reaction rate: The rate constant, or the specific rate constant, is the proportionality constant in the equation that expresses the relationship between the rate of a chemical reaction and the concentrations of the reacting substances. The measurement and interpretation of reactions constitute the branch of chemistry known as…

Jerry Reinsdorf: …Comiskey Park (now known as Guaranteed Rate Field), which opened in 1991, was subsidized by taxpayers and contained a large number of premium-priced seats. Similarly, in 1994 Reinsdorf unveiled the new United Center to replace Chicago Stadium—another iconic Chicago sports arena—for the Bulls. Later that year, when players of Major…

insurance: Rate making: Closely associated with underwriting is the rate-making function. If, for example, the underwriter decides that the most important factor in discriminating between different risk characteristics is age, the rates will be differentiated according to age.

radiation measurement: Counting systems: …be indicated electronically using a rate meter. This unit provides an output signal that is proportional to the rate at which accepted pulses are occurring averaged over a response time that is normally adjustable by the user. Long response times minimize the fluctuations in the output signal due to the…

human development: Types and rates of human growth: …to the next, expressed as rate of growth per year. If growth is thought of as a form of motion, the height attained at successive ages can be considered the distance travelled, and the rate of growth, the velocity. The velocity or rate of growth reflects the child’s state at…

Interest is the price paid for the use of credit or money. The interest rate is the price paid, expressed as a percentage—typically on an annualized basis—of the underlying credit amount. When you borrow money, perhaps to buy a house or a car or to attend college, you pay interest. When you deposit

Hungary: Demographic trends: …Hungary has experienced a negative natural increase rate (meaning the number of deaths has outpaced the number of births). These demographic trends were influenced by the urbanization and modernization process. As modernization spread from urban areas (where people generally have fewer children) into the countryside, so did the declining birth…

Arthur Laffer: …propounded the idea that lowering tax rates could result in higher revenues. His theory on taxes influenced U.S. economic policy in the 1980s, which during the presidency of Ronald Reagan (1981–89) became known as Reaganomics.

separation and purification: Separations based on rates: Rate separation processes are based on differences in the kinetic properties of the components of a mixture, such as the velocity of migration in a medium or of diffusion through semipermeable barriers.

income tax: International variations in rate structures: …be said about variations in rate structures. The important variants in these structures are (1) the starting point and levels of first-bracket rates, (2) the top bracket or maximum marginal rates, and (3) the income range within which rates rise from the lowest to the highest levels.

Rihanna: Later works: Rated R, Talk That Talk, and Unapologetic: …that followed later that year, Rated R, much of which she cowrote, was marked by icily stark production and brooding lyrics that touched on revenge. Although her sales declined somewhat, she scored another major hit with “Rude Boy.” Rihanna returned to less-portentous fare on the dance-friendly Loud (2010). In early…

ratel, (Mellivora capensis), badgerlike member of the weasel family (Mustelidae) noted for its fondness for honey. Ratels live in covered and forested regions of Africa and southern Asia. The adult stands 25–30 cm (10–12 inches) at the shoulder and has a heavily built, thick-skinned body about

government budget: Local government finance in the United Kingdom: …was a property tax called rates.

Henri-René Lenormand: His best-known play, Les Ratés (1920; “The Failures”), traces the physical and moral disintegration of a playwright and his mistress, a mediocre actress, who, under the pressure of adversity, end their lives in murder and suicide. To elucidate the conflicts of the human psyche, Lenormand often chose abnormal…

ratfish, any of certain sharks of the chimaera (q.v.)

Tara: …a vast oval enclosure called Ráth na Riógh (“Fortress of the Kings”). Near the centre of this are two conjoined earthworks: Forradh (“Royal Seat”) and Teach Cormaic (“Cormac’s House”). On the latter is a pillar stone, often thought to be the inauguration stone of the kings of Tara. The other…

Kristallnacht: …7 of the German diplomat Ernst vom Rath by a Polish-Jewish student, Herschel Grynszpan. News of Rath’s death on November 9 reached Adolf Hitler in Munich, Germany, where he was celebrating the anniversary of the abortive 1923 Beer Hall Putsch. There, Minister of Propaganda Joseph Goebbels, after conferring with Hitler,…

Lübeck: …Henry III), and the magnificent Rathaus (city hall), built in a combination of Gothic and Renaissance styles. Waterways and parklands outline the inner city, where the moat and ramparts once shielded it from attack. Two towered gates are remnants of the medieval fortifications: the Burgtor (1444), which received a new…

Rathayatra, Hindu festival of India, observed by taking an image of a deity in a procession (yatra) through the streets in a chariot (ratha). This affords darshan (auspicious viewing) of the deity to worshippers who, because of caste or sectarian restrictions, are not admitted to the sanctuary. It

Central Asian arts: Sculpture and painting: …scroll paintings such as the Rathayātrā Scroll (1617; Chhatrapati Shivaji Maharaj Vastu Sangrahalaya). Its planar intricacies reveal a new and vital aspect of Nepalese painting, an immediacy of emotion and action of its protagonists, the figures of which are placed on an opaque, velvety ground. The colours of these book…

Basil Rathbone was a British character actor whose portrayal of Sherlock Holmes highlighted a long and varied stage and screen career. Upon graduating from Repton school in England in 1910, Rathbone made his stage debut in Shakespeare’s The Taming of the Shrew in 1911. A number of other

Basil Rathbone was a British character actor whose portrayal of Sherlock Holmes highlighted a long and varied stage and screen career. Upon graduating from Repton school in England in 1910, Rathbone made his stage debut in Shakespeare’s The Taming of the Shrew in 1911. A number of other

hypophosphatasia, rare hereditary disorder characterized by very low levels of tissue and serum alkaline phosphatase (the enzyme necessary in cell processes such as muscle metabolism and bone formation). The disease is more common in females. Growth of the infant is retarded; permanent stunting may

Mary Jane Rathbun was an American marine zoologist known for establishing the basic taxonomic information on Crustacea. In 1881, at the urging of her brother, Richard Rathbun, of the U.S. Fish Commission, she volunteered to work at the Woods Hole Marine Research Center in Massachusetts. Her

Emil Rathenau was a German industrialist and a leading figure in the early European electrical industry. In 1883 he founded the Deutsche Edison-Gesellschaft to manufacture products based on Thomas A. Edison’s patents, for which he had purchased the European rights. The firm was renamed

Walther Rathenau was a German-Jewish statesman, industrialist, and philosopher who organized Germany’s economy on a war footing during World War I and, after the war, as minister of reconstruction and foreign minister, was instrumental in beginning reparations payments under the Treaty of

Dan Rather is an American newscaster and author who covered some of the most important historical events of his time, including the civil rights movement, the Vietnam War, and the Watergate scandal, during his four decades with CBS. Rather grew up in Texas, where his father laid pipeline for oil

Dan Rather is an American newscaster and author who covered some of the most important historical events of his time, including the civil rights movement, the Vietnam War, and the Watergate scandal, during his four decades with CBS. Rather grew up in Texas, where his father laid pipeline for oil

Martin H. Rathke: …embryonic structure, now known as Rathke’s pouch, from which the anterior lobe of the pituitary gland develops.

Martin H. Rathke was a German anatomist who first described the gill slits and gill arches in the embryos of mammals and birds. He also first described in 1839 the embryonic structure, now known as Rathke’s pouch, from which the anterior lobe of the pituitary gland develops. Rathke ended a 10-year

Martin H. Rathke was a German anatomist who first described the gill slits and gill arches in the embryos of mammals and birds. He also first described in 1839 the embryonic structure, now known as Rathke’s pouch, from which the anterior lobe of the pituitary gland develops. Rathke ended a 10-year

Moyle: …coast of Ireland, Moyle included Rathlin Island, Northern Ireland’s only populated island, and had 42 miles (68 km) of bays, headlands, and sheer basalt cliffs dissected by wooded glens. The Antrim Mountains extend through the eastern portion of Moyle, reaching an elevation of 1,817 feet (554 metres) at Trostan Mountain…

Rajyavardhan Singh Rathore is an Indian politician and former rifle shooter who won his country’s first individual Olympic silver medal when he placed second in the men’s double-trap event at the Athens 2004 Olympic Games. Rathore attended the Indian National Defence Academy and joined the Indian

gastropod: Classification: …or terrestrial and carnivorous (Rathouisiidae); about 200 species. Superorder Basommatophora Mantle cavity present; eyes at base of 1 pair of tentacles; male and female gonopore separate, usually on right side of body; shell conical to patelliform; mostly freshwater but a few land and marine taxa; about 1,000 species. (No…

coneflower: Plants of the genus Ratibida have yellow ray flowers, brownish disk flowers, and segmented leaves. Prairie coneflower (Ratibida columnaris) and R. pinnata are grown in wildflower gardens. The third genus, Rudbeckia, has about 25 annual, biennial, and perennial species with simple or segmented leaves, yellow ray flowers, and brown…

Racibórz, city, southwestern Śląskie województwo (province), south-central Poland, on the upper Oder River. According to tradition, Racibórz was founded by a Slavic tribal ruler, Prince Racibor, in the 9th century and was united with Poland in the 10th. It was granted municipal rights in the 13th

Wolfgang Ratke was a German educational reformer, especially in the teaching of languages, whose pioneering achievements laid the groundwork for the work of Comenius. Ratke was educated in Hamburg, and he studied theology (without obtaining a degree) at the University of Rostock. Having abandoned a

Wolfgang Ratke was a German educational reformer, especially in the teaching of languages, whose pioneering achievements laid the groundwork for the work of Comenius. Ratke was educated in Hamburg, and he studied theology (without obtaining a degree) at the University of Rostock. Having abandoned a

Wolfgang Ratke was a German educational reformer, especially in the teaching of languages, whose pioneering achievements laid the groundwork for the work of Comenius. Ratke was educated in Hamburg, and he studied theology (without obtaining a degree) at the University of Rostock. Having abandoned a

diplomacy: Diplomatic agreements: Treaties and conventions require ratification, an executive act of final approval. In democratic countries parliamentary approval is deemed advisable for important treaties. In the United States the Senate must consent by a two-thirds vote. Elsewhere, legislative involvement is less drastic but has increased since World War II. In Britain…

radio: Ratings systems: ) As radio grew into a commercial force, it became necessary to determine the popularity of particular shows, as this would affect the price of the program’s advertising time. In 1930 the Association of National Advertisers, along with the Cooperative Analysis of Broadcasting, devised…

Motion Picture Association: …the MPAA set up a rating board that classified films as G, M, R, and X. After various changes the MPA ratings are now as follows: G, for general audiences; PG, parental guidance suggested; PG-13, parents strongly cautioned, because film contains material inappropriate for children under 13; R, restricted to…

insurance: Rate making: …claims experience by setting up rating bureaus to calculate rates based on industrywide experience. They may have an agreement that all member companies must use the rates thus developed. The rationale for such agreements is that they help insurers meet the criteria of adequacy and fairness. Rating bureaus are used…

rating rule, in yacht racing, rule used to classify sailing yachts of different designs to enable them to compete on relatively equal terms. The competition may be either among yachts in a particular rating class or on a handicap basis, with the highest-rated boat giving up time allowances to all

personality assessment: Rating scales: The rating scale is one of the oldest and most versatile of assessment techniques. Rating scales present users with an item and ask them to select from a number of choices. The rating scale is similar in some respects to a multiple choice…

Andreas Gursky: Ratingen Swimming Pool (1987) shows a lush green landscape dotted with tiny figures swimming and relaxing by the pool. The scene was photographed from a considerable distance at a slightly elevated perspective. Though shot far from the pool, the image captures every element of the…

ratio, Quotient of two values. The ratio of a to b can be written a:b or as the fraction a/b. In either case, a is the antecedent and b the consequent. Ratios arise whenever comparisons are made. They are usually reduced to lowest terms for simplicity. Thus, a school with 1,000 students and 50

business finance: Financial ratio analysis: A firm’s balance sheet contains many items that, taken by themselves, have no clear meaning. Financial ratio analysis is a way of appraising their relative importance. The ratio of current assets to current liabilities, for example, gives the analyst an idea of…

Claudio Aquaviva: This work, Ratio atque institutio studiorum (“The Reason and Establishment of Studies”), was first published in 1586, at which time it was distributed to Jesuit schools for criticism and revision. The definitive text (1599) unified Jesuit teaching throughout the world, yet allowed for adaptation to local needs.…

psychological testing: Types of measurement scales: Ratio scales not only provide equal units but also have absolute zero points; examples include measures of weight and distance.

infinite series: …reformulated slightly and called the ratio test: if an > 0 and if an + 1/an ≤ r for some r < 1 for every n, then a1 + a2 +⋯ converges. For example, the ratio test proves the convergence of the series

Jonathan Edwards: Early life and ministry: …the outlines of a “Rational Account” of the doctrines of Christianity in terms of contemporary philosophy. In the essay “Of Being,” he argued from the inconceivability of absolute Nothing to the existence of God as the eternal omnipresent Being. It was also inconceivable to him that anything should exist…

rational choice theory, school of thought based on the assumption that individuals choose a course of action that is most in line with their personal preferences. Rational choice theory is used to model human decision making, especially in the context of microeconomics, where it helps economists

neoinstitutionalism: Rational choice institutionalism: Rational choice institutionalism, which has its roots in economics and organizational theory, examines institutions as systems of rules and incentives. Rules are contested so that one group of political actors can gain leverage over another. Political decision making is explained through modeling…

rational choice theory, school of thought based on the assumption that individuals choose a course of action that is most in line with their personal preferences. Rational choice theory is used to model human decision making, especially in the context of microeconomics, where it helps economists

historiography: From explanation to interpretation: …a similar vein, Vico’s “rational civil theology” recognizes that “men have themselves made this world of nations” but goes on to assert that “this world without doubt has issued from a mind often diverse, at times quite contrary, and always superior to the particular ends that men had proposed…

therapeutics: Behavioral therapy: Rational emotive therapy aims at altering inaccurate or irrational thoughts that lead to negative emotions or maladaptive behaviour. Other behavioral approaches attempt to modify physical responses. Neurofeedback, for example, uses sensitive electronic devices and the principles of reinforcement to provide continuous visual or auditory “feedback,”…

business cycle: Rational expectations theories: In the early 1970s the American economist Robert Lucas developed what came to be known as the “Lucas critique” of both monetarist and Keynesian theories of the business cycle. Building on rational expectations concepts introduced by the American economist John Muth, Lucas…

elementary algebra: Algebraic expressions: …of polynomials, one obtains the rational functions. Examples of such rational functions are 2/3x and (a + bx2)/(c + dx2 + ex5). Working with rational functions allows one to introduce the expression 1/x and its powers, 1/x2, 1/x3, … (often written x−1,

urban planning: Competing models: …universal method—also known as “the rational model”—whereby experts would evaluate alternatives in relation to a specified set of goals and then choose the optimum solution. The rational model was briefly hegemonic, but this scientific approach to public-policy making was quickly challenged by critics who argued that the human consequences…

rational number, in arithmetic, a number that can be represented as the quotient p/q of two integers such that q ≠ 0. In addition to all the fractions, the set of rational numbers includes all the integers, each of which can be written as a quotient with the integer as the numerator and 1 as the

consumption: The rational optimization framework: In their studies of consumption, economists generally draw upon a common theoretical framework by assuming that consumers base their expenditures on a rational and informed assessment of their current and future economic circumstances. This “rational optimization” assumption is untestable, however, without additional…

phytotherapy: History of phytotherapy: In 1997 the book Rational Phytotherapy was published under the stewardship of American pharmacognosist Varro Tyler. The work was an English translation of the German book Rationale Phytotherapie: Ratgeber für die Ärztliche Praxis (3rd ed., 1996), written by Volker Schulz and Rudolf Hänsel.

rational psychology, Metaphysical discipline that attempted to determine the nature of the human soul by a priori reasoning. In Christian Wolff’s division of metaphysics, rational psychology was one of three disciplines included under the heading of “special metaphysics” (the others being rational

rational root theorem, in algebra, theorem that for a polynomial equation in one variable with integer coefficients to have a solution (root) that is a rational number, the leading coefficient (the coefficient of the highest power) must be divisible by the denominator of the fraction and the

rational root theorem, in algebra, theorem that for a polynomial equation in one variable with integer coefficients to have a solution (root) that is a rational number, the leading coefficient (the coefficient of the highest power) must be divisible by the denominator of the fraction and the

Miura Baien: He formulated the jōrigaku (“rationalist studies”) doctrine, which was a precursor to modern scientific and philosophical thought in Japan.

organization theory: Key questions, units of analysis, and debates: The rational system perspective focuses on the formal structures of an organization and sees the organization as a group of people who work together to pursue specific goals. The natural system perspective advances the idea that informal and interpersonal structures within an organization are more important…

Gemeinschaft and Gesellschaft: …the creation of Kürwille (rational will) and is typified by modern, cosmopolitan societies with their government bureaucracies and large industrial organizations. In the Gesellschaft, rational self-interest and calculating conduct act to weaken the traditional bonds of family, kinship, and religion that permeate the Gemeinschaft’s structure. In the Gesellschaft, human…

therapeutics: Behavioral therapy: Rational emotive therapy aims at altering inaccurate or irrational thoughts that lead to negative emotions or maladaptive behaviour. Other behavioral approaches attempt to modify physical responses. Neurofeedback, for example, uses sensitive electronic devices and the principles of reinforcement to provide continuous visual or auditory “feedback,”…

Guillaume Durand: Of his liturgical works, the Rationale divinorum officiorum (c. 1285–91), a general treatise on the liturgy and its symbolism, is considered one of the most important medieval books on divine worship. The Speculum was printed at least 39 times between 1473 and 1678, and the Rationale even more.

Jeremy Bentham: Mature works: Thus, the Rationale of Judicial Evidence, 5 vol. (1827), was put in its finished state by John Stuart Mill and the Book of Fallacies (1824) by Peregrine Bingham. The services of Étienne Dumont in recasting as well as translating the works of Bentham were still more important.

Jeremy Bentham: Early life and works: …Rationale of Reward (1825) and The Rationale of Punishment (1830). In 1785 Bentham started, by way of Italy and Constantinople, on a visit to his brother, Samuel Bentham, an engineer in the Russian armed forces; and it was in Russia that he wrote his Defence of Usury (published 1787). This,…

James Martineau: …of Scripture, and in his Rationale of Religious Inquiry (1836) he declared that “the last appeal in all researches into religious truth must be to the judgment of the human mind.” Appointed professor of mental and moral philosophy at Manchester New College in 1840, Martineau taught there (and from 1869…

Jeremy Bentham: Early life and works: …eventually appeared in English as The Rationale of Reward (1825) and The Rationale of Punishment (1830). In 1785 Bentham started, by way of Italy and Constantinople, on a visit to his brother, Samuel Bentham, an engineer in the Russian armed forces; and it was in Russia that he wrote his…

phytotherapy: History of phytotherapy: In 1997 the book Rational Phytotherapy was published under the stewardship of American pharmacognosist Varro Tyler. The work was an English translation of the German book Rationale Phytotherapie: Ratgeber für die Ärztliche Praxis (3rd ed., 1996), written by Volker Schulz and Rudolf Hänsel.

rationalism, in Western philosophy, the view that regards reason as the chief source and test of knowledge. Holding that reality itself has an inherently logical structure, the rationalist asserts that a class of truths exists that the intellect can grasp directly. There are, according to the

Michael Oakeshott: …most famous work, however, is Rationalism in Politics (1962), an essay that criticizes the modern tendency to elevate formal theory above practical knowledge. Oakeshott is also known for his original reading of the 17th-century English philosopher Thomas Hobbes. In his introduction (1946) to Hobbes’s Leviathan, Oakeshott reclaims Hobbes as a…

rationality, the use of knowledge to attain goals. (Read Britannica’s biography of Steven Pinker, author of this entry.) Rationality has a normative dimension, namely how an agent ought to reason in order to attain some goal, and a descriptive or psychological dimension, namely how human beings do

organizational analysis: Origins of the discipline: …this development, which he called rationalization, underlay the rise of the modern state bureaucracy. According to Weber, organizations were able to develop unparalleled calculability and efficiency by combining two structures: (1) a system of explicit rules, upheld by clearly marked jurisdictions between offices and by permanent files documenting the processing…

defense mechanism: Psychoanalysts emphasize that the use of a defense mechanism is a normal part of personality function and not in and of itself a sign of psychological disorder.…

rationing, government policy consisting of the planned and restrictive allocation of scarce resources and consumer goods, usually practiced during times of war, famine, or some other national emergency. Rationing may be of several types. Informal rationing, which precedes the imposition of formal

Regensburg, city, Bavaria Land (state), southeastern Germany. It lies on the right bank of the Danube River along its most northerly course, where it is joined by the Regen River, about 65 miles (105 km) northeast of Munich. Regensburg is an important cultural, industrial, and commercial centre and

Rhaetian Alps, segment of the Central Alps extending along the Italian-Swiss and Austrian-Swiss borders but lying mainly in Graubünden canton, eastern Switzerland. The mountains are bounded by the Lepontine Alps and Splügen Pass (west-southwest), the Hinterrhein River (west), the Lechtaler Alps

ratite, any bird whose sternum (breastbone) is smooth, or raftlike, because it lacks a keel to which flight muscles could be anchored. All species of ratites are thus unable to fly. They are a peculiar and puzzling group, with anatomic anomalies. The group includes some of the largest birds of all

Wolfgang Ratke was a German educational reformer, especially in the teaching of languages, whose pioneering achievements laid the groundwork for the work of Comenius. Ratke was educated in Hamburg, and he studied theology (without obtaining a degree) at the University of Rostock. Having abandoned a

Ratlam, city, western Madhya Pradesh state, central India. It is situated at an elevation of about 1,575 feet (480 metres) above sea level on the Malwa Plateau, about 45 miles (72 km) west-northwest of Ujjain. Ratlam is a major rail junction, an agricultural trade centre, and a major industrial

knot: The clove hitch, also called a builder’s knot or a ratline hitch, is made by passing the rope’s end around an object and then crossing it over the rope’s standing part to form a loop, then passing the end around the object again to form a…

Alexei Ratmansky is a Russian ballet dancer and choreographer known for his exceptional musicality, seemingly limitless energy, and stylistic versatility. As artistic director of the Bolshoi Ballet (2004–08), he rescued the company from a financial and artistic quagmire, largely by diversifying its

Alexei Ratmansky is a Russian ballet dancer and choreographer known for his exceptional musicality, seemingly limitless energy, and stylistic versatility. As artistic director of the Bolshoi Ballet (2004–08), he rescued the company from a financial and artistic quagmire, largely by diversifying its

Ratnagiri, town, southwestern Maharashtra state, western India. It is situated on the Arabian Sea coast at the mouth of the Kajali River. Ratnagiri became an administrative capital under the Bijapur rulers. In 1731 it came under the control of Satara kings, and in 1818 it was surrendered to the

Mani Ratnam is an Indian filmmaker noted for his popular films in both Tamil and Hindi cinema. Ratnam was the son of film producer Ratnam Iyer. He obtained a management degree at the Jamnalal Bajaj Institute of Management Studies at the University of Bombay (now the University of Mumbai) before

Ratnapura, town, southwestern Sri Lanka. It is situated southeast of Colombo, on the Kalu River. Dominating the town is a hill on which the Portuguese built a fort. Ratnapura (Sinhalese: “City of Gems”) is Sri Lanka’s chief source of precious and semiprecious stones (including rubies, sapphires,

Ratnasambhava, in Vajrayana Buddhism, one of the five “self-born” celestial buddhas. See

Jainism: Theories of knowledge as applied to liberation: …to the Three Jewels (ratnatraya) of right knowledge, right faith, and right practice (respectively, samyagjnana, samyagdarshana, and samyakcharitra).

South Asian arts: The theatre: …are attributed three charming plays: Ratnāvalī and Priyadarśikā, both of which are of the harem type; and Nāgānanda (“The Joy of the Serpents”), inspired by Buddhism and illustrating the generosity of the snake deity Jīmūtavāhana.

Gregory Ratoff was a Russian-born actor and director who appeared in a number of supporting roles before embarking on a directing career that featured a diverse range of films. Ratoff trained in the Russian theatre before serving with the tsar’s army during the Russian Revolution (1917). In the

Raton, city, seat (1897) of Colfax county, northeastern New Mexico, U.S. It lies at the southern end of Raton Pass (7,834 feet [2,388 metres] above sea level) in the Sangre de Cristo Range, near the Colorado state line. Located on the old Santa Fe Trail and settled in 1871, it was used as a

bulbil: Bulbils, called offsets when full-sized, fall or are removed and planted to produce new plants. They are especially common among such plants as onions and lilies.

sugarcane: Culture: …of cane propagation is by ratooning, in which, when the cane is harvested, a portion of stalk is left underground to give rise to a succeeding growth of cane, the ratoon or stubble crop. The ratooning process is usually repeated three times so that three economical crops are taken from…