Differential Calculus
that branch of mathematics which has for its object the explanation of the method of deriving one determinate function from another by the process of differentiation. If in any determinate function of one variable we give to the variable a constant increment, and find the corresponding increment of the function, and then divide the increment of the function by the increment of the variable, we shall find a ratio which will in general be dependent upon the increment of the variable. If now we pass to the limit of this ratio, by making the increment of the variable equal to 0, we shall in general obtain a function of the original variable, which is called the differential coefficient of the function. If this be multiplied by the differential of the variable, the result is called the differential of the function. Any function of a single variable will have one, and only one, differential coefficient, and consequently it will have but one differential of the same order. The differential calculus consists of two parts. The first embraces the science of the differential calculus, and explains the methods of finding the differentials and successive differentials of all determinate functions. The second treats of the application of the differential calculus to the other branches of mathematics, as algebra, analytical geometry, etc. See CALCUJUS.
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Differential Thermometer
an instrument for determining very minute differences of temperature. Leslie's differential thermometer consists of two glass bulbs containing air connected by a bent tube containing some sulphuric acid, the movement of which (as the air expands and contracts) serves to indicate any slight difference of temperature between the two bulbs.
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Diffraction
a term applied to certain phenomena connected with the modification that rays of light undergo in passing close to the edge of an opaque body. Thus when a beam of direct sunlight is admitted into dark room a through a narrow slit, and falls upon a screen placed to receive it, there appears a line of white light bordered by colored fringes; these fringes are produced by diffraction.
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Diffusion
a word having several applications. (1) The act of diffusing or spreading about of a liquid, fluid, etc.; (2) a spreading or diffusing abroad of a matter; (3) the state of being spread or dispersed widely; (4) the act of spreading, extending or propagating widely, as the diffusion of knowledge; (5) copiousness, exuberance of style, prolixity, verbosity. Diffusion of gases is the passing of one gas into the space occupied by another. The name given to that phenomenon by which the composition of the atmosphere is kept uniform, or nearly so. Gases diffuse into one another according to a fixed law, that is, inversely as the square root of their densities. Diffusion of heat is a term applied to those modes by which the equilibrium of heat is effected-viz., conduction, radiation, and convention. Diffusion of liquids: When two liquids that are capable of mixing are put in contact they gradually diffuse one into the other, notwithstanding the action of gravity.
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Digamma
the name given to a letter in the oldest Greek alphabet, which early fell into disuse, being retained longest in the Æolian dialect. It is considered to have had the power of the English w or v, and is frequently represented in Latin by u (v): thus, Gr. oikos Lat. vicus, Eng. wick; Gr. oinos Lat. vinum, Eng. wine. See ALPHABET.
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Digit
a term applied to the 10 symbols of number, 0, 1, 2, etc., to 9; thus 305 is said to be a number of three digits. Numbers were originally indicated by the fingers, and hence the name. Astronomers use digit to signify a twelfth-part of the diameter of the sun or moon, and speak of an eclipse of seven digits, meaning that seven-twelfths of the diameter is covered. See NOTATION.
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Digitalin
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C35H56014, A glucoside found in the leaves of Digitalis purpurea (foxglove). It occurs as a white, amorphous powder, or in granular masses, almost insoluble in cold water. water, readily soluble in alcohol. Used in medicine as a heart stimulant, and in Bright's dis- It is claimed that the drug is not ease. cumulative in its action, thereby differing from various preparations of digitalis leaves. In large doses it is poisonous, and in case of poisoning emetics should be given, followed by alcoholic stimulants or camphor.
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Digitalis
a genus of plants belonging to the natural order Scrophulariaceæ. They are natives of Europe and western Asia. There are numerous species, all of them tall herbs. D. purpurea is the common foxglove. The dried leaves of the foxglove are used in medicine, as powder, infusion, or tincture, or in the form of the active principle, digitalin. D. purpurea belongs to the order Scrophulariaceæ, and is very useful in cases of heart disease. The powdered leaves or an extract of D. purpurea, ochroleuca, lævigata, ferruginea, and other species, overdoses produce vomiting, vertigo, and other symptoms, followed even by death.
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Digitaria
finger-grass, a genus of grasses so named from the digitate spikes. There are two species: D. sanguinalis, or cock's-foot finger-grass, and D. humifusa, smooth finger-grass.
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Digitigrada
a section of the order Carnivora, comprising the lions, tigers, cats, dogs, etc., in which the heel is raised above the ground, so that the animals walk more or less on the tips of the toes. The other two sections are the Pinnigrada and the Plantigrada. The section Digitigrada is divided into the families Mustelidæ, Viverridæ, Canidæ Hyænidæ, and Felide. The first two are aberrant, being semiplantigrade.
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Dijon
the chief town in the French department of Côte-d'Or, formerly capital of the old duchy of Burgundy, lies, spread out on a fertile plain at the foot of Mont Afrique (1,916 feet), at the junction of the Ouche and Suzon, and on the Canal de Bourgogne, 196 miles S. E. of Paris by rail. Its importance as a railway center has rendered it of consequence in the inner line of French defenses. On the death of Charles the Bold it came with Burgundy into the possession of France in 1477. In October, 1870, after a sharp engagement before the city, Dijon capitulated to a German force. There was again severe fighting here in January, 1871. Pop. about 75,000.
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