an altitude of about 100 km (62 mi), as Theodore von Kármán calculated, a vehicle would have to travel faster than orbital velocity to derive sufficient aerodynamic lift from the atmosphere to support itself.
- The United States designates people who travel above an altitude of 50 mi (80 km) as astronauts.
- NASA's Space Shuttle used 400,000 ft, or 75.76 miles (120 km), as its re-entry altitude (termed the Entry Interface), which roughly marks the boundary where atmospheric drag becomes noticeable, thus beginning the process of switching from steering with thrusters to maneuvering with aerodynamic control surfaces.
In 2009, scientists reported detailed measurements with a Supra-Thermal Ion Imager (an instrument that measures the direction and speed of ions), which allowed them to establish a boundary at 118 km (73.3 mi) above Earth. The boundary represents the midpoint of a gradual transition over tens of kilometers from the relatively gentle winds of the Earth's atmosphere to the more violent flows of charged particles in space, which can reach speeds well over 268 m/s (880 ft/s).
The Outer Space Treaty provides the basic framework for international space law. It covers the legal use of outer space by nation states, and includes in its definition of outer space, the Moon, and other celestial bodies. The treaty states that outer space is free for all nation states to explore and is not subject to claims of national sovereignty, calling outer space the "province of all mankind". This status as a common heritage of mankind has been used, though not without opposition, to enforce the right to access and shared use of outer space for all nations equally, particularly non-spacefaring nations. It also prohibits the development of nuclear weapons in outer space. The treaty was passed by the United Nations General Assembly in 1963 and signed in 1967 by the USSR, the United States of America and the United Kingdom. As of 2017, 105 state parties have either ratified or acceded to the treaty. An additional 25 states signed the treaty, without ratifying it.
Since 1958, outer space has been the subject of multiple United Nations resolutions. Of these, more than 50 have been concerning the international co-operation in the peaceful uses of outer space and preventing an arms race in space. Four additional space law treaties have been negotiated and drafted by the UN's Committee on the Peaceful Uses of Outer Space. Still, there remains no legal prohibition against deploying conventional weapons in space, and anti-satellite weapons have been successfully tested by the US, USSR, China, and in 2019, India. The 1979 Moon Treaty turned the jurisdiction of all heavenly bodies (including the orbits around such bodies) over to the international community. The treaty has not been ratified by any nation that currently practices human spaceflight.
In 1976, eight equatorial states (Ecuador, Colombia, Brazil, Congo, Zaire, Uganda, Kenya, and Indonesia) met in Bogotá, Colombia. With their "Declaration of the First Meeting of Equatorial Countries", or "the Bogotá Declaration", they claimed control of the segment of the geosynchronous orbital path corresponding to each country. These claims are not internationally accepted.
Discovery, exploration and applicationsEdit
In 350 BCE, Greek philosopher Aristotle suggested that nature abhors a vacuum, a principle that became known as the horror vacui. This concept built upon a 5th-century BCE ontological argument by the Greek philosopher Parmenides, who denied the possible existence of a void in space. Based on this idea that a vacuum could not exist, in the West it was widely held for many centuries that space could not be empty. As late as the 17th century, the French philosopher René Descartes argued that the entirety of space must be filled.
In ancient China, the 2nd-century astronomer Zhang Heng became convinced that space must be infinite, extending well beyond the mechanism that supported the Sun and the stars. The surviving books of the Hsüan Yeh school said that the heavens were boundless, "empty and void of substance". Likewise, the "sun, moon, and the company of stars float in the empty space, moving or standing still".
The Italian scientist Galileo Galilei knew that air had mass and so was subject to gravity. In 1640, he demonstrated that an established force resisted the formation of a vacuum. It would remain for his pupil Evangelista Torricelli to create an apparatus that would produce a partial vacuum in 1643. This experiment resulted in the first mercury barometer and created a scientific sensation in Europe. The French mathematician Blaise Pascal reasoned that if the column of mercury was supported by air, then the column ought to be shorter at higher altitude where the air pressure is lower. In 1648, his brother-in-law, Florin Périer, repeated the experiment on the Puy de Dôme mountain in central France and found that the column was shorter by three inches. This decrease in pressure was further demonstrated by carrying a half-full balloon up a mountain and watching it gradually expand, then contract upon descent.
In 1650, German scientist Otto von Guericke constructed the first vacuum pump: a device that would further refute the principle of horror vacui. He correctly noted that the atmosphere of the Earth surrounds the planet like a shell, with the density gradually declining with altitude. He concluded that there must be a vacuum between the Earth and the Moon.
Back in the 15th century, German theologian Nicolaus Cusanus speculated that the Universe lacked a center and a circumference. He believed that the Universe, while not infinite, could not be held as finite as it lacked any bounds within which it could be contained. These ideas led to speculations as to the infinite dimension of space by the Italian philosopher Giordano Bruno in the 16th century. He extended the Copernican heliocentric cosmology to the concept of an infinite Universe filled with a substance he called aether, which did not resist the motion of heavenly bodies. English philosopher William Gilbert arrived at a similar conclusion, arguing that the stars are visible to us only because they are surrounded by a thin aether or a void. This concept of an aether originated with ancient Greek philosophers, including Aristotle, who conceived of it as the medium through which the heavenly bodies move.
The concept of a Universe filled with a luminiferous aether retained support among some scientists until the early 20th century. This form of aether was viewed as the medium through which light could propagate. In 1887, the Michelson–Morley experiment tried to detect the Earth's motion through this medium by looking for changes in the speed of light depending on the direction of the planet's motion. The null result indicated something was wrong with the concept. The idea of the luminiferous aether was then abandoned. It was replaced by Albert Einstein's theory of special relativity, which holds that the speed of light in a vacuum is a fixed constant, independent of the observer's motion or frame of reference.
The first professional astronomer to support the concept of an infinite Universe was the Englishman Thomas Digges in 1576. But the scale of the Universe remained unknown until the first successful measurement of the distance to a nearby star in 1838 by the German astronomer Friedrich Bessel. He showed that the star system 61 Cygni had a parallax of just 0.31 arcseconds (compared to the modern value of 0.287″). This corresponds to a distance of over 10 light years. In 1917, Heber Curtis noted that novae in spiral nebulae were, on average, 10 magnitudes fainter than galactic novae, suggesting that the former are 100 times further away. The distance to the Andromeda Galaxy was determined in 1923 by American astronomer Edwin Hubble by measuring the brightness of cepheid variables in that galaxy, a new technique discovered by Henrietta Leavitt. This established that the Andromeda galaxy, and by extension all galaxies, lay well outside the Milky Way.
The modern concept of outer space is based on the "Big Bang" cosmology, first proposed in 1931 by the Belgian physicist Georges Lemaître. This theory holds that the universe originated from a very dense form that has since undergone continuous expansion.
The earliest known estimate of the temperature of outer space was by the Swiss physicist Charles É. Guillaume in 1896. Using the estimated radiation of the background stars, he concluded that space must be heated to a temperature of 5–6 K. British physicist Arthur Eddington made a similar calculation to derive a temperature of 3.18 K in 1926. German physicist Erich Regener used the total measured energy of cosmic rays to estimate an intergalactic temperature of 2.8 K in 1933. American physicists Ralph Alpher and Robert Herman predicted 5 K for the temperature of space in 1948, based on the gradual decrease in background energy following the then-new Big Bang theory. The modern measurement of the cosmic microwave background is about 2.7K.
The term outward space was used in 1842 by the English poet Lady Emmeline Stuart-Wortley in her poem "The Maiden of Moscow". The expression outer space was used as an astronomical term by Alexander von Humboldt in 1845. It was later popularized in the writings of H. G. Wells in 1901. The shorter term space is older, first used to mean the region beyond Earth's sky in John Milton's Paradise Lost in 1667. "Spaceborne" denotes existing in outer space, especially if carried by a spacecraft; similarly, "space-based" means based in outer space or using space technology.
Exploration and applicationEdit
For most of human history, space was explored by observations made from the Earth's surface—initially with the unaided eye and then with the telescope. Before reliable rocket technology, the closest that humans had come to reaching outer space was through balloon flights. In 1935, the U.S. Explorer II crewed balloon flight reached an altitude of 22 km (14 mi). This was greatly exceeded in 1942 when the third launch of the German A-4 rocket climbed to an altitude of about 80 km (50 mi). In 1957, the uncrewed satellite Sputnik 1 was launched by a Russian R-7 rocket, achieving Earth orbit at an altitude of 215–939 kilometres (134–583 mi). This was followed by the first human spaceflight in 1961, when Yuri Gagarin was sent into orbit on Vostok 1. The first humans to escape low-Earth orbit were Frank Borman, Jim Lovell and William Anders in 1968 on board the U.S. Apollo 8, which achieved lunar orbit and reached a maximum distance of 377,349 km (234,474 mi) from the Earth.
The first spacecraft to reach escape velocity was the Soviet Luna 1, which performed a fly-by of the Moon in 1959. In 1961, Venera 1 became the first planetary probe. It revealed the presence of the solar wind and performed the first fly-by of Venus, although contact was lost before reaching Venus. The first successful planetary mission was the 1962 fly-by of Venus by Mariner 2. The first fly-by of Mars was by Mariner 4 in 1964. Since that time, uncrewed spacecraft have successfully examined each of the Solar System's planets, as well their moons and many minor planets and comets. They remain a fundamental tool for the exploration of outer space, as well as for observation of the Earth. In August 2012, Voyager 1 became the first man-made object to leave the Solar System and enter interstellar space.
The absence of air makes outer space an ideal location for astronomy at all wavelengths of the electromagnetic spectrum. This is evidenced by the spectacular pictures sent back by the Hubble Space Telescope, allowing light from more than 13 billion years ago—almost to the time of the Big Bang—to be observed. Not every location in space is ideal for a telescope. The interplanetary zodiacal dust emits a diffuse near-infrared radiation that can mask the emission of faint sources such as extrasolar planets. Moving an infrared telescope out past the dust increases its effectiveness. Likewise, a site like the Daedalus crater on the far side of the Moon could shield a radio telescope from the radio frequency interference that hampers Earth-based observations.
Uncrewed spacecraft in Earth orbit are an essential technology of modern civilization. They allow direct monitoring of weather conditions, relay long-range communications like television, provide a means of precise navigation, and allow remote sensing of the Earth. The latter role serves a wide variety of purposes, including tracking soil moisture for agriculture, prediction of water outflow from seasonal snow packs, detection of diseases in plants and trees, and surveillance of military activities.
The deep vacuum of space could make it an attractive environment for certain industrial processes, such as those requiring ultraclean surfaces. Like asteroid mining, space manufacturing would require a large financial investment with little prospect of immediate return. An important factor in the total expense is the high cost of placing mass into Earth orbit: $8,000–$27,000 per kg, according to a 2006 estimate (allowing for inflation since then). The cost of access to space has declined since 2013. Partially reusable rockets such as the Falcon 9 have lowered access to space below 3500 dollars per kilogram. With these new rockets the cost to send materials into space remains prohibitively high for many industries. Proposed concepts for addressing this issue include, fully reusable launch systems, non-rocket spacelaunch, momentum exchange tethers, and space elevators.
Interstellar travel for a human crew remains at present only a theoretical possibility. The distances to the nearest stars mean it would require new technological developments and the ability to safely sustain crews for journeys lasting several decades. For example, the Daedalus Project study, which proposed a spacecraft powered by the fusion of deuterium and helium-3, would require 36 years to reach the "nearby" Alpha Centauri system. Other proposed interstellar propulsion systems include light sails, ramjets, and beam-powered propulsion. More advanced propulsion systems could use antimatter as a fuel, potentially reaching relativistic velocities.
- Animals in space
- Earth's location in the Universe
- List of government space agencies
- List of topics in space
- Olbers' paradox
- Outline of space science
- Space and survival
- Space environment
- Space race
- Space station
- Space technology
- Space weather
- Space weathering
- Timeline of knowledge about the interstellar and intergalactic medium
- Timeline of Solar System exploration
- Timeline of spaceflight
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When it comes to the future of spaceflight, the Moon is the place to be. Several missions are set to land on the Moon in the next few years in an effort to establish a human presence on the lunar surface. Although they’re meant to bolster lunar activity, those landings, however, could in turn have a negative effect on spacecraft orbiting the Moon.
A recent study, newly uploaded to the preprint arXiv, examined the potential damage caused by lunar landers, which can eject dust from the surface of the Moon and send it into orbit as they land on the surface. With enough Moon landings in the future, a cloud of pesky lunar dust particles could get in the way of orbiting spacecraft.
Lunar dust has always been an issue for Moon missions. Astronauts from NASA’s Apollo program reported annoying difficulties in dealing with dust from the Moon’s surface, those electrically charged, fine particles of regolith that stick on any surface. As Apollo astronauts entered and exited the lunar module, dust got everywhere and “it clogged mechanisms, interfered with instruments, caused radiators to overheat and even tore up their spacesuits,” according to NASA.
As NASA prepares to land on the Moon as part of its Artemis program, the space agency is now aware of the trials and tribulations of lunar dust when it comes to its astronauts. Frequent Moon landings, however, could have larger impacts on orbiters or space stations in lunar orbit, according to the new pre-print, which has yet to go through peer review. Planetary physicist Philip Metzger from the University of Central Florida co-authored the new study.
The Artemis program will involve several lunar landings in the coming years, with Artemis 3 scheduled for launch in late 2025, followed by Artemis 4 in 2028. Afterwards, NASA wants to establish a steady flow of astronauts headed for the Moon. The space agency isn’t the only one with longterm lunar ambitions; China recently revealed its own plan to land astronauts on the Moon by 2030 and establish a sustainable presence on the surface as well.
The study found that large lunar landers would kick up clouds of dust from the surface of the Moon, sending this “ejecta,” in the parlance of scientists, tens of thousands of particles into orbit. A 40-ton lunar lander could accelerate surface dust to speeds of around 10,000 miles per hour (16,000 kilometers per hour), which is enough to place a large cloud of particles into lunar orbit.
NASA’s future Lunar Gateway, designed to be a space station in a highly elongated “halo” orbit around the Moon, would pass through this dusty sheet but will likely suffer little to no damage, the scientists claim. Other orbiting spacecraft flying closer to the Moon, on the other hand, “will sustain extensive damage with hundreds of millions of impacts per square meter,” according to the paper.
Even if the high-velocity impact of the particles doesn’t damage the spacecraft, the dust itself will. “As you know, regolith particulates are very, very fine,” William Schonberg, an engineering professor at Missouri University of Science and Technology, told Gizmodo in an email. “So even if they don’t do any impact damage, they can still ‘settle’ on critical functional surfaces and components of lunar orbiting spacecraft and nearby lunar habitats or worksites and so can easily ‘gum up’ that functionality.”
As Schonberg points out, the dust could also pose a risk to future lunar habitats built on the surface of the Moon. “That’s probably why recent lunar sci-fi shows have lunar take-off and landing sites far removed from any surface habitats, right?” he added.
So as the new study shows, lunar dust is not just annoying to deal with on the surface of the Moon, it could be a major hazard for lunar spacecraft in the future. NASA and other agencies with their landers set for the Moon should keep its dusty surface in mind. |
What is Linear Programming?
In here, the variables are non-negative and satisfy a set of linear inequalities (called linear constraints) and the problems have the goal to find the optimal value (maximum or minimum) of a linear function of several variables (called objective function) with respect to the conditions. Variables are sometimes called decision variables and are non-negative in nature.
Students can refer to the short notes and MCQ questions along with separate solution pdf of this chapter for quick revision from the links below:
- Linear Programming Study Notes PDF
- Linear Programming MCQ Practice Questions PDF
- Linear Programming MCQ Practice Solutions PDF
CBSE Class 12 Maths Notes Chapter 12 Linear Programming – Related Links
- Linear Programming – Basics
- Linear Programming For Class 12
- Linear programming problem (LPP)
- Types of Linear Programming
- Linear Programming Problems
- Linear Programming Problems – Graphical Method
Feasible region (or solution region) is referred to the common region represented by all the boundaries including the non-negative boundaries x ≥ 0, y ≥ 0.
In an objective function, the optimal solution of any point in the feasible region gives the optimal value (maximum or minimum).
Theorems of Linear Programming
There are theorems which will help in solving problems of linear programming and they are:
- Let P be the feasible region and let S = ax + by be the objective function. The optimal value must occur at a corner point of the feasible region when S has an optimal value and the variables x and y are subject to boundaries described by linear inequalities.
- Let P be the feasible region and let S = ax + by be the objective function. If P is constrained, then the objective function S has both minimum and maximum value of P and each of these occurs at a corner point (vertex) of P
Corner Point Method
This method has some steps such as :
- The feasible region of the linear programming problem is to be found and its corner points (vertices) should be determined.
- The objective function Z = ax + by at each corner point should be evaluated. Let’s assume that M and m respectively be the largest and smallest values at these points
- M and m respectively are the maximum and minimum values of the objective function if the feasible region is bounded
When the feasible region is not bounded then,
- The objective function has no maximum value unless Z is the maximum value of the objective function if the open half plane determined by ax + by > Z doesn’t have any point in common with the feasible region.
- The function has no minimum value unless S is the minimum value of the objective function if the open half plane determined by ax + by < S which doesn’t have any point in common with the feasible region.
|NCERT Solutions for Class 12 Maths Chapter 12|
|NCERT Exemplar for Class 12 Maths Chapter 12|
- Assuming that there is no shortage of the other ingredients used in making the cakes, the cake requires 300g of flour and 35g of fat, and another kind of cake requires 200g of flour and 60g of fat. Find the maximum number of cakes which can be made from 10kg of flour and 2kg of fat.
Frequently asked Questions on CBSE Class 12 Maths Notes Chapter 12: Linear Programming
What is ‘Linear Programming’?
Linear programming is a process of optimising the problems which are subjected to certain constraints.
What is ‘Absolute Maxima’?
An absolute maximum point is a point where the function obtains its greatest possible value.
What is ‘Non-negative restriction’?
Non-negativity restriction indicates that all decision variables must take on values equal to or greater than zero. |
In computing, a fixed-point number representation is a real data type for a number that has a fixed number of digits after (and sometimes also before) the radix point (after the decimal point '.' in English decimal notation). Fixed-point number representation can be compared to the more complicated (and more computationally demanding) floating-point number representation.
Fixed-point numbers are useful for representing fractional values, usually in base 2 or base 10, when the executing processor has no floating point unit (FPU) or if fixed-point provides improved performance or accuracy for the application at hand. Older or low-cost embedded microprocessors and microcontrollers do not have an FPU.
A value of a fixed-point data type is essentially an integer that is scaled by an implicit specific factor determined by the type. For example, the value 1.23 can be represented as 1230 in a fixed-point data type with scaling factor of 1/1000, and the value 1,230,000 can be represented as 1230 with a scaling factor of 1000. Unlike floating-point data types, the scaling factor is the same for all values of the same type, and does not change during the entire computation.
The scaling factor is usually a power of 10 (for human convenience) or a power of 2 (for computational efficiency). However, other scaling factors may be used occasionally, e.g. a time value in hours may be represented as a fixed-point type with a scale factor of 1/3600 to obtain values with one-second accuracy.
The maximum value of a fixed-point type is simply the largest value that can be represented in the underlying integer type multiplied by the scaling factor; and similarly for the minimum value.
To convert a number from a fixed point type with scaling factor R to another type with scaling factor S, the underlying integer must be multiplied by R and divided by S; that is, multiplied by the ratio R/S. Thus, for example, to convert the value 1.23 = 123/100 from a type with scaling factor R=1/100 to one with scaling factor S=1/1000, the underlying integer 123 must be multiplied by (1/100)/(1/1000) = 10, yielding the representation 1230/1000. If S does not divide R (in particular, if the new scaling factor S is greater than the original R), the new integer will have to be rounded. The rounding rules and methods are usually part of the language's specification.
To add or subtract two values of the same fixed-point type, it is sufficient to add or subtract the underlying integers, and keep their common scaling factor. The result can be exactly represented in the same type, as long as no overflow occurs (i.e. provided that the sum of the two integers fits in the underlying integer type). If the numbers have different fixed-point types, with different scaling factors, then one of them must be converted to the other before the sum.
To multiply two fixed-point numbers, it suffices to multiply the two underlying integers, and assume that the scaling factor of the result is the product of their scaling factors. This operation involves no rounding. For example, multiplying the numbers 123 scaled by 1/1000 (0.123) and 25 scaled by 1/10 (2.5) yields the integer 123×25 = 3075 scaled by (1/1000)×(1/10) = 1/10000, that is 3075/10000 = 0.3075. If the two operands belong to the same fixed-point type, and the result is also to be represented in that type, then the product of the two integers must be explicitly multiplied by the common scaling factor; in this case the result may have to be rounded, and overflow may occur. For example, if the common scaling factor is 1/100, multiplying 1.23 by 0.25 entails multiplying 123 by 25 to yield 3075 with an intermediate scaling factor of 1/10000. This then must be multiplied by 1/100 to yield either 31 (0.31) or 30 (0.30), depending on the rounding method used, to result in a final scale factor of 1/100.
To divide two fixed-point numbers, one takes the integer quotient of their underlying integers, and assumes that the scaling factor is the quotient of their scaling factors. The first division involves rounding in general. For example, division of 3456 scaled by 1/100 (34.56) and 1234 scaled by 1/1000 (1.234) yields the integer 3456÷1234 = 3 (rounded) with scale factor (1/100)/(1/1000) = 10, that is, 30. One can obtain a more accurate result by first converting the dividend to a more precise type: in the same example, converting 3456 scaled by 1/100 (34.56) to 3,456,000 scaled by 1/100000, before dividing by 1234 scaled by 1/1000 (1.234), would yield 3456000÷1234 = 2801 (rounded) with scaling factor (1/100000)/(1/1000) = 1/100, that is 28.01 (instead of 30). If both operands and the desired result all have the same scaling factor, then the quotient of the two integers must be explicitly multiplied by that common scaling factor.
Binary vs. decimal
The two most common classes of fixed-point types are decimal and binary. Decimal fixed-point types have a scaling factor that is a power of ten; for binary fixed-point types it is a power of two.
Binary fixed-point types are most commonly used, because the rescaling operations can be implemented as fast bit shifts. Binary fixed-point numbers can represent fractional powers of two exactly, but, like binary floating-point numbers, cannot exactly represent fractional powers of ten. If exact fractional powers of ten are desired, then a decimal format should be used. For example, one-tenth (0.1) and one-hundredth (0.01) can be represented only approximately by binary fixed-point or binary floating-point representations, while they can be represented exactly in decimal fixed-point or decimal floating-point representations. These representations may be encoded in many ways, including binary-coded decimal (BCD).
There are various notations used to represent word length and radix point in a binary fixed-point number. In the following list, f represents the number of fractional bits, m the number of magnitude or integer bits, s the number of sign bits, and b the total number of bits.
- Qf: The "Q" prefix. For example, Q15 represents a number with 15 fractional bits. This notation is ambiguous since it does not specify the word length, however it is usually assumed that the word length is either 16 or 32 bits depending on the target processor in use.
- Qm.f: The unambiguous form of the "Q" notation. Since the entire word is a 2's complement integer, a sign bit is implied. For example, Q1.30 describes a number with 1 integer bit and 30 fractional bits stored as a 32-bit 2's complement integer.
- fxm.b: The "fx" prefix is similar to the above, but uses the word length as the second item in the dotted pair. For example, fx1.16 describes a number with 1 magnitude bit and 15 fractional bits in a 16 bit word.
- s:m:f: Yet other notations include a sign bit, such as this one used in the PS2 GS User's Guide. It also differs from conventional usage by using a colon instead of a period as the separator. For example, in this notation, 0:8:0 represents an unsigned 8-bit integer.
- (p,q) Used in the PL/I programming language, to specify p total digits (not including sign) with q after the radix point. q can be positive or negative, and the radix binary or decimal.
Precision loss and overflow
Because fixed point operations can produce results that have more digits than the operands, information loss is possible. For instance, the result of fixed point multiplication could potentially have as many digits as the sum of the number of digits in the two operands. In order to fit the result into the same number of digits as the operands, the answer must be rounded or truncated. If this is the case, the choice of which digits to keep is very important. When multiplying two fixed point numbers with the same format, for instance with integer digits, and fractional digits, the answer could have up to integer digits, and fractional digits.
For simplicity, many fixed-point multiply procedures use the same result format as the operands. This has the effect of keeping the middle digits; the I-number of least significant integer digits, and the Q-number of most significant fractional digits. Fractional digits lost below this value represent a precision loss which is common in fractional multiplication. If any integer digits are lost, however, the value will be radically inaccurate. Some model-based fixed-point packages allow specifying a result format different from the input formats, enabling the user to maximize precision and avoid overflow.
Some operations, like divide, often have built-in result limiting so that any positive overflow results in the largest possible number that can be represented by the current format. Likewise, negative overflow results in the largest negative number represented by the current format. This built in limiting is often referred to as saturation.
Computer language implementations
Very few computer languages include built-in support for fixed point values other than with the radix point immediately to the right of the least significant digit, because for most applications, binary or decimal floating-point representations are usually simpler to use and accurate enough. Floating-point representations are easier to use than fixed-point representations, because they can handle a wider dynamic range and do not require programmers to specify the number of digits after the radix point. However, if they are needed, fixed-point numbers can be implemented even in programming languages like C and C++, which do not commonly include such support.
A common use of fixed-point BCD numbers is for storing monetary values, where the inexact values of binary floating-point numbers are often a liability. Historically, fixed-point representations were the norm for decimal data types; for example, in PL/I or COBOL. The Ada programming language includes built-in support for both fixed-point (binary and decimal) and floating-point. JOVIAL and Coral 66 also provide both floating- and fixed-point types.
ISO/IEC TR 18037 specifies fixed-point data types for the C programming language; vendors are expected to implement the language extensions for fixed point arithmetic in coming years. Fixed-point support is implemented in GCC.
Software application examples
- libfixmath is a recent open-source library for the manipulation of fixed point numbers, it currently supports Q16.16 and Q0.32 formats and provides an interface similar to math.h.
- The Nest Labs Utilities library, provides a limited set of macros and functions for fixed point numbers, particularly when dealing with those numbers in the context of sensor sampling and sensor outputs.
- GnuCash is an application for tracking money which is written in C. It switched from a floating-point representation of money to a fixed-point implementation as of version 1.6. This change was made to trade the less predictable rounding errors of floating-point representations for more control over rounding (for example, to the nearest cent).
- Tremor, Toast and MAD are software libraries which decode the Ogg Vorbis, GSM Full Rate and MP3 audio formats respectively. These codecs use fixed-point arithmetic because many audio decoding hardware devices do not have an FPU (partly to save money, but primarily to save power - integer units are much smaller in silicon area than an FPU) and audio decoding requires performance to the extent a software implementation of floating-point on low-speed devices would not produce output in real time.
- All 3D graphics engines on Sony's original PlayStation, Sega's Saturn, Nintendo's Game Boy Advance (only 2D), Nintendo DS (2D and 3D), Nintendo Gamecube and GP2X Wiz video game systems use fixed-point arithmetic for the same reason as Tremor and Toast: to gain throughput on an architecture without an FPU (e.g. the PlayStation included hardware support for 4.12bit values in its transformation coprocessor).
- The OpenGL ES 1.x specification includes a fixed point profile, as it is an API aimed for embedded systems, which do not always have an FPU.
- TeX font metric files use 32-bit signed fixed-point numbers, with 12 bits to the left of the decimal, extensively.
- The dc and bc programs are arbitrary precision calculators, but only keep track of a (user-specified) fixed number of fractional digits.
- VisSim A visually programmed block diagram language supporting a fixed-point block set to allow simulation and automatic code generation of fixed-point operations. Both word size and radix point can be specified on an operator basis.
- Fractint represents numbers as Q2.29 fixed-point numbers, to speed up drawing on old PCs with 386 or 486SX processors, which lacked an FPU.
- Doom was the last first-person shooter title by id Software to use a 16.16 fixed point representation for all of its non-integer computations, including map system, geometry, rendering, player movement etc. This was done in order for the game to be playable on 386 and 486SX CPUs without an FPU. For compatibility reasons, this representation is still used in modern Doom source ports.
- SystemC provides signed and unsigned fixed point data types.
- Wavpack is a fixed-point, lossless audio compressor. Its creator, David Bryant, justifies the decision to implement fixed instead of floating point: " I believe that integer operations are less susceptible to subtle chip to chip variations that could corrupt the lossless nature of the compression."
- fixed point numbers are sometimes used for storing and manipulating images and video frames. Processors with SIMD units aimed at image processing may include instructions suitable for handling packed fixed point data.
- The Q# programming language for the Azure quantum computers, that implement quantum logic gates, contains a standard numeric library for performing fixed-point arithmetic on registers of qubits.
- Texas Instruments, TMS320C64x DSP Library Programmer's Reference, Appendix A.2
- "MathWorks Fixed-Point Toolbox Documentation Glossary". mathworks.com.
- Inc., solidThinking. "VisSim is now solidThinking Embed". www.vissim.com.
- PS2 GS User's Guide, Chapter 7.1 "Explanatory Notes"
- VisSim Fixed-Point User Guide|http://www.vissim.com/downloads/doc/EmbeddedControlsDeveloper_UGv80.pdf
- JTC1/SC22/WG14, status of TR 18037: Embedded C
- GCC wiki, Fixed-Point Arithmetic Support
- Using GCC, section 5.13 Fixed-Point Types
- PostgreSQL manual, section 8.1.2. Arbitrary Precision Numbers
- "Google Code Archive - Long-term storage for Google Code Project Hosting". code.google.com.
- "Dolphin Emulator". Dolphin Emulator.
- Fractint, A Little Code
- "WavPack Technical Description". www.wavpack.com. Retrieved 2015-07-13.
- "Introduction to the Quantum Numerics Library". Retrieved 2019-11-13.
|The Wikibook Floating Point has a page on the topic of: Fixed-Point Numbers|
|The Wikibook Embedded Systems has a page on the topic of: Fixed-Point Arithmetic| |
Key unit competence
Think critically using mathematical logic to understand and perform operations on the set of real numbers and its subsets using the properties of algebraic structures.
Work in groups.
1. Discuss the following: What are sets? What are real numbers?
2. Carry out research on sets of numbers to determine the meanings of natural numbers, integers, rational numbers and irrational numbers.
The one-to-one correspondence between the real numbers and the points on the number line is familiar to us all. Corresponding to each real number there is exactly one point on the line: corresponding to each point on the line there is exactly one real number.
4.2 Properties of real numbers
Subsets of real numbers
If a and b are any two real numbers, then either a < b or b < a or a = b. The sum and product of any two positive real numbers are both positive.
If a < 0 then (– a) >0.
If a < b then (a – b) > 0. This means that the point on the number line corresponding to a is to the right of the point corresponding to b.
The elementary rules for inequalities are:
1. If a < b and c is any real number then a + c < b + c . That is we may add (or subtract) any real number to (or from) both sides of an inequality.
2. (a) If a < b and c > 0, then ac < bc. (b) If a < b and c < 0, then ac > bc. We may multiply (or divide) both sides of an inequality by a positive real number, but when we multiply (or divide) both sides of an inequality by a negative real number we must change the direction of the inequality sign.
3. (a) If 0 < a < b then 0 < a2 < b2.
(b) If a < b < 0 then a2 > b2. We may square both sides of an inequality if both sides are positive. However if both sides are negative we may square both sides but we must reverse the direction of the inequality sign and then both sides become positive. If one side is positive and the other negative we cannot use the same rule. For example, –2 < 3 and (–2)2 < 32 , but –3 < 2 and (–3)2 > 22.
That is we may take the reciprocal of both sides of an inequality only if both sides have the same sign and, in each possible case, we must reverse the direction of the inequality sign.
4.3 Absolute value functions
In groups of four, research on the meaning of absolute value. Present your findings to the rest of the class for discussion. Make use of diagrams and examples.
There is a technical definition for absolute value, but you could easily never need it. For now, you should view the absolute value of a number as its distance from zero.
Let us look at the number line.
The absolute value of x, denoted "| x |" (and which is read as "the absolute value of x"), is the distance of x from zero. This is why absolute value is never negative; absolute value only asks "how far?", not "in which direction?" This means not only that | 3 | = 3, because 3 is three units to the right of zero, but also that | –3 | = 3, because –3 is three units to the left of zero.
Note: The absolute-value notation is bars, not parentheses or brackets. Use the proper notation. The other notations do not mean the same thing.
As this illustrates, if you take the negative of an absolute value, you will get a negative number for your answer.
Sometimes we order numbers according to their size. We denote the size or absolute value of the real numbers x by |x|, called the modulus of x.
4.4 Powers and radicals
1. In pairs, revise the meaning of the term 'power'. Give the definition.
2. Research and derive the rules of exponential expressions.
The power of a number says how many times we use the number in a multiplication. It is written as a small number to the right and above the base number. Another name for power is index or exponent.
When a real number a is raised to the index m to give am , the result is a power of a. When am is formed, m is sometimes called the power, but it is more correctly called the index to which a is raised.
The rules used to manipulate exponential expressions should already be familiar with the reader. These rules may be summarized as follows:
Research on the meaning of the term radical. Discuss your findings with the rest of the class. Your teacher will assist you get a concise meaning of the term.
2. Every positive number has two square roots, one of which is positive and the other negative.
3. The square root of zero is zero.
4. Negative real numbers have no real square roots.
If a3 = b, then b is the cube of a and a is the cube root of b. This time we say the cube root of b since 23 = 8 but (–2)3 = –8.
1. No definition is needed to specify which cube root is meant since a real number has one and only one cube root in the real number system.
2. Every positive number has one and only one cube root which is positive.
3. The cube root of zero is zero.
4. Every negative number has one and only one cube root which is negative.
In general, if n is an even positive integer then in the real number system:
1. If a > 0, a has two nth roots, one positive and another negative.
2. If a = 0, a has one nth root which is zero.
3. If a < 0, a has no real nth roots.
If n is an odd positive integer (not 1) then in the real number system,
1. If a > 0, a has one nth root which is positive.
2. If a = 0, a has one nth root which is zero.
3. If a < 0, a has one nth root which is negative.
The process of squaring both sides is used in solving irrational equations, i.e., equations involving surd expressions. It is therefore always necessary to check any solution obtained.
4.5 Decimal logarithms
Discuss in groups of four and give two examples for each.
1. What is a decimal?
2. What is a logarithm?
The logarithm of a positive number, in base 10, is its power of 10. For instance:
Note: If no base is indicated we assume that it is base 10.
The laws of logarithms
Your teacher will guide you in deriving the laws of logarithms. Use numerous examples to practise using them.
The logarithm can be used in solving exponential equations.
Application of exponents in real life |
Trigonometry is the branch of mathematics dealing with the measures of the sides and angles of a triangle. Using trigonometric ratios, one can determine the side and angle measures (i.e. "solve the triangle") using minimal information.
What is a right triangle?
A right triangle is any triangle where one angle measures 90º. A right triangle consists of two small sides, across from the smaller angles, and a longer side, across from the right angle. The sides of a right triangle have special names. The two smaller ones are called legs, and the longer side is called the hypotenuse (pronounced hi-POT-uh-noose).
Notice that the bottom-left angle is 90 degrees. The sides labelled "opposite" and "adjacent" are the legs, and the names are in reference to the angle "a". These terms will always be used when discussing sides of a right triangle, and will always be given in reference to some angle. Remember, the hypotenuse is always the longest side and is always across from the right angle.
Let's practice what we've learned.
For the triangle below, fill in the blanks.
What is the length of the hypotenuse? _________
What is the length of the side opposte angle "a"? _________
What is the length of the side adjacent to angle "a"?_________
The correct answers are 10 feet, 8 feet, and 6 feet respectively.
Rotating a right triangle does not alter the names of the sides. Consider the following triangle: Can you name the hypotenuse, adjacent and opposite sides?
(6 feet is incorrect (should be 5 feet), since h^2 = a^2 + b^2 = 9 + 16 = 25, the square root being 5)
Even though this right angle has been rotated, the sides are still named with respect to the angle "a". See if you can identify the sides of the triangle below. Remember that everything is from the point of view of angle "a".
What is the length of the hypotenuse? ___________feet
What is the length of the side opposite angle "a"? ___________feet
What is the length of side adjacent to angle "a"? ___________feet
(Two of the answers are incorrect. The opposite angle should be 3 feet, and the adjacent angle should be 4 feet)
The correct answers are 5 feet, 3 feet, 4 feet, respectively.
The three most common trigonometric ratios are sine (abbreviated "sin"), cosine (abbreviated "cos"), and tangent (abbreviated "tan"). These trigonometric ratios can be determined contingent on the information you have available. If the angle measure is given, entering sin(x), cos(x), or tan(x) in most scientific calculators (where "x" is the angle measure) will yield the sine, cosine, and tangent of the given value. The three other ratios are cosecant (abbreviated "csc"), secant (abbreviated "sec"), and cotangent (abbreviated "cot" or "ctn"), the reciprocal functions of the sine, cosine, and tangent respectively.
Soh Cah Toa
In a right triangle, if you are given at least two of the side measures, you can determine the sine, cosine, or tangent using a method commonly referred to by the mnenomic device Soh Cah Toa. What this refers to is:
- Soh: sine = opposite / hypotenuse
- Cah: cosine = adjacent / hypotenuse
- Toa: tangent = opposite / adjacent
The terms opposite and adjacent are in relation to the reference angle, which is the angle your calculations are based upon. In Figure 1, since angle A is the reference angle, then the side opposite of that angle is side a. While there are two sides adjacent to angle A, side b is designated as the hypotenuse so side c is the adjacent side. Therefore, in Figure 1:
- sin(A) = a/b
- cos(A) = c/b
- tan(A) = a/c
Please note that "sin(A)" is read as "sine of A," "cos(A)" is read as "cosine of A," and "tan(A)" is read as "tangent of A."
For example, if a = 7 and c = 14, you would need to find the tangent of angle A, as the other two ratios require the hypotenuse which is unavailable. As the tangent is the opposite divided by the adjacent, you would get tan(A) = 7/14, which can be simplified to one-half.
- Note: Please make sure first that your calculator gives angle measures in degrees.
When determining the measures of a triangle, the sines, cosines, and tangents have a function: determining the angle measure. Above, it was determined that the tangent of the reference angle, A, is 1/2. If you entered tan-1(1/2) into a scientific calculator, you will see that you will get the angle measure of A, which is approximately 26.6°. You now have two angle measures: 26.6° and 90°, since this is a right triangle. Since the sum of all angles in a triangle is 180°, subtract the two known angle measures from 180 and you will get the third angle measure: 63.4°.
Solving the side and angle measures of triangles will be covered in more depth in Chapter 19.
- Geometry Main Page
- Geometry/Chapter 1 Definitions and Reasoning (Introduction)
- Geometry/Chapter 2 Proofs
- Geometry/Chapter 3 Logical Arguments
- Geometry/Chapter 4 Congruence and Similarity
- Geometry/Chapter 5 Triangle: Congruence and Similiarity
- Geometry/Chapter 6 Triangle: Inequality Theorem
- Geometry/Chapter 7 Parallel Lines, Quadrilaterals, and Circles
- Geometry/Chapter 8 Perimeters, Areas, Volumes
- Geometry/Chapter 9 Prisms, Pyramids, Spheres
- Geometry/Chapter 10 Polygons
- Geometry/Chapter 11
- Geometry/Chapter 12 Angles: Interior and Exterior
- Geometry/Chapter 13 Angles: Complementary, Supplementary, Vertical
- Geometry/Chapter 14 Pythagorean Theorem: Proof
- Geometry/Chapter 15 Pythagorean Theorem: Distance and Triangles
- Geometry/Chapter 16 Constructions
- Geometry/Chapter 17 Coordinate Geometry
- Geometry/Chapter 18 Trigonometry
- Geometry/Chapter 19 Trigonometry: Solving Triangles
- Geometry/Chapter 20 Special Right Triangles
- Geometry/Chapter 21 Chords, Secants, Tangents, Inscribed Angles, Circumscribed Angles
- Geometry/Chapter 22 Rigid Motion
- Geometry/Appendix A Formulae
- Geometry/Appendix B Answers to problems
- Appendix C. Geometry/Postulates & Definitions
- Appendix D. Geometry/The SMSG Postulates for Euclidean Geometry |
Just like a physician measures a person’s temperature in order to check his or her health, a new project from the European Space Agency (ESA) hopes to track temperatures of the Earth’s surface by satellite. This project, called GlobTemperature, will be a compilation of data from different satellite sensors that are taking measurements of surface temperatures, similar to a doctor’s thermometer. GlobTemperature will combine all of this information about surface temperature from the Earth’s land, water, and ice and make it available to scientists in a single collection online.
The reasoning behind the project is the potential temperature measurements from satellites have for unlocking previous limitations on studying the Earth. Up until now, climatologists and meteorologists have relied mainly on air temperature measurements to determine weather and climate patterns because of problems with data from satellites. Data about the Earth’s temperatures from satellites is extremely complex and come in a variety of formats. Satellite data is also filled with gaps because of things like cloud cover. Plus, it is challenging to translate solid land surface temperatures from satellites to air temperatures, which are more frequently used.
The ESA is hoping to change all that with the availability of GlobTemperature. The data gathered through the project could have a wide variety of uses because land surface temperatures are essential for understanding life on the Earth. Surface temperatures play important roles in many natural processes like the emission of gases from the surface of the planet to the atmosphere, the sensitivity of vegetation, and the convection of the atmosphere that produces weather patterns. The temperatures of the Earth’s land over time can play an important role as clues in climate change, too.
Ultimately, the goal of the project is to better meet user’s needs when it comes to satellite data on Earth surface temperatures. One of the uses for GlobTemperature currently in development is to provide a more accurate depiction of day and night temperatures. To demonstrate how this satellite data can benefit scientists, five case studies in different regions of the globe are being done. There is also an open user consultation being planned for June of 2014, and GlobTemperature is intended to continue for the next three years.
See: Taking Earth’s Temperature – European Space Agency
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In mathematics, a group is a set equipped with a binary operation that combines any two elements to form a third element in such a way that conditions called group axioms are satisfied, namely associativity, identity and invertibility. These conditions are familiar from many mathematical structures, such as number systems: for example, the integers endowed with the addition operation form a group. The formulation of the axioms is, however, detached from the concrete nature of the group and its operation. This allows one to handle entities of very different mathematical origins in a flexible way, while retaining essential structural aspects of many objects in abstract algebra and beyond. The ubiquity of groups in numerous areas—both within and outside mathematics—makes them a central organizing principle of contemporary mathematics.
Groups share a fundamental kinship with the notion of symmetry. For example, a symmetry group encodes symmetry features of a geometrical object: the group consists of the set of transformations that leave the object unchanged and the operation of combining two such transformations by performing one after the other. Lie groups arise as symmetry groups in geometry but appear also in the Standard Model of particle physics. The Poincaré group is a Lie group consisting of the symmetries of spacetime in special relativity. Point groups describe symmetry in molecular chemistry.
The concept of a group arose from the study of polynomial equations, starting with Évariste Galois in the 1830s, who introduced the term of group (groupe, in French) for the symmetry group of the roots of an equation, now called a Galois group. After contributions from other fields such as number theory and geometry, the group notion was generalized and firmly established around 1870. Modern group theory—an active mathematical discipline—studies groups in their own right. To explore groups, mathematicians have devised various notions to break groups into smaller, better-understandable pieces, such as subgroups, quotient groups and simple groups. In addition to their abstract properties, group theorists also study the different ways in which a group can be expressed concretely, both from a point of view of representation theory (that is, through the representations of the group) and of computational group theory. A theory has been developed for finite groups, which culminated with the classification of finite simple groups, completed in 2004. Since the mid-1980s, geometric group theory, which studies finitely generated groups as geometric objects, has become an active area in group theory.
Formally, the group is the ordered pair of a set and a binary operation on this set that satisfies the group axioms. The set is called the underlying set of the group, and the operation is called the group operation or the group law.
A group and its underlying set are thus two different mathematical objects. To avoid cumbersome notation, it is common to abuse notation by using the same symbol to denote both. This reflects also an informal way of thinking: that the group is the same as the set except that it has been enriched by additional structure provided by the operation.
Two figures in the plane are congruent if one can be changed into the other using a combination of rotations, reflections, and translations. Any figure is congruent to itself. However, some figures are congruent to themselves in more than one way, and these extra congruences are called symmetries. A square has eight symmetries. These are:
Given this set of symmetries and the described operation, the group axioms can be understood as follows.
Geometry was a second field in which groups were used systematically, especially symmetry groups as part of Felix Klein's 1872 Erlangen program. After novel geometries such as hyperbolic and projective geometry had emerged, Klein used group theory to organize them in a more coherent way. Further advancing these ideas, Sophus Lie founded the study of Lie groups in 1884.
The third field contributing to group theory was number theory. Certain abelian group structures had been used implicitly in Carl Friedrich Gauss' number-theoretical work Disquisitiones Arithmeticae (1798), and more explicitly by Leopold Kronecker. In 1847, Ernst Kummer made early attempts to prove Fermat's Last Theorem by developing groups describing factorization into prime numbers.
The convergence of these various sources into a uniform theory of groups started with Camille Jordan's Traité des substitutions et des équations algébriques (1870). Walther von Dyck (1882) introduced the idea of specifying a group by means of generators and relations, and was also the first to give an axiomatic definition of an "abstract group", in the terminology of the time. As of the 20th century, groups gained wide recognition by the pioneering work of Ferdinand Georg Frobenius and William Burnside, who worked on representation theory of finite groups, Richard Brauer's modular representation theory and Issai Schur's papers. The theory of Lie groups, and more generally locally compact groups was studied by Hermann Weyl, Élie Cartan and many others. Its algebraic counterpart, the theory of algebraic groups, was first shaped by Claude Chevalley (from the late 1930s) and later by the work of Armand Borel and Jacques Tits.
The University of Chicago's 1960–61 Group Theory Year brought together group theorists such as Daniel Gorenstein, John G. Thompson and Walter Feit, laying the foundation of a collaboration that, with input from numerous other mathematicians, led to the classification of finite simple groups, with the final step taken by Aschbacher and Smith in 2004. This project exceeded previous mathematical endeavours by its sheer size, in both length of proof and number of researchers. Research concerning this classification proof is ongoing. These days, group theory is still a highly active mathematical branch,[b] impacting many other fields, as the examples below illustrate.
Basic facts about all groups that can be obtained directly from the group axioms are commonly subsumed under elementary group theory. For example, repeated applications of the associativity axiom show that the unambiguity of
Individual axioms may be "weakened" to assert only the existence of a left identity and left inverses. From these one-sided axioms, one can prove that the left identity is also a right identity and a left inverse is also a right inverse for the same element. Since they define exactly the same structures as groups, collectively the axioms are no weaker.
When studying sets, one uses concepts such as subset, function, and quotient by an equivalence relation. When studying groups, one instead subgroups, homomorphisms, and quotient groups. These are the appropriate analogues that take into account the existence of the group structure.[c]
In some situations the set of cosets of a subgroup can be endowed with a group law, giving a quotient group or factor group. For this to be possible, the subgroup has to be normal. Given any normal subgroup N, the quotient group is defined by
Groups are also applied in many other mathematical areas. Mathematical objects are often examined by associating groups to them and studying the properties of the corresponding groups. For example, Henri Poincaré founded what is now called algebraic topology by introducing the fundamental group. By means of this connection, topological properties such as proximity and continuity translate into properties of groups.[h] For example, elements of the fundamental group are represented by loops. The second image shows some loops in a plane minus a point. The blue loop is considered null-homotopic (and thus irrelevant), because it can be continuously shrunk to a point. The presence of the hole prevents the orange loop from being shrunk to a point. The fundamental group of the plane with a point deleted turns out to be infinite cyclic, generated by the orange loop (or any other loop winding once around the hole). This way, the fundamental group detects the hole.
In more recent applications, the influence has also been reversed to motivate geometric constructions by a group-theoretical background.[i] In a similar vein, geometric group theory employs geometric concepts, for example in the study of hyperbolic groups. Further branches crucially applying groups include algebraic geometry and number theory.
In addition to the above theoretical applications, many practical applications of groups exist. Cryptography relies on the combination of the abstract group theory approach together with algorithmical knowledge obtained in computational group theory, in particular when implemented for finite groups. Applications of group theory are not restricted to mathematics; sciences such as physics, chemistry and computer science benefit from the concept.
Many number systems, such as the integers and the rationals enjoy a naturally given group structure. In some cases, such as with the rationals, both addition and multiplication operations give rise to group structures. Such number systems are predecessors to more general algebraic structures known as rings and fields. Further abstract algebraic concepts such as modules, vector spaces and algebras also form groups.
The desire for the existence of multiplicative inverses suggests considering fractions
The study of finitely generated abelian groups is quite mature, including the ; and reflecting this state of affairs, many group-related notions, such as center and commutator, describe the extent to which a given group is not abelian.
Symmetry groups are groups consisting of symmetries of given mathematical objects, principally geometric entities, such as the symmetry group of the square given as an introductory example above, although they also arise in algebra such as the symmetries among the roots of polynomial equations dealt with in Galois theory (see below). Conceptually, group theory can be thought of as the study of symmetry.[q] Symmetries in mathematics greatly simplify the study of geometrical or analytical objects. A group is said to act on another mathematical object X if every group element can be associated to some operation on X and the composition of these operations follows the group law. For example, an element of the (2,3,7) triangle group acts on a triangular tiling of the hyperbolic plane by permuting the triangles. By a group action, the group pattern is connected to the structure of the object being acted on.
In chemical fields, such as crystallography, space groups and point groups describe molecular symmetries and crystal symmetries. These symmetries underlie the chemical and physical behavior of these systems, and group theory enables simplification of quantum mechanical analysis of these properties. For example, group theory is used to show that optical transitions between certain quantum levels cannot occur simply because of the symmetry of the states involved.
Not only are groups useful to assess the implications of symmetries in molecules, but surprisingly they also predict that molecules sometimes can change symmetry. The Jahn–Teller effect is a distortion of a molecule of high symmetry when it adopts a particular ground state of lower symmetry from a set of possible ground states that are related to each other by the symmetry operations of the molecule.
Likewise, group theory helps predict the changes in physical properties that occur when a material undergoes a phase transition, for example, from a cubic to a tetrahedral crystalline form. An example is ferroelectric materials, where the change from a paraelectric to a ferroelectric state occurs at the Curie temperature and is related to a change from the high-symmetry paraelectric state to the lower symmetry ferroelectric state, accompanied by a so-called soft phonon mode, a vibrational lattice mode that goes to zero frequency at the transition.
Finite symmetry groups such as the Mathieu groups are used in coding theory, which is in turn applied in error correction of transmitted data, and in CD players. Another application is differential Galois theory, which characterizes functions having antiderivatives of a prescribed form, giving group-theoretic criteria for when solutions of certain differential equations are well-behaved.[r] Geometric properties that remain stable under group actions are investigated in (geometric) invariant theory.
A group action gives further means to study the object being acted on.[t] On the other hand, it also yields information about the group. Group representations are an organizing principle in the theory of finite groups, Lie groups, algebraic groups and topological groups, especially (locally) compact groups.
Modern Galois theory generalizes the above type of Galois groups by shifting to field theory and considering field extensions formed as the splitting field of a polynomial. This theory establishes—via the fundamental theorem of Galois theory—a precise relationship between fields and groups, underlining once again the ubiquity of groups in mathematics.
This way of defining groups lends itself to generalizations such as the notion of a group objects in a category. Briefly this is an object (that is, examples of another mathematical structure) which comes with transformations (called morphisms) that mimic the group axioms.
A Lie group is a group that also has the structure of a differentiable manifold; informally, this means that it looks locally like a Euclidean space of some fixed dimension. Again, the definition requires the additional structure, here the manifold structure, to be compatible: the multiplication and inverse maps are required to be smooth.
Lie groups are of fundamental importance in modern physics: Noether's theorem links continuous symmetries to conserved quantities. Rotation, as well as translations in space and time are basic symmetries of the laws of mechanics. They can, for instance, be used to construct simple models—imposing, say, axial symmetry on a situation will typically lead to significant simplification in the equations one needs to solve to provide a physical description.[x] Another example is the group of Lorentz transformations, which relate measurements of time and velocity of two observers in motion relative to each other. They can be deduced in a purely group-theoretical way, by expressing the transformations as a rotational symmetry of Minkowski space. The latter serves—in the absence of significant gravitation—as a model of spacetime in special relativity. The full symmetry group of Minkowski space, i.e., including translations, is known as the Poincaré group. By the above, it plays a pivotal role in special relativity and, by implication, for quantum field theories. Symmetries that vary with location are central to the modern description of physical interactions with the help of gauge theory. An important example of a gauge theory is the Standard Model, which describes three of the four known fundamental forces and classifies all known elementary particles. |
|Invented by||W. Pugh|
|Time complexity in big O notation|
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In computer science, a skip list is a data structure that allows fast search within an ordered sequence of elements. Fast search is made possible by maintaining a linked hierarchy of subsequences, with each successive subsequence skipping over fewer elements than the previous one. Searching starts in the sparsest subsequence until two consecutive elements have been found, one smaller and one larger than or equal to the element searched for. Via the linked hierarchy, these two elements link to elements of the next sparsest subsequence, where searching is continued until finally we are searching in the full sequence. The elements that are skipped over may be chosen probabilistically or deterministically, with the former being more common.
A skip list is built in layers. The bottom layer is an ordinary ordered linked list. Each higher layer acts as an "express lane" for the lists below, where an element in layer i appears in layer i+1 with some fixed probability p (two commonly used values for p are 1/2 or 1/4). On average, each element appears in 1/(1-p) lists, and the tallest element (usually a special head element at the front of the skip list) in all the lists. The skip list contains lists.
A search for a target element begins at the head element in the top list, and proceeds horizontally until the current element is greater than or equal to the target. If the current element is equal to the target, it has been found. If the current element is greater than the target, or the search reaches the end of the linked list, the procedure is repeated after returning to the previous element and dropping down vertically to the next lower list. The expected number of steps in each linked list is at most 1/p, which can be seen by tracing the search path backwards from the target until reaching an element that appears in the next higher list or reaching the beginning of the current list. Therefore, the total expected cost of a search is which is when p is a constant. By choosing different values of p, it is possible to trade search costs against storage costs.
The elements used for a skip list can contain more than one pointer since they can participate in more than one list.
Insertions and deletions are implemented much like the corresponding linked-list operations, except that "tall" elements must be inserted into or deleted from more than one linked list.
operations, which force us to visit every node in ascending order (such as printing the entire list), provide the opportunity to perform a behind-the-scenes derandomization of the level structure of the skip-list in an optimal way, bringing the skip list to search time. (Choose the level of the i'th finite node to be 1 plus the number of times we can repeatedly divide i by 2 before it becomes odd. Also, i=0 for the negative infinity header as we have the usual special case of choosing the highest possible level for negative and/or positive infinite nodes.) However this also allows someone to know where all of the higher-than-level 1 nodes are and delete them.
Alternatively, we could make the level structure quasi-random in the following way:
make all nodes level 1 j ← 1 while the number of nodes at level j > 1 do for each i'th node at level j do if i is odd if i is not the last node at level j randomly choose whether to promote it to level j+1 else do not promote end if else if i is even and node i-1 was not promoted promote it to level j+1 end if repeat j ← j + 1 repeat
Like the derandomized version, quasi-randomization is only done when there is some other reason to be running an operation (which visits every node).
The advantage of this quasi-randomness is that it doesn't give away nearly as much level-structure related information to an adversarial user as the de-randomized one. This is desirable because an adversarial user who is able to tell which nodes are not at the lowest level can pessimize performance by simply deleting higher-level nodes. (Bethea and Reiter however argue that nonetheless an adversary can use probabilistic and timing methods to force performance degradation.) The search performance is still guaranteed to be logarithmic.
It would be tempting to make the following "optimization": In the part which says "Next, for each ith...", forget about doing a coin-flip for each even-odd pair. Just flip a coin once to decide whether to promote only the even ones or only the odd ones. Instead of coin flips, there would only be of them. Unfortunately, this gives the adversarial user a 50/50 chance of being correct upon guessing that all of the even numbered nodes (among the ones at level 1 or higher) are higher than level one. This is despite the property that he has a very low probability of guessing that a particular node is at level N for some integer N.
A skip list does not provide the same absolute worst-case performance guarantees as more traditional balanced tree data structures, because it is always possible (though with very low probability) that the coin-flips used to build the skip list will produce a badly balanced structure. However, they work well in practice, and the randomized balancing scheme has been argued to be easier to implement than the deterministic balancing schemes used in balanced binary search trees. Skip lists are also useful in parallel computing, where insertions can be done in different parts of the skip list in parallel without any global rebalancing of the data structure. Such parallelism can be especially advantageous for resource discovery in an ad-hoc wireless network because a randomized skip list can be made robust to the loss of any single node.
As described above, a skiplist is capable of fast insertion and removal of values from a sorted sequence, but it has only slow lookups of values at a given position in the sequence (i.e. return the 500th value); however, with a minor modification the speed of random access indexed lookups can be improved to .
For every link, also store the width of the link. The width is defined as the number of bottom layer links being traversed by each of the higher layer "express lane" links.
For example, here are the widths of the links in the example at the top of the page:
1 10 o---> o---------------------------------------------------------> o Top level 1 3 2 5 o---> o---------------> o---------> o---------------------------> o Level 3 1 2 1 2 3 2 o---> o---------> o---> o---------> o---------------> o---------> o Level 2 1 1 1 1 1 1 1 1 1 1 1 o---> o---> o---> o---> o---> o---> o---> o---> o---> o---> o---> o Bottom level Head 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th NIL Node Node Node Node Node Node Node Node Node Node
Notice that the width of a higher level link is the sum of the component links below it (i.e. the width 10 link spans the links of widths 3, 2 and 5 immediately below it). Consequently, the sum of all widths is the same on every level (10 + 1 = 1 + 3 + 2 + 5 = 1 + 2 + 1 + 2 + 5).
To index the skip list and find the i'th value, traverse the skip list while counting down the widths of each traversed link. Descend a level whenever the upcoming width would be too large.
For example, to find the node in the fifth position (Node 5), traverse a link of width 1 at the top level. Now four more steps are needed but the next width on this level is ten which is too large, so drop one level. Traverse one link of width 3. Since another step of width 2 would be too far, drop down to the bottom level. Now traverse the final link of width 1 to reach the target running total of 5 (1+3+1).
function lookupByPositionIndex(i) node ← head i ← i + 1 # don't count the head as a step for level from top to bottom do while i ≥ node.width[level] do # if next step is not too far i ← i - node.width[level] # subtract the current width node ← node.next[level] # traverse forward at the current level repeat repeat return node.value end function
This method of implementing indexing is detailed in Section 3.4 Linear List Operations in "A skip list cookbook" by William Pugh.
To quote the author:
- Skip lists are a probabilistic data structure that seem likely to supplant balanced trees as the implementation method of choice for many applications. Skip list algorithms have the same asymptotic expected time bounds as balanced trees and are simpler, faster and use less space.
List of applications and frameworks that use skip lists:
- MemSQL uses skip lists as its prime indexing structure for its database technology.
- Cyrus IMAP server offers a "skiplist" backend DB implementation (source file)
- Lucene uses skip lists to search delta-encoded posting lists in logarithmic time.
- QMap (up to Qt 4) template class of Qt that provides a dictionary.
- Redis, an ANSI-C open-source persistent key/value store for Posix systems, uses skip lists in its implementation of ordered sets.
- nessDB, a very fast key-value embedded Database Storage Engine (Using log-structured-merge (LSM) trees), uses skip lists for its memtable.
- skipdb is an open-source database format using ordered key/value pairs.
- ConcurrentSkipListSet and ConcurrentSkipListMap in the Java 1.6 API.
- Speed Tables are a fast key-value datastore for Tcl that use skiplists for indexes and lockless shared memory.
- leveldb, a fast key-value storage library written at Google that provides an ordered mapping from string keys to string values
- Con Kolivas' MuQSS Scheduler for the Linux kernel uses skip lists
- SkiMap uses skip lists as base data structure to build a more complex 3D Sparse Grid for Robot Mapping systems.
Skip lists are used for efficient statistical computations of running medians (also known as moving medians). Skip lists are also used in distributed applications (where the nodes represent physical computers, and pointers represent network connections) and for implementing highly scalable concurrent priority queues with less lock contention, or even without locking, as well as lockless concurrent dictionaries. There are also several US patents for using skip lists to implement (lockless) priority queues and concurrent dictionaries.
- Papadakis, Thomas (1993). Skip Lists and Probabilistic Analysis of Algorithms (PDF) (Ph.D.). University of Waterloo.
- Pugh, W. (1990). "Skip lists: A probabilistic alternative to balanced trees" (PDF). Communications of the ACM. 33 (6): 668. doi:10.1145/78973.78977.
- Munro, J. Ian; Papadakis, Thomas; Sedgewick, Robert (1992). "Deterministic skip lists" (PDF). Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms (SODA '92). Orlando, Florida, USA: Society for Industrial and Applied Mathematics, Philadelphia, PA, USA. pp. 367–375. doi:10.1145/139404.139478.
- Bethea, Darrell; Reiter, Michael K. (September 21–23, 2009). Data Structures with Unpredictable Timing (PDF). ESORICS 2009, 14th European Symposium on Research in Computer Security. Saint-Malo, France. pp. 456–471, §4 "Skip Lists". doi:10.1007/978-3-642-04444-1_28. ISBN 3-642-04443-3.
- Shah, Gauri (2003). Distributed Data Structures for Peer-to-Peer Systems (PDF) (Ph.D. thesis). Yale University.
- Pugh, William (April 1989). Concurrent Maintenance of Skip Lists (PS, PDF) (Technical report). Dept. of Computer Science, U. Maryland. CS-TR-2222.
- "Redis ordered set implementation".
- "LKML: Con Kolivas: [ANNOUNCE] Multiple Queue Skiplist Scheduler version 0.120". lkml.org. Retrieved 2017-05-11.
- Gregorio, Daniele De; Stefano, Luigi Di (2017). "SkiMap: An Efficient Mapping Framework for Robot Navigation". arXiv: [cs.CV].
- Shavit, N.; Lotan, I. (2000). "Skiplist-based concurrent priority queues". Proceedings 14th International Parallel and Distributed Processing Symposium. IPDPS 2000 (PDF). p. 263. doi:10.1109/IPDPS.2000.845994. ISBN 0-7695-0574-0.
- Sundell, H.; Tsigas, P. (2003). "Fast and lock-free concurrent priority queues for multi-thread systems". Proceedings International Parallel and Distributed Processing Symposium. p. 11. doi:10.1109/IPDPS.2003.1213189. ISBN 0-7695-1926-1.
- Fomitchev, Mikhail; Ruppert, Eric (2004). Lock-free linked lists and skip lists (PDF). Proc. Annual ACM Symp. on Principles of Distributed Computing (PODC). pp. 50–59. doi:10.1145/1011767.1011776. ISBN 1581138024.
- Bajpai, R.; Dhara, K. K.; Krishnaswamy, V. (2008). "QPID: A Distributed Priority Queue with Item Locality". 2008 IEEE International Symposium on Parallel and Distributed Processing with Applications. p. 215. doi:10.1109/ISPA.2008.90. ISBN 978-0-7695-3471-8.
- Sundell, H. K.; Tsigas, P. (2004). "Scalable and lock-free concurrent dictionaries". Proceedings of the 2004 ACM symposium on Applied computing - SAC '04 (PDF). p. 1438. doi:10.1145/967900.968188. ISBN 1581138121.
- US patent 7937378
|Wikimedia Commons has media related to Skip list.|
- "Skip list" entry in the Dictionary of Algorithms and Data Structures
- Skip Lists: A Linked List with Self-Balancing BST-Like Properties on MSDN in C# 2.0
- Why Skip Lists?
- Skip Lists lecture (MIT OpenCourseWare: Introduction to Algorithms)
- Open Data Structures - Chapter 4 - Skiplists
- Skip trees, an alternative data structure to skip lists in a concurrent approach
- Skip tree graphs, a distributed version of skip trees
- More on skip tree graphs, a distributed version of skip trees
- Skip List Applet by Kubo Kovac
- Thomas Wenger's demo applet on skiplists |
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