time-division: see multiplexing.

labor, division of: see division of labor.

division of labor, in economics, the specialization of the functions and roles involved in production. Division of labor is closely tied with the standardization of production, the introduction and perfection of machinery, and the development of large-scale industry. Among the different categories of division of labor are territorial, in which certain geographical regions specialize in producing certain products, exchanging their surplus for goods produced elsewhere; temporal, in which separate processes are performed by different industrial groups in manufacturing one product, as the making of bread by farmers, millers, and bakers; and occupational, in which goods produced in the same industrial group are worked by a number of persons, each applying one or more processes and skills. Modern mass-production techniques are based on the last type. The proficiency attained through experience at one task and the time saved by concentration on one phase of an operation are such that the total production is many times what it would be had each worker made the complete article. The classic example is that given by Adam Smith, advocate of free trade (of which the division of labor is the underlying principle), in which 10 men, each performing one or more of the 18 operations necessary to make a pin, together produce 48,000 pins a day, whereas working separately they could not make 200. Problems created by the division of labor include the monotony of concentration on routine tasks, technological unemployment for people whose skills are not in demand, and eventually chronic unemployment if the economy does not expand quickly enough to reabsorb the displaced labor. Each variant of the division of labor has its own peculiar problems of distribution.

division, fundamental operation in arithmetic; the inverse of multiplication. Division may be indicated by the symbol ÷, as in 15 ÷ 3, or simply by a fraction, 15/3. The number that is being divided, e.g. 15, is called the dividend and the number dividing into it, e.g. 3, the divisor. The result of division is called the quotient. If the dividend is an exact (integral) multiple of the divisor, then the division will be exact, the quotient being the factor by which the divisor must be multiplied to yield the dividend (in the above example the quotient 5 multiplied by the divisor 3 equals the dividend 15). If the dividend is not an exact multiple of the divisor there will be a remainder expressed as a fraction with the divisor as the denominator; e.g., 16/3 = 51/3, where 1/3 is the remainder. A division in which the divisor b is larger than the dividend a is simply indicated by the fraction a/b, with no actual operation being carried out. In terms of multiplication either of the symbols 1/b or b^-1 is called the multiplicative inverse of b with the property that the product of a number and its inverse equals 1, or b · b^-1 =1. The division of a by b is equivalent to the multiplication of a by the multiplicative inverse of b, i.e., a ÷ b = a · (1/b) = a · b^-1; for example, when a = 25 and b = 5, then 1/b = 1/5 and 25 ÷ 5 = 25 · (1/5) = 5.

division, in taxonomy: see classification.

cell division: see cell; mitosis; meiosis.

Rainbow Division, nickname of the 42d Division of the U.S. army. The first U.S. combat division to arrive in France in World War I, it participated in the second battle of the Marne, fought in the counteroffensive at Château-Thierry, and spearheaded attacks at Saint-Mihiel and in the Meuse-Argonne sector. Throughout the war the division suffered heavy losses. It later became a part of the National Guard.

Cassini's division: see Saturn.

(German panzer, “armoured”) Self-contained military unit of the German army, built around the capabilities of armoured vehicles. In World War II, it consisted of a tank brigade with four battalions; a motorized infantry brigade with four rifle battalions; an artillery regiment; and reconnaissance, antitank, and military-engineering battalions and service units. Germany had six panzer divisions in 1939 and 20 by 1941. It remains the principal offensive element of the German army.

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Division of the legislative, executive, and judicial functions of government among separate and independent bodies. Such a separation limits the possibility of arbitrary excesses by government, since the sanction of all three branches is required for the making, executing, and administering of laws. The concept received its first modern formulation in the work of Charles-Louis de Secondat, baron de La Brède et de Montesquieu, who declared it the best way to safeguard liberty; he influenced the framers of the Constitution of the United States, who in turn influenced the writers of 19th- and 20th-century constitutions. Seealso checks and balances.

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Specialization in the production process. Complex jobs can usually be less expensively completed by a large number of people each performing a small number of specialized tasks than by one person attempting to complete the entire job. The idea that specialization reduces costs, and thereby the price the consumer pays, is embedded in the principle of comparative advantage. Division of labour is the basic principle underlying the assembly line in mass production systems. See Émile Durkheim.

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