Page:The New International Encyclopædia 1st ed. v. 06.djvu/381

DIVING BEETLE. The medium-sized forms belong to the genera Aeilius and Colymbetes, the former having the wings finely punctured, and the latter striated. The larvæ of all forms can easily be kept in confinement if fed on bits of cooked or raw meat.

 DIVINING-ROD (often called virgula divina, baculus divinatorius, caduccus or wand of Mercury, rod of Aaron, etc.). A forked branch, usually of hazel, and sometimes of iron, and even of brass and copper, by which it has been pretended that minerals and water have been discovered beneath the surface of the earth. The rod, when suspended by the two prongs, sometimes between the balls of the thumbs, is supposed to show by a decided inclination the spot under which the concealed mine or spring is situated. Other powers are ascribed to the divining-rod, but this is the chief. Many persons, even of some pretensions to scientific knowledge, have been believers in the occult power ascribed to this magic wand. Agricola, Sperlingius. and Kirchmayer all believe in its supernatural influence. Bayle, in his dictionary, under the word abaris, gives some ingenious arguments both for and against the divining-rod. In a work published in 1847 and 1851, entitled On the Truth Contained in Popular Superstitions, Dr. Herbert Mayo gives a curious collection of alleged discoveries made by this divining-rod.  DIVISCH,, (1696–1765). An Austrian scientist, born in Senftenberg. He entered the Præmonstrant Order, and became pastor at Brendiz. In 1754—and thus two years after Franklin’s kite experiment—he erected in an open field the first lightning-conductor on the Continent. The apparatus was destroyed by the peasants, who attributed to it the drought of the succeeding summer.  DIVISIBILITY; (from Lat. divisibilis, divisible, from dividere, to divide). That property of quantity, matter, or extension, through which it is either actually or potentially separable into parts. Whether matter is or is not indefinitely divisible, is a question which has occupied the minds of philosophers since very early times. The diffusion of odors through the air for long periods from odoriferous bodies without their suffering any sensible change of weight, and the tinging of great quantities of fluid by very minute portions of coloring matter, are cases commonly appealed to in proof of the great divisibility of substances. On the other hand, abstractly speaking, matter must be conceived as infinitely divisible for the reason that the division of matter is necessarily the division of the space it occupies: and the infinite divisibility of space may be demonstrated geometrically. All this does not prove, however, that matter is capable of undergoing indefinite subdivision by processes actually taking place in nature. In fact, the atomic hypothesis, which seems to be the only one capable of correlating and explaining a great variety of facts brought to light by the physical sciences, indicates that there is a definite limit to the divisibility of matter: that a substance could not be divided into smaller parts than its molecules without losing its essential properties, and that by no natural process at present known could a substance be divided into smaller parts than the atoms of its component elements. See, ; , ; and.  DIVISIBILITY. See.  DIVISION (OF. devision, division, Fr. division, from Lat. divisio, from dividere, to divide). In logic, the process of distributing all the objects included in the denotation [sic] (q.v.) of a (q.v.) into mutually exclusive classes, each of which is marked off from the others by the possession of some distinctive attribute. Logical division must not be confounded with physical division. In the former the whole (called genus) can be predicated of the resultant parts (called species, see ); in the latter such predication is not possible. Thus, when Cuvier divided his order of (q.v.) into homo, simia, lemur, and vespertilio, he performed a logical division because the whole thus divided, primate, is predicable of every one of the parts obtained; in other words, it can be said that man is a primate. But when a man is dissected into head, trunk, feet, etc., the division is not logical, but physical, because the whole cannot be predicated of the parts; we cannot say that the head is a man. Traditional logic generally gives the following rules for correct division: First, the division must be exhaustive; i.e. the sum of the denotations of the species must be exactly equal to the denotation of the genus. Second, the division must be exclusive: i.e. no object found in the denotation of any species must be found in the denotation of any other species. Third, in order to secure conformity to the above rules the division should be based on some one characteristic in regard to which the various objects in the denotation of the concept to be divided differ from each other. This characteristic used as the basis of division is called the fundamentum divisionis. Thus when plane triangles are divided into scalene, isosceles, and equilateral triangles, the fundamentum divisionis is the relative length of the sides of triangles.  DIVISION. In mathematics, one of the four fundamental processes of arithmetic, the one by which we find one of two factors when the product and the other factors are given. The given factor is called the divisor, the given product is called the dividend, and the result (i.e. the required factor) is called the quotient. The definition of division leads to the following identity: dividend = divisor × quotient + remainder. If the remainder is zero, the division is said to be exact. The common symbols for division are: $a⁄b$, a ÷ b; a : b; a/b, ab$-1$, in which a is the dividend and b the divisor. Two forms of division are recognized in elementary arithmetic, the one based on the idea of measurement and the other on the idea of partition. The fonner is the case of dividing one number by another of the same kind, and the latter that of dividing a concrete by an abstract number.

The usual tests of the correctness of division are: (a) multiply the quotient by the divisor and add the remainder, the result equaling the dividend; (b) compare the excesses of nines in the identity of division. See.

Simple tests of the divisibility of numbers by 2, 4, 5, 6, 8, 9, 10, 11 are: (a) a number is divisible by 2, 4, or 8 if the number represented